Workflow nets (WF-nets) are Petri nets which represent workflows. Soundness is a criterion of logical correctness defined for WF-nets. It is known that soundness verification is intractable. In this paper, we propose a method to verify soundness using a Linear Temporal Logic (LTL) model checking tool, SPIN. We give an LTL necessary and sufficient condition to verify soundness for WF-nets without livelock. Acyclic WF-nets have no livelock, but cyclic WF-nets may have livelock. We also give a necessary and sufficient condition to verify livelock. Meanwhile, we show that any LTL model checking tool cannot verify soundness for WF-nets with livelock. We give necessary conditions to verify soundness for them. Those conditions enable us to use SPIN even if a given WF-net has livelock. We also develop a tool to verify soundness based on our method. We show effectiveness of our method by comparing our tool with existing soundness verification tools on verification time for 200 cyclic ACWF-nets.