Mining Bitcoin with Antminer S1/S3 is like trying to run Mafia III on a Celeron from 2010 with Integrated Graphics. The game maybe will start, but you'll not be able to play...
Yes , nowadays mining Bitcoin with an Antminer S1 or S3 is not profitable even if you have free electricity (you will mine very little bitcoin now with increased difficulty).
Nowadays people use S7 antminer which is the normal one now and it is not profitable if you don't have free or very cheap electricity.
The only Antminer which can mine coin for you nowadays is the S9 just released not long ago. This is the best miner to mine bitcoins now.
If you are asking about an altcoin there are quite some that are profitable via GPU mining. Just have a more thorough look at this section of the forum.