Fitch-Style Proof Help

Question

I'm having some trouble solving a Fitch Proof, Here's how far I've gotten.

Any Help is appreciated.

Thank You

Answer 1

I don't get how you intend to go from what you've done to the goal. Let me suggest a different approach.

Your goal is $\forall x\left(\left(\text{Large}(x)\lor \text{Cube}(x)\right)\to \text{Dodec}(x)\right)$.

It's reasonable to take a constant $a$ such that $\text{Large}(a)\lor \text{Cube}(a)$.

Just because it is allowed, I suggest eliminating $\forall$ from the premises with $a$.

Now performing $\lor$-$\text{Elim}$ on $\text{Large}(a)\lor \text{Cube}(a)$ is one way to go.

If $\text{Large}(a)$ holds, then $\text{Dodec}(a)$ follows from the second premise (not exactly, but close enough).

If $\text{Cube}(a)$ holds, you can get a contradiction from the first premise and you can infer whatever you want, namely $\text{Dodec}(a)$.

Eliminating the disjunction and tying loose ends finalizes the proof.

Hover your mouse over the grey area below to see the suggested proof.