TSTP Solution File: GRP602-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP602-1 : 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 : n001.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
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP602-1 : 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
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 00:00:51 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.38 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 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): inverse(double_divide(inverse(double_divide(X, inverse(double_divide(Y, double_divide(X, Z))))), Z)) = Y.
% 0.18/0.41
% 0.18/0.41 Lemma 3: multiply(X, multiply(multiply(double_divide(Y, X), Z), Y)) = Z.
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(X, multiply(multiply(double_divide(Y, X), Z), Y))
% 0.18/0.41 = { by axiom 1 (multiply) }
% 0.18/0.41 multiply(X, multiply(inverse(double_divide(Z, double_divide(Y, X))), Y))
% 0.18/0.41 = { by axiom 1 (multiply) }
% 0.18/0.41 multiply(X, inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))))
% 0.18/0.41 = { by axiom 1 (multiply) }
% 0.18/0.41 inverse(double_divide(inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))), X))
% 0.18/0.41 = { by axiom 2 (single_axiom) }
% 0.18/0.41 Z
% 0.18/0.41
% 0.18/0.41 Lemma 4: multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X) = multiply(Z, multiply(W, Y)).
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)
% 0.18/0.41 = { by lemma 3 R->L }
% 0.18/0.41 multiply(Z, multiply(multiply(double_divide(Y, Z), multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)), Y))
% 0.18/0.41 = { by lemma 3 }
% 0.18/0.41 multiply(Z, multiply(W, Y))
% 0.18/0.41
% 0.18/0.41 Lemma 5: multiply(double_divide(X, Y), multiply(Y, multiply(Z, X))) = Z.
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(double_divide(X, Y), multiply(Y, multiply(Z, X)))
% 0.18/0.41 = { by lemma 4 R->L }
% 0.18/0.41 multiply(double_divide(X, Y), multiply(multiply(double_divide(W, double_divide(X, Y)), Z), W))
% 0.18/0.41 = { by lemma 3 }
% 0.18/0.41 Z
% 0.18/0.41
% 0.18/0.41 Lemma 6: multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, Y)) = double_divide(Z, X).
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, Y))
% 0.18/0.41 = { by lemma 5 R->L }
% 0.18/0.41 multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, multiply(double_divide(Z, X), multiply(X, multiply(Y, Z)))))
% 0.18/0.41 = { by lemma 5 }
% 0.18/0.41 double_divide(Z, X)
% 0.18/0.41
% 0.18/0.41 Lemma 7: double_divide(X, multiply(double_divide(multiply(Y, X), Z), Y)) = Z.
% 0.18/0.41 Proof:
% 0.18/0.41 double_divide(X, multiply(double_divide(multiply(Y, X), Z), Y))
% 0.18/0.41 = { by lemma 6 R->L }
% 0.18/0.41 multiply(double_divide(multiply(multiply(double_divide(multiply(Y, X), Z), Y), multiply(Y, X)), double_divide(multiply(Y, X), Z)), multiply(double_divide(multiply(Y, X), Z), Y))
% 0.18/0.41 = { by lemma 5 R->L }
% 0.18/0.41 multiply(double_divide(multiply(multiply(double_divide(multiply(Y, X), Z), Y), multiply(Y, X)), double_divide(multiply(Y, X), Z)), multiply(double_divide(multiply(Y, X), Z), multiply(Z, multiply(multiply(double_divide(multiply(Y, X), Z), Y), multiply(Y, X)))))
% 0.18/0.41 = { by lemma 5 }
% 0.18/0.41 Z
% 0.18/0.41
% 0.18/0.41 Lemma 8: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(multiply(X, inverse(X)), Y)
% 0.18/0.41 = { by lemma 3 R->L }
% 0.18/0.41 multiply(multiply(X, inverse(X)), multiply(inverse(X), multiply(multiply(double_divide(Z, inverse(X)), Y), Z)))
% 0.18/0.41 = { by lemma 7 R->L }
% 0.18/0.41 multiply(multiply(X, inverse(X)), multiply(inverse(double_divide(multiply(inverse(X), multiply(multiply(double_divide(Z, inverse(X)), Y), Z)), multiply(double_divide(multiply(multiply(X, inverse(X)), multiply(inverse(X), multiply(multiply(double_divide(Z, inverse(X)), Y), Z))), X), multiply(X, inverse(X))))), multiply(multiply(double_divide(Z, inverse(X)), Y), Z)))
% 0.18/0.41 = { by axiom 1 (multiply) R->L }
% 0.18/0.41 multiply(multiply(X, inverse(X)), multiply(multiply(multiply(double_divide(multiply(multiply(X, inverse(X)), multiply(inverse(X), multiply(multiply(double_divide(Z, inverse(X)), Y), Z))), X), multiply(X, inverse(X))), multiply(inverse(X), multiply(multiply(double_divide(Z, inverse(X)), Y), Z))), multiply(multiply(double_divide(Z, inverse(X)), Y), Z)))
% 0.18/0.41 = { by lemma 6 }
% 0.18/0.41 multiply(multiply(X, inverse(X)), multiply(multiply(double_divide(multiply(multiply(double_divide(Z, inverse(X)), Y), Z), multiply(X, inverse(X))), multiply(inverse(X), multiply(multiply(double_divide(Z, inverse(X)), Y), Z))), multiply(multiply(double_divide(Z, inverse(X)), Y), Z)))
% 0.18/0.41 = { by lemma 3 }
% 0.18/0.41 multiply(inverse(X), multiply(multiply(double_divide(Z, inverse(X)), Y), Z))
% 0.18/0.41 = { by lemma 3 }
% 0.18/0.41 Y
% 0.18/0.41
% 0.18/0.41 Lemma 9: double_divide(multiply(X, Y), double_divide(Y, multiply(Z, X))) = Z.
% 0.18/0.41 Proof:
% 0.18/0.41 double_divide(multiply(X, Y), double_divide(Y, multiply(Z, X)))
% 0.18/0.41 = { by lemma 6 R->L }
% 0.18/0.41 double_divide(multiply(X, Y), multiply(double_divide(multiply(multiply(Z, X), multiply(X, Y)), Z), multiply(Z, X)))
% 0.18/0.41 = { by lemma 7 }
% 0.18/0.41 Z
% 0.18/0.41
% 0.18/0.41 Lemma 10: multiply(Y, multiply(X, Z)) = multiply(X, multiply(Y, Z)).
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(Y, multiply(X, Z))
% 0.18/0.41 = { by lemma 8 R->L }
% 0.18/0.41 multiply(multiply(multiply(W, inverse(W)), Y), multiply(X, Z))
% 0.18/0.41 = { by lemma 4 R->L }
% 0.18/0.41 multiply(multiply(double_divide(multiply(Y, Z), double_divide(Z, multiply(multiply(W, inverse(W)), Y))), X), multiply(Y, Z))
% 0.18/0.41 = { by lemma 9 }
% 0.18/0.41 multiply(multiply(multiply(W, inverse(W)), X), multiply(Y, Z))
% 0.18/0.41 = { by lemma 8 }
% 0.18/0.41 multiply(X, multiply(Y, Z))
% 0.18/0.41
% 0.18/0.41 Lemma 11: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(X, multiply(Y, inverse(Y)))
% 0.18/0.41 = { by lemma 10 }
% 0.18/0.41 multiply(Y, multiply(X, inverse(Y)))
% 0.18/0.41 = { by lemma 9 R->L }
% 0.18/0.41 multiply(double_divide(multiply(multiply(double_divide(Z, X), inverse(Y)), Z), double_divide(Z, multiply(Y, multiply(double_divide(Z, X), inverse(Y))))), multiply(X, inverse(Y)))
% 0.18/0.41 = { by lemma 10 }
% 0.18/0.41 multiply(double_divide(multiply(multiply(double_divide(Z, X), inverse(Y)), Z), double_divide(Z, multiply(double_divide(Z, X), multiply(Y, inverse(Y))))), multiply(X, inverse(Y)))
% 0.18/0.41 = { by lemma 8 R->L }
% 0.18/0.41 multiply(double_divide(multiply(multiply(double_divide(Z, X), inverse(Y)), Z), double_divide(Z, multiply(double_divide(multiply(multiply(Y, inverse(Y)), Z), X), multiply(Y, inverse(Y))))), multiply(X, inverse(Y)))
% 0.18/0.41 = { by lemma 7 }
% 0.18/0.41 multiply(double_divide(multiply(multiply(double_divide(Z, X), inverse(Y)), Z), X), multiply(X, inverse(Y)))
% 0.18/0.41 = { by lemma 3 R->L }
% 0.18/0.41 multiply(double_divide(multiply(multiply(double_divide(Z, X), inverse(Y)), Z), X), multiply(X, multiply(X, multiply(multiply(double_divide(Z, X), inverse(Y)), Z))))
% 0.18/0.41 = { by lemma 5 }
% 0.18/0.41 X
% 0.18/0.41
% 0.18/0.41 Lemma 12: multiply(Y, X) = multiply(X, Y).
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(Y, X)
% 0.18/0.41 = { by lemma 11 R->L }
% 0.18/0.41 multiply(Y, multiply(X, multiply(Z, inverse(Z))))
% 0.18/0.41 = { by lemma 10 R->L }
% 0.18/0.41 multiply(X, multiply(Y, multiply(Z, inverse(Z))))
% 0.18/0.41 = { by lemma 11 }
% 0.18/0.41 multiply(X, Y)
% 0.18/0.41
% 0.18/0.41 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(multiply(inverse(b2), b2), a2)
% 0.18/0.41 = { by lemma 12 R->L }
% 0.18/0.41 multiply(a2, multiply(inverse(b2), b2))
% 0.18/0.41 = { by lemma 12 R->L }
% 0.18/0.41 multiply(a2, multiply(b2, inverse(b2)))
% 0.18/0.41 = { by lemma 11 }
% 0.18/0.41 a2
% 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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