Consider the following premises. If Barbara sleeps, then Mary is playing squash. Richard is a carpenter. If it is overcast, then Charles is a cashier. If Mary plays squash, then Charles is a cashier. Barbara is sleeping or it is overcast. Can we infer the following from them? Charles is a cashier.
 From the fact that if Barbara sleeps, then Mary is playing squash, and that if Mary plays squash, then Charles is a cashier we can infer that if Barbara sleeps, then Charles is a cashier. Finally, from the fact that if Barbara sleeps, then Charles is a cashier, that if it is overcast, then Charles is a cashier, and that Barbara is sleeping or it is overcast we can infer that Charles is a cashier. Therefore, the answer is yes.