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A cell-free (CF) massive multiple-input-multiple-output (mMIMO) system can provide uniform spectral efficiency (SE) with simple signal processing. On the other hand, a recently introduced technology called hybrid relay-reflecting intelligent surface (HR-RIS) can customize the physical propagation environment by simultaneously reflecting and amplifying radio waves in preferred directions. Thus, it is natural that incorporating HR-RIS into CF mMIMO can be a symbiotic convergence of these two technologies for future wireless communications. This motivates us to consider an HR-RIS-aided CF mMIMO system to utilize their combined benefits. We first model the uplink/downlink channels and derive the minimum-mean-square-error estimate of the effective channels. We then present a comprehensive analysis of SE performance of the considered system. Specifically, we derive closed-form expressions for the uplink …