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A stunned Verbeek sat on the bench shaking his head while Joachim Loew, in his 50th game as Germany coach, punched the air in celebration.
Hoping to hold out for a draw, Verbeek used Cahill as a forward and packed his midfield. But with Cahill isolated up front instead of controlling the midfield, Australia had no answer to Germany's swift passing and running game.
"It was not an easy game for us," Verbeek said. "We tried to make it very difficult for them and use our speed, but we didn't have the ball in the first 20 minutes."
Any slim hope Australia had of coming back evaporated with Cahill's 56th-minute ejection.
Klose missed two more good chances before Mueller made it 3-0 in the 68th minute, dragging the ball back to avoid Scott Chipperfield's lunge and firing a low shot in off the post.
Cacau rounded off the scoring in the 70th, just two minutes after coming on for Klose.
While Germany is in excellent shape for advancement already, the Socceroos are desperate.
"The next game is a final," Verbeek said of the match with Ghana. "We have to win that game."
Copyright 2010 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.
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