TSTP Solution File: GRP594-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP594-1 : 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 : n008.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 01:19:02 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP594-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % 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 : n008.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 20:23:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.40 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.40
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.20/0.41 Axiom 2 (single_axiom): inverse(double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(Z, Y)))))) = Z.
% 0.20/0.41
% 0.20/0.41 Lemma 3: multiply(multiply(multiply(X, Y), Z), double_divide(Z, X)) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(multiply(multiply(X, Y), Z), double_divide(Z, X))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 multiply(multiply(inverse(double_divide(Y, X)), Z), double_divide(Z, X))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 multiply(inverse(double_divide(Z, inverse(double_divide(Y, X)))), double_divide(Z, X))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 inverse(double_divide(double_divide(Z, X), inverse(double_divide(Z, inverse(double_divide(Y, X))))))
% 0.20/0.41 = { by axiom 2 (single_axiom) }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 4: multiply(multiply(X, Y), double_divide(Y, multiply(multiply(Z, X), W))) = double_divide(W, Z).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(multiply(X, Y), double_divide(Y, multiply(multiply(Z, X), W)))
% 0.20/0.41 = { by lemma 3 R->L }
% 0.20/0.41 multiply(multiply(multiply(multiply(multiply(Z, X), W), double_divide(W, Z)), Y), double_divide(Y, multiply(multiply(Z, X), W)))
% 0.20/0.41 = { by lemma 3 }
% 0.20/0.41 double_divide(W, Z)
% 0.20/0.41
% 0.20/0.41 Lemma 5: double_divide(multiply(X, double_divide(Y, multiply(Z, X))), Z) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 double_divide(multiply(X, double_divide(Y, multiply(Z, X))), Z)
% 0.20/0.41 = { by lemma 4 R->L }
% 0.20/0.41 multiply(multiply(X, double_divide(Y, multiply(Z, X))), double_divide(double_divide(Y, multiply(Z, X)), multiply(multiply(Z, X), multiply(X, double_divide(Y, multiply(Z, X))))))
% 0.20/0.41 = { by lemma 3 R->L }
% 0.20/0.41 multiply(multiply(multiply(multiply(multiply(Z, X), multiply(X, double_divide(Y, multiply(Z, X)))), Y), double_divide(Y, multiply(Z, X))), double_divide(double_divide(Y, multiply(Z, X)), multiply(multiply(Z, X), multiply(X, double_divide(Y, multiply(Z, X))))))
% 0.20/0.41 = { by lemma 3 }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 6: multiply(X, multiply(Y, double_divide(Z, multiply(X, Y)))) = inverse(Z).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(X, multiply(Y, double_divide(Z, multiply(X, Y))))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 inverse(double_divide(multiply(Y, double_divide(Z, multiply(X, Y))), X))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 inverse(Z)
% 0.20/0.41
% 0.20/0.41 Lemma 7: multiply(inverse(X), double_divide(double_divide(multiply(Y, X), Z), Z)) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(inverse(X), double_divide(double_divide(multiply(Y, X), Z), Z))
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 multiply(multiply(multiply(Z, Y), multiply(multiply(Y, X), double_divide(X, multiply(multiply(Z, Y), multiply(Y, X))))), double_divide(double_divide(multiply(Y, X), Z), Z))
% 0.20/0.41 = { by lemma 4 }
% 0.20/0.41 multiply(multiply(multiply(Z, Y), double_divide(multiply(Y, X), Z)), double_divide(double_divide(multiply(Y, X), Z), Z))
% 0.20/0.41 = { by lemma 3 }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 8: multiply(X, double_divide(Y, X)) = inverse(Y).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(X, double_divide(Y, X))
% 0.20/0.41 = { by lemma 7 R->L }
% 0.20/0.41 multiply(X, double_divide(multiply(inverse(double_divide(Y, multiply(X, Y))), double_divide(double_divide(multiply(Y, double_divide(Y, multiply(X, Y))), X), X)), X))
% 0.20/0.41 = { by lemma 7 R->L }
% 0.20/0.41 multiply(X, double_divide(multiply(inverse(double_divide(Y, multiply(X, Y))), double_divide(multiply(inverse(double_divide(Y, multiply(X, Y))), double_divide(double_divide(multiply(double_divide(multiply(Y, double_divide(Y, multiply(X, Y))), X), double_divide(Y, multiply(X, Y))), multiply(X, inverse(double_divide(Y, multiply(X, Y))))), multiply(X, inverse(double_divide(Y, multiply(X, Y)))))), X)), X))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 multiply(X, double_divide(multiply(inverse(double_divide(Y, multiply(X, Y))), double_divide(multiply(double_divide(multiply(Y, double_divide(Y, multiply(X, Y))), X), double_divide(Y, multiply(X, Y))), multiply(X, inverse(double_divide(Y, multiply(X, Y)))))), X))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 multiply(X, multiply(double_divide(multiply(Y, double_divide(Y, multiply(X, Y))), X), double_divide(Y, multiply(X, Y))))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 multiply(X, multiply(Y, double_divide(Y, multiply(X, Y))))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 inverse(Y)
% 0.20/0.41
% 0.20/0.41 Lemma 9: multiply(inverse(X), multiply(Y, X)) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(inverse(X), multiply(Y, X))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 inverse(double_divide(multiply(Y, X), inverse(X)))
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 multiply(inverse(X), double_divide(double_divide(multiply(Y, X), inverse(X)), inverse(X)))
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(multiply(inverse(b2), b2), a2)
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 multiply(inverse(double_divide(b2, inverse(b2))), a2)
% 0.20/0.41 = { by lemma 3 R->L }
% 0.20/0.41 multiply(inverse(double_divide(b2, inverse(b2))), multiply(multiply(multiply(inverse(b2), a2), b2), double_divide(b2, inverse(b2))))
% 0.20/0.41 = { by lemma 9 }
% 0.20/0.41 multiply(multiply(inverse(b2), a2), b2)
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 multiply(multiply(inverse(b2), a2), double_divide(multiply(multiply(a2, b2), double_divide(b2, multiply(multiply(inverse(b2), a2), multiply(a2, b2)))), multiply(inverse(b2), a2)))
% 0.20/0.41 = { by lemma 4 }
% 0.20/0.41 multiply(multiply(inverse(b2), a2), double_divide(double_divide(multiply(a2, b2), inverse(b2)), multiply(inverse(b2), a2)))
% 0.20/0.41 = { by lemma 8 }
% 0.20/0.41 inverse(double_divide(multiply(a2, b2), inverse(b2)))
% 0.20/0.41 = { by axiom 1 (multiply) R->L }
% 0.20/0.41 multiply(inverse(b2), multiply(a2, b2))
% 0.20/0.41 = { by lemma 9 }
% 0.20/0.41 a2
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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