%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP110-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 10:09:17 AM UTC 2026
% Result : Unsatisfiable 0.46s 0.52s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP110-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 09:22:21 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.52 Command-line arguments: --no-flatten-goal
% 0.46/0.52
% 0.46/0.52 % SZS status Unsatisfiable
% 0.46/0.52
% 0.46/0.56 % SZS output start Proof
% 0.46/0.56 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.46/0.56 Axiom 2 (single_axiom): inverse(double_divide(inverse(double_divide(inverse(double_divide(X, Y)), Z)), double_divide(X, Z))) = Y.
% 0.46/0.56
% 0.46/0.56 Lemma 3: multiply(double_divide(X, Y), multiply(Y, multiply(Z, X))) = Z.
% 0.46/0.56 Proof:
% 0.46/0.56 multiply(double_divide(X, Y), multiply(Y, multiply(Z, X)))
% 0.46/0.56 = { by axiom 1 (multiply) }
% 0.46/0.56 multiply(double_divide(X, Y), multiply(Y, inverse(double_divide(X, Z))))
% 0.46/0.56 = { by axiom 1 (multiply) }
% 0.46/0.56 multiply(double_divide(X, Y), inverse(double_divide(inverse(double_divide(X, Z)), Y)))
% 0.46/0.56 = { by axiom 1 (multiply) }
% 0.46/0.56 inverse(double_divide(inverse(double_divide(inverse(double_divide(X, Z)), Y)), double_divide(X, Y)))
% 0.46/0.57 = { by axiom 2 (single_axiom) }
% 0.46/0.57 Z
% 0.46/0.57
% 0.46/0.57 Lemma 4: multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X) = Z.
% 0.46/0.57 Proof:
% 0.46/0.57 multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X)
% 0.46/0.57 = { by lemma 3 R->L }
% 0.46/0.57 multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), multiply(double_divide(Y, Z), multiply(Z, multiply(X, Y))))
% 0.46/0.57 = { by lemma 3 }
% 0.46/0.57 Z
% 0.46/0.57
% 0.46/0.57 Lemma 5: multiply(double_divide(X, Y), multiply(Y, Z)) = double_divide(multiply(X, W), double_divide(W, Z)).
% 0.46/0.57 Proof:
% 0.46/0.57 multiply(double_divide(X, Y), multiply(Y, Z))
% 0.46/0.57 = { by lemma 4 R->L }
% 0.46/0.57 multiply(double_divide(X, Y), multiply(Y, multiply(double_divide(multiply(X, W), double_divide(W, Z)), X)))
% 0.46/0.57 = { by lemma 3 }
% 0.46/0.57 double_divide(multiply(X, W), double_divide(W, Z))
% 0.46/0.57
% 0.46/0.57 Lemma 6: double_divide(multiply(multiply(X, multiply(Y, Z)), W), double_divide(W, Y)) = double_divide(Z, X).
% 0.46/0.57 Proof:
% 0.46/0.57 double_divide(multiply(multiply(X, multiply(Y, Z)), W), double_divide(W, Y))
% 0.46/0.57 = { by lemma 5 R->L }
% 0.46/0.57 multiply(double_divide(multiply(X, multiply(Y, Z)), V), multiply(V, Y))
% 0.46/0.57 = { by lemma 3 R->L }
% 0.46/0.57 multiply(double_divide(multiply(X, multiply(Y, Z)), V), multiply(V, multiply(double_divide(Z, X), multiply(X, multiply(Y, Z)))))
% 0.46/0.57 = { by lemma 3 }
% 0.46/0.57 double_divide(Z, X)
% 0.46/0.57
% 0.46/0.57 Lemma 7: double_divide(multiply(X, W), double_divide(W, Z)) = double_divide(multiply(X, Y), double_divide(Y, Z)).
% 0.46/0.57 Proof:
% 0.46/0.57 double_divide(multiply(X, W), double_divide(W, Z))
% 0.46/0.57 = { by lemma 3 R->L }
% 0.46/0.57 multiply(double_divide(X, V), multiply(V, multiply(double_divide(multiply(X, W), double_divide(W, Z)), X)))
% 0.46/0.57 = { by lemma 4 }
% 0.46/0.57 multiply(double_divide(X, V), multiply(V, Z))
% 0.46/0.57 = { by lemma 4 R->L }
% 0.46/0.57 multiply(double_divide(X, V), multiply(V, multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X)))
% 0.46/0.57 = { by lemma 3 }
% 0.46/0.57 double_divide(multiply(X, Y), double_divide(Y, Z))
% 0.46/0.57
% 0.46/0.57 Lemma 8: multiply(double_divide(W, Y), multiply(Z, W)) = multiply(double_divide(X, Y), multiply(Z, X)).
% 0.46/0.57 Proof:
% 0.46/0.57 multiply(double_divide(W, Y), multiply(Z, W))
% 0.46/0.57 = { by axiom 1 (multiply) }
% 0.46/0.57 inverse(double_divide(multiply(Z, W), double_divide(W, Y)))
% 0.46/0.57 = { by lemma 7 }
% 0.46/0.57 inverse(double_divide(multiply(Z, X), double_divide(X, Y)))
% 0.46/0.57 = { by axiom 1 (multiply) R->L }
% 0.46/0.57 multiply(double_divide(X, Y), multiply(Z, X))
% 0.46/0.57
% 0.46/0.57 Lemma 9: double_divide(Z, double_divide(Z, Y)) = double_divide(X, double_divide(X, Y)).
% 0.46/0.57 Proof:
% 0.46/0.57 double_divide(Z, double_divide(Z, Y))
% 0.46/0.57 = { by lemma 6 R->L }
% 0.46/0.57 double_divide(multiply(multiply(double_divide(Z, Y), multiply(W, Z)), V), double_divide(V, W))
% 0.46/0.57 = { by lemma 8 }
% 0.46/0.57 double_divide(multiply(multiply(double_divide(X, Y), multiply(W, X)), V), double_divide(V, W))
% 0.46/0.57 = { by lemma 6 }
% 0.46/0.57 double_divide(X, double_divide(X, Y))
% 0.46/0.57
% 0.46/0.57 Lemma 10: double_divide(W, double_divide(W, double_divide(X, Z))) = double_divide(X, double_divide(Y, double_divide(Y, Z))).
% 0.46/0.57 Proof:
% 0.46/0.57 double_divide(W, double_divide(W, double_divide(X, Z)))
% 0.46/0.57 = { by lemma 9 }
% 0.46/0.57 double_divide(X, double_divide(X, double_divide(X, Z)))
% 0.46/0.57 = { by lemma 9 R->L }
% 0.46/0.57 double_divide(X, double_divide(Y, double_divide(Y, Z)))
% 0.46/0.57
% 0.46/0.57 Lemma 11: multiply(double_divide(multiply(X, Y), double_divide(Y, X)), Z) = Z.
% 0.46/0.57 Proof:
% 0.46/0.57 multiply(double_divide(multiply(X, Y), double_divide(Y, X)), Z)
% 0.46/0.57 = { by lemma 5 R->L }
% 0.46/0.57 multiply(multiply(double_divide(X, W), multiply(W, X)), Z)
% 0.46/0.57 = { by lemma 8 }
% 0.46/0.57 multiply(multiply(double_divide(Z, W), multiply(W, Z)), Z)
% 0.46/0.57 = { by lemma 5 }
% 0.46/0.57 multiply(double_divide(multiply(Z, V), double_divide(V, Z)), Z)
% 0.46/0.57 = { by lemma 4 }
% 0.46/0.57 Z
% 0.46/0.57
% 0.46/0.57 Lemma 12: double_divide(X, double_divide(X, double_divide(Y, Z))) = double_divide(Y, Z).
% 0.46/0.57 Proof:
% 0.46/0.57 double_divide(X, double_divide(X, double_divide(Y, Z)))
% 0.46/0.57 = { by lemma 6 R->L }
% 0.46/0.57 double_divide(X, double_divide(X, double_divide(multiply(multiply(Z, multiply(W, Y)), Y), double_divide(Y, W))))
% 0.46/0.57 = { by lemma 10 }
% 0.46/0.57 double_divide(multiply(multiply(Z, multiply(W, Y)), Y), double_divide(Y, double_divide(Y, double_divide(Y, W))))
% 0.46/0.57 = { by lemma 11 R->L }
% 0.46/0.57 double_divide(multiply(multiply(Z, multiply(double_divide(multiply(W, Y), double_divide(Y, W)), multiply(W, Y))), Y), double_divide(Y, double_divide(Y, double_divide(Y, W))))
% 0.46/0.57 = { by axiom 1 (multiply) }
% 0.46/0.57 double_divide(multiply(multiply(Z, inverse(double_divide(multiply(W, Y), double_divide(multiply(W, Y), double_divide(Y, W))))), Y), double_divide(Y, double_divide(Y, double_divide(Y, W))))
% 0.46/0.57 = { by lemma 9 R->L }
% 0.46/0.57 double_divide(multiply(multiply(Z, inverse(double_divide(Y, double_divide(Y, double_divide(Y, W))))), Y), double_divide(Y, double_divide(Y, double_divide(Y, W))))
% 0.46/0.57 = { by axiom 1 (multiply) R->L }
% 0.46/0.57 double_divide(multiply(multiply(Z, multiply(double_divide(Y, double_divide(Y, W)), Y)), Y), double_divide(Y, double_divide(Y, double_divide(Y, W))))
% 0.46/0.57 = { by lemma 6 }
% 0.46/0.57 double_divide(Y, Z)
% 0.46/0.57
% 0.46/0.57 Lemma 13: multiply(double_divide(multiply(X, Y), double_divide(Z, W)), X) = double_divide(Y, double_divide(Z, W)).
% 0.46/0.58 Proof:
% 0.46/0.58 multiply(double_divide(multiply(X, Y), double_divide(Z, W)), X)
% 0.46/0.58 = { by lemma 12 R->L }
% 0.46/0.58 multiply(double_divide(multiply(X, Y), double_divide(Y, double_divide(Y, double_divide(Z, W)))), X)
% 0.46/0.58 = { by lemma 4 }
% 0.46/0.58 double_divide(Y, double_divide(Z, W))
% 0.46/0.58
% 0.46/0.58 Lemma 14: double_divide(X, double_divide(X, Y)) = Y.
% 0.46/0.58 Proof:
% 0.46/0.58 double_divide(X, double_divide(X, Y))
% 0.46/0.58 = { by lemma 13 R->L }
% 0.46/0.58 multiply(double_divide(multiply(Z, X), double_divide(X, Y)), Z)
% 0.46/0.58 = { by lemma 4 }
% 0.46/0.58 Y
% 0.46/0.58
% 0.46/0.58 Lemma 15: multiply(double_divide(X, Y), X) = inverse(Y).
% 0.46/0.58 Proof:
% 0.46/0.58 multiply(double_divide(X, Y), X)
% 0.46/0.58 = { by axiom 1 (multiply) }
% 0.46/0.58 inverse(double_divide(X, double_divide(X, Y)))
% 0.46/0.58 = { by lemma 14 }
% 0.46/0.58 inverse(Y)
% 0.46/0.58
% 0.46/0.58 Lemma 16: double_divide(multiply(X, Y), Z) = double_divide(Y, multiply(Z, X)).
% 0.46/0.58 Proof:
% 0.46/0.58 double_divide(multiply(X, Y), Z)
% 0.46/0.58 = { by lemma 11 R->L }
% 0.46/0.58 double_divide(multiply(double_divide(multiply(W, V), double_divide(V, W)), multiply(X, Y)), Z)
% 0.46/0.58 = { by lemma 3 R->L }
% 0.46/0.58 multiply(double_divide(double_divide(multiply(W, V), double_divide(V, W)), U), multiply(U, multiply(double_divide(multiply(double_divide(multiply(W, V), double_divide(V, W)), multiply(X, Y)), Z), double_divide(multiply(W, V), double_divide(V, W)))))
% 0.46/0.58 = { by lemma 3 R->L }
% 0.46/0.58 multiply(double_divide(double_divide(multiply(W, V), double_divide(V, W)), U), multiply(U, multiply(double_divide(multiply(double_divide(multiply(W, V), double_divide(V, W)), multiply(X, Y)), multiply(double_divide(X, T), multiply(T, multiply(Z, X)))), double_divide(multiply(W, V), double_divide(V, W)))))
% 0.46/0.58 = { by lemma 5 }
% 0.46/0.58 multiply(double_divide(double_divide(multiply(W, V), double_divide(V, W)), U), multiply(U, multiply(double_divide(multiply(double_divide(multiply(W, V), double_divide(V, W)), multiply(X, Y)), double_divide(multiply(X, Y), double_divide(Y, multiply(Z, X)))), double_divide(multiply(W, V), double_divide(V, W)))))
% 0.46/0.58 = { by lemma 4 }
% 0.46/0.58 multiply(double_divide(double_divide(multiply(W, V), double_divide(V, W)), U), multiply(U, double_divide(Y, multiply(Z, X))))
% 0.46/0.58 = { by lemma 5 }
% 0.46/0.58 double_divide(multiply(double_divide(multiply(W, V), double_divide(V, W)), Y), double_divide(Y, double_divide(Y, multiply(Z, X))))
% 0.46/0.58 = { by lemma 10 R->L }
% 0.46/0.58 double_divide(S, double_divide(S, double_divide(multiply(double_divide(multiply(W, V), double_divide(V, W)), Y), multiply(Z, X))))
% 0.46/0.58 = { by lemma 14 }
% 0.46/0.58 double_divide(multiply(double_divide(multiply(W, V), double_divide(V, W)), Y), multiply(Z, X))
% 0.46/0.58 = { by lemma 11 }
% 0.46/0.58 double_divide(Y, multiply(Z, X))
% 0.46/0.58
% 0.46/0.58 Lemma 17: multiply(double_divide(X, inverse(X)), Y) = Y.
% 0.46/0.58 Proof:
% 0.46/0.58 multiply(double_divide(X, inverse(X)), Y)
% 0.46/0.58 = { by lemma 15 R->L }
% 0.46/0.58 multiply(double_divide(X, multiply(double_divide(X, X), X)), Y)
% 0.46/0.58 = { by lemma 16 R->L }
% 0.46/0.58 multiply(double_divide(multiply(X, X), double_divide(X, X)), Y)
% 0.46/0.58 = { by lemma 11 }
% 0.46/0.58 Y
% 0.46/0.58
% 0.46/0.58 Lemma 18: multiply(inverse(X), Y) = double_divide(X, inverse(Y)).
% 0.46/0.58 Proof:
% 0.46/0.58 multiply(inverse(X), Y)
% 0.46/0.58 = { by lemma 17 R->L }
% 0.46/0.58 multiply(double_divide(X, inverse(X)), multiply(inverse(X), Y))
% 0.46/0.58 = { by lemma 5 }
% 0.46/0.58 double_divide(multiply(X, X), double_divide(X, Y))
% 0.46/0.58 = { by lemma 16 }
% 0.46/0.58 double_divide(X, multiply(double_divide(X, Y), X))
% 0.46/0.58 = { by lemma 15 }
% 0.46/0.58 double_divide(X, inverse(Y))
% 0.46/0.58
% 0.46/0.58 Lemma 19: inverse(multiply(X, Y)) = double_divide(Y, X).
% 0.46/0.58 Proof:
% 0.46/0.58 inverse(multiply(X, Y))
% 0.46/0.58 = { by lemma 14 R->L }
% 0.46/0.58 double_divide(Y, double_divide(Y, inverse(multiply(X, Y))))
% 0.46/0.58 = { by lemma 18 R->L }
% 0.46/0.58 double_divide(Y, multiply(inverse(Y), multiply(X, Y)))
% 0.46/0.58 = { by lemma 17 R->L }
% 0.46/0.58 double_divide(Y, multiply(double_divide(Y, inverse(Y)), multiply(inverse(Y), multiply(X, Y))))
% 0.46/0.58 = { by lemma 3 }
% 0.46/0.58 double_divide(Y, X)
% 0.46/0.58
% 0.46/0.58 Lemma 20: multiply(X, double_divide(Y, inverse(Y))) = X.
% 0.46/0.58 Proof:
% 0.46/0.58 multiply(X, double_divide(Y, inverse(Y)))
% 0.46/0.58 = { by lemma 14 R->L }
% 0.46/0.58 multiply(double_divide(Z, double_divide(Z, X)), double_divide(Y, inverse(Y)))
% 0.46/0.58 = { by lemma 17 R->L }
% 0.46/0.58 multiply(double_divide(multiply(double_divide(Y, inverse(Y)), Z), double_divide(Z, X)), double_divide(Y, inverse(Y)))
% 0.46/0.58 = { by lemma 4 }
% 0.46/0.58 X
% 0.46/0.58
% 0.46/0.58 Lemma 21: inverse(inverse(X)) = X.
% 0.46/0.58 Proof:
% 0.46/0.58 inverse(inverse(X))
% 0.46/0.58 = { by lemma 15 R->L }
% 0.46/0.58 inverse(multiply(double_divide(Y, X), Y))
% 0.46/0.58 = { by lemma 19 }
% 0.46/0.58 double_divide(Y, double_divide(Y, X))
% 0.46/0.58 = { by lemma 14 }
% 0.46/0.58 X
% 0.46/0.58
% 0.46/0.58 Lemma 22: double_divide(X, double_divide(Y, X)) = Y.
% 0.46/0.58 Proof:
% 0.46/0.58 double_divide(X, double_divide(Y, X))
% 0.46/0.58 = { by lemma 19 R->L }
% 0.46/0.58 inverse(multiply(double_divide(Y, X), X))
% 0.46/0.58 = { by lemma 20 R->L }
% 0.46/0.58 inverse(multiply(double_divide(Y, X), multiply(X, double_divide(Z, inverse(Z)))))
% 0.46/0.58 = { by lemma 5 }
% 0.46/0.58 inverse(double_divide(multiply(Y, Z), double_divide(Z, double_divide(Z, inverse(Z)))))
% 0.46/0.58 = { by lemma 16 }
% 0.46/0.58 inverse(double_divide(Z, multiply(double_divide(Z, double_divide(Z, inverse(Z))), Y)))
% 0.46/0.58 = { by lemma 14 }
% 0.46/0.58 inverse(double_divide(Z, multiply(inverse(Z), Y)))
% 0.46/0.58 = { by lemma 18 }
% 0.46/0.58 inverse(double_divide(Z, double_divide(Z, inverse(Y))))
% 0.46/0.58 = { by lemma 14 }
% 0.46/0.58 inverse(inverse(Y))
% 0.46/0.58 = { by lemma 21 }
% 0.46/0.58 Y
% 0.46/0.58
% 0.46/0.58 Lemma 23: double_divide(X, Y) = double_divide(Y, X).
% 0.46/0.58 Proof:
% 0.46/0.58 double_divide(X, Y)
% 0.46/0.58 = { by lemma 14 R->L }
% 0.46/0.58 double_divide(Y, double_divide(Y, double_divide(X, Y)))
% 0.46/0.58 = { by lemma 22 }
% 0.46/0.58 double_divide(Y, X)
% 0.46/0.58
% 0.46/0.58 Lemma 24: multiply(Y, X) = multiply(X, Y).
% 0.46/0.58 Proof:
% 0.46/0.58 multiply(Y, X)
% 0.46/0.58 = { by lemma 22 R->L }
% 0.46/0.58 multiply(double_divide(multiply(X, Y), double_divide(Y, multiply(X, Y))), X)
% 0.46/0.58 = { by lemma 4 }
% 0.46/0.58 multiply(X, Y)
% 0.46/0.58
% 0.46/0.58 Lemma 25: double_divide(X, double_divide(Y, inverse(Y))) = inverse(X).
% 0.46/0.58 Proof:
% 0.46/0.58 double_divide(X, double_divide(Y, inverse(Y)))
% 0.46/0.58 = { by lemma 6 R->L }
% 0.46/0.58 double_divide(multiply(multiply(double_divide(Y, inverse(Y)), multiply(Z, X)), W), double_divide(W, Z))
% 0.46/0.58 = { by lemma 17 }
% 0.46/0.58 double_divide(multiply(multiply(Z, X), W), double_divide(W, Z))
% 0.46/0.58 = { by lemma 16 }
% 0.46/0.58 double_divide(W, multiply(double_divide(W, Z), multiply(Z, X)))
% 0.46/0.58 = { by lemma 5 }
% 0.46/0.58 double_divide(W, double_divide(multiply(W, W), double_divide(W, X)))
% 0.46/0.58 = { by lemma 16 }
% 0.46/0.58 double_divide(W, double_divide(W, multiply(double_divide(W, X), W)))
% 0.46/0.58 = { by lemma 14 }
% 0.46/0.58 multiply(double_divide(W, X), W)
% 0.46/0.58 = { by lemma 15 }
% 0.46/0.58 inverse(X)
% 0.46/0.58
% 0.46/0.58 Lemma 26: multiply(X, Y) = double_divide(inverse(X), inverse(Y)).
% 0.46/0.58 Proof:
% 0.46/0.58 multiply(X, Y)
% 0.46/0.58 = { by lemma 14 R->L }
% 0.46/0.58 double_divide(inverse(X), double_divide(inverse(X), multiply(X, Y)))
% 0.46/0.58 = { by lemma 24 }
% 0.46/0.58 double_divide(inverse(X), double_divide(inverse(X), multiply(Y, X)))
% 0.46/0.58 = { by lemma 23 R->L }
% 0.46/0.58 double_divide(inverse(X), double_divide(multiply(Y, X), inverse(X)))
% 0.46/0.58 = { by lemma 25 R->L }
% 0.46/0.58 double_divide(inverse(X), double_divide(multiply(Y, X), double_divide(X, double_divide(Z, inverse(Z)))))
% 0.46/0.58 = { by lemma 7 R->L }
% 0.46/0.58 double_divide(inverse(X), double_divide(multiply(Y, Z), double_divide(Z, double_divide(Z, inverse(Z)))))
% 0.46/0.58 = { by lemma 16 }
% 0.46/0.58 double_divide(inverse(X), double_divide(Z, multiply(double_divide(Z, double_divide(Z, inverse(Z))), Y)))
% 0.46/0.58 = { by lemma 14 }
% 0.46/0.58 double_divide(inverse(X), double_divide(Z, multiply(inverse(Z), Y)))
% 0.46/0.58 = { by lemma 18 }
% 0.46/0.58 double_divide(inverse(X), double_divide(Z, double_divide(Z, inverse(Y))))
% 0.46/0.58 = { by lemma 14 }
% 0.46/0.58 double_divide(inverse(X), inverse(Y))
% 0.46/0.58
% 0.46/0.58 Lemma 27: multiply(X, inverse(X)) = double_divide(Y, inverse(Y)).
% 0.46/0.58 Proof:
% 0.46/0.58 multiply(X, inverse(X))
% 0.46/0.58 = { by lemma 24 }
% 0.46/0.58 multiply(inverse(X), X)
% 0.46/0.58 = { by lemma 14 R->L }
% 0.46/0.58 multiply(double_divide(Z, double_divide(Z, inverse(X))), X)
% 0.46/0.58 = { by lemma 18 R->L }
% 0.46/0.58 multiply(double_divide(Z, multiply(inverse(Z), X)), X)
% 0.46/0.58 = { by lemma 16 R->L }
% 0.46/0.58 multiply(double_divide(multiply(X, Z), inverse(Z)), X)
% 0.46/0.58 = { by lemma 25 R->L }
% 0.46/0.58 multiply(double_divide(multiply(X, Z), double_divide(Z, double_divide(Y, inverse(Y)))), X)
% 0.46/0.58 = { by lemma 13 }
% 0.46/0.58 double_divide(Z, double_divide(Z, double_divide(Y, inverse(Y))))
% 0.46/0.58 = { by lemma 12 }
% 0.46/0.58 double_divide(Y, inverse(Y))
% 0.46/0.58
% 0.46/0.58 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)).
% 0.46/0.58 Proof:
% 0.46/0.58 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.46/0.58 = { by lemma 24 R->L }
% 0.46/0.58 tuple(multiply(a1, inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.46/0.58 = { by lemma 24 R->L }
% 0.46/0.58 tuple(multiply(a1, inverse(a1)), multiply(a2, multiply(inverse(b2), b2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.46/0.58 = { by lemma 24 R->L }
% 0.46/0.58 tuple(multiply(a1, inverse(a1)), multiply(a2, multiply(b2, inverse(b2))), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.46/0.58 = { by lemma 24 R->L }
% 0.46/0.58 tuple(multiply(a1, inverse(a1)), multiply(a2, multiply(b2, inverse(b2))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.46/0.58 = { by lemma 27 }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), multiply(a2, multiply(b2, inverse(b2))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.46/0.58 = { by lemma 27 }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), multiply(a2, double_divide(Y, inverse(Y))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.46/0.58 = { by lemma 20 }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.46/0.58 = { by lemma 26 }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), inverse(multiply(a3, b3))), multiply(a4, b4))
% 0.46/0.58 = { by lemma 19 }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), double_divide(b3, a3)), multiply(a4, b4))
% 0.46/0.58 = { by lemma 23 }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), double_divide(a3, b3)), multiply(a4, b4))
% 0.46/0.58 = { by lemma 26 }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), double_divide(a3, b3)), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.58 = { by lemma 23 R->L }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), double_divide(b3, a3)), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.58 = { by lemma 19 R->L }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(c3), inverse(multiply(a3, b3))), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.58 = { by lemma 26 R->L }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, multiply(c3, multiply(a3, b3)), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.58 = { by lemma 3 R->L }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, multiply(double_divide(double_divide(b3, c3), double_divide(Z, inverse(Z))), multiply(double_divide(Z, inverse(Z)), multiply(multiply(c3, multiply(a3, b3)), double_divide(b3, c3)))), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.58 = { by lemma 25 }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, multiply(inverse(double_divide(b3, c3)), multiply(double_divide(Z, inverse(Z)), multiply(multiply(c3, multiply(a3, b3)), double_divide(b3, c3)))), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.58 = { by lemma 17 }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, multiply(inverse(double_divide(b3, c3)), multiply(multiply(c3, multiply(a3, b3)), double_divide(b3, c3))), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.58 = { by lemma 24 R->L }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, multiply(inverse(double_divide(b3, c3)), multiply(double_divide(b3, c3), multiply(c3, multiply(a3, b3)))), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.58 = { by lemma 3 }
% 0.46/0.58 tuple(double_divide(X, inverse(X)), a2, multiply(inverse(double_divide(b3, c3)), a3), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.59 = { by lemma 26 }
% 0.46/0.59 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(inverse(double_divide(b3, c3))), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.59 = { by lemma 21 }
% 0.46/0.59 tuple(double_divide(X, inverse(X)), a2, double_divide(double_divide(b3, c3), inverse(a3)), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.59 = { by lemma 23 }
% 0.46/0.59 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), double_divide(b3, c3)), double_divide(inverse(a4), inverse(b4)))
% 0.46/0.59 = { by lemma 26 R->L }
% 0.46/0.59 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.46/0.59 = { by lemma 23 R->L }
% 0.46/0.59 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), double_divide(c3, b3)), multiply(a4, b4))
% 0.46/0.59 = { by lemma 19 R->L }
% 0.46/0.59 tuple(double_divide(X, inverse(X)), a2, double_divide(inverse(a3), inverse(multiply(b3, c3))), multiply(a4, b4))
% 0.46/0.59 = { by lemma 26 R->L }
% 0.46/0.59 tuple(double_divide(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.46/0.59 = { by lemma 27 R->L }
% 0.46/0.59 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.46/0.59 = { by lemma 24 }
% 0.46/0.59 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.46/0.59 = { by lemma 24 }
% 0.46/0.59 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.46/0.59 % SZS output end Proof
% 0.46/0.59
% 0.46/0.59 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------