Can you point to any examples of major scientific discoveries that were accomplished by the "Proof by Elimination" method you propose?
Certainly eliminating hypotheses that disagree with the evidence is a significant *part* of science. But at least as big a part (and I am leaving out other parts) is deducing consequences of theories (preferably ones not resulting from other theories you know about) and testing to see if those hypothesized consequences are there. For example, evolutionary theory predicts the existence of transitional fossils (though how many depends on the version of the theory) and that DNA in related creatures will be similar. That is one of the problems with "Intelligent Design" as science -- no such predictions that I have seen.
There are probably a few things where your "process of elimination" view of science works. These would be simple things with a small number of variables where one could construct the set of all possible theories.
But let's get real. In the realm of science, you are talking about biology, the development of life, the physical parameters of the universe, and other areas that are quite complex and where many things are not fully understood. To claim that all possible theories are considered in these areas so as to prove something by process of elimination is preposterous.
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