This is turning into an interesting project...Deskjet 712c is not a recent product it appears.
Now we have this ..for reference:
HPLIP
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HPLIP is an HP developed solution for printing, scanning, and faxing with HP inkjet and laser based printers in Linux..
The HPLIP project provides printing support for 1,330 printer models, including Deskjet, Officejet, Photosmart, PSC (Print Scan Copy), Business Inkjet, LaserJet, Edgeline MFP, and LaserJet MFP. (Note: Not all models are currently supported. See Supported Printers for more information.)
The current version of the HPLIP solution is version 2.8.5 (Download) (Release Notes).Latest News 
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Deskjet 712c NOT supported by HPLIP.
Doing moe searching.....
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HP Linux Imaging and Printing(HPLIP) 2.7.10
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HP Linux Imaging and Printing(HPLIP) 2.7.10 was presented for free download to install, add, update, setup HP Multifunction. please check your digital device manufacturer HP, device category Multifunction, device model, operating system, driver version according to HP Linux Imaging and Printing(HPLIP) 2.7.10.
- Version:
- 2.7.10
- Release:
- 5 Jul 2007
- Update:
- 6 Dec 2007
- License:
- Free Driver
These distros are currently supported:
- SUSE Linux (10.0, 10.1, 10.2, 10.3)
- Fedora (3.0, 4.0, 5.0, 5, 5.92, 6.0, 6, 7.0)
- PCLinuxOS (2006.0, 2007.0)
- IGOS (1.0)
- Ubuntu (5.04, 5.1, 6.06, 6.10, 7.04, 7.10)
There are small number of printers that are not supported: HP Color LaserJet 1500, HP Color LaserJet 1600, HP Color LaserJet 2600, HP Deskjet 1000C, HP Deskjet 200, HP Deskjet 320, HP Deskjet 340C, HP Deskjet 710C,
HP Deskjet 712C,
HP Deskjet 720C, HP Deskjet 722C, HP Deskjet 820C, HP Deskjet Plus, LaserJet 1000, LaserJet 1005, HP LaserJet 3100, HP LaserJet 3150, HP Photosmart Pro b9100 series.