Proof the above premises and hypothesis using Indirect proof:

Premise $1$: $P\to \mathrm{\neg}R$

Premise $2$: $Q\to S$

Premise $3$: $(R\vee S)\to T$

Premise $4$: $\mathrm{\neg}T$

Hypothesis: $P\vee Q$

Premise $1$: $P\to \mathrm{\neg}R$

Premise $2$: $Q\to S$

Premise $3$: $(R\vee S)\to T$

Premise $4$: $\mathrm{\neg}T$

Hypothesis: $P\vee Q$