Consider the following premises. For all x_6, if x_6 were a carpenter, then x_6 is a sailor. For all x_6, if x_6 were a sailor, then x_6 is making tea. For all x_6, if x_6 were a server, then x_6 is a carpenter. For all x_6, if x_6 makes tea, then x_6 is a server. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which the fact that x_6 makes tea does not imply that x_6 is a sailor.
 From the fact that for all x_6, if x_6 were a server, then x_6 is a carpenter, and that for all x_6, if x_6 were a carpenter, then x_6 is a sailor we can infer that for all x_6, if x_6 were a server, then x_6 is a sailor via universal transitivity. From the fact that for all x_6, if x_6 makes tea, then x_6 is a server, and that for all x_6, if x_6 were a server, then x_6 is a sailor we can infer that for all x_6, if x_6 makes tea, then x_6 is a sailor via universal transitivity. From the fact that for all x_6, if x_6 makes tea, then x_6 is a sailor, and that for all x_6, if x_6 were a sailor, then x_6 is making tea we can infer that for all x_6, x_6 will make tea if and only if x_6 is a sailor via universal biconditional introduction. Finally, from the fact that for all x_6, x_6 will make tea if and only if x_6 is a sailor we can infer that for all x_6, if x_6 makes tea, then x_6 is a sailor via universal biconditional elimination, which contradicts that There is at least one x_6 for which the fact that x_6 makes tea does not imply that x_6 is a sailor. Therefore, the answer is no.