Export the problems P0-P2 and W0-W2 to TPTP THF.
Contains all the formulas used.
Problem 0: sequence (0,1)
Problem 1: sequence (1,0,0)
Problem 0: sequence (1,0,1)
Contains all the conjecture sequents used.
Problem 0 with witness: sequence (0,1)
Problem 1 with witness : sequence (1,0,0)
Problem 2 with witness: sequence (1,0,1)
Problem 2 with different witness: sequence (1,0,1)
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.