You're mixing up where the negation goes. The lemma says that in any configuration which starts finite and never dies out, there DOES exist at least one lifeli

You're mixing up where the negation goes. The lemma says that in any configuration which starts finite and never dies out, there DOES exist at least one lifeline which DOESN'T go in a forbidden direction. (There are almost certainly lots of other lifelines which do go in forbidden directions, that's fine.) An example of a lifeline in a southeastward spaceship that never goes S or SE: http://www.xamuel.com/images/lifeline.gif http://www.xamuel.com/images/lifeline.gif The proof I outlined above was published in the Elect. J. of Combinatorics (last section): http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i1p31 http://www.combinatorics.org/ojs/index.php/eljc/article/view...