You don't actually need a counter, since Perl already provides one: $.

my $max_lines = 800;
if (($. - 1) % $max_lines == 0) {
   my $file_num  = int(($. - 1) / $max_lines) + 1;
   my $file_name = "file${file_num}.txt";
   open($fh_out, '>', $file_name)
      or die("Unable to create file \"$file_name\": $!\n");
}
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