Seems pretty straightforward:

open (INFILE,$filename) or die "a slow, suffocating death: $!";
$segment=1;
ENDLESS: while (1) {
    open (OUTFILE,">".$filename.$segment.$extension);
    foreach (1..56) {
        $line=<INFILE> or end ENDLESS;
        print OUTFILE $line;
    }
    close OUTFILE;
    $segment++;
}
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The variable names should be pretty self-explanatory. Hope that helps, Brother Ade