if the code finds that $NumProc String exists at the exact same position in the next line it would wipe out the next line, keeping only the first line found.

Taking you at your word, here's an SSCCE:

use strict;
use warnings;

use Test::More tests => 1;

my @in = split (/\n/, <<EOT);
aaa Foo: 1234 xyz
bbb Foo: 1234 yzx
ccc Foo: 1234 yxz
ddd Foo: 2345 zyx
EOT

my @want = split (/\n/, <<EOT); 
aaa Foo: 1234 xyz
ddd Foo: 2345 zyx
EOT

my $number;
my $index;
my %seen;
my @out;

for my $line (@in) {
    if ($line =~ /Foo: ([\d]{4})/) {
        $number = $1;
        $index  = index ($number, $line);
    } else {
        $number = '';
        $index = -1;
    }

    push @out, $line unless $number ne '' && $seen{$number}++ && index
+ ($number, $line) == $index;
}

is_deeply (\@out, \@want);
[download]

There's a good few assumptions in there and I've entirely ignored that your data looks like XML (which, if it is, is probably a better route for your specific needs) but it should give you an idea of one way you might proceed.