Edit: There has to be an adjustment to my question as the number of permutations far exceeds 1 trillion which would lead to the main program doing way more than 1 trillion operations. Therefore, the number of operations allowed for the programs will be chosen such that they exceed the number of operations the main program will take to create all those permutations and compare the stored results in memory. Keep this in mind while reading the question.
Is following task achievable?
Find the first program which is larger than 1 million in symbol size which produces a NEW sequence of symbols as output within less than a trillion operations. New sequence as in not having been generated by any other program with less than a million symbols in size and within a trillion operations.
One could consider writing a main program which creates all permutations of symbols valid to our programming language up to a million symbols in length.
Store those permutations as source code to a program and then run each of the code in a separate thread up to a trillion operations.
If a program returns with a finite sequence of symbols as output within 1 trillion operations, store that output in memory.
When all programs with less than a million symbols in size finished, the main program would then generate permutations of symbols with more than a million symbols in size and run a trillion operations on them.
Every such program which would produce a finite sequence of symbols as output within 1 trillion operations would have its output compared to the outputs stored in memory.
If the output is new, hence not stored in memory, one would think that we completed our task. We found the first program that is more than 1 million symbols in size and which produces a new finite sequence of symbols within 1 trillion operations.
But we did not! Our main program which is much smaller in size can simply output that same sequence, as it is the program checking each output and compares it to those stored in memory.
This might be closely related to berry's paradox.
However, this program could actually be written and if we had fast enough computers to actually perform all those operations in the future, the program should give us an output at some point. But seemingly the output would be wrong as it leads to the contradiction.
Does this mean that there exist no first program with more than a million symbols in length that outputs a new first sequence within 1 trillion operations? How can such a program not exist at all?