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Lukas Podolski, Miroslav Klose, Thomas Mueller and substitute Cacau were all on target in the best match of the tournament so far.
Joachim Loew’s side were simply too good for Australia, although the Socceroos’ cause was not helped by the dismissal of Tim Cahill early in the second half, Euro.
But, even before Australia were reduced to 10 men, the three-times world champions had proved their class with the excellent Mesut Ozil conducting the show.