%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP108-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:16 AM UTC 2026
% Result : Unsatisfiable 0.06s 0.36s
% Output : Proof 0.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP108-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 09:19:21 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.36 Command-line arguments: --no-flatten-goal
% 0.06/0.36
% 0.06/0.36 % SZS status Unsatisfiable
% 0.06/0.36
% 0.06/0.37 % SZS output start Proof
% 0.06/0.37 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.06/0.37 Axiom 2 (single_axiom): inverse(double_divide(inverse(double_divide(X, inverse(double_divide(Y, double_divide(X, Z))))), Z)) = Y.
% 0.06/0.37
% 0.06/0.37 Lemma 3: multiply(X, multiply(multiply(double_divide(Y, X), Z), Y)) = Z.
% 0.06/0.37 Proof:
% 0.06/0.37 multiply(X, multiply(multiply(double_divide(Y, X), Z), Y))
% 0.06/0.37 = { by axiom 1 (multiply) }
% 0.06/0.37 multiply(X, multiply(inverse(double_divide(Z, double_divide(Y, X))), Y))
% 0.06/0.37 = { by axiom 1 (multiply) }
% 0.06/0.37 multiply(X, inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))))
% 0.06/0.37 = { by axiom 1 (multiply) }
% 0.06/0.37 inverse(double_divide(inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))), X))
% 0.06/0.37 = { by axiom 2 (single_axiom) }
% 0.06/0.37 Z
% 0.06/0.37
% 0.06/0.37 Lemma 4: multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X) = multiply(Z, multiply(W, Y)).
% 0.06/0.37 Proof:
% 0.06/0.37 multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)
% 0.06/0.37 = { by lemma 3 R->L }
% 0.06/0.37 multiply(Z, multiply(multiply(double_divide(Y, Z), multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)), Y))
% 0.06/0.37 = { by lemma 3 }
% 0.06/0.37 multiply(Z, multiply(W, Y))
% 0.06/0.37
% 0.06/0.37 Lemma 5: multiply(double_divide(X, Y), multiply(Y, multiply(Z, X))) = Z.
% 0.06/0.37 Proof:
% 0.06/0.37 multiply(double_divide(X, Y), multiply(Y, multiply(Z, X)))
% 0.06/0.37 = { by lemma 4 R->L }
% 0.06/0.37 multiply(double_divide(X, Y), multiply(multiply(double_divide(W, double_divide(X, Y)), Z), W))
% 0.06/0.38 = { by lemma 3 }
% 0.06/0.38 Z
% 0.06/0.38
% 0.06/0.38 Lemma 6: multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X) = Z.
% 0.06/0.38 Proof:
% 0.06/0.38 multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X)
% 0.06/0.38 = { by lemma 5 R->L }
% 0.06/0.38 multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), multiply(double_divide(Y, Z), multiply(Z, multiply(X, Y))))
% 0.06/0.38 = { by lemma 5 }
% 0.06/0.38 Z
% 0.06/0.38
% 0.06/0.38 Lemma 7: multiply(double_divide(X, Y), multiply(Y, Z)) = double_divide(multiply(X, W), double_divide(W, Z)).
% 0.06/0.38 Proof:
% 0.06/0.38 multiply(double_divide(X, Y), multiply(Y, Z))
% 0.06/0.38 = { by lemma 6 R->L }
% 0.06/0.38 multiply(double_divide(X, Y), multiply(Y, multiply(double_divide(multiply(X, W), double_divide(W, Z)), X)))
% 0.06/0.38 = { by lemma 5 }
% 0.06/0.38 double_divide(multiply(X, W), double_divide(W, Z))
% 0.06/0.38
% 0.06/0.38 Lemma 8: double_divide(multiply(X, Y), double_divide(Y, multiply(Z, X))) = Z.
% 0.06/0.38 Proof:
% 0.06/0.38 double_divide(multiply(X, Y), double_divide(Y, multiply(Z, X)))
% 0.06/0.38 = { by lemma 7 R->L }
% 0.06/0.38 multiply(double_divide(X, W), multiply(W, multiply(Z, X)))
% 0.06/0.38 = { by lemma 5 }
% 0.06/0.38 Z
% 0.06/0.38
% 0.06/0.38 Lemma 9: multiply(multiply(X, Z), multiply(Y, W)) = multiply(multiply(X, Y), multiply(Z, W)).
% 0.06/0.38 Proof:
% 0.06/0.38 multiply(multiply(X, Z), multiply(Y, W))
% 0.06/0.38 = { by lemma 8 R->L }
% 0.06/0.38 multiply(multiply(double_divide(multiply(Y, W), double_divide(W, multiply(X, Y))), Z), multiply(Y, W))
% 0.06/0.38 = { by lemma 4 }
% 0.06/0.38 multiply(multiply(X, Y), multiply(Z, W))
% 0.06/0.38
% 0.06/0.38 Lemma 10: multiply(multiply(X, Y), multiply(inverse(X), Z)) = multiply(Y, Z).
% 0.06/0.38 Proof:
% 0.06/0.38 multiply(multiply(X, Y), multiply(inverse(X), Z))
% 0.06/0.38 = { by lemma 8 R->L }
% 0.06/0.38 multiply(multiply(X, Y), multiply(inverse(double_divide(multiply(Y, Z), double_divide(Z, multiply(X, Y)))), Z))
% 0.06/0.38 = { by axiom 1 (multiply) R->L }
% 0.06/0.38 multiply(multiply(X, Y), multiply(multiply(double_divide(Z, multiply(X, Y)), multiply(Y, Z)), Z))
% 0.06/0.38 = { by lemma 3 }
% 0.06/0.38 multiply(Y, Z)
% 0.06/0.38
% 0.06/0.38 Lemma 11: multiply(multiply(X, inverse(X)), multiply(Y, Z)) = multiply(Y, Z).
% 0.06/0.38 Proof:
% 0.06/0.38 multiply(multiply(X, inverse(X)), multiply(Y, Z))
% 0.06/0.38 = { by lemma 9 }
% 0.06/0.38 multiply(multiply(X, Y), multiply(inverse(X), Z))
% 0.06/0.38 = { by lemma 10 }
% 0.06/0.38 multiply(Y, Z)
% 0.06/0.38
% 0.06/0.38 Lemma 12: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.06/0.38 Proof:
% 0.06/0.38 multiply(multiply(X, inverse(X)), Y)
% 0.06/0.38 = { by lemma 6 R->L }
% 0.06/0.38 multiply(multiply(X, inverse(X)), multiply(double_divide(multiply(Z, W), double_divide(W, Y)), Z))
% 0.06/0.38 = { by lemma 11 }
% 0.06/0.38 multiply(double_divide(multiply(Z, W), double_divide(W, Y)), Z)
% 0.06/0.38 = { by lemma 6 }
% 0.06/0.38 Y
% 0.06/0.38
% 0.06/0.38 Lemma 13: multiply(multiply(X, multiply(Y, Z)), W) = multiply(Y, multiply(multiply(X, Z), W)).
% 0.06/0.38 Proof:
% 0.06/0.38 multiply(multiply(X, multiply(Y, Z)), W)
% 0.06/0.38 = { by lemma 10 R->L }
% 0.06/0.38 multiply(multiply(double_divide(Z, X), multiply(X, multiply(Y, Z))), multiply(inverse(double_divide(Z, X)), W))
% 0.06/0.38 = { by lemma 5 }
% 0.06/0.38 multiply(Y, multiply(inverse(double_divide(Z, X)), W))
% 0.06/0.38 = { by axiom 1 (multiply) R->L }
% 0.06/0.38 multiply(Y, multiply(multiply(X, Z), W))
% 0.06/0.38
% 0.06/0.38 Lemma 14: double_divide(multiply(X, multiply(Y, multiply(Z, W))), double_divide(W, X)) = double_divide(Y, Z).
% 0.06/0.38 Proof:
% 0.06/0.38 double_divide(multiply(X, multiply(Y, multiply(Z, W))), double_divide(W, X))
% 0.06/0.38 = { by lemma 12 R->L }
% 0.06/0.38 double_divide(multiply(X, multiply(multiply(multiply(V, inverse(V)), Y), multiply(Z, W))), double_divide(W, X))
% 0.06/0.38 = { by lemma 9 R->L }
% 0.06/0.38 double_divide(multiply(X, multiply(multiply(multiply(V, inverse(V)), Z), multiply(Y, W))), double_divide(W, X))
% 0.06/0.38 = { by lemma 12 }
% 0.06/0.38 double_divide(multiply(X, multiply(Z, multiply(Y, W))), double_divide(W, X))
% 0.06/0.38 = { by lemma 12 R->L }
% 0.06/0.38 double_divide(multiply(X, multiply(Z, multiply(multiply(multiply(U, inverse(U)), Y), W))), double_divide(W, X))
% 0.06/0.38 = { by lemma 13 R->L }
% 0.06/0.38 double_divide(multiply(X, multiply(multiply(multiply(U, inverse(U)), multiply(Z, Y)), W)), double_divide(W, X))
% 0.06/0.38 = { by lemma 12 }
% 0.06/0.38 double_divide(multiply(X, multiply(multiply(Z, Y), W)), double_divide(W, X))
% 0.06/0.38 = { by lemma 13 R->L }
% 0.06/0.38 double_divide(multiply(multiply(Z, multiply(X, Y)), W), double_divide(W, X))
% 0.06/0.38 = { by lemma 7 R->L }
% 0.06/0.38 multiply(double_divide(multiply(Z, multiply(X, Y)), T), multiply(T, X))
% 0.06/0.38 = { by lemma 5 R->L }
% 0.06/0.38 multiply(double_divide(multiply(Z, multiply(X, Y)), T), multiply(T, multiply(double_divide(Y, Z), multiply(Z, multiply(X, Y)))))
% 0.06/0.38 = { by lemma 5 }
% 0.06/0.38 double_divide(Y, Z)
% 0.06/0.38
% 0.06/0.38 Lemma 15: double_divide(multiply(X, Z), Y) = double_divide(multiply(X, Y), Z).
% 0.06/0.38 Proof:
% 0.06/0.38 double_divide(multiply(X, Z), Y)
% 0.06/0.38 = { by lemma 14 R->L }
% 0.06/0.38 double_divide(multiply(W, multiply(multiply(X, Z), multiply(Y, V))), double_divide(V, W))
% 0.06/0.38 = { by lemma 9 }
% 0.06/0.38 double_divide(multiply(W, multiply(multiply(X, Y), multiply(Z, V))), double_divide(V, W))
% 0.06/0.38 = { by lemma 14 }
% 0.06/0.38 double_divide(multiply(X, Y), Z)
% 0.06/0.38
% 0.06/0.38 Lemma 16: inverse(double_divide(X, Y)) = multiply(X, Y).
% 0.06/0.38 Proof:
% 0.06/0.38 inverse(double_divide(X, Y))
% 0.06/0.38 = { by lemma 12 R->L }
% 0.06/0.38 inverse(double_divide(multiply(multiply(Z, inverse(Z)), X), Y))
% 0.06/0.38 = { by lemma 15 R->L }
% 0.06/0.38 inverse(double_divide(multiply(multiply(Z, inverse(Z)), Y), X))
% 0.06/0.38 = { by lemma 12 }
% 0.06/0.38 inverse(double_divide(Y, X))
% 0.06/0.38 = { by axiom 1 (multiply) R->L }
% 0.06/0.38 multiply(X, Y)
% 0.06/0.38
% 0.06/0.38 Lemma 17: multiply(Y, X) = multiply(X, Y).
% 0.06/0.38 Proof:
% 0.06/0.38 multiply(Y, X)
% 0.06/0.38 = { by lemma 16 R->L }
% 0.06/0.38 inverse(double_divide(Y, X))
% 0.06/0.38 = { by axiom 1 (multiply) R->L }
% 0.06/0.38 multiply(X, Y)
% 0.06/0.38
% 0.06/0.38 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4)).
% 0.06/0.38 Proof:
% 0.06/0.38 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.06/0.38 = { by lemma 17 R->L }
% 0.06/0.38 tuple(multiply(a1, inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.06/0.38 = { by lemma 17 R->L }
% 0.06/0.38 tuple(multiply(a1, inverse(a1)), multiply(multiply(b2, inverse(b2)), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.06/0.38 = { by lemma 12 }
% 0.06/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.06/0.38 = { by lemma 17 R->L }
% 0.06/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.06/0.38 = { by lemma 17 }
% 0.06/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(c3, multiply(b3, a3)), multiply(a4, b4))
% 0.06/0.38 = { by axiom 1 (multiply) }
% 0.06/0.38 tuple(multiply(a1, inverse(a1)), a2, inverse(double_divide(multiply(b3, a3), c3)), multiply(a4, b4))
% 0.06/0.38 = { by lemma 15 R->L }
% 0.06/0.38 tuple(multiply(a1, inverse(a1)), a2, inverse(double_divide(multiply(b3, c3), a3)), multiply(a4, b4))
% 0.06/0.38 = { by lemma 16 }
% 0.06/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(multiply(b3, c3), a3), multiply(a4, b4))
% 0.06/0.38 = { by lemma 17 R->L }
% 0.06/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.06/0.38 = { by lemma 17 }
% 0.06/0.38 tuple(multiply(a1, inverse(a1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.06/0.38 = { by lemma 5 R->L }
% 0.06/0.38 tuple(multiply(double_divide(X, Y), multiply(Y, multiply(multiply(a1, inverse(a1)), X))), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.06/0.38 = { by lemma 6 R->L }
% 0.06/0.38 tuple(multiply(double_divide(X, Y), multiply(Y, multiply(multiply(a1, inverse(a1)), multiply(double_divide(multiply(Z, W), double_divide(W, X)), Z)))), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.06/0.38 = { by lemma 11 }
% 0.06/0.38 tuple(multiply(double_divide(X, Y), multiply(Y, multiply(double_divide(multiply(Z, W), double_divide(W, X)), Z))), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.06/0.38 = { by lemma 11 R->L }
% 0.06/0.38 tuple(multiply(double_divide(X, Y), multiply(Y, multiply(multiply(b1, inverse(b1)), multiply(double_divide(multiply(Z, W), double_divide(W, X)), Z)))), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.06/0.38 = { by lemma 6 }
% 0.06/0.38 tuple(multiply(double_divide(X, Y), multiply(Y, multiply(multiply(b1, inverse(b1)), X))), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.06/0.38 = { by lemma 5 }
% 0.06/0.38 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.06/0.38 = { by lemma 17 }
% 0.06/0.38 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.06/0.38 % SZS output end Proof
% 0.06/0.38
% 0.06/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------