Typical bottom-up, forward-chaining reasoning systems such as hyperresolution lack goaldirectedness while typical top-down, backward-chaining reasoning systems like Prolog or model elimination repeatedly solve the same goals. Reasoning systems that are goal-directed and avoid repeatedly solving the same goals can be constructed by formulating the topdown methods metatheoretically for execution by a bottom-up reasoning system (hence, "upside-down meta-interpretation" is being used). This also facilitates the use of flexible search strategies, such as merit-ordered search, that are common to bottom-up interpreters. The model elimination theorem proving procedure, its extension by an assumption rule for abduction and its restriction to Horn clauses, are adapted here for such upside-down metainterpretation. This work can be regarded as an extension of the magic set method for query evaluation in deductive databases to both non-Horn clauses and abductive reasoning.