%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP078-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 10:09:13 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP078-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:20:56 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 Command-line arguments: --no-flatten-goal
% 0.19/0.46
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.19/0.49 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.19/0.49 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.19/0.49 Axiom 4 (single_axiom): double_divide(double_divide(identity, X), double_divide(identity, double_divide(double_divide(double_divide(X, Y), identity), double_divide(Z, Y)))) = Z.
% 0.19/0.49
% 0.19/0.49 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.19/0.49 Proof:
% 0.19/0.49 inverse(double_divide(X, Y))
% 0.19/0.49 = { by axiom 1 (inverse) }
% 0.19/0.49 double_divide(double_divide(X, Y), identity)
% 0.19/0.49 = { by axiom 3 (multiply) R->L }
% 0.19/0.49 multiply(Y, X)
% 0.19/0.49
% 0.19/0.49 Lemma 6: double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(Y, X), double_divide(Z, Y)))) = Z.
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(Y, X), double_divide(Z, Y))))
% 0.19/0.49 = { by lemma 5 R->L }
% 0.19/0.49 double_divide(double_divide(identity, X), double_divide(identity, double_divide(inverse(double_divide(X, Y)), double_divide(Z, Y))))
% 0.19/0.49 = { by axiom 1 (inverse) }
% 0.19/0.49 double_divide(double_divide(identity, X), double_divide(identity, double_divide(double_divide(double_divide(X, Y), identity), double_divide(Z, Y))))
% 0.19/0.49 = { by axiom 4 (single_axiom) }
% 0.19/0.49 Z
% 0.19/0.49
% 0.19/0.49 Lemma 7: double_divide(double_divide(identity, X), double_divide(identity, inverse(multiply(inverse(Y), X)))) = Y.
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(double_divide(identity, X), double_divide(identity, inverse(multiply(inverse(Y), X))))
% 0.19/0.49 = { by axiom 1 (inverse) }
% 0.19/0.49 double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(inverse(Y), X), identity)))
% 0.19/0.49 = { by axiom 2 (identity) }
% 0.19/0.49 double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(inverse(Y), X), double_divide(Y, inverse(Y)))))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.49 Y
% 0.19/0.49
% 0.19/0.49 Lemma 8: multiply(inverse(X), X) = inverse(identity).
% 0.19/0.49 Proof:
% 0.19/0.49 multiply(inverse(X), X)
% 0.19/0.49 = { by lemma 5 R->L }
% 0.19/0.49 inverse(double_divide(X, inverse(X)))
% 0.19/0.49 = { by axiom 2 (identity) R->L }
% 0.19/0.49 inverse(identity)
% 0.19/0.49
% 0.19/0.49 Lemma 9: double_divide(double_divide(identity, X), double_divide(identity, inverse(inverse(identity)))) = X.
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(double_divide(identity, X), double_divide(identity, inverse(inverse(identity))))
% 0.19/0.49 = { by lemma 8 R->L }
% 0.19/0.49 double_divide(double_divide(identity, X), double_divide(identity, inverse(multiply(inverse(X), X))))
% 0.19/0.49 = { by lemma 7 }
% 0.19/0.49 X
% 0.19/0.49
% 0.19/0.49 Lemma 10: double_divide(identity, inverse(inverse(identity))) = identity.
% 0.19/0.49 Proof:
% 0.19/0.49 double_divide(identity, inverse(inverse(identity)))
% 0.19/0.49 = { by lemma 9 R->L }
% 0.19/0.49 double_divide(double_divide(identity, double_divide(identity, inverse(inverse(identity)))), double_divide(identity, inverse(inverse(identity))))
% 0.19/0.49 = { by axiom 2 (identity) }
% 0.19/0.49 double_divide(double_divide(double_divide(identity, inverse(identity)), double_divide(identity, inverse(inverse(identity)))), double_divide(identity, inverse(inverse(identity))))
% 0.19/0.49 = { by lemma 9 }
% 0.19/0.49 double_divide(inverse(identity), double_divide(identity, inverse(inverse(identity))))
% 0.19/0.49 = { by axiom 1 (inverse) }
% 0.19/0.49 double_divide(double_divide(identity, identity), double_divide(identity, inverse(inverse(identity))))
% 0.19/0.49 = { by lemma 9 }
% 0.19/0.49 identity
% 0.19/0.49
% 0.19/0.49 Lemma 11: inverse(identity) = identity.
% 0.19/0.49 Proof:
% 0.19/0.49 inverse(identity)
% 0.19/0.49 = { by lemma 7 R->L }
% 0.19/0.49 double_divide(double_divide(identity, X), double_divide(identity, inverse(multiply(inverse(inverse(identity)), X))))
% 0.19/0.49 = { by axiom 1 (inverse) }
% 0.19/0.49 double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(inverse(inverse(identity)), X), identity)))
% 0.19/0.49 = { by lemma 10 R->L }
% 0.19/0.49 double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(inverse(inverse(identity)), X), double_divide(identity, inverse(inverse(identity))))))
% 0.19/0.49 = { by lemma 6 }
% 0.19/0.50 identity
% 0.19/0.50
% 0.19/0.50 Lemma 12: multiply(X, identity) = X.
% 0.19/0.50 Proof:
% 0.19/0.50 multiply(X, identity)
% 0.19/0.50 = { by lemma 5 R->L }
% 0.19/0.50 inverse(double_divide(identity, X))
% 0.19/0.50 = { by axiom 1 (inverse) }
% 0.19/0.50 double_divide(double_divide(identity, X), identity)
% 0.19/0.50 = { by lemma 10 R->L }
% 0.19/0.50 double_divide(double_divide(identity, X), double_divide(identity, inverse(inverse(identity))))
% 0.19/0.50 = { by lemma 9 }
% 0.19/0.50 X
% 0.19/0.50
% 0.19/0.50 Lemma 13: double_divide(identity, inverse(X)) = X.
% 0.19/0.50 Proof:
% 0.19/0.50 double_divide(identity, inverse(X))
% 0.19/0.50 = { by lemma 12 R->L }
% 0.19/0.50 multiply(double_divide(identity, inverse(X)), identity)
% 0.19/0.50 = { by lemma 5 R->L }
% 0.19/0.50 inverse(double_divide(identity, double_divide(identity, inverse(X))))
% 0.19/0.50 = { by axiom 1 (inverse) }
% 0.19/0.50 double_divide(double_divide(identity, double_divide(identity, inverse(X))), identity)
% 0.19/0.50 = { by axiom 2 (identity) }
% 0.19/0.50 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, inverse(identity)))
% 0.19/0.50 = { by lemma 11 R->L }
% 0.19/0.50 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, inverse(inverse(identity))))
% 0.19/0.50 = { by lemma 8 R->L }
% 0.19/0.50 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, inverse(multiply(inverse(double_divide(identity, inverse(X))), double_divide(identity, inverse(X))))))
% 0.19/0.50 = { by lemma 5 }
% 0.19/0.50 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, inverse(multiply(multiply(inverse(X), identity), double_divide(identity, inverse(X))))))
% 0.19/0.50 = { by lemma 12 }
% 0.19/0.50 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, inverse(multiply(inverse(X), double_divide(identity, inverse(X))))))
% 0.19/0.50 = { by lemma 7 }
% 0.19/0.50 X
% 0.19/0.50
% 0.19/0.50 Lemma 14: double_divide(X, multiply(inverse(Y), inverse(X))) = Y.
% 0.19/0.50 Proof:
% 0.19/0.50 double_divide(X, multiply(inverse(Y), inverse(X)))
% 0.19/0.50 = { by lemma 13 R->L }
% 0.19/0.50 double_divide(X, double_divide(identity, inverse(multiply(inverse(Y), inverse(X)))))
% 0.19/0.50 = { by lemma 13 R->L }
% 0.19/0.50 double_divide(double_divide(identity, inverse(X)), double_divide(identity, inverse(multiply(inverse(Y), inverse(X)))))
% 0.19/0.50 = { by lemma 7 }
% 0.19/0.50 Y
% 0.19/0.50
% 0.19/0.50 Lemma 15: multiply(identity, X) = inverse(inverse(X)).
% 0.19/0.50 Proof:
% 0.19/0.50 multiply(identity, X)
% 0.19/0.50 = { by lemma 5 R->L }
% 0.19/0.50 inverse(double_divide(X, identity))
% 0.19/0.50 = { by axiom 1 (inverse) R->L }
% 0.19/0.50 inverse(inverse(X))
% 0.19/0.50
% 0.19/0.50 Lemma 16: inverse(inverse(X)) = X.
% 0.19/0.50 Proof:
% 0.19/0.50 inverse(inverse(X))
% 0.19/0.50 = { by lemma 7 R->L }
% 0.19/0.50 double_divide(double_divide(identity, Y), double_divide(identity, inverse(multiply(inverse(inverse(inverse(X))), Y))))
% 0.19/0.50 = { by axiom 1 (inverse) }
% 0.19/0.50 double_divide(double_divide(identity, Y), double_divide(identity, double_divide(multiply(inverse(inverse(inverse(X))), Y), identity)))
% 0.19/0.50 = { by lemma 14 R->L }
% 0.19/0.50 double_divide(double_divide(identity, Y), double_divide(identity, double_divide(multiply(inverse(inverse(inverse(X))), Y), double_divide(X, multiply(inverse(identity), inverse(X))))))
% 0.19/0.50 = { by lemma 11 }
% 0.19/0.50 double_divide(double_divide(identity, Y), double_divide(identity, double_divide(multiply(inverse(inverse(inverse(X))), Y), double_divide(X, multiply(identity, inverse(X))))))
% 0.19/0.50 = { by lemma 15 }
% 0.19/0.50 double_divide(double_divide(identity, Y), double_divide(identity, double_divide(multiply(inverse(inverse(inverse(X))), Y), double_divide(X, inverse(inverse(inverse(X)))))))
% 0.19/0.50 = { by lemma 6 }
% 0.19/0.50 X
% 0.19/0.50
% 0.19/0.50 Lemma 17: double_divide(identity, X) = inverse(X).
% 0.19/0.50 Proof:
% 0.19/0.50 double_divide(identity, X)
% 0.19/0.50 = { by lemma 16 R->L }
% 0.19/0.50 double_divide(identity, inverse(inverse(X)))
% 0.19/0.50 = { by lemma 13 }
% 0.19/0.50 inverse(X)
% 0.19/0.50
% 0.19/0.50 Lemma 18: double_divide(X, double_divide(Y, X)) = Y.
% 0.19/0.50 Proof:
% 0.19/0.50 double_divide(X, double_divide(Y, X))
% 0.19/0.50 = { by lemma 12 R->L }
% 0.19/0.50 double_divide(X, multiply(double_divide(Y, X), identity))
% 0.19/0.50 = { by lemma 5 R->L }
% 0.19/0.50 double_divide(X, inverse(double_divide(identity, double_divide(Y, X))))
% 0.19/0.50 = { by lemma 17 R->L }
% 0.19/0.50 double_divide(X, double_divide(identity, double_divide(identity, double_divide(Y, X))))
% 0.19/0.50 = { by lemma 13 R->L }
% 0.19/0.50 double_divide(double_divide(identity, inverse(X)), double_divide(identity, double_divide(identity, double_divide(Y, X))))
% 0.19/0.50 = { by lemma 11 R->L }
% 0.19/0.50 double_divide(double_divide(identity, inverse(X)), double_divide(identity, double_divide(inverse(identity), double_divide(Y, X))))
% 0.19/0.50 = { by lemma 8 R->L }
% 0.19/0.50 double_divide(double_divide(identity, inverse(X)), double_divide(identity, double_divide(multiply(inverse(inverse(X)), inverse(X)), double_divide(Y, X))))
% 0.19/0.50 = { by lemma 16 }
% 0.19/0.50 double_divide(double_divide(identity, inverse(X)), double_divide(identity, double_divide(multiply(X, inverse(X)), double_divide(Y, X))))
% 0.19/0.50 = { by lemma 6 }
% 0.19/0.50 Y
% 0.19/0.50
% 0.19/0.50 Lemma 19: double_divide(double_divide(X, Y), X) = Y.
% 0.19/0.50 Proof:
% 0.19/0.50 double_divide(double_divide(X, Y), X)
% 0.19/0.50 = { by lemma 18 R->L }
% 0.19/0.50 double_divide(double_divide(X, Y), double_divide(Y, double_divide(X, Y)))
% 0.19/0.50 = { by lemma 18 }
% 0.19/0.50 Y
% 0.19/0.50
% 0.19/0.50 Lemma 20: double_divide(X, inverse(Y)) = multiply(inverse(X), Y).
% 0.19/0.50 Proof:
% 0.19/0.50 double_divide(X, inverse(Y))
% 0.19/0.50 = { by lemma 17 R->L }
% 0.19/0.50 double_divide(X, double_divide(identity, Y))
% 0.19/0.50 = { by lemma 7 R->L }
% 0.19/0.50 double_divide(double_divide(double_divide(identity, Y), double_divide(identity, inverse(multiply(inverse(X), Y)))), double_divide(identity, Y))
% 0.19/0.50 = { by lemma 19 }
% 0.19/0.50 double_divide(identity, inverse(multiply(inverse(X), Y)))
% 0.19/0.50 = { by lemma 13 }
% 0.19/0.50 multiply(inverse(X), Y)
% 0.19/0.50
% 0.19/0.50 Lemma 21: inverse(multiply(X, Y)) = double_divide(Y, X).
% 0.19/0.50 Proof:
% 0.19/0.50 inverse(multiply(X, Y))
% 0.19/0.50 = { by lemma 5 R->L }
% 0.19/0.50 inverse(inverse(double_divide(Y, X)))
% 0.19/0.50 = { by lemma 16 }
% 0.19/0.50 double_divide(Y, X)
% 0.19/0.50
% 0.19/0.50 Lemma 22: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.19/0.50 Proof:
% 0.19/0.50 multiply(X, multiply(inverse(X), Y))
% 0.19/0.50 = { by lemma 20 R->L }
% 0.19/0.50 multiply(X, double_divide(X, inverse(Y)))
% 0.19/0.50 = { by lemma 21 R->L }
% 0.19/0.50 multiply(X, inverse(multiply(inverse(Y), X)))
% 0.19/0.50 = { by lemma 19 R->L }
% 0.19/0.50 double_divide(double_divide(multiply(inverse(Y), X), multiply(X, inverse(multiply(inverse(Y), X)))), multiply(inverse(Y), X))
% 0.19/0.50 = { by lemma 16 R->L }
% 0.19/0.50 double_divide(double_divide(multiply(inverse(Y), X), multiply(inverse(inverse(X)), inverse(multiply(inverse(Y), X)))), multiply(inverse(Y), X))
% 0.19/0.50 = { by lemma 14 }
% 0.19/0.50 double_divide(inverse(X), multiply(inverse(Y), X))
% 0.19/0.50 = { by lemma 17 R->L }
% 0.19/0.50 double_divide(double_divide(identity, X), multiply(inverse(Y), X))
% 0.19/0.50 = { by lemma 13 R->L }
% 0.19/0.50 double_divide(double_divide(identity, X), double_divide(identity, inverse(multiply(inverse(Y), X))))
% 0.19/0.50 = { by lemma 7 }
% 0.19/0.50 Y
% 0.19/0.50
% 0.19/0.50 Lemma 23: double_divide(multiply(inverse(X), Y), X) = inverse(Y).
% 0.19/0.50 Proof:
% 0.19/0.50 double_divide(multiply(inverse(X), Y), X)
% 0.19/0.50 = { by lemma 13 R->L }
% 0.19/0.50 double_divide(identity, inverse(double_divide(multiply(inverse(X), Y), X)))
% 0.19/0.50 = { by lemma 5 }
% 0.19/0.50 double_divide(identity, multiply(X, multiply(inverse(X), Y)))
% 0.19/0.50 = { by lemma 22 }
% 0.19/0.50 double_divide(identity, Y)
% 0.19/0.50 = { by lemma 17 }
% 0.19/0.50 inverse(Y)
% 0.19/0.50
% 0.19/0.50 Lemma 24: double_divide(X, Y) = multiply(inverse(X), inverse(Y)).
% 0.19/0.50 Proof:
% 0.19/0.50 double_divide(X, Y)
% 0.19/0.50 = { by lemma 22 R->L }
% 0.19/0.50 double_divide(multiply(inverse(Y), multiply(inverse(inverse(Y)), X)), Y)
% 0.19/0.50 = { by lemma 23 }
% 0.19/0.50 inverse(multiply(inverse(inverse(Y)), X))
% 0.19/0.50 = { by lemma 21 }
% 0.19/0.50 double_divide(X, inverse(inverse(Y)))
% 0.19/0.50 = { by lemma 20 }
% 0.19/0.50 multiply(inverse(X), inverse(Y))
% 0.19/0.50
% 0.19/0.50 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3)) = tuple(identity, a2, multiply(a3, multiply(b3, c3))).
% 0.19/0.50 Proof:
% 0.19/0.50 tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3))
% 0.19/0.50 = { by lemma 15 }
% 0.19/0.50 tuple(multiply(inverse(a1), a1), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.19/0.51 = { by lemma 8 }
% 0.19/0.51 tuple(inverse(identity), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.19/0.51 = { by lemma 11 }
% 0.19/0.51 tuple(identity, inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.19/0.51 = { by lemma 16 }
% 0.19/0.51 tuple(identity, a2, multiply(multiply(a3, b3), c3))
% 0.19/0.51 = { by lemma 16 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(multiply(a3, inverse(inverse(b3))), c3))
% 0.19/0.51 = { by lemma 16 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), c3))
% 0.19/0.51 = { by lemma 22 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), c3))))
% 0.19/0.51 = { by lemma 24 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(double_divide(inverse(a3), inverse(b3)), c3))))
% 0.19/0.51 = { by lemma 21 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(inverse(multiply(inverse(b3), inverse(a3))), c3))))
% 0.19/0.51 = { by lemma 20 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(a3, multiply(inverse(a3), double_divide(multiply(inverse(b3), inverse(a3)), inverse(c3)))))
% 0.19/0.51 = { by lemma 12 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(double_divide(multiply(inverse(b3), inverse(a3)), inverse(c3)), identity))))
% 0.19/0.51 = { by lemma 5 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(a3, multiply(inverse(a3), inverse(double_divide(identity, double_divide(multiply(inverse(b3), inverse(a3)), inverse(c3)))))))
% 0.19/0.51 = { by lemma 12 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(a3, multiply(multiply(inverse(a3), identity), inverse(double_divide(identity, double_divide(multiply(inverse(b3), inverse(a3)), inverse(c3)))))))
% 0.19/0.51 = { by lemma 5 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(a3, multiply(inverse(double_divide(identity, inverse(a3))), inverse(double_divide(identity, double_divide(multiply(inverse(b3), inverse(a3)), inverse(c3)))))))
% 0.19/0.51 = { by lemma 24 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(a3, double_divide(double_divide(identity, inverse(a3)), double_divide(identity, double_divide(multiply(inverse(b3), inverse(a3)), inverse(c3))))))
% 0.19/0.51 = { by lemma 23 R->L }
% 0.19/0.51 tuple(identity, a2, multiply(a3, double_divide(double_divide(identity, inverse(a3)), double_divide(identity, double_divide(multiply(inverse(b3), inverse(a3)), double_divide(multiply(inverse(inverse(b3)), c3), inverse(b3)))))))
% 0.19/0.51 = { by lemma 6 }
% 0.19/0.51 tuple(identity, a2, multiply(a3, multiply(inverse(inverse(b3)), c3)))
% 0.19/0.51 = { by lemma 16 }
% 0.19/0.51 tuple(identity, a2, multiply(a3, multiply(b3, c3)))
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51
% 0.19/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------