The critical issue here is that the two answer choices you pick
must create sentences with identical meaning. "Irreconcilable" creates a different sentence meaning than that the one made with "conjectural". Thus, you're better off picking any other pair, rather than two words that individually seem to work - if even if the two words individually make the sentence work, if they don't create identical meanings, the answer is automatically wrong.
"Putative" can be used to suggest a bit of uncertainty, and in the context of this question, can be used to refer to something "seeming to be the case".
This would match with "conjectural", and contrast with "proven" in the sentence.
Rohit1988
Are you sure the answer is B and C ? Shouldn’t it be C and F ?
Putative (B) means reputed and it doesn’t seem to fit in this context