you forgot a quote here:

system "/home/rebecca/bs127/Predator/predator -fpredator.txt input_seq
+uence.txt <---
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Im assuming it is right in your script. You could try to use 'backticks' to catch the output:

my $output = `/home/rebecca/bs127/Predator/predator input_sequence.txt
+`;
open (FILE, ">predator.txt") or die $!;
print FILE $output;
close (FILE) or die $!;
[download]

About permissions, has your script got write permissions for the local directory?

hope it helps