The ultrahigh demand for faster computers is currently tackled by traditional methods such as size scaling (for increasing the number of devices), but this is rapidly becoming almost impossible, due to physical and lithographic limitations. To boost the speed of computers without increasing the number of logic devices, one of the most feasible solutions is to increase the number of operations performed by a device, which is largely impossible to achieve using current silicon-based logic devices. Multiple operations in phase-change-based logic devices have been achieved using crystallization; however, they can achieve mostly speeds of several hundreds of nanoseconds. A difficulty also arises from the trade-off between the speed of crystallization and long-term stability of the amorphous phase. We here instead control the process of melting through premelting disordering effects, while maintaining the superior advantage of phase-change-based logic devices over silicon-based logic devices. A melting speed of just 900 ps was achieved to perform multiple Boolean algebraic operations (e.g., NOR and NOT). Ab initio molecular-dynamics simulations and in situ electrical characterization revealed the origin (i.e., bond buckling of atoms) and kinetics (e.g., discontinuouslike behavior) of melting through premelting disordering, which were key to increasing the melting speeds. By a subtle investigation of the well-characterized phase-transition behavior, this simple method provides an elegant solution to boost significantly the speed of phase-change-based in-memory logic devices, thus paving the way for achieving computers that can perform computations approaching terahertz processing rates.