#!/usr/bin/perl -w

use strict;

my %log;

foreach(<DATA>) {
  chomp;
  if(!/^$/){
    /.+(EVENT\d)/;
    $log{$1} = $_;
  }
}

print map { "$log{$_}\n" } sort keys %log; 

__DATA__
09:12:50:861 EVENT1 #Don't want this line
09:13:09:467 EVENT1 #Don't want this line
09:13:09:837 EVENT1
09:13:38:059 EVENT2
09:14:03:115 EVENT3
09:14:04:076 EVENT4
09:14:11:376 EVENT1
09:14:34:049 EVENT2
09:14:34:990 EVENT3 #Don't want this line
09:14:34:990 EVENT3
09:14:34:990 EVENT4