Such a claim is like that of someone who insists that the very same thing is both existent and nonexistent, or both eternal and created, or who maintains of a body that it is at once standing and sitting, moving and motionless. Given this, its self-contradiction is too obvious to require any formal proof.
When the Christians say, “He is one in essence and three in attributes,” we reply: Had you been content to say simply that He is one yet possesses multiple attributes, the vast majority of Muslims would not object; what they reject is your restricting those attributes to exactly three. That restriction is false for several reasons:
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In your own theology the Father is the substance, not an attribute. Consequently, He could have only the attributes of life and knowledge, which would leave one substance with two hypostases, whereas you affirm three.
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The Lord’s attributes are by no means limited to life and knowledge; He is also described as possessing power and many others.
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You sometimes interpret the Holy Spirit as life, at other times as power, and at yet other times as existence. Likewise you explain the Word sometimes as knowledge, sometimes as wisdom, and sometimes as speech.
The flaws in your attempt to establish precisely three attributes are therefore manifold, and yet you go further by turning each of those attributes into a god—declaring life to be a god and knowledge to be a god. This is patently false.
As for those, among Muslims and others, who deny the reality of divine attributes altogether, they answer you from different angles, as when some of them say: “If one were to ask, ‘Do you not maintain that the parts…’”