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open( LINKS, "+<", "filename" );
while (<LINKS>) {
...
   # when all done adding updates at the end...
   seek LINKS, $lastread, 0; # jump back for next read:
}

   ...
   next if exists( $fetched{$url} );
   ...

while (-s "list1") {
   open( INP, "<list1" ) or die $!;
...
}

print "list1 is empty now.  We must be done.\n";