"Man's inhumanity against man" is when humans deny the worth and dignity of other humans and take actions against others that are cruel and pitiless. The underlying presupposition (i.e., the primary conditional; the conditional assumption; the foundational belief) is that humans have intrinsic worth and dignity that requires compassionate and kindly treated. When the dignity and worth is denied, humans act against other humans in ways that are harmful and destructive. This denial of worth and dignity and the consequent pitiless cruel behaviors have come to be called the inhumanity of man against man or man's inhumanity to man.
Though Ivan Denisovich is a story about a Soviet prison camp, where many Article 58 political prisoners serve ten-year terms, its primary theme is ironically man's humanity to man. Yes, being a prison camp in the Soviet's frozen waste lands, there are examples of the secondary theme of man's inhumanity to man, yet you'll note that every instance of inhumanity is followed or preceded by an instance of humanity. Yes, there are prisoners who steal from each other, but these are outnumbered by those who allow others to earn extra money or food rations without preventing them and without jealousy. The primary theme of man's humanity to man is displayed in the way prisoners share with each other, protect each other's food rations, advise and help each other.
Shukov [Ivan] saw that Tsezar realized the danger. he was bustling here and there, but too late. ... Pityingly, Shukov gave him some advice:
'Sit here till the last moment, Tsezar Markovich ... till everyone has left. ... [then] come out and say you're feeling bad. ... That's the way ...'
As an example of the the secondary theme of inhumanity, one dramatic illustration of man's inhumanity to man is evident in the way the guards rigorously give and enforce punishments. Punishments might be "with work" or "without work." Punishment without work will mean broken health or death to the prisoner punished. In this punishment, daily rations are cut to below subsistence caloric levels so prisoners cannot withstand the effects of the cold, and they were not permitted to work to fend off the cold by activity. The guards' unflinching adherence to these punishments demonstrates man's inhumanity to man:
They knew the [lock-up] cells ... You slept on bare boards, and if you'd any teeth left to eat with after all the chattering they'd be doing, they gave you three hundred grammes of bread day after day and hot skilly only on the third, sixth, and ninth.
Ten days. Ten days 'hard' in the cells--if you sat them out the the end your health would be ruined .... hospitalization for you till you croaked. ...
As for those who got fifteen days 'hard' ... they went straight into a hole in the cold earth.
Another illustration of this secondary theme of inhumanity is the punishment allotted to soldiers who had served in World War II. Under the Soviet Article 58, those who were captured prisoners of war who were held or who escaped were given ten-year prison terms for supposedly becoming enemy spies against the Soviet State. The horrible cruelty of this is demonstrated by the old prisoner whom Ivan meets, whose hair had fallen out "long ago," who had been given one ten-year prison term after another:
He'd been told that this old man had spent years without number in camps and prisons, .... Whenever one ten-year stretch had run out they shoved another on to him right away.