Solved! I'll answer my question. In short, install HP printers (and wifi printer) through the CUPS, "Printers" dialog in Mint 14 - NOT using HPLIP!
After researching the problem, a link to installing using CUPS on Ubuntu 12.04 explains how to do it:http://blog.sudobits.com/2012/04/13/how ... ntu-12-04/
Make sure the USB cable is plugged. In this case, go to Preferences/Printers. Dialog box opens and click the “+” button at the bottom left. The gnome-control-center box opens; click “network” in the list. Next box appears and I added the address of the printer – 192.168.1.1.106. Checked “Search by Address”, and it loaded the wifi printer for the HP C4750! Ran some test printer pages w/o the USB cable and it works perfectly – all through CUPS and NOT HPLIP. BTW, CUPS will recognize the USB cable connection and automatically add the hard wired printer perfectly.
Printer wifi address idea can be found near the bottom of this page: http://forums.gentoo.org/viewtopic-t-854466.html
The address can be obtained by running the “Wireless Network Test Report” on the Scan function of the HP wifi printer. It is a self test, prints 2 pages and will tell the status of the printer - including the IP address of the printer.
After the printer was installed through CUPS, two icons show up in the “Printers” dialog box (one icon for the USB and one for the wifi printer- the second icon is the wifi) on Mint 14 but not in the HPLIP, confirming that HP has not written or updated HPLIP for Mint 14 yet.