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We use a computer-aided approach to prove that there are no standard compactClifford-Klein forms of homogeneous spaces of exceptional Lie groups. Thisyields further support for Kobayashi's conjecture about possible compactClifford-Klein forms. On one hand, our approach is based on the algorithmsdeveloped in this work which eliminate the majority of possibilities. On theother hand, we complete the proof using the algorithmic methods of classifyingsemisimple subalgebras in simple real Lie algebras developed by Faccin and deGraaf, as well as by calculating invariants like a-hyperbolic rank.

Non-existence of standard compact Clifford-Klein forms of homogeneous spaces of exceptional Lie groups