Conversation so far:
What happened with the deposition of Patrice Lumumba?
Kasa-Vubu announced that he had dismissed Patrice Lumumba and six of his ministers for the massacres in South Kasai and for involving the Soviets in the Congo.
Did Kasa-Vubu depose Patrice Lumumba?
Patrice Lumumba denounced his dismissal over the radio as illegitimate, and in turn labeled Kasa-Vubu a traitor and declared him deposed.

Question: How did they solve this problem?
Self-contained rewrite: How did Kasa-Vubu and Patrice Lumumba solve the problem of declaring each other deposed?