class CERES extends AnyRef
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def
apply(endsequent: HOLSequent, projections: Set[LKProof], rp: ResolutionProof): LKProof
Applies the CERES method to a first order proof with equality.
Applies the CERES method to a first order proof with equality. Internally this is handled by the ResolutionToLKProof method.
- endsequent
The end-sequent of the original proof
- projections
The projections of the original proof
- rp
A resolution refutation
- returns
an LK Proof in Atomic Cut Normal Form (ACNF) i.e. without quantified cuts
- def apply(p: LKProof, pred: (HOLFormula) ⇒ Boolean, prover: ResolutionProver): LKProof
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def
apply(p: LKProof, pred: (HOLFormula) ⇒ Boolean): LKProof
Applies the CERES method to a first order proof with equality.
Applies the CERES method to a first order proof with equality. Internally this is handled by the RobinsoToLK method.
- p
a first-order LKProof without strong quantifiers in the end-sequent (i.e. structural rules, cut, logical rules, equational rules but no definitions, schema,higher order)
- pred
a predicate to specify which cut formulas to eliminate (e.g. x => containsQuantifiers(x) to keep propositional cuts intact)
- returns
an LK Proof where all cuts are quantifier-free
- def apply(p: LKProof, prover: ResolutionProver): LKProof
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def
apply(p: LKProof): LKProof
Applies the CERES method to a first order proof with equality.
Applies the CERES method to a first order proof with equality. Internally this is handled by the RobinsoToLK method.
- p
a first-order LKProof (structural rules, cut, logical rules, equational rules but no definitions, schema,higher order) also each formula must be a FOLFormula, since the prover9 interface returns proofs from the FOL layer
- returns
an LK Proof in Atomic Cut Normal Form (ACNF) i.e. without quantified cuts
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- def ensuring(cond: (CERES) ⇒ Boolean, msg: ⇒ Any): CERES
- def ensuring(cond: (CERES) ⇒ Boolean): CERES
- def ensuring(cond: Boolean, msg: ⇒ Any): CERES
- def ensuring(cond: Boolean): CERES
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def
findMatchingProjection(endsequent: HOLSequent, projections: Set[LKProof])(input_clause: Input): LKProof
Finds the matching projection of an input clause in the set of projections.
Finds the matching projection of an input clause in the set of projections.
- endsequent
The common end-sequent of all projections.
- projections
The set of projections.
- input_clause
The clause we need to project to.
- returns
An LK proof endsequent x input_clause contained in projections
- Note
This method is passed to ResolutionToLKProof, which handles the simulation of the reflexivity introduction rule by itself.
- def formatted(fmtstr: String): String
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- def →[B](y: B): (CERES, B)