Machine learning techniques based on Data Mining are employed for automatic assertion generation in hardware digital design verification. This paper presents a new mining technique to extract all design properties from simulation traces. The extracted properties cover all possible design assertions either at system level or Register Transfer Logic (RTL) verification depending on the simulated design level. It can afterwards be tuned or filtered to match a certain desired abstraction level. The new technique is based on a Breadth-First Decision Tree (BF-DT) search algorithm. The innovated algorithm maps the input simulation traces to a search tree that covers all possible input combinations, and prunes the redundant paths. The proposed technique is tested against recently innovated mining techniques for some basic digital design functions as a proof of concept for the gained efficiency. The main advantage of the new technique is the possibility to extract all the design properties from the simulation traces achieving hundred-percent coverage in a reasonably efficient time for millions of simulation traces.