1) Explanation

Let's break down the sentence to understand the meaning required for the blank:
- "Far from $\qquad$ the more belligerent parties involved in the delicate negotiation,"
- The phrase "Far from" sets up a direct contrast. Whatever the mayor's proposal appeared to do (or intended to do) for the "belligerent parties," the actual effect was the opposite. "Belligerent" means hostile or aggressive. In a "delicate negotiation," one would ideally want to calm or satisfy belligerent parties.
- "the mayor's most recent proposal incensed even the more moderate members of the negotiating teams."
- This second part describes the actual effect of the proposal. "Incensed" means to make someone very angry. The proposal angered even the moderate members, implying it certainly didn't appease the belligerent ones.

Combining these, if the proposal angered even moderate members, it clearly did not calm or satisfy the belligerent ones. The blank needs words that mean to calm, soothe, or satisfy, acting as an antonym to "incensed" and what one would hope for in a "delicate negotiation."

Let's evaluate the given options:
- A. mollifying: Appease the anger or anxiety of (someone). This fits perfectly. If the mayor was far from mollifying the belligerent parties, it means he didn't calm them down.
- B. acknowledging: Accept or admit the existence or truth of. This doesn't fit the context of calming or satisfying parties in a negotiation.
- C. appeasing: Pacify or placate (someone) by acceding to their demands; relieve or satisfy (a demand or a feeling). This is a strong synonym for "mollifying" and also fits the context of calming angry parties in a negotiation.
- D. aggravating: Make (a problem, injury, or offense) worse or more serious. This describes the actual effect (incensing), not what the mayor was "far from" doing. This is a strong distractor because it describes the outcome, but the "Far from" structure requires the opposite of the outcome.
- E. aggrieving: Cause distress to. Similar to aggravating, this describes causing a negative effect, not the calming effect that the "far from" structure implies.
- F. ejecting: Force or throw (someone) out. This is irrelevant to the context of negotiations.

Conclusion:
The sentence sets up a clear contrast: the mayor's proposal failed to calm or satisfy the difficult parties, and instead made even the moderate ones angry. Therefore, the words that fit the blank must mean to calm or appease. Both "mollifying" and "appeasing" convey this meaning.

The correct answers are A. mollifying and C. appeasing.