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Chris Woakes took six wickets for 17 runs and Stuart Broad 4-19 in an Ireland second innings that lasted just 15.4 overs.
The visitors had been set a seemingly modest 182 to win on the third day of a match scheduled for a maximum of four days rather than the usual five allocated to a Test.
But they ended up being bowled out for the seventh-lowest completed innings score in Test history and lowest since 1955 as their dreams of a maiden win in the format were blown away in a match in which they had dismissed England for 85 in the hosts' first innings.