The paper considers the space of orderings ( X R ( x , y ) , G R ( x , y ) ) of the field of rational functions over R in two variables. It is shown that the pp conjecture fails to hold for such a space; an example of a positive primitive formula which is not product-free and one-related is investigated and it is proven, that although the formula holds true for every finite subspace of ( X R ( x , y ) , G R ( x , y ) ) , it is false in general. This provides a negative answer to one of the questions raised in [M. Marshall, Open questions in the theory of spaces of orderings, J. Symbolic Logic 67 (2002) 341–352]. This work is a sequel to the previous results presented in [P. Gładki, M. Marshall, The pp conjecture for spaces of orderings of rational conics, J. Algebra Appl. 6 (2) (2007) 245–257]. Both spaces of orderings of conic sections and the space ( X R ( x , y ) , G R ( x , y ) ) are important examples of spaces of stability index 2 that are within the scope of our research.