Billed me for international sms's I did NOT send

I received my billing for the month of October, stating that I sms'ed R150 worth of sms's to an international number over a 21 day period. I phoned in, lodged the query, the guy said that it had to me who had sent it because the computer says it was sent from my number. His suggestion to resolve the matter was that I should phone the number to find out who it belongs to. As if that would sort it out? I kept explaining that I did not send the sms's and that I would know if someone else would have, as it was over 21 days, from early the morning to late at night. I live alone, so it could not have been from my phone. He then kept me on hold for over 20 minutes and I put the phone down, obviously he did that so I would go away. Its despicable how they just keep telling you the same thing over and over. He said that they could not do anything about it. So what do I do? Don't pay the bill, and they shut my phone off. So now what?