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This paper describes the design of a multiprocessor COOL system to be implemented with superconductor Rapid Single-Flux-Quantum (RSFQ) technology that is being developed at SUNY (Stony Brook, USA) within the framework of the Hybrid Technology MultiThreaded architecture (HTMT) project. The objective of the current phase of the project is the proof-of-concept study of a computer that could be built with novel technologies such as RSFQ, optical networks, processors-in-memory, and holographic memory in order to achieve petaflops-level performance within a reasonable hardware and power budget by 2007. The COOL system design is based on a new multithreaded COOL-I architecture which supports two-level multithreading to hide latencies associated with memory and arithmetic operations in superconductor SPELL processors. Preliminary simulation results show that a COOL system with 4096 66-GHz processors can achieve petaflops-level performance on computationally-intensive parallel program kernels.