%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP080-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 0.18s 0.46s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP080-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.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 09:18:16 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 Command-line arguments: --no-flatten-goal
% 0.18/0.46
% 0.18/0.46 % SZS status Unsatisfiable
% 0.18/0.46
% 0.18/0.48 % SZS output start Proof
% 0.18/0.48 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.18/0.48 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.18/0.48 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.18/0.48 Axiom 4 (single_axiom): double_divide(double_divide(identity, double_divide(X, double_divide(Y, identity))), double_divide(double_divide(Y, double_divide(Z, X)), identity)) = Z.
% 0.18/0.48
% 0.18/0.48 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.18/0.48 Proof:
% 0.18/0.48 inverse(double_divide(X, Y))
% 0.18/0.48 = { by axiom 1 (inverse) }
% 0.18/0.48 double_divide(double_divide(X, Y), identity)
% 0.18/0.48 = { by axiom 3 (multiply) R->L }
% 0.18/0.48 multiply(Y, X)
% 0.18/0.48
% 0.18/0.48 Lemma 6: double_divide(double_divide(identity, double_divide(X, inverse(Y))), multiply(double_divide(Z, X), Y)) = Z.
% 0.18/0.48 Proof:
% 0.18/0.48 double_divide(double_divide(identity, double_divide(X, inverse(Y))), multiply(double_divide(Z, X), Y))
% 0.18/0.48 = { by lemma 5 R->L }
% 0.18/0.48 double_divide(double_divide(identity, double_divide(X, inverse(Y))), inverse(double_divide(Y, double_divide(Z, X))))
% 0.18/0.48 = { by axiom 1 (inverse) }
% 0.18/0.48 double_divide(double_divide(identity, double_divide(X, inverse(Y))), double_divide(double_divide(Y, double_divide(Z, X)), identity))
% 0.18/0.48 = { by axiom 1 (inverse) }
% 0.18/0.48 double_divide(double_divide(identity, double_divide(X, double_divide(Y, identity))), double_divide(double_divide(Y, double_divide(Z, X)), identity))
% 0.18/0.48 = { by axiom 4 (single_axiom) }
% 0.18/0.48 Z
% 0.18/0.48
% 0.18/0.48 Lemma 7: inverse(identity) = identity.
% 0.18/0.48 Proof:
% 0.18/0.48 inverse(identity)
% 0.18/0.48 = { by lemma 6 R->L }
% 0.18/0.48 double_divide(double_divide(identity, double_divide(inverse(identity), inverse(identity))), multiply(double_divide(inverse(identity), inverse(identity)), identity))
% 0.18/0.48 = { by lemma 5 R->L }
% 0.18/0.48 double_divide(double_divide(identity, double_divide(inverse(identity), inverse(identity))), inverse(double_divide(identity, double_divide(inverse(identity), inverse(identity)))))
% 0.18/0.48 = { by axiom 2 (identity) R->L }
% 0.18/0.48 identity
% 0.18/0.48
% 0.18/0.48 Lemma 8: multiply(identity, X) = inverse(inverse(X)).
% 0.18/0.48 Proof:
% 0.18/0.48 multiply(identity, X)
% 0.18/0.48 = { by lemma 5 R->L }
% 0.18/0.48 inverse(double_divide(X, identity))
% 0.18/0.48 = { by axiom 1 (inverse) R->L }
% 0.18/0.49 inverse(inverse(X))
% 0.18/0.49
% 0.18/0.49 Lemma 9: double_divide(identity, multiply(double_divide(X, Y), Y)) = X.
% 0.18/0.49 Proof:
% 0.18/0.49 double_divide(identity, multiply(double_divide(X, Y), Y))
% 0.18/0.49 = { by lemma 7 R->L }
% 0.18/0.49 double_divide(inverse(identity), multiply(double_divide(X, Y), Y))
% 0.18/0.49 = { by axiom 1 (inverse) }
% 0.18/0.49 double_divide(double_divide(identity, identity), multiply(double_divide(X, Y), Y))
% 0.18/0.49 = { by axiom 2 (identity) }
% 0.18/0.49 double_divide(double_divide(identity, double_divide(Y, inverse(Y))), multiply(double_divide(X, Y), Y))
% 0.18/0.49 = { by lemma 6 }
% 0.18/0.49 X
% 0.18/0.49
% 0.18/0.49 Lemma 10: double_divide(identity, inverse(inverse(inverse(X)))) = X.
% 0.18/0.49 Proof:
% 0.18/0.49 double_divide(identity, inverse(inverse(inverse(X))))
% 0.18/0.49 = { by lemma 8 R->L }
% 0.18/0.49 double_divide(identity, multiply(identity, inverse(X)))
% 0.18/0.49 = { by axiom 2 (identity) }
% 0.18/0.49 double_divide(identity, multiply(double_divide(X, inverse(X)), inverse(X)))
% 0.18/0.49 = { by lemma 9 }
% 0.18/0.49 X
% 0.18/0.49
% 0.18/0.49 Lemma 11: multiply(inverse(inverse(inverse(X))), identity) = inverse(X).
% 0.18/0.49 Proof:
% 0.18/0.49 multiply(inverse(inverse(inverse(X))), identity)
% 0.18/0.49 = { by lemma 5 R->L }
% 0.18/0.49 inverse(double_divide(identity, inverse(inverse(inverse(X)))))
% 0.18/0.49 = { by lemma 10 }
% 0.18/0.49 inverse(X)
% 0.18/0.49
% 0.18/0.49 Lemma 12: double_divide(identity, inverse(X)) = inverse(inverse(X)).
% 0.18/0.49 Proof:
% 0.18/0.49 double_divide(identity, inverse(X))
% 0.18/0.49 = { by lemma 11 R->L }
% 0.18/0.49 double_divide(identity, multiply(inverse(inverse(inverse(X))), identity))
% 0.18/0.49 = { by axiom 1 (inverse) }
% 0.18/0.49 double_divide(identity, multiply(double_divide(inverse(inverse(X)), identity), identity))
% 0.18/0.49 = { by lemma 9 }
% 0.18/0.49 inverse(inverse(X))
% 0.18/0.49
% 0.18/0.49 Lemma 13: inverse(inverse(inverse(inverse(X)))) = X.
% 0.18/0.49 Proof:
% 0.18/0.49 inverse(inverse(inverse(inverse(X))))
% 0.18/0.49 = { by lemma 12 R->L }
% 0.18/0.49 double_divide(identity, inverse(inverse(inverse(X))))
% 0.18/0.49 = { by lemma 10 }
% 0.18/0.49 X
% 0.18/0.49
% 0.18/0.49 Lemma 14: multiply(X, identity) = inverse(inverse(X)).
% 0.18/0.49 Proof:
% 0.18/0.49 multiply(X, identity)
% 0.18/0.49 = { by lemma 13 R->L }
% 0.18/0.49 multiply(inverse(inverse(inverse(inverse(X)))), identity)
% 0.18/0.49 = { by lemma 11 }
% 0.18/0.49 inverse(inverse(X))
% 0.18/0.49
% 0.18/0.49 Lemma 15: multiply(X, multiply(double_divide(X, Y), Z)) = double_divide(Y, inverse(Z)).
% 0.18/0.49 Proof:
% 0.18/0.49 multiply(X, multiply(double_divide(X, Y), Z))
% 0.18/0.49 = { by lemma 6 R->L }
% 0.18/0.49 multiply(double_divide(double_divide(identity, double_divide(Y, inverse(Z))), multiply(double_divide(X, Y), Z)), multiply(double_divide(X, Y), Z))
% 0.18/0.49 = { by lemma 10 R->L }
% 0.18/0.49 double_divide(identity, inverse(inverse(inverse(multiply(double_divide(double_divide(identity, double_divide(Y, inverse(Z))), multiply(double_divide(X, Y), Z)), multiply(double_divide(X, Y), Z))))))
% 0.18/0.49 = { by lemma 14 R->L }
% 0.18/0.49 double_divide(identity, inverse(multiply(multiply(double_divide(double_divide(identity, double_divide(Y, inverse(Z))), multiply(double_divide(X, Y), Z)), multiply(double_divide(X, Y), Z)), identity)))
% 0.18/0.49 = { by lemma 5 R->L }
% 0.18/0.49 double_divide(identity, inverse(inverse(double_divide(identity, multiply(double_divide(double_divide(identity, double_divide(Y, inverse(Z))), multiply(double_divide(X, Y), Z)), multiply(double_divide(X, Y), Z))))))
% 0.18/0.49 = { by lemma 9 }
% 0.18/0.49 double_divide(identity, inverse(inverse(double_divide(identity, double_divide(Y, inverse(Z))))))
% 0.18/0.49 = { by lemma 12 }
% 0.18/0.49 inverse(inverse(inverse(double_divide(identity, double_divide(Y, inverse(Z))))))
% 0.18/0.49 = { by lemma 5 }
% 0.18/0.49 inverse(inverse(multiply(double_divide(Y, inverse(Z)), identity)))
% 0.18/0.49 = { by lemma 14 }
% 0.18/0.49 inverse(inverse(inverse(inverse(double_divide(Y, inverse(Z))))))
% 0.18/0.49 = { by lemma 13 }
% 0.18/0.49 double_divide(Y, inverse(Z))
% 0.18/0.49
% 0.18/0.49 Lemma 16: double_divide(inverse(X), inverse(Y)) = multiply(X, inverse(inverse(Y))).
% 0.18/0.49 Proof:
% 0.18/0.49 double_divide(inverse(X), inverse(Y))
% 0.18/0.49 = { by lemma 15 R->L }
% 0.18/0.49 multiply(X, multiply(double_divide(X, inverse(X)), Y))
% 0.18/0.49 = { by axiom 2 (identity) R->L }
% 0.18/0.49 multiply(X, multiply(identity, Y))
% 0.18/0.49 = { by lemma 8 }
% 0.18/0.49 multiply(X, inverse(inverse(Y)))
% 0.18/0.49
% 0.18/0.49 Lemma 17: inverse(inverse(X)) = X.
% 0.18/0.49 Proof:
% 0.18/0.49 inverse(inverse(X))
% 0.18/0.49 = { by lemma 12 R->L }
% 0.18/0.49 double_divide(identity, inverse(X))
% 0.18/0.49 = { by lemma 7 R->L }
% 0.18/0.49 double_divide(inverse(identity), inverse(X))
% 0.18/0.49 = { by lemma 16 }
% 0.18/0.49 multiply(identity, inverse(inverse(X)))
% 0.18/0.49 = { by lemma 8 }
% 0.18/0.49 inverse(inverse(inverse(inverse(X))))
% 0.18/0.49 = { by lemma 13 }
% 0.18/0.49 X
% 0.18/0.49
% 0.18/0.49 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))).
% 0.18/0.49 Proof:
% 0.18/0.49 tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3))
% 0.18/0.49 = { by lemma 8 }
% 0.18/0.49 tuple(multiply(inverse(a1), a1), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.18/0.49 = { by lemma 5 R->L }
% 0.18/0.49 tuple(inverse(double_divide(a1, inverse(a1))), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.18/0.49 = { by axiom 2 (identity) R->L }
% 0.18/0.49 tuple(inverse(identity), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.18/0.49 = { by lemma 7 }
% 0.18/0.49 tuple(identity, inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.18/0.49 = { by lemma 17 }
% 0.18/0.49 tuple(identity, a2, multiply(multiply(a3, b3), c3))
% 0.18/0.49 = { by lemma 13 R->L }
% 0.18/0.49 tuple(identity, a2, multiply(multiply(a3, inverse(inverse(inverse(inverse(b3))))), c3))
% 0.18/0.49 = { by lemma 13 R->L }
% 0.18/0.49 tuple(identity, a2, multiply(multiply(a3, inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(b3))))))))), c3))
% 0.18/0.49 = { by lemma 16 R->L }
% 0.18/0.49 tuple(identity, a2, multiply(double_divide(inverse(a3), inverse(inverse(inverse(inverse(inverse(inverse(inverse(b3)))))))), c3))
% 0.18/0.49 = { by lemma 13 }
% 0.18/0.49 tuple(identity, a2, multiply(double_divide(inverse(a3), inverse(inverse(inverse(b3)))), c3))
% 0.18/0.49 = { by lemma 17 R->L }
% 0.18/0.49 tuple(identity, a2, inverse(inverse(multiply(double_divide(inverse(a3), inverse(inverse(inverse(b3)))), c3))))
% 0.18/0.49 = { by lemma 12 R->L }
% 0.18/0.49 tuple(identity, a2, double_divide(identity, inverse(multiply(double_divide(inverse(a3), inverse(inverse(inverse(b3)))), c3))))
% 0.18/0.49 = { by lemma 15 R->L }
% 0.18/0.49 tuple(identity, a2, multiply(a3, multiply(double_divide(a3, identity), multiply(double_divide(inverse(a3), inverse(inverse(inverse(b3)))), c3))))
% 0.18/0.49 = { by axiom 1 (inverse) R->L }
% 0.18/0.49 tuple(identity, a2, multiply(a3, multiply(inverse(a3), multiply(double_divide(inverse(a3), inverse(inverse(inverse(b3)))), c3))))
% 0.18/0.49 = { by lemma 15 }
% 0.18/0.49 tuple(identity, a2, multiply(a3, double_divide(inverse(inverse(inverse(b3))), inverse(c3))))
% 0.18/0.49 = { by lemma 17 R->L }
% 0.18/0.49 tuple(identity, a2, multiply(a3, double_divide(inverse(inverse(inverse(inverse(inverse(b3))))), inverse(c3))))
% 0.18/0.49 = { by lemma 16 }
% 0.18/0.49 tuple(identity, a2, multiply(a3, multiply(inverse(inverse(inverse(inverse(b3)))), inverse(inverse(c3)))))
% 0.18/0.49 = { by lemma 17 }
% 0.18/0.49 tuple(identity, a2, multiply(a3, multiply(inverse(inverse(inverse(inverse(b3)))), c3)))
% 0.18/0.49 = { by lemma 13 }
% 0.18/0.49 tuple(identity, a2, multiply(a3, multiply(b3, c3)))
% 0.18/0.49 % SZS output end Proof
% 0.18/0.49
% 0.18/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------