Here is a complete solution which uses Algorithm::QuineMcCluskey (this module throws a number of warnings but seems to work). I only tested it on your one expression, so if you are using it, let me know whether it works well or not.

use strict; 
use warnings; 
use List::Util 'sum'; 
use Algorithm::QuineMcCluskey;

my $bool = 'Fred&Teddy&(Fred|Teddy)|(Fred)&(John)'; 
my @vars = keys %{{ map { $_ => 1 } $bool =~ /\b(\w+)\b/g }}; 
$bool =~ s/($_)/\$b\{${1}\}/g for @vars; 
my $n = @vars; 
my @table; 
my %b; 
for (0..2**$n-1) { 
  @b{@vars} = split //, sprintf "%0${n}b", $_; 
  push @table, $_ if eval $bool; 
} 

my $q = new Algorithm::QuineMcCluskey( width => $n, minterms => \@tabl
+e );
my( $result )= $q->solve();
$result =~ s/\+/|/g;
$result =~ s/([A-Z])'/!$1/g;
$result =~ s#([A-Z]+)# join( "&", map { $vars[ord($_)-ord("A")] } spli
+t //, $1 ) #ge;
print "$result\n";
[download]

Update: I could not help playing a little with this code. If one uses the vec function instead of a hash for the variables, one can shorten the code to:

use strict; 
use warnings; 
use Algorithm::QuineMcCluskey;

my $bool = 'Fred&Teddy&(Fred|Teddy)|(Fred)&(John)'; 
my @vars = keys %{{ map { $_ => 1 } $bool =~ /\b(\w+)\b/g }}; 
$bool =~ s/$vars[-$_]/vec(\$_,$_-1,1)/g for 1..@vars; 

my($result) = Algorithm::QuineMcCluskey->new( 
                                             width => scalar @vars, 
                                             minterms => [ grep { eval
+ $bool } 0..2**@vars-1 ] 
                                            )->solve();
$result =~ s/\+/|/g;
$result =~ s/([A-Z])'/!$1/g;
$result =~ s#([A-Z]+)# join( "&", map { $vars[ord($_)-ord("A")] } spli
+t //, $1 ) #ge;
print "$result\n";
[download]

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