Suppose that x is over the domain of all things and I have the following predicates:
H(x) = x is a person, J(x) = x is named John, F(x,y) = x is happier than y, a = John Smith
My interpretation of this sentence is that it's equivalent to saying "there exists a person who is happier than every person, and their name is NOT named John"
My attempt at translating this sentence is: ∃x(H(x) ^ ∀y((H(y) → F(x,y)) → ¬J(x)))
but the programme I'm using is telling me that it's not correct, can someone please guide me on how to correct my symbolic statement? Thank you so much.