Prove replacement only?

Question

Help with this logic proof. Must use only replacement rules. No inference rules or other assumptions. I'm stuck. I'm told it should take no more than 16 lines.

Premise: (~P v Q) v (~P ^ Q)

Conclusion: ~P v Q

Answer 1

1. (~P v Q) v (~P ⋅ Q)

2. ( (~P v Q) v (~P) ) ⋅ ( (~P v Q) v Q) ...... 1 Distribution

3. ( ( Q v ~P ) v (~P) ) ⋅ ( (~P v Q) v Q) ..... 2 Commutativity

4. ( Q v (~P v ~P) ) ⋅ ( ~P v (Q v Q) ) ..... 3 Associativity

5. ( Q v (~P) ) ⋅ ( ~P v (Q) ) ..... 4 Tautology

6. ( ~P v Q ) ⋅ ( ~P v Q ) ..... 5 Commutativity

7. ~P v Q ..... 6 Tautology