OK, taking a little liberty here, it's been 14 years since the last time I worked this particular problem. 
Theorem 1: any logic problem can be proven in a finite amount of time.
Suppose Th.1 were true. Then it would be possible to prove the general case of algorithmic correctness of an arbitrarily complex system, since such algorithms and and complexities can be described as logic.
Godel's theorem is commonly known to stand in the field of algorithms, that an arbitrarily complex algorithmic system cannot be proven correct. This is a contradiction to the example. Proving Godel's theorem false would be functionally equivalent to proving P=NP, which is known to be intractible.
Given a contradiction to Th. 1 exists, Th.1 must therefore be false, and it cannot be proven that no exception exists to the original theorem that Reason applies to every question.

Theorem 1: any logic problem can be proven in a finite amount of time.
Suppose Th.1 were true. Then it would be possible to prove the general case of algorithmic correctness of an arbitrarily complex system, since such algorithms and and complexities can be described as logic.
Godel's theorem is commonly known to stand in the field of algorithms, that an arbitrarily complex algorithmic system cannot be proven correct. This is a contradiction to the example. Proving Godel's theorem false would be functionally equivalent to proving P=NP, which is known to be intractible.
Given a contradiction to Th. 1 exists, Th.1 must therefore be false, and it cannot be proven that no exception exists to the original theorem that Reason applies to every question.