A human is not a part of a species, it is an instance of a species :)
Contradiction management is a very interisting topic, and contradictions are inherent to Wikidata model. We can't expect everything is consistent considering Wikidata only reflects sources, and that 2 sources can disagree in an essentially inconsistent way.
We could expect however that several statements extracted from the same source should be consistent themselves, but it might be rare that we will have enough statements that will be sourced to draw useful inferences. This can lead to subproblems like computing the maximum set of consistent sources on a part of the graph or finding the sources that leads to contradiction when took together.
However, we already have qualifiers that marks a source in contradiction with another : "statement disputed by". We could assume that the sources involved are probably inconsistent with each other.
Or we could simply drop the consistency checks out of the inference way :) And leave it to the constraint system : if an inference draws a path that leads to constraint violation, then community will be notified. To avoid explosion, the scope of inerences could be limited (not trying to compute the transitive closure of the inferences rules application). We could use some sort of "partial consistency" notion, such as those used in constraint programming.
Thinking about it I can imagine constraint problems such as "considering an inference I deduced some way, is it fully consistent with the set of sources we have, or is there a set of sources that implies the inference is not true ?" -> Is the inference a tautology or is the infererence only satisfiable in a problem where each statements maps to a variable, the different sources are values for the domain of the variables, and the sources must be consistent wrt. what we know they says on Wikidata ?