Object

at.logic.gapt.examples

PigeonHolePrinciple

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object PigeonHolePrinciple

Constructs a formula representing the pigeon hole principle. More precisely: PigeonHolePrinciple( p, h ) states that if p pigeons are put into h holes then there is a hole which contains two pigeons. PigeonHolePrinciple( p, h ) is a tautology iff p > h.

Since we want to avoid empty disjunctions, we assume > 1 pigeons.

Source
FormulaSequences.scala
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  1. final def !=(arg0: Any): Boolean

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  2. final def ##(): Int

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  3. final def ==(arg0: Any): Boolean

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  4. def apply(ps: Int, hs: Int): FOLFormula

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    ps

    the number of pigeons

    hs

    the number of holes

  5. final def asInstanceOf[T0]: T0

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  6. def atom(p: Int, h: Int): FOLAtom

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  7. def clone(): AnyRef

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  8. final def eq(arg0: AnyRef): Boolean

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  10. def finalize(): Unit

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  11. final def getClass(): Class[_]

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  12. def hashCode(): Int

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  13. def hole(i: Int): FOLConst

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  14. final def isInstanceOf[T0]: Boolean

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  15. final def ne(arg0: AnyRef): Boolean

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  16. final def notify(): Unit

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  17. final def notifyAll(): Unit

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  18. def pigeon(i: Int): FOLConst

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  19. val rel: String

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  20. final def synchronized[T0](arg0: ⇒ T0): T0

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  21. def toString(): String

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  22. final def wait(): Unit

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  24. final def wait(arg0: Long): Unit

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