iPhone wifi connection log file? I have an iPhone 5s with the latest version of iOS.  The wireless (and bluetooth) card has stopped working (tested at the Genius Bar) just a couple weeks out of warranty.  Apple wants $250+ to replace the phone.

I wonder if I can determine when the phone last connected to a wifi network?  If I can determine that it has not connected to my home wifi prior to expiration of the warranty, Apple may have an obligation to replace the phone without charge.

Does a log file exist (and if so where can I find it) that would show the information I need?
Logs are available via Xcode, however they are overwritten pretty quickly in order to prevent from consuming large amounts of memory on the device.  Usually you can only get a few days worth of logs at most.  That means that the logs you are seeking have certainly already been deleted from the device.  These are the same diagnostic logs that are available at the Genius bar.  They are useful for troubleshooting current issues, but they are not usefully for determining how long you have had a problem.