Within satisfaction problems or any decision or other problem which is reducible to a satisfaction problem, the invention tracks the paths along which implications propagate and identifies conditional contradictions and subsequently moves the contradictions back down the implicational paths toward assumptions or other unreasoned assertions in order to expel the contradictions. The action is completed in less time than is incurred by existing methods and thus provides a performance improvement to the devices, software, or processes which address such problems. Such problems are addressed by devices, software, and processes related to many technical fields, including: ore refining; pipeline routing; yarn manufacture; fabric cutting; sawyering; mechanical component design; structural design of data processing systems; design and analysis of circuits or semiconductor masks; inspection and guarding of containers, pipes, and galleries; sensor array operations; orbital satellite operations; data compression; chemical analysis; design and analysis of proteins.
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