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gapt.examples.sequence

SumExampleProof

object SumExampleProof extends ProofSequence

Functions to construct the straightforward cut-free FOL LK proofs of the sequents

P(sn(0),0), ∀x,y. P(s(x),y) → P(x,s(y)) :- P(0,sn(0))

where n is an Integer parameter >= 0.

This sequent is shown to have no cut-free proof which can be compressed by a single cut with a single quantifier in S. Eberhard, S. Hetzl: On the compressibility of finite languages and formal proofs, submitted, 2015.

Source
SumExampleProof.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(n: Int): LKProof

    n

    An integer >= 0.

    returns

    A proof of P(sn(0),0), ∀x,y. P(s(x),y) → P(x,s(y)) :- P(0,sn(0))

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    SumExampleProofProofSequence
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