Unity and Trinity Contradiction

[Bork]

Proof that the orthodox christian God doesnt exist:

Orthodox Christians believe that the father, the son, and the holy ghost are three distinct entities. They also believe that each is wholly God.

The above beliefs entail that 3 equals one or that identity is not transitive. It is impossible for 3 to equal one or for identity to not be transitive. Hence, orthodox christians believe in an impossible God. Hence, the God they believe in doesn't exist.

http://www.catholic.net/RCC/Catechism/3/l3.html