B777 air carrier First Officer reported pressurization system failure in cruise flight and returned to departure airport for uneventful landing.

Narrative

I was the Relief Pilot at the time of the event. I was woken up when I heard flight attendants take your jumpseats" which appeared to come over the PA into the bunk and the audio from the oxygen mask mic could be heard. I then sensed a descent initiate. A couple of minutes later once the flight attendants were asked to "check in" after reaching a safe altitude; I was then called back into the cockpit via the flight deck. Once I entered back into the flight deck I was briefed of the descent that had occurred as a result of a failure of the pressurization system and a CABIN ALT WARNING. I gathered my bearings and saw we were just outside ZZZZ at 9;000ft. We then started devising a plan together for a diversion and confirmed once again with the cabin crew to ensure everyone was okay and there was no visible damage to the aircraft that could've resulted in our issue. My role at this point as the Relief Pilot was to set up the communications via the SATCOM in preparation for the Captain to speak with Dispatch/Maintenance Control; I also monitored the flight path while the FO (First Officer) flew the aircraft. I commenced obtaining weather information via the sources on my ipad. We entered a hold before we made a decision where to divert. As a crew; along with the input from Dispatch and Maintenance Control we agreed that our best course of action was to return to ZZZ. An alternate of ZZZZ was not favorable due to weather. Once we commenced our diversion since we were overweight we then began the discussion regarding fuel dumping which we later coordinated ATC. We recorded the position and shared with our dispatcher. We then confirmed via our FOM diversion guide that we had considered all possible challenges that came with our situation. Upon arrival; Maintenance inspected the aircraft and advised "Both outflow valves closed; Maintenance confirmed initial findings (found ice in the air hook up; check valve broken and confirmed CABIN ALT WARNING)"."