Update: I generated a file1 of 1000 lines (factors(A..Z)Seq(0..9)Pos(0..1000). And a file2 of 1000 triples of A..Z. Processing with your code ran for over 1.5 hours before I abandoned it; with my code it took less than a second. HTH.

Try this. On cursory inspection (and using only the tiny amount of data provided), I think it should be quite a bit quicker than your brute force iteration/comparison method:

#! perl -slw
use strict;
use Inline::Files;

my( %file1, %facBySeq, %seqByFac );

while( <FILE_1> ) {
    my( $fac, $seq, $pos ) = split ' ';
    push @{ $file1{ $fac }{ $seq } }, $pos;
    $facBySeq{ $seq }{ $fac } = 1;
    $seqByFac{ $fac }{ $seq } = 1;
}

while( <FILE_2> ) {
    my @facs = split ' ';
    for my $seq ( keys %{ $seqByFac{ $facs[ 0 ] } } ) {
        if( exists $facBySeq{ $seq }{ $facs[ 1 ] }
        and exists $facBySeq{ $seq }{ $facs[ 2 ] } ) {
            for my $pos1 ( @{ $file1{ $facs[ 0 ] }{ $seq } } ) {
                for my $pos2 ( @{ $file1{ $facs[ 1 ] }{ $seq } } ) {
                    for my $pos3 ( @{ $file1{ $facs[ 2 ] }{ $seq } } )
+ {
                        print join ' ', $facs[0], $seq, $pos1, $facs[ 
+1 ], $seq, $pos2, $facs[ 2 ], $seq, $pos3;
                    }
                }
            }
        }
    }
}

__FILE_1__
A seq1 20
B seq2 25
B seq2 80
B seq1 40
C seq1 25
D seq2 30
E seq2 45
__FILE_2__
A B C
B D E
[download]

Outputs:

[ 8:24:45.48] C:\test>1109868.pl
A seq1 20 B seq1 40 C seq1 25
B seq2 25 D seq2 30 E seq2 45
B seq2 80 D seq2 30 E seq2 45
[download]

Basically, it just constructs a couple of ancilliary indexes using hashes to avoid much of the iteration. (Note:The Inline::Files just allowed me to put all the test data and code in a single file.)

Thank you very much for your reply (code). It is really taking very less time to complete.