TSTP Solution File: GRP600-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP600-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n003.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 01:19:04 EDT 2023
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP600-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.12/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 21:02:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.38 Command-line arguments: --no-flatten-goal
% 0.18/0.38
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.18/0.40 Axiom 2 (single_axiom): double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y))))) = Z.
% 0.18/0.40
% 0.18/0.40 Lemma 3: double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X)) = Z.
% 0.18/0.40 Proof:
% 0.18/0.40 double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X))
% 0.18/0.40 = { by axiom 1 (multiply) }
% 0.18/0.40 double_divide(double_divide(X, Y), multiply(inverse(double_divide(inverse(Z), Y)), X))
% 0.18/0.40 = { by axiom 1 (multiply) }
% 0.18/0.40 double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y)))))
% 0.18/0.40 = { by axiom 2 (single_axiom) }
% 0.18/0.40 Z
% 0.18/0.40
% 0.18/0.40 Lemma 4: multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X)) = inverse(Y).
% 0.18/0.40 Proof:
% 0.18/0.40 multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X))
% 0.18/0.40 = { by axiom 1 (multiply) }
% 0.18/0.40 inverse(double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.18/0.40 = { by lemma 3 }
% 0.18/0.40 inverse(Y)
% 0.18/0.40
% 0.18/0.40 Lemma 5: multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y) = inverse(W).
% 0.18/0.40 Proof:
% 0.18/0.40 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y)
% 0.18/0.40 = { by lemma 3 R->L }
% 0.18/0.40 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.18/0.40 = { by lemma 4 }
% 0.18/0.40 inverse(W)
% 0.18/0.40
% 0.18/0.40 Lemma 6: multiply(multiply(inverse(X), inverse(Y)), X) = inverse(Y).
% 0.18/0.40 Proof:
% 0.18/0.40 multiply(multiply(inverse(X), inverse(Y)), X)
% 0.18/0.40 = { by lemma 3 R->L }
% 0.18/0.40 multiply(multiply(inverse(X), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))), X)
% 0.18/0.40 = { by lemma 5 R->L }
% 0.18/0.40 multiply(multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(X)), double_divide(Z, W)), inverse(Y)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))), X)
% 0.18/0.40 = { by lemma 5 }
% 0.18/0.40 inverse(Y)
% 0.18/0.40
% 0.18/0.40 Lemma 7: double_divide(double_divide(X, inverse(X)), multiply(Y, Z)) = double_divide(Z, Y).
% 0.18/0.40 Proof:
% 0.18/0.40 double_divide(double_divide(X, inverse(X)), multiply(Y, Z))
% 0.18/0.40 = { by axiom 1 (multiply) }
% 0.18/0.40 double_divide(double_divide(X, inverse(X)), inverse(double_divide(Z, Y)))
% 0.18/0.40 = { by lemma 6 R->L }
% 0.18/0.40 double_divide(double_divide(X, inverse(X)), multiply(multiply(inverse(X), inverse(double_divide(Z, Y))), X))
% 0.18/0.40 = { by lemma 3 }
% 0.18/0.40 double_divide(Z, Y)
% 0.18/0.40
% 0.18/0.40 Lemma 8: double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), inverse(Z)) = X.
% 0.18/0.40 Proof:
% 0.18/0.40 double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), inverse(Z))
% 0.18/0.40 = { by lemma 4 R->L }
% 0.18/0.40 double_divide(double_divide(double_divide(inverse(X), Y), multiply(Y, inverse(Z))), multiply(multiply(multiply(Y, inverse(Z)), inverse(X)), double_divide(inverse(X), Y)))
% 0.18/0.40 = { by lemma 3 }
% 0.18/0.40 X
% 0.18/0.40
% 0.18/0.40 Lemma 9: double_divide(double_divide(X, inverse(Y)), inverse(Y)) = X.
% 0.18/0.40 Proof:
% 0.18/0.40 double_divide(double_divide(X, inverse(Y)), inverse(Y))
% 0.18/0.41 = { by lemma 3 R->L }
% 0.18/0.41 double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(X))), Z)), multiply(multiply(multiply(multiply(W, inverse(inverse(X))), Z), inverse(double_divide(V, inverse(V)))), double_divide(Z, W))), multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(X))), Z), inverse(double_divide(V, inverse(V)))), double_divide(Z, W)), inverse(X)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(X))), Z)))), inverse(Y)), inverse(Y))
% 0.18/0.41 = { by lemma 3 }
% 0.18/0.41 double_divide(double_divide(double_divide(double_divide(V, inverse(V)), multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(X))), Z), inverse(double_divide(V, inverse(V)))), double_divide(Z, W)), inverse(X)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(X))), Z)))), inverse(Y)), inverse(Y))
% 0.18/0.41 = { by lemma 5 }
% 0.18/0.41 double_divide(double_divide(double_divide(double_divide(V, inverse(V)), multiply(inverse(double_divide(V, inverse(V))), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(X))), Z)))), inverse(Y)), inverse(Y))
% 0.18/0.41 = { by lemma 3 }
% 0.18/0.41 double_divide(double_divide(double_divide(double_divide(V, inverse(V)), multiply(inverse(double_divide(V, inverse(V))), inverse(X))), inverse(Y)), inverse(Y))
% 0.18/0.41 = { by lemma 7 }
% 0.18/0.41 double_divide(double_divide(double_divide(inverse(X), inverse(double_divide(V, inverse(V)))), inverse(Y)), inverse(Y))
% 0.18/0.41 = { by axiom 1 (multiply) R->L }
% 0.18/0.41 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(V), V)), inverse(Y)), inverse(Y))
% 0.18/0.41 = { by lemma 6 R->L }
% 0.18/0.41 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(V), V)), multiply(multiply(inverse(double_divide(V, inverse(V))), inverse(Y)), double_divide(V, inverse(V)))), inverse(Y))
% 0.18/0.41 = { by axiom 1 (multiply) }
% 0.18/0.41 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(V), V)), multiply(inverse(double_divide(inverse(Y), inverse(double_divide(V, inverse(V))))), double_divide(V, inverse(V)))), inverse(Y))
% 0.18/0.41 = { by lemma 6 R->L }
% 0.18/0.41 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(V), V)), multiply(multiply(multiply(inverse(V), inverse(double_divide(inverse(Y), inverse(double_divide(V, inverse(V)))))), V), double_divide(V, inverse(V)))), inverse(Y))
% 0.18/0.41 = { by lemma 4 }
% 0.18/0.41 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(V), V)), inverse(double_divide(inverse(Y), inverse(double_divide(V, inverse(V)))))), inverse(Y))
% 0.18/0.41 = { by axiom 1 (multiply) R->L }
% 0.18/0.41 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(V), V)), multiply(inverse(double_divide(V, inverse(V))), inverse(Y))), inverse(Y))
% 0.18/0.41 = { by axiom 1 (multiply) R->L }
% 0.18/0.41 double_divide(double_divide(double_divide(inverse(X), multiply(inverse(V), V)), multiply(multiply(inverse(V), V), inverse(Y))), inverse(Y))
% 0.18/0.41 = { by lemma 8 }
% 0.18/0.41 X
% 0.18/0.41
% 0.18/0.41 Lemma 10: double_divide(double_divide(inverse(X), inverse(inverse(Y))), inverse(X)) = Y.
% 0.18/0.41 Proof:
% 0.18/0.41 double_divide(double_divide(inverse(X), inverse(inverse(Y))), inverse(X))
% 0.18/0.41 = { by lemma 7 R->L }
% 0.18/0.41 double_divide(double_divide(double_divide(inverse(Y), inverse(inverse(Y))), multiply(inverse(inverse(Y)), inverse(X))), inverse(X))
% 0.18/0.41 = { by lemma 8 }
% 0.18/0.41 Y
% 0.18/0.41
% 0.18/0.41 Lemma 11: inverse(inverse(X)) = X.
% 0.18/0.41 Proof:
% 0.18/0.41 inverse(inverse(X))
% 0.18/0.41 = { by lemma 9 R->L }
% 0.18/0.41 double_divide(double_divide(inverse(inverse(X)), inverse(inverse(X))), inverse(inverse(X)))
% 0.18/0.41 = { by lemma 10 }
% 0.18/0.41 X
% 0.18/0.41
% 0.18/0.41 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(a, b)
% 0.18/0.41 = { by axiom 1 (multiply) }
% 0.18/0.41 inverse(double_divide(b, a))
% 0.18/0.41 = { by lemma 10 R->L }
% 0.18/0.41 inverse(double_divide(double_divide(double_divide(inverse(inverse(a)), inverse(inverse(b))), inverse(inverse(a))), a))
% 0.18/0.41 = { by lemma 11 }
% 0.18/0.41 inverse(double_divide(double_divide(double_divide(a, inverse(inverse(b))), inverse(inverse(a))), a))
% 0.18/0.41 = { by lemma 11 }
% 0.18/0.41 inverse(double_divide(double_divide(double_divide(a, b), inverse(inverse(a))), a))
% 0.18/0.41 = { by lemma 11 }
% 0.18/0.41 inverse(double_divide(double_divide(double_divide(a, b), a), a))
% 0.18/0.41 = { by lemma 11 R->L }
% 0.18/0.41 inverse(double_divide(double_divide(double_divide(a, b), a), inverse(inverse(a))))
% 0.18/0.41 = { by lemma 11 R->L }
% 0.18/0.41 inverse(double_divide(double_divide(double_divide(a, b), inverse(inverse(a))), inverse(inverse(a))))
% 0.18/0.41 = { by lemma 9 }
% 0.18/0.41 inverse(double_divide(a, b))
% 0.18/0.41 = { by axiom 1 (multiply) R->L }
% 0.18/0.41 multiply(b, a)
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41
% 0.18/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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