By "proton" I mean a thingy that creates a potential well where an electron bops around, and by "hydrogen atom" I mean a single of these with a single electron in it, and by "have" I mean that when the electron has high enough energy you don't call it an hydrogen atom but "a proton here and an electron over there". This is of course a tautology.

By "one" I mean S(0) (and by "0" I mean the empty set), which is also a tautology. And if you don't know what I mean by "exactly" then you don't understand the parent quote anyway.

Admittedly a good counterexample would involve an exact truth that is not a tautology.