What does it really mean [not able not to sin] according to Augustine?

"then logically this person still has the ability not to sin."

I think this is the logical answer from scripture as well. Neither X or Y are the correct biblical answer, and not just from the New Testament - from the Old Testament as well, and from the ante-Nicene Church that leans more toward Pelagian, free will and the ability to cease from sin.

Let's start with Man's nature however. God tells us explicitly what the curse was. In the Garden, after the sin of Eve - who then tempted Adam, God curses them in the order of their responsibility. The Serpent (Satan) first, then Eve, then Adam.

Let's go through that to understand the curse placed on mankind. Let's look for key concepts here that Augustine and his intellectual heirs claim.

1) Does God say man has lost free will?

2) Does God proclaim from this point forward that man cannot stop sinning?

The curse on Eve:

Genesis 3:16 NASB - To the woman He said, "I will greatly multiply Your pain in childbirth, In pain you will bring forth children; Yet your desire will be for your husband, And he will rule over you."

the curse on Adam:

Genesis 3:17-19 NASB - Then to Adam He said, "Because you have listened to the voice of your wife, and have eaten from the tree about which I commanded you, saying, 'You shall not eat from it'; Cursed is the ground because of you; In toil you will eat of it All the days of your life. "Both thorns and thistles it shall grow for you; And you will eat the plants of the field; By the sweat of your face You will eat bread, Till you return to the ground, Because from it you were taken; For you are dust, And to dust you shall return."

Nowhere in a plain reading of scripture from the curse do we see a loss of free will, and a transmission of sin through s*m*n. (Traducionism) God cursed the women in childbirth, which is why Paul says this:

1 Timothy 2:15 NASB - But [women] will be preserved through the bearing of children if they continue in faith and love and sanctity with self-restraint.

and God cursed man with labor pains over the now cursed Earth. The Earth was cursed for the sake of Adam's sin. We also see this as a truth in the very next chapter with Abel and Cain.

Genesis 4:3-4 NASB - So it came about in the course of time that Cain brought an offering to the LORD of the fruit of the ground. Abel, on his part also brought of the firstlings of his flock and of their fat portions. And the LORD had regard for Abel and for his offering;

Abel brought His best, Cain brought the fruit of the ground - what type of fruit grows on the ground? I don't think the book of Jasher is inspired, but I do think they are correct in their interpretation here - that Cain brought rotten fruit to the alter of God.

In fact, we see the fruit of Abel's effort from Heb 11.

Hebrews 11:4 NASB - By faith Abel offered to God a better sacrifice than Cain, through which he obtained the testimony that he was righteous, God testifying about his gifts, and through faith, though he is dead, he still speaks.

Abel's faith in God and free will moved Him to provide a better sacrifice to God than Cain provided. And Cain was moved toward jealousy of the love God showed Abel and moved toward temptation, evil desire -

Genesis 4:5-7 NASB - but for Cain and for his offering He had no regard. So Cain became very angry and his countenance fell. Then the LORD said to Cain, "Why are you angry? And why has your countenance fallen? "If you do well, will not [your countenance] be lifted up? And if you do not do well, sin is crouching at the door; and its desire is for you, but you must master it."

According to God, immediately after the fall, and the curse - Cain had the ability to rule over the sinful desire. He had the ability to not sin, to not murder His brother. Any other interpretation of scripture here, denying Cain's God given ability makes God a liar. Let's say for instance, you take a hard determinism approach of the world, and that God causes everything to have foreknowledge. The logical implications of that are dreadful here. It means not only was God lying to Cain, but He had no actual ability to rule over His sinful desire as God told Him, but God ultimately caused Him to murder Abel.

As I stated from the beginning - this idea is not only contrary to the word of God, it's contrary to what the early Church taught and believed.

Tertullian:

I find, then, that man was constituted free by God. He was master of his own will and power…For a law would not be imposed upon one who did not have it in his power to render that obedience which is due to law. Nor again, would the penalty of death be threatened against sin, if a contempt of the law were impossible to man in the liberty of his will…Man is free, with a will either for obedience of resistance. (c. 207, Vol. 3, pp. 300-301)

Irenaeus:

”Let your light so shine before men, that they may see your good deeds”…And ”Why call me, Lord, Lord, and do not do the things that I say?’…All such passages demonstrate the independent will of man…For it is in man’s power to disobey God and to forfeit what is good.” (c.180, Vol. 1, p. 519)

Ignatius:

I do not mean to say that there are two different human natures, but all humanity is made the same, sometimes belonging to God and sometimes to the devil. If anyone is truly spiritual they are a person of God; but if they are irreligious and not spiritual then they are a person of the devil, made such not by nature, but by their own choice. Pg.61 vol. 1.

Now related to Birth before showing the passage from Clement, let's go to clear scripture on that from two sources, Moses and Ezekiel.

Deuteronomy 1:39 NASB - 'Moreover, your little ones who you said would become a prey, and your sons, who this day have no knowledge of good or evil, shall enter there, and I will give it to them and they shall possess it.

Ezekiel 18:20 NASB - "The person who sins will die. The son will not bear the punishment for the father's iniquity, nor will the father bear the punishment for the son's iniquity; the righteousness of the righteous will be upon himself, and the wickedness of the wicked will be upon himself.

Clement:

Thus although we are born neither good nor bad, we become on or the other and having formed habits, we are with difficulty drawn from them. Pg 273 vol.8

As you can see from scripture and the teachers prior to Augustine - the only conclusion is that both X and Y are incorrect. Man is born with free will, and prior to knowledge of sin, we are neither good nor evil - we are born with the ability to cease from sin, and that is what Paul means by being "free from sin" - not just the condemnation, but the desire.

Origen:

Certain ones of those [Gnostic’s] who hold different opinions misuse these passages. They essentially destroy free will by introducing ruined natures incapable of salvation and by introducing others as being saved in such a way that they cannot be lost.

Now as for what Augustine logically meant?

I think He leaned toward the ability to never cease from sin, it's well known He remained in bondage to lust and sinful desires.