Class

at.logic.gapt.proofs.resolution

Splitting

Related Doc: package resolution

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case class Splitting(splittingClause: ResolutionProof, part1: HOLClause, part2: HOLClause, case1: ResolutionProof, case2: ResolutionProof) extends ResolutionProof with Product with Serializable

DPLL-style splitting as used in SPASS.

This inference is very similar to an or-elimination rule in natural deduction; splittingClause is the proof of a disjunction, and then we do a case analysis: first, we consider the case that part1 is true and derive a contradiction. Second, we consider the case that part2 is true and part1 is false.

  (splittingClause)     (case1)            (case2)
                        [part1]        [part2] [¬part1]
   part1 ∨ part2           ⊥                 ⊥
  -----------------------------------------------------
                          ⊥

Source
resolution.scala
Linear Supertypes
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Inherited
  1. Splitting
  2. Serializable
  3. Serializable
  4. ResolutionProof
  5. SequentProof
  6. DagProof
  7. Product
  8. Equals
  9. AnyRef
  10. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
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Instance Constructors

  1. new Splitting(splittingClause: ResolutionProof, part1: HOLClause, part2: HOLClause, case1: ResolutionProof, case2: ResolutionProof)

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Value Members

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

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    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any
  3. def +(other: String): String

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    Implicit information
    This member is added by an implicit conversion from Splitting to any2stringadd[Splitting] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Splitting, B)

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    Implicit information
    This member is added by an implicit conversion from Splitting to ArrowAssoc[Splitting] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any
  6. val addInputClauses1: Set[HOLClause]

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  7. val addInputClauses2: Set[HOLClause]

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  8. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any
  9. def auxFormulas: Seq[Seq[HOLAtom]]

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    A list of lists containing the auxiliary formulas of the rule.

    A list of lists containing the auxiliary formulas of the rule. The first list constains the auxiliary formulas in the first premise and so on.

    Definition Classes
    SequentProof
  10. def auxIndices: Seq[Seq[SequentIndex]]

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    A list of lists of SequentIndices denoting the auxiliary formula(s) of the rule.

    A list of lists of SequentIndices denoting the auxiliary formula(s) of the rule. The first list contains the auxiliary formulas in the first premise and so on.

    Definition Classes
    SplittingSequentProof
  11. val case1: ResolutionProof

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  12. val case2: ResolutionProof

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  13. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  14. def conclusion: Sequent[Nothing]

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    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    SplittingSequentProof
  15. def dagLike: DagLikeOps[ResolutionProof]

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    Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see DagProof.DagLikeOps for a list.

    Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see DagProof.DagLikeOps for a list.

    Definition Classes
    DagProof
  16. def depth: Int

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    Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.

    Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.

    Definition Classes
    DagProof
  17. def ensuring(cond: (Splitting) ⇒ Boolean, msg: ⇒ Any): Splitting

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    Implicit information
    This member is added by an implicit conversion from Splitting to Ensuring[Splitting] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  18. def ensuring(cond: (Splitting) ⇒ Boolean): Splitting

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    Implicit information
    This member is added by an implicit conversion from Splitting to Ensuring[Splitting] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: Boolean, msg: ⇒ Any): Splitting

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    Implicit information
    This member is added by an implicit conversion from Splitting to Ensuring[Splitting] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. def ensuring(cond: Boolean): Splitting

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    Implicit information
    This member is added by an implicit conversion from Splitting to Ensuring[Splitting] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. final def eq(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  22. def equals(that: Any): Boolean

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    Definition Classes
    DagProof → Equals → AnyRef → Any
  23. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  24. def formatted(fmtstr: String): String

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    Implicit information
    This member is added by an implicit conversion from Splitting to StringFormat[Splitting] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  25. final def getClass(): Class[_]

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    Definition Classes
    AnyRef → Any
  26. val groundNegPart1: Seq[Sequent[HOLAtom]]

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  27. val hashCode: Int

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    Definition Classes
    DagProof → AnyRef → Any
  28. def immediateSubProofs: Seq[ResolutionProof]

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    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    SplittingDagProof
  29. val inputClauses: Set[HOLClause]

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    Definition Classes
    SplittingResolutionProof
  30. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  31. def longName: String

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    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  32. def mainFormulas: Seq[HOLAtom]

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    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  33. def mainIndices: Seq[Nothing]

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    A list of SequentIndices denoting the main formula(s) of the rule.

    A list of SequentIndices denoting the main formula(s) of the rule.

    Definition Classes
    SplittingSequentProof
  34. def name: String

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    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    DagProof
  35. final def ne(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  36. final def notify(): Unit

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    Definition Classes
    AnyRef
  37. final def notifyAll(): Unit

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    Definition Classes
    AnyRef
  38. def occConnectors: Seq[OccConnector[HOLAtom]]

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    A list of occurrence connectors, one for each immediate subproof.

    A list of occurrence connectors, one for each immediate subproof.

    Definition Classes
    SplittingSequentProof
  39. val part1: HOLClause

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  40. val part2: HOLClause

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  41. def premises: Seq[Sequent[HOLAtom]]

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    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  42. val splittingClause: ResolutionProof

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  43. def stepString(subProofLabels: Map[Any, String]): String

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    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  44. def subProofs: Set[ResolutionProof]

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    Set of all (transitive) sub-proofs including this.

    Set of all (transitive) sub-proofs including this.

    Definition Classes
    DagProof
  45. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef
  46. def toString(): String

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    Definition Classes
    DagProof → AnyRef → Any
  47. def treeLike: TreeLikeOps[ResolutionProof]

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    Operations that view the sub-proofs as a tree, see DagProof.TreeLikeOps for a list.

    Operations that view the sub-proofs as a tree, see DagProof.TreeLikeOps for a list.

    Definition Classes
    DagProof
  48. final def wait(): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  49. final def wait(arg0: Long, arg1: Int): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  50. final def wait(arg0: Long): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  51. def [B](y: B): (Splitting, B)

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    Implicit information
    This member is added by an implicit conversion from Splitting to ArrowAssoc[Splitting] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Serializable

Inherited from Serializable

Inherited from ResolutionProof

Inherited from DagProof[ResolutionProof]

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from Splitting to any2stringadd[Splitting]

Inherited by implicit conversion StringFormat from Splitting to StringFormat[Splitting]

Inherited by implicit conversion Ensuring from Splitting to Ensuring[Splitting]

Inherited by implicit conversion ArrowAssoc from Splitting to ArrowAssoc[Splitting]

Ungrouped