What seems to get somewhat bypassed in the total depravity doctrine is the role of Satan in deceiving man to disobedience and also influencing Cain to murder Abel.
St. Irenaeus ( about 175 AD) when preaching from Genesis seems to focus on the role of Satan in the fall of Adam & the depravity of Cain:
15. But, lest man should conceive thoughts too high, and be exalted and uplifted, as though he had no lord, because of the authority and freedom granted to him, and so should transgress against his maker God, overpassing his measure, and entertain selfish imaginings of pride in opposition to God; a law was given to him by God, in order that he might perceive that he had as lord the Lord of all. And He set him certain limitations, so that, if he should keep the commandment of God, he should ever remain such as he was, that is to say, immortal; but, if he should not keep it, he should become mortal and be dissolved to earth from whence his formation had been taken. Now the commandment was this:
Of every tree that is in the Paradise thou shalt freely eat; but of that tree alone from which is the knowledge of good 84and evil, of it thou shalt not eat; for in the day thou eatest, thou shalt surely die.
16. This commandment the man kept not, but was disobedient to God, being led astray by the angel who, for the great gifts of God which He had given to man, was envious and jealous of him,
107 and both brought himself to nought and made man sinful, persuading him to disobey the commandment of God. So the angel, becoming by his falsehood the author and originator of sin, himself was struck down, having offended against God, and man he caused to be cast out from Paradise. And, because through the guidance of his disposition he apostatized and departed from God, he was called Satan, according to the Hebrew word; that is, Apostate:
108 a but he is also called Slanderer. Now God cursed the serpent which carried and conveyed the Slanderer; and this malediction came on the beast himself and on the angel hidden and concealed in him, even on Satan; and man He put away from His presence, removing him and making him to dwell on the way to Paradise
109 at that time; because Paradise receiveth not the sinful.
17. And when they were put out of Paradise, Adam and his wife. Eve fell into many troubles of anxious grief, going about with sorrow and toil
85and lamentation in this world. For under the beams of this sun man tilled the earth, and it put forth thorns and thistles, the punishment of sin. Then was fulfilled that which was written:
Adam knew his wife, and she conceived and bore Cain; and after him
she bare Abel. Now the apostate angel, who led man into disobedience and made him sinful and caused his expulsion from Paradise, not content with the first evil, wrought a second on the brothers; for filling Cain with his spirit he made him a fratricide. And so Abel died, slain by his brother; signifying thenceforth that certain should be persecuted and oppressed and slain, the unrighteous slaying and persecuting the righteous. And upon this God was angered yet more, and cursed Cain; and it came to pass that everyone of that race in successive generations was made like to the begetter. And God
raised up another son to Adam,
instead of Abel who was slain.
18. And for a very long while wickedness extended and spread, and reached and laid hold upon the whole race of mankind, until a very small seed of righteousness remained among them
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