B747-400 flight crew reported shutting down #1 during cruise in response to a fire warning. Crew followed QRH and diverted safely to alternate.

Narrative

Status message ENG 1 FIRE LP A annunciated in flight. Extinguished after 10 min. This was followed by Status message ENG 1 FIRE LP B. After 10 mins it extinguished. These messages alternated.The mechanic was called to the flight deck to make him aware. The mechanic interrogated the MCDU (Multipurpose Control Display Unit) and identified that we had an intermittent fault in both loops.Shortly after; DET FIRE /OVHT 1 EICAS message annunciated.QRH procedure accomplished. The Dispatcher was contacted via ACARS and advised of the issue; that we didn't have fire or overheat detection; and we asked where the Company would like us to go; as continuing wasn't appropriate.The Dispatcher advised ZZZ as our diversion airport and sent a revised flight plan and fuel burn via ACARS.The second crew (who were on their rest in the bunks) were awakened so they could assist and be involved in the briefing.We were preparing for the diversion when a Master Warning FIRE ENG 1 annunciated with associated warning bell.The memory items were conducted and QRH procedure completed as per the manual.The fire light extinguished after the engine fire handle was pulled.The engine was shutdown; a request for priority handling was given to ATC; descent to flight level 240 requested.We advised ATC of the requirement to divert to ZZZ; the requirement to dump fuel; the nature of the issue and that the fire indication had extinguished after engine shutdown.We diverted towards ZZZ and dumped approximately 28;000 kg enroute to reduce us to below max landing weight.Landing calculations performed and an appropriate runway negotiated with ATC.The Company was advised that a request for priority handling had been issued and that we were enroute to ZZZ and an ETA provided.A standard approach (with an engine shutdown) was conducted as per the manual and company SOP's via ILS XXL.The approach; landing and taxi were uneventful.The aircraft was taxied to parking; checklists and paperwork completed.A review of the event was conducted with crew to discuss how it was handled; to ensure they were ok; what was learned and whether anything could have been handled differently or improved upon.The Chief Pilot was phoned by the Captain to advise him of the situation.Operations decided to send the crew to a hotel and the crew signed off.