and(implies(not(not(implies(not(v), some(r, u)))), not(and(not(implies(u, not(w))), and(v, or(implies(w, w), all(r, v)))))), not(implies(not(not(implies(not(v), some(r, u)))), not(and(not(implies(u, not(w))), and(v, or(implies(w, w), all(r, v)))))))