Chasing 309 to remain in the hunt for a last four berth, South Africa's survival bid petered out on 259-9.
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Disciplined Pakistan bowling saw Shadab Khan and Wahab Riaz take three wickets each as South Africa surrendered without a fight.
Faf du Plessis's side had already been roughed up by Haris Sohail's brilliant 59-ball innings of 89 in Pakistan's total of 308-7 from their 50 overs.
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