Sorry. Too many experiences to really buy the logic "it can be done, it has not been done, hence contradiction". Indeed e.g. the proof of Fermat's theorem (Wikipedia: After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995; it was described as a "stunning advance" in the citation for Wiles's Abel Prize award in 2016.) would be a contradiction of that logic. (Indeed, I am very confident that mathematics is a much more developed a mature field then IT).

The only time such an argument had been yielded and has some value is in my (not so, I guess) humble opinion when I think Fermi used the argument that if there was a lower energy level of water there surely would have been an animal by now that used this extra energy by converting water to this state (although I cannot find a link to this quite so quickly, so perhaps the argument was slightly different).