Strange Cat Invading our Home. Help!

We have a very sweet little NEUTERED female cat. She has a cat flat to
go in and out of the house. Over the past few months we have noticed
that she was getting thin even though we kept giving her larger bowls
of food. Now we know why : a strange cat comes in and beats her up,
urinates inside the house, eats her food and is a bl***y nuisance. We
have tried putting one of those (harmless) spring loaded traps down,
hoping that if we caught it we could sprinkle it with water to try and
deter it from coming here. It ripped the door off the cage and escaped.
THREE times. Then we tried putting a booby trap on the cat flap: as
soon as it came through the flap, a trap door would drop and stop it
getting out. Then we could sprinkle it with water etc. This time, it
ripped the trap door off its screws and escaped. It has now discovered
how to lift up the flap and escape.In the morning, we find all the food
has gone, the trap door has fallen down but there is NO CAT to be
found. Houdini had nothing on this animal. Any ideas please? It is
driving my husband crazy being outwitted by a cat. We cant put any
repellents etc; down as we have a cat ourselves. It is also costing a
fortune in food and cleansing materials to try and get the stink of cat
pee out of the house.