Central limit theorem and increment conditions

Let φ be a convex function defined on R⁺, with φ(0) = 0 and lim_x→0φ(x)/x=0. We show that there exists a uniformly bounded process (X_t) on [0,1] with continuous sample paths that satisfies the increment condition for every u < t, E(φ(| X_t− X_u|)) ⩽ t − u. but that fails the CLT.