List of all possible reasoning tasks - satisfiability and theorem proving only? What is the exhaustive list of reasoning tasks? As far as I can understand, then any logical reasoning reduces to 2 tasks only: 1) satisfiability problem (finding the assignment of the variables) and 2) theorem proving (deducing general statement from the other statements). 

https://en.wikipedia.org/wiki/Logical_reasoning lists 3 types of reasoning: 1) deductive; 2) inductive; 3) analogical. But, as far as I understand, then each of those types reduces to some methods/heuristics of forming some statements and again - in the final step one of two reasoning tasks is applied - SAT or theorem proving.

Logic programming in essence if SAT problem as well (at least for stable model semantics/fixed poing semantics): one compiles the list of implicational statements and then tries to find the assignment of variables under which no internal dynamics happen further.

So - are there only those 2 reasoning tasks - SAT and theorem proving? Of course, there are many logics in which those tasks can be completed, but that is other problem, see, e.g. https://kwarc.info/people/frabe/Research/rabe_howto_14.pdf and https://uniformal.github.io/

The question is important when one tries to implement cognitive architecture (https://en.wikipedia.org/wiki/Cognitive_architecture and http://bicasociety.org/cogarch/architectures.php) - one should be sure about the exhaustive list or reasoning tasks to certify that some implementation achieves some generality.

My question is of even more important when one considers neural networks. One can ask - what is the exhaustive list of reasoning tasks that neural networks should be able to do? Of course, generally there are evidence about Turing completeness of neural networks, but my question concerns the cognitive/reasoning subset of general computations.
There is no exhaustive list of reasoning tasks, as the phrase "reasoning task" does not have a precise definition.

Don't put too much weight on categorizations.  They're a descriptive tool that might help you get a high-level overview of a field, but they're inherently subjective, incomplete, and imperfect.  There's tons of work on artificial reasoning, and there are many ways one could potentially put a mental framework around it -- there's no one right answer about how to do that.