nTape6

gapt.examples.nTape6
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.

Attributes

Graph
Supertypes
class Object
trait Matchable
class Any
Self type
nTape6.type

Members list

Type members

Classlikes

object formulas

Contains all the formulas used.

Contains all the formulas used.

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
formulas.type
object sequents

Contains all the conjecture sequents used.

Contains all the conjecture sequents used.

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
sequents.type

Value members

Concrete methods

def export(path: String, separate_axioms: Boolean): Unit

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

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

Attributes

Concrete fields

val fn: String
val p0: Sequent[Formula]

Problem 0: sequence (0,1)

Problem 0: sequence (0,1)

Attributes

val p1: Sequent[Formula]

Problem 1: sequence (1,0,0)

Problem 1: sequence (1,0,0)

Attributes

val p2: Sequent[Formula]

Problem 0: sequence (1,0,1)

Problem 0: sequence (1,0,1)

Attributes

val w0: Sequent[Formula]

Problem 0 with witness: sequence (0,1)

Problem 0 with witness: sequence (0,1)

Attributes

val w1: Sequent[Formula]

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

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

Attributes

val w2: Sequent[Formula]

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

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

Attributes

val w2b: Sequent[Formula]

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

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

Attributes