I am so close to solving this problem: (Language Logic and Proof 8.36).
All I need to do to complete the proof is show that P <-> Q and P -> ~Q is a contradiction (the problem has a similar form to this)
How can I do this? Intuitively, P <-> Q is (P -> Q) ^ (Q -> P) which can be translated to
(~P V Q) ^ (~Q V P) and that
P->~Q has this form (~P V ~Q) which is not equivalent to either of the above expressions (let alone both of them!).
Am I missing something really obvious? Is there another way to complete this problem?