As a matter of fact, both are fine.

Something + has proved helpful + in + gerund
http://paknews.com/flash.php?id=13&date1=2003-12-30
Look at headline

Something + has proved helpful + to + verb?
http://www.cambridge-efl.org/rs_notes/0 ... tes1_5.cfm
Look at the first sentence of the third paragraph

Both are idiomatic. I would prefer the former with the gerund form but I believe that while the the original question's error is clearly explained, the chicken question has an error which makes it preferable to choose E over A
A) a cannon shooting dead chickens at airplanes has proved helpful to demonstrate what kind of damage
In the above, the emphasis is put on the subject in bold "a cannon". The portion in green is an adjective clause and it is given second order importance vis a vis the subject. It seems that it is the subject, the cannon itself which has proved helpful to... while it should really be the act of shooting which has proved helpful to...
E) a cannon that shoots dead chickens at airplanes has proved helpful in demonstrating
In the above, the portion in red is a restrictive clause. The emphasis is shifted to the restrictive clause and it is because of it that whatever happens happens. Hence, it is because the cannon shoots chicken and the very act of shooting chickens which has proved helpful in demonstrating... not the cannon itself for not every cannon can demonstrate...

I'll try to show another example of the "shift of emphasis" when using restrictive clauses.
Ex: The garage that belongs to my uncle is filled with cars. --> why is the garage filled with cars? Because if belongs to my uncle. As you can see, a restrictive clause gives crucial information to whatever verb comes after; it explains why the verb is.
Ex: The garage belonging to my uncle is filled with cars --> the portion in blue is an adjective clause. It is not crucial in explaining the very reason of the verb coming after. The adjective clause could be replaced by a simple adjective. Let's change it by adjective "blue"
The blue garage is filled with cars: Is it because the garage is blue that makes it being filled with cars? No. It is just a garage which happens to be blue and which is filled with cars.

All of this to say the importance of restrictive vs adjective clauses. Whenever there is a restrictive clause, you should know that it is that clause which explains why what comes after has a very reason of being. Therefore, in the "chicken" question, the use of either idioms is fine but it is the use of restrictive vs adjective clause which makes the difference.