TSTP Solution File: GRP579-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP579-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:18:59 EDT 2023
% Result : Unsatisfiable 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP579-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 02:45:25 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.46 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.46
% 0.21/0.46 % SZS status Unsatisfiable
% 0.21/0.46
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.21/0.49 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.21/0.49 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.21/0.49 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.
% 0.21/0.49
% 0.21/0.49 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.21/0.49 Proof:
% 0.21/0.49 inverse(double_divide(X, Y))
% 0.21/0.49 = { by axiom 1 (inverse) }
% 0.21/0.49 double_divide(double_divide(X, Y), identity)
% 0.21/0.49 = { by axiom 3 (multiply) R->L }
% 0.21/0.49 multiply(Y, X)
% 0.21/0.49
% 0.21/0.49 Lemma 6: double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), inverse(Y))), inverse(identity)) = Z.
% 0.21/0.49 Proof:
% 0.21/0.49 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), inverse(Y))), inverse(identity))
% 0.21/0.49 = { by axiom 1 (inverse) }
% 0.21/0.49 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), inverse(Y))), double_divide(identity, identity))
% 0.21/0.49 = { by axiom 1 (inverse) }
% 0.21/0.49 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), double_divide(Y, identity))), double_divide(identity, identity))
% 0.21/0.49 = { by axiom 4 (single_axiom) }
% 0.21/0.49 Z
% 0.21/0.49
% 0.21/0.49 Lemma 7: double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity)) = multiply(X, Y).
% 0.21/0.49 Proof:
% 0.21/0.49 double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity))
% 0.21/0.49 = { by axiom 2 (identity) }
% 0.21/0.49 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), inverse(double_divide(Y, X))), inverse(Y))), inverse(identity))
% 0.21/0.49 = { by lemma 6 }
% 0.21/0.49 inverse(double_divide(Y, X))
% 0.21/0.49 = { by lemma 5 }
% 0.21/0.49 multiply(X, Y)
% 0.21/0.49
% 0.21/0.49 Lemma 8: double_divide(double_divide(double_divide(X, double_divide(identity, Y)), Z), inverse(X)) = double_divide(double_divide(Y, Z), inverse(identity)).
% 0.21/0.49 Proof:
% 0.21/0.49 double_divide(double_divide(double_divide(X, double_divide(identity, Y)), Z), inverse(X))
% 0.21/0.49 = { by lemma 6 R->L }
% 0.21/0.49 double_divide(double_divide(Y, double_divide(double_divide(double_divide(identity, Y), double_divide(double_divide(double_divide(X, double_divide(identity, Y)), Z), inverse(X))), inverse(identity))), inverse(identity))
% 0.21/0.49 = { by lemma 6 }
% 0.21/0.49 double_divide(double_divide(Y, Z), inverse(identity))
% 0.21/0.49
% 0.21/0.49 Lemma 9: double_divide(inverse(X), inverse(identity)) = multiply(X, identity).
% 0.21/0.49 Proof:
% 0.21/0.49 double_divide(inverse(X), inverse(identity))
% 0.21/0.49 = { by axiom 1 (inverse) }
% 0.21/0.49 double_divide(double_divide(X, identity), inverse(identity))
% 0.21/0.49 = { by axiom 2 (identity) }
% 0.21/0.49 double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
% 0.21/0.49 = { by lemma 7 }
% 0.21/0.49 multiply(X, identity)
% 0.21/0.49
% 0.21/0.49 Lemma 10: double_divide(multiply(X, Y), inverse(identity)) = multiply(double_divide(Y, X), identity).
% 0.21/0.49 Proof:
% 0.21/0.49 double_divide(multiply(X, Y), inverse(identity))
% 0.21/0.49 = { by lemma 5 R->L }
% 0.21/0.49 double_divide(inverse(double_divide(Y, X)), inverse(identity))
% 0.21/0.49 = { by lemma 9 }
% 0.21/0.49 multiply(double_divide(Y, X), identity)
% 0.21/0.49
% 0.21/0.49 Lemma 11: double_divide(multiply(X, Y), inverse(X)) = multiply(double_divide(identity, Y), identity).
% 0.21/0.49 Proof:
% 0.21/0.49 double_divide(multiply(X, Y), inverse(X))
% 0.21/0.49 = { by lemma 7 R->L }
% 0.21/0.49 double_divide(double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity)), inverse(X))
% 0.21/0.49 = { by lemma 8 }
% 0.21/0.49 double_divide(double_divide(inverse(Y), inverse(identity)), inverse(identity))
% 0.21/0.49 = { by lemma 9 }
% 0.21/0.49 double_divide(multiply(Y, identity), inverse(identity))
% 0.21/0.49 = { by lemma 10 }
% 0.21/0.49 multiply(double_divide(identity, Y), identity)
% 0.21/0.49
% 0.21/0.49 Lemma 12: multiply(double_divide(identity, X), identity) = multiply(inverse(X), identity).
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(double_divide(identity, X), identity)
% 0.21/0.49 = { by lemma 11 R->L }
% 0.21/0.49 double_divide(multiply(identity, X), inverse(identity))
% 0.21/0.49 = { by lemma 10 }
% 0.21/0.49 multiply(double_divide(X, identity), identity)
% 0.21/0.49 = { by axiom 1 (inverse) R->L }
% 0.21/0.49 multiply(inverse(X), identity)
% 0.21/0.49
% 0.21/0.49 Lemma 13: inverse(inverse(X)) = multiply(identity, X).
% 0.21/0.49 Proof:
% 0.21/0.49 inverse(inverse(X))
% 0.21/0.49 = { by axiom 1 (inverse) }
% 0.21/0.49 inverse(double_divide(X, identity))
% 0.21/0.49 = { by lemma 5 }
% 0.21/0.49 multiply(identity, X)
% 0.21/0.49
% 0.21/0.49 Lemma 14: inverse(identity) = identity.
% 0.21/0.49 Proof:
% 0.21/0.49 inverse(identity)
% 0.21/0.49 = { by axiom 2 (identity) }
% 0.21/0.49 inverse(double_divide(identity, inverse(identity)))
% 0.21/0.49 = { by lemma 5 }
% 0.21/0.49 multiply(inverse(identity), identity)
% 0.21/0.49 = { by lemma 12 R->L }
% 0.21/0.49 multiply(double_divide(identity, identity), identity)
% 0.21/0.49 = { by lemma 11 R->L }
% 0.21/0.49 double_divide(multiply(multiply(identity, identity), identity), inverse(multiply(identity, identity)))
% 0.21/0.49 = { by lemma 13 R->L }
% 0.21/0.49 double_divide(multiply(inverse(inverse(identity)), identity), inverse(multiply(identity, identity)))
% 0.21/0.49 = { by lemma 12 R->L }
% 0.21/0.49 double_divide(multiply(double_divide(identity, inverse(identity)), identity), inverse(multiply(identity, identity)))
% 0.21/0.49 = { by axiom 2 (identity) R->L }
% 0.21/0.49 double_divide(multiply(identity, identity), inverse(multiply(identity, identity)))
% 0.21/0.49 = { by axiom 2 (identity) R->L }
% 0.21/0.49 identity
% 0.21/0.49
% 0.21/0.49 Lemma 15: multiply(identity, X) = multiply(X, identity).
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(identity, X)
% 0.21/0.49 = { by lemma 5 R->L }
% 0.21/0.49 inverse(double_divide(X, identity))
% 0.21/0.49 = { by axiom 1 (inverse) }
% 0.21/0.49 double_divide(double_divide(X, identity), identity)
% 0.21/0.49 = { by lemma 14 R->L }
% 0.21/0.49 double_divide(double_divide(X, identity), inverse(identity))
% 0.21/0.49 = { by lemma 14 R->L }
% 0.21/0.49 double_divide(double_divide(X, inverse(identity)), inverse(identity))
% 0.21/0.49 = { by axiom 1 (inverse) }
% 0.21/0.49 double_divide(double_divide(X, double_divide(identity, identity)), inverse(identity))
% 0.21/0.49 = { by lemma 14 R->L }
% 0.21/0.49 double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
% 0.21/0.49 = { by lemma 7 }
% 0.21/0.49 multiply(X, identity)
% 0.21/0.49
% 0.21/0.49 Lemma 16: double_divide(double_divide(inverse(X), Y), inverse(X)) = multiply(Y, identity).
% 0.21/0.49 Proof:
% 0.21/0.49 double_divide(double_divide(inverse(X), Y), inverse(X))
% 0.21/0.49 = { by axiom 1 (inverse) }
% 0.21/0.49 double_divide(double_divide(double_divide(X, identity), Y), inverse(X))
% 0.21/0.49 = { by axiom 2 (identity) }
% 0.21/0.49 double_divide(double_divide(double_divide(X, double_divide(identity, inverse(identity))), Y), inverse(X))
% 0.21/0.49 = { by lemma 8 }
% 0.21/0.49 double_divide(double_divide(inverse(identity), Y), inverse(identity))
% 0.21/0.49 = { by lemma 14 }
% 0.21/0.49 double_divide(double_divide(identity, Y), inverse(identity))
% 0.21/0.49 = { by lemma 14 }
% 0.21/0.49 double_divide(double_divide(identity, Y), identity)
% 0.21/0.49 = { by axiom 1 (inverse) R->L }
% 0.21/0.49 inverse(double_divide(identity, Y))
% 0.21/0.49 = { by lemma 5 }
% 0.21/0.49 multiply(Y, identity)
% 0.21/0.49
% 0.21/0.49 Lemma 17: multiply(identity, multiply(X, identity)) = X.
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(identity, multiply(X, identity))
% 0.21/0.49 = { by lemma 15 }
% 0.21/0.49 multiply(multiply(X, identity), identity)
% 0.21/0.49 = { by lemma 16 R->L }
% 0.21/0.49 multiply(double_divide(double_divide(inverse(Y), X), inverse(Y)), identity)
% 0.21/0.49 = { by axiom 1 (inverse) }
% 0.21/0.49 multiply(double_divide(double_divide(double_divide(Y, identity), X), inverse(Y)), identity)
% 0.21/0.49 = { by lemma 14 R->L }
% 0.21/0.49 multiply(double_divide(double_divide(double_divide(Y, inverse(identity)), X), inverse(Y)), identity)
% 0.21/0.49 = { by lemma 16 R->L }
% 0.21/0.49 double_divide(double_divide(inverse(identity), double_divide(double_divide(double_divide(Y, inverse(identity)), X), inverse(Y))), inverse(identity))
% 0.21/0.49 = { by lemma 6 }
% 0.21/0.49 X
% 0.21/0.49
% 0.21/0.49 Lemma 18: double_divide(identity, X) = inverse(X).
% 0.21/0.49 Proof:
% 0.21/0.49 double_divide(identity, X)
% 0.21/0.49 = { by lemma 17 R->L }
% 0.21/0.49 multiply(identity, multiply(double_divide(identity, X), identity))
% 0.21/0.49 = { by lemma 12 }
% 0.21/0.49 multiply(identity, multiply(inverse(X), identity))
% 0.21/0.49 = { by lemma 17 }
% 0.21/0.49 inverse(X)
% 0.21/0.49
% 0.21/0.49 Lemma 19: inverse(inverse(X)) = multiply(X, identity).
% 0.21/0.49 Proof:
% 0.21/0.49 inverse(inverse(X))
% 0.21/0.49 = { by lemma 18 R->L }
% 0.21/0.49 inverse(double_divide(identity, X))
% 0.21/0.49 = { by lemma 5 }
% 0.21/0.49 multiply(X, identity)
% 0.21/0.49
% 0.21/0.49 Lemma 20: multiply(identity, inverse(X)) = inverse(X).
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(identity, inverse(X))
% 0.21/0.49 = { by lemma 13 R->L }
% 0.21/0.49 inverse(inverse(inverse(X)))
% 0.21/0.49 = { by lemma 13 }
% 0.21/0.49 inverse(multiply(identity, X))
% 0.21/0.49 = { by lemma 7 R->L }
% 0.21/0.49 inverse(double_divide(double_divide(identity, double_divide(identity, inverse(X))), inverse(identity)))
% 0.21/0.49 = { by lemma 5 }
% 0.21/0.49 multiply(inverse(identity), double_divide(identity, double_divide(identity, inverse(X))))
% 0.21/0.49 = { by lemma 18 }
% 0.21/0.49 multiply(inverse(identity), inverse(double_divide(identity, inverse(X))))
% 0.21/0.49 = { by lemma 5 }
% 0.21/0.49 multiply(inverse(identity), multiply(inverse(X), identity))
% 0.21/0.49 = { by lemma 14 }
% 0.21/0.49 multiply(identity, multiply(inverse(X), identity))
% 0.21/0.49 = { by lemma 17 }
% 0.21/0.49 inverse(X)
% 0.21/0.49
% 0.21/0.49 Lemma 21: multiply(X, identity) = X.
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(X, identity)
% 0.21/0.49 = { by lemma 19 R->L }
% 0.21/0.49 inverse(inverse(X))
% 0.21/0.49 = { by lemma 20 R->L }
% 0.21/0.49 multiply(identity, inverse(inverse(X)))
% 0.21/0.49 = { by lemma 19 }
% 0.21/0.49 multiply(identity, multiply(X, identity))
% 0.21/0.49 = { by lemma 17 }
% 0.21/0.49 X
% 0.21/0.49
% 0.21/0.49 Lemma 22: multiply(identity, X) = X.
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(identity, X)
% 0.21/0.49 = { by lemma 15 }
% 0.21/0.49 multiply(X, identity)
% 0.21/0.49 = { by lemma 21 }
% 0.21/0.49 X
% 0.21/0.49
% 0.21/0.49 Lemma 23: multiply(Y, X) = multiply(X, Y).
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(Y, X)
% 0.21/0.49 = { by lemma 5 R->L }
% 0.21/0.49 inverse(double_divide(X, Y))
% 0.21/0.49 = { by axiom 1 (inverse) }
% 0.21/0.49 double_divide(double_divide(X, Y), identity)
% 0.21/0.49 = { by lemma 14 R->L }
% 0.21/0.49 double_divide(double_divide(X, Y), inverse(identity))
% 0.21/0.49 = { by lemma 21 R->L }
% 0.21/0.49 double_divide(double_divide(X, multiply(Y, identity)), inverse(identity))
% 0.21/0.49 = { by lemma 19 R->L }
% 0.21/0.49 double_divide(double_divide(X, inverse(inverse(Y))), inverse(identity))
% 0.21/0.49 = { by lemma 18 R->L }
% 0.21/0.49 double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity))
% 0.21/0.49 = { by lemma 7 }
% 0.21/0.49 multiply(X, Y)
% 0.21/0.49
% 0.21/0.49 Lemma 24: double_divide(Y, X) = double_divide(X, Y).
% 0.21/0.49 Proof:
% 0.21/0.49 double_divide(Y, X)
% 0.21/0.49 = { by lemma 22 R->L }
% 0.21/0.49 multiply(identity, double_divide(Y, X))
% 0.21/0.49 = { by lemma 13 R->L }
% 0.21/0.49 inverse(inverse(double_divide(Y, X)))
% 0.21/0.49 = { by lemma 5 }
% 0.21/0.49 inverse(multiply(X, Y))
% 0.21/0.49 = { by axiom 1 (inverse) }
% 0.21/0.49 double_divide(multiply(X, Y), identity)
% 0.21/0.49 = { by lemma 14 R->L }
% 0.21/0.49 double_divide(multiply(X, Y), inverse(identity))
% 0.21/0.49 = { by lemma 23 }
% 0.21/0.49 double_divide(multiply(Y, X), inverse(identity))
% 0.21/0.49 = { by lemma 10 }
% 0.21/0.49 multiply(double_divide(X, Y), identity)
% 0.21/0.49 = { by lemma 21 }
% 0.21/0.49 double_divide(X, Y)
% 0.21/0.49
% 0.21/0.49 Lemma 25: multiply(inverse(X), double_divide(Y, inverse(X))) = inverse(Y).
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(inverse(X), double_divide(Y, inverse(X)))
% 0.21/0.49 = { by lemma 24 }
% 0.21/0.49 multiply(inverse(X), double_divide(inverse(X), Y))
% 0.21/0.49 = { by lemma 5 R->L }
% 0.21/0.49 inverse(double_divide(double_divide(inverse(X), Y), inverse(X)))
% 0.21/0.49 = { by lemma 16 }
% 0.21/0.49 inverse(multiply(Y, identity))
% 0.21/0.49 = { by lemma 9 R->L }
% 0.21/0.49 inverse(double_divide(inverse(Y), inverse(identity)))
% 0.21/0.49 = { by lemma 5 }
% 0.21/0.49 multiply(inverse(identity), inverse(Y))
% 0.21/0.49 = { by lemma 14 }
% 0.21/0.49 multiply(identity, inverse(Y))
% 0.21/0.49 = { by lemma 20 }
% 0.21/0.50 inverse(Y)
% 0.21/0.50
% 0.21/0.50 Lemma 26: multiply(X, inverse(Y)) = double_divide(Y, inverse(X)).
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(X, inverse(Y))
% 0.21/0.50 = { by lemma 23 }
% 0.21/0.50 multiply(inverse(Y), X)
% 0.21/0.50 = { by lemma 5 R->L }
% 0.21/0.50 inverse(double_divide(X, inverse(Y)))
% 0.21/0.50 = { by lemma 21 R->L }
% 0.21/0.50 multiply(inverse(double_divide(X, inverse(Y))), identity)
% 0.21/0.50 = { by lemma 12 R->L }
% 0.21/0.50 multiply(double_divide(identity, double_divide(X, inverse(Y))), identity)
% 0.21/0.50 = { by lemma 11 R->L }
% 0.21/0.50 double_divide(multiply(inverse(Y), double_divide(X, inverse(Y))), inverse(inverse(Y)))
% 0.21/0.50 = { by lemma 25 }
% 0.21/0.50 double_divide(inverse(X), inverse(inverse(Y)))
% 0.21/0.50 = { by lemma 19 }
% 0.21/0.50 double_divide(inverse(X), multiply(Y, identity))
% 0.21/0.50 = { by lemma 21 }
% 0.21/0.50 double_divide(inverse(X), Y)
% 0.21/0.50 = { by lemma 24 R->L }
% 0.21/0.50 double_divide(Y, inverse(X))
% 0.21/0.50
% 0.21/0.50 Lemma 27: multiply(inverse(X), Y) = double_divide(X, inverse(Y)).
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(inverse(X), Y)
% 0.21/0.50 = { by lemma 23 }
% 0.21/0.50 multiply(Y, inverse(X))
% 0.21/0.50 = { by lemma 26 }
% 0.21/0.50 double_divide(X, inverse(Y))
% 0.21/0.50
% 0.21/0.50 Lemma 28: multiply(X, double_divide(X, Y)) = inverse(Y).
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(X, double_divide(X, Y))
% 0.21/0.50 = { by lemma 24 }
% 0.21/0.50 multiply(X, double_divide(Y, X))
% 0.21/0.50 = { by lemma 21 R->L }
% 0.21/0.50 multiply(X, double_divide(Y, multiply(X, identity)))
% 0.21/0.50 = { by lemma 19 R->L }
% 0.21/0.50 multiply(X, double_divide(Y, inverse(inverse(X))))
% 0.21/0.50 = { by lemma 22 R->L }
% 0.21/0.50 multiply(multiply(identity, X), double_divide(Y, inverse(inverse(X))))
% 0.21/0.50 = { by lemma 13 R->L }
% 0.21/0.50 multiply(inverse(inverse(X)), double_divide(Y, inverse(inverse(X))))
% 0.21/0.50 = { by lemma 25 }
% 0.21/0.50 inverse(Y)
% 0.21/0.50
% 0.21/0.50 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(multiply(a3, b3), c3)
% 0.21/0.50 = { by lemma 23 R->L }
% 0.21/0.50 multiply(c3, multiply(a3, b3))
% 0.21/0.50 = { by lemma 21 R->L }
% 0.21/0.50 multiply(c3, multiply(a3, multiply(b3, identity)))
% 0.21/0.50 = { by lemma 19 R->L }
% 0.21/0.50 multiply(c3, multiply(a3, inverse(inverse(b3))))
% 0.21/0.50 = { by lemma 28 R->L }
% 0.21/0.50 multiply(c3, multiply(a3, multiply(multiply(b3, c3), double_divide(multiply(b3, c3), inverse(b3)))))
% 0.21/0.50 = { by lemma 11 }
% 0.21/0.50 multiply(c3, multiply(a3, multiply(multiply(b3, c3), multiply(double_divide(identity, c3), identity))))
% 0.21/0.50 = { by lemma 21 }
% 0.21/0.50 multiply(c3, multiply(a3, multiply(multiply(b3, c3), double_divide(identity, c3))))
% 0.21/0.50 = { by lemma 18 }
% 0.21/0.50 multiply(c3, multiply(a3, multiply(multiply(b3, c3), inverse(c3))))
% 0.21/0.50 = { by lemma 26 }
% 0.21/0.50 multiply(c3, multiply(a3, double_divide(c3, inverse(multiply(b3, c3)))))
% 0.21/0.50 = { by lemma 18 R->L }
% 0.21/0.50 multiply(c3, multiply(a3, double_divide(c3, double_divide(identity, multiply(b3, c3)))))
% 0.21/0.50 = { by lemma 5 R->L }
% 0.21/0.50 multiply(c3, inverse(double_divide(double_divide(c3, double_divide(identity, multiply(b3, c3))), a3)))
% 0.21/0.50 = { by lemma 25 R->L }
% 0.21/0.50 multiply(c3, multiply(inverse(c3), double_divide(double_divide(double_divide(c3, double_divide(identity, multiply(b3, c3))), a3), inverse(c3))))
% 0.21/0.50 = { by lemma 8 }
% 0.21/0.50 multiply(c3, multiply(inverse(c3), double_divide(double_divide(multiply(b3, c3), a3), inverse(identity))))
% 0.21/0.50 = { by lemma 27 }
% 0.21/0.50 multiply(c3, double_divide(c3, inverse(double_divide(double_divide(multiply(b3, c3), a3), inverse(identity)))))
% 0.21/0.50 = { by lemma 5 }
% 0.21/0.50 multiply(c3, double_divide(c3, multiply(inverse(identity), double_divide(multiply(b3, c3), a3))))
% 0.21/0.50 = { by lemma 27 }
% 0.21/0.50 multiply(c3, double_divide(c3, double_divide(identity, inverse(double_divide(multiply(b3, c3), a3)))))
% 0.21/0.50 = { by lemma 18 }
% 0.21/0.50 multiply(c3, double_divide(c3, inverse(inverse(double_divide(multiply(b3, c3), a3)))))
% 0.21/0.50 = { by lemma 19 }
% 0.21/0.50 multiply(c3, double_divide(c3, multiply(double_divide(multiply(b3, c3), a3), identity)))
% 0.21/0.50 = { by lemma 10 R->L }
% 0.21/0.50 multiply(c3, double_divide(c3, double_divide(multiply(a3, multiply(b3, c3)), inverse(identity))))
% 0.21/0.50 = { by lemma 14 }
% 0.21/0.50 multiply(c3, double_divide(c3, double_divide(multiply(a3, multiply(b3, c3)), identity)))
% 0.21/0.50 = { by axiom 1 (inverse) R->L }
% 0.21/0.50 multiply(c3, double_divide(c3, inverse(multiply(a3, multiply(b3, c3)))))
% 0.21/0.50 = { by lemma 28 }
% 0.21/0.50 inverse(inverse(multiply(a3, multiply(b3, c3))))
% 0.21/0.50 = { by lemma 19 }
% 0.21/0.50 multiply(multiply(a3, multiply(b3, c3)), identity)
% 0.21/0.50 = { by lemma 21 }
% 0.21/0.50 multiply(a3, multiply(b3, c3))
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50
% 0.21/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------