Object

at.logic.gapt.examples

nTape6

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object nTape6

The object nTape6 generates hard problems for higher order theorem provers containing an axiomatization of if-then-else. Formulas: f1,f2 ... if-then-else axiomatizations f3,f4 ... properties of the successor function (0 is no successor and a number is always different from its successor) conclusion0 ... there exists a function h s.t. h(0) = 1, h(1) = 0 conclusion1 ... there exists a function h s.t. h(0) = 1, h(1) = 0, h(2) = 0 conclusion2 ... there exists a function h s.t. h(0) = 1, h(1) = 0, h(2) = 1 w1 ... witness for sc w2 ... witness for sc2

The problems are (in sequent notation):

P0: f1, f2 :- conclusion0 P1: f1, f2, f3, f4 :- conclusion1 P2: f1, f2, f3, f4 :- conclusion2

The generated filenames are "ntape6-${i}-without-witness.tptp" for i = 0 to 2.

To show that there are actual witnesses for the function h, we provide a witness, where the witness w1 can be used for both W0 and W1:

W0: { w1 :- } x P0 W1: { w1 :- } x P1 W2: { w2 :- } x P2

The generated filenames are "ntape6-${i}-with-witness.tptp" for i = 0 to 2.

Source
nTape6.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. final def asInstanceOf[T0]: T0

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  6. final def eq(arg0: AnyRef): Boolean

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  7. def equals(arg0: Any): Boolean

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  8. def export(path: String = "."): Unit

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    Export the problems P0-P2 and W0-W2 to TPTP THF.

  9. def finalize(): Unit

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  10. val fn: String

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  11. object formulas

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    Contains all the formulas used.

  12. final def getClass(): Class[_]

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  13. def hashCode(): Int

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  14. final def isInstanceOf[T0]: Boolean

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  15. final def ne(arg0: AnyRef): Boolean

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  16. final def notify(): Unit

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  17. final def notifyAll(): Unit

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  18. val p0: Sequent[HOLFormula]

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    Problem 0: sequence (0,1)

  19. val p1: Sequent[HOLFormula]

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    Problem 1: sequence (1,0,0)

  20. val p2: Sequent[HOLFormula]

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    Problem 0: sequence (1,0,1)

  21. object sequents

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    Contains all the conjecture sequents used.

  22. final def synchronized[T0](arg0: ⇒ T0): T0

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  23. def toString(): String

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  24. val w0: Sequent[HOLFormula]

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    Problem 0 with witness: sequence (0,1)

  25. val w1: Sequent[HOLFormula]

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    Problem 1 with witness : sequence (1,0,0)

  26. val w2: Sequent[HOLFormula]

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    Problem 2 with witness: sequence (1,0,1)

  27. val w2b: Sequent[HOLFormula]

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    Problem 2 with different witness: sequence (1,0,1)

  28. final def wait(): Unit

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  29. final def wait(arg0: Long, arg1: Int): Unit

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  30. final def wait(arg0: Long): Unit

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