In the era of the rapid development of the Internet, the threshold for information spreading has become lower. Most of the time, rumors, as a special kind of information, are harmful to society. And once the rumor appears, the truth will follow. Considering that the rumor and truth compete with each other like light and darkness in reality, in this paper, we study a rumor spreading model in the homogeneous network called 2SIH2R, in which there are both spreader1(people who spread the rumor) and spreader2(people who spread the truth). In this model, we introduced discernible mechanism and confrontation mechanism to quantify the level of people's cognitive abilities and the competition between the rumor and truth. By mean-field equations, steady-state analysis and numerical simulations in a generated network which is closed and homogeneous, some significant results can be given: the higher discernible rate of the rumor, the smaller influence of the rumor; the stronger confrontation degree of the rumor, the smaller influence of the rumor; the large average degree of the network, the greater influence of the rumor but the shorter duration. The model and simulation results provide a quantitative reference for revealing and controlling the spread of the rumor.