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If gods may not actually exist, then their logical possibility or impossibility is irrelevant.

There are many things that cannot be seen with the naked eye, like oxygen, gravity and static electricity, but we know these exist because these things have effects, whether we regard them as logically impossible or not.

The gods of all major religions that have been presented to the people of the world have no known effects, therefore they should be considered as non-existent, whether they are regarded as logically pssible or not.

Again, for example, no dogs exist in my house presently, and it is irrelevant whether or not it is logically possible.