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Logic obfuscation is a prominent approach to protect intellectual property within integrated circuits during fabrication. Many attacks on logic locking have been proposed, particularly in the Boolean satifiability (SAT) attack family, leading to the development of stronger obfuscation techniques. Some obfuscation techniques, including Full-Lock and InterLock, resist SAT attacks by inserting SAT-hard instances into the design, making the SAT attack infeasible. In this work, we observe that this class of obfuscation leaves most of the original design topology visible to an attacker, who can reverse-engineer the original design given the functionality of the SAT-hard instance. We show that an attacker can expose the SAT-hard instance functionality of Full-Lock or InterLock with a polynomial number of queries of its inputs and outputs. We then develop a mathematical framework showing how the functionality can be inferred using only a black-box oracle, as is commonly used in attacks in the literature. Using this framework, we develop a novel attack that allows a SAT-capable attacker to efficiently unlock designs obfuscated with Full-Lock. Our attack recovers the intellectual property from these obfuscation techniques that were previously thought secure. We empirically demonstrate the potency of our novel sensitization attack against benchmark circuits obfuscated with Full-Lock.