Consider the following premises. For all z_1, if z_1 cooks, then z_1 is an artist. For all z_1, z_1 is a scientist or z_1 will not play squash. For all z_1, if z_1 were a scientist, then z_1 is cooking. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_1 for which the fact that z_1 plays squash does not imply that z_1 is an artist.
 From the fact that for all z_1, if z_1 were a scientist, then z_1 is cooking, and that for all z_1, if z_1 cooks, then z_1 is an artist we can infer that for all z_1, if z_1 were a scientist, then z_1 is an artist via universal transitivity. From the fact that for all z_1, z_1 is a scientist or z_1 will not play squash we can infer that for all z_1, if z_1 plays squash, then z_1 is a scientist via universal rewriting. Finally, from the fact that for all z_1, if z_1 plays squash, then z_1 is a scientist, and that for all z_1, if z_1 were a scientist, then z_1 is an artist we can infer that for all z_1, if z_1 plays squash, then z_1 is an artist via universal transitivity, which contradicts that There is at least one z_1 for which the fact that z_1 plays squash does not imply that z_1 is an artist. Therefore, the answer is no.