abstract class AnalysisWithCeresOmega extends AnyRef
The generic template for using ceres_omega to analyze a proof. It performs the following steps:
1) eliminate definitions (AnalysisWithCeresOmega.input_proof
2) eliminate definitions (AnalysisWithCeresOmega.preprocessed_input_proof1
3) expand non-atomic axioms (AnalysisWithCeresOmega.preprocessed_input_proof2)
4) make the proof regular (AnalysisWithCeresOmega.preprocessed_input_proof)
5) convert it to lk_sk (AnalysisWithCeresOmega.lksk_proof)
6) compute the struct, css and projections (AnalysisWithCeresOmega.css,
AnalysisWithCeresOmega.projections, AnalysisWithCeresOmega.struct)
7) map the css to first-order by lambda lifting and erasure of types (AnalysisWithCeresOmega.fol_css)
8) try to find a refutation of the css (AnalysisWithCeresOmega.fol_refutation)
9) reintroduce types (might fail because type erasure is a heuristic which is unsound in general) (no method available, included in step 11)
10) reintroduce terms abstracted away by lambda lifting (no method available, included in step 11)
11) construct an r_al proof from the refutation (AnalysisWithCeresOmega.ral_refutation)
12) construct the acnf (AnalysisWithCeresOmega.acnf)
13) construct the expansion proof (with atomic cuts) (AnalysisWithCeresOmega.expansion_proof)
14) print statistics (AnalysisWithCeresOmega.printStatistics)
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Instance Constructors
- new AnalysisWithCeresOmega()
Abstract Value Members
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abstract
def
proofdb(): ExtendedProofDatabase
The proof database to start from.
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abstract
def
root_proof(): String
The name of the root proof to start with
Concrete Value Members
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final
def
!=(arg0: Any): Boolean
- Definition Classes
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final
def
##(): Int
- Definition Classes
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-
def
+(other: String): String
- Implicit
- This member is added by an implicit conversion from AnalysisWithCeresOmega to any2stringadd[AnalysisWithCeresOmega] performed by method any2stringadd in scala.Predef.
- Definition Classes
- any2stringadd
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def
->[B](y: B): (AnalysisWithCeresOmega, B)
- Implicit
- This member is added by an implicit conversion from AnalysisWithCeresOmega to ArrowAssoc[AnalysisWithCeresOmega] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc
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- @inline()
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final
def
==(arg0: Any): Boolean
- Definition Classes
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lazy val
abstracted_constants_map: expr.fol.replaceAbstractions.ConstantsMap
The first order export of the preprocessed characteristic sequent set (preprocessed_css), together with the map of replacing constants.
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lazy val
acnf: LKProof
The simulation of the ral_refutation on the projections i.e.
The simulation of the ral_refutation on the projections i.e. an LKsk proof where cuts only work on atom formulas
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final
def
asInstanceOf[T0]: T0
- Definition Classes
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def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
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- @throws( ... )
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lazy val
css: Set[HOLSequent]
The characteristic sequent set of the preprocessed_input_proof.
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def
ensuring(cond: (AnalysisWithCeresOmega) ⇒ Boolean, msg: ⇒ Any): AnalysisWithCeresOmega
- Implicit
- This member is added by an implicit conversion from AnalysisWithCeresOmega to Ensuring[AnalysisWithCeresOmega] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: (AnalysisWithCeresOmega) ⇒ Boolean): AnalysisWithCeresOmega
- Implicit
- This member is added by an implicit conversion from AnalysisWithCeresOmega to Ensuring[AnalysisWithCeresOmega] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: Boolean, msg: ⇒ Any): AnalysisWithCeresOmega
- Implicit
- This member is added by an implicit conversion from AnalysisWithCeresOmega to Ensuring[AnalysisWithCeresOmega] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
-
def
ensuring(cond: Boolean): AnalysisWithCeresOmega
- Implicit
- This member is added by an implicit conversion from AnalysisWithCeresOmega to Ensuring[AnalysisWithCeresOmega] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
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final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
equals(arg0: Any): Boolean
- Definition Classes
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lazy val
expansion_proof: ExpansionProofWithCut
The expansion proof of the cut-free proof acnf.
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lazy val
expansion_proof_fol_deep: FOLFormula
A first-order conversion of the deep formula of the expansion_proof.
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def
export_thf(filename: String): Unit
Exports the preprocessed characteristic sequent (preprocessed_css) set to the TPTP THF format
Exports the preprocessed characteristic sequent (preprocessed_css) set to the TPTP THF format
- filename
The name of the file to export to
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def
finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] )
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lazy val
fol_css: List[Sequent[FOLAtom]]
The first order export of the preprocessed characteristic sequent set (preprocessed_css), together with the map of replacing constants.
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lazy val
fol_refutation: ResolutionProof
The first order refutation of the first order characteristic sequent set (fol_css)
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lazy val
fol_refutation_expansion_proof: ExpansionProofWithCut
The expansion proof of the first-order refutation (fol_refutation).
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def
formatted(fmtstr: String): String
- Implicit
- This member is added by an implicit conversion from AnalysisWithCeresOmega to StringFormat[AnalysisWithCeresOmega] performed by method StringFormat in scala.Predef.
- Definition Classes
- StringFormat
- Annotations
- @inline()
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final
def
getClass(): Class[_]
- Definition Classes
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def
hashCode(): Int
- Definition Classes
- AnyRef → Any
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lazy val
input_proof: LKProof
The input LK proof, extracted by the name root_proof from the proof database (proofdb)
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
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lazy val
lksk_proof: LKProof
The processed input proof converted to LKsk.
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final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
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final
def
notify(): Unit
- Definition Classes
- AnyRef
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final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
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lazy val
preprocessed_css: List[HOLSequent]
The characteristic sequent set (css) after removal of labels and subsumption
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lazy val
preprocessed_input_proof: LKProof
The input proof (TAPEPROOF) after definition elimination(preprocessed_input_proof1, expansion of logical axioms to atomic axioms (preprocessed_input_proof2) and regularization (preprocessed_input_proof3)
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lazy val
preprocessed_input_proof1: LKProof
The input proof (TAPEPROOF) after preprocessing step 1: definition elimination
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lazy val
preprocessed_input_proof2: LKProof
The input proof after preprocessing step 2: expansion of logical axioms to atomic axioms
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lazy val
preprocessed_input_proof3: LKProof
The input proof preprocessing step 3: regularization
- def printStatistics(): Unit
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def
print_css_thf(): Unit
Prints the preprocessed characteristic sequent set in TPTP THF format.
Prints the preprocessed characteristic sequent set in TPTP THF format. Use export_thf to write it to a file.
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lazy val
projections: Set[LKProof]
The set of projections of the preprocessed_input_proof.
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lazy val
ral_refutation: ResolutionProof
The ral version of the first-order refutation (fol_refutation), with all necessary simplifications undone
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lazy val
reproved_deep: ResolutionProof
The proof of the deep formula of the expansion_proof.
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def
skip_strategy(): (HOLFormula) ⇒ Boolean
Determines if and which cuts should be taken into accoutn for cut-elimination.
Determines if and which cuts should be taken into accoutn for cut-elimination. Default: propositional cuts are skipped.
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lazy val
struct: Struct[HOLFormula]
The struct of the proof.
The struct of the proof. It is an intermediate representation of the characteristic sequent set.
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final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
- def thf_reproving_deep(filename: Option[String]): String
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def
timeout(): Duration
Timeout for call to theorem provers.
Timeout for call to theorem provers.
- returns
the timeout as duration. default: 60 seconds
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def
toString(): String
- Definition Classes
- AnyRef → Any
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final
def
wait(): Unit
- Definition Classes
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- @throws( ... )
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final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
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final
def
wait(arg0: Long): Unit
- Definition Classes
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def
→[B](y: B): (AnalysisWithCeresOmega, B)
- Implicit
- This member is added by an implicit conversion from AnalysisWithCeresOmega to ArrowAssoc[AnalysisWithCeresOmega] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc