If Hamlet has either won a Hugo Award and is written by Tolkien, or neither has won a Hugo Award nor is written by Tolkien, then Hamlet has neither won a Hugo Award nor is written by Neil Gaiman.
¬(Win(hamlet, hugoAward) ⊕ WrittenBy(hamlet, tolkien)) → (¬Win(hamlet, hugoAward) ∧ (¬WrittenBy(hamlet, neilGaiman)))