TSTP Solution File: GRP578-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP578-1 : 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 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP578-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:04:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.39 Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.39
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.20/0.42 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.20/0.42 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.20/0.42 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.
% 0.20/0.42
% 0.20/0.42 Lemma 5: double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), inverse(Y))), inverse(identity)) = Z.
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), inverse(Y))), inverse(identity))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), inverse(Y))), double_divide(identity, identity))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), Z), double_divide(Y, identity))), double_divide(identity, identity))
% 0.20/0.42 = { by axiom 4 (single_axiom) }
% 0.20/0.42 Z
% 0.20/0.42
% 0.20/0.42 Lemma 6: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.20/0.42 Proof:
% 0.20/0.42 inverse(double_divide(X, Y))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 double_divide(double_divide(X, Y), identity)
% 0.20/0.42 = { by axiom 3 (multiply) R->L }
% 0.20/0.42 multiply(Y, X)
% 0.20/0.42
% 0.20/0.42 Lemma 7: double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity)) = multiply(X, Y).
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity))
% 0.20/0.42 = { by axiom 2 (identity) }
% 0.20/0.42 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), inverse(double_divide(Y, X))), inverse(Y))), inverse(identity))
% 0.20/0.42 = { by lemma 5 }
% 0.20/0.42 inverse(double_divide(Y, X))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 multiply(X, Y)
% 0.20/0.42
% 0.20/0.42 Lemma 8: double_divide(inverse(X), inverse(identity)) = multiply(X, identity).
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(inverse(X), inverse(identity))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 double_divide(double_divide(X, identity), inverse(identity))
% 0.20/0.42 = { by axiom 2 (identity) }
% 0.20/0.42 double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 multiply(X, identity)
% 0.20/0.42
% 0.20/0.42 Lemma 9: double_divide(double_divide(X, double_divide(multiply(X, Y), inverse(Y))), inverse(identity)) = identity.
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(double_divide(X, double_divide(multiply(X, Y), inverse(Y))), inverse(identity))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 double_divide(double_divide(X, double_divide(inverse(double_divide(Y, X)), inverse(Y))), inverse(identity))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 double_divide(double_divide(X, double_divide(double_divide(double_divide(Y, X), identity), inverse(Y))), inverse(identity))
% 0.20/0.42 = { by lemma 5 }
% 0.20/0.42 identity
% 0.20/0.42
% 0.20/0.42 Lemma 10: multiply(double_divide(multiply(X, Y), inverse(Y)), X) = inverse(identity).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(double_divide(multiply(X, Y), inverse(Y)), X)
% 0.20/0.42 = { by lemma 7 R->L }
% 0.20/0.42 double_divide(double_divide(double_divide(multiply(X, Y), inverse(Y)), double_divide(identity, inverse(X))), inverse(identity))
% 0.20/0.42 = { by lemma 9 R->L }
% 0.20/0.42 double_divide(double_divide(double_divide(multiply(X, Y), inverse(Y)), double_divide(double_divide(double_divide(X, double_divide(multiply(X, Y), inverse(Y))), inverse(identity)), inverse(X))), inverse(identity))
% 0.20/0.42 = { by lemma 5 }
% 0.20/0.42 inverse(identity)
% 0.20/0.42
% 0.20/0.42 Lemma 11: multiply(inverse(X), X) = inverse(identity).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(inverse(X), X)
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 inverse(double_divide(X, inverse(X)))
% 0.20/0.42 = { by axiom 2 (identity) R->L }
% 0.20/0.42 inverse(identity)
% 0.20/0.42
% 0.20/0.42 Lemma 12: multiply(identity, X) = inverse(inverse(X)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(identity, X)
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 inverse(double_divide(X, identity))
% 0.20/0.42 = { by axiom 1 (inverse) R->L }
% 0.20/0.42 inverse(inverse(X))
% 0.20/0.42
% 0.20/0.42 Lemma 13: multiply(inverse(inverse(identity)), identity) = identity.
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(inverse(inverse(identity)), identity)
% 0.20/0.42 = { by lemma 8 R->L }
% 0.20/0.42 double_divide(inverse(inverse(inverse(identity))), inverse(identity))
% 0.20/0.42 = { by lemma 10 R->L }
% 0.20/0.42 double_divide(inverse(inverse(inverse(identity))), multiply(double_divide(multiply(inverse(inverse(identity)), inverse(identity)), inverse(inverse(identity))), inverse(inverse(identity))))
% 0.20/0.42 = { by lemma 11 }
% 0.20/0.42 double_divide(inverse(inverse(inverse(identity))), multiply(double_divide(inverse(identity), inverse(inverse(identity))), inverse(inverse(identity))))
% 0.20/0.42 = { by axiom 2 (identity) R->L }
% 0.20/0.42 double_divide(inverse(inverse(inverse(identity))), multiply(identity, inverse(inverse(identity))))
% 0.20/0.42 = { by lemma 12 }
% 0.20/0.42 double_divide(inverse(inverse(inverse(identity))), inverse(inverse(inverse(inverse(identity)))))
% 0.20/0.42 = { by axiom 2 (identity) R->L }
% 0.20/0.42 identity
% 0.20/0.42
% 0.20/0.42 Lemma 14: double_divide(multiply(double_divide(identity, X), Y), inverse(Y)) = multiply(X, identity).
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(multiply(double_divide(identity, X), Y), inverse(Y))
% 0.20/0.42 = { by lemma 5 R->L }
% 0.20/0.42 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))
% 0.20/0.42 = { by lemma 9 }
% 0.20/0.42 double_divide(double_divide(X, identity), inverse(identity))
% 0.20/0.42 = { by axiom 1 (inverse) R->L }
% 0.20/0.42 double_divide(inverse(X), inverse(identity))
% 0.20/0.42 = { by lemma 8 }
% 0.20/0.42 multiply(X, identity)
% 0.20/0.42
% 0.20/0.42 Lemma 15: inverse(inverse(identity)) = inverse(identity).
% 0.20/0.42 Proof:
% 0.20/0.42 inverse(inverse(identity))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 double_divide(inverse(identity), identity)
% 0.20/0.42 = { by lemma 13 R->L }
% 0.20/0.42 double_divide(inverse(identity), multiply(inverse(inverse(identity)), identity))
% 0.20/0.42 = { by lemma 13 R->L }
% 0.20/0.42 double_divide(inverse(multiply(inverse(inverse(identity)), identity)), multiply(inverse(inverse(identity)), identity))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 double_divide(inverse(multiply(inverse(inverse(identity)), identity)), inverse(double_divide(identity, inverse(inverse(identity)))))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 double_divide(inverse(inverse(double_divide(identity, inverse(inverse(identity))))), inverse(double_divide(identity, inverse(inverse(identity)))))
% 0.20/0.42 = { by lemma 12 R->L }
% 0.20/0.42 double_divide(multiply(identity, double_divide(identity, inverse(inverse(identity)))), inverse(double_divide(identity, inverse(inverse(identity)))))
% 0.20/0.42 = { by axiom 2 (identity) }
% 0.20/0.42 double_divide(multiply(double_divide(identity, inverse(identity)), double_divide(identity, inverse(inverse(identity)))), inverse(double_divide(identity, inverse(inverse(identity)))))
% 0.20/0.42 = { by lemma 14 }
% 0.20/0.42 multiply(inverse(identity), identity)
% 0.20/0.42 = { by lemma 11 }
% 0.20/0.42 inverse(identity)
% 0.20/0.42
% 0.20/0.42 Lemma 16: inverse(identity) = identity.
% 0.20/0.42 Proof:
% 0.20/0.42 inverse(identity)
% 0.20/0.42 = { by lemma 15 R->L }
% 0.20/0.42 inverse(inverse(identity))
% 0.20/0.42 = { by lemma 12 R->L }
% 0.20/0.42 multiply(identity, identity)
% 0.20/0.42 = { by lemma 8 R->L }
% 0.20/0.42 double_divide(inverse(identity), inverse(identity))
% 0.20/0.42 = { by lemma 15 R->L }
% 0.20/0.42 double_divide(inverse(identity), inverse(inverse(identity)))
% 0.20/0.42 = { by axiom 2 (identity) R->L }
% 0.20/0.42 identity
% 0.20/0.42
% 0.20/0.42 Lemma 17: multiply(X, identity) = inverse(inverse(X)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, identity)
% 0.20/0.42 = { by lemma 7 R->L }
% 0.20/0.42 double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
% 0.20/0.42 = { by lemma 16 }
% 0.20/0.42 double_divide(double_divide(X, double_divide(identity, identity)), inverse(identity))
% 0.20/0.42 = { by axiom 1 (inverse) R->L }
% 0.20/0.42 double_divide(double_divide(X, inverse(identity)), inverse(identity))
% 0.20/0.42 = { by lemma 16 }
% 0.20/0.42 double_divide(double_divide(X, identity), inverse(identity))
% 0.20/0.42 = { by lemma 16 }
% 0.20/0.42 double_divide(double_divide(X, identity), identity)
% 0.20/0.42 = { by axiom 1 (inverse) R->L }
% 0.20/0.42 inverse(double_divide(X, identity))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 multiply(identity, X)
% 0.20/0.42 = { by lemma 12 }
% 0.20/0.42 inverse(inverse(X))
% 0.20/0.42
% 0.20/0.42 Lemma 18: double_divide(multiply(X, Y), inverse(identity)) = multiply(double_divide(Y, X), identity).
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(multiply(X, Y), inverse(identity))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 double_divide(inverse(double_divide(Y, X)), inverse(identity))
% 0.20/0.42 = { by lemma 8 }
% 0.20/0.42 multiply(double_divide(Y, X), identity)
% 0.20/0.42
% 0.20/0.42 Lemma 19: inverse(inverse(inverse(inverse(X)))) = inverse(inverse(X)).
% 0.20/0.42 Proof:
% 0.20/0.42 inverse(inverse(inverse(inverse(X))))
% 0.20/0.42 = { by lemma 17 R->L }
% 0.20/0.42 inverse(inverse(multiply(X, identity)))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 inverse(inverse(inverse(double_divide(identity, X))))
% 0.20/0.42 = { by lemma 17 R->L }
% 0.20/0.42 inverse(multiply(double_divide(identity, X), identity))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 inverse(inverse(double_divide(identity, double_divide(identity, X))))
% 0.20/0.42 = { by lemma 17 R->L }
% 0.20/0.42 multiply(double_divide(identity, double_divide(identity, X)), identity)
% 0.20/0.42 = { by lemma 18 R->L }
% 0.20/0.42 double_divide(multiply(double_divide(identity, X), identity), inverse(identity))
% 0.20/0.42 = { by lemma 14 }
% 0.20/0.42 multiply(X, identity)
% 0.20/0.42 = { by lemma 17 }
% 0.20/0.42 inverse(inverse(X))
% 0.20/0.42
% 0.20/0.42 Lemma 20: inverse(inverse(multiply(identity, X))) = multiply(identity, X).
% 0.20/0.42 Proof:
% 0.20/0.42 inverse(inverse(multiply(identity, X)))
% 0.20/0.42 = { by lemma 12 }
% 0.20/0.42 inverse(inverse(inverse(inverse(X))))
% 0.20/0.42 = { by lemma 19 }
% 0.20/0.42 inverse(inverse(X))
% 0.20/0.42 = { by lemma 12 R->L }
% 0.20/0.42 multiply(identity, X)
% 0.20/0.42
% 0.20/0.42 Lemma 21: multiply(inverse(identity), multiply(identity, X)) = inverse(multiply(inverse(X), identity)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(inverse(identity), multiply(identity, X))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 inverse(double_divide(multiply(identity, X), inverse(identity)))
% 0.20/0.42 = { by lemma 12 }
% 0.20/0.42 inverse(double_divide(inverse(inverse(X)), inverse(identity)))
% 0.20/0.42 = { by lemma 8 }
% 0.20/0.42 inverse(multiply(inverse(X), identity))
% 0.20/0.42
% 0.20/0.42 Lemma 22: double_divide(identity, multiply(identity, X)) = inverse(multiply(identity, X)).
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(identity, multiply(identity, X))
% 0.20/0.42 = { by lemma 20 R->L }
% 0.20/0.42 double_divide(identity, inverse(inverse(multiply(identity, X))))
% 0.20/0.42 = { by lemma 12 R->L }
% 0.20/0.42 double_divide(identity, multiply(identity, multiply(identity, X)))
% 0.20/0.42 = { by lemma 16 R->L }
% 0.20/0.42 double_divide(identity, multiply(inverse(identity), multiply(identity, X)))
% 0.20/0.42 = { by lemma 21 }
% 0.20/0.42 double_divide(identity, inverse(multiply(inverse(X), identity)))
% 0.20/0.42 = { by lemma 16 R->L }
% 0.20/0.42 double_divide(inverse(identity), inverse(multiply(inverse(X), identity)))
% 0.20/0.42 = { by lemma 10 R->L }
% 0.20/0.42 double_divide(multiply(double_divide(multiply(multiply(inverse(X), identity), double_divide(identity, inverse(X))), inverse(double_divide(identity, inverse(X)))), multiply(inverse(X), identity)), inverse(multiply(inverse(X), identity)))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 double_divide(multiply(double_divide(multiply(inverse(double_divide(identity, inverse(X))), double_divide(identity, inverse(X))), inverse(double_divide(identity, inverse(X)))), multiply(inverse(X), identity)), inverse(multiply(inverse(X), identity)))
% 0.20/0.42 = { by lemma 11 }
% 0.20/0.42 double_divide(multiply(double_divide(inverse(identity), inverse(double_divide(identity, inverse(X)))), multiply(inverse(X), identity)), inverse(multiply(inverse(X), identity)))
% 0.20/0.42 = { by lemma 16 }
% 0.20/0.42 double_divide(multiply(double_divide(identity, inverse(double_divide(identity, inverse(X)))), multiply(inverse(X), identity)), inverse(multiply(inverse(X), identity)))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 double_divide(multiply(double_divide(identity, multiply(inverse(X), identity)), multiply(inverse(X), identity)), inverse(multiply(inverse(X), identity)))
% 0.20/0.42 = { by lemma 14 }
% 0.20/0.42 multiply(multiply(inverse(X), identity), identity)
% 0.20/0.42 = { by lemma 17 }
% 0.20/0.42 inverse(inverse(multiply(inverse(X), identity)))
% 0.20/0.42 = { by lemma 21 R->L }
% 0.20/0.42 inverse(multiply(inverse(identity), multiply(identity, X)))
% 0.20/0.42 = { by lemma 16 }
% 0.20/0.42 inverse(multiply(identity, multiply(identity, X)))
% 0.20/0.42 = { by lemma 12 }
% 0.20/0.42 inverse(inverse(inverse(multiply(identity, X))))
% 0.20/0.42 = { by lemma 20 }
% 0.20/0.42 inverse(multiply(identity, X))
% 0.20/0.42
% 0.20/0.42 Goal 1 (prove_these_axioms_2): multiply(identity, a2) = a2.
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(identity, a2)
% 0.20/0.42 = { by lemma 20 R->L }
% 0.20/0.42 inverse(inverse(multiply(identity, a2)))
% 0.20/0.42 = { by lemma 17 R->L }
% 0.20/0.42 multiply(multiply(identity, a2), identity)
% 0.20/0.42 = { by lemma 16 R->L }
% 0.20/0.42 multiply(multiply(identity, a2), inverse(identity))
% 0.20/0.42 = { by lemma 10 R->L }
% 0.20/0.42 multiply(multiply(identity, a2), multiply(double_divide(multiply(a2, identity), inverse(identity)), a2))
% 0.20/0.42 = { by lemma 18 }
% 0.20/0.42 multiply(multiply(identity, a2), multiply(multiply(double_divide(identity, a2), identity), a2))
% 0.20/0.42 = { by lemma 17 }
% 0.20/0.42 multiply(multiply(identity, a2), multiply(inverse(inverse(double_divide(identity, a2))), a2))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 multiply(multiply(identity, a2), multiply(inverse(multiply(a2, identity)), a2))
% 0.20/0.42 = { by lemma 17 }
% 0.20/0.42 multiply(multiply(identity, a2), multiply(inverse(inverse(inverse(a2))), a2))
% 0.20/0.42 = { by lemma 12 R->L }
% 0.20/0.42 multiply(multiply(identity, a2), multiply(inverse(multiply(identity, a2)), a2))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 multiply(multiply(identity, a2), inverse(double_divide(a2, inverse(multiply(identity, a2)))))
% 0.20/0.42 = { by axiom 1 (inverse) }
% 0.20/0.42 multiply(multiply(identity, a2), double_divide(double_divide(a2, inverse(multiply(identity, a2))), identity))
% 0.20/0.42 = { by lemma 16 R->L }
% 0.20/0.42 multiply(multiply(identity, a2), double_divide(double_divide(a2, inverse(multiply(identity, a2))), inverse(identity)))
% 0.20/0.42 = { by lemma 22 R->L }
% 0.20/0.42 multiply(multiply(identity, a2), double_divide(double_divide(a2, double_divide(identity, multiply(identity, a2))), inverse(identity)))
% 0.20/0.42 = { by lemma 12 }
% 0.20/0.42 multiply(multiply(identity, a2), double_divide(double_divide(a2, double_divide(identity, inverse(inverse(a2)))), inverse(identity)))
% 0.20/0.42 = { by lemma 19 R->L }
% 0.20/0.42 multiply(multiply(identity, a2), double_divide(double_divide(a2, double_divide(identity, inverse(inverse(inverse(inverse(a2)))))), inverse(identity)))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 multiply(multiply(identity, a2), multiply(a2, inverse(inverse(inverse(a2)))))
% 0.20/0.43 = { by lemma 12 R->L }
% 0.20/0.43 multiply(multiply(identity, a2), multiply(a2, inverse(multiply(identity, a2))))
% 0.20/0.43 = { by lemma 6 R->L }
% 0.20/0.43 inverse(double_divide(multiply(a2, inverse(multiply(identity, a2))), multiply(identity, a2)))
% 0.20/0.43 = { by axiom 1 (inverse) }
% 0.20/0.43 double_divide(double_divide(multiply(a2, inverse(multiply(identity, a2))), multiply(identity, a2)), identity)
% 0.20/0.43 = { by lemma 16 R->L }
% 0.20/0.43 double_divide(double_divide(multiply(a2, inverse(multiply(identity, a2))), multiply(identity, a2)), inverse(identity))
% 0.20/0.43 = { by lemma 20 R->L }
% 0.20/0.43 double_divide(double_divide(multiply(a2, inverse(multiply(identity, a2))), inverse(inverse(multiply(identity, a2)))), inverse(identity))
% 0.20/0.43 = { by lemma 17 R->L }
% 0.20/0.43 double_divide(double_divide(multiply(a2, inverse(multiply(identity, a2))), multiply(multiply(identity, a2), identity)), inverse(identity))
% 0.20/0.43 = { by lemma 14 R->L }
% 0.20/0.43 double_divide(double_divide(multiply(a2, inverse(multiply(identity, a2))), double_divide(multiply(double_divide(identity, multiply(identity, a2)), multiply(identity, a2)), inverse(multiply(identity, a2)))), inverse(identity))
% 0.20/0.43 = { by lemma 16 R->L }
% 0.20/0.43 double_divide(double_divide(multiply(a2, inverse(multiply(identity, a2))), double_divide(multiply(double_divide(inverse(identity), multiply(identity, a2)), multiply(identity, a2)), inverse(multiply(identity, a2)))), inverse(identity))
% 0.20/0.43 = { by lemma 12 }
% 0.20/0.43 double_divide(double_divide(multiply(a2, inverse(multiply(identity, a2))), double_divide(multiply(double_divide(inverse(identity), inverse(inverse(a2))), multiply(identity, a2)), inverse(multiply(identity, a2)))), inverse(identity))
% 0.20/0.43 = { by lemma 11 R->L }
% 0.20/0.43 double_divide(double_divide(multiply(a2, inverse(multiply(identity, a2))), double_divide(multiply(double_divide(multiply(inverse(inverse(a2)), inverse(a2)), inverse(inverse(a2))), multiply(identity, a2)), inverse(multiply(identity, a2)))), inverse(identity))
% 0.20/0.43 = { by lemma 12 R->L }
% 0.20/0.43 double_divide(double_divide(multiply(a2, inverse(multiply(identity, a2))), double_divide(multiply(double_divide(multiply(multiply(identity, a2), inverse(a2)), inverse(inverse(a2))), multiply(identity, a2)), inverse(multiply(identity, a2)))), inverse(identity))
% 0.20/0.43 = { by lemma 10 }
% 0.20/0.43 double_divide(double_divide(multiply(a2, inverse(multiply(identity, a2))), double_divide(inverse(identity), inverse(multiply(identity, a2)))), inverse(identity))
% 0.20/0.43 = { by lemma 16 }
% 0.20/0.43 double_divide(double_divide(multiply(a2, inverse(multiply(identity, a2))), double_divide(identity, inverse(multiply(identity, a2)))), inverse(identity))
% 0.20/0.43 = { by lemma 7 }
% 0.20/0.43 multiply(multiply(a2, inverse(multiply(identity, a2))), multiply(identity, a2))
% 0.20/0.43 = { by lemma 6 R->L }
% 0.20/0.43 multiply(inverse(double_divide(inverse(multiply(identity, a2)), a2)), multiply(identity, a2))
% 0.20/0.43 = { by axiom 1 (inverse) }
% 0.20/0.43 multiply(double_divide(double_divide(inverse(multiply(identity, a2)), a2), identity), multiply(identity, a2))
% 0.20/0.43 = { by lemma 6 R->L }
% 0.20/0.43 inverse(double_divide(multiply(identity, a2), double_divide(double_divide(inverse(multiply(identity, a2)), a2), identity)))
% 0.20/0.43 = { by axiom 1 (inverse) }
% 0.20/0.43 double_divide(double_divide(multiply(identity, a2), double_divide(double_divide(inverse(multiply(identity, a2)), a2), identity)), identity)
% 0.20/0.43 = { by lemma 16 R->L }
% 0.20/0.43 double_divide(double_divide(multiply(identity, a2), double_divide(double_divide(inverse(multiply(identity, a2)), a2), inverse(identity))), identity)
% 0.20/0.43 = { by lemma 16 R->L }
% 0.20/0.43 double_divide(double_divide(multiply(identity, a2), double_divide(double_divide(inverse(multiply(identity, a2)), a2), inverse(identity))), inverse(identity))
% 0.20/0.43 = { by lemma 22 R->L }
% 0.20/0.43 double_divide(double_divide(multiply(identity, a2), double_divide(double_divide(double_divide(identity, multiply(identity, a2)), a2), inverse(identity))), inverse(identity))
% 0.20/0.43 = { by lemma 5 }
% 0.20/0.43 a2
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------