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I'm stuck on trying to find an unsatisfiable conjunction of the form $a \wedge b \wedge c$ where:

  • $a \wedge b$ is satisfiable
  • $a \wedge c$ is satisfiable
  • $b \wedge c$ is satisfiable
  • $a, b, c$ are boolean literals from Linear Integer Arithmetic, i.e. $x \leq y$, $\neg(3 = 5)$, $z = z$, etc.

Is there no such case that this is possible (is there a proof for it), or am I just missing an obvious example?

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1 Answer 1

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$(x< y) \land (y < z) \land (z < x)$

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