perl -MList::Util=reduce 
-nle"$p{reduce{$p{$a}=1;$a=qq[$a/$::b]}split'/'}=1}{print for sort keys%p" 
junk.dat

/admin
/admin/test
/core
/core/system
/core/system/init.conf
/demo
/demo/test
/demo/test/core
/demo/test/core/newfile.cgi
/demo/test/file1234.cgi