Presumably you have reason to be believe that the algorithm for producing Guids is not producing truly random numbers, but is in fact cycling with a period << 2^128.

e.g. RFC4122 method used to derive GUIDs which fixes the values of some bits.

Proof of cycling is going to depend upon the possible size of the period.

For small periods, hash table of hash(GUID) -> GUID with replacement on collision
if GUIDs do not match (terminate if they do) might be an approach. Consider also only doing the replacement a random fraction of the time.

Ultimately if the maximum period between collisions is large enough (and isn't known in advance) any method is only going to yield a probability that the collision would be found if it existed.

Note that if the method of generating Guids is clock based (see the RFC), then it may not be possible to determine if collisions exist because either (a) you won't be able to wait long enough for the clock to wrap round, or (b) you can't request enough Guids within a clock tick to force a collision.

Alternatively you might be able to show a statistical relationship between the bits in the Guid, or a correlation of bits between Guids. Such a relationship might make it highly probable that the algorithm is flawed without necessarily being able to find an actual collision.

Of course, if you just want to prove that Guids can collide, then a mathematical proof, not a program, is the answer.