The objective of this study is to compare the efficacy and safety of Tipranavir/ritonavir (TPV/r, 500mg/200mg twice daily) to the safety and efficacy of Darunavir/ritonavir (DRV/r 600 mg /100 mg twice daily) in combination with investigator selected optimised background regimens in patients who are three-class (Nucleoside reverse transcriptase inhibitors (NRTI), Nonnucleoside reverse transcriptase inhibitors (NNRTI), and Protease inhibitor (PI)) treatment-experienced (a minimum of 3-months duration for each class) with resistance to more than one PI on the screening virtual phenotype resistance testing.