Use an Indirect Proof. Begin by assuming (Aea ∧ Cfc), use the first premise to derive Beb, the third to derive Cbf, and the second to derive a contradiction. Some of your subproofs will likewise be Indirect Proofs; using existential generalisation to derive their contradictions.

Assuming, that the thing you call IP operates as expected (derive a contradiction from an assumption, thereby deducing that the negation of the assumption holds).

Use an Indirect Proof.

Begin by assuming (Aea ∧ Cfc), use the first premise to derive Beb, the third to derive Cbf, and the second to derive a contradiction.

Some of your subproofs will likewise be Indirect Proofs; using existential generalisation to derive their contradictions.

Assuming, that the thing you call IP operates as expected (derive a contradiction from an assumption, thereby deducing that the negation of the assumption holds).