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  • object nTape6

    The object nTape6 generates hard problems for higher order theorem provers containing an axiomatization of if-then-else.

    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.

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object formulas

Contains all the formulas used.

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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  5. def clone(): AnyRef
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    @throws( ... )
  6. val conclusion0: HOLFormula
  7. val conclusion1: HOLFormula
  8. val conclusion2: HOLFormula
  9. final def eq(arg0: AnyRef): Boolean
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  10. def equals(arg0: Any): Boolean
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  11. val f1: HOLFormula
  12. val f2: HOLFormula
  13. val f3: HOLFormula
  14. val f4: HOLFormula
  15. def finalize(): Unit
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  16. final def getClass(): Class[_]
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  18. final def isInstanceOf[T0]: Boolean
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  19. final def ne(arg0: AnyRef): Boolean
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  20. final def notify(): Unit
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  21. final def notifyAll(): Unit
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  22. val s1: String
  23. val s2: String
  24. val s3: String
  25. val s4: String
  26. val s5: String
  27. val s6: String
  28. val s7: String
  29. val sc: String
  30. val sc1: String
  31. val sc2: String
  32. implicit val signature: LLKSignature
  33. final def synchronized[T0](arg0: ⇒ T0): T0
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  34. def toString(): String
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  35. val w1: HOLFormula
  36. val w2: HOLFormula
  37. val w3: HOLFormula
  38. final def wait(): Unit
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  39. final def wait(arg0: Long, arg1: Int): Unit
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  40. final def wait(arg0: Long): Unit
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