Your first example is not grammatical, and its meaning is consequently unclear.
Your variants of the first example are all grammatical, but they do not mean what you probably intended by the first example.
Part of the problem is that "justify" is frequently used instead of "try to justify." MW defines the word to mean "to prove or show [something] to be right, just, or reasonable."
Moreover, the variants are orders not to use your intelligence in order to find valid reasons for your idleness. I greatly doubt that is what you are trying to say.
Here is what I suspect you mean by your first example:
Do not claim that your intelligence justifies your idleness.
More simply
Your intelligence does not justify your idleness.
Your mention of an "instrumental case" suggests to me that you are trying to use a form that exists in your native language. Case is seldom a useful concept in English, which has only remnants of inflection.
EDIT:
I shall not try to explain differences between Russian and English because I know no Russian. I know that Russian that suffixes on the ends of words (inflections) heavily affect meaning. English is much, much less reliant on suffixes to create meaning. English, however, is heavily dependent on lexical means to create meaning. For example,
"Justify" may be used in the following way
Person X justified his actions
means
Person X argued successfully that his actions were correct.
Notice that the subject is a person, and the meaning relates to the phyical action of speaking or writing as well as implying a result from that action.
Some people also say
Person X justified his actions
to mean
Person X tried to argue that his actions were correct, but was not successful
I prefer using "try to justify" in that case to avoid ambiguity. But again, a person is the subject, and the meaning relates to a physical action.
However, "justify" can be used in a different way
Y justifies X's actions
means
Y is the reason that X's actions were correct
Now the subject is not a person, and the meaning does not relate to a physical action, but rather to a logical relationship.
Your example was trying to squeeze both meanings into a single sentence.
Now you can do many things in English, but you cannot make a single utterance of one word convey two different meanings in the same sentence. You could use a word in two different senses in one sentence if the word is used two different times. That would be grammatical, but would usually be bad style.
Don't try to justify your idleness by saying that your intelligence justifies it
That is grammatical, but I would never write it. The shifting meanings of "justify" make it confusing.
