TSTP Solution File: GRP596-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP596-1 : 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 : n014.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 01:19:03 EDT 2023
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% 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 : GRP596-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n014.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 20:57:45 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.41 Command-line arguments: --no-flatten-goal
% 0.21/0.41
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.21/0.43 Axiom 2 (single_axiom): inverse(double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(Z, Y)))))) = Z.
% 0.21/0.43
% 0.21/0.43 Lemma 3: multiply(multiply(multiply(X, Y), Z), double_divide(Z, X)) = Y.
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(multiply(multiply(X, Y), Z), double_divide(Z, X))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 multiply(multiply(inverse(double_divide(Y, X)), Z), double_divide(Z, X))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 multiply(inverse(double_divide(Z, inverse(double_divide(Y, X)))), double_divide(Z, X))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 inverse(double_divide(double_divide(Z, X), inverse(double_divide(Z, inverse(double_divide(Y, X))))))
% 0.21/0.43 = { by axiom 2 (single_axiom) }
% 0.21/0.43 Y
% 0.21/0.43
% 0.21/0.43 Lemma 4: multiply(X, double_divide(double_divide(Y, Z), multiply(Z, X))) = Y.
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(X, double_divide(double_divide(Y, Z), multiply(Z, X)))
% 0.21/0.43 = { by lemma 3 R->L }
% 0.21/0.43 multiply(multiply(multiply(multiply(Z, X), Y), double_divide(Y, Z)), double_divide(double_divide(Y, Z), multiply(Z, X)))
% 0.21/0.43 = { by lemma 3 }
% 0.21/0.43 Y
% 0.21/0.43
% 0.21/0.43 Lemma 5: double_divide(double_divide(X, Y), multiply(Y, Z)) = multiply(multiply(X, W), double_divide(W, Z)).
% 0.21/0.43 Proof:
% 0.21/0.44 double_divide(double_divide(X, Y), multiply(Y, Z))
% 0.21/0.44 = { by lemma 3 R->L }
% 0.21/0.44 multiply(multiply(multiply(Z, double_divide(double_divide(X, Y), multiply(Y, Z))), W), double_divide(W, Z))
% 0.21/0.44 = { by lemma 4 }
% 0.21/0.44 multiply(multiply(X, W), double_divide(W, Z))
% 0.21/0.44
% 0.21/0.44 Lemma 6: multiply(multiply(W, Y), double_divide(Z, W)) = multiply(multiply(X, Y), double_divide(Z, X)).
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(multiply(W, Y), double_divide(Z, W))
% 0.21/0.44 = { by axiom 1 (multiply) }
% 0.21/0.44 inverse(double_divide(double_divide(Z, W), multiply(W, Y)))
% 0.21/0.44 = { by lemma 5 }
% 0.21/0.44 inverse(multiply(multiply(Z, V), double_divide(V, Y)))
% 0.21/0.44 = { by lemma 5 R->L }
% 0.21/0.44 inverse(double_divide(double_divide(Z, X), multiply(X, Y)))
% 0.21/0.44 = { by axiom 1 (multiply) R->L }
% 0.21/0.44 multiply(multiply(X, Y), double_divide(Z, X))
% 0.21/0.44
% 0.21/0.44 Lemma 7: multiply(X, multiply(multiply(Y, Z), double_divide(Z, X))) = Y.
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(X, multiply(multiply(Y, Z), double_divide(Z, X)))
% 0.21/0.44 = { by lemma 5 R->L }
% 0.21/0.44 multiply(X, double_divide(double_divide(Y, W), multiply(W, X)))
% 0.21/0.44 = { by lemma 4 }
% 0.21/0.44 Y
% 0.21/0.44
% 0.21/0.44 Lemma 8: multiply(X, multiply(multiply(Y, Z), double_divide(Z, Y))) = X.
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(X, multiply(multiply(Y, Z), double_divide(Z, Y)))
% 0.21/0.44 = { by lemma 6 }
% 0.21/0.44 multiply(X, multiply(multiply(X, Z), double_divide(Z, X)))
% 0.21/0.44 = { by lemma 7 }
% 0.21/0.44 X
% 0.21/0.44
% 0.21/0.44 Lemma 9: multiply(Z, double_divide(Y, Z)) = multiply(X, double_divide(Y, X)).
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(Z, double_divide(Y, Z))
% 0.21/0.44 = { by lemma 8 R->L }
% 0.21/0.44 multiply(multiply(Z, multiply(multiply(W, V), double_divide(V, W))), double_divide(Y, Z))
% 0.21/0.44 = { by lemma 6 }
% 0.21/0.44 multiply(multiply(X, multiply(multiply(W, V), double_divide(V, W))), double_divide(Y, X))
% 0.21/0.44 = { by lemma 8 }
% 0.21/0.44 multiply(X, double_divide(Y, X))
% 0.21/0.44
% 0.21/0.44 Lemma 10: multiply(multiply(X, Y), multiply(Z, double_divide(Y, Z))) = X.
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(multiply(X, Y), multiply(Z, double_divide(Y, Z)))
% 0.21/0.44 = { by lemma 9 }
% 0.21/0.44 multiply(multiply(X, Y), multiply(multiply(X, Y), double_divide(Y, multiply(X, Y))))
% 0.21/0.44 = { by lemma 7 }
% 0.21/0.44 X
% 0.21/0.44
% 0.21/0.44 Lemma 11: double_divide(multiply(X, double_divide(Y, X)), Z) = multiply(multiply(Y, W), double_divide(W, Z)).
% 0.21/0.44 Proof:
% 0.21/0.44 double_divide(multiply(X, double_divide(Y, X)), Z)
% 0.21/0.44 = { by lemma 3 R->L }
% 0.21/0.44 multiply(multiply(multiply(multiply(multiply(Z, Y), multiply(X, double_divide(Y, X))), double_divide(multiply(X, double_divide(Y, X)), Z)), W), double_divide(W, multiply(multiply(Z, Y), multiply(X, double_divide(Y, X)))))
% 0.21/0.44 = { by lemma 3 }
% 0.21/0.44 multiply(multiply(Y, W), double_divide(W, multiply(multiply(Z, Y), multiply(X, double_divide(Y, X)))))
% 0.21/0.44 = { by lemma 10 }
% 0.21/0.44 multiply(multiply(Y, W), double_divide(W, Z))
% 0.21/0.44
% 0.21/0.44 Lemma 12: multiply(X, double_divide(double_divide(multiply(Y, Z), inverse(Z)), X)) = Y.
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(X, double_divide(double_divide(multiply(Y, Z), inverse(Z)), X))
% 0.21/0.44 = { by lemma 9 }
% 0.21/0.44 multiply(inverse(Z), double_divide(double_divide(multiply(Y, Z), inverse(Z)), inverse(Z)))
% 0.21/0.44 = { by lemma 3 R->L }
% 0.21/0.44 multiply(inverse(multiply(multiply(multiply(Y, Z), W), double_divide(W, Y))), double_divide(double_divide(multiply(Y, Z), inverse(Z)), inverse(Z)))
% 0.21/0.44 = { by lemma 5 R->L }
% 0.21/0.44 multiply(inverse(double_divide(double_divide(multiply(Y, Z), inverse(Z)), multiply(inverse(Z), Y))), double_divide(double_divide(multiply(Y, Z), inverse(Z)), inverse(Z)))
% 0.21/0.44 = { by axiom 1 (multiply) R->L }
% 0.21/0.44 multiply(multiply(multiply(inverse(Z), Y), double_divide(multiply(Y, Z), inverse(Z))), double_divide(double_divide(multiply(Y, Z), inverse(Z)), inverse(Z)))
% 0.21/0.44 = { by lemma 3 }
% 0.21/0.44 Y
% 0.21/0.44
% 0.21/0.44 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(a, b)
% 0.21/0.44 = { by lemma 3 R->L }
% 0.21/0.44 multiply(multiply(multiply(multiply(X, a), multiply(Y, double_divide(X, Y))), double_divide(multiply(Y, double_divide(X, Y)), X)), b)
% 0.21/0.44 = { by axiom 1 (multiply) }
% 0.21/0.44 multiply(multiply(inverse(double_divide(multiply(Y, double_divide(X, Y)), multiply(X, a))), double_divide(multiply(Y, double_divide(X, Y)), X)), b)
% 0.21/0.44 = { by lemma 11 }
% 0.21/0.44 multiply(multiply(inverse(multiply(multiply(X, a), double_divide(a, multiply(X, a)))), double_divide(multiply(Y, double_divide(X, Y)), X)), b)
% 0.21/0.44 = { by lemma 11 }
% 0.21/0.44 multiply(multiply(inverse(multiply(multiply(X, a), double_divide(a, multiply(X, a)))), multiply(multiply(X, Z), double_divide(Z, X))), b)
% 0.21/0.44 = { by lemma 8 }
% 0.21/0.44 multiply(inverse(multiply(multiply(X, a), double_divide(a, multiply(X, a)))), b)
% 0.21/0.44 = { by lemma 10 R->L }
% 0.21/0.44 multiply(inverse(multiply(multiply(X, a), double_divide(a, multiply(X, a)))), multiply(multiply(b, a), multiply(multiply(X, a), double_divide(a, multiply(X, a)))))
% 0.21/0.44 = { by lemma 8 R->L }
% 0.21/0.44 multiply(multiply(inverse(multiply(multiply(X, a), double_divide(a, multiply(X, a)))), multiply(multiply(b, a), multiply(multiply(X, a), double_divide(a, multiply(X, a))))), multiply(multiply(W, V), double_divide(V, W)))
% 0.21/0.44 = { by lemma 12 R->L }
% 0.21/0.44 multiply(U, double_divide(double_divide(multiply(multiply(multiply(inverse(multiply(multiply(X, a), double_divide(a, multiply(X, a)))), multiply(multiply(b, a), multiply(multiply(X, a), double_divide(a, multiply(X, a))))), multiply(multiply(W, V), double_divide(V, W))), double_divide(multiply(multiply(W, V), double_divide(V, W)), inverse(multiply(multiply(X, a), double_divide(a, multiply(X, a)))))), inverse(double_divide(multiply(multiply(W, V), double_divide(V, W)), inverse(multiply(multiply(X, a), double_divide(a, multiply(X, a))))))), U))
% 0.21/0.44 = { by lemma 3 }
% 0.21/0.44 multiply(U, double_divide(double_divide(multiply(multiply(b, a), multiply(multiply(X, a), double_divide(a, multiply(X, a)))), inverse(double_divide(multiply(multiply(W, V), double_divide(V, W)), inverse(multiply(multiply(X, a), double_divide(a, multiply(X, a))))))), U))
% 0.21/0.44 = { by axiom 1 (multiply) R->L }
% 0.21/0.44 multiply(U, double_divide(double_divide(multiply(multiply(b, a), multiply(multiply(X, a), double_divide(a, multiply(X, a)))), multiply(inverse(multiply(multiply(X, a), double_divide(a, multiply(X, a)))), multiply(multiply(W, V), double_divide(V, W)))), U))
% 0.21/0.44 = { by lemma 8 }
% 0.21/0.44 multiply(U, double_divide(double_divide(multiply(multiply(b, a), multiply(multiply(X, a), double_divide(a, multiply(X, a)))), inverse(multiply(multiply(X, a), double_divide(a, multiply(X, a))))), U))
% 0.21/0.44 = { by lemma 12 }
% 0.21/0.44 multiply(b, a)
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44
% 0.21/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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