Science - Proof of Propositional Logics

I am being asked if I can prove P, L, Q? (without using resolution-refutation).

Propositional clauses:
1. P -> V
2. !P -> (!V and F)
3. (V or F) -> Q
4. Q -> L

From here I was able, with resolution-refutation, to determine that we cannot prove P but we should be able to prove Q and L… After that I am completely stuck on how to proceed as I am not allowed to prove the question with that approach – only to help me see what answers I should get…

I assume I must either use Forward-Chaining or Backward-Chaining to solve the problems – but no knowledge is given, only implications – so how is one supposed to use either? In all my readings usually we would be given something like F=True (knowledge) or something similar and the chaining would come down to that – but with only implications I can’t see how anything can be proven…

All my attempts (and there have been many) have only added to my confusion.
Any help/hints would be greatly appreciated.

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