Let A be a directed graph.  A is definable iff there is a first order
formula phi(x) such that A satisfies phi[a] and A satisfies (there
exists a unique x)phi(x).  A is nameable iff every a in A is
definable. The question is to show that every finite rigid directed
graph is nameable.

Desired timeframe: 5 days

Let A be a rigid directed graph over vertex set {1,2,...,n}.
Define the following formulae over the variable set {x1,x2,...,xn}:

phi1(x1,...,xn) == AND over {i,j | 1 <= i < j <= n} of (xi <> xj)

phi2(x1,...,xn) == AND over {i,j | 1 <= i, j <= n s.t. (i,j) in A} of R(xi,xj)

phi3(x1,...,xn) == AND over {i,j | 1 <= i, j <= n s.t. (i,j) not in A}
of (not R(xi,xj)

For a in {1,2,...,n}, the following formula phi(x) defines a:

phi(x) == EXISTS {x1,x2,...,xn} (x = xa) and phi1 and phi2 and phi3

what is R in the phi2 formula?