  An approach to universal (meta-)logical reasoning in classical higher-order
logic is employed to explore and study simplifications of Kurt G\"odel's modal
ontological argument. Some argument premises are modified, others are dropped,
modal collapse is avoided and validity is shown already in weak modal logics K
and T. Key to the gained simplifications of G\"odel's original theory is the
exploitation of a link to the notions of filter and ultrafilter from topology.
The paper illustrates how modern knowledge representation and reasoning
technology for quantified non-classical logics can contribute new knowledge to
other disciplines. The contributed material is also well suited to support
teaching of non-trivial logic formalisms in classroom.
