It is considered that a key to overcoming the limitations of classical artificial intelligence is to process distributed representations of information without symbolizing them. However, conventional neural networks require local or symbolic representations to perform complicated processing. Here we present a brain-like inference engine consisting of a nonmonotone neural network that makes inferences based only upon distributed representations. This engine deduces a conclusion according to state transitions of the network along a trajectory attractor formed in a large-scale dynamic system. It has the powerful capability of analogical reasoning. We also construct a simple inference system and demonstrate its many advantages; for example, it can perform nonmonotonic reasoning simply and naturally.