I believe everything exists.

[Existentialist]

Anything that one's imagination can bring into existence, exists. It exists in one's internal reality, in the mind. But many of these things are non-existent in one's external reality, the universe around us. We usually use the word 'exist' as shorthand for 'something that appears to exist in our external reality'. So a non-existent thing in my external reality can exist in my internal reality. A non-existent thing therefore exists.