I would go for the "or anything option".
My first option would be to simply talk to the company you used to pay and ask how the system operates, what number it calls and how to disable it. They presumably get the calls and ignore them because you don't have a contact any more so they may be helpful.
Second option would be to set it off several times quite quickly at a known date and time and then look at the telephone bill.
You have said the system is using an autodialer which is why I am thinking in terms of a serial line, a modem and a telephone.
If neither of the above work and you have a PC with a RS232 serial port you can probably tap into the line between the security system to display what the system is sending to the modem.
If on the other hand you actually have a networked system, so there is no autodialing involved, you might use something like Wireshark to capture and decode the communications.