1.Qe8? threat: 2.Qxe5+ Bb2 3.Qxb2#

1...Bb2 2.Qa8+ Ba3 3.Qxa3+ Ba2+ 4.Qxa2#

but: 1...Ba2+!

1.Qxb5! threat: 2.Qxe5+ Bb2 3.Qxb2#

1...Ba2+ 2.Kxc2 threat: 3.Qxe5+ Bb2 4.Qxb2#

               2...Bb3+ 3.Qxb3 threat: 4.Qb1#

                              3...Bb2 4.Qxb2#

1...Bb2 2.Qa4+ Ba3 3.Qxa3+ Ba2+ 4.Qxa2#

Minimal engraving. Refutation a false trail is one of the defenses in the solution.