No, the conditions are still poor. As long as it is a prism, it can be proved.

Although B 1C 1 is parallel to BC, the main problem is that AA 1 BB 1 CC 1 cannot be equal.

To prove that two lines are parallel, it is necessary to prove that they are perpendicular to the same plane. But the condition only proves that B 1C 1BC is a plane, while A 1F and AD are not perpendicular to this plane because they are perpendicular to two different straight lines in the plane. They are all perpendicular to only one.

Hope to adopt, thank you.