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In this paper, we propose a new search technique for ATPG, called CONCAT , which (a) is based on AND/OR reasoning, (b) integrates conflict driven learning, and (c) avoids over specification of test vectors. The technique works seamlessly (i) between Boolean and non-Boolean gates in industrial designs, (ii) across phases in latch-based designs, (iii) between justification and propagation tasks in sequential ATPG, and (iv) across faults in the fault list. Experimental results on combinational ISCAS circuits against SAT-based ATPG, show that we can reduce the test vector specification by upto 74%, with consistent improvement in performance and capacity. We integrated the CONCAT technique into Intel's existing ATPG tool, called Aztec, and obtained upto 67% speed-up and upto 14% more ATPG effectiveness on industrial designs.