  The $t$-vertex condition, for an integer $t\ge 2$, was introduced by Hestenes
and Higman in 1971, providing a combinatorial invariant defined on edges and
non-edges of a graph. Finite rank 3 graphs satisfy the condition for all values
of $t$. Moreover, a long-standing conjecture of M. Klin asserts the existence
of an integer $t_0$ such that a graph satisfies the $t_0$-vertex condition if
and only if it is a rank 3 graph.
  We construct the first infinite family of non-rank 3 strongly regular graphs
satisfying the $7$-vertex condition. This implies that the Klin parameter $t_0$
is at least 8. The examples are the point graphs of a certain family of
generalised quadrangles.
