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Shelton showed he could be a threat over the next two weeks as he broke Thiem again to close out the second set.
World number one Jannik Sinner quelled the challenge of big-serving 14th seed Ben Shelton with a 6-2 6-4 7-6(9) victory.
Karolina Muchova overwhelmed Sorana Cirstea and will meet American Coco Gauff in the semifinals.