TSTP Solution File: GRP613-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP613-1 : 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 : n017.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 01:19:07 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP613-1 : 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
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 20:04:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.40 Command-line arguments: --no-flatten-goal
% 0.20/0.40
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.20/0.42 Axiom 2 (single_axiom): double_divide(inverse(double_divide(inverse(double_divide(X, inverse(Y))), Z)), double_divide(X, Z)) = Y.
% 0.20/0.42
% 0.20/0.42 Lemma 3: double_divide(multiply(X, multiply(inverse(Y), Z)), double_divide(Z, X)) = Y.
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(multiply(X, multiply(inverse(Y), Z)), double_divide(Z, X))
% 0.20/0.42 = { by axiom 1 (multiply) }
% 0.20/0.42 double_divide(multiply(X, inverse(double_divide(Z, inverse(Y)))), double_divide(Z, X))
% 0.20/0.42 = { by axiom 1 (multiply) }
% 0.20/0.42 double_divide(inverse(double_divide(inverse(double_divide(Z, inverse(Y))), X)), double_divide(Z, X))
% 0.20/0.42 = { by axiom 2 (single_axiom) }
% 0.20/0.42 Y
% 0.20/0.42
% 0.20/0.42 Lemma 4: multiply(double_divide(X, Y), multiply(Y, multiply(inverse(Z), X))) = inverse(Z).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(double_divide(X, Y), multiply(Y, multiply(inverse(Z), X)))
% 0.20/0.42 = { by axiom 1 (multiply) }
% 0.20/0.42 inverse(double_divide(multiply(Y, multiply(inverse(Z), X)), double_divide(X, Y)))
% 0.20/0.42 = { by lemma 3 }
% 0.20/0.42 inverse(Z)
% 0.20/0.42
% 0.20/0.42 Lemma 5: multiply(X, multiply(double_divide(Y, Z), multiply(inverse(W), multiply(Z, multiply(inverse(X), Y))))) = inverse(W).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, multiply(double_divide(Y, Z), multiply(inverse(W), multiply(Z, multiply(inverse(X), Y)))))
% 0.20/0.42 = { by lemma 3 R->L }
% 0.20/0.42 multiply(double_divide(multiply(Z, multiply(inverse(X), Y)), double_divide(Y, Z)), multiply(double_divide(Y, Z), multiply(inverse(W), multiply(Z, multiply(inverse(X), Y)))))
% 0.20/0.42 = { by lemma 4 }
% 0.20/0.42 inverse(W)
% 0.20/0.42
% 0.20/0.42 Lemma 6: multiply(X, multiply(inverse(Y), inverse(X))) = inverse(Y).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, multiply(inverse(Y), inverse(X)))
% 0.20/0.42 = { by lemma 3 R->L }
% 0.20/0.42 multiply(X, multiply(double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z)), inverse(X)))
% 0.20/0.42 = { by lemma 5 R->L }
% 0.20/0.42 multiply(X, multiply(double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z)), multiply(inverse(Y), multiply(double_divide(W, Z), multiply(inverse(X), multiply(Z, multiply(inverse(inverse(Y)), W)))))))
% 0.20/0.42 = { by lemma 5 }
% 0.20/0.42 inverse(Y)
% 0.20/0.42
% 0.20/0.42 Lemma 7: double_divide(inverse(X), double_divide(inverse(Y), Y)) = X.
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(inverse(X), double_divide(inverse(Y), Y))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 double_divide(multiply(Y, multiply(inverse(X), inverse(Y))), double_divide(inverse(Y), Y))
% 0.20/0.42 = { by lemma 3 }
% 0.20/0.42 X
% 0.20/0.42
% 0.20/0.42 Lemma 8: double_divide(multiply(X, Y), double_divide(inverse(Z), Z)) = double_divide(Y, X).
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(multiply(X, Y), double_divide(inverse(Z), Z))
% 0.20/0.42 = { by axiom 1 (multiply) }
% 0.20/0.42 double_divide(inverse(double_divide(Y, X)), double_divide(inverse(Z), Z))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 double_divide(Y, X)
% 0.20/0.42
% 0.20/0.42 Lemma 9: double_divide(inverse(X), double_divide(multiply(inverse(X), Y), double_divide(Y, inverse(Z)))) = Z.
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(inverse(X), double_divide(multiply(inverse(X), Y), double_divide(Y, inverse(Z))))
% 0.20/0.42 = { by lemma 4 R->L }
% 0.20/0.42 double_divide(multiply(double_divide(Y, inverse(Z)), multiply(inverse(Z), multiply(inverse(X), Y))), double_divide(multiply(inverse(X), Y), double_divide(Y, inverse(Z))))
% 0.20/0.42 = { by lemma 3 }
% 0.20/0.42 Z
% 0.20/0.42
% 0.20/0.42 Lemma 10: double_divide(inverse(X), double_divide(inverse(X), Y)) = Y.
% 0.20/0.42 Proof:
% 0.20/0.43 double_divide(inverse(X), double_divide(inverse(X), Y))
% 0.20/0.43 = { by lemma 3 R->L }
% 0.20/0.43 double_divide(inverse(X), double_divide(inverse(X), double_divide(multiply(double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z)), multiply(inverse(Y), multiply(double_divide(W, Z), multiply(inverse(double_divide(inverse(V), V)), multiply(Z, multiply(inverse(inverse(Y)), W)))))), double_divide(multiply(double_divide(W, Z), multiply(inverse(double_divide(inverse(V), V)), multiply(Z, multiply(inverse(inverse(Y)), W)))), double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z))))))
% 0.20/0.43 = { by lemma 3 }
% 0.20/0.43 double_divide(inverse(X), double_divide(inverse(X), double_divide(multiply(double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z)), multiply(inverse(Y), multiply(double_divide(W, Z), multiply(inverse(double_divide(inverse(V), V)), multiply(Z, multiply(inverse(inverse(Y)), W)))))), double_divide(inverse(V), V))))
% 0.20/0.43 = { by lemma 5 }
% 0.20/0.43 double_divide(inverse(X), double_divide(inverse(X), double_divide(multiply(double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z)), inverse(double_divide(inverse(V), V))), double_divide(inverse(V), V))))
% 0.20/0.43 = { by lemma 3 }
% 0.20/0.43 double_divide(inverse(X), double_divide(inverse(X), double_divide(multiply(inverse(Y), inverse(double_divide(inverse(V), V))), double_divide(inverse(V), V))))
% 0.20/0.43 = { by lemma 8 }
% 0.20/0.43 double_divide(inverse(X), double_divide(inverse(X), double_divide(inverse(double_divide(inverse(V), V)), inverse(Y))))
% 0.20/0.43 = { by axiom 1 (multiply) R->L }
% 0.20/0.43 double_divide(inverse(X), double_divide(inverse(X), double_divide(multiply(V, inverse(V)), inverse(Y))))
% 0.20/0.43 = { by lemma 6 R->L }
% 0.20/0.43 double_divide(inverse(X), double_divide(multiply(double_divide(inverse(V), V), multiply(inverse(X), inverse(double_divide(inverse(V), V)))), double_divide(multiply(V, inverse(V)), inverse(Y))))
% 0.20/0.43 = { by axiom 1 (multiply) }
% 0.20/0.43 double_divide(inverse(X), double_divide(multiply(double_divide(inverse(V), V), inverse(double_divide(inverse(double_divide(inverse(V), V)), inverse(X)))), double_divide(multiply(V, inverse(V)), inverse(Y))))
% 0.20/0.43 = { by lemma 6 R->L }
% 0.20/0.43 double_divide(inverse(X), double_divide(multiply(double_divide(inverse(V), V), multiply(V, multiply(inverse(double_divide(inverse(double_divide(inverse(V), V)), inverse(X))), inverse(V)))), double_divide(multiply(V, inverse(V)), inverse(Y))))
% 0.20/0.43 = { by lemma 4 }
% 0.20/0.43 double_divide(inverse(X), double_divide(inverse(double_divide(inverse(double_divide(inverse(V), V)), inverse(X))), double_divide(multiply(V, inverse(V)), inverse(Y))))
% 0.20/0.43 = { by axiom 1 (multiply) R->L }
% 0.20/0.43 double_divide(inverse(X), double_divide(multiply(inverse(X), inverse(double_divide(inverse(V), V))), double_divide(multiply(V, inverse(V)), inverse(Y))))
% 0.20/0.43 = { by axiom 1 (multiply) R->L }
% 0.20/0.43 double_divide(inverse(X), double_divide(multiply(inverse(X), multiply(V, inverse(V))), double_divide(multiply(V, inverse(V)), inverse(Y))))
% 0.20/0.43 = { by lemma 9 }
% 0.20/0.43 Y
% 0.20/0.43
% 0.20/0.43 Lemma 11: double_divide(inverse(X), double_divide(inverse(inverse(Y)), inverse(X))) = Y.
% 0.20/0.43 Proof:
% 0.20/0.43 double_divide(inverse(X), double_divide(inverse(inverse(Y)), inverse(X)))
% 0.20/0.43 = { by lemma 8 R->L }
% 0.20/0.43 double_divide(inverse(X), double_divide(multiply(inverse(X), inverse(inverse(Y))), double_divide(inverse(inverse(Y)), inverse(Y))))
% 0.20/0.43 = { by lemma 9 }
% 0.20/0.43 Y
% 0.20/0.43
% 0.20/0.43 Lemma 12: inverse(inverse(X)) = X.
% 0.20/0.43 Proof:
% 0.20/0.43 inverse(inverse(X))
% 0.20/0.43 = { by lemma 10 R->L }
% 0.20/0.43 double_divide(inverse(inverse(X)), double_divide(inverse(inverse(X)), inverse(inverse(X))))
% 0.20/0.43 = { by lemma 11 }
% 0.20/0.43 X
% 0.20/0.43
% 0.20/0.43 Lemma 13: multiply(Y, X) = multiply(X, Y).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(Y, X)
% 0.20/0.43 = { by axiom 1 (multiply) }
% 0.20/0.43 inverse(double_divide(X, Y))
% 0.20/0.43 = { by lemma 11 R->L }
% 0.20/0.43 inverse(double_divide(X, double_divide(inverse(inverse(X)), double_divide(inverse(inverse(Y)), inverse(inverse(X))))))
% 0.20/0.43 = { by lemma 12 }
% 0.20/0.43 inverse(double_divide(X, double_divide(X, double_divide(inverse(inverse(Y)), inverse(inverse(X))))))
% 0.20/0.43 = { by lemma 12 }
% 0.20/0.43 inverse(double_divide(X, double_divide(X, double_divide(Y, inverse(inverse(X))))))
% 0.20/0.43 = { by lemma 12 }
% 0.20/0.43 inverse(double_divide(X, double_divide(X, double_divide(Y, X))))
% 0.20/0.43 = { by lemma 12 R->L }
% 0.20/0.43 inverse(double_divide(X, double_divide(inverse(inverse(X)), double_divide(Y, X))))
% 0.20/0.43 = { by lemma 12 R->L }
% 0.20/0.43 inverse(double_divide(inverse(inverse(X)), double_divide(inverse(inverse(X)), double_divide(Y, X))))
% 0.20/0.43 = { by lemma 10 }
% 0.20/0.43 inverse(double_divide(Y, X))
% 0.20/0.43 = { by axiom 1 (multiply) R->L }
% 0.20/0.43 multiply(X, Y)
% 0.20/0.43
% 0.20/0.43 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(inverse(a1), a1)
% 0.20/0.43 = { by lemma 13 R->L }
% 0.20/0.43 multiply(a1, inverse(a1))
% 0.20/0.43 = { by axiom 1 (multiply) }
% 0.20/0.43 inverse(double_divide(inverse(a1), a1))
% 0.20/0.43 = { by lemma 7 R->L }
% 0.20/0.43 inverse(double_divide(inverse(a1), double_divide(inverse(a1), double_divide(inverse(b1), b1))))
% 0.20/0.43 = { by lemma 10 }
% 0.20/0.43 inverse(double_divide(inverse(b1), b1))
% 0.20/0.43 = { by axiom 1 (multiply) R->L }
% 0.20/0.43 multiply(b1, inverse(b1))
% 0.20/0.43 = { by lemma 13 }
% 0.20/0.43 multiply(inverse(b1), b1)
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------