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foreach my $intersect_file (@intersect_keys) {
    my $execs = $system_file_data{$intersect_file};  # Array ref
...
       print("$exec\n");
    }
}

foreach my $intersect_file (@intersect_keys) {
    foreach my $exec (@{ $system_file_data{$intersect_file} }) {
       print("$exec\n");
    }
}