%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP076-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP076-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % 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 09:16:09 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 Command-line arguments: --no-flatten-goal
% 0.20/0.48
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.20/0.52 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.20/0.52 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.20/0.52 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(double_divide(X, Y), Z), double_divide(Y, identity))), double_divide(identity, identity)) = Z.
% 0.20/0.52
% 0.20/0.52 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.20/0.52 Proof:
% 0.20/0.52 inverse(double_divide(X, Y))
% 0.20/0.52 = { by axiom 1 (inverse) }
% 0.20/0.52 double_divide(double_divide(X, Y), identity)
% 0.20/0.52 = { by axiom 3 (multiply) R->L }
% 0.20/0.52 multiply(Y, X)
% 0.20/0.52
% 0.20/0.52 Lemma 6: multiply(identity, X) = inverse(inverse(X)).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(identity, X)
% 0.20/0.52 = { by lemma 5 R->L }
% 0.20/0.52 inverse(double_divide(X, identity))
% 0.20/0.52 = { by axiom 1 (inverse) R->L }
% 0.20/0.52 inverse(inverse(X))
% 0.20/0.52
% 0.20/0.52 Lemma 7: double_divide(double_divide(X, double_divide(double_divide(double_divide(X, Y), Z), inverse(Y))), inverse(identity)) = Z.
% 0.20/0.52 Proof:
% 0.20/0.52 double_divide(double_divide(X, double_divide(double_divide(double_divide(X, Y), Z), inverse(Y))), inverse(identity))
% 0.20/0.52 = { by axiom 1 (inverse) }
% 0.20/0.52 double_divide(double_divide(X, double_divide(double_divide(double_divide(X, Y), Z), inverse(Y))), double_divide(identity, identity))
% 0.20/0.52 = { by axiom 1 (inverse) }
% 0.20/0.52 double_divide(double_divide(X, double_divide(double_divide(double_divide(X, Y), Z), double_divide(Y, identity))), double_divide(identity, identity))
% 0.20/0.52 = { by axiom 4 (single_axiom) }
% 0.20/0.52 Z
% 0.20/0.52
% 0.20/0.52 Lemma 8: double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity)) = multiply(Y, X).
% 0.20/0.52 Proof:
% 0.20/0.52 double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity))
% 0.20/0.52 = { by axiom 2 (identity) }
% 0.20/0.52 double_divide(double_divide(X, double_divide(double_divide(double_divide(X, Y), inverse(double_divide(X, Y))), inverse(Y))), inverse(identity))
% 0.20/0.52 = { by lemma 7 }
% 0.20/0.52 inverse(double_divide(X, Y))
% 0.20/0.52 = { by lemma 5 }
% 0.20/0.52 multiply(Y, X)
% 0.20/0.52
% 0.20/0.52 Lemma 9: double_divide(double_divide(double_divide(inverse(X), Y), Z), inverse(Y)) = double_divide(double_divide(X, Z), inverse(identity)).
% 0.20/0.52 Proof:
% 0.20/0.52 double_divide(double_divide(double_divide(inverse(X), Y), Z), inverse(Y))
% 0.20/0.52 = { by axiom 1 (inverse) }
% 0.20/0.52 double_divide(double_divide(double_divide(double_divide(X, identity), Y), Z), inverse(Y))
% 0.20/0.52 = { by lemma 7 R->L }
% 0.20/0.52 double_divide(double_divide(X, double_divide(double_divide(double_divide(X, identity), double_divide(double_divide(double_divide(double_divide(X, identity), Y), Z), inverse(Y))), inverse(identity))), inverse(identity))
% 0.20/0.52 = { by lemma 7 }
% 0.20/0.52 double_divide(double_divide(X, Z), inverse(identity))
% 0.20/0.52
% 0.20/0.52 Lemma 10: multiply(X, inverse(inverse(Y))) = multiply(X, Y).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(X, inverse(inverse(Y)))
% 0.20/0.52 = { by axiom 1 (inverse) }
% 0.20/0.52 multiply(X, double_divide(inverse(Y), identity))
% 0.20/0.52 = { by lemma 8 R->L }
% 0.20/0.52 double_divide(double_divide(double_divide(inverse(Y), identity), double_divide(identity, inverse(X))), inverse(identity))
% 0.20/0.52 = { by lemma 9 }
% 0.20/0.52 double_divide(double_divide(Y, double_divide(identity, inverse(X))), inverse(identity))
% 0.20/0.52 = { by lemma 8 }
% 0.20/0.52 multiply(X, Y)
% 0.20/0.52
% 0.20/0.52 Lemma 11: inverse(inverse(inverse(inverse(X)))) = inverse(inverse(X)).
% 0.20/0.52 Proof:
% 0.20/0.52 inverse(inverse(inverse(inverse(X))))
% 0.20/0.52 = { by lemma 6 R->L }
% 0.20/0.52 multiply(identity, inverse(inverse(X)))
% 0.20/0.52 = { by lemma 10 }
% 0.20/0.52 multiply(identity, X)
% 0.20/0.52 = { by lemma 6 }
% 0.20/0.52 inverse(inverse(X))
% 0.20/0.52
% 0.20/0.52 Lemma 12: double_divide(inverse(X), inverse(identity)) = inverse(inverse(X)).
% 0.20/0.52 Proof:
% 0.20/0.52 double_divide(inverse(X), inverse(identity))
% 0.20/0.52 = { by axiom 1 (inverse) }
% 0.20/0.52 double_divide(double_divide(X, identity), inverse(identity))
% 0.20/0.52 = { by axiom 2 (identity) }
% 0.20/0.52 double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
% 0.20/0.52 = { by lemma 8 }
% 0.20/0.52 multiply(identity, X)
% 0.20/0.52 = { by lemma 6 }
% 0.20/0.52 inverse(inverse(X))
% 0.20/0.52
% 0.20/0.52 Lemma 13: multiply(inverse(X), X) = inverse(identity).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(inverse(X), X)
% 0.20/0.52 = { by lemma 5 R->L }
% 0.20/0.52 inverse(double_divide(X, inverse(X)))
% 0.20/0.52 = { by axiom 2 (identity) R->L }
% 0.20/0.52 inverse(identity)
% 0.20/0.52
% 0.20/0.52 Lemma 14: inverse(inverse(identity)) = inverse(identity).
% 0.20/0.52 Proof:
% 0.20/0.52 inverse(inverse(identity))
% 0.20/0.52 = { by lemma 11 R->L }
% 0.20/0.52 inverse(inverse(inverse(inverse(identity))))
% 0.20/0.52 = { by lemma 12 R->L }
% 0.20/0.52 inverse(double_divide(inverse(inverse(identity)), inverse(identity)))
% 0.20/0.52 = { by lemma 5 }
% 0.20/0.52 multiply(inverse(identity), inverse(inverse(identity)))
% 0.20/0.52 = { by lemma 10 }
% 0.20/0.52 multiply(inverse(identity), identity)
% 0.20/0.52 = { by lemma 13 }
% 0.20/0.52 inverse(identity)
% 0.20/0.52
% 0.20/0.52 Lemma 15: inverse(identity) = identity.
% 0.20/0.52 Proof:
% 0.20/0.52 inverse(identity)
% 0.20/0.52 = { by lemma 14 R->L }
% 0.20/0.52 inverse(inverse(identity))
% 0.20/0.52 = { by lemma 12 R->L }
% 0.20/0.52 double_divide(inverse(identity), inverse(identity))
% 0.20/0.52 = { by lemma 14 R->L }
% 0.20/0.52 double_divide(inverse(identity), inverse(inverse(identity)))
% 0.20/0.52 = { by axiom 2 (identity) R->L }
% 0.20/0.52 identity
% 0.20/0.52
% 0.20/0.52 Lemma 16: multiply(multiply(X, inverse(Y)), Y) = X.
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(multiply(X, inverse(Y)), Y)
% 0.20/0.52 = { by lemma 5 R->L }
% 0.20/0.52 inverse(double_divide(Y, multiply(X, inverse(Y))))
% 0.20/0.52 = { by axiom 1 (inverse) }
% 0.20/0.52 double_divide(double_divide(Y, multiply(X, inverse(Y))), identity)
% 0.20/0.52 = { by lemma 15 R->L }
% 0.20/0.52 double_divide(double_divide(Y, multiply(X, inverse(Y))), inverse(identity))
% 0.20/0.52 = { by axiom 1 (inverse) }
% 0.20/0.52 double_divide(double_divide(Y, multiply(X, double_divide(Y, identity))), inverse(identity))
% 0.20/0.52 = { by lemma 5 R->L }
% 0.20/0.52 double_divide(double_divide(Y, inverse(double_divide(double_divide(Y, identity), X))), inverse(identity))
% 0.20/0.52 = { by axiom 1 (inverse) }
% 0.20/0.52 double_divide(double_divide(Y, double_divide(double_divide(double_divide(Y, identity), X), identity)), inverse(identity))
% 0.20/0.52 = { by lemma 15 R->L }
% 0.20/0.52 double_divide(double_divide(Y, double_divide(double_divide(double_divide(Y, identity), X), inverse(identity))), inverse(identity))
% 0.20/0.52 = { by lemma 7 }
% 0.20/0.52 X
% 0.20/0.52
% 0.20/0.52 Lemma 17: multiply(X, inverse(multiply(Y, Z))) = multiply(X, double_divide(Z, Y)).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(X, inverse(multiply(Y, Z)))
% 0.20/0.52 = { by lemma 5 R->L }
% 0.20/0.52 multiply(X, inverse(inverse(double_divide(Z, Y))))
% 0.20/0.52 = { by lemma 10 }
% 0.20/0.52 multiply(X, double_divide(Z, Y))
% 0.20/0.52
% 0.20/0.52 Lemma 18: double_divide(multiply(X, inverse(Y)), inverse(X)) = inverse(inverse(Y)).
% 0.20/0.52 Proof:
% 0.20/0.52 double_divide(multiply(X, inverse(Y)), inverse(X))
% 0.20/0.52 = { by lemma 5 R->L }
% 0.20/0.52 double_divide(inverse(double_divide(inverse(Y), X)), inverse(X))
% 0.20/0.52 = { by axiom 1 (inverse) }
% 0.20/0.52 double_divide(double_divide(double_divide(inverse(Y), X), identity), inverse(X))
% 0.20/0.52 = { by lemma 9 }
% 0.20/0.52 double_divide(double_divide(Y, identity), inverse(identity))
% 0.20/0.52 = { by axiom 1 (inverse) R->L }
% 0.20/0.52 double_divide(inverse(Y), inverse(identity))
% 0.20/0.52 = { by lemma 12 }
% 0.20/0.52 inverse(inverse(Y))
% 0.20/0.52
% 0.20/0.52 Lemma 19: double_divide(multiply(X, Y), inverse(X)) = inverse(inverse(inverse(Y))).
% 0.20/0.52 Proof:
% 0.20/0.52 double_divide(multiply(X, Y), inverse(X))
% 0.20/0.52 = { by lemma 10 R->L }
% 0.20/0.52 double_divide(multiply(X, inverse(inverse(Y))), inverse(X))
% 0.20/0.52 = { by lemma 18 }
% 0.20/0.52 inverse(inverse(inverse(Y)))
% 0.20/0.52
% 0.20/0.52 Lemma 20: multiply(inverse(X), multiply(X, Y)) = inverse(inverse(Y)).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(inverse(X), multiply(X, Y))
% 0.20/0.52 = { by lemma 5 R->L }
% 0.20/0.52 inverse(double_divide(multiply(X, Y), inverse(X)))
% 0.20/0.52 = { by lemma 19 }
% 0.20/0.52 inverse(inverse(inverse(inverse(Y))))
% 0.20/0.52 = { by lemma 11 }
% 0.20/0.52 inverse(inverse(Y))
% 0.20/0.52
% 0.20/0.52 Lemma 21: inverse(inverse(multiply(X, Y))) = multiply(inverse(inverse(X)), Y).
% 0.20/0.52 Proof:
% 0.20/0.52 inverse(inverse(multiply(X, Y)))
% 0.20/0.52 = { by lemma 20 R->L }
% 0.20/0.52 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
% 0.20/0.52 = { by lemma 20 }
% 0.20/0.52 multiply(inverse(inverse(X)), inverse(inverse(Y)))
% 0.20/0.52 = { by lemma 10 }
% 0.20/0.52 multiply(inverse(inverse(X)), Y)
% 0.20/0.52
% 0.20/0.52 Lemma 22: inverse(multiply(inverse(inverse(X)), Y)) = inverse(multiply(X, Y)).
% 0.20/0.52 Proof:
% 0.20/0.52 inverse(multiply(inverse(inverse(X)), Y))
% 0.20/0.52 = { by lemma 21 R->L }
% 0.20/0.52 inverse(inverse(inverse(multiply(X, Y))))
% 0.20/0.52 = { by lemma 5 R->L }
% 0.20/0.52 inverse(inverse(inverse(inverse(double_divide(Y, X)))))
% 0.20/0.52 = { by lemma 11 }
% 0.20/0.52 inverse(inverse(double_divide(Y, X)))
% 0.20/0.52 = { by lemma 5 }
% 0.20/0.52 inverse(multiply(X, Y))
% 0.20/0.52
% 0.20/0.52 Lemma 23: multiply(inverse(inverse(X)), identity) = inverse(inverse(X)).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(inverse(inverse(X)), identity)
% 0.20/0.52 = { by lemma 5 R->L }
% 0.20/0.52 inverse(double_divide(identity, inverse(inverse(X))))
% 0.20/0.52 = { by lemma 15 R->L }
% 0.20/0.52 inverse(double_divide(inverse(identity), inverse(inverse(X))))
% 0.20/0.52 = { by lemma 13 R->L }
% 0.20/0.52 inverse(double_divide(multiply(inverse(X), X), inverse(inverse(X))))
% 0.20/0.52 = { by lemma 19 }
% 0.20/0.52 inverse(inverse(inverse(inverse(X))))
% 0.20/0.52 = { by lemma 11 }
% 0.20/0.52 inverse(inverse(X))
% 0.20/0.52
% 0.20/0.52 Lemma 24: multiply(X, double_divide(identity, Y)) = multiply(X, inverse(Y)).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(X, double_divide(identity, Y))
% 0.20/0.52 = { by lemma 17 R->L }
% 0.20/0.52 multiply(X, inverse(multiply(Y, identity)))
% 0.20/0.52 = { by lemma 22 R->L }
% 0.20/0.52 multiply(X, inverse(multiply(inverse(inverse(Y)), identity)))
% 0.20/0.52 = { by lemma 23 }
% 0.20/0.52 multiply(X, inverse(inverse(inverse(Y))))
% 0.20/0.52 = { by lemma 10 }
% 0.20/0.52 multiply(X, inverse(Y))
% 0.20/0.52
% 0.20/0.52 Lemma 25: multiply(identity, X) = X.
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(identity, X)
% 0.20/0.52 = { by lemma 15 R->L }
% 0.20/0.52 multiply(inverse(identity), X)
% 0.20/0.52 = { by lemma 13 R->L }
% 0.20/0.52 multiply(multiply(inverse(double_divide(identity, multiply(X, identity))), double_divide(identity, multiply(X, identity))), X)
% 0.20/0.52 = { by lemma 5 }
% 0.20/0.52 multiply(multiply(multiply(multiply(X, identity), identity), double_divide(identity, multiply(X, identity))), X)
% 0.20/0.52 = { by lemma 15 R->L }
% 0.20/0.52 multiply(multiply(multiply(multiply(X, inverse(identity)), identity), double_divide(identity, multiply(X, identity))), X)
% 0.20/0.52 = { by lemma 15 R->L }
% 0.20/0.52 multiply(multiply(multiply(multiply(X, inverse(identity)), inverse(identity)), double_divide(identity, multiply(X, identity))), X)
% 0.20/0.53 = { by lemma 14 R->L }
% 0.20/0.53 multiply(multiply(multiply(multiply(X, inverse(inverse(identity))), inverse(identity)), double_divide(identity, multiply(X, identity))), X)
% 0.20/0.53 = { by lemma 16 }
% 0.20/0.53 multiply(multiply(X, double_divide(identity, multiply(X, identity))), X)
% 0.20/0.53 = { by lemma 24 }
% 0.20/0.53 multiply(multiply(X, inverse(multiply(X, identity))), X)
% 0.20/0.53 = { by lemma 17 }
% 0.20/0.53 multiply(multiply(X, double_divide(identity, X)), X)
% 0.20/0.53 = { by lemma 24 }
% 0.20/0.53 multiply(multiply(X, inverse(X)), X)
% 0.20/0.53 = { by lemma 16 }
% 0.20/0.53 X
% 0.20/0.53
% 0.20/0.53 Lemma 26: inverse(inverse(X)) = X.
% 0.20/0.53 Proof:
% 0.20/0.53 inverse(inverse(X))
% 0.20/0.53 = { by lemma 6 R->L }
% 0.20/0.53 multiply(identity, X)
% 0.20/0.53 = { by lemma 25 }
% 0.20/0.53 X
% 0.20/0.53
% 0.20/0.53 Lemma 27: multiply(inverse(X), identity) = inverse(inverse(inverse(X))).
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(inverse(X), identity)
% 0.20/0.53 = { by lemma 8 R->L }
% 0.20/0.53 double_divide(double_divide(identity, double_divide(identity, inverse(inverse(X)))), inverse(identity))
% 0.20/0.53 = { by lemma 11 R->L }
% 0.20/0.53 double_divide(double_divide(identity, double_divide(identity, inverse(inverse(inverse(inverse(X)))))), inverse(identity))
% 0.20/0.53 = { by lemma 8 }
% 0.20/0.53 multiply(inverse(inverse(inverse(X))), identity)
% 0.20/0.53 = { by lemma 23 }
% 0.20/0.53 inverse(inverse(inverse(X)))
% 0.20/0.53
% 0.20/0.53 Lemma 28: inverse(multiply(X, Y)) = double_divide(Y, X).
% 0.20/0.53 Proof:
% 0.20/0.53 inverse(multiply(X, Y))
% 0.20/0.53 = { by lemma 26 R->L }
% 0.20/0.53 inverse(inverse(inverse(multiply(X, Y))))
% 0.20/0.53 = { by lemma 27 R->L }
% 0.20/0.53 multiply(inverse(multiply(X, Y)), identity)
% 0.20/0.53 = { by lemma 5 R->L }
% 0.20/0.53 multiply(inverse(inverse(double_divide(Y, X))), identity)
% 0.20/0.53 = { by lemma 23 }
% 0.20/0.53 inverse(inverse(double_divide(Y, X)))
% 0.20/0.53 = { by lemma 26 }
% 0.20/0.53 double_divide(Y, X)
% 0.20/0.53
% 0.20/0.53 Lemma 29: multiply(double_divide(X, Y), Y) = inverse(X).
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(double_divide(X, Y), Y)
% 0.20/0.53 = { by lemma 28 R->L }
% 0.20/0.53 multiply(inverse(multiply(Y, X)), Y)
% 0.20/0.53 = { by lemma 16 R->L }
% 0.20/0.53 multiply(inverse(multiply(Y, X)), multiply(multiply(Y, inverse(inverse(X))), inverse(X)))
% 0.20/0.53 = { by lemma 10 }
% 0.20/0.53 multiply(inverse(multiply(Y, X)), multiply(multiply(Y, X), inverse(X)))
% 0.20/0.53 = { by lemma 20 }
% 0.20/0.53 inverse(inverse(inverse(X)))
% 0.20/0.53 = { by lemma 26 }
% 0.20/0.53 inverse(X)
% 0.20/0.53
% 0.20/0.53 Lemma 30: double_divide(X, inverse(Y)) = multiply(inverse(X), Y).
% 0.20/0.53 Proof:
% 0.20/0.53 double_divide(X, inverse(Y))
% 0.20/0.53 = { by lemma 16 R->L }
% 0.20/0.53 multiply(multiply(double_divide(X, inverse(Y)), inverse(Y)), Y)
% 0.20/0.53 = { by lemma 29 }
% 0.20/0.53 multiply(inverse(X), Y)
% 0.20/0.53
% 0.20/0.53 Lemma 31: multiply(multiply(X, multiply(Y, inverse(Z))), Z) = multiply(X, Y).
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(multiply(X, multiply(Y, inverse(Z))), Z)
% 0.20/0.53 = { by lemma 25 R->L }
% 0.20/0.53 multiply(multiply(X, multiply(multiply(identity, Y), inverse(Z))), Z)
% 0.20/0.53 = { by lemma 5 R->L }
% 0.20/0.53 multiply(multiply(X, multiply(inverse(double_divide(Y, identity)), inverse(Z))), Z)
% 0.20/0.53 = { by lemma 26 R->L }
% 0.20/0.53 multiply(multiply(X, multiply(inverse(inverse(inverse(double_divide(Y, identity)))), inverse(Z))), Z)
% 0.20/0.53 = { by lemma 18 R->L }
% 0.20/0.53 multiply(multiply(X, multiply(double_divide(multiply(Z, inverse(inverse(double_divide(Y, identity)))), inverse(Z)), inverse(Z))), Z)
% 0.20/0.53 = { by lemma 29 }
% 0.20/0.53 multiply(multiply(X, inverse(multiply(Z, inverse(inverse(double_divide(Y, identity)))))), Z)
% 0.20/0.53 = { by lemma 28 }
% 0.20/0.53 multiply(multiply(X, double_divide(inverse(inverse(double_divide(Y, identity))), Z)), Z)
% 0.20/0.53 = { by lemma 20 R->L }
% 0.20/0.53 multiply(multiply(X, double_divide(multiply(inverse(Z), multiply(Z, double_divide(Y, identity))), Z)), Z)
% 0.20/0.53 = { by lemma 28 R->L }
% 0.20/0.53 multiply(multiply(X, inverse(multiply(Z, multiply(inverse(Z), multiply(Z, double_divide(Y, identity)))))), Z)
% 0.20/0.53 = { by lemma 22 R->L }
% 0.20/0.53 multiply(multiply(X, inverse(multiply(inverse(inverse(Z)), multiply(inverse(Z), multiply(Z, double_divide(Y, identity)))))), Z)
% 0.20/0.53 = { by lemma 20 }
% 0.20/0.53 multiply(multiply(X, inverse(inverse(inverse(multiply(Z, double_divide(Y, identity)))))), Z)
% 0.20/0.53 = { by lemma 26 }
% 0.20/0.53 multiply(multiply(X, inverse(multiply(Z, double_divide(Y, identity)))), Z)
% 0.20/0.53 = { by lemma 28 }
% 0.20/0.53 multiply(multiply(X, double_divide(double_divide(Y, identity), Z)), Z)
% 0.20/0.53 = { by lemma 5 R->L }
% 0.20/0.53 multiply(inverse(double_divide(double_divide(double_divide(Y, identity), Z), X)), Z)
% 0.20/0.53 = { by lemma 30 R->L }
% 0.20/0.53 double_divide(double_divide(double_divide(double_divide(Y, identity), Z), X), inverse(Z))
% 0.20/0.53 = { by lemma 7 R->L }
% 0.20/0.53 double_divide(double_divide(Y, double_divide(double_divide(double_divide(Y, identity), double_divide(double_divide(double_divide(double_divide(Y, identity), Z), X), inverse(Z))), inverse(identity))), inverse(identity))
% 0.20/0.53 = { by lemma 7 }
% 0.20/0.53 double_divide(double_divide(Y, X), inverse(identity))
% 0.20/0.53 = { by lemma 30 }
% 0.20/0.53 multiply(inverse(double_divide(Y, X)), identity)
% 0.20/0.53 = { by lemma 27 }
% 0.20/0.53 inverse(inverse(inverse(double_divide(Y, X))))
% 0.20/0.53 = { by lemma 26 }
% 0.20/0.53 inverse(double_divide(Y, X))
% 0.20/0.53 = { by lemma 5 }
% 0.20/0.53 multiply(X, Y)
% 0.20/0.53
% 0.20/0.53 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))).
% 0.20/0.53 Proof:
% 0.20/0.53 tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3))
% 0.20/0.53 = { by lemma 6 }
% 0.20/0.53 tuple(multiply(inverse(a1), a1), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.20/0.53 = { by lemma 13 }
% 0.20/0.53 tuple(inverse(identity), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.20/0.53 = { by lemma 15 }
% 0.20/0.53 tuple(identity, inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.20/0.53 = { by lemma 26 }
% 0.20/0.53 tuple(identity, a2, multiply(multiply(a3, b3), c3))
% 0.20/0.53 = { by lemma 26 R->L }
% 0.20/0.53 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), b3), c3))
% 0.20/0.53 = { by lemma 21 R->L }
% 0.20/0.53 tuple(identity, a2, multiply(inverse(inverse(multiply(a3, b3))), c3))
% 0.20/0.53 = { by lemma 6 R->L }
% 0.20/0.53 tuple(identity, a2, multiply(multiply(identity, multiply(a3, b3)), c3))
% 0.20/0.53 = { by lemma 31 R->L }
% 0.20/0.53 tuple(identity, a2, multiply(multiply(identity, multiply(multiply(a3, multiply(b3, inverse(inverse(c3)))), inverse(c3))), c3))
% 0.20/0.53 = { by lemma 31 }
% 0.20/0.53 tuple(identity, a2, multiply(identity, multiply(a3, multiply(b3, inverse(inverse(c3))))))
% 0.20/0.53 = { by lemma 10 }
% 0.20/0.53 tuple(identity, a2, multiply(identity, multiply(a3, multiply(b3, c3))))
% 0.20/0.53 = { by lemma 25 }
% 0.20/0.53 tuple(identity, a2, multiply(a3, multiply(b3, c3)))
% 0.20/0.53 % SZS output end Proof
% 0.20/0.53
% 0.20/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------