The following logical offering, as an attempt to demonstrate there is no God, is taken from the CARM atheism discussion board.  I have reproduced it here.  Following is an analysis.

1. If God exists, God must be omnipotent. (If not, he is not God)
2. If God is omnipotent then:
   1. God is omnipotent because he willed that he would be omnipotent or
   2. he is omnipotent without having willed himself omnipotent.
3. A cannot be true because God could not will himself omnipotent prior to being omnipotent.
4. If A cannot be true, then A is not true.
5. If A is not true, then God is not the source of his own omnipotence.
6. Any entity that is not the source of all potency within reality is not God.
7. Therefore no entity can fulfill the requirements for being a God.
8. If no entity can fulfill the requirements for being a God, then there is no God.
   1. Premise: If God exists, God must be omnipotent. (If not, he is not God).
      1. Response:  This is reasonable.  However, omnipotence does not mean that God can do anything.  Omnipotence means that God can do anything that is consistent with his nature.  God could not violate his own essence and nature.  Some would then say that God is not omnipotent.  So be it.  But, by what logic can anyone claim that a creature or object can behave in a manner contrary to its own nature?  If this can be established, then omnipotence can be defined as being able to do anything, including violating one’s own nature (behaving in a manner contrary to the nature and abilities and restrictions of its own nature).  If this cannot be logically established, then omnipotence must be the ability to do anything that is consistent with one’s nature, attributes, and essence. We see this reflected in the Bible when it says, for example, that God cannot lie (Titus 1:2).  This is a logical necessity since to lie would be a self-contradiction; and if God is true, then he cannot be self-contradictory.
   2. Premise: If God is omnipotent, then:
      1. Premise:  God is omnipotent because he willed that he would be omnipotent or . . .
         1. Response:  Omnipotence would be an attribute of God.  An attribute of God is a natural part of God’s being.  Therefore, God would not will omnipotence in that he was not omnipotent and then decided he would be omnipotent.  This would be a change in His nature and violates the biblical doctrine of God’s immutability – that he changes not (Psalm 90:2; Heb. 13:8).
      2. Premise: . . . he is omnipotent without having willed himself omnipotent.
         1. Response:  This would be a more logical statement.
   3. Premise: A cannot be true because God could not will himself omnipotent prior to being omnipotent.
      1. Response:  Correct.
   4. Premise: If A cannot be true, then A is not true.
      1. Response: This is logically correct since if A cannot be true, then it is not true.
   5. Premise: If A is not true, then God is not the source of his own omnipotence.
      1. Response:  The problem here is that Premise 2A does not apply to the conclusion of Premise 5.  The negation of 2A is simply that God did not will to become omnipotent because he already was omnipotent since omnipotence is part of his nature.  To will something means to make a decision and act upon it.  In this case, it would imply that God willed to change his nature (by becoming omnipotent when He wasn’t), which would pose the logical problem of God becoming something he was not, which would be in violation of his previous nature.  How does something not omnipotent become omnipotent?  Where would it get its “all power” from–something greater than itself?  If so, this would mean that God was not God since there is an omnipotent source greater than God.  So, Premise 5 cannot be true. Second, since God is, by definition, already omnipotent, then he is the source of his own omnipotence, and this further contradicts Premise 5.  But, He is not the source in that he became something he was not or originated something in Himself that was previously non-existent.  This would mean God changed, and that would violate the definition of God (at least the Christian one).  He is the source in that it exists within His own nature.  As God is, his omnipotence is.Third, since 2A is not correct and 2B is correct, the argument should have addressed this possibility in contrast to 2A since it raised it.  It did, after all, offer two possibilities and did not negate the second.  Instead, it ignored 2B as a logical alternative, thereby demonstrating that the argument is insufficient.
   6. Premise: Any entity that is not the source of all potency within reality is not God.
      1. Response:  Since Premise 5 has been shown to be faulty, Premise 6 is not a logical necessity.
   7. Premise: Therefore no entity can fulfill the requirements for being a God.
      1. Response:  Since Premise 6 has been shown to be faulty, Premise 7 is not a logical necessity.
   8. Premise: If no entity can fulfill the requirements for being a God, then there is no God.
      1. Response: Since Premise 7 has been shown to be faulty, Premise 8 is not a logical necessity.

Logic is good for finding errors in thinking.  The error in this argument rests in Premise 5.  Therefore, the concluding argument is not logically necessary, and this does not suffice as proof that God does not exist.