%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP105-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 0.07s 0.42s
% Output : Proof 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP105-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/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 09:19:04 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.42 Command-line arguments: --no-flatten-goal
% 0.07/0.42
% 0.07/0.42 % SZS status Unsatisfiable
% 0.07/0.42
% 1.01/0.47 % SZS output start Proof
% 1.01/0.47 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 1.01/0.47 Axiom 2 (single_axiom): double_divide(inverse(double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(Z))))), Y) = Z.
% 1.01/0.47
% 1.01/0.47 Lemma 3: double_divide(multiply(multiply(inverse(X), Y), double_divide(Y, Z)), Z) = X.
% 1.01/0.47 Proof:
% 1.01/0.47 double_divide(multiply(multiply(inverse(X), Y), double_divide(Y, Z)), Z)
% 1.01/0.47 = { by axiom 1 (multiply) }
% 1.01/0.47 double_divide(multiply(inverse(double_divide(Y, inverse(X))), double_divide(Y, Z)), Z)
% 1.01/0.47 = { by axiom 1 (multiply) }
% 1.01/0.47 double_divide(inverse(double_divide(double_divide(Y, Z), inverse(double_divide(Y, inverse(X))))), Z)
% 1.01/0.47 = { by axiom 2 (single_axiom) }
% 1.01/0.47 X
% 1.01/0.47
% 1.01/0.47 Lemma 4: multiply(X, multiply(multiply(inverse(Y), Z), double_divide(Z, X))) = inverse(Y).
% 1.01/0.47 Proof:
% 1.01/0.47 multiply(X, multiply(multiply(inverse(Y), Z), double_divide(Z, X)))
% 1.01/0.47 = { by axiom 1 (multiply) }
% 1.01/0.47 inverse(double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, X)), X))
% 1.01/0.47 = { by lemma 3 }
% 1.01/0.47 inverse(Y)
% 1.01/0.47
% 1.01/0.47 Lemma 5: double_divide(multiply(inverse(X), X), inverse(Y)) = Y.
% 1.01/0.47 Proof:
% 1.01/0.47 double_divide(multiply(inverse(X), X), inverse(Y))
% 1.01/0.47 = { by lemma 4 R->L }
% 1.01/0.47 double_divide(multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), double_divide(Z, inverse(Y)))), X), inverse(Y))
% 1.01/0.47 = { by lemma 3 R->L }
% 1.01/0.47 double_divide(multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), double_divide(Z, inverse(Y)))), double_divide(multiply(multiply(inverse(X), Z), double_divide(Z, inverse(Y))), inverse(Y))), inverse(Y))
% 1.01/0.47 = { by lemma 3 }
% 1.01/0.47 Y
% 1.01/0.47
% 1.01/0.47 Lemma 6: multiply(inverse(X), multiply(inverse(Y), Y)) = inverse(X).
% 1.01/0.47 Proof:
% 1.01/0.47 multiply(inverse(X), multiply(inverse(Y), Y))
% 1.01/0.47 = { by axiom 1 (multiply) }
% 1.01/0.47 inverse(double_divide(multiply(inverse(Y), Y), inverse(X)))
% 1.01/0.47 = { by lemma 5 }
% 1.01/0.47 inverse(X)
% 1.01/0.47
% 1.01/0.47 Lemma 7: double_divide(multiply(inverse(X), X), multiply(Y, Z)) = double_divide(Z, Y).
% 1.01/0.47 Proof:
% 1.01/0.47 double_divide(multiply(inverse(X), X), multiply(Y, Z))
% 1.01/0.47 = { by axiom 1 (multiply) }
% 1.01/0.47 double_divide(multiply(inverse(X), X), inverse(double_divide(Z, Y)))
% 1.01/0.47 = { by lemma 5 }
% 1.01/0.47 double_divide(Z, Y)
% 1.01/0.47
% 1.01/0.47 Lemma 8: double_divide(multiply(inverse(X), double_divide(Y, Z)), multiply(Z, Y)) = X.
% 1.01/0.47 Proof:
% 1.01/0.47 double_divide(multiply(inverse(X), double_divide(Y, Z)), multiply(Z, Y))
% 1.01/0.47 = { by lemma 6 R->L }
% 1.01/0.47 double_divide(multiply(multiply(inverse(X), multiply(inverse(W), W)), double_divide(Y, Z)), multiply(Z, Y))
% 1.01/0.47 = { by lemma 7 R->L }
% 1.01/0.47 double_divide(multiply(multiply(inverse(X), multiply(inverse(W), W)), double_divide(multiply(inverse(W), W), multiply(Z, Y))), multiply(Z, Y))
% 1.01/0.47 = { by lemma 3 }
% 1.01/0.47 X
% 1.01/0.47
% 1.01/0.47 Lemma 9: double_divide(multiply(inverse(X), Y), inverse(Y)) = X.
% 1.01/0.47 Proof:
% 1.01/0.47 double_divide(multiply(inverse(X), Y), inverse(Y))
% 1.01/0.47 = { by lemma 4 R->L }
% 1.01/0.47 double_divide(multiply(inverse(X), Y), multiply(Z, multiply(multiply(inverse(Y), W), double_divide(W, Z))))
% 1.01/0.47 = { by lemma 3 R->L }
% 1.01/0.47 double_divide(multiply(inverse(X), double_divide(multiply(multiply(inverse(Y), W), double_divide(W, Z)), Z)), multiply(Z, multiply(multiply(inverse(Y), W), double_divide(W, Z))))
% 1.01/0.47 = { by lemma 8 }
% 1.01/0.47 X
% 1.01/0.47
% 1.01/0.47 Lemma 10: multiply(inverse(X), multiply(inverse(Y), X)) = inverse(Y).
% 1.01/0.47 Proof:
% 1.01/0.47 multiply(inverse(X), multiply(inverse(Y), X))
% 1.01/0.47 = { by axiom 1 (multiply) }
% 1.01/0.47 inverse(double_divide(multiply(inverse(Y), X), inverse(X)))
% 1.01/0.47 = { by lemma 9 }
% 1.01/0.47 inverse(Y)
% 1.01/0.47
% 1.01/0.47 Lemma 11: double_divide(inverse(X), inverse(multiply(inverse(X), Y))) = Y.
% 1.01/0.47 Proof:
% 1.01/0.47 double_divide(inverse(X), inverse(multiply(inverse(X), Y)))
% 1.01/0.47 = { by lemma 10 R->L }
% 1.01/0.47 double_divide(multiply(inverse(Y), multiply(inverse(X), Y)), inverse(multiply(inverse(X), Y)))
% 1.01/0.48 = { by lemma 9 }
% 1.01/0.48 Y
% 1.01/0.48
% 1.01/0.48 Lemma 12: multiply(inverse(X), Y) = double_divide(inverse(Y), inverse(inverse(X))).
% 1.01/0.48 Proof:
% 1.01/0.48 multiply(inverse(X), Y)
% 1.01/0.48 = { by lemma 11 R->L }
% 1.01/0.48 double_divide(inverse(Y), inverse(multiply(inverse(Y), multiply(inverse(X), Y))))
% 1.01/0.48 = { by lemma 10 }
% 1.01/0.48 double_divide(inverse(Y), inverse(inverse(X)))
% 1.01/0.48
% 1.01/0.48 Lemma 13: multiply(multiply(X, Y), double_divide(multiply(X, Y), inverse(inverse(Z)))) = inverse(Z).
% 1.01/0.48 Proof:
% 1.01/0.48 multiply(multiply(X, Y), double_divide(multiply(X, Y), inverse(inverse(Z))))
% 1.01/0.48 = { by axiom 1 (multiply) }
% 1.01/0.48 multiply(multiply(X, Y), double_divide(inverse(double_divide(Y, X)), inverse(inverse(Z))))
% 1.01/0.48 = { by lemma 12 R->L }
% 1.01/0.48 multiply(multiply(X, Y), multiply(inverse(Z), double_divide(Y, X)))
% 1.01/0.48 = { by lemma 6 R->L }
% 1.01/0.48 multiply(multiply(X, Y), multiply(multiply(inverse(Z), multiply(inverse(W), W)), double_divide(Y, X)))
% 1.01/0.48 = { by lemma 7 R->L }
% 1.01/0.48 multiply(multiply(X, Y), multiply(multiply(inverse(Z), multiply(inverse(W), W)), double_divide(multiply(inverse(W), W), multiply(X, Y))))
% 1.01/0.48 = { by lemma 4 }
% 1.01/0.48 inverse(Z)
% 1.01/0.48
% 1.01/0.48 Lemma 14: double_divide(X, double_divide(inverse(inverse(Y)), inverse(inverse(X)))) = Y.
% 1.01/0.48 Proof:
% 1.01/0.48 double_divide(X, double_divide(inverse(inverse(Y)), inverse(inverse(X))))
% 1.01/0.48 = { by lemma 12 R->L }
% 1.01/0.48 double_divide(X, multiply(inverse(X), inverse(Y)))
% 1.01/0.48 = { by lemma 9 R->L }
% 1.01/0.48 double_divide(double_divide(multiply(inverse(X), inverse(Y)), inverse(inverse(Y))), multiply(inverse(X), inverse(Y)))
% 1.01/0.48 = { by lemma 3 R->L }
% 1.01/0.48 double_divide(multiply(multiply(inverse(double_divide(double_divide(multiply(inverse(X), inverse(Y)), inverse(inverse(Y))), multiply(inverse(X), inverse(Y)))), Z), double_divide(Z, W)), W)
% 1.01/0.48 = { by axiom 1 (multiply) R->L }
% 1.01/0.48 double_divide(multiply(multiply(multiply(multiply(inverse(X), inverse(Y)), double_divide(multiply(inverse(X), inverse(Y)), inverse(inverse(Y)))), Z), double_divide(Z, W)), W)
% 1.01/0.48 = { by lemma 13 }
% 1.01/0.48 double_divide(multiply(multiply(inverse(Y), Z), double_divide(Z, W)), W)
% 1.01/0.48 = { by lemma 3 }
% 1.01/0.48 Y
% 1.01/0.48
% 1.01/0.48 Lemma 15: double_divide(inverse(inverse(multiply(inverse(X), X))), inverse(Y)) = Y.
% 1.01/0.48 Proof:
% 1.01/0.48 double_divide(inverse(inverse(multiply(inverse(X), X))), inverse(Y))
% 1.01/0.48 = { by lemma 6 R->L }
% 1.01/0.48 double_divide(inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))), inverse(Y))
% 1.01/0.48 = { by lemma 6 R->L }
% 1.01/0.48 double_divide(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))), inverse(Y))
% 1.01/0.48 = { by lemma 5 }
% 1.01/0.48 Y
% 1.01/0.48
% 1.01/0.48 Lemma 16: multiply(inverse(X), X) = double_divide(Y, inverse(Y)).
% 1.01/0.48 Proof:
% 1.01/0.48 multiply(inverse(X), X)
% 1.01/0.48 = { by lemma 14 R->L }
% 1.01/0.48 double_divide(Y, double_divide(inverse(inverse(multiply(inverse(X), X))), inverse(inverse(Y))))
% 1.01/0.48 = { by lemma 15 }
% 1.01/0.48 double_divide(Y, inverse(Y))
% 1.01/0.48
% 1.01/0.48 Lemma 17: double_divide(double_divide(inverse(X), inverse(inverse(Y))), inverse(X)) = Y.
% 1.01/0.48 Proof:
% 1.01/0.48 double_divide(double_divide(inverse(X), inverse(inverse(Y))), inverse(X))
% 1.01/0.48 = { by lemma 13 R->L }
% 1.01/0.48 double_divide(double_divide(multiply(multiply(Z, W), double_divide(multiply(Z, W), inverse(inverse(X)))), inverse(inverse(Y))), inverse(X))
% 1.01/0.48 = { by axiom 1 (multiply) }
% 1.01/0.48 double_divide(double_divide(inverse(double_divide(double_divide(multiply(Z, W), inverse(inverse(X))), multiply(Z, W))), inverse(inverse(Y))), inverse(X))
% 1.01/0.48 = { by lemma 12 R->L }
% 1.01/0.48 double_divide(multiply(inverse(Y), double_divide(double_divide(multiply(Z, W), inverse(inverse(X))), multiply(Z, W))), inverse(X))
% 1.01/0.48 = { by lemma 13 R->L }
% 1.01/0.48 double_divide(multiply(inverse(Y), double_divide(double_divide(multiply(Z, W), inverse(inverse(X))), multiply(Z, W))), multiply(multiply(Z, W), double_divide(multiply(Z, W), inverse(inverse(X)))))
% 1.01/0.48 = { by lemma 8 }
% 1.01/0.48 Y
% 1.01/0.48
% 1.01/0.48 Lemma 18: multiply(double_divide(X, inverse(X)), Y) = Y.
% 1.01/0.48 Proof:
% 1.01/0.48 multiply(double_divide(X, inverse(X)), Y)
% 1.01/0.48 = { by lemma 16 R->L }
% 1.01/0.48 multiply(multiply(inverse(Z), Z), Y)
% 1.01/0.48 = { by lemma 5 R->L }
% 1.01/0.48 double_divide(multiply(inverse(Z), Z), inverse(multiply(multiply(inverse(Z), Z), Y)))
% 1.01/0.48 = { by axiom 1 (multiply) }
% 1.01/0.48 double_divide(inverse(double_divide(Z, inverse(Z))), inverse(multiply(multiply(inverse(Z), Z), Y)))
% 1.01/0.48 = { by lemma 10 R->L }
% 1.01/0.48 double_divide(multiply(inverse(Y), multiply(inverse(double_divide(Z, inverse(Z))), Y)), inverse(multiply(multiply(inverse(Z), Z), Y)))
% 1.01/0.48 = { by axiom 1 (multiply) R->L }
% 1.01/0.48 double_divide(multiply(inverse(Y), multiply(multiply(inverse(Z), Z), Y)), inverse(multiply(multiply(inverse(Z), Z), Y)))
% 1.01/0.48 = { by lemma 12 }
% 1.01/0.48 double_divide(double_divide(inverse(multiply(multiply(inverse(Z), Z), Y)), inverse(inverse(Y))), inverse(multiply(multiply(inverse(Z), Z), Y)))
% 1.01/0.48 = { by lemma 17 }
% 1.01/0.48 Y
% 1.01/0.48
% 1.01/0.48 Lemma 19: double_divide(double_divide(X, Y), Y) = X.
% 1.01/0.48 Proof:
% 1.01/0.48 double_divide(double_divide(X, Y), Y)
% 1.01/0.48 = { by lemma 18 R->L }
% 1.01/0.48 double_divide(multiply(double_divide(Z, inverse(Z)), double_divide(X, Y)), Y)
% 1.01/0.48 = { by lemma 16 R->L }
% 1.01/0.48 double_divide(multiply(multiply(inverse(X), X), double_divide(X, Y)), Y)
% 1.01/0.48 = { by lemma 3 }
% 1.01/0.48 X
% 1.01/0.48
% 1.01/0.48 Lemma 20: inverse(inverse(X)) = X.
% 1.01/0.48 Proof:
% 1.01/0.48 inverse(inverse(X))
% 1.01/0.48 = { by lemma 19 R->L }
% 1.01/0.48 double_divide(double_divide(inverse(inverse(X)), inverse(inverse(X))), inverse(inverse(X)))
% 1.01/0.48 = { by lemma 17 }
% 1.01/0.49 X
% 1.01/0.49
% 1.01/0.49 Lemma 21: double_divide(X, double_divide(Y, X)) = Y.
% 1.01/0.49 Proof:
% 1.01/0.49 double_divide(X, double_divide(Y, X))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 double_divide(X, double_divide(Y, inverse(inverse(X))))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 double_divide(X, double_divide(Y, inverse(inverse(inverse(inverse(X))))))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 double_divide(X, double_divide(inverse(inverse(Y)), inverse(inverse(inverse(inverse(X))))))
% 1.01/0.49 = { by lemma 12 R->L }
% 1.01/0.49 double_divide(X, multiply(inverse(inverse(inverse(X))), inverse(Y)))
% 1.01/0.49 = { by axiom 1 (multiply) }
% 1.01/0.49 double_divide(X, inverse(double_divide(inverse(Y), inverse(inverse(inverse(X))))))
% 1.01/0.49 = { by lemma 12 R->L }
% 1.01/0.49 double_divide(X, inverse(multiply(inverse(inverse(X)), Y)))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 double_divide(inverse(inverse(X)), inverse(multiply(inverse(inverse(X)), Y)))
% 1.01/0.49 = { by lemma 11 }
% 1.01/0.49 Y
% 1.01/0.49
% 1.01/0.49 Lemma 22: double_divide(X, Y) = double_divide(Y, X).
% 1.01/0.49 Proof:
% 1.01/0.49 double_divide(X, Y)
% 1.01/0.49 = { by lemma 21 R->L }
% 1.01/0.49 double_divide(Y, double_divide(double_divide(X, Y), Y))
% 1.01/0.49 = { by lemma 19 }
% 1.01/0.49 double_divide(Y, X)
% 1.01/0.49
% 1.01/0.49 Lemma 23: multiply(multiply(X, Y), Z) = double_divide(inverse(Z), inverse(multiply(X, Y))).
% 1.01/0.49 Proof:
% 1.01/0.49 multiply(multiply(X, Y), Z)
% 1.01/0.49 = { by axiom 1 (multiply) }
% 1.01/0.49 multiply(inverse(double_divide(Y, X)), Z)
% 1.01/0.49 = { by lemma 12 }
% 1.01/0.49 double_divide(inverse(Z), inverse(inverse(double_divide(Y, X))))
% 1.01/0.49 = { by axiom 1 (multiply) R->L }
% 1.01/0.49 double_divide(inverse(Z), inverse(multiply(X, Y)))
% 1.01/0.49
% 1.01/0.49 Lemma 24: multiply(X, Y) = double_divide(inverse(Y), inverse(X)).
% 1.01/0.49 Proof:
% 1.01/0.49 multiply(X, Y)
% 1.01/0.49 = { by lemma 18 R->L }
% 1.01/0.49 multiply(multiply(double_divide(Z, inverse(Z)), X), Y)
% 1.01/0.49 = { by lemma 23 }
% 1.01/0.49 double_divide(inverse(Y), inverse(multiply(double_divide(Z, inverse(Z)), X)))
% 1.01/0.49 = { by lemma 18 }
% 1.01/0.49 double_divide(inverse(Y), inverse(X))
% 1.01/0.49
% 1.01/0.49 Lemma 25: inverse(double_divide(X, Y)) = double_divide(inverse(X), inverse(Y)).
% 1.01/0.49 Proof:
% 1.01/0.49 inverse(double_divide(X, Y))
% 1.01/0.49 = { by lemma 22 R->L }
% 1.01/0.49 inverse(double_divide(Y, X))
% 1.01/0.49 = { by axiom 1 (multiply) R->L }
% 1.01/0.49 multiply(X, Y)
% 1.01/0.49 = { by lemma 24 }
% 1.01/0.49 double_divide(inverse(Y), inverse(X))
% 1.01/0.49 = { by lemma 22 }
% 1.01/0.49 double_divide(inverse(X), inverse(Y))
% 1.01/0.49
% 1.01/0.49 Lemma 26: multiply(inverse(X), X) = double_divide(inverse(Y), inverse(inverse(Y))).
% 1.01/0.49 Proof:
% 1.01/0.49 multiply(inverse(X), X)
% 1.01/0.49 = { by lemma 11 R->L }
% 1.01/0.49 double_divide(inverse(Y), inverse(multiply(inverse(Y), multiply(inverse(X), X))))
% 1.01/0.49 = { by lemma 6 }
% 1.01/0.49 double_divide(inverse(Y), inverse(inverse(Y)))
% 1.01/0.49
% 1.01/0.49 Lemma 27: double_divide(double_divide(X, inverse(Y)), double_divide(Y, inverse(Z))) = double_divide(Z, inverse(X)).
% 1.01/0.49 Proof:
% 1.01/0.49 double_divide(double_divide(X, inverse(Y)), double_divide(Y, inverse(Z)))
% 1.01/0.49 = { by lemma 22 R->L }
% 1.01/0.49 double_divide(double_divide(Y, inverse(Z)), double_divide(X, inverse(Y)))
% 1.01/0.49 = { by lemma 22 R->L }
% 1.01/0.49 double_divide(double_divide(Y, inverse(Z)), double_divide(inverse(Y), X))
% 1.01/0.49 = { by lemma 22 R->L }
% 1.01/0.49 double_divide(double_divide(inverse(Y), X), double_divide(Y, inverse(Z)))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 double_divide(double_divide(inverse(Y), X), double_divide(Y, inverse(inverse(inverse(Z)))))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 double_divide(double_divide(inverse(Y), X), double_divide(inverse(inverse(Y)), inverse(inverse(inverse(Z)))))
% 1.01/0.49 = { by lemma 25 R->L }
% 1.01/0.49 double_divide(double_divide(inverse(Y), X), inverse(double_divide(inverse(Y), inverse(inverse(Z)))))
% 1.01/0.49 = { by lemma 12 R->L }
% 1.01/0.49 double_divide(double_divide(inverse(Y), X), inverse(multiply(inverse(Z), Y)))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 double_divide(double_divide(inverse(Y), inverse(inverse(X))), inverse(multiply(inverse(Z), Y)))
% 1.01/0.49 = { by lemma 25 R->L }
% 1.01/0.49 double_divide(inverse(double_divide(Y, inverse(X))), inverse(multiply(inverse(Z), Y)))
% 1.01/0.49 = { by lemma 23 R->L }
% 1.01/0.49 multiply(multiply(inverse(Z), Y), double_divide(Y, inverse(X)))
% 1.01/0.49 = { by lemma 11 R->L }
% 1.01/0.49 double_divide(inverse(X), inverse(multiply(inverse(X), multiply(multiply(inverse(Z), Y), double_divide(Y, inverse(X))))))
% 1.01/0.49 = { by lemma 4 }
% 1.01/0.49 double_divide(inverse(X), inverse(inverse(Z)))
% 1.01/0.49 = { by lemma 20 }
% 1.01/0.49 double_divide(inverse(X), Z)
% 1.01/0.49 = { by lemma 22 }
% 1.01/0.49 double_divide(Z, inverse(X))
% 1.01/0.49
% 1.01/0.49 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)).
% 1.01/0.49 Proof:
% 1.01/0.49 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 1.01/0.49 = { by lemma 26 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 1.01/0.49 = { by lemma 26 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), multiply(double_divide(inverse(Y), inverse(inverse(Y))), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 1.01/0.49 = { by lemma 18 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 1.01/0.49 = { by lemma 23 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), inverse(multiply(a3, b3))), multiply(a4, b4))
% 1.01/0.49 = { by lemma 24 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), inverse(double_divide(inverse(b3), inverse(a3)))), multiply(a4, b4))
% 1.01/0.49 = { by axiom 1 (multiply) R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), multiply(inverse(a3), inverse(b3))), multiply(a4, b4))
% 1.01/0.49 = { by lemma 24 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), double_divide(inverse(inverse(b3)), inverse(inverse(a3)))), multiply(a4, b4))
% 1.01/0.49 = { by lemma 24 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), double_divide(inverse(inverse(b3)), inverse(inverse(a3)))), double_divide(inverse(b4), inverse(a4)))
% 1.01/0.49 = { by lemma 20 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), double_divide(b3, inverse(inverse(a3)))), double_divide(inverse(b4), inverse(a4)))
% 1.01/0.49 = { by lemma 20 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), double_divide(b3, a3)), double_divide(inverse(b4), inverse(a4)))
% 1.01/0.49 = { by lemma 22 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), double_divide(a3, b3)), double_divide(inverse(b4), inverse(a4)))
% 1.01/0.49 = { by lemma 22 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), double_divide(a3, b3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), double_divide(a3, inverse(inverse(b3)))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), double_divide(a3, inverse(inverse(inverse(inverse(b3)))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), double_divide(inverse(inverse(a3)), inverse(inverse(inverse(inverse(b3)))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 25 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), inverse(double_divide(inverse(a3), inverse(inverse(inverse(b3)))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 12 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(c3), inverse(multiply(inverse(inverse(b3)), a3))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 27 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(multiply(inverse(inverse(b3)), a3), inverse(a3)), double_divide(a3, inverse(inverse(c3)))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 9 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(b3), double_divide(a3, inverse(inverse(c3)))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 20 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(b3), double_divide(a3, c3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 22 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(b3), double_divide(c3, a3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 22 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(c3, a3), inverse(b3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(c3, inverse(inverse(a3))), inverse(b3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 20 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), inverse(b3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 27 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, inverse(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(a3)))), double_divide(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(a3)), inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 15 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, inverse(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(a3)))), double_divide(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), double_divide(inverse(inverse(multiply(inverse(Z), Z))), inverse(inverse(a3)))), inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 12 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, inverse(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(a3)))), double_divide(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), multiply(inverse(a3), inverse(multiply(inverse(Z), Z)))), inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by axiom 1 (multiply) }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, inverse(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(a3)))), double_divide(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(double_divide(inverse(multiply(inverse(Z), Z)), inverse(a3)))), inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 24 R->L }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, inverse(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(a3)))), double_divide(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(multiply(a3, multiply(inverse(Z), Z)))), inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by axiom 1 (multiply) }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, inverse(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(a3)))), double_divide(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(inverse(double_divide(multiply(inverse(Z), Z), a3)))), inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.49 = { by lemma 17 }
% 1.01/0.49 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, inverse(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(a3)))), double_divide(multiply(inverse(Z), Z), a3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 16 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, inverse(double_divide(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3)))), inverse(a3)))), double_divide(double_divide(W, inverse(W)), a3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 25 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(inverse(inverse(double_divide(inverse(inverse(c3)), inverse(inverse(a3))))), inverse(inverse(a3)))), double_divide(double_divide(W, inverse(W)), a3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 20 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), inverse(inverse(a3)))), double_divide(double_divide(W, inverse(W)), a3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 20 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), a3)), double_divide(double_divide(W, inverse(W)), a3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 16 R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), a3)), double_divide(multiply(inverse(V), V), a3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 14 R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), a3)), double_divide(U, double_divide(inverse(inverse(double_divide(multiply(inverse(V), V), a3))), inverse(inverse(U))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by axiom 1 (multiply) R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), a3)), double_divide(U, double_divide(inverse(multiply(a3, multiply(inverse(V), V))), inverse(inverse(U))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 24 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), a3)), double_divide(U, double_divide(inverse(double_divide(inverse(multiply(inverse(V), V)), inverse(a3))), inverse(inverse(U))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by axiom 1 (multiply) R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), a3)), double_divide(U, double_divide(multiply(inverse(a3), inverse(multiply(inverse(V), V))), inverse(inverse(U))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 12 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), a3)), double_divide(U, double_divide(double_divide(inverse(inverse(multiply(inverse(V), V))), inverse(inverse(a3))), inverse(inverse(U))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 15 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), a3)), double_divide(U, double_divide(inverse(a3), inverse(inverse(U))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 20 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), a3)), double_divide(U, double_divide(inverse(a3), U))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 21 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), a3)), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 22 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(a3), double_divide(b3, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(a3))), a3))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 22 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(a3), double_divide(b3, double_divide(a3, double_divide(inverse(inverse(c3)), inverse(inverse(a3)))))), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 14 }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(a3), double_divide(b3, c3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 22 R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(a3), double_divide(c3, b3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 22 R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(c3, b3), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 20 R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(c3, inverse(inverse(b3))), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 20 R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(b3))), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 1.01/0.50 = { by lemma 24 R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(double_divide(inverse(inverse(c3)), inverse(inverse(b3))), inverse(a3)), multiply(b4, a4))
% 1.01/0.50 = { by lemma 24 R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(multiply(inverse(b3), inverse(c3)), inverse(a3)), multiply(b4, a4))
% 1.01/0.50 = { by axiom 1 (multiply) }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(double_divide(inverse(c3), inverse(b3))), inverse(a3)), multiply(b4, a4))
% 1.01/0.50 = { by lemma 24 R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, multiply(a3, double_divide(inverse(c3), inverse(b3))), multiply(b4, a4))
% 1.01/0.50 = { by lemma 24 R->L }
% 1.01/0.50 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 1.01/0.50 = { by lemma 26 R->L }
% 1.01/0.50 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 1.01/0.50 % SZS output end Proof
% 1.01/0.50
% 1.01/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------