(A) \(\displaystyle \exists x(F(x) \land S(x)) \rightarrow (y)(M(y) \rightarrow W(y))\)

(B) \(\displaystyle \exists y(M(y) \land \lnot W(y))\)

1. \(\displaystyle \exists y(M(y) \land \lnot W(y))\) by (B)

2. \(\displaystyle \lnot (y) \lnot (M(y) \land \lnot W(y))\) by (1)

3. \(\displaystyle \lnot (y) (\lnot M(y) \lor W(y))\) by (2)

4. \(\displaystyle \lnot (y) (M(y) \rightarrow W(y))\) by (3)

5. \(\displaystyle \lnot (y)(M(y) \rightarrow W(y)) \rightarrow \lnot \exists x(F(x) \land S(x))\) by (A)

6. \(\displaystyle \lnot \exists x (F(x) \land S(x))\) by (4), (5) MP

7. \(\displaystyle (x) \lnot (F(x) \land S(x))\) by (6)

8. \(\displaystyle (x)(\lnot F(x) \lor \lnot S(x))\) by (7)

9. \(\displaystyle (x)(F(x) \rightarrow \lnot S(x))\) by (8)