%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP107-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 0.63s 0.52s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP107-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 09:19:33 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.63/0.52 Command-line arguments: --no-flatten-goal
% 0.63/0.52
% 0.63/0.52 % SZS status Unsatisfiable
% 0.63/0.52
% 0.63/0.55 % SZS output start Proof
% 0.63/0.55 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.63/0.55 Axiom 2 (single_axiom): double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y))))) = Z.
% 0.63/0.55
% 0.63/0.55 Lemma 3: double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X)) = Z.
% 0.63/0.55 Proof:
% 0.63/0.55 double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X))
% 0.63/0.55 = { by axiom 1 (multiply) }
% 0.63/0.55 double_divide(double_divide(X, Y), multiply(inverse(double_divide(inverse(Z), Y)), X))
% 0.63/0.55 = { by axiom 1 (multiply) }
% 0.63/0.55 double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y)))))
% 0.63/0.55 = { by axiom 2 (single_axiom) }
% 0.63/0.55 Z
% 0.63/0.55
% 0.63/0.55 Lemma 4: multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X)) = inverse(Y).
% 0.63/0.55 Proof:
% 0.63/0.55 multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X))
% 0.63/0.55 = { by axiom 1 (multiply) }
% 0.63/0.55 inverse(double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.63/0.55 = { by lemma 3 }
% 0.63/0.55 inverse(Y)
% 0.63/0.55
% 0.63/0.55 Lemma 5: multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y) = inverse(W).
% 0.63/0.55 Proof:
% 0.63/0.55 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y)
% 0.63/0.55 = { by lemma 3 R->L }
% 0.63/0.55 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.63/0.55 = { by lemma 4 }
% 0.63/0.55 inverse(W)
% 0.63/0.55
% 0.63/0.55 Lemma 6: double_divide(double_divide(X, inverse(X)), multiply(Y, Z)) = double_divide(Z, Y).
% 0.63/0.55 Proof:
% 0.63/0.55 double_divide(double_divide(X, inverse(X)), multiply(Y, Z))
% 0.63/0.55 = { by axiom 1 (multiply) }
% 0.63/0.55 double_divide(double_divide(X, inverse(X)), inverse(double_divide(Z, Y)))
% 0.63/0.55 = { by lemma 5 R->L }
% 0.63/0.55 double_divide(double_divide(X, inverse(X)), multiply(multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(double_divide(Z, Y)))), V), inverse(X)), double_divide(V, W)), inverse(double_divide(Z, Y))), double_divide(double_divide(V, W), multiply(multiply(W, inverse(inverse(double_divide(Z, Y)))), V))), X))
% 0.63/0.55 = { by lemma 5 }
% 0.63/0.55 double_divide(double_divide(X, inverse(X)), multiply(multiply(inverse(X), double_divide(double_divide(V, W), multiply(multiply(W, inverse(inverse(double_divide(Z, Y)))), V))), X))
% 0.63/0.55 = { by lemma 3 }
% 0.63/0.55 double_divide(double_divide(X, inverse(X)), multiply(multiply(inverse(X), inverse(double_divide(Z, Y))), X))
% 0.63/0.55 = { by lemma 3 }
% 0.63/0.55 double_divide(Z, Y)
% 0.63/0.55
% 0.63/0.55 Lemma 7: double_divide(X, multiply(inverse(X), inverse(Y))) = Y.
% 0.63/0.55 Proof:
% 0.63/0.55 double_divide(X, multiply(inverse(X), inverse(Y)))
% 0.63/0.55 = { by lemma 3 R->L }
% 0.63/0.55 double_divide(X, multiply(inverse(X), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))))
% 0.63/0.55 = { by lemma 5 R->L }
% 0.63/0.55 double_divide(X, multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W)), inverse(Y)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))))
% 0.63/0.55 = { by lemma 3 R->L }
% 0.63/0.55 double_divide(double_divide(double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z)), multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W))), multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W)), inverse(Y)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))))
% 0.63/0.55 = { by lemma 3 }
% 0.63/0.55 Y
% 0.63/0.55
% 0.63/0.55 Lemma 8: double_divide(inverse(X), multiply(inverse(Y), Y)) = X.
% 0.63/0.55 Proof:
% 0.63/0.55 double_divide(inverse(X), multiply(inverse(Y), Y))
% 0.63/0.55 = { by axiom 1 (multiply) }
% 0.63/0.55 double_divide(inverse(X), inverse(double_divide(Y, inverse(Y))))
% 0.63/0.55 = { by lemma 6 R->L }
% 0.63/0.55 double_divide(double_divide(Y, inverse(Y)), multiply(inverse(double_divide(Y, inverse(Y))), inverse(X)))
% 0.63/0.55 = { by lemma 7 }
% 0.63/0.55 X
% 0.63/0.55
% 0.63/0.56 Lemma 9: multiply(multiply(inverse(X), X), inverse(Y)) = inverse(Y).
% 0.63/0.56 Proof:
% 0.63/0.56 multiply(multiply(inverse(X), X), inverse(Y))
% 0.63/0.56 = { by axiom 1 (multiply) }
% 0.63/0.56 inverse(double_divide(inverse(Y), multiply(inverse(X), X)))
% 0.63/0.56 = { by lemma 8 }
% 0.63/0.56 inverse(Y)
% 0.63/0.56
% 0.63/0.56 Lemma 10: double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), inverse(Z)) = X.
% 0.63/0.56 Proof:
% 0.63/0.56 double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), inverse(Z))
% 0.63/0.56 = { by lemma 4 R->L }
% 0.63/0.56 double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), multiply(multiply(multiply(Y, inverse(Z)), inverse(X)), double_divide(inverse(X), Y)))
% 0.63/0.56 = { by lemma 3 }
% 0.63/0.56 X
% 0.63/0.56
% 0.63/0.56 Lemma 11: double_divide(double_divide(X, inverse(Y)), inverse(Y)) = X.
% 0.63/0.56 Proof:
% 0.63/0.56 double_divide(double_divide(X, inverse(Y)), inverse(Y))
% 0.63/0.56 = { by lemma 8 R->L }
% 0.63/0.56 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(Z), Z)), inverse(Y)), inverse(Y))
% 0.63/0.56 = { by lemma 9 R->L }
% 0.63/0.56 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(Z), Z)), multiply(multiply(inverse(Z), Z), inverse(Y))), inverse(Y))
% 0.63/0.56 = { by lemma 10 }
% 0.63/0.56 X
% 0.63/0.56
% 0.63/0.56 Lemma 12: double_divide(double_divide(inverse(X), inverse(inverse(Y))), inverse(X)) = Y.
% 0.63/0.56 Proof:
% 0.63/0.56 double_divide(double_divide(inverse(X), inverse(inverse(Y))), inverse(X))
% 0.63/0.56 = { by lemma 6 R->L }
% 0.63/0.56 double_divide(double_divide(double_divide(inverse(Y), inverse(inverse(Y))), multiply(inverse(inverse(Y)), inverse(X))), inverse(X))
% 0.63/0.56 = { by lemma 10 }
% 0.63/0.56 Y
% 0.63/0.56
% 0.63/0.56 Lemma 13: inverse(inverse(X)) = X.
% 0.63/0.56 Proof:
% 0.63/0.56 inverse(inverse(X))
% 0.63/0.56 = { by lemma 11 R->L }
% 0.63/0.56 double_divide(double_divide(inverse(inverse(X)), inverse(inverse(X))), inverse(inverse(X)))
% 0.63/0.56 = { by lemma 12 }
% 0.63/0.56 X
% 0.63/0.56
% 0.63/0.56 Lemma 14: double_divide(double_divide(X, Y), X) = Y.
% 0.63/0.56 Proof:
% 0.63/0.56 double_divide(double_divide(X, Y), X)
% 0.63/0.56 = { by lemma 13 R->L }
% 0.63/0.56 double_divide(double_divide(X, Y), inverse(inverse(X)))
% 0.63/0.56 = { by lemma 13 R->L }
% 0.63/0.56 double_divide(double_divide(X, inverse(inverse(Y))), inverse(inverse(X)))
% 0.63/0.56 = { by lemma 13 R->L }
% 0.63/0.56 double_divide(double_divide(inverse(inverse(X)), inverse(inverse(Y))), inverse(inverse(X)))
% 0.63/0.56 = { by lemma 12 }
% 0.63/0.56 Y
% 0.63/0.56
% 0.63/0.56 Lemma 15: double_divide(Y, X) = double_divide(X, Y).
% 0.63/0.56 Proof:
% 0.63/0.56 double_divide(Y, X)
% 0.63/0.56 = { by lemma 14 R->L }
% 0.63/0.56 double_divide(double_divide(double_divide(X, Y), X), X)
% 0.63/0.56 = { by lemma 13 R->L }
% 0.63/0.56 double_divide(double_divide(double_divide(X, Y), X), inverse(inverse(X)))
% 0.63/0.56 = { by lemma 13 R->L }
% 0.63/0.56 double_divide(double_divide(double_divide(X, Y), inverse(inverse(X))), inverse(inverse(X)))
% 0.63/0.56 = { by lemma 11 }
% 0.63/0.56 double_divide(X, Y)
% 0.63/0.56
% 0.63/0.56 Lemma 16: multiply(X, double_divide(X, Y)) = inverse(Y).
% 0.63/0.56 Proof:
% 0.63/0.56 multiply(X, double_divide(X, Y))
% 0.63/0.56 = { by lemma 15 }
% 0.63/0.56 multiply(X, double_divide(Y, X))
% 0.63/0.56 = { by lemma 13 R->L }
% 0.63/0.56 multiply(X, double_divide(Y, inverse(inverse(X))))
% 0.63/0.56 = { by lemma 13 R->L }
% 0.63/0.56 multiply(inverse(inverse(X)), double_divide(Y, inverse(inverse(X))))
% 0.63/0.56 = { by lemma 8 R->L }
% 0.63/0.56 multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), multiply(inverse(Z), Z)), inverse(inverse(X))))
% 0.63/0.56 = { by lemma 9 R->L }
% 0.63/0.56 multiply(inverse(inverse(X)), double_divide(double_divide(inverse(Y), multiply(inverse(Z), Z)), multiply(multiply(inverse(Z), Z), inverse(inverse(X)))))
% 0.63/0.56 = { by lemma 4 R->L }
% 0.63/0.56 multiply(multiply(multiply(multiply(multiply(inverse(Z), Z), inverse(inverse(X))), inverse(Y)), double_divide(inverse(Y), multiply(inverse(Z), Z))), double_divide(double_divide(inverse(Y), multiply(inverse(Z), Z)), multiply(multiply(inverse(Z), Z), inverse(inverse(X)))))
% 0.63/0.56 = { by lemma 4 }
% 0.63/0.56 inverse(Y)
% 0.63/0.56
% 0.63/0.56 Lemma 17: inverse(double_divide(X, Y)) = multiply(X, Y).
% 0.63/0.56 Proof:
% 0.63/0.56 inverse(double_divide(X, Y))
% 0.63/0.56 = { by lemma 15 }
% 0.63/0.56 inverse(double_divide(Y, X))
% 0.63/0.56 = { by axiom 1 (multiply) R->L }
% 0.63/0.56 multiply(X, Y)
% 0.63/0.56
% 0.63/0.56 Lemma 18: multiply(Y, X) = multiply(X, Y).
% 0.63/0.56 Proof:
% 0.63/0.56 multiply(Y, X)
% 0.63/0.56 = { by lemma 17 R->L }
% 0.63/0.56 inverse(double_divide(Y, X))
% 0.63/0.56 = { by axiom 1 (multiply) R->L }
% 0.63/0.56 multiply(X, Y)
% 0.63/0.56
% 0.63/0.56 Lemma 19: inverse(multiply(X, Y)) = double_divide(X, Y).
% 0.63/0.56 Proof:
% 0.63/0.56 inverse(multiply(X, Y))
% 0.63/0.56 = { by lemma 18 }
% 0.63/0.56 inverse(multiply(Y, X))
% 0.63/0.56 = { by lemma 17 R->L }
% 0.63/0.56 inverse(inverse(double_divide(Y, X)))
% 0.63/0.56 = { by lemma 13 }
% 0.63/0.56 double_divide(Y, X)
% 0.63/0.56 = { by lemma 15 R->L }
% 0.63/0.56 double_divide(X, Y)
% 0.63/0.56
% 0.63/0.56 Lemma 20: multiply(X, Y) = double_divide(inverse(X), inverse(Y)).
% 0.63/0.56 Proof:
% 0.63/0.56 multiply(X, Y)
% 0.63/0.56 = { by lemma 7 R->L }
% 0.63/0.56 multiply(X, double_divide(X, multiply(inverse(X), inverse(Y))))
% 0.63/0.56 = { by lemma 16 }
% 0.63/0.56 inverse(multiply(inverse(X), inverse(Y)))
% 0.63/0.56 = { by lemma 19 }
% 0.63/0.56 double_divide(inverse(X), inverse(Y))
% 0.63/0.56
% 0.63/0.56 Lemma 21: multiply(X, inverse(X)) = double_divide(Y, inverse(Y)).
% 0.63/0.56 Proof:
% 0.63/0.56 multiply(X, inverse(X))
% 0.63/0.56 = { by lemma 18 }
% 0.63/0.56 multiply(inverse(X), X)
% 0.63/0.56 = { by lemma 8 R->L }
% 0.63/0.56 multiply(inverse(X), double_divide(inverse(X), multiply(inverse(Y), Y)))
% 0.63/0.56 = { by lemma 16 }
% 0.63/0.56 inverse(multiply(inverse(Y), Y))
% 0.63/0.56 = { by lemma 19 }
% 0.63/0.56 double_divide(inverse(Y), Y)
% 0.63/0.56 = { by lemma 15 R->L }
% 0.63/0.56 double_divide(Y, inverse(Y))
% 0.63/0.56
% 0.63/0.56 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)).
% 0.63/0.56 Proof:
% 0.63/0.56 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.63/0.56 = { by lemma 18 R->L }
% 0.63/0.56 tuple(multiply(a1, inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.63/0.56 = { by lemma 18 R->L }
% 0.63/0.56 tuple(multiply(a1, inverse(a1)), multiply(multiply(b2, inverse(b2)), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.63/0.56 = { by lemma 18 R->L }
% 0.63/0.56 tuple(multiply(a1, inverse(a1)), multiply(a2, multiply(b2, inverse(b2))), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.63/0.56 = { by lemma 18 R->L }
% 0.63/0.56 tuple(multiply(a1, inverse(a1)), multiply(a2, multiply(b2, inverse(b2))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.63/0.56 = { by lemma 21 }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), multiply(a2, multiply(b2, inverse(b2))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.63/0.56 = { by lemma 21 }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), multiply(a2, double_divide(Y, inverse(Y))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.63/0.56 = { by lemma 20 }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), double_divide(inverse(a2), inverse(double_divide(Y, inverse(Y)))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.63/0.56 = { by axiom 1 (multiply) R->L }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), double_divide(inverse(a2), multiply(inverse(Y), Y)), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.63/0.56 = { by lemma 8 }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.63/0.56 = { by lemma 20 }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), inverse(multiply(a3, b3))), multiply(a4, b4))
% 0.63/0.56 = { by lemma 19 }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), double_divide(a3, b3)), multiply(a4, b4))
% 0.63/0.56 = { by lemma 20 }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), double_divide(a3, b3)), double_divide(inverse(a4), inverse(b4)))
% 0.63/0.56 = { by lemma 3 R->L }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, double_divide(double_divide(double_divide(a3, b3), multiply(multiply(b3, inverse(inverse(c3))), a3)), double_divide(a3, b3)), double_divide(inverse(a4), inverse(b4)))
% 0.63/0.56 = { by lemma 14 }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, multiply(multiply(b3, inverse(inverse(c3))), a3), double_divide(inverse(a4), inverse(b4)))
% 0.63/0.56 = { by lemma 20 }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(multiply(b3, inverse(inverse(c3)))), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 0.63/0.56 = { by lemma 19 }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, double_divide(double_divide(b3, inverse(inverse(c3))), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 0.63/0.56 = { by lemma 15 R->L }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), double_divide(b3, inverse(inverse(c3)))), double_divide(inverse(a4), inverse(b4)))
% 0.63/0.56 = { by lemma 13 }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), double_divide(b3, c3)), double_divide(inverse(a4), inverse(b4)))
% 0.63/0.56 = { by lemma 20 R->L }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.63/0.56 = { by lemma 19 R->L }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), inverse(multiply(b3, c3))), multiply(a4, b4))
% 0.63/0.56 = { by lemma 20 R->L }
% 0.63/0.56 tuple(double_divide(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.63/0.56 = { by lemma 21 R->L }
% 0.63/0.56 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.63/0.56 = { by lemma 18 }
% 0.63/0.56 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.63/0.56 = { by lemma 18 }
% 0.63/0.56 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.63/0.56 % SZS output end Proof
% 0.63/0.56
% 0.63/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------