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I checked the tool (TU Kaiserslautern - Computer Science - Embedded Systems Group: Teaching ( it is generating the proof tree for validity only like following {} |- {phi} but how can I make it to calculate the satisfiability proof like {phi} |- {} ?

in * TF "Emb. Sys. and Rob." by (2.9k points)

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On slide 12, you can see that SAT(φ) holds iff not VALID(¬φ) holds. Hence, to use the sequent calculus (tool) to generate a satisfying assignment, you try to prove that ¬φ is valid. If that proof fails with a counterexample to ¬φ, you have a satisfying assignment for φ. See also slice 108 of the propositional logic chapter that discusses that in detail.
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Got your point.
Thanks for the explanation.

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