Godel's Mathematical Proof of God's Existence

Godel was a brilliant mathematician at Princeton and a close friend of Einstein (he only ate food prepared by his wife or Albert). Among his more unusual theories was a design for a time machine that Einstein agreed would allow travel backwards. . . if certain physical properties of the universe exist (and most scientist now believe they don't).

He developed a mathematical proof of God which reads as follows:

Axiom 1. (Dichotomy) A property positive if and only if its negation is negative.
Axiom 2. (Closure) A property is positive if it necessarily contains positive property.
Theorem 1. A positive property is logically consistent (i.e., possibly it has some instance).
Definition. Something is God-like if and only if it possesses all positive properties.
Axiom 3. Being God-like is a positive property.
Axiom 4. Being a positive property is (logical, hence) necessary.
Definition. A property P is the essence of x if and only if x has P and P is necessarily minimal.
Theorem 2. If x is God-like, then being God-like is the essence of x.
Definition. NE(x): necessarily exists if it has an essential property.
Axiom 5. Being NE is God-like.
Theorem 3. Necessarily there is some x such that x is God-like.

Maybe it's just me but it doesn't seem overly convincing, but, then again, I majored in English.