The vulnerability of neural networks to adversarial perturbations has necessitated formal verification techniques that can rigorously certify the quality of neural networks. As the state-of-the-art, branch and bound (BaB) is a "divide-and-conquer" strategy that applies off-the-shelf verifiers to sub-problems for which they perform better. While BaB can identify the sub-problems that are necessary to be split, it explores the space of these sub-problems in a naive "first-come-first-serve" manner, thereby suffering from an issue of inefficiency to reach a verification conclusion. To bridge this gap, we introduce an order over different sub-problems produced by BaB, concerning with their different likelihoods of containing counterexamples. Based on this order, we propose a novel verification framework Oliva that explores the sub-problem space by prioritizing those sub-problems that are more likely to find counterexamples, in order to efficiently reach the conclusion of the verification. Even if no counterexample can be found in any sub-problem, it only changes the order of visiting different sub-problem and so will not lead to a performance degradation. Specifically, Oliva has two variants, including $Oliva^{GR}$, a greedy strategy that always prioritizes the sub-problems that are more likely to find counterexamples, and $Oliva^{SA}$, a balanced strategy inspired by simulated annealing that gradually shifts from exploration to exploitation to locate the globally optimal sub-problems. We experimentally evaluate the performance of Oliva on 690 verification problems spanning over 5 models with datasets MNIST and CIFAR10. Compared to the state-of-the-art approaches, we demonstrate the speedup of Oliva for up to 25X in MNIST, and up to 80X in CIFAR10.