Incorrectness logic (IL) based on under-approximation is effective at finding real program bugs. The prior work utilises bi-abductive specification inference mechanism to infer IL specifications for analysing large-scale C projects. However, this approach does not work well with object-oriented (OO) programs because it does not account for class inheritance and method overriding. In our work, we present an IL specification inference system that tackles these issues. At its core, we encode type information in our bi-abductive reasoning and propagate type constraints throughout the analysis. The direct benefit is that we can efficiently identify bugs caused by improper usage of the casting operator, which cannot be handled by the existing specification inference. Meanwhile, our system can reduce false positives while finding more true bugs because of not losing OO-type information. Furthermore, we model dynamic dispatching calls by inferring dynamic specifications, where the possible types of the calling object at runtime are bounded by the type constraints. We prototype our system in ILoop and evaluate it using real-world projects. Experimental results show that it finds 400% more class-cast-exceptions compared with Error Prone and improves the precision of finding null-pointer-exceptions by 27.0% compared with Pulse.