Don't try and use an invalid filehandle. You always should check the return value from system calls such as open to find out if they failed or not before trying to use their products.

open FIRST, $first_file or die "Can't open '$first_file' for reading: 
+$!\n";
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Update: Also printing to a filehandle opened for reading doesn't make much sense (even if it opened successfully). You need to (re)read perlopentut.