Software systems have evolved to the age of Artificial Intelligence (AI), consisting of independent autonomous agents interacting with each other in dynamic and unpredictable environments. In this kind of environment it is often very difficult to predict all the interactions between the agents. Hence verification of an interaction between multiple agents has become a key research area in AI. In this paper we model and verify an Automatic Meeting Scheduling (AMS) problem having multiple agent communication. The AMS problem helps us to emulate a real life scenario where multiple agents can argue over the defined constraints. A weighted strength based argumentation scheme is proposed, where each argument is weighed against each other to determine the strongest evidence. The argumentation model described in the paper have six agents: Initiator, Scheduler and four Participant agents. We have formalized the agent interactions using Computation Tree Logic (CTL) and verified the scheme by providing suitable specifications (SPEC) in a symbolic model verifier tool called, NuSMV.