Spreading truths is recognized as a feasible strategy for inhibiting rumors. This paper is devoted to assessing the effectiveness of the truth-spreading strategy. An individual-level rumor-truth spreading model (the generic URTU model) is derived. Under the model, two criteria for the termination of a rumor are presented. These criteria capture the influence of the network structures on the effectiveness of the truth-spreading strategy. Extensive simulations show that, when the rumor or the truth terminates, the dynamics of a simplified URTU model (the linear URTU model) fits well with the actual rumor-truth interplay process. Therefore, the generic URTU model forms a theoretical basis for assessing the effectiveness of the truth-spreading strategy for restraining rumors.