%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP109-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 0.16s 0.49s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP109-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n011.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 09:19:45 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.49 Command-line arguments: --no-flatten-goal
% 0.16/0.49
% 0.16/0.49 % SZS status Unsatisfiable
% 0.16/0.49
% 0.16/0.52 % SZS output start Proof
% 0.16/0.52 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.16/0.52 Axiom 2 (single_axiom): double_divide(inverse(double_divide(X, inverse(double_divide(inverse(Y), double_divide(X, Z))))), Z) = Y.
% 0.16/0.52
% 0.16/0.52 Lemma 3: double_divide(multiply(multiply(double_divide(X, Y), inverse(Z)), X), Y) = Z.
% 0.16/0.52 Proof:
% 0.16/0.52 double_divide(multiply(multiply(double_divide(X, Y), inverse(Z)), X), Y)
% 0.16/0.52 = { by axiom 1 (multiply) }
% 0.16/0.52 double_divide(multiply(inverse(double_divide(inverse(Z), double_divide(X, Y))), X), Y)
% 0.16/0.52 = { by axiom 1 (multiply) }
% 0.16/0.52 double_divide(inverse(double_divide(X, inverse(double_divide(inverse(Z), double_divide(X, Y))))), Y)
% 0.16/0.52 = { by axiom 2 (single_axiom) }
% 0.16/0.52 Z
% 0.16/0.52
% 0.16/0.52 Lemma 4: multiply(X, multiply(multiply(double_divide(Y, X), inverse(Z)), Y)) = inverse(Z).
% 0.16/0.52 Proof:
% 0.16/0.52 multiply(X, multiply(multiply(double_divide(Y, X), inverse(Z)), Y))
% 0.16/0.52 = { by axiom 1 (multiply) }
% 0.16/0.52 inverse(double_divide(multiply(multiply(double_divide(Y, X), inverse(Z)), Y), X))
% 0.16/0.52 = { by lemma 3 }
% 0.16/0.52 inverse(Z)
% 0.16/0.52
% 0.16/0.52 Lemma 5: multiply(multiply(double_divide(X, double_divide(Y, Z)), inverse(W)), X) = multiply(Z, multiply(inverse(W), Y)).
% 0.16/0.52 Proof:
% 0.16/0.52 multiply(multiply(double_divide(X, double_divide(Y, Z)), inverse(W)), X)
% 0.16/0.52 = { by axiom 1 (multiply) }
% 0.16/0.52 inverse(double_divide(X, multiply(double_divide(X, double_divide(Y, Z)), inverse(W))))
% 0.16/0.52 = { by lemma 3 R->L }
% 0.16/0.52 inverse(double_divide(multiply(multiply(double_divide(Y, Z), inverse(double_divide(X, multiply(double_divide(X, double_divide(Y, Z)), inverse(W))))), Y), Z))
% 0.16/0.52 = { by axiom 1 (multiply) R->L }
% 0.16/0.52 inverse(double_divide(multiply(multiply(double_divide(Y, Z), multiply(multiply(double_divide(X, double_divide(Y, Z)), inverse(W)), X)), Y), Z))
% 0.16/0.52 = { by lemma 4 }
% 0.16/0.52 inverse(double_divide(multiply(inverse(W), Y), Z))
% 0.16/0.52 = { by axiom 1 (multiply) R->L }
% 0.16/0.52 multiply(Z, multiply(inverse(W), Y))
% 0.16/0.52
% 0.16/0.52 Lemma 6: multiply(double_divide(X, Y), multiply(Y, multiply(inverse(Z), X))) = inverse(Z).
% 0.16/0.52 Proof:
% 0.16/0.52 multiply(double_divide(X, Y), multiply(Y, multiply(inverse(Z), X)))
% 0.16/0.52 = { by lemma 5 R->L }
% 0.16/0.52 multiply(double_divide(X, Y), multiply(multiply(double_divide(W, double_divide(X, Y)), inverse(Z)), W))
% 0.16/0.52 = { by lemma 4 }
% 0.16/0.52 inverse(Z)
% 0.16/0.52
% 0.16/0.52 Lemma 7: double_divide(inverse(X), multiply(X, inverse(Y))) = Y.
% 0.16/0.52 Proof:
% 0.16/0.52 double_divide(inverse(X), multiply(X, inverse(Y)))
% 0.16/0.52 = { by lemma 4 R->L }
% 0.16/0.52 double_divide(multiply(multiply(X, inverse(Y)), multiply(multiply(double_divide(Z, multiply(X, inverse(Y))), inverse(X)), Z)), multiply(X, inverse(Y)))
% 0.16/0.52 = { by lemma 3 R->L }
% 0.16/0.52 double_divide(multiply(multiply(double_divide(multiply(multiply(double_divide(Z, multiply(X, inverse(Y))), inverse(X)), Z), multiply(X, inverse(Y))), inverse(Y)), multiply(multiply(double_divide(Z, multiply(X, inverse(Y))), inverse(X)), Z)), multiply(X, inverse(Y)))
% 0.16/0.52 = { by lemma 3 }
% 0.16/0.52 Y
% 0.16/0.52
% 0.16/0.52 Lemma 8: double_divide(inverse(X), multiply(X, multiply(Y, Z))) = double_divide(Z, Y).
% 0.16/0.52 Proof:
% 0.16/0.52 double_divide(inverse(X), multiply(X, multiply(Y, Z)))
% 0.16/0.52 = { by axiom 1 (multiply) }
% 0.16/0.52 double_divide(inverse(X), multiply(X, inverse(double_divide(Z, Y))))
% 0.16/0.52 = { by lemma 7 }
% 0.16/0.52 double_divide(Z, Y)
% 0.16/0.52
% 0.16/0.52 Lemma 9: double_divide(multiply(inverse(X), Y), Z) = double_divide(multiply(Z, Y), inverse(X)).
% 0.16/0.52 Proof:
% 0.16/0.53 double_divide(multiply(inverse(X), Y), Z)
% 0.16/0.53 = { by lemma 8 R->L }
% 0.16/0.53 double_divide(inverse(double_divide(Y, Z)), multiply(double_divide(Y, Z), multiply(Z, multiply(inverse(X), Y))))
% 0.16/0.53 = { by lemma 6 }
% 0.16/0.53 double_divide(inverse(double_divide(Y, Z)), inverse(X))
% 0.16/0.53 = { by axiom 1 (multiply) R->L }
% 0.16/0.53 double_divide(multiply(Z, Y), inverse(X))
% 0.16/0.53
% 0.16/0.53 Lemma 10: multiply(multiply(X, inverse(Y)), inverse(X)) = inverse(Y).
% 0.16/0.53 Proof:
% 0.16/0.53 multiply(multiply(X, inverse(Y)), inverse(X))
% 0.16/0.53 = { by axiom 1 (multiply) }
% 0.16/0.53 inverse(double_divide(inverse(X), multiply(X, inverse(Y))))
% 0.16/0.53 = { by lemma 7 }
% 0.16/0.53 inverse(Y)
% 0.16/0.53
% 0.16/0.53 Lemma 11: double_divide(inverse(multiply(X, inverse(Y))), inverse(Y)) = X.
% 0.16/0.53 Proof:
% 0.16/0.53 double_divide(inverse(multiply(X, inverse(Y))), inverse(Y))
% 0.16/0.53 = { by lemma 10 R->L }
% 0.16/0.53 double_divide(inverse(multiply(X, inverse(Y))), multiply(multiply(X, inverse(Y)), inverse(X)))
% 0.16/0.53 = { by lemma 7 }
% 0.16/0.53 X
% 0.16/0.53
% 0.16/0.53 Lemma 12: multiply(X, inverse(Y)) = double_divide(inverse(inverse(Y)), inverse(X)).
% 0.16/0.53 Proof:
% 0.16/0.53 multiply(X, inverse(Y))
% 0.16/0.53 = { by lemma 11 R->L }
% 0.16/0.53 double_divide(inverse(multiply(multiply(X, inverse(Y)), inverse(X))), inverse(X))
% 0.16/0.53 = { by lemma 10 }
% 0.16/0.53 double_divide(inverse(inverse(Y)), inverse(X))
% 0.16/0.53
% 0.16/0.53 Lemma 13: multiply(X, multiply(multiply(double_divide(Y, X), multiply(Z, W)), Y)) = multiply(Z, W).
% 0.16/0.53 Proof:
% 0.16/0.53 multiply(X, multiply(multiply(double_divide(Y, X), multiply(Z, W)), Y))
% 0.16/0.53 = { by axiom 1 (multiply) }
% 0.16/0.53 multiply(X, multiply(multiply(double_divide(Y, X), inverse(double_divide(W, Z))), Y))
% 0.16/0.53 = { by lemma 4 }
% 0.16/0.53 inverse(double_divide(W, Z))
% 0.16/0.53 = { by axiom 1 (multiply) R->L }
% 0.16/0.53 multiply(Z, W)
% 0.16/0.53
% 0.16/0.53 Lemma 14: multiply(double_divide(X, Y), multiply(Y, multiply(multiply(Z, W), X))) = multiply(Z, W).
% 0.16/0.53 Proof:
% 0.16/0.53 multiply(double_divide(X, Y), multiply(Y, multiply(multiply(Z, W), X)))
% 0.16/0.53 = { by lemma 13 R->L }
% 0.16/0.53 multiply(double_divide(X, Y), multiply(Y, multiply(multiply(double_divide(X, Y), multiply(multiply(double_divide(V, double_divide(X, Y)), multiply(Z, W)), V)), X)))
% 0.16/0.53 = { by lemma 13 }
% 0.16/0.53 multiply(double_divide(X, Y), multiply(multiply(double_divide(V, double_divide(X, Y)), multiply(Z, W)), V))
% 0.16/0.53 = { by lemma 13 }
% 0.16/0.53 multiply(Z, W)
% 0.16/0.53
% 0.16/0.53 Lemma 15: double_divide(X, double_divide(X, multiply(Y, Z))) = multiply(Y, Z).
% 0.16/0.53 Proof:
% 0.16/0.53 double_divide(X, double_divide(X, multiply(Y, Z)))
% 0.16/0.53 = { by lemma 8 R->L }
% 0.16/0.53 double_divide(inverse(inverse(W)), multiply(inverse(W), multiply(double_divide(X, multiply(Y, Z)), X)))
% 0.16/0.53 = { by axiom 1 (multiply) }
% 0.16/0.53 double_divide(inverse(inverse(W)), inverse(double_divide(multiply(double_divide(X, multiply(Y, Z)), X), inverse(W))))
% 0.16/0.53 = { by lemma 12 R->L }
% 0.16/0.53 multiply(double_divide(multiply(double_divide(X, multiply(Y, Z)), X), inverse(W)), inverse(W))
% 0.16/0.53 = { by lemma 9 R->L }
% 0.16/0.53 multiply(double_divide(multiply(inverse(W), X), double_divide(X, multiply(Y, Z))), inverse(W))
% 0.16/0.53 = { by lemma 6 R->L }
% 0.16/0.53 multiply(double_divide(multiply(inverse(W), X), double_divide(X, multiply(Y, Z))), multiply(double_divide(X, multiply(Y, Z)), multiply(multiply(Y, Z), multiply(inverse(W), X))))
% 0.16/0.53 = { by lemma 14 }
% 0.16/0.53 multiply(Y, Z)
% 0.16/0.53
% 0.16/0.53 Lemma 16: multiply(X, inverse(Y)) = double_divide(inverse(X), Y).
% 0.16/0.53 Proof:
% 0.16/0.53 multiply(X, inverse(Y))
% 0.16/0.53 = { by lemma 15 R->L }
% 0.16/0.53 double_divide(inverse(X), double_divide(inverse(X), multiply(X, inverse(Y))))
% 0.16/0.53 = { by lemma 7 }
% 0.16/0.53 double_divide(inverse(X), Y)
% 0.16/0.53
% 0.16/0.53 Lemma 17: double_divide(inverse(X), double_divide(inverse(X), Y)) = Y.
% 0.16/0.53 Proof:
% 0.16/0.53 double_divide(inverse(X), double_divide(inverse(X), Y))
% 0.16/0.53 = { by lemma 16 R->L }
% 0.16/0.53 double_divide(inverse(X), multiply(X, inverse(Y)))
% 0.16/0.53 = { by lemma 7 }
% 0.16/0.53 Y
% 0.16/0.53
% 0.16/0.53 Lemma 18: double_divide(double_divide(inverse(X), Y), inverse(X)) = Y.
% 0.16/0.53 Proof:
% 0.16/0.53 double_divide(double_divide(inverse(X), Y), inverse(X))
% 0.16/0.53 = { by lemma 16 R->L }
% 0.16/0.53 double_divide(multiply(X, inverse(Y)), inverse(X))
% 0.16/0.53 = { by axiom 1 (multiply) }
% 0.16/0.53 double_divide(inverse(double_divide(inverse(Y), X)), inverse(X))
% 0.16/0.53 = { by lemma 16 R->L }
% 0.16/0.53 double_divide(inverse(multiply(Y, inverse(X))), inverse(X))
% 0.16/0.53 = { by lemma 11 }
% 0.16/0.53 Y
% 0.16/0.53
% 0.16/0.53 Lemma 19: multiply(X, inverse(Y)) = double_divide(Y, inverse(X)).
% 0.16/0.53 Proof:
% 0.16/0.53 multiply(X, inverse(Y))
% 0.16/0.53 = { by lemma 18 R->L }
% 0.16/0.53 double_divide(double_divide(inverse(X), multiply(X, inverse(Y))), inverse(X))
% 0.16/0.53 = { by lemma 7 }
% 0.16/0.53 double_divide(Y, inverse(X))
% 0.16/0.53
% 0.16/0.53 Lemma 20: double_divide(inverse(X), Y) = double_divide(Y, inverse(X)).
% 0.16/0.53 Proof:
% 0.16/0.53 double_divide(inverse(X), Y)
% 0.16/0.53 = { by lemma 18 R->L }
% 0.16/0.53 double_divide(double_divide(inverse(X), double_divide(inverse(X), Y)), inverse(X))
% 0.16/0.53 = { by lemma 17 }
% 0.16/0.53 double_divide(Y, inverse(X))
% 0.16/0.53
% 0.16/0.53 Lemma 21: inverse(inverse(X)) = X.
% 0.16/0.53 Proof:
% 0.16/0.53 inverse(inverse(X))
% 0.16/0.53 = { by lemma 6 R->L }
% 0.16/0.53 inverse(multiply(double_divide(multiply(inverse(Y), Z), double_divide(Z, inverse(X))), multiply(double_divide(Z, inverse(X)), multiply(inverse(X), multiply(inverse(Y), Z)))))
% 0.16/0.53 = { by lemma 6 }
% 0.16/0.53 inverse(multiply(double_divide(multiply(inverse(Y), Z), double_divide(Z, inverse(X))), inverse(Y)))
% 0.16/0.53 = { by lemma 9 }
% 0.16/0.53 inverse(multiply(double_divide(multiply(double_divide(Z, inverse(X)), Z), inverse(Y)), inverse(Y)))
% 0.16/0.53 = { by lemma 12 }
% 0.16/0.53 inverse(double_divide(inverse(inverse(Y)), inverse(double_divide(multiply(double_divide(Z, inverse(X)), Z), inverse(Y)))))
% 0.16/0.53 = { by axiom 1 (multiply) R->L }
% 0.16/0.53 inverse(double_divide(inverse(inverse(Y)), multiply(inverse(Y), multiply(double_divide(Z, inverse(X)), Z))))
% 0.16/0.53 = { by lemma 8 }
% 0.16/0.53 inverse(double_divide(Z, double_divide(Z, inverse(X))))
% 0.16/0.53 = { by lemma 17 R->L }
% 0.16/0.53 double_divide(inverse(W), double_divide(inverse(W), inverse(double_divide(Z, double_divide(Z, inverse(X))))))
% 0.16/0.53 = { by lemma 19 R->L }
% 0.16/0.53 double_divide(inverse(W), multiply(double_divide(Z, double_divide(Z, inverse(X))), inverse(inverse(W))))
% 0.16/0.53 = { by lemma 20 }
% 0.16/0.53 double_divide(multiply(double_divide(Z, double_divide(Z, inverse(X))), inverse(inverse(W))), inverse(W))
% 0.16/0.53 = { by lemma 3 R->L }
% 0.16/0.53 double_divide(multiply(double_divide(Z, double_divide(Z, inverse(X))), inverse(inverse(W))), double_divide(multiply(multiply(double_divide(Z, double_divide(Z, inverse(X))), inverse(inverse(W))), Z), double_divide(Z, inverse(X))))
% 0.16/0.53 = { by lemma 14 R->L }
% 0.16/0.53 double_divide(multiply(double_divide(Z, inverse(X)), multiply(inverse(X), multiply(multiply(double_divide(Z, double_divide(Z, inverse(X))), inverse(inverse(W))), Z))), double_divide(multiply(multiply(double_divide(Z, double_divide(Z, inverse(X))), inverse(inverse(W))), Z), double_divide(Z, inverse(X))))
% 0.16/0.53 = { by lemma 5 R->L }
% 0.16/0.53 double_divide(multiply(multiply(double_divide(V, double_divide(multiply(multiply(double_divide(Z, double_divide(Z, inverse(X))), inverse(inverse(W))), Z), double_divide(Z, inverse(X)))), inverse(X)), V), double_divide(multiply(multiply(double_divide(Z, double_divide(Z, inverse(X))), inverse(inverse(W))), Z), double_divide(Z, inverse(X))))
% 0.16/0.53 = { by lemma 3 }
% 0.16/0.53 X
% 0.16/0.53
% 0.16/0.53 Lemma 22: double_divide(Y, X) = double_divide(X, Y).
% 0.16/0.53 Proof:
% 0.16/0.53 double_divide(Y, X)
% 0.16/0.53 = { by lemma 21 R->L }
% 0.16/0.53 double_divide(inverse(inverse(Y)), X)
% 0.16/0.53 = { by lemma 20 }
% 0.16/0.53 double_divide(X, inverse(inverse(Y)))
% 0.16/0.53 = { by lemma 21 }
% 0.16/0.53 double_divide(X, Y)
% 0.16/0.53
% 0.16/0.53 Lemma 23: inverse(double_divide(X, Y)) = multiply(X, Y).
% 0.16/0.53 Proof:
% 0.16/0.53 inverse(double_divide(X, Y))
% 0.16/0.53 = { by lemma 22 }
% 0.16/0.53 inverse(double_divide(Y, X))
% 0.16/0.53 = { by axiom 1 (multiply) R->L }
% 0.16/0.53 multiply(X, Y)
% 0.16/0.53
% 0.16/0.53 Lemma 24: multiply(X, Y) = multiply(Y, X).
% 0.16/0.53 Proof:
% 0.16/0.53 multiply(X, Y)
% 0.16/0.53 = { by lemma 23 R->L }
% 0.16/0.53 inverse(double_divide(X, Y))
% 0.16/0.53 = { by axiom 1 (multiply) R->L }
% 0.16/0.53 multiply(Y, X)
% 0.16/0.53
% 0.16/0.53 Lemma 25: multiply(X, multiply(Y, Z)) = double_divide(inverse(X), double_divide(Y, Z)).
% 0.16/0.53 Proof:
% 0.16/0.53 multiply(X, multiply(Y, Z))
% 0.16/0.53 = { by lemma 24 R->L }
% 0.16/0.53 multiply(X, multiply(Z, Y))
% 0.16/0.53 = { by lemma 15 R->L }
% 0.16/0.53 double_divide(inverse(X), double_divide(inverse(X), multiply(X, multiply(Z, Y))))
% 0.16/0.53 = { by lemma 8 }
% 0.16/0.53 double_divide(inverse(X), double_divide(Y, Z))
% 0.16/0.53
% 0.16/0.53 Lemma 26: double_divide(inverse(X), double_divide(Y, inverse(Z))) = double_divide(Z, double_divide(X, Y)).
% 0.16/0.53 Proof:
% 0.16/0.53 double_divide(inverse(X), double_divide(Y, inverse(Z)))
% 0.16/0.53 = { by lemma 20 R->L }
% 0.16/0.53 double_divide(inverse(X), double_divide(inverse(Z), Y))
% 0.16/0.53 = { by lemma 25 R->L }
% 0.16/0.53 multiply(X, multiply(inverse(Z), Y))
% 0.16/0.53 = { by lemma 13 R->L }
% 0.16/0.53 multiply(W, multiply(multiply(double_divide(V, W), multiply(X, multiply(inverse(Z), Y))), V))
% 0.16/0.53 = { by axiom 1 (multiply) }
% 0.16/0.53 multiply(W, multiply(multiply(double_divide(V, W), inverse(double_divide(multiply(inverse(Z), Y), X))), V))
% 0.16/0.53 = { by lemma 9 }
% 0.16/0.53 multiply(W, multiply(multiply(double_divide(V, W), inverse(double_divide(multiply(X, Y), inverse(Z)))), V))
% 0.16/0.53 = { by axiom 1 (multiply) R->L }
% 0.16/0.53 multiply(W, multiply(multiply(double_divide(V, W), multiply(inverse(Z), multiply(X, Y))), V))
% 0.16/0.53 = { by lemma 13 }
% 0.16/0.53 multiply(inverse(Z), multiply(X, Y))
% 0.16/0.53 = { by lemma 25 }
% 0.16/0.53 double_divide(inverse(inverse(Z)), double_divide(X, Y))
% 0.16/0.53 = { by lemma 21 }
% 0.16/0.53 double_divide(Z, double_divide(X, Y))
% 0.16/0.53
% 0.16/0.53 Lemma 27: double_divide(X, double_divide(Y, inverse(Y))) = inverse(X).
% 0.16/0.53 Proof:
% 0.16/0.53 double_divide(X, double_divide(Y, inverse(Y)))
% 0.16/0.53 = { by lemma 11 R->L }
% 0.16/0.53 double_divide(inverse(multiply(double_divide(X, double_divide(Y, inverse(Y))), inverse(double_divide(Z, multiply(multiply(double_divide(W, Z), inverse(V)), W))))), inverse(double_divide(Z, multiply(multiply(double_divide(W, Z), inverse(V)), W))))
% 0.16/0.53 = { by axiom 1 (multiply) R->L }
% 0.16/0.53 double_divide(inverse(multiply(double_divide(X, double_divide(Y, inverse(Y))), multiply(multiply(multiply(double_divide(W, Z), inverse(V)), W), Z))), inverse(double_divide(Z, multiply(multiply(double_divide(W, Z), inverse(V)), W))))
% 0.16/0.53 = { by axiom 1 (multiply) }
% 0.16/0.53 double_divide(inverse(inverse(double_divide(multiply(multiply(multiply(double_divide(W, Z), inverse(V)), W), Z), double_divide(X, double_divide(Y, inverse(Y)))))), inverse(double_divide(Z, multiply(multiply(double_divide(W, Z), inverse(V)), W))))
% 0.16/0.53 = { by lemma 21 }
% 0.16/0.53 double_divide(double_divide(multiply(multiply(multiply(double_divide(W, Z), inverse(V)), W), Z), double_divide(X, double_divide(Y, inverse(Y)))), inverse(double_divide(Z, multiply(multiply(double_divide(W, Z), inverse(V)), W))))
% 0.16/0.53 = { by lemma 22 R->L }
% 0.16/0.53 double_divide(double_divide(double_divide(X, double_divide(Y, inverse(Y))), multiply(multiply(multiply(double_divide(W, Z), inverse(V)), W), Z)), inverse(double_divide(Z, multiply(multiply(double_divide(W, Z), inverse(V)), W))))
% 0.16/0.53 = { by lemma 23 }
% 0.16/0.53 double_divide(double_divide(double_divide(X, double_divide(Y, inverse(Y))), multiply(multiply(multiply(double_divide(W, Z), inverse(V)), W), Z)), multiply(Z, multiply(multiply(double_divide(W, Z), inverse(V)), W)))
% 0.16/0.53 = { by lemma 22 R->L }
% 0.16/0.53 double_divide(multiply(Z, multiply(multiply(double_divide(W, Z), inverse(V)), W)), double_divide(double_divide(X, double_divide(Y, inverse(Y))), multiply(multiply(multiply(double_divide(W, Z), inverse(V)), W), Z)))
% 0.16/0.53 = { by lemma 24 }
% 0.16/0.53 double_divide(multiply(Z, multiply(multiply(double_divide(W, Z), inverse(V)), W)), double_divide(double_divide(X, double_divide(Y, inverse(Y))), multiply(Z, multiply(multiply(double_divide(W, Z), inverse(V)), W))))
% 0.16/0.53 = { by lemma 4 }
% 0.16/0.53 double_divide(inverse(V), double_divide(double_divide(X, double_divide(Y, inverse(Y))), multiply(Z, multiply(multiply(double_divide(W, Z), inverse(V)), W))))
% 0.16/0.53 = { by lemma 4 }
% 0.16/0.53 double_divide(inverse(V), double_divide(double_divide(X, double_divide(Y, inverse(Y))), inverse(V)))
% 0.16/0.53 = { by lemma 25 R->L }
% 0.16/0.53 multiply(V, multiply(double_divide(X, double_divide(Y, inverse(Y))), inverse(V)))
% 0.16/0.53 = { by lemma 26 R->L }
% 0.16/0.53 multiply(V, multiply(double_divide(inverse(Y), double_divide(inverse(Y), inverse(X))), inverse(V)))
% 0.16/0.53 = { by lemma 3 R->L }
% 0.16/0.53 multiply(double_divide(multiply(multiply(double_divide(inverse(Y), double_divide(inverse(Y), inverse(X))), inverse(V)), inverse(Y)), double_divide(inverse(Y), inverse(X))), multiply(double_divide(inverse(Y), double_divide(inverse(Y), inverse(X))), inverse(V)))
% 0.16/0.53 = { by lemma 14 R->L }
% 0.16/0.53 multiply(double_divide(multiply(multiply(double_divide(inverse(Y), double_divide(inverse(Y), inverse(X))), inverse(V)), inverse(Y)), double_divide(inverse(Y), inverse(X))), multiply(double_divide(inverse(Y), inverse(X)), multiply(inverse(X), multiply(multiply(double_divide(inverse(Y), double_divide(inverse(Y), inverse(X))), inverse(V)), inverse(Y)))))
% 0.16/0.53 = { by lemma 6 }
% 0.16/0.53 inverse(X)
% 0.16/0.53
% 0.16/0.53 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)).
% 0.16/0.53 Proof:
% 0.16/0.53 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.16/0.53 = { by lemma 24 }
% 0.16/0.53 tuple(multiply(a1, inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.16/0.53 = { by lemma 19 }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.16/0.53 = { by lemma 24 }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), multiply(a2, multiply(inverse(b2), b2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.16/0.53 = { by lemma 24 }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), multiply(a2, multiply(b2, inverse(b2))), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.16/0.53 = { by lemma 19 }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), multiply(a2, double_divide(b2, inverse(b2))), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.16/0.53 = { by lemma 24 }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), multiply(a2, double_divide(b2, inverse(b2))), multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.16/0.53 = { by lemma 25 }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), multiply(a2, double_divide(b2, inverse(b2))), double_divide(inverse(c3), double_divide(a3, b3)), multiply(a4, b4))
% 0.16/0.53 = { by lemma 26 R->L }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), multiply(a2, double_divide(b2, inverse(b2))), double_divide(inverse(a3), double_divide(b3, inverse(inverse(c3)))), multiply(a4, b4))
% 0.16/0.53 = { by lemma 21 }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), multiply(a2, double_divide(b2, inverse(b2))), double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.16/0.53 = { by lemma 24 R->L }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), multiply(double_divide(b2, inverse(b2)), a2), double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.16/0.53 = { by axiom 1 (multiply) }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), inverse(double_divide(a2, double_divide(b2, inverse(b2)))), double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.16/0.53 = { by lemma 27 }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), inverse(inverse(a2)), double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.16/0.53 = { by lemma 21 }
% 0.16/0.53 tuple(double_divide(a1, inverse(a1)), a2, double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.16/0.53 = { by lemma 17 R->L }
% 0.16/0.53 tuple(double_divide(inverse(X), double_divide(inverse(X), double_divide(a1, inverse(a1)))), a2, double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.16/0.53 = { by lemma 27 }
% 0.16/0.53 tuple(double_divide(inverse(X), inverse(inverse(X))), a2, double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.16/0.53 = { by lemma 27 R->L }
% 0.16/0.53 tuple(double_divide(inverse(X), double_divide(inverse(X), double_divide(b1, inverse(b1)))), a2, double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.16/0.53 = { by lemma 17 }
% 0.16/0.53 tuple(double_divide(b1, inverse(b1)), a2, double_divide(inverse(a3), double_divide(b3, c3)), multiply(a4, b4))
% 0.16/0.53 = { by lemma 25 R->L }
% 0.16/0.53 tuple(double_divide(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.16/0.53 = { by lemma 24 R->L }
% 0.16/0.53 tuple(double_divide(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.16/0.53 = { by lemma 19 R->L }
% 0.16/0.53 tuple(multiply(b1, inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.16/0.53 = { by lemma 24 R->L }
% 0.16/0.53 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.16/0.53 % SZS output end Proof
% 0.16/0.53
% 0.16/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------