my $cnt=0;
while (my $line = <>) {
  $cnt++ if $line =~ /formulae/;
  last if $cnt>1;
}
if ($cnt>1) {
  # got what we wanted
} else {
  # word didn't appear twice
}
[download]

I'm sure it can be done more succinctly, but this should make obvious what is going on.

UPDATE: ops! thanks Albannach. fixed code above.