I slightly modified my script:

#!/usr/bin/perl

use feature 'say';
use warnings;
use strict;

my $file = 'words.txt';
open my $IN, '<', $file or die "$!";
my %words;
while (my $word = <$IN>) {
    chomp $word;
    undef $words{$word};
}

my %reported;
for my $word (keys %words) {
    my $length = length $word;
    for my $pos (0 .. $length - 1) {
        my $skip_itself = ! $pos;
        for my $len (1 .. $length - $pos - $skip_itself) {
            my $subword = substr($word, $pos, $len);
            next if exists $reported{$subword};
            next if $word eq $subword . q{s}
                 or $word eq $subword . q{'s};
            if (exists $words{$subword}) {
                say "$subword";
                undef $reported{$subword};
            }
        }
    }
}
[download]

I used english.0 from this archive as words.txt: http://downloads.sourceforge.net/wordlist/ispell-enwl-3.1.20.zip. Your script took 58s, whilest mine only 6s (on Pentium 4, 2.8 GHz). The results were different, though: your output contains the word indistinguishableness that mine does not; my list contained 911 more words than yours (e.g. you, wraps or tribe's).

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