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In recent years, several electronic design automation (EDA) problems in testing and verification have been formulated as Boolean satisfiability (SAT) instances due to the development of efficient general-purpose SAT solvers. Problem-specific learning techniques and heuristics can be integrated into the SAT solver to further speed-up the search for a satisfying assignment. In this paper, we target the problem of generating a complete test-suite for the path delay fault (PDF) model. We provide an incremental satisfiability framework that learns from (1) static logic implications, (2) segment-specific clauses, and (3) unsatisfiability cores of each untestable partial PDF. These learning techniques improvise the test generation for path delay faults that have common testable and/or untestable segments. The experimental results show that a significant portion of PDFs can be excluded dynamically in the proposed incremental SAT formulation for large benchmark circuits, thus potentially achieving speed-ups for PDF test generation.