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The semi-final between Germany and Spain in Durban was interrupted briefly in the fourth minute when the fan ran onto the pitch to protest about the exclusion of a player from Italy's squad.
FIFA spokesperson Nicolas Maingot said on Thursday that police were investigating the matter but that the breach in security was "certainly not acceptable."
Maingot says FIFA "will tighten the controls again."
The fan entered the field near Germany goalkeeper Manuel Neuer's net and sprinted almost to midfield before he was caught by security and escorted away by police.
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