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gapt.examples

PigeonHolePrinciple

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

    ps

    the number of pigeons

    hs

    the number of holes

  5. final def asInstanceOf[T0]: T0
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  6. def clone(): AnyRef
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  10. def hashCode(): Int
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  11. def hole(i: Int): FOLConst
  12. def inHole(p: Int, h: Int): FOLAtom
  13. final def isInstanceOf[T0]: Boolean
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  14. final def ne(arg0: AnyRef): Boolean
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  16. final def notifyAll(): Unit
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  17. def pigeon(i: Int): FOLConst
  18. val rel: String

    The binary relation symbol.

  19. final def synchronized[T0](arg0: => T0): T0
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  20. def toString(): String
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  21. final def wait(arg0: Long, arg1: Int): Unit
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