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In this paper, we present a novel and accurate method for identifying design for testability (DFT) solutions for register-transfer level (RTL) circuits. Test generation proceeds by abstracting the circuit components using input/output propagation rules so that any justification/propagation event can be captured as a Boolean implication. Consequently, the RTL test generation problem is reduced to a satisfiability (SAT) instance. If a given SAT instance is not satisfiable, then we identify Boolean implications (also known as the unsatisfiable segment) that are responsible for unsatisfiability. We show that adding DFT elements is equivalent to modifying these clauses such that the unsatisfiable segment becomes satisfiable. The proposed DFT technique is both fast and accurate as it is applicable to RTL and mixed gate-level/RTL circuits and uses exact unsatisfiability conditions to identify the DFT solutions.