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Star Trek: First Contact - timeline
World War III begins.
World War III ends and the Earth is left devastated by the nuclear carnage of it.
4th April: The Enterprise arrives from 2373 to prevent the Borg murder of Zephram Cochrane, the inventor of the warp drive.
5th April: Humans make their first contact with the Vulcans.
War, disease and famine are all gone by this time.
The Enterprise travels back to 2063 to stop the Borg murder of Zephram Cochrane, the inventor of the warp drive.