How do I prove that FedEx caused my package to be stolen when their own records say they made proper delivery?

With UPS you can put through a tracer and file a claim but I'm not sure about FEDEX. Next time you get a delivery of this type, make them require a signature for the merchandise or pick it up at the UPS or FEDEX terminal yourself, otherwise I have heard of them leaving packages clear at the end of people's driveways. All they care about is dropping off the package at the address. They don't care if you get it or not evidently unless you require a signature.