My approach in this case is to take potentially duplicate inputs and make them hash keys, like so:

while ($i = <STDIN>) {
    chomp $i;
    if ($i) {
        $buffer{$i} = 1;
    }
    else {
        last;
    }
}
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and then output with

sort keys %buffer.

On systems without case sensitivity of paths you should uc or lc the inputted paths as well.