Atheism is the absence of reason..

[Tiberius]

It's been a long time since I've picked apart logical arguments, but it's a fun thing to do.

FAITH = BELIEF WITHOUT EVIDENCE
KNOWING = BELIEF THROUGH EVIDENCE

BELIEF = ACCEPTANCE OF CLAIM with or without EVIDENCE (Correctness)
DISBELIEF = REJECTION OF CLAIM with or without EVIDENCE (incorrectness)

DO YOU AGREE TO THESE DEFINTIONS? THEY ARE VERY NEUTRAL.

I wouldn't say I "agree" to those definitions; the fact that they are "very neutral" is irrelevant, but let's go with them for now.

CONSTRUCT 1
Premise 1: No one can define God. (True)
Premise 2: No one KNOWS if God exists or not..(True)
Conclusion: Any CLAIM to KNOW is a lie. (Valid and Sound)

Premise 1 is incorrect. There are many definitions of God. Luckily though, Premise 1 appears to be completely irrelevant to the conclusion of Construct 1. However, the conclusion as it is is still invalid, because it says "Any CLAIM to KNOW". If the argument was to be logical, it should read:

Premise 1: A claim to know something which nobody knows is a lie.
Premise 2: Nobody knows if God exists or not.
Conclusion: A claim to know whether God exists or not is a lie.

CONSTRUCT 2
Premise 1: Believers HAVE FAITH God Exists. (True)
Premise 2: To HAVE FAITH is claim existence but without evidence (ie. not knowing.) (True)
Conclusion: Believers do not claim to KNOW God exists.(See conlcusion 1.). (VALID AND SOUND)

This one is actually pretty logical and sound. No issues here.

CONSTRUCT 3
Premise 1: Atheists disbelieve God Exists. (TRUE)
Premise 2: To disbelieve is to falsify a belief based on evidence. (ie. Knowing) (true)
Conclusion: Atheists claim to KNOW the Truth about God's existence. (see conclusion1. )
(Valid & Sound)

Uh oh. The guy doesn't understand his own definitions! According to his earlier definition:

DISBELIEF = REJECTION OF CLAIM with or without EVIDENCE.

Now, in Premise 2, he's changed it entirely. Not only is it not about rejecting a claim, it's now about "falsifying a belief", and is "based on evidence".

So whilst the conclusion is logical, it is not sound.

Premise 1: If any claim to know is a lie
Premise 2: And Atheists claim to know
Conclsuoin : Atheists lie.

So, this isn't even a logical argument. Premise 1 isn't a premise, it's a conditional. It's also based on that flawed Conclusion or Construct 1 which I had to fix, so let's do some fixing here:

Premise 1: A claim to know whether God exists or not is a lie.
Premise 2: Atheists claim to know whether God exists or not.
Conclusion: Atheists lie.

Now, the argument is logically valid, however because Premise 2 is based off Construct 3, and Construct 3 is not sound, the entire argument here is not sound.