The possibility of cluster-state generation on the basis of mixing radiation from two independent lasers in an asymmetric Mach-Zehnder interferometer is shown in this paper. The formulation of the problem is close to that considered before by Menicucci (Phys. Rev. A 83, 62314 (2011)) and Yokouama et al. (Nature Photonics 7, 982 (2013)). The specificity of the current consideration is that our sources of squeezed light (phase-locked sub-Poissonian lasers) radiate bright light in a mixed state, in contrast to an optical parametric oscillator in the subthreshold mode. We also take into account the multimode structure of the radiation, not restricting ourselves to only a constant component of the field-noise characteristics. To set the cluster state, the van Loock-Furusawa separability criterion is used.