Disproving a Negative

I seem to be hearing a lot of talk about it being impossible to prove the nonexistence of something. It seems to me that their are multiple ways to prove the nonexistence of non existent objects/beings. For example if any object/being is contradictory by virtue of its existence (married bachelor, or circular square) it is proof of its nonexistence. Also why can’t I prove that (for example) no 10 year old US senators exist? If it is possible to prove that certain objects or beings do not exist shouldn’t it then be possible (albeit difficult) to prove that god does not exist.

Just a random thought.

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