%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP077-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:13 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.55s
% Output : Proof 1.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP077-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n020.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 09:19:04 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.55 Command-line arguments: --no-flatten-goal
% 0.18/0.55
% 0.18/0.55 % SZS status Unsatisfiable
% 0.18/0.55
% 1.33/0.61 % SZS output start Proof
% 1.33/0.61 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 1.33/0.61 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 1.33/0.61 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 1.33/0.61 Axiom 4 (single_axiom): double_divide(X, double_divide(double_divide(double_divide(identity, double_divide(double_divide(X, identity), double_divide(Y, Z))), Y), identity)) = Z.
% 1.33/0.61
% 1.33/0.61 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 1.33/0.61 Proof:
% 1.33/0.61 inverse(double_divide(X, Y))
% 1.33/0.61 = { by axiom 1 (inverse) }
% 1.33/0.61 double_divide(double_divide(X, Y), identity)
% 1.33/0.61 = { by axiom 3 (multiply) R->L }
% 1.33/0.61 multiply(Y, X)
% 1.33/0.61
% 1.33/0.61 Lemma 6: double_divide(X, multiply(Y, double_divide(identity, double_divide(inverse(X), double_divide(Y, Z))))) = Z.
% 1.33/0.61 Proof:
% 1.33/0.61 double_divide(X, multiply(Y, double_divide(identity, double_divide(inverse(X), double_divide(Y, Z)))))
% 1.33/0.61 = { by axiom 1 (inverse) }
% 1.33/0.61 double_divide(X, multiply(Y, double_divide(identity, double_divide(double_divide(X, identity), double_divide(Y, Z)))))
% 1.33/0.61 = { by lemma 5 R->L }
% 1.33/0.61 double_divide(X, inverse(double_divide(double_divide(identity, double_divide(double_divide(X, identity), double_divide(Y, Z))), Y)))
% 1.33/0.61 = { by axiom 1 (inverse) }
% 1.33/0.61 double_divide(X, double_divide(double_divide(double_divide(identity, double_divide(double_divide(X, identity), double_divide(Y, Z))), Y), identity))
% 1.33/0.61 = { by axiom 4 (single_axiom) }
% 1.33/0.61 Z
% 1.33/0.61
% 1.33/0.61 Lemma 7: double_divide(X, multiply(Y, double_divide(identity, inverse(inverse(X))))) = inverse(Y).
% 1.33/0.61 Proof:
% 1.33/0.61 double_divide(X, multiply(Y, double_divide(identity, inverse(inverse(X)))))
% 1.33/0.61 = { by axiom 1 (inverse) }
% 1.33/0.61 double_divide(X, multiply(Y, double_divide(identity, double_divide(inverse(X), identity))))
% 1.33/0.61 = { by axiom 2 (identity) }
% 1.33/0.61 double_divide(X, multiply(Y, double_divide(identity, double_divide(inverse(X), double_divide(Y, inverse(Y))))))
% 1.33/0.61 = { by lemma 6 }
% 1.33/0.62 inverse(Y)
% 1.33/0.62
% 1.33/0.62 Lemma 8: multiply(identity, X) = inverse(inverse(X)).
% 1.33/0.62 Proof:
% 1.33/0.62 multiply(identity, X)
% 1.33/0.62 = { by lemma 5 R->L }
% 1.33/0.62 inverse(double_divide(X, identity))
% 1.33/0.62 = { by axiom 1 (inverse) R->L }
% 1.33/0.62 inverse(inverse(X))
% 1.33/0.62
% 1.33/0.62 Lemma 9: multiply(inverse(X), X) = inverse(identity).
% 1.33/0.62 Proof:
% 1.33/0.62 multiply(inverse(X), X)
% 1.33/0.62 = { by lemma 5 R->L }
% 1.33/0.62 inverse(double_divide(X, inverse(X)))
% 1.33/0.62 = { by axiom 2 (identity) R->L }
% 1.33/0.62 inverse(identity)
% 1.33/0.62
% 1.33/0.62 Lemma 10: inverse(multiply(inverse(inverse(X)), identity)) = double_divide(X, inverse(identity)).
% 1.33/0.62 Proof:
% 1.33/0.62 inverse(multiply(inverse(inverse(X)), identity))
% 1.33/0.62 = { by lemma 5 R->L }
% 1.33/0.62 inverse(inverse(double_divide(identity, inverse(inverse(X)))))
% 1.33/0.62 = { by lemma 7 R->L }
% 1.33/0.62 double_divide(X, multiply(inverse(double_divide(identity, inverse(inverse(X)))), double_divide(identity, inverse(inverse(X)))))
% 1.33/0.62 = { by lemma 9 }
% 1.33/0.62 double_divide(X, inverse(identity))
% 1.33/0.62
% 1.33/0.62 Lemma 11: double_divide(X, multiply(inverse(X), identity)) = inverse(identity).
% 1.33/0.62 Proof:
% 1.33/0.62 double_divide(X, multiply(inverse(X), identity))
% 1.33/0.62 = { by axiom 2 (identity) }
% 1.33/0.62 double_divide(X, multiply(inverse(X), double_divide(identity, inverse(identity))))
% 1.33/0.62 = { by lemma 7 R->L }
% 1.33/0.62 double_divide(X, multiply(inverse(X), double_divide(identity, double_divide(inverse(X), multiply(identity, double_divide(identity, inverse(inverse(inverse(X)))))))))
% 1.33/0.62 = { by lemma 8 }
% 1.33/0.62 double_divide(X, multiply(inverse(X), double_divide(identity, double_divide(inverse(X), inverse(inverse(double_divide(identity, inverse(inverse(inverse(X))))))))))
% 1.33/0.62 = { by lemma 5 }
% 1.33/0.62 double_divide(X, multiply(inverse(X), double_divide(identity, double_divide(inverse(X), inverse(multiply(inverse(inverse(inverse(X))), identity))))))
% 1.33/0.62 = { by lemma 10 }
% 1.33/0.62 double_divide(X, multiply(inverse(X), double_divide(identity, double_divide(inverse(X), double_divide(inverse(X), inverse(identity))))))
% 1.33/0.62 = { by lemma 6 }
% 1.33/0.62 inverse(identity)
% 1.33/0.62
% 1.33/0.62 Lemma 12: inverse(identity) = identity.
% 1.33/0.62 Proof:
% 1.33/0.62 inverse(identity)
% 1.33/0.62 = { by lemma 11 R->L }
% 1.33/0.62 double_divide(identity, multiply(inverse(identity), identity))
% 1.33/0.62 = { by lemma 9 }
% 1.33/0.62 double_divide(identity, inverse(identity))
% 1.33/0.62 = { by axiom 2 (identity) R->L }
% 1.33/0.62 identity
% 1.33/0.62
% 1.33/0.62 Lemma 13: double_divide(identity, multiply(X, identity)) = inverse(X).
% 1.33/0.62 Proof:
% 1.33/0.62 double_divide(identity, multiply(X, identity))
% 1.33/0.62 = { by axiom 2 (identity) }
% 1.33/0.62 double_divide(identity, multiply(X, double_divide(identity, inverse(identity))))
% 1.33/0.62 = { by lemma 12 R->L }
% 1.33/0.62 double_divide(identity, multiply(X, double_divide(identity, inverse(inverse(identity)))))
% 1.33/0.62 = { by lemma 7 }
% 1.33/0.62 inverse(X)
% 1.33/0.62
% 1.33/0.62 Lemma 14: multiply(multiply(X, identity), identity) = inverse(inverse(X)).
% 1.33/0.62 Proof:
% 1.33/0.62 multiply(multiply(X, identity), identity)
% 1.33/0.62 = { by lemma 5 R->L }
% 1.33/0.62 inverse(double_divide(identity, multiply(X, identity)))
% 1.33/0.62 = { by lemma 13 }
% 1.33/0.62 inverse(inverse(X))
% 1.33/0.62
% 1.33/0.62 Lemma 15: inverse(multiply(X, identity)) = double_divide(identity, inverse(inverse(X))).
% 1.33/0.62 Proof:
% 1.33/0.62 inverse(multiply(X, identity))
% 1.33/0.62 = { by lemma 13 R->L }
% 1.33/0.62 double_divide(identity, multiply(multiply(X, identity), identity))
% 1.33/0.62 = { by lemma 14 }
% 1.33/0.62 double_divide(identity, inverse(inverse(X)))
% 1.33/0.62
% 1.33/0.62 Lemma 16: double_divide(identity, inverse(inverse(inverse(multiply(X, Y))))) = multiply(X, Y).
% 1.33/0.62 Proof:
% 1.33/0.62 double_divide(identity, inverse(inverse(inverse(multiply(X, Y)))))
% 1.33/0.62 = { by lemma 15 R->L }
% 1.33/0.62 inverse(multiply(inverse(multiply(X, Y)), identity))
% 1.33/0.62 = { by lemma 5 R->L }
% 1.33/0.62 inverse(multiply(inverse(inverse(double_divide(Y, X))), identity))
% 1.33/0.62 = { by lemma 10 }
% 1.33/0.62 double_divide(double_divide(Y, X), inverse(identity))
% 1.33/0.62 = { by lemma 12 }
% 1.33/0.62 double_divide(double_divide(Y, X), identity)
% 1.33/0.62 = { by axiom 1 (inverse) R->L }
% 1.33/0.62 inverse(double_divide(Y, X))
% 1.33/0.62 = { by lemma 5 }
% 1.33/0.62 multiply(X, Y)
% 1.33/0.62
% 1.33/0.62 Lemma 17: double_divide(identity, inverse(X)) = multiply(X, identity).
% 1.33/0.62 Proof:
% 1.33/0.62 double_divide(identity, inverse(X))
% 1.33/0.62 = { by axiom 1 (inverse) }
% 1.33/0.62 double_divide(identity, double_divide(X, identity))
% 1.33/0.62 = { by lemma 12 R->L }
% 1.33/0.62 double_divide(identity, double_divide(X, inverse(identity)))
% 1.33/0.62 = { by lemma 10 R->L }
% 1.33/0.62 double_divide(identity, inverse(multiply(inverse(inverse(X)), identity)))
% 1.33/0.62 = { by lemma 5 R->L }
% 1.33/0.62 double_divide(identity, inverse(inverse(double_divide(identity, inverse(inverse(X))))))
% 1.33/0.62 = { by lemma 15 R->L }
% 1.33/0.62 double_divide(identity, inverse(inverse(inverse(multiply(X, identity)))))
% 1.33/0.62 = { by lemma 16 }
% 1.33/0.62 multiply(X, identity)
% 1.33/0.62
% 1.33/0.62 Lemma 18: inverse(inverse(multiply(X, Y))) = multiply(X, Y).
% 1.33/0.62 Proof:
% 1.33/0.62 inverse(inverse(multiply(X, Y)))
% 1.33/0.62 = { by axiom 1 (inverse) }
% 1.33/0.62 double_divide(inverse(multiply(X, Y)), identity)
% 1.33/0.62 = { by lemma 12 R->L }
% 1.33/0.62 double_divide(inverse(multiply(X, Y)), inverse(identity))
% 1.33/0.62 = { by lemma 12 R->L }
% 1.33/0.62 double_divide(inverse(multiply(X, Y)), inverse(inverse(identity)))
% 1.33/0.62 = { by lemma 11 R->L }
% 1.33/0.62 double_divide(inverse(multiply(X, Y)), inverse(double_divide(multiply(X, Y), multiply(inverse(multiply(X, Y)), identity))))
% 1.33/0.62 = { by lemma 5 }
% 1.33/0.62 double_divide(inverse(multiply(X, Y)), multiply(multiply(inverse(multiply(X, Y)), identity), multiply(X, Y)))
% 1.33/0.62 = { by lemma 16 R->L }
% 1.33/0.62 double_divide(inverse(multiply(X, Y)), multiply(multiply(inverse(multiply(X, Y)), identity), double_divide(identity, inverse(inverse(inverse(multiply(X, Y)))))))
% 1.33/0.62 = { by lemma 7 }
% 1.33/0.62 inverse(multiply(inverse(multiply(X, Y)), identity))
% 1.33/0.62 = { by lemma 15 }
% 1.33/0.62 double_divide(identity, inverse(inverse(inverse(multiply(X, Y)))))
% 1.33/0.62 = { by lemma 16 }
% 1.33/0.62 multiply(X, Y)
% 1.33/0.62
% 1.33/0.62 Lemma 19: multiply(multiply(X, Y), identity) = multiply(X, Y).
% 1.33/0.62 Proof:
% 1.33/0.62 multiply(multiply(X, Y), identity)
% 1.33/0.62 = { by lemma 17 R->L }
% 1.33/0.62 double_divide(identity, inverse(multiply(X, Y)))
% 1.33/0.62 = { by lemma 18 R->L }
% 1.33/0.62 double_divide(identity, inverse(inverse(inverse(multiply(X, Y)))))
% 1.33/0.62 = { by lemma 16 }
% 1.33/0.62 multiply(X, Y)
% 1.33/0.62
% 1.33/0.62 Lemma 20: multiply(X, identity) = inverse(inverse(X)).
% 1.33/0.62 Proof:
% 1.33/0.62 multiply(X, identity)
% 1.33/0.62 = { by lemma 19 R->L }
% 1.33/0.62 multiply(multiply(X, identity), identity)
% 1.33/0.62 = { by lemma 14 }
% 1.33/0.62 inverse(inverse(X))
% 1.33/0.62
% 1.33/0.62 Lemma 21: inverse(inverse(inverse(X))) = inverse(X).
% 1.33/0.62 Proof:
% 1.33/0.62 inverse(inverse(inverse(X)))
% 1.33/0.62 = { by lemma 20 R->L }
% 1.33/0.62 multiply(inverse(X), identity)
% 1.33/0.62 = { by lemma 17 R->L }
% 1.33/0.62 double_divide(identity, inverse(inverse(X)))
% 1.33/0.62 = { by lemma 20 R->L }
% 1.33/0.62 double_divide(identity, multiply(X, identity))
% 1.33/0.62 = { by lemma 13 }
% 1.33/0.62 inverse(X)
% 1.33/0.62
% 1.33/0.62 Lemma 22: multiply(multiply(X, inverse(Y)), Y) = inverse(inverse(X)).
% 1.33/0.62 Proof:
% 1.33/0.62 multiply(multiply(X, inverse(Y)), Y)
% 1.33/0.62 = { by lemma 21 R->L }
% 1.33/0.62 multiply(multiply(X, inverse(inverse(inverse(Y)))), Y)
% 1.33/0.62 = { by lemma 20 R->L }
% 1.33/0.62 multiply(multiply(X, multiply(inverse(Y), identity)), Y)
% 1.33/0.62 = { by lemma 17 R->L }
% 1.33/0.62 multiply(multiply(X, double_divide(identity, inverse(inverse(Y)))), Y)
% 1.33/0.62 = { by lemma 5 R->L }
% 1.33/0.62 inverse(double_divide(Y, multiply(X, double_divide(identity, inverse(inverse(Y))))))
% 1.33/0.62 = { by lemma 7 }
% 1.33/0.62 inverse(inverse(X))
% 1.33/0.62
% 1.33/0.62 Lemma 23: multiply(inverse(inverse(X)), Y) = multiply(X, inverse(inverse(Y))).
% 1.33/0.62 Proof:
% 1.33/0.62 multiply(inverse(inverse(X)), Y)
% 1.33/0.62 = { by lemma 22 R->L }
% 1.33/0.62 multiply(multiply(multiply(X, inverse(inverse(Y))), inverse(Y)), Y)
% 1.33/0.62 = { by lemma 22 }
% 1.33/0.62 inverse(inverse(multiply(X, inverse(inverse(Y)))))
% 1.33/0.62 = { by lemma 18 }
% 1.33/0.62 multiply(X, inverse(inverse(Y)))
% 1.33/0.62
% 1.33/0.62 Lemma 24: multiply(inverse(multiply(X, Y)), Z) = multiply(double_divide(Y, X), inverse(inverse(Z))).
% 1.33/0.62 Proof:
% 1.33/0.62 multiply(inverse(multiply(X, Y)), Z)
% 1.33/0.62 = { by lemma 5 R->L }
% 1.33/0.62 multiply(inverse(inverse(double_divide(Y, X))), Z)
% 1.33/0.62 = { by lemma 23 }
% 1.33/0.62 multiply(double_divide(Y, X), inverse(inverse(Z)))
% 1.33/0.62
% 1.33/0.62 Lemma 25: multiply(inverse(X), inverse(inverse(Y))) = multiply(inverse(X), Y).
% 1.33/0.62 Proof:
% 1.33/0.62 multiply(inverse(X), inverse(inverse(Y)))
% 1.33/0.62 = { by lemma 21 R->L }
% 1.33/0.62 multiply(inverse(X), inverse(inverse(inverse(inverse(Y)))))
% 1.33/0.62 = { by lemma 23 R->L }
% 1.33/0.62 multiply(inverse(inverse(inverse(X))), inverse(inverse(Y)))
% 1.33/0.62 = { by lemma 20 R->L }
% 1.33/0.62 multiply(multiply(inverse(X), identity), inverse(inverse(Y)))
% 1.33/0.62 = { by lemma 17 R->L }
% 1.33/0.62 multiply(double_divide(identity, inverse(inverse(X))), inverse(inverse(Y)))
% 1.33/0.62 = { by lemma 24 R->L }
% 1.33/0.62 multiply(inverse(multiply(inverse(inverse(X)), identity)), Y)
% 1.33/0.62 = { by lemma 10 }
% 1.33/0.62 multiply(double_divide(X, inverse(identity)), Y)
% 1.33/0.62 = { by lemma 12 }
% 1.33/0.62 multiply(double_divide(X, identity), Y)
% 1.33/0.62 = { by axiom 1 (inverse) R->L }
% 1.33/0.62 multiply(inverse(X), Y)
% 1.33/0.62
% 1.33/0.62 Lemma 26: inverse(multiply(X, inverse(inverse(Y)))) = double_divide(Y, inverse(inverse(X))).
% 1.33/0.62 Proof:
% 1.33/0.62 inverse(multiply(X, inverse(inverse(Y))))
% 1.33/0.62 = { by lemma 20 R->L }
% 1.33/0.62 inverse(multiply(X, multiply(Y, identity)))
% 1.33/0.62 = { by lemma 12 R->L }
% 1.33/0.62 inverse(multiply(X, multiply(Y, inverse(identity))))
% 1.33/0.62 = { by lemma 12 R->L }
% 1.33/0.62 inverse(multiply(X, multiply(Y, inverse(inverse(identity)))))
% 1.33/0.62 = { by lemma 23 R->L }
% 1.33/0.62 inverse(multiply(X, multiply(inverse(inverse(Y)), identity)))
% 1.33/0.62 = { by lemma 5 R->L }
% 1.33/0.62 inverse(multiply(X, inverse(double_divide(identity, inverse(inverse(Y))))))
% 1.33/0.62 = { by lemma 7 R->L }
% 1.33/0.62 double_divide(Y, multiply(multiply(X, inverse(double_divide(identity, inverse(inverse(Y))))), double_divide(identity, inverse(inverse(Y)))))
% 1.33/0.62 = { by lemma 22 }
% 1.33/0.63 double_divide(Y, inverse(inverse(X)))
% 1.33/0.63
% 1.33/0.63 Lemma 27: inverse(multiply(inverse(X), Y)) = double_divide(Y, inverse(X)).
% 1.33/0.63 Proof:
% 1.33/0.63 inverse(multiply(inverse(X), Y))
% 1.33/0.63 = { by lemma 25 R->L }
% 1.33/0.63 inverse(multiply(inverse(X), inverse(inverse(Y))))
% 1.33/0.63 = { by lemma 26 }
% 1.33/0.63 double_divide(Y, inverse(inverse(inverse(X))))
% 1.33/0.63 = { by lemma 21 }
% 1.33/0.63 double_divide(Y, inverse(X))
% 1.33/0.63
% 1.33/0.63 Lemma 28: multiply(multiply(X, multiply(Y, Z)), inverse(multiply(Y, Z))) = inverse(inverse(X)).
% 1.33/0.63 Proof:
% 1.33/0.63 multiply(multiply(X, multiply(Y, Z)), inverse(multiply(Y, Z)))
% 1.33/0.63 = { by lemma 5 R->L }
% 1.33/0.63 multiply(multiply(X, multiply(Y, Z)), inverse(inverse(double_divide(Z, Y))))
% 1.33/0.63 = { by lemma 5 R->L }
% 1.33/0.63 multiply(multiply(X, inverse(double_divide(Z, Y))), inverse(inverse(double_divide(Z, Y))))
% 1.33/0.63 = { by lemma 20 R->L }
% 1.33/0.63 multiply(multiply(X, inverse(double_divide(Z, Y))), multiply(double_divide(Z, Y), identity))
% 1.33/0.63 = { by lemma 12 R->L }
% 1.33/0.63 multiply(multiply(X, inverse(double_divide(Z, Y))), multiply(double_divide(Z, Y), inverse(identity)))
% 1.33/0.63 = { by lemma 12 R->L }
% 1.33/0.63 multiply(multiply(X, inverse(double_divide(Z, Y))), multiply(double_divide(Z, Y), inverse(inverse(identity))))
% 1.33/0.63 = { by lemma 23 R->L }
% 1.33/0.63 multiply(multiply(X, inverse(double_divide(Z, Y))), multiply(inverse(inverse(double_divide(Z, Y))), identity))
% 1.33/0.63 = { by axiom 1 (inverse) }
% 1.33/0.63 multiply(multiply(X, double_divide(double_divide(Z, Y), identity)), multiply(inverse(inverse(double_divide(Z, Y))), identity))
% 1.33/0.63 = { by lemma 12 R->L }
% 1.33/0.63 multiply(multiply(X, double_divide(double_divide(Z, Y), inverse(identity))), multiply(inverse(inverse(double_divide(Z, Y))), identity))
% 1.33/0.63 = { by lemma 10 R->L }
% 1.33/0.63 multiply(multiply(X, inverse(multiply(inverse(inverse(double_divide(Z, Y))), identity))), multiply(inverse(inverse(double_divide(Z, Y))), identity))
% 1.33/0.63 = { by lemma 22 }
% 1.33/0.63 inverse(inverse(X))
% 1.33/0.63
% 1.33/0.63 Lemma 29: multiply(inverse(X), double_divide(inverse(X), Y)) = inverse(Y).
% 1.33/0.63 Proof:
% 1.33/0.63 multiply(inverse(X), double_divide(inverse(X), Y))
% 1.33/0.63 = { by lemma 25 R->L }
% 1.33/0.63 multiply(inverse(X), inverse(inverse(double_divide(inverse(X), Y))))
% 1.33/0.63 = { by lemma 5 }
% 1.33/0.63 multiply(inverse(X), inverse(multiply(Y, inverse(X))))
% 1.33/0.63 = { by lemma 7 R->L }
% 1.33/0.63 multiply(double_divide(Z, multiply(X, double_divide(identity, inverse(inverse(Z))))), inverse(multiply(Y, inverse(X))))
% 1.33/0.63 = { by axiom 1 (inverse) }
% 1.33/0.63 multiply(double_divide(Z, multiply(X, double_divide(identity, double_divide(inverse(Z), identity)))), inverse(multiply(Y, inverse(X))))
% 1.33/0.63 = { by lemma 6 R->L }
% 1.33/0.63 multiply(double_divide(Z, multiply(X, double_divide(identity, double_divide(inverse(Z), double_divide(X, multiply(inverse(Y), double_divide(identity, double_divide(inverse(X), double_divide(inverse(Y), identity))))))))), inverse(multiply(Y, inverse(X))))
% 1.33/0.63 = { by axiom 1 (inverse) R->L }
% 1.33/0.63 multiply(double_divide(Z, multiply(X, double_divide(identity, double_divide(inverse(Z), double_divide(X, multiply(inverse(Y), double_divide(identity, double_divide(inverse(X), inverse(inverse(Y)))))))))), inverse(multiply(Y, inverse(X))))
% 1.33/0.63 = { by lemma 27 R->L }
% 1.33/0.63 multiply(double_divide(Z, multiply(X, double_divide(identity, double_divide(inverse(Z), double_divide(X, multiply(inverse(Y), double_divide(identity, inverse(multiply(inverse(inverse(Y)), inverse(X)))))))))), inverse(multiply(Y, inverse(X))))
% 1.33/0.63 = { by lemma 17 }
% 1.33/0.63 multiply(double_divide(Z, multiply(X, double_divide(identity, double_divide(inverse(Z), double_divide(X, multiply(inverse(Y), multiply(multiply(inverse(inverse(Y)), inverse(X)), identity))))))), inverse(multiply(Y, inverse(X))))
% 1.33/0.63 = { by lemma 19 }
% 1.33/0.63 multiply(double_divide(Z, multiply(X, double_divide(identity, double_divide(inverse(Z), double_divide(X, multiply(inverse(Y), multiply(inverse(inverse(Y)), inverse(X)))))))), inverse(multiply(Y, inverse(X))))
% 1.33/0.63 = { by lemma 6 }
% 1.33/0.63 multiply(multiply(inverse(Y), multiply(inverse(inverse(Y)), inverse(X))), inverse(multiply(Y, inverse(X))))
% 1.33/0.63 = { by lemma 23 }
% 1.33/0.63 multiply(multiply(inverse(Y), multiply(Y, inverse(inverse(inverse(X))))), inverse(multiply(Y, inverse(X))))
% 1.33/0.63 = { by lemma 21 }
% 1.33/0.63 multiply(multiply(inverse(Y), multiply(Y, inverse(X))), inverse(multiply(Y, inverse(X))))
% 1.33/0.63 = { by lemma 28 }
% 1.33/0.63 inverse(inverse(inverse(Y)))
% 1.33/0.63 = { by lemma 21 }
% 1.33/0.63 inverse(Y)
% 1.33/0.63
% 1.33/0.63 Lemma 30: double_divide(X, multiply(Y, inverse(X))) = inverse(Y).
% 1.33/0.63 Proof:
% 1.33/0.63 double_divide(X, multiply(Y, inverse(X)))
% 1.33/0.63 = { by axiom 1 (inverse) }
% 1.33/0.63 double_divide(X, multiply(Y, double_divide(X, identity)))
% 1.33/0.63 = { by lemma 12 R->L }
% 1.33/0.63 double_divide(X, multiply(Y, double_divide(X, inverse(identity))))
% 1.33/0.63 = { by lemma 10 R->L }
% 1.33/0.63 double_divide(X, multiply(Y, inverse(multiply(inverse(inverse(X)), identity))))
% 1.33/0.63 = { by lemma 5 R->L }
% 1.33/0.63 double_divide(X, multiply(Y, inverse(inverse(double_divide(identity, inverse(inverse(X)))))))
% 1.33/0.63 = { by lemma 23 R->L }
% 1.33/0.63 double_divide(X, multiply(inverse(inverse(Y)), double_divide(identity, inverse(inverse(X)))))
% 1.33/0.63 = { by lemma 7 }
% 1.33/0.63 inverse(inverse(inverse(Y)))
% 1.33/0.63 = { by lemma 21 }
% 1.33/0.63 inverse(Y)
% 1.33/0.63
% 1.33/0.63 Lemma 31: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 1.33/0.63 Proof:
% 1.33/0.63 inverse(multiply(inverse(X), Y))
% 1.33/0.63 = { by lemma 29 R->L }
% 1.33/0.63 multiply(inverse(Y), double_divide(inverse(Y), multiply(inverse(X), Y)))
% 1.33/0.63 = { by lemma 25 R->L }
% 1.33/0.63 multiply(inverse(Y), double_divide(inverse(Y), multiply(inverse(X), inverse(inverse(Y)))))
% 1.33/0.63 = { by lemma 30 }
% 1.33/0.63 multiply(inverse(Y), inverse(inverse(X)))
% 1.33/0.63 = { by lemma 25 }
% 1.33/0.63 multiply(inverse(Y), X)
% 1.33/0.63
% 1.33/0.63 Lemma 32: double_divide(X, inverse(Y)) = multiply(inverse(X), Y).
% 1.33/0.63 Proof:
% 1.33/0.63 double_divide(X, inverse(Y))
% 1.33/0.63 = { by lemma 21 R->L }
% 1.33/0.63 double_divide(X, inverse(inverse(inverse(Y))))
% 1.33/0.63 = { by lemma 20 R->L }
% 1.33/0.63 double_divide(X, multiply(inverse(Y), identity))
% 1.33/0.63 = { by lemma 5 R->L }
% 1.33/0.63 double_divide(X, inverse(double_divide(identity, inverse(Y))))
% 1.33/0.63 = { by lemma 27 R->L }
% 1.33/0.63 inverse(multiply(inverse(double_divide(identity, inverse(Y))), X))
% 1.33/0.63 = { by lemma 5 }
% 1.33/0.63 inverse(multiply(multiply(inverse(Y), identity), X))
% 1.33/0.63 = { by lemma 17 R->L }
% 1.33/0.63 inverse(multiply(double_divide(identity, inverse(inverse(Y))), X))
% 1.33/0.63 = { by lemma 15 R->L }
% 1.33/0.63 inverse(multiply(inverse(multiply(Y, identity)), X))
% 1.33/0.63 = { by lemma 31 }
% 1.33/0.63 multiply(inverse(X), multiply(Y, identity))
% 1.33/0.63 = { by lemma 20 }
% 1.33/0.63 multiply(inverse(X), inverse(inverse(Y)))
% 1.33/0.63 = { by lemma 25 }
% 1.33/0.63 multiply(inverse(X), Y)
% 1.33/0.63
% 1.33/0.63 Lemma 33: inverse(inverse(X)) = X.
% 1.33/0.63 Proof:
% 1.33/0.63 inverse(inverse(X))
% 1.33/0.63 = { by lemma 20 R->L }
% 1.33/0.63 multiply(X, identity)
% 1.33/0.63 = { by lemma 5 R->L }
% 1.33/0.63 inverse(double_divide(identity, X))
% 1.33/0.63 = { by lemma 29 R->L }
% 1.33/0.63 multiply(inverse(Y), double_divide(inverse(Y), double_divide(identity, X)))
% 1.33/0.63 = { by lemma 25 R->L }
% 1.33/0.63 multiply(inverse(Y), inverse(inverse(double_divide(inverse(Y), double_divide(identity, X)))))
% 1.33/0.63 = { by lemma 20 R->L }
% 1.33/0.63 multiply(inverse(Y), multiply(double_divide(inverse(Y), double_divide(identity, X)), identity))
% 1.33/0.63 = { by lemma 5 R->L }
% 1.33/0.63 multiply(inverse(Y), inverse(double_divide(identity, double_divide(inverse(Y), double_divide(identity, X)))))
% 1.33/0.63 = { by lemma 32 R->L }
% 1.33/0.63 double_divide(Y, inverse(inverse(double_divide(identity, double_divide(inverse(Y), double_divide(identity, X))))))
% 1.33/0.63 = { by lemma 8 R->L }
% 1.33/0.63 double_divide(Y, multiply(identity, double_divide(identity, double_divide(inverse(Y), double_divide(identity, X)))))
% 1.33/0.63 = { by lemma 6 }
% 1.33/0.63 X
% 1.33/0.63
% 1.33/0.63 Lemma 34: inverse(multiply(X, Y)) = double_divide(Y, X).
% 1.33/0.63 Proof:
% 1.33/0.63 inverse(multiply(X, Y))
% 1.33/0.63 = { by lemma 5 R->L }
% 1.33/0.63 inverse(inverse(double_divide(Y, X)))
% 1.33/0.63 = { by lemma 33 }
% 1.33/0.63 double_divide(Y, X)
% 1.33/0.63
% 1.33/0.63 Lemma 35: double_divide(X, Y) = multiply(inverse(X), inverse(Y)).
% 1.33/0.63 Proof:
% 1.33/0.63 double_divide(X, Y)
% 1.33/0.63 = { by lemma 34 R->L }
% 1.33/0.63 inverse(multiply(Y, X))
% 1.33/0.63 = { by lemma 33 R->L }
% 1.33/0.63 inverse(multiply(Y, inverse(inverse(X))))
% 1.33/0.63 = { by lemma 26 }
% 1.33/0.63 double_divide(X, inverse(inverse(Y)))
% 1.33/0.63 = { by lemma 32 }
% 1.33/0.63 multiply(inverse(X), inverse(Y))
% 1.33/0.63
% 1.33/0.63 Lemma 36: multiply(X, double_divide(X, Y)) = inverse(Y).
% 1.33/0.63 Proof:
% 1.33/0.63 multiply(X, double_divide(X, Y))
% 1.33/0.63 = { by lemma 33 R->L }
% 1.33/0.63 multiply(X, double_divide(inverse(inverse(X)), Y))
% 1.33/0.63 = { by lemma 20 R->L }
% 1.33/0.63 multiply(X, double_divide(multiply(X, identity), Y))
% 1.33/0.63 = { by lemma 17 R->L }
% 1.33/0.63 multiply(X, double_divide(double_divide(identity, inverse(X)), Y))
% 1.33/0.63 = { by lemma 33 R->L }
% 1.33/0.63 multiply(X, inverse(inverse(double_divide(double_divide(identity, inverse(X)), Y))))
% 1.33/0.63 = { by lemma 23 R->L }
% 1.33/0.63 multiply(inverse(inverse(X)), double_divide(double_divide(identity, inverse(X)), Y))
% 1.33/0.63 = { by lemma 32 R->L }
% 1.33/0.63 double_divide(inverse(X), inverse(double_divide(double_divide(identity, inverse(X)), Y)))
% 1.33/0.63 = { by lemma 5 }
% 1.33/0.64 double_divide(inverse(X), multiply(Y, double_divide(identity, inverse(X))))
% 1.33/0.64 = { by lemma 33 R->L }
% 1.33/0.64 double_divide(inverse(X), multiply(Y, double_divide(identity, inverse(inverse(inverse(X))))))
% 1.33/0.64 = { by lemma 7 }
% 1.33/0.64 inverse(Y)
% 1.33/0.64
% 1.33/0.64 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3)) = tuple(identity, a2, multiply(a3, multiply(b3, c3))).
% 1.33/0.64 Proof:
% 1.33/0.64 tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3))
% 1.33/0.64 = { by lemma 8 }
% 1.33/0.64 tuple(multiply(inverse(a1), a1), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 1.33/0.64 = { by lemma 9 }
% 1.33/0.64 tuple(inverse(identity), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 1.33/0.64 = { by lemma 12 }
% 1.33/0.64 tuple(identity, inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 1.33/0.64 = { by lemma 33 }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(a3, b3), c3))
% 1.33/0.64 = { by lemma 33 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(a3, inverse(inverse(b3))), c3))
% 1.33/0.64 = { by lemma 23 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), b3), c3))
% 1.33/0.64 = { by lemma 31 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), c3))
% 1.33/0.64 = { by lemma 35 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(inverse(double_divide(b3, a3)), c3))
% 1.33/0.64 = { by lemma 6 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(inverse(double_divide(double_divide(a3, multiply(c3, double_divide(identity, double_divide(inverse(a3), double_divide(c3, b3))))), a3)), c3))
% 1.33/0.64 = { by lemma 34 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(inverse(inverse(multiply(a3, double_divide(a3, multiply(c3, double_divide(identity, double_divide(inverse(a3), double_divide(c3, b3)))))))), c3))
% 1.33/0.64 = { by lemma 36 }
% 1.33/0.64 tuple(identity, a2, multiply(inverse(inverse(inverse(multiply(c3, double_divide(identity, double_divide(inverse(a3), double_divide(c3, b3))))))), c3))
% 1.33/0.64 = { by lemma 33 }
% 1.33/0.64 tuple(identity, a2, multiply(inverse(multiply(c3, double_divide(identity, double_divide(inverse(a3), double_divide(c3, b3))))), c3))
% 1.33/0.64 = { by lemma 33 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(inverse(multiply(c3, inverse(inverse(double_divide(identity, double_divide(inverse(a3), double_divide(c3, b3))))))), c3))
% 1.33/0.64 = { by lemma 8 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(inverse(multiply(c3, multiply(identity, double_divide(identity, double_divide(inverse(a3), double_divide(c3, b3)))))), c3))
% 1.33/0.64 = { by lemma 36 }
% 1.33/0.64 tuple(identity, a2, multiply(inverse(multiply(c3, inverse(double_divide(inverse(a3), double_divide(c3, b3))))), c3))
% 1.33/0.64 = { by lemma 5 }
% 1.33/0.64 tuple(identity, a2, multiply(inverse(multiply(c3, multiply(double_divide(c3, b3), inverse(a3)))), c3))
% 1.33/0.64 = { by lemma 35 }
% 1.33/0.64 tuple(identity, a2, multiply(inverse(multiply(c3, multiply(multiply(inverse(c3), inverse(b3)), inverse(a3)))), c3))
% 1.33/0.64 = { by lemma 30 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(double_divide(multiply(multiply(inverse(c3), inverse(b3)), inverse(a3)), multiply(multiply(c3, multiply(multiply(inverse(c3), inverse(b3)), inverse(a3))), inverse(multiply(multiply(inverse(c3), inverse(b3)), inverse(a3))))), c3))
% 1.33/0.64 = { by lemma 28 }
% 1.33/0.64 tuple(identity, a2, multiply(double_divide(multiply(multiply(inverse(c3), inverse(b3)), inverse(a3)), inverse(inverse(c3))), c3))
% 1.33/0.64 = { by lemma 32 }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(inverse(multiply(multiply(inverse(c3), inverse(b3)), inverse(a3))), inverse(c3)), c3))
% 1.33/0.64 = { by lemma 24 }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(double_divide(inverse(a3), multiply(inverse(c3), inverse(b3))), inverse(inverse(inverse(c3)))), c3))
% 1.33/0.64 = { by lemma 21 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(double_divide(inverse(inverse(inverse(a3))), multiply(inverse(c3), inverse(b3))), inverse(inverse(inverse(c3)))), c3))
% 1.33/0.64 = { by lemma 20 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(double_divide(multiply(inverse(a3), identity), multiply(inverse(c3), inverse(b3))), inverse(inverse(inverse(c3)))), c3))
% 1.33/0.64 = { by lemma 17 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(double_divide(double_divide(identity, inverse(inverse(a3))), multiply(inverse(c3), inverse(b3))), inverse(inverse(inverse(c3)))), c3))
% 1.33/0.64 = { by lemma 34 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(inverse(multiply(multiply(inverse(c3), inverse(b3)), double_divide(identity, inverse(inverse(a3))))), inverse(inverse(inverse(c3)))), c3))
% 1.33/0.64 = { by lemma 36 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(multiply(a3, double_divide(a3, multiply(multiply(inverse(c3), inverse(b3)), double_divide(identity, inverse(inverse(a3)))))), inverse(inverse(inverse(c3)))), c3))
% 1.33/0.64 = { by lemma 7 }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(multiply(a3, inverse(multiply(inverse(c3), inverse(b3)))), inverse(inverse(inverse(c3)))), c3))
% 1.33/0.64 = { by lemma 23 R->L }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(inverse(inverse(multiply(a3, inverse(multiply(inverse(c3), inverse(b3)))))), inverse(c3)), c3))
% 1.33/0.64 = { by lemma 18 }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(multiply(a3, inverse(multiply(inverse(c3), inverse(b3)))), inverse(c3)), c3))
% 1.33/0.64 = { by lemma 31 }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(multiply(a3, multiply(inverse(inverse(b3)), c3)), inverse(c3)), c3))
% 1.33/0.64 = { by lemma 23 }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(multiply(a3, multiply(b3, inverse(inverse(c3)))), inverse(c3)), c3))
% 1.33/0.64 = { by lemma 33 }
% 1.33/0.64 tuple(identity, a2, multiply(multiply(multiply(a3, multiply(b3, c3)), inverse(c3)), c3))
% 1.33/0.64 = { by lemma 22 }
% 1.33/0.64 tuple(identity, a2, inverse(inverse(multiply(a3, multiply(b3, c3)))))
% 1.33/0.64 = { by lemma 18 }
% 1.33/0.64 tuple(identity, a2, multiply(a3, multiply(b3, c3)))
% 1.33/0.64 % SZS output end Proof
% 1.33/0.64
% 1.33/0.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------