I have an old exam-question but don't know how to solve this type of problems. So If someone could give me a hint it would be much appreciated.
Is the following entailment valid?
$$ (p \rightarrow q) \rightarrow r, \neg r\land \neg s, (q \rightarrow p) \lor t, t \rightarrow (r \lor p) \vdash t $$
If I assume that the right handside is false$(\neg t)$ and show that the left handside holds, then the entailment is not valid. But how?
For $$ \neg r \land \neg s $$ to be true then both r and s must be false. And if r is false then $$(p \rightarrow q)$$ must be false. And since $$(q \rightarrow p)$$ must be true, then p is true and q is false.
When t is negated, all premises is satisfiable and therefor the entailment is not valid. Am I right?