the script doesn't do what you describe, first of all your only incrementing once:

else {
  ($num=$num1++);
  print $num;
  print "\n";
}
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an then you want to loop, but without test (that should be == not =) and you are confusing until with unless (see perlsyn#Compound Statements)

unless ($num1=$num2) {
  print $num2;
}
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IMHO you wanted something like

else {
  $num=$num1;
  while ( $num <= $num2 ) {
     print $num;
     $num++
  }
}
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UPDATE: corrected $num != $num1 confusion