We adopt pKTN, the Petri-net-based Knowledge Transitive Network, which is an AI approach representing first-order predicate logic (FOL) in the form of a network, and present a successful algorithm for deductive inference. During deduction, the pKTN is expanded to a network with AND/OR-tree structure, in which we need to solve an 'ill-posed' problem, finding a symbolically consistent subtree out of a given redundant tree. For this problem, a token-based algorithm named ELISE (ELiminating Inconsistency by SElection) was proposed, but existing ELISE was only applicable to non-redundant (well-posed) problems. In this paper, we seriously revise the algorithm of ELISE, make it applicable to redundant (ill-posed) problems of the pKTN, and examine the validity of the algorithm with some preliminary experiments. Since ELISE is a distributed algorithm that makes only transitions relevant to a query fire, we expect that the pKTN can now be a powerful method to construct a large logical database equipped with an efficient reasoning tool.