Consider the following premises. Mary is a soldier if and only if Thomas is sad. If Thomas were a lawyer, then Mary is a soldier. For all z_3, z_3 is sad or z_3 is a lawyer. Can we infer the following from them? Mary is not a soldier.
 From the fact that for all z_3, z_3 is sad or z_3 is a lawyer we can infer that Thomas is sad or Thomas is a lawyer. From the fact that Mary is a soldier if and only if Thomas is sad we can infer that if Thomas were sad, then Mary is a soldier. Finally, from the fact that if Thomas were sad, then Mary is a soldier, that if Thomas were a lawyer, then Mary is a soldier, and that Thomas is sad or Thomas is a lawyer we can infer that Mary is a soldier, which contradicts that Mary is not a soldier. Therefore, the answer is no.