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She also was simply outplayed by Cornet, a 32-year-old from France who beat past major champions Simona Halep at the Australian Open, Jelena Ostapenko at the French Open and Iga Swiatek at Wimbledon, ending the No. 1-ranked woman's 37-match winning streak at Wimbledon.
Djokovic announced his withdrawal from the year's last Grand Slam tournament on Twitter.
Coric signalled his return to full fitness from shoulder surgery and showed that he will be a threat at the US Open.
Taylor Fritz blasted his way to a 6-3, 6-2 win over Australian Nick Kyrgios while Cameron Norrie fought back to beat former world No. 1 Andy Murray 3-6, 6,-3 6-4 in an all-British clash.
The three-day team event pits six of Europe's top players against six from the rest of the world.
The top seed overwhelmed Britain's Cameron Norrie 2-6 6-3 6-2 6-4 in the second semifinal.
The Spaniard was injured during the quarterfinal match against Taylor Fritz.
The Spaniard had appeared close to retiring mid-match with an abdominal injury.
The top seed bounced back from two sets down to win 5-7 2-6 6-3 6-2 6-2.
He will next face unseeded Chilean Cristian Garin, who beat Kyrgios's compatriot Alex De Minaur to enter the last eight.