TSTP Solution File: GRP583-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP583-1 : 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 : n005.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 01:19:00 EDT 2023
% Result : Unsatisfiable 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP583-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.13 % 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 : n005.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 : Mon Aug 28 23:03:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.48 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.48
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48
% 0.21/0.52 % SZS output start Proof
% 0.21/0.52 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.21/0.52 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.21/0.52 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.21/0.52 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(identity, Y), double_divide(Z, double_divide(Y, X)))), double_divide(identity, identity)) = Z.
% 0.21/0.52
% 0.21/0.52 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.21/0.52 Proof:
% 0.21/0.52 inverse(double_divide(X, Y))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(double_divide(X, Y), identity)
% 0.21/0.52 = { by axiom 3 (multiply) R->L }
% 0.21/0.52 multiply(Y, X)
% 0.21/0.52
% 0.21/0.52 Lemma 6: double_divide(double_divide(X, double_divide(double_divide(identity, Y), double_divide(Z, double_divide(Y, X)))), inverse(identity)) = Z.
% 0.21/0.52 Proof:
% 0.21/0.52 double_divide(double_divide(X, double_divide(double_divide(identity, Y), double_divide(Z, double_divide(Y, X)))), inverse(identity))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(double_divide(X, double_divide(double_divide(identity, Y), double_divide(Z, double_divide(Y, X)))), double_divide(identity, identity))
% 0.21/0.52 = { by axiom 4 (single_axiom) }
% 0.21/0.52 Z
% 0.21/0.52
% 0.21/0.52 Lemma 7: double_divide(double_divide(identity, double_divide(double_divide(identity, X), double_divide(Y, inverse(X)))), inverse(identity)) = Y.
% 0.21/0.52 Proof:
% 0.21/0.52 double_divide(double_divide(identity, double_divide(double_divide(identity, X), double_divide(Y, inverse(X)))), inverse(identity))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(double_divide(identity, double_divide(double_divide(identity, X), double_divide(Y, double_divide(X, identity)))), inverse(identity))
% 0.21/0.52 = { by lemma 6 }
% 0.21/0.52 Y
% 0.21/0.52
% 0.21/0.52 Lemma 8: double_divide(double_divide(identity, multiply(X, identity)), inverse(identity)) = X.
% 0.21/0.52 Proof:
% 0.21/0.52 double_divide(double_divide(identity, multiply(X, identity)), inverse(identity))
% 0.21/0.52 = { by lemma 5 R->L }
% 0.21/0.52 double_divide(double_divide(identity, inverse(double_divide(identity, X))), inverse(identity))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(double_divide(identity, double_divide(double_divide(identity, X), identity)), inverse(identity))
% 0.21/0.52 = { by axiom 2 (identity) }
% 0.21/0.52 double_divide(double_divide(identity, double_divide(double_divide(identity, X), double_divide(X, inverse(X)))), inverse(identity))
% 0.21/0.52 = { by lemma 7 }
% 0.21/0.52 X
% 0.21/0.52
% 0.21/0.52 Lemma 9: inverse(identity) = identity.
% 0.21/0.52 Proof:
% 0.21/0.52 inverse(identity)
% 0.21/0.52 = { by lemma 8 R->L }
% 0.21/0.52 double_divide(double_divide(identity, multiply(inverse(identity), identity)), inverse(identity))
% 0.21/0.52 = { by lemma 5 R->L }
% 0.21/0.52 double_divide(double_divide(identity, inverse(double_divide(identity, inverse(identity)))), inverse(identity))
% 0.21/0.52 = { by axiom 2 (identity) R->L }
% 0.21/0.52 double_divide(double_divide(identity, inverse(identity)), inverse(identity))
% 0.21/0.52 = { by axiom 2 (identity) R->L }
% 0.21/0.52 double_divide(identity, inverse(identity))
% 0.21/0.52 = { by axiom 2 (identity) R->L }
% 0.21/0.52 identity
% 0.21/0.52
% 0.21/0.52 Lemma 10: inverse(inverse(X)) = multiply(identity, X).
% 0.21/0.52 Proof:
% 0.21/0.52 inverse(inverse(X))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 inverse(double_divide(X, identity))
% 0.21/0.52 = { by lemma 5 }
% 0.21/0.52 multiply(identity, X)
% 0.21/0.52
% 0.21/0.52 Lemma 11: double_divide(double_divide(X, double_divide(inverse(identity), double_divide(Y, double_divide(identity, X)))), inverse(identity)) = Y.
% 0.21/0.52 Proof:
% 0.21/0.52 double_divide(double_divide(X, double_divide(inverse(identity), double_divide(Y, double_divide(identity, X)))), inverse(identity))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(double_divide(X, double_divide(double_divide(identity, identity), double_divide(Y, double_divide(identity, X)))), inverse(identity))
% 0.21/0.52 = { by lemma 6 }
% 0.21/0.52 Y
% 0.21/0.52
% 0.21/0.52 Lemma 12: double_divide(double_divide(inverse(X), double_divide(double_divide(identity, X), inverse(Y))), inverse(identity)) = Y.
% 0.21/0.52 Proof:
% 0.21/0.52 double_divide(double_divide(inverse(X), double_divide(double_divide(identity, X), inverse(Y))), inverse(identity))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(double_divide(inverse(X), double_divide(double_divide(identity, X), double_divide(Y, identity))), inverse(identity))
% 0.21/0.52 = { by axiom 2 (identity) }
% 0.21/0.52 double_divide(double_divide(inverse(X), double_divide(double_divide(identity, X), double_divide(Y, double_divide(X, inverse(X))))), inverse(identity))
% 0.21/0.52 = { by lemma 6 }
% 0.21/0.52 Y
% 0.21/0.52
% 0.21/0.52 Lemma 13: double_divide(multiply(inverse(X), identity), X) = identity.
% 0.21/0.52 Proof:
% 0.21/0.52 double_divide(multiply(inverse(X), identity), X)
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(multiply(double_divide(X, identity), identity), X)
% 0.21/0.52 = { by lemma 9 R->L }
% 0.21/0.52 double_divide(multiply(double_divide(X, inverse(identity)), identity), X)
% 0.21/0.52 = { by lemma 9 R->L }
% 0.21/0.52 double_divide(multiply(double_divide(X, inverse(identity)), inverse(identity)), X)
% 0.21/0.52 = { by lemma 7 R->L }
% 0.21/0.52 double_divide(double_divide(identity, double_divide(double_divide(identity, identity), double_divide(double_divide(multiply(double_divide(X, inverse(identity)), inverse(identity)), X), inverse(identity)))), inverse(identity))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(double_divide(identity, double_divide(double_divide(identity, identity), double_divide(double_divide(multiply(double_divide(X, double_divide(identity, identity)), inverse(identity)), X), inverse(identity)))), inverse(identity))
% 0.21/0.52 = { by lemma 5 R->L }
% 0.21/0.52 double_divide(double_divide(identity, double_divide(double_divide(identity, identity), double_divide(double_divide(inverse(double_divide(inverse(identity), double_divide(X, double_divide(identity, identity)))), X), inverse(identity)))), inverse(identity))
% 0.21/0.52 = { by lemma 11 R->L }
% 0.21/0.52 double_divide(double_divide(identity, double_divide(double_divide(identity, identity), double_divide(double_divide(inverse(double_divide(inverse(identity), double_divide(X, double_divide(identity, identity)))), double_divide(double_divide(identity, double_divide(inverse(identity), double_divide(X, double_divide(identity, identity)))), inverse(identity))), inverse(identity)))), inverse(identity))
% 0.21/0.52 = { by lemma 12 }
% 0.21/0.52 double_divide(double_divide(identity, double_divide(double_divide(identity, identity), identity)), inverse(identity))
% 0.21/0.52 = { by axiom 1 (inverse) R->L }
% 0.21/0.52 double_divide(double_divide(identity, inverse(double_divide(identity, identity))), inverse(identity))
% 0.21/0.52 = { by lemma 5 }
% 0.21/0.52 double_divide(double_divide(identity, multiply(identity, identity)), inverse(identity))
% 0.21/0.52 = { by lemma 8 }
% 0.21/0.52 identity
% 0.21/0.52
% 0.21/0.52 Lemma 14: multiply(identity, X) = X.
% 0.21/0.52 Proof:
% 0.21/0.52 multiply(identity, X)
% 0.21/0.52 = { by lemma 10 R->L }
% 0.21/0.52 inverse(inverse(X))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(inverse(X), identity)
% 0.21/0.52 = { by lemma 9 R->L }
% 0.21/0.52 double_divide(inverse(X), inverse(identity))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(double_divide(X, identity), inverse(identity))
% 0.21/0.52 = { by lemma 9 R->L }
% 0.21/0.52 double_divide(double_divide(X, inverse(identity)), inverse(identity))
% 0.21/0.52 = { by lemma 9 R->L }
% 0.21/0.52 double_divide(double_divide(X, inverse(inverse(identity))), inverse(identity))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(double_divide(X, double_divide(inverse(identity), identity)), inverse(identity))
% 0.21/0.52 = { by lemma 13 R->L }
% 0.21/0.52 double_divide(double_divide(X, double_divide(inverse(identity), double_divide(multiply(inverse(double_divide(identity, X)), identity), double_divide(identity, X)))), inverse(identity))
% 0.21/0.52 = { by lemma 11 }
% 0.21/0.52 multiply(inverse(double_divide(identity, X)), identity)
% 0.21/0.52 = { by lemma 5 }
% 0.21/0.52 multiply(multiply(X, identity), identity)
% 0.21/0.52 = { by lemma 5 R->L }
% 0.21/0.52 inverse(double_divide(identity, multiply(X, identity)))
% 0.21/0.52 = { by axiom 1 (inverse) }
% 0.21/0.52 double_divide(double_divide(identity, multiply(X, identity)), identity)
% 0.21/0.52 = { by lemma 9 R->L }
% 0.21/0.52 double_divide(double_divide(identity, multiply(X, identity)), inverse(identity))
% 0.21/0.52 = { by lemma 8 }
% 0.21/0.52 X
% 0.21/0.52
% 0.21/0.52 Lemma 15: double_divide(double_divide(X, Y), multiply(Y, X)) = identity.
% 0.21/0.52 Proof:
% 0.21/0.52 double_divide(double_divide(X, Y), multiply(Y, X))
% 0.21/0.52 = { by lemma 5 R->L }
% 0.21/0.52 double_divide(double_divide(X, Y), inverse(double_divide(X, Y)))
% 0.21/0.52 = { by axiom 2 (identity) R->L }
% 0.21/0.52 identity
% 0.21/0.52
% 0.21/0.52 Lemma 16: double_divide(identity, X) = inverse(X).
% 0.21/0.52 Proof:
% 0.21/0.52 double_divide(identity, X)
% 0.21/0.52 = { by lemma 12 R->L }
% 0.21/0.52 double_divide(double_divide(inverse(X), double_divide(double_divide(identity, X), inverse(double_divide(identity, X)))), inverse(identity))
% 0.21/0.52 = { by axiom 2 (identity) R->L }
% 0.21/0.52 double_divide(double_divide(inverse(X), identity), inverse(identity))
% 0.21/0.52 = { by axiom 1 (inverse) R->L }
% 0.21/0.52 double_divide(inverse(inverse(X)), inverse(identity))
% 0.21/0.52 = { by lemma 10 }
% 0.21/0.52 double_divide(multiply(identity, X), inverse(identity))
% 0.21/0.52 = { by lemma 9 }
% 0.21/0.52 double_divide(multiply(identity, X), identity)
% 0.21/0.52 = { by axiom 1 (inverse) R->L }
% 0.21/0.52 inverse(multiply(identity, X))
% 0.21/0.52 = { by lemma 10 R->L }
% 0.21/0.52 inverse(inverse(inverse(X)))
% 0.21/0.52 = { by lemma 10 }
% 0.21/0.52 multiply(identity, inverse(X))
% 0.21/0.52 = { by lemma 14 }
% 0.21/0.52 inverse(X)
% 0.21/0.52
% 0.21/0.52 Lemma 17: multiply(X, identity) = X.
% 0.21/0.52 Proof:
% 0.21/0.53 multiply(X, identity)
% 0.21/0.53 = { by lemma 14 R->L }
% 0.21/0.53 multiply(multiply(identity, X), identity)
% 0.21/0.53 = { by lemma 10 R->L }
% 0.21/0.53 multiply(inverse(inverse(X)), identity)
% 0.21/0.53 = { by lemma 7 R->L }
% 0.21/0.53 double_divide(double_divide(identity, double_divide(double_divide(identity, X), double_divide(multiply(inverse(inverse(X)), identity), inverse(X)))), inverse(identity))
% 0.21/0.53 = { by lemma 13 }
% 0.21/0.53 double_divide(double_divide(identity, double_divide(double_divide(identity, X), identity)), inverse(identity))
% 0.21/0.53 = { by axiom 1 (inverse) R->L }
% 0.21/0.53 double_divide(double_divide(identity, inverse(double_divide(identity, X))), inverse(identity))
% 0.21/0.53 = { by lemma 5 }
% 0.21/0.53 double_divide(double_divide(identity, multiply(X, identity)), inverse(identity))
% 0.21/0.53 = { by lemma 8 }
% 0.21/0.53 X
% 0.21/0.53
% 0.21/0.53 Lemma 18: inverse(multiply(double_divide(inverse(X), double_divide(Y, double_divide(X, Z))), Z)) = inverse(Y).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(multiply(double_divide(inverse(X), double_divide(Y, double_divide(X, Z))), Z))
% 0.21/0.53 = { by lemma 16 R->L }
% 0.21/0.53 inverse(multiply(double_divide(double_divide(identity, X), double_divide(Y, double_divide(X, Z))), Z))
% 0.21/0.53 = { by lemma 5 R->L }
% 0.21/0.53 inverse(inverse(double_divide(Z, double_divide(double_divide(identity, X), double_divide(Y, double_divide(X, Z))))))
% 0.21/0.53 = { by lemma 10 }
% 0.21/0.53 multiply(identity, double_divide(Z, double_divide(double_divide(identity, X), double_divide(Y, double_divide(X, Z)))))
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 multiply(inverse(identity), double_divide(Z, double_divide(double_divide(identity, X), double_divide(Y, double_divide(X, Z)))))
% 0.21/0.53 = { by lemma 5 R->L }
% 0.21/0.53 inverse(double_divide(double_divide(Z, double_divide(double_divide(identity, X), double_divide(Y, double_divide(X, Z)))), inverse(identity)))
% 0.21/0.53 = { by lemma 6 }
% 0.21/0.53 inverse(Y)
% 0.21/0.53
% 0.21/0.53 Lemma 19: multiply(double_divide(X, inverse(Y)), inverse(Y)) = inverse(X).
% 0.21/0.53 Proof:
% 0.21/0.53 multiply(double_divide(X, inverse(Y)), inverse(Y))
% 0.21/0.53 = { by lemma 5 R->L }
% 0.21/0.53 inverse(double_divide(inverse(Y), double_divide(X, inverse(Y))))
% 0.21/0.53 = { by lemma 17 R->L }
% 0.21/0.53 inverse(multiply(double_divide(inverse(Y), double_divide(X, inverse(Y))), identity))
% 0.21/0.53 = { by axiom 1 (inverse) }
% 0.21/0.53 inverse(multiply(double_divide(inverse(Y), double_divide(X, double_divide(Y, identity))), identity))
% 0.21/0.53 = { by lemma 18 }
% 0.21/0.53 inverse(X)
% 0.21/0.53
% 0.21/0.53 Lemma 20: inverse(multiply(Y, X)) = double_divide(X, Y).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(multiply(Y, X))
% 0.21/0.53 = { by axiom 1 (inverse) }
% 0.21/0.53 double_divide(multiply(Y, X), identity)
% 0.21/0.53 = { by lemma 15 R->L }
% 0.21/0.53 double_divide(multiply(Y, X), double_divide(double_divide(X, Y), multiply(Y, X)))
% 0.21/0.53 = { by lemma 14 R->L }
% 0.21/0.53 double_divide(multiply(Y, X), double_divide(double_divide(X, Y), multiply(identity, multiply(Y, X))))
% 0.21/0.53 = { by lemma 10 R->L }
% 0.21/0.53 double_divide(multiply(Y, X), double_divide(double_divide(X, Y), inverse(inverse(multiply(Y, X)))))
% 0.21/0.53 = { by lemma 14 R->L }
% 0.21/0.53 double_divide(multiply(identity, multiply(Y, X)), double_divide(double_divide(X, Y), inverse(inverse(multiply(Y, X)))))
% 0.21/0.53 = { by lemma 10 R->L }
% 0.21/0.53 double_divide(inverse(inverse(multiply(Y, X))), double_divide(double_divide(X, Y), inverse(inverse(multiply(Y, X)))))
% 0.21/0.53 = { by lemma 16 R->L }
% 0.21/0.53 double_divide(double_divide(identity, inverse(multiply(Y, X))), double_divide(double_divide(X, Y), inverse(inverse(multiply(Y, X)))))
% 0.21/0.53 = { by lemma 17 R->L }
% 0.21/0.53 multiply(double_divide(double_divide(identity, inverse(multiply(Y, X))), double_divide(double_divide(X, Y), inverse(inverse(multiply(Y, X))))), identity)
% 0.21/0.53 = { by lemma 5 R->L }
% 0.21/0.53 inverse(double_divide(identity, double_divide(double_divide(identity, inverse(multiply(Y, X))), double_divide(double_divide(X, Y), inverse(inverse(multiply(Y, X)))))))
% 0.21/0.53 = { by lemma 19 R->L }
% 0.21/0.53 multiply(double_divide(double_divide(identity, double_divide(double_divide(identity, inverse(multiply(Y, X))), double_divide(double_divide(X, Y), inverse(inverse(multiply(Y, X)))))), inverse(identity)), inverse(identity))
% 0.21/0.53 = { by lemma 7 }
% 0.21/0.53 multiply(double_divide(X, Y), inverse(identity))
% 0.21/0.53 = { by lemma 9 }
% 0.21/0.53 multiply(double_divide(X, Y), identity)
% 0.21/0.53 = { by lemma 17 }
% 0.21/0.53 double_divide(X, Y)
% 0.21/0.53
% 0.21/0.53 Lemma 21: double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(X))), inverse(identity)) = X.
% 0.21/0.53 Proof:
% 0.21/0.53 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(X))), inverse(identity))
% 0.21/0.53 = { by axiom 1 (inverse) }
% 0.21/0.53 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), double_divide(X, identity))), inverse(identity))
% 0.21/0.53 = { by axiom 2 (identity) }
% 0.21/0.53 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), double_divide(X, double_divide(identity, inverse(identity))))), inverse(identity))
% 0.21/0.53 = { by lemma 11 }
% 0.21/0.53 X
% 0.21/0.53
% 0.21/0.53 Lemma 22: double_divide(Y, X) = double_divide(X, Y).
% 0.21/0.53 Proof:
% 0.21/0.53 double_divide(Y, X)
% 0.21/0.53 = { by lemma 14 R->L }
% 0.21/0.53 double_divide(Y, multiply(identity, X))
% 0.21/0.53 = { by lemma 10 R->L }
% 0.21/0.53 double_divide(Y, inverse(inverse(X)))
% 0.21/0.53 = { by axiom 1 (inverse) }
% 0.21/0.53 double_divide(Y, double_divide(inverse(X), identity))
% 0.21/0.53 = { by lemma 20 R->L }
% 0.21/0.53 inverse(multiply(double_divide(inverse(X), identity), Y))
% 0.21/0.53 = { by lemma 13 R->L }
% 0.21/0.53 inverse(multiply(double_divide(inverse(X), double_divide(multiply(inverse(double_divide(X, Y)), identity), double_divide(X, Y))), Y))
% 0.21/0.53 = { by lemma 18 }
% 0.21/0.53 inverse(multiply(inverse(double_divide(X, Y)), identity))
% 0.21/0.53 = { by lemma 20 }
% 0.21/0.53 double_divide(identity, inverse(double_divide(X, Y)))
% 0.21/0.53 = { by lemma 17 R->L }
% 0.21/0.53 multiply(double_divide(identity, inverse(double_divide(X, Y))), identity)
% 0.21/0.53 = { by lemma 5 R->L }
% 0.21/0.53 inverse(double_divide(identity, double_divide(identity, inverse(double_divide(X, Y)))))
% 0.21/0.53 = { by axiom 1 (inverse) }
% 0.21/0.53 double_divide(double_divide(identity, double_divide(identity, inverse(double_divide(X, Y)))), identity)
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 double_divide(double_divide(identity, double_divide(inverse(identity), inverse(double_divide(X, Y)))), identity)
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 double_divide(double_divide(identity, double_divide(inverse(identity), inverse(double_divide(X, Y)))), inverse(identity))
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.54 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(X, Y)))), inverse(identity))
% 0.21/0.54 = { by lemma 21 }
% 0.21/0.54 double_divide(X, Y)
% 0.21/0.54
% 0.21/0.54 Lemma 23: multiply(X, Y) = multiply(Y, X).
% 0.21/0.54 Proof:
% 0.21/0.54 multiply(X, Y)
% 0.21/0.54 = { by lemma 5 R->L }
% 0.21/0.54 inverse(double_divide(Y, X))
% 0.21/0.54 = { by lemma 17 R->L }
% 0.21/0.54 multiply(inverse(double_divide(Y, X)), identity)
% 0.21/0.54 = { by lemma 14 R->L }
% 0.21/0.54 multiply(identity, multiply(inverse(double_divide(Y, X)), identity))
% 0.21/0.54 = { by lemma 10 R->L }
% 0.21/0.54 inverse(inverse(multiply(inverse(double_divide(Y, X)), identity)))
% 0.21/0.54 = { by lemma 18 R->L }
% 0.21/0.54 inverse(inverse(multiply(double_divide(inverse(Y), double_divide(multiply(inverse(double_divide(Y, X)), identity), double_divide(Y, X))), X)))
% 0.21/0.54 = { by lemma 10 }
% 0.21/0.54 multiply(identity, multiply(double_divide(inverse(Y), double_divide(multiply(inverse(double_divide(Y, X)), identity), double_divide(Y, X))), X))
% 0.21/0.54 = { by lemma 14 }
% 0.21/0.54 multiply(double_divide(inverse(Y), double_divide(multiply(inverse(double_divide(Y, X)), identity), double_divide(Y, X))), X)
% 0.21/0.54 = { by lemma 13 }
% 0.21/0.54 multiply(double_divide(inverse(Y), identity), X)
% 0.21/0.54 = { by axiom 1 (inverse) R->L }
% 0.21/0.54 multiply(inverse(inverse(Y)), X)
% 0.21/0.54 = { by lemma 10 }
% 0.21/0.54 multiply(multiply(identity, Y), X)
% 0.21/0.54 = { by lemma 14 }
% 0.21/0.54 multiply(Y, X)
% 0.21/0.54
% 0.21/0.54 Lemma 24: multiply(double_divide(inverse(X), inverse(Y)), inverse(X)) = Y.
% 0.21/0.54 Proof:
% 0.21/0.54 multiply(double_divide(inverse(X), inverse(Y)), inverse(X))
% 0.21/0.54 = { by lemma 5 R->L }
% 0.21/0.54 inverse(double_divide(inverse(X), double_divide(inverse(X), inverse(Y))))
% 0.21/0.54 = { by axiom 1 (inverse) }
% 0.21/0.54 double_divide(double_divide(inverse(X), double_divide(inverse(X), inverse(Y))), identity)
% 0.21/0.54 = { by lemma 9 R->L }
% 0.21/0.54 double_divide(double_divide(inverse(X), double_divide(inverse(X), inverse(Y))), inverse(identity))
% 0.21/0.54 = { by lemma 18 R->L }
% 0.21/0.54 double_divide(double_divide(inverse(X), double_divide(inverse(multiply(double_divide(inverse(Z), double_divide(X, double_divide(Z, W))), W)), inverse(Y))), inverse(identity))
% 0.21/0.54 = { by lemma 16 R->L }
% 0.21/0.54 double_divide(double_divide(inverse(X), double_divide(double_divide(identity, multiply(double_divide(inverse(Z), double_divide(X, double_divide(Z, W))), W)), inverse(Y))), inverse(identity))
% 0.21/0.54 = { by lemma 18 R->L }
% 0.21/0.54 double_divide(double_divide(inverse(multiply(double_divide(inverse(Z), double_divide(X, double_divide(Z, W))), W)), double_divide(double_divide(identity, multiply(double_divide(inverse(Z), double_divide(X, double_divide(Z, W))), W)), inverse(Y))), inverse(identity))
% 0.21/0.54 = { by lemma 12 }
% 0.21/0.54 Y
% 0.21/0.54
% 0.21/0.54 Lemma 25: double_divide(X, double_divide(Y, double_divide(Z, double_divide(X, inverse(Y))))) = inverse(Z).
% 0.21/0.54 Proof:
% 0.21/0.54 double_divide(X, double_divide(Y, double_divide(Z, double_divide(X, inverse(Y)))))
% 0.21/0.54 = { by lemma 22 }
% 0.21/0.54 double_divide(X, double_divide(Y, double_divide(Z, double_divide(inverse(Y), X))))
% 0.21/0.54 = { by lemma 14 R->L }
% 0.21/0.54 double_divide(X, double_divide(multiply(identity, Y), double_divide(Z, double_divide(inverse(Y), X))))
% 0.21/0.54 = { by lemma 20 R->L }
% 0.21/0.54 inverse(multiply(double_divide(multiply(identity, Y), double_divide(Z, double_divide(inverse(Y), X))), X))
% 0.21/0.54 = { by lemma 10 R->L }
% 0.21/0.54 inverse(multiply(double_divide(inverse(inverse(Y)), double_divide(Z, double_divide(inverse(Y), X))), X))
% 0.21/0.54 = { by lemma 18 }
% 0.21/0.54 inverse(Z)
% 0.21/0.54
% 0.21/0.54 Lemma 26: double_divide(inverse(X), multiply(X, Y)) = inverse(Y).
% 0.21/0.54 Proof:
% 0.21/0.54 double_divide(inverse(X), multiply(X, Y))
% 0.21/0.54 = { by lemma 5 R->L }
% 0.21/0.54 double_divide(inverse(X), inverse(double_divide(Y, X)))
% 0.21/0.54 = { by lemma 16 R->L }
% 0.21/0.54 double_divide(inverse(X), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by lemma 14 R->L }
% 0.21/0.54 double_divide(multiply(identity, inverse(X)), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by lemma 10 R->L }
% 0.21/0.54 double_divide(inverse(inverse(inverse(X))), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by axiom 1 (inverse) }
% 0.21/0.54 double_divide(double_divide(inverse(inverse(X)), identity), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by lemma 9 R->L }
% 0.21/0.54 double_divide(double_divide(inverse(inverse(X)), inverse(identity)), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by axiom 1 (inverse) }
% 0.21/0.54 double_divide(double_divide(double_divide(inverse(X), identity), inverse(identity)), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by lemma 15 R->L }
% 0.21/0.54 double_divide(double_divide(double_divide(inverse(X), double_divide(double_divide(identity, identity), multiply(identity, identity))), inverse(identity)), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by lemma 14 }
% 0.21/0.54 double_divide(double_divide(double_divide(inverse(X), double_divide(double_divide(identity, identity), identity)), inverse(identity)), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by axiom 1 (inverse) R->L }
% 0.21/0.54 double_divide(double_divide(double_divide(inverse(X), double_divide(inverse(identity), identity)), inverse(identity)), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by lemma 15 R->L }
% 0.21/0.54 double_divide(double_divide(double_divide(inverse(X), double_divide(inverse(identity), double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(identity, inverse(X))))), multiply(double_divide(inverse(identity), inverse(double_divide(identity, inverse(X)))), inverse(identity))))), inverse(identity)), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by lemma 24 }
% 0.21/0.54 double_divide(double_divide(double_divide(inverse(X), double_divide(inverse(identity), double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(identity, inverse(X))))), double_divide(identity, inverse(X))))), inverse(identity)), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by lemma 11 }
% 0.21/0.54 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(double_divide(identity, inverse(X))))), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by lemma 5 }
% 0.21/0.54 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), multiply(inverse(X), identity))), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by lemma 17 }
% 0.21/0.54 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(X))), double_divide(identity, double_divide(Y, X)))
% 0.21/0.54 = { by lemma 21 R->L }
% 0.21/0.54 double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(X))), double_divide(identity, double_divide(Y, double_divide(double_divide(inverse(identity), double_divide(inverse(identity), inverse(X))), inverse(identity)))))
% 0.21/0.54 = { by lemma 25 }
% 0.21/0.54 inverse(Y)
% 0.21/0.54
% 0.21/0.54 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.21/0.54 Proof:
% 0.21/0.54 multiply(multiply(a3, b3), c3)
% 0.21/0.54 = { by lemma 14 R->L }
% 0.21/0.54 multiply(identity, multiply(multiply(a3, b3), c3))
% 0.21/0.54 = { by lemma 10 R->L }
% 0.21/0.54 inverse(inverse(multiply(multiply(a3, b3), c3)))
% 0.21/0.54 = { by lemma 18 R->L }
% 0.21/0.54 inverse(inverse(multiply(double_divide(inverse(c3), double_divide(multiply(multiply(a3, b3), c3), double_divide(c3, double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3)))))), double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))))))
% 0.21/0.54 = { by lemma 25 }
% 0.21/0.54 inverse(inverse(multiply(double_divide(inverse(c3), inverse(b3)), double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))))))
% 0.21/0.54 = { by lemma 20 }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), double_divide(inverse(c3), inverse(b3))))
% 0.21/0.54 = { by lemma 22 }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), double_divide(inverse(b3), inverse(c3))))
% 0.21/0.54 = { by lemma 24 R->L }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), double_divide(inverse(b3), multiply(double_divide(inverse(inverse(b3)), inverse(inverse(c3))), inverse(inverse(b3))))))
% 0.21/0.54 = { by lemma 10 }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), double_divide(inverse(b3), multiply(double_divide(multiply(identity, b3), inverse(inverse(c3))), inverse(inverse(b3))))))
% 0.21/0.54 = { by lemma 14 }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), double_divide(inverse(b3), multiply(double_divide(b3, inverse(inverse(c3))), inverse(inverse(b3))))))
% 0.21/0.54 = { by lemma 10 }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), double_divide(inverse(b3), multiply(double_divide(b3, inverse(inverse(c3))), multiply(identity, b3)))))
% 0.21/0.54 = { by lemma 14 }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), double_divide(inverse(b3), multiply(double_divide(b3, inverse(inverse(c3))), b3))))
% 0.21/0.54 = { by lemma 10 }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), double_divide(inverse(b3), multiply(double_divide(b3, multiply(identity, c3)), b3))))
% 0.21/0.54 = { by lemma 14 }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), double_divide(inverse(b3), multiply(double_divide(b3, c3), b3))))
% 0.21/0.54 = { by lemma 23 }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), double_divide(inverse(b3), multiply(b3, double_divide(b3, c3)))))
% 0.21/0.54 = { by lemma 26 }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), inverse(double_divide(b3, c3))))
% 0.21/0.54 = { by lemma 5 }
% 0.21/0.54 inverse(double_divide(double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3))), multiply(c3, b3)))
% 0.21/0.54 = { by lemma 22 R->L }
% 0.21/0.54 inverse(double_divide(multiply(c3, b3), double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3)))))
% 0.21/0.54 = { by lemma 23 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), inverse(c3)))))
% 0.21/0.54 = { by lemma 26 R->L }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), double_divide(inverse(multiply(a3, b3)), multiply(multiply(a3, b3), c3))))))
% 0.21/0.54 = { by lemma 22 R->L }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), double_divide(multiply(multiply(a3, b3), c3), inverse(multiply(a3, b3)))))))
% 0.21/0.54 = { by axiom 1 (inverse) }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), double_divide(multiply(multiply(a3, b3), c3), double_divide(multiply(a3, b3), identity))))))
% 0.21/0.54 = { by axiom 2 (identity) }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(b3, double_divide(multiply(multiply(a3, b3), c3), double_divide(multiply(multiply(a3, b3), c3), double_divide(multiply(a3, b3), double_divide(multiply(multiply(a3, b3), c3), inverse(multiply(multiply(a3, b3), c3)))))))))
% 0.21/0.54 = { by lemma 25 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(b3, inverse(multiply(a3, b3)))))
% 0.21/0.54 = { by lemma 22 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), b3)))
% 0.21/0.54 = { by lemma 17 R->L }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), multiply(b3, identity))))
% 0.21/0.54 = { by lemma 9 R->L }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), multiply(b3, inverse(identity)))))
% 0.21/0.54 = { by lemma 11 R->L }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), multiply(double_divide(double_divide(inverse(a3), double_divide(inverse(identity), double_divide(b3, double_divide(identity, inverse(a3))))), inverse(identity)), inverse(identity)))))
% 0.21/0.54 = { by lemma 19 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), inverse(double_divide(inverse(a3), double_divide(inverse(identity), double_divide(b3, double_divide(identity, inverse(a3)))))))))
% 0.21/0.54 = { by lemma 5 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), multiply(double_divide(inverse(identity), double_divide(b3, double_divide(identity, inverse(a3)))), inverse(a3)))))
% 0.21/0.54 = { by lemma 9 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), multiply(double_divide(identity, double_divide(b3, double_divide(identity, inverse(a3)))), inverse(a3)))))
% 0.21/0.54 = { by lemma 16 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), multiply(inverse(double_divide(b3, double_divide(identity, inverse(a3)))), inverse(a3)))))
% 0.21/0.54 = { by lemma 5 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), multiply(multiply(double_divide(identity, inverse(a3)), b3), inverse(a3)))))
% 0.21/0.54 = { by lemma 16 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), multiply(multiply(inverse(inverse(a3)), b3), inverse(a3)))))
% 0.21/0.54 = { by lemma 10 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), multiply(multiply(multiply(identity, a3), b3), inverse(a3)))))
% 0.21/0.54 = { by lemma 14 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), double_divide(inverse(multiply(a3, b3)), multiply(multiply(a3, b3), inverse(a3)))))
% 0.21/0.54 = { by lemma 26 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), inverse(inverse(a3))))
% 0.21/0.54 = { by lemma 10 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), multiply(identity, a3)))
% 0.21/0.54 = { by lemma 14 }
% 0.21/0.54 inverse(double_divide(multiply(b3, c3), a3))
% 0.21/0.54 = { by lemma 20 R->L }
% 0.21/0.54 inverse(inverse(multiply(a3, multiply(b3, c3))))
% 0.21/0.54 = { by lemma 10 }
% 0.21/0.54 multiply(identity, multiply(a3, multiply(b3, c3)))
% 0.21/0.54 = { by lemma 14 }
% 0.21/0.54 multiply(a3, multiply(b3, c3))
% 0.21/0.54 % SZS output end Proof
% 0.21/0.54
% 0.21/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------