%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 0.12s 0.48s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:21:14 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.48 Command-line arguments: --no-flatten-goal
% 0.12/0.48
% 0.12/0.48 % SZS status Unsatisfiable
% 0.12/0.48
% 0.62/0.51 % SZS output start Proof
% 0.62/0.51 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.62/0.51 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.62/0.51 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.62/0.51 Axiom 4 (single_axiom): double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(Y, Z), double_divide(identity, identity)), double_divide(X, Z))) = Y.
% 0.62/0.51
% 0.62/0.51 Lemma 5: double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(Y, Z), inverse(identity)), double_divide(X, Z))) = Y.
% 0.62/0.51 Proof:
% 0.62/0.51 double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(Y, Z), inverse(identity)), double_divide(X, Z)))
% 0.62/0.51 = { by axiom 1 (inverse) }
% 0.62/0.51 double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(Y, Z), double_divide(identity, identity)), double_divide(X, Z)))
% 0.62/0.51 = { by axiom 4 (single_axiom) }
% 0.62/0.51 Y
% 0.62/0.51
% 0.62/0.51 Lemma 6: double_divide(double_divide(identity, X), double_divide(identity, double_divide(X, inverse(Y)))) = Y.
% 0.62/0.51 Proof:
% 0.62/0.51 double_divide(double_divide(identity, X), double_divide(identity, double_divide(X, inverse(Y))))
% 0.62/0.51 = { by axiom 2 (identity) }
% 0.62/0.51 double_divide(double_divide(identity, X), double_divide(double_divide(identity, inverse(identity)), double_divide(X, inverse(Y))))
% 0.62/0.51 = { by axiom 2 (identity) }
% 0.62/0.51 double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(Y, inverse(Y)), inverse(identity)), double_divide(X, inverse(Y))))
% 0.62/0.51 = { by lemma 5 }
% 0.62/0.51 Y
% 0.62/0.51
% 0.62/0.51 Lemma 7: double_divide(double_divide(identity, X), inverse(identity)) = X.
% 0.62/0.51 Proof:
% 0.62/0.51 double_divide(double_divide(identity, X), inverse(identity))
% 0.62/0.51 = { by axiom 1 (inverse) }
% 0.62/0.51 double_divide(double_divide(identity, X), double_divide(identity, identity))
% 0.62/0.51 = { by axiom 2 (identity) }
% 0.62/0.51 double_divide(double_divide(identity, X), double_divide(identity, double_divide(X, inverse(X))))
% 0.62/0.51 = { by lemma 6 }
% 0.62/0.51 X
% 0.62/0.51
% 0.62/0.51 Lemma 8: inverse(identity) = identity.
% 0.62/0.51 Proof:
% 0.62/0.51 inverse(identity)
% 0.62/0.51 = { by lemma 7 R->L }
% 0.62/0.51 double_divide(double_divide(identity, inverse(identity)), inverse(identity))
% 0.62/0.51 = { by axiom 2 (identity) R->L }
% 0.62/0.51 double_divide(identity, inverse(identity))
% 0.62/0.51 = { by axiom 2 (identity) R->L }
% 0.62/0.51 identity
% 0.62/0.51
% 0.62/0.51 Lemma 9: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.62/0.51 Proof:
% 0.62/0.51 inverse(double_divide(X, Y))
% 0.62/0.51 = { by axiom 1 (inverse) }
% 0.62/0.51 double_divide(double_divide(X, Y), identity)
% 0.62/0.51 = { by axiom 3 (multiply) R->L }
% 0.62/0.51 multiply(Y, X)
% 0.62/0.51
% 0.62/0.51 Lemma 10: multiply(X, identity) = X.
% 0.62/0.51 Proof:
% 0.62/0.51 multiply(X, identity)
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 inverse(double_divide(identity, X))
% 0.62/0.52 = { by axiom 1 (inverse) }
% 0.62/0.52 double_divide(double_divide(identity, X), identity)
% 0.62/0.52 = { by lemma 8 R->L }
% 0.62/0.52 double_divide(double_divide(identity, X), inverse(identity))
% 0.62/0.52 = { by lemma 7 }
% 0.62/0.52 X
% 0.62/0.52
% 0.62/0.52 Lemma 11: double_divide(double_divide(X, Y), multiply(Y, X)) = identity.
% 0.62/0.52 Proof:
% 0.62/0.52 double_divide(double_divide(X, Y), multiply(Y, X))
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 double_divide(double_divide(X, Y), inverse(double_divide(X, Y)))
% 0.62/0.52 = { by axiom 2 (identity) R->L }
% 0.62/0.52 identity
% 0.62/0.52
% 0.62/0.52 Lemma 12: double_divide(identity, inverse(X)) = X.
% 0.62/0.52 Proof:
% 0.62/0.52 double_divide(identity, inverse(X))
% 0.62/0.52 = { by lemma 7 R->L }
% 0.62/0.52 double_divide(double_divide(identity, double_divide(identity, inverse(X))), inverse(identity))
% 0.62/0.52 = { by axiom 1 (inverse) }
% 0.62/0.52 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, identity))
% 0.62/0.52 = { by lemma 11 R->L }
% 0.62/0.52 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, double_divide(double_divide(identity, inverse(X)), multiply(inverse(X), identity))))
% 0.62/0.52 = { by lemma 10 }
% 0.62/0.52 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, double_divide(double_divide(identity, inverse(X)), inverse(X))))
% 0.62/0.52 = { by lemma 6 }
% 0.62/0.52 X
% 0.62/0.52
% 0.62/0.52 Lemma 13: double_divide(identity, X) = inverse(X).
% 0.62/0.52 Proof:
% 0.62/0.52 double_divide(identity, X)
% 0.62/0.52 = { by lemma 10 R->L }
% 0.62/0.52 multiply(double_divide(identity, X), identity)
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 inverse(double_divide(identity, double_divide(identity, X)))
% 0.62/0.52 = { by lemma 8 R->L }
% 0.62/0.52 inverse(double_divide(inverse(identity), double_divide(identity, X)))
% 0.62/0.52 = { by axiom 1 (inverse) }
% 0.62/0.52 inverse(double_divide(double_divide(identity, identity), double_divide(identity, X)))
% 0.62/0.52 = { by lemma 12 R->L }
% 0.62/0.52 inverse(double_divide(double_divide(identity, identity), double_divide(identity, double_divide(identity, inverse(X)))))
% 0.62/0.52 = { by lemma 6 }
% 0.62/0.52 inverse(X)
% 0.62/0.52
% 0.62/0.52 Lemma 14: multiply(identity, X) = inverse(inverse(X)).
% 0.62/0.52 Proof:
% 0.62/0.52 multiply(identity, X)
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 inverse(double_divide(X, identity))
% 0.62/0.52 = { by axiom 1 (inverse) R->L }
% 0.62/0.52 inverse(inverse(X))
% 0.62/0.52
% 0.62/0.52 Lemma 15: inverse(inverse(X)) = X.
% 0.62/0.52 Proof:
% 0.62/0.52 inverse(inverse(X))
% 0.62/0.52 = { by lemma 13 R->L }
% 0.62/0.52 inverse(double_divide(identity, X))
% 0.62/0.52 = { by lemma 9 }
% 0.62/0.52 multiply(X, identity)
% 0.62/0.52 = { by lemma 10 }
% 0.62/0.52 X
% 0.62/0.52
% 0.62/0.52 Lemma 16: double_divide(X, double_divide(Y, X)) = Y.
% 0.62/0.52 Proof:
% 0.62/0.52 double_divide(X, double_divide(Y, X))
% 0.62/0.52 = { by lemma 15 R->L }
% 0.62/0.52 double_divide(X, inverse(inverse(double_divide(Y, X))))
% 0.62/0.52 = { by lemma 14 R->L }
% 0.62/0.52 double_divide(X, multiply(identity, double_divide(Y, X)))
% 0.62/0.52 = { by lemma 8 R->L }
% 0.62/0.52 double_divide(X, multiply(inverse(identity), double_divide(Y, X)))
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 double_divide(X, inverse(double_divide(double_divide(Y, X), inverse(identity))))
% 0.62/0.52 = { by axiom 1 (inverse) }
% 0.62/0.52 double_divide(X, double_divide(double_divide(double_divide(Y, X), inverse(identity)), identity))
% 0.62/0.52 = { by lemma 12 R->L }
% 0.62/0.52 double_divide(double_divide(identity, inverse(X)), double_divide(double_divide(double_divide(Y, X), inverse(identity)), identity))
% 0.62/0.52 = { by lemma 11 R->L }
% 0.62/0.52 double_divide(double_divide(identity, inverse(X)), double_divide(double_divide(double_divide(Y, X), inverse(identity)), double_divide(double_divide(identity, X), multiply(X, identity))))
% 0.62/0.52 = { by lemma 13 }
% 0.62/0.52 double_divide(double_divide(identity, inverse(X)), double_divide(double_divide(double_divide(Y, X), inverse(identity)), double_divide(inverse(X), multiply(X, identity))))
% 0.62/0.52 = { by lemma 10 }
% 0.62/0.52 double_divide(double_divide(identity, inverse(X)), double_divide(double_divide(double_divide(Y, X), inverse(identity)), double_divide(inverse(X), X)))
% 0.62/0.52 = { by lemma 5 }
% 0.62/0.52 Y
% 0.62/0.52
% 0.62/0.52 Lemma 17: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.62/0.52 Proof:
% 0.62/0.52 multiply(inverse(X), multiply(X, Y))
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 multiply(inverse(X), inverse(double_divide(Y, X)))
% 0.62/0.52 = { by axiom 1 (inverse) }
% 0.62/0.52 multiply(inverse(X), double_divide(double_divide(Y, X), identity))
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 inverse(double_divide(double_divide(double_divide(Y, X), identity), inverse(X)))
% 0.62/0.52 = { by lemma 13 R->L }
% 0.62/0.52 double_divide(identity, double_divide(double_divide(double_divide(Y, X), identity), inverse(X)))
% 0.62/0.52 = { by lemma 8 R->L }
% 0.62/0.52 double_divide(inverse(identity), double_divide(double_divide(double_divide(Y, X), identity), inverse(X)))
% 0.62/0.52 = { by lemma 8 R->L }
% 0.62/0.52 double_divide(inverse(identity), double_divide(double_divide(double_divide(Y, X), inverse(identity)), inverse(X)))
% 0.62/0.52 = { by lemma 13 R->L }
% 0.62/0.52 double_divide(double_divide(identity, identity), double_divide(double_divide(double_divide(Y, X), inverse(identity)), inverse(X)))
% 0.62/0.52 = { by lemma 13 R->L }
% 0.62/0.52 double_divide(double_divide(identity, identity), double_divide(double_divide(double_divide(Y, X), inverse(identity)), double_divide(identity, X)))
% 0.62/0.52 = { by lemma 5 }
% 0.62/0.52 Y
% 0.62/0.52
% 0.62/0.52 Lemma 18: multiply(X, double_divide(X, Y)) = inverse(Y).
% 0.62/0.52 Proof:
% 0.62/0.52 multiply(X, double_divide(X, Y))
% 0.62/0.52 = { by lemma 12 R->L }
% 0.62/0.52 multiply(X, double_divide(identity, inverse(double_divide(X, Y))))
% 0.62/0.52 = { by lemma 9 }
% 0.62/0.52 multiply(X, double_divide(identity, multiply(Y, X)))
% 0.62/0.52 = { by lemma 13 }
% 0.62/0.52 multiply(X, inverse(multiply(Y, X)))
% 0.62/0.52 = { by lemma 17 R->L }
% 0.62/0.52 multiply(multiply(inverse(Y), multiply(Y, X)), inverse(multiply(Y, X)))
% 0.62/0.52 = { by lemma 13 R->L }
% 0.62/0.52 multiply(multiply(inverse(Y), multiply(Y, X)), double_divide(identity, multiply(Y, X)))
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 multiply(inverse(double_divide(multiply(Y, X), inverse(Y))), double_divide(identity, multiply(Y, X)))
% 0.62/0.52 = { by lemma 13 R->L }
% 0.62/0.52 multiply(double_divide(identity, double_divide(multiply(Y, X), inverse(Y))), double_divide(identity, multiply(Y, X)))
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 inverse(double_divide(double_divide(identity, multiply(Y, X)), double_divide(identity, double_divide(multiply(Y, X), inverse(Y)))))
% 0.62/0.52 = { by lemma 6 }
% 0.62/0.52 inverse(Y)
% 0.62/0.52
% 0.62/0.52 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))).
% 0.62/0.52 Proof:
% 0.62/0.52 tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3))
% 0.62/0.52 = { by lemma 14 }
% 0.62/0.52 tuple(multiply(inverse(a1), a1), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 tuple(inverse(double_divide(a1, inverse(a1))), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.62/0.52 = { by axiom 2 (identity) R->L }
% 0.62/0.52 tuple(inverse(identity), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.62/0.52 = { by lemma 8 }
% 0.62/0.52 tuple(identity, inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.62/0.52 = { by lemma 15 }
% 0.62/0.52 tuple(identity, a2, multiply(multiply(a3, b3), c3))
% 0.62/0.52 = { by lemma 15 R->L }
% 0.62/0.52 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), b3), c3))
% 0.62/0.52 = { by lemma 15 R->L }
% 0.62/0.52 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), c3))
% 0.62/0.52 = { by lemma 17 R->L }
% 0.62/0.52 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), multiply(inverse(b3), multiply(b3, c3))))
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), inverse(double_divide(multiply(b3, c3), inverse(b3)))))
% 0.62/0.52 = { by lemma 10 R->L }
% 0.62/0.52 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), multiply(inverse(double_divide(multiply(b3, c3), inverse(b3))), identity)))
% 0.62/0.52 = { by lemma 9 R->L }
% 0.62/0.52 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), inverse(double_divide(identity, inverse(double_divide(multiply(b3, c3), inverse(b3)))))))
% 0.62/0.52 = { by lemma 13 R->L }
% 0.62/0.52 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), double_divide(identity, double_divide(identity, inverse(double_divide(multiply(b3, c3), inverse(b3)))))))
% 0.62/0.52 = { by lemma 16 R->L }
% 0.62/0.52 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), double_divide(double_divide(double_divide(identity, identity), double_divide(identity, double_divide(identity, inverse(double_divide(multiply(b3, c3), inverse(b3)))))), double_divide(double_divide(identity, double_divide(identity, inverse(double_divide(multiply(b3, c3), inverse(b3))))), double_divide(double_divide(identity, identity), double_divide(identity, double_divide(identity, inverse(double_divide(multiply(b3, c3), inverse(b3))))))))))
% 0.62/0.52 = { by lemma 16 }
% 0.62/0.52 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), double_divide(double_divide(double_divide(identity, identity), double_divide(identity, double_divide(identity, inverse(double_divide(multiply(b3, c3), inverse(b3)))))), double_divide(identity, identity))))
% 0.62/0.52 = { by lemma 6 }
% 0.62/0.52 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), double_divide(double_divide(multiply(b3, c3), inverse(b3)), double_divide(identity, identity))))
% 0.62/0.53 = { by lemma 13 }
% 0.62/0.53 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), double_divide(double_divide(multiply(b3, c3), inverse(b3)), inverse(identity))))
% 0.62/0.53 = { by lemma 18 R->L }
% 0.62/0.53 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), multiply(inverse(a3), double_divide(inverse(a3), inverse(b3)))), double_divide(double_divide(multiply(b3, c3), inverse(b3)), inverse(identity))))
% 0.62/0.53 = { by lemma 17 }
% 0.62/0.53 tuple(identity, a2, multiply(double_divide(inverse(a3), inverse(b3)), double_divide(double_divide(multiply(b3, c3), inverse(b3)), inverse(identity))))
% 0.62/0.53 = { by lemma 9 R->L }
% 0.62/0.53 tuple(identity, a2, inverse(double_divide(double_divide(double_divide(multiply(b3, c3), inverse(b3)), inverse(identity)), double_divide(inverse(a3), inverse(b3)))))
% 0.62/0.53 = { by lemma 18 R->L }
% 0.62/0.53 tuple(identity, a2, multiply(double_divide(identity, inverse(a3)), double_divide(double_divide(identity, inverse(a3)), double_divide(double_divide(double_divide(multiply(b3, c3), inverse(b3)), inverse(identity)), double_divide(inverse(a3), inverse(b3))))))
% 0.62/0.53 = { by lemma 5 }
% 0.62/0.53 tuple(identity, a2, multiply(double_divide(identity, inverse(a3)), multiply(b3, c3)))
% 0.62/0.53 = { by lemma 13 }
% 0.62/0.53 tuple(identity, a2, multiply(inverse(inverse(a3)), multiply(b3, c3)))
% 0.62/0.53 = { by lemma 15 }
% 0.62/0.53 tuple(identity, a2, multiply(a3, multiply(b3, c3)))
% 0.62/0.53 % SZS output end Proof
% 0.62/0.53
% 0.62/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------