%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP102-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.12s 0.49s
% Output : Proof 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP102-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 09:19:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.49 Command-line arguments: --no-flatten-goal
% 0.12/0.49
% 0.12/0.49 % SZS status Unsatisfiable
% 0.12/0.49
% 0.73/0.54 % SZS output start Proof
% 0.73/0.54 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.73/0.54 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.73/0.54 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.73/0.54 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), double_divide(Y, identity))), double_divide(identity, identity)) = Z.
% 0.73/0.54
% 0.73/0.54 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.73/0.54 Proof:
% 0.73/0.54 inverse(double_divide(X, Y))
% 0.73/0.54 = { by axiom 1 (inverse) }
% 0.73/0.54 double_divide(double_divide(X, Y), identity)
% 0.73/0.54 = { by axiom 3 (multiply) R->L }
% 0.73/0.54 multiply(Y, X)
% 0.73/0.54
% 0.73/0.54 Lemma 6: multiply(inverse(X), X) = inverse(identity).
% 0.73/0.54 Proof:
% 0.73/0.54 multiply(inverse(X), X)
% 0.73/0.54 = { by lemma 5 R->L }
% 0.73/0.54 inverse(double_divide(X, inverse(X)))
% 0.73/0.54 = { by axiom 2 (identity) R->L }
% 0.73/0.54 inverse(identity)
% 0.73/0.54
% 0.73/0.54 Lemma 7: double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), inverse(Y))), inverse(identity)) = Z.
% 0.73/0.54 Proof:
% 0.73/0.54 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), inverse(Y))), inverse(identity))
% 0.73/0.54 = { by axiom 1 (inverse) }
% 0.73/0.54 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), inverse(Y))), double_divide(identity, identity))
% 0.73/0.54 = { by axiom 1 (inverse) }
% 0.73/0.54 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), double_divide(Y, identity))), double_divide(identity, identity))
% 0.73/0.54 = { by axiom 4 (single_axiom) }
% 0.73/0.54 Z
% 0.73/0.54
% 0.73/0.54 Lemma 8: double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity)) = multiply(X, Y).
% 0.73/0.54 Proof:
% 0.73/0.54 double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity))
% 0.73/0.54 = { by axiom 2 (identity) }
% 0.73/0.54 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), inverse(double_divide(Y, X))), inverse(Y))), inverse(identity))
% 0.73/0.54 = { by lemma 7 }
% 0.73/0.54 inverse(double_divide(Y, X))
% 0.73/0.54 = { by lemma 5 }
% 0.73/0.54 multiply(X, Y)
% 0.73/0.54
% 0.73/0.54 Lemma 9: double_divide(inverse(X), inverse(identity)) = multiply(X, identity).
% 0.73/0.54 Proof:
% 0.73/0.54 double_divide(inverse(X), inverse(identity))
% 0.73/0.54 = { by axiom 1 (inverse) }
% 0.73/0.54 double_divide(double_divide(X, identity), inverse(identity))
% 0.73/0.54 = { by axiom 2 (identity) }
% 0.73/0.54 double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
% 0.73/0.54 = { by lemma 8 }
% 0.73/0.54 multiply(X, identity)
% 0.73/0.54
% 0.73/0.54 Lemma 10: inverse(multiply(X, identity)) = multiply(inverse(identity), inverse(X)).
% 0.73/0.54 Proof:
% 0.73/0.54 inverse(multiply(X, identity))
% 0.73/0.54 = { by lemma 9 R->L }
% 0.73/0.54 inverse(double_divide(inverse(X), inverse(identity)))
% 0.73/0.54 = { by lemma 5 }
% 0.73/0.54 multiply(inverse(identity), inverse(X))
% 0.73/0.54
% 0.73/0.54 Lemma 11: double_divide(double_divide(X, double_divide(multiply(X, Y), inverse(Y))), inverse(identity)) = identity.
% 0.73/0.54 Proof:
% 0.73/0.54 double_divide(double_divide(X, double_divide(multiply(X, Y), inverse(Y))), inverse(identity))
% 0.73/0.54 = { by lemma 5 R->L }
% 0.73/0.54 double_divide(double_divide(X, double_divide(inverse(double_divide(Y, X)), inverse(Y))), inverse(identity))
% 0.73/0.54 = { by axiom 1 (inverse) }
% 0.73/0.54 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), identity), inverse(Y))), inverse(identity))
% 0.73/0.54 = { by lemma 7 }
% 0.73/0.54 identity
% 0.73/0.54
% 0.73/0.54 Lemma 12: inverse(identity) = identity.
% 0.73/0.54 Proof:
% 0.73/0.54 inverse(identity)
% 0.73/0.54 = { by lemma 6 R->L }
% 0.73/0.54 multiply(inverse(identity), identity)
% 0.73/0.54 = { by lemma 9 R->L }
% 0.73/0.54 double_divide(inverse(inverse(identity)), inverse(identity))
% 0.73/0.54 = { by axiom 1 (inverse) }
% 0.73/0.54 double_divide(double_divide(inverse(identity), identity), inverse(identity))
% 0.73/0.54 = { by axiom 2 (identity) }
% 0.73/0.54 double_divide(double_divide(inverse(identity), double_divide(inverse(inverse(identity)), inverse(inverse(inverse(identity))))), inverse(identity))
% 0.73/0.54 = { by lemma 6 R->L }
% 0.73/0.54 double_divide(double_divide(inverse(identity), double_divide(inverse(multiply(inverse(identity), identity)), inverse(inverse(inverse(identity))))), inverse(identity))
% 0.73/0.54 = { by lemma 10 }
% 0.73/0.54 double_divide(double_divide(inverse(identity), double_divide(multiply(inverse(identity), inverse(inverse(identity))), inverse(inverse(inverse(identity))))), inverse(identity))
% 0.73/0.54 = { by lemma 11 }
% 0.73/0.54 identity
% 0.73/0.54
% 0.73/0.54 Lemma 13: multiply(identity, X) = inverse(inverse(X)).
% 0.73/0.54 Proof:
% 0.73/0.54 multiply(identity, X)
% 0.73/0.54 = { by lemma 5 R->L }
% 0.73/0.54 inverse(double_divide(X, identity))
% 0.73/0.54 = { by axiom 1 (inverse) R->L }
% 0.73/0.54 inverse(inverse(X))
% 0.73/0.54
% 0.73/0.54 Lemma 14: multiply(X, identity) = inverse(inverse(X)).
% 0.73/0.54 Proof:
% 0.73/0.54 multiply(X, identity)
% 0.73/0.54 = { by lemma 8 R->L }
% 0.73/0.54 double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
% 0.73/0.54 = { by lemma 12 }
% 0.73/0.54 double_divide(double_divide(X, double_divide(identity, identity)), inverse(identity))
% 0.73/0.54 = { by axiom 1 (inverse) R->L }
% 0.73/0.54 double_divide(double_divide(X, inverse(identity)), inverse(identity))
% 0.73/0.54 = { by lemma 12 }
% 0.73/0.54 double_divide(double_divide(X, identity), inverse(identity))
% 0.73/0.54 = { by lemma 12 }
% 0.73/0.54 double_divide(double_divide(X, identity), identity)
% 0.73/0.55 = { by axiom 1 (inverse) R->L }
% 0.73/0.55 inverse(double_divide(X, identity))
% 0.73/0.55 = { by lemma 5 }
% 0.73/0.55 multiply(identity, X)
% 0.73/0.55 = { by lemma 13 }
% 0.73/0.55 inverse(inverse(X))
% 0.73/0.55
% 0.73/0.55 Lemma 15: double_divide(multiply(X, Y), inverse(identity)) = multiply(double_divide(Y, X), identity).
% 0.73/0.55 Proof:
% 0.73/0.55 double_divide(multiply(X, Y), inverse(identity))
% 0.73/0.55 = { by lemma 5 R->L }
% 0.73/0.55 double_divide(inverse(double_divide(Y, X)), inverse(identity))
% 0.73/0.55 = { by lemma 9 }
% 0.73/0.55 multiply(double_divide(Y, X), identity)
% 0.73/0.55
% 0.73/0.55 Lemma 16: double_divide(multiply(double_divide(identity, X), Y), inverse(Y)) = inverse(inverse(X)).
% 0.73/0.55 Proof:
% 0.73/0.55 double_divide(multiply(double_divide(identity, X), Y), inverse(Y))
% 0.73/0.55 = { by lemma 7 R->L }
% 0.73/0.55 double_divide(double_divide(X, double_divide(double_divide(double_divide(identity, X), double_divide(multiply(double_divide(identity, X), Y), inverse(Y))), inverse(identity))), inverse(identity))
% 0.73/0.55 = { by lemma 11 }
% 0.73/0.55 double_divide(double_divide(X, identity), inverse(identity))
% 0.73/0.55 = { by axiom 1 (inverse) R->L }
% 0.73/0.55 double_divide(inverse(X), inverse(identity))
% 0.73/0.55 = { by lemma 9 }
% 0.73/0.55 multiply(X, identity)
% 0.73/0.55 = { by lemma 14 }
% 0.73/0.55 inverse(inverse(X))
% 0.73/0.55
% 0.73/0.55 Lemma 17: inverse(inverse(inverse(inverse(X)))) = inverse(inverse(X)).
% 0.73/0.55 Proof:
% 0.73/0.55 inverse(inverse(inverse(inverse(X))))
% 0.73/0.55 = { by lemma 13 R->L }
% 0.73/0.55 inverse(multiply(identity, inverse(X)))
% 0.73/0.55 = { by lemma 12 R->L }
% 0.73/0.55 inverse(multiply(inverse(identity), inverse(X)))
% 0.73/0.55 = { by lemma 10 R->L }
% 0.73/0.55 inverse(inverse(multiply(X, identity)))
% 0.73/0.55 = { by lemma 5 R->L }
% 0.73/0.55 inverse(inverse(inverse(double_divide(identity, X))))
% 0.73/0.55 = { by lemma 13 R->L }
% 0.73/0.55 multiply(identity, inverse(double_divide(identity, X)))
% 0.73/0.55 = { by lemma 12 R->L }
% 0.73/0.55 multiply(inverse(identity), inverse(double_divide(identity, X)))
% 0.73/0.55 = { by lemma 10 R->L }
% 0.73/0.55 inverse(multiply(double_divide(identity, X), identity))
% 0.73/0.55 = { by lemma 5 R->L }
% 0.73/0.55 inverse(inverse(double_divide(identity, double_divide(identity, X))))
% 0.73/0.55 = { by lemma 14 R->L }
% 0.73/0.55 multiply(double_divide(identity, double_divide(identity, X)), identity)
% 0.73/0.55 = { by lemma 15 R->L }
% 0.73/0.55 double_divide(multiply(double_divide(identity, X), identity), inverse(identity))
% 0.73/0.55 = { by lemma 16 }
% 0.73/0.55 inverse(inverse(X))
% 0.73/0.55
% 0.73/0.55 Lemma 18: multiply(multiply(X, double_divide(identity, Y)), Y) = X.
% 0.73/0.55 Proof:
% 0.73/0.55 multiply(multiply(X, double_divide(identity, Y)), Y)
% 0.73/0.55 = { by lemma 5 R->L }
% 0.73/0.55 inverse(double_divide(Y, multiply(X, double_divide(identity, Y))))
% 0.73/0.55 = { by axiom 1 (inverse) }
% 0.73/0.55 double_divide(double_divide(Y, multiply(X, double_divide(identity, Y))), identity)
% 0.73/0.55 = { by lemma 12 R->L }
% 0.73/0.55 double_divide(double_divide(Y, multiply(X, double_divide(identity, Y))), inverse(identity))
% 0.73/0.55 = { by lemma 5 R->L }
% 0.73/0.55 double_divide(double_divide(Y, inverse(double_divide(double_divide(identity, Y), X))), inverse(identity))
% 0.73/0.55 = { by axiom 1 (inverse) }
% 0.73/0.55 double_divide(double_divide(Y, double_divide(double_divide(double_divide(identity, Y), X), identity)), inverse(identity))
% 0.73/0.55 = { by lemma 12 R->L }
% 0.73/0.55 double_divide(double_divide(Y, double_divide(double_divide(double_divide(identity, Y), X), inverse(identity))), inverse(identity))
% 0.73/0.55 = { by lemma 7 }
% 0.73/0.55 X
% 0.73/0.55
% 0.73/0.55 Lemma 19: inverse(inverse(X)) = X.
% 0.73/0.55 Proof:
% 0.73/0.55 inverse(inverse(X))
% 0.73/0.55 = { by lemma 17 R->L }
% 0.73/0.55 inverse(inverse(inverse(inverse(X))))
% 0.73/0.55 = { by lemma 13 R->L }
% 0.73/0.55 inverse(multiply(identity, inverse(X)))
% 0.73/0.55 = { by lemma 12 R->L }
% 0.73/0.55 inverse(multiply(inverse(identity), inverse(X)))
% 0.73/0.55 = { by lemma 10 R->L }
% 0.73/0.55 inverse(inverse(multiply(X, identity)))
% 0.73/0.55 = { by lemma 12 R->L }
% 0.73/0.55 inverse(inverse(multiply(X, inverse(identity))))
% 0.73/0.55 = { by lemma 14 R->L }
% 0.73/0.55 multiply(multiply(X, inverse(identity)), identity)
% 0.73/0.55 = { by axiom 1 (inverse) }
% 0.73/0.55 multiply(multiply(X, double_divide(identity, identity)), identity)
% 0.73/0.55 = { by lemma 18 }
% 0.73/0.55 X
% 0.73/0.55
% 0.73/0.55 Lemma 20: double_divide(identity, inverse(inverse(X))) = inverse(inverse(inverse(X))).
% 0.73/0.55 Proof:
% 0.73/0.55 double_divide(identity, inverse(inverse(X)))
% 0.73/0.55 = { by lemma 12 R->L }
% 0.73/0.55 double_divide(inverse(identity), inverse(inverse(X)))
% 0.73/0.55 = { by lemma 7 R->L }
% 0.73/0.55 double_divide(double_divide(double_divide(double_divide(multiply(inverse(X), X), inverse(X)), double_divide(double_divide(double_divide(inverse(X), double_divide(multiply(inverse(X), X), inverse(X))), inverse(identity)), inverse(inverse(X)))), inverse(identity)), inverse(inverse(X)))
% 0.73/0.55 = { by lemma 11 }
% 0.73/0.55 double_divide(double_divide(double_divide(double_divide(multiply(inverse(X), X), inverse(X)), double_divide(identity, inverse(inverse(X)))), inverse(identity)), inverse(inverse(X)))
% 0.73/0.55 = { by lemma 8 }
% 0.73/0.55 double_divide(multiply(double_divide(multiply(inverse(X), X), inverse(X)), inverse(X)), inverse(inverse(X)))
% 0.73/0.55 = { by lemma 6 }
% 0.73/0.55 double_divide(multiply(double_divide(inverse(identity), inverse(X)), inverse(X)), inverse(inverse(X)))
% 0.73/0.55 = { by lemma 12 }
% 0.73/0.55 double_divide(multiply(double_divide(identity, inverse(X)), inverse(X)), inverse(inverse(X)))
% 0.73/0.55 = { by lemma 16 }
% 0.73/0.55 inverse(inverse(inverse(X)))
% 0.73/0.55
% 0.73/0.55 Lemma 21: multiply(inverse(inverse(inverse(Y))), X) = multiply(X, inverse(Y)).
% 0.73/0.55 Proof:
% 0.73/0.55 multiply(inverse(inverse(inverse(Y))), X)
% 0.73/0.55 = { by lemma 5 R->L }
% 0.73/0.55 inverse(double_divide(X, inverse(inverse(inverse(Y)))))
% 0.73/0.55 = { by axiom 1 (inverse) }
% 0.73/0.55 double_divide(double_divide(X, inverse(inverse(inverse(Y)))), identity)
% 0.73/0.55 = { by lemma 12 R->L }
% 0.73/0.55 double_divide(double_divide(X, inverse(inverse(inverse(Y)))), inverse(identity))
% 0.73/0.55 = { by lemma 20 R->L }
% 0.73/0.55 double_divide(double_divide(X, double_divide(identity, inverse(inverse(Y)))), inverse(identity))
% 0.73/0.55 = { by lemma 8 }
% 0.73/0.55 multiply(X, inverse(Y))
% 0.73/0.55
% 0.73/0.55 Lemma 22: multiply(Y, X) = multiply(X, Y).
% 0.73/0.55 Proof:
% 0.73/0.55 multiply(Y, X)
% 0.73/0.55 = { by lemma 19 R->L }
% 0.73/0.55 multiply(Y, inverse(inverse(X)))
% 0.73/0.55 = { by lemma 21 R->L }
% 0.73/0.55 multiply(inverse(inverse(inverse(inverse(X)))), Y)
% 0.73/0.55 = { by lemma 17 }
% 0.73/0.55 multiply(inverse(inverse(X)), Y)
% 0.73/0.55 = { by lemma 19 }
% 0.73/0.56 multiply(X, Y)
% 0.73/0.56
% 0.73/0.56 Lemma 23: inverse(multiply(X, Y)) = double_divide(X, Y).
% 0.73/0.56 Proof:
% 0.73/0.56 inverse(multiply(X, Y))
% 0.73/0.56 = { by axiom 1 (inverse) }
% 0.73/0.56 double_divide(multiply(X, Y), identity)
% 0.73/0.56 = { by lemma 12 R->L }
% 0.73/0.56 double_divide(multiply(X, Y), inverse(identity))
% 0.73/0.56 = { by lemma 22 }
% 0.73/0.56 double_divide(multiply(Y, X), inverse(identity))
% 0.73/0.56 = { by lemma 15 }
% 0.73/0.56 multiply(double_divide(X, Y), identity)
% 0.73/0.56 = { by lemma 14 }
% 0.73/0.56 inverse(inverse(double_divide(X, Y)))
% 0.73/0.56 = { by lemma 19 }
% 0.73/0.56 double_divide(X, Y)
% 0.73/0.56
% 0.73/0.56 Lemma 24: double_divide(Y, X) = double_divide(X, Y).
% 0.73/0.56 Proof:
% 0.73/0.56 double_divide(Y, X)
% 0.73/0.56 = { by lemma 23 R->L }
% 0.73/0.56 inverse(multiply(Y, X))
% 0.73/0.56 = { by lemma 5 R->L }
% 0.73/0.56 inverse(inverse(double_divide(X, Y)))
% 0.73/0.56 = { by lemma 19 }
% 0.73/0.56 double_divide(X, Y)
% 0.73/0.56
% 0.73/0.56 Lemma 25: double_divide(identity, X) = inverse(X).
% 0.73/0.56 Proof:
% 0.73/0.56 double_divide(identity, X)
% 0.73/0.56 = { by lemma 19 R->L }
% 0.73/0.56 double_divide(identity, inverse(inverse(X)))
% 0.73/0.56 = { by lemma 20 }
% 0.73/0.56 inverse(inverse(inverse(X)))
% 0.73/0.56 = { by lemma 19 }
% 0.73/0.56 inverse(X)
% 0.73/0.56
% 0.73/0.56 Lemma 26: multiply(inverse(X), multiply(X, inverse(Y))) = inverse(Y).
% 0.73/0.56 Proof:
% 0.73/0.56 multiply(inverse(X), multiply(X, inverse(Y)))
% 0.73/0.56 = { by lemma 22 }
% 0.73/0.56 multiply(inverse(X), multiply(inverse(Y), X))
% 0.73/0.56 = { by lemma 25 R->L }
% 0.73/0.56 multiply(inverse(X), multiply(double_divide(identity, Y), X))
% 0.73/0.56 = { by lemma 5 R->L }
% 0.73/0.56 inverse(double_divide(multiply(double_divide(identity, Y), X), inverse(X)))
% 0.73/0.56 = { by lemma 16 }
% 0.73/0.56 inverse(inverse(inverse(Y)))
% 0.73/0.56 = { by lemma 19 }
% 0.73/0.56 inverse(Y)
% 0.73/0.56
% 0.73/0.56 Lemma 27: inverse(double_divide(X, Y)) = multiply(X, Y).
% 0.73/0.56 Proof:
% 0.73/0.56 inverse(double_divide(X, Y))
% 0.73/0.56 = { by lemma 24 }
% 0.73/0.56 inverse(double_divide(Y, X))
% 0.73/0.56 = { by lemma 23 R->L }
% 0.73/0.56 inverse(inverse(multiply(Y, X)))
% 0.73/0.56 = { by lemma 19 }
% 0.73/0.56 multiply(Y, X)
% 0.73/0.56 = { by lemma 22 R->L }
% 0.73/0.56 multiply(X, Y)
% 0.73/0.56
% 0.73/0.56 Lemma 28: double_divide(X, inverse(Y)) = multiply(Y, inverse(X)).
% 0.73/0.56 Proof:
% 0.73/0.56 double_divide(X, inverse(Y))
% 0.73/0.56 = { by lemma 19 R->L }
% 0.73/0.56 inverse(inverse(double_divide(X, inverse(Y))))
% 0.73/0.56 = { by lemma 26 R->L }
% 0.73/0.56 multiply(inverse(X), multiply(X, inverse(inverse(double_divide(X, inverse(Y))))))
% 0.73/0.56 = { by lemma 22 R->L }
% 0.73/0.56 multiply(inverse(X), multiply(inverse(inverse(double_divide(X, inverse(Y)))), X))
% 0.73/0.56 = { by lemma 19 }
% 0.73/0.56 multiply(inverse(X), multiply(double_divide(X, inverse(Y)), X))
% 0.73/0.56 = { by lemma 22 R->L }
% 0.73/0.56 multiply(inverse(X), multiply(X, double_divide(X, inverse(Y))))
% 0.73/0.56 = { by lemma 24 }
% 0.73/0.56 multiply(inverse(X), multiply(X, double_divide(inverse(Y), X)))
% 0.73/0.56 = { by lemma 27 R->L }
% 0.73/0.56 multiply(inverse(X), inverse(double_divide(X, double_divide(inverse(Y), X))))
% 0.73/0.56 = { by axiom 1 (inverse) }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(inverse(Y), X)), identity))
% 0.73/0.56 = { by lemma 12 R->L }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(inverse(Y), X)), inverse(identity)))
% 0.73/0.56 = { by lemma 19 R->L }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(inverse(Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by lemma 25 R->L }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(double_divide(identity, Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by lemma 12 R->L }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(double_divide(inverse(identity), Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by lemma 12 R->L }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(double_divide(inverse(inverse(identity)), Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by lemma 16 R->L }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(double_divide(double_divide(multiply(double_divide(identity, identity), double_divide(Z, multiply(X, double_divide(identity, Z)))), inverse(double_divide(Z, multiply(X, double_divide(identity, Z))))), Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by axiom 1 (inverse) R->L }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(double_divide(double_divide(multiply(inverse(identity), double_divide(Z, multiply(X, double_divide(identity, Z)))), inverse(double_divide(Z, multiply(X, double_divide(identity, Z))))), Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by lemma 12 }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(double_divide(double_divide(multiply(identity, double_divide(Z, multiply(X, double_divide(identity, Z)))), inverse(double_divide(Z, multiply(X, double_divide(identity, Z))))), Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by lemma 13 }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(double_divide(double_divide(inverse(inverse(double_divide(Z, multiply(X, double_divide(identity, Z))))), inverse(double_divide(Z, multiply(X, double_divide(identity, Z))))), Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by lemma 5 }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(double_divide(double_divide(inverse(multiply(multiply(X, double_divide(identity, Z)), Z)), inverse(double_divide(Z, multiply(X, double_divide(identity, Z))))), Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by lemma 5 }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(double_divide(double_divide(inverse(multiply(multiply(X, double_divide(identity, Z)), Z)), multiply(multiply(X, double_divide(identity, Z)), Z)), Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by lemma 18 }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(double_divide(double_divide(inverse(X), multiply(multiply(X, double_divide(identity, Z)), Z)), Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by lemma 18 }
% 0.73/0.56 multiply(inverse(X), double_divide(double_divide(X, double_divide(double_divide(double_divide(inverse(X), X), Y), inverse(inverse(X)))), inverse(identity)))
% 0.73/0.56 = { by lemma 7 }
% 0.73/0.56 multiply(inverse(X), Y)
% 0.73/0.56 = { by lemma 22 R->L }
% 0.73/0.56 multiply(Y, inverse(X))
% 0.73/0.56
% 0.73/0.56 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3), multiply(a4, b4)) = tuple(identity, a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4)).
% 0.73/0.56 Proof:
% 0.73/0.56 tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.73/0.56 = { by lemma 13 }
% 0.73/0.56 tuple(multiply(inverse(a1), a1), inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.73/0.56 = { by lemma 6 }
% 0.73/0.56 tuple(inverse(identity), inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.73/0.56 = { by lemma 12 }
% 0.73/0.56 tuple(identity, inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.73/0.56 = { by lemma 19 }
% 0.73/0.56 tuple(identity, a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.73/0.56 = { by lemma 22 R->L }
% 0.73/0.56 tuple(identity, a2, multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.73/0.56 = { by lemma 19 R->L }
% 0.73/0.56 tuple(identity, a2, multiply(inverse(inverse(c3)), multiply(a3, b3)), multiply(a4, b4))
% 0.73/0.56 = { by lemma 17 R->L }
% 0.73/0.56 tuple(identity, a2, multiply(inverse(inverse(inverse(inverse(c3)))), multiply(a3, b3)), multiply(a4, b4))
% 0.73/0.56 = { by lemma 22 }
% 0.73/0.56 tuple(identity, a2, multiply(inverse(inverse(inverse(inverse(c3)))), multiply(b3, a3)), multiply(a4, b4))
% 0.73/0.56 = { by lemma 19 R->L }
% 0.73/0.56 tuple(identity, a2, multiply(inverse(inverse(inverse(inverse(inverse(inverse(c3)))))), multiply(b3, a3)), multiply(a4, b4))
% 0.73/0.56 = { by lemma 21 }
% 0.73/0.56 tuple(identity, a2, multiply(multiply(b3, a3), inverse(inverse(inverse(inverse(c3))))), multiply(a4, b4))
% 0.73/0.56 = { by lemma 27 R->L }
% 0.73/0.56 tuple(identity, a2, multiply(inverse(double_divide(b3, a3)), inverse(inverse(inverse(inverse(c3))))), multiply(a4, b4))
% 0.73/0.56 = { by lemma 7 R->L }
% 0.73/0.56 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(double_divide(b3, a3), multiply(inverse(double_divide(b3, a3)), inverse(inverse(inverse(inverse(c3)))))), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.56 = { by lemma 19 R->L }
% 0.73/0.56 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(inverse(inverse(double_divide(b3, a3))), multiply(inverse(double_divide(b3, a3)), inverse(inverse(inverse(inverse(c3)))))), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.56 = { by lemma 19 R->L }
% 0.73/0.56 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(inverse(inverse(double_divide(b3, a3))), multiply(inverse(inverse(inverse(double_divide(b3, a3)))), inverse(inverse(inverse(inverse(c3)))))), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.57 = { by lemma 17 R->L }
% 0.73/0.57 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(inverse(inverse(inverse(inverse(double_divide(b3, a3))))), multiply(inverse(inverse(inverse(double_divide(b3, a3)))), inverse(inverse(inverse(inverse(c3)))))), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.57 = { by lemma 24 }
% 0.73/0.57 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(multiply(inverse(inverse(inverse(double_divide(b3, a3)))), inverse(inverse(inverse(inverse(c3))))), inverse(inverse(inverse(inverse(double_divide(b3, a3)))))), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.57 = { by lemma 19 R->L }
% 0.73/0.57 tuple(identity, a2, double_divide(double_divide(a3, double_divide(inverse(inverse(double_divide(multiply(inverse(inverse(inverse(double_divide(b3, a3)))), inverse(inverse(inverse(inverse(c3))))), inverse(inverse(inverse(inverse(double_divide(b3, a3)))))))), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.57 = { by lemma 14 R->L }
% 0.73/0.57 tuple(identity, a2, double_divide(double_divide(a3, double_divide(multiply(double_divide(multiply(inverse(inverse(inverse(double_divide(b3, a3)))), inverse(inverse(inverse(inverse(c3))))), inverse(inverse(inverse(inverse(double_divide(b3, a3)))))), identity), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.57 = { by lemma 15 R->L }
% 0.73/0.57 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(multiply(inverse(inverse(inverse(inverse(double_divide(b3, a3))))), multiply(inverse(inverse(inverse(double_divide(b3, a3)))), inverse(inverse(inverse(inverse(c3)))))), inverse(identity)), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.57 = { by lemma 26 }
% 0.73/0.57 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(inverse(inverse(inverse(inverse(c3)))), inverse(identity)), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.57 = { by lemma 9 }
% 0.73/0.57 tuple(identity, a2, double_divide(double_divide(a3, double_divide(multiply(inverse(inverse(inverse(c3))), identity), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.57 = { by lemma 14 }
% 0.73/0.57 tuple(identity, a2, double_divide(double_divide(a3, double_divide(inverse(inverse(inverse(inverse(inverse(c3))))), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.57 = { by lemma 19 }
% 0.73/0.57 tuple(identity, a2, double_divide(double_divide(a3, double_divide(inverse(inverse(inverse(c3))), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.73/0.57 = { by lemma 28 }
% 0.73/0.57 tuple(identity, a2, multiply(identity, inverse(double_divide(a3, double_divide(inverse(inverse(inverse(c3))), inverse(b3))))), multiply(a4, b4))
% 0.73/0.57 = { by lemma 13 }
% 0.73/0.57 tuple(identity, a2, inverse(inverse(inverse(double_divide(a3, double_divide(inverse(inverse(inverse(c3))), inverse(b3)))))), multiply(a4, b4))
% 0.73/0.57 = { by lemma 19 }
% 0.73/0.57 tuple(identity, a2, inverse(double_divide(a3, double_divide(inverse(inverse(inverse(c3))), inverse(b3)))), multiply(a4, b4))
% 0.73/0.57 = { by lemma 27 }
% 0.73/0.57 tuple(identity, a2, multiply(a3, double_divide(inverse(inverse(inverse(c3))), inverse(b3))), multiply(a4, b4))
% 0.73/0.57 = { by lemma 28 }
% 0.73/0.57 tuple(identity, a2, multiply(a3, multiply(b3, inverse(inverse(inverse(inverse(c3)))))), multiply(a4, b4))
% 0.73/0.57 = { by lemma 8 R->L }
% 0.73/0.57 tuple(identity, a2, multiply(a3, double_divide(double_divide(b3, double_divide(identity, inverse(inverse(inverse(inverse(inverse(c3))))))), inverse(identity))), multiply(a4, b4))
% 0.73/0.57 = { by lemma 17 }
% 0.73/0.57 tuple(identity, a2, multiply(a3, double_divide(double_divide(b3, double_divide(identity, inverse(inverse(inverse(c3))))), inverse(identity))), multiply(a4, b4))
% 0.73/0.57 = { by lemma 8 }
% 0.73/0.57 tuple(identity, a2, multiply(a3, multiply(b3, inverse(inverse(c3)))), multiply(a4, b4))
% 0.73/0.57 = { by lemma 19 }
% 0.73/0.57 tuple(identity, a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.73/0.57 = { by lemma 22 }
% 0.73/0.57 tuple(identity, a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.73/0.57 % SZS output end Proof
% 0.73/0.57
% 0.73/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------