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.