Clique Divergent Clockwork Graphs and Partial Orders

S. Hazan V. Neumann-Lara proved in 1996 that every finite partially ordered set whose comparability graph is clique-null has the fixed point property and they asked whether the converse is true. In this work we answer that question in the negative by exhibiting a finite poset with the fixed point property whose comparability graph is clique-divergent.