TSTP Solution File: GRP604-1 by Twee---2.5.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : GRP604-1 : TPTP v8.2.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 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 : Mon Jun 24 07:12:56 EDT 2024
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP604-1 : TPTP v8.2.0. Bugfixed v2.7.0.
% 0.07/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n001.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 : Thu Jun 20 12:43:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.42 Command-line arguments: --no-flatten-goal
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.20/0.44 Axiom 2 (single_axiom): inverse(double_divide(inverse(double_divide(X, inverse(double_divide(Y, double_divide(X, Z))))), Z)) = Y.
% 0.20/0.44
% 0.20/0.44 Lemma 3: multiply(X, multiply(multiply(double_divide(Y, X), Z), Y)) = Z.
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(X, multiply(multiply(double_divide(Y, X), Z), Y))
% 0.20/0.44 = { by axiom 1 (multiply) }
% 0.20/0.44 multiply(X, multiply(inverse(double_divide(Z, double_divide(Y, X))), Y))
% 0.20/0.44 = { by axiom 1 (multiply) }
% 0.20/0.44 multiply(X, inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))))
% 0.20/0.44 = { by axiom 1 (multiply) }
% 0.20/0.44 inverse(double_divide(inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))), X))
% 0.20/0.44 = { by axiom 2 (single_axiom) }
% 0.20/0.44 Z
% 0.20/0.44
% 0.20/0.44 Lemma 4: multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X) = multiply(Z, multiply(W, Y)).
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)
% 0.20/0.44 = { by lemma 3 R->L }
% 0.20/0.44 multiply(Z, multiply(multiply(double_divide(Y, Z), multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)), Y))
% 0.20/0.44 = { by lemma 3 }
% 0.20/0.44 multiply(Z, multiply(W, Y))
% 0.20/0.44
% 0.20/0.44 Lemma 5: multiply(double_divide(X, Y), multiply(Y, multiply(Z, X))) = Z.
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(double_divide(X, Y), multiply(Y, multiply(Z, X)))
% 0.20/0.44 = { by lemma 4 R->L }
% 0.20/0.44 multiply(double_divide(X, Y), multiply(multiply(double_divide(W, double_divide(X, Y)), Z), W))
% 0.20/0.44 = { by lemma 3 }
% 0.20/0.44 Z
% 0.20/0.44
% 0.20/0.44 Lemma 6: multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X) = Z.
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X)
% 0.20/0.44 = { by lemma 5 R->L }
% 0.20/0.44 multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), multiply(double_divide(Y, Z), multiply(Z, multiply(X, Y))))
% 0.20/0.44 = { by lemma 5 }
% 0.20/0.44 Z
% 0.20/0.44
% 0.20/0.44 Lemma 7: double_divide(multiply(X, Y), double_divide(Y, Z)) = multiply(double_divide(X, W), multiply(W, Z)).
% 0.20/0.44 Proof:
% 0.20/0.44 double_divide(multiply(X, Y), double_divide(Y, Z))
% 0.20/0.44 = { by lemma 5 R->L }
% 0.20/0.44 multiply(double_divide(X, W), multiply(W, multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X)))
% 0.20/0.44 = { by lemma 6 }
% 0.20/0.44 multiply(double_divide(X, W), multiply(W, Z))
% 0.20/0.44
% 0.20/0.44 Lemma 8: multiply(multiply(double_divide(X, Y), multiply(Y, Z)), X) = Z.
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(multiply(double_divide(X, Y), multiply(Y, Z)), X)
% 0.20/0.44 = { by lemma 7 R->L }
% 0.20/0.44 multiply(double_divide(multiply(X, W), double_divide(W, Z)), X)
% 0.20/0.44 = { by lemma 6 }
% 0.20/0.44 Z
% 0.20/0.44
% 0.20/0.44 Lemma 9: multiply(multiply(X, multiply(Y, Z)), W) = multiply(Y, multiply(multiply(X, Z), W)).
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(multiply(X, multiply(Y, Z)), W)
% 0.20/0.44 = { by lemma 3 R->L }
% 0.20/0.44 multiply(multiply(double_divide(Z, X), multiply(X, multiply(Y, Z))), multiply(multiply(double_divide(W, multiply(double_divide(Z, X), multiply(X, multiply(Y, Z)))), multiply(multiply(X, multiply(Y, Z)), W)), W))
% 0.20/0.44 = { by axiom 1 (multiply) }
% 0.20/0.44 multiply(multiply(double_divide(Z, X), multiply(X, multiply(Y, Z))), multiply(inverse(double_divide(multiply(multiply(X, multiply(Y, Z)), W), double_divide(W, multiply(double_divide(Z, X), multiply(X, multiply(Y, Z)))))), W))
% 0.20/0.44 = { by lemma 7 }
% 0.20/0.44 multiply(multiply(double_divide(Z, X), multiply(X, multiply(Y, Z))), multiply(inverse(multiply(double_divide(multiply(X, multiply(Y, Z)), V), multiply(V, multiply(double_divide(Z, X), multiply(X, multiply(Y, Z)))))), W))
% 0.20/0.44 = { by lemma 5 }
% 0.20/0.44 multiply(multiply(double_divide(Z, X), multiply(X, multiply(Y, Z))), multiply(inverse(double_divide(Z, X)), W))
% 0.20/0.44 = { by lemma 5 }
% 0.20/0.44 multiply(Y, multiply(inverse(double_divide(Z, X)), W))
% 0.20/0.44 = { by axiom 1 (multiply) R->L }
% 0.20/0.44 multiply(Y, multiply(multiply(X, Z), W))
% 0.20/0.44
% 0.20/0.44 Lemma 10: multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(multiply(X, Y), Z)
% 0.20/0.44 = { by lemma 8 R->L }
% 0.20/0.44 multiply(multiply(double_divide(W, V), multiply(V, multiply(multiply(X, Y), Z))), W)
% 0.20/0.44 = { by lemma 4 R->L }
% 0.20/0.44 multiply(multiply(double_divide(W, V), multiply(multiply(double_divide(U, double_divide(Z, V)), multiply(X, Y)), U)), W)
% 0.20/0.44 = { by lemma 9 }
% 0.20/0.44 multiply(multiply(double_divide(W, V), multiply(X, multiply(multiply(double_divide(U, double_divide(Z, V)), Y), U))), W)
% 0.20/0.45 = { by lemma 4 }
% 0.20/0.45 multiply(multiply(double_divide(W, V), multiply(X, multiply(V, multiply(Y, Z)))), W)
% 0.20/0.45 = { by lemma 9 }
% 0.20/0.45 multiply(X, multiply(multiply(double_divide(W, V), multiply(V, multiply(Y, Z))), W))
% 0.20/0.45 = { by lemma 8 }
% 0.20/0.45 multiply(X, multiply(Y, Z))
% 0.20/0.45
% 0.20/0.45 Lemma 11: multiply(double_divide(W, Y), multiply(Z, W)) = multiply(double_divide(X, Y), multiply(Z, X)).
% 0.20/0.45 Proof:
% 0.20/0.45 multiply(double_divide(W, Y), multiply(Z, W))
% 0.20/0.45 = { by axiom 1 (multiply) }
% 0.20/0.45 inverse(double_divide(multiply(Z, W), double_divide(W, Y)))
% 0.20/0.45 = { by lemma 7 }
% 0.20/0.45 inverse(multiply(double_divide(Z, V), multiply(V, Y)))
% 0.20/0.45 = { by lemma 7 R->L }
% 0.20/0.45 inverse(double_divide(multiply(Z, X), double_divide(X, Y)))
% 0.20/0.45 = { by axiom 1 (multiply) R->L }
% 0.20/0.45 multiply(double_divide(X, Y), multiply(Z, X))
% 0.20/0.45
% 0.20/0.45 Lemma 12: multiply(multiply(double_divide(X, Y), multiply(Y, X)), Z) = Z.
% 0.20/0.45 Proof:
% 0.20/0.45 multiply(multiply(double_divide(X, Y), multiply(Y, X)), Z)
% 0.20/0.45 = { by lemma 11 }
% 0.20/0.45 multiply(multiply(double_divide(Z, Y), multiply(Y, Z)), Z)
% 0.20/0.45 = { by lemma 8 }
% 0.20/0.45 Z
% 0.20/0.45
% 0.20/0.45 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.20/0.45 Proof:
% 0.20/0.45 multiply(a, b)
% 0.20/0.45 = { by lemma 5 R->L }
% 0.20/0.45 multiply(a, multiply(double_divide(a, a), multiply(a, multiply(b, a))))
% 0.20/0.45 = { by lemma 10 R->L }
% 0.20/0.45 multiply(a, multiply(double_divide(a, a), multiply(multiply(a, b), a)))
% 0.20/0.45 = { by lemma 9 R->L }
% 0.20/0.45 multiply(a, multiply(multiply(a, multiply(double_divide(a, a), b)), a))
% 0.20/0.45 = { by lemma 10 R->L }
% 0.20/0.45 multiply(multiply(a, multiply(a, multiply(double_divide(a, a), b))), a)
% 0.20/0.45 = { by lemma 3 R->L }
% 0.20/0.45 multiply(multiply(a, multiply(a, multiply(double_divide(a, a), multiply(X, multiply(multiply(double_divide(Y, X), b), Y))))), a)
% 0.20/0.45 = { by lemma 4 R->L }
% 0.20/0.45 multiply(multiply(a, multiply(a, multiply(multiply(double_divide(Z, double_divide(multiply(multiply(double_divide(Y, X), b), Y), double_divide(a, a))), X), Z))), a)
% 0.20/0.45 = { by lemma 9 R->L }
% 0.20/0.45 multiply(multiply(a, multiply(multiply(double_divide(Z, double_divide(multiply(multiply(double_divide(Y, X), b), Y), double_divide(a, a))), multiply(a, X)), Z)), a)
% 0.20/0.45 = { by lemma 4 }
% 0.20/0.45 multiply(multiply(a, multiply(double_divide(a, a), multiply(multiply(a, X), multiply(multiply(double_divide(Y, X), b), Y)))), a)
% 0.20/0.45 = { by lemma 10 }
% 0.20/0.45 multiply(multiply(a, multiply(double_divide(a, a), multiply(a, multiply(X, multiply(multiply(double_divide(Y, X), b), Y))))), a)
% 0.20/0.45 = { by lemma 3 }
% 0.20/0.45 multiply(multiply(a, multiply(double_divide(a, a), multiply(a, b))), a)
% 0.20/0.45 = { by lemma 10 R->L }
% 0.20/0.45 multiply(multiply(a, multiply(multiply(double_divide(a, a), a), b)), a)
% 0.20/0.45 = { by lemma 12 R->L }
% 0.20/0.45 multiply(multiply(a, multiply(multiply(double_divide(a, a), multiply(multiply(double_divide(W, V), multiply(V, W)), a)), b)), a)
% 0.20/0.45 = { by lemma 11 }
% 0.20/0.45 multiply(multiply(a, multiply(multiply(double_divide(b, a), multiply(multiply(double_divide(W, V), multiply(V, W)), b)), b)), a)
% 0.20/0.45 = { by lemma 12 }
% 0.20/0.45 multiply(multiply(a, multiply(multiply(double_divide(b, a), b), b)), a)
% 0.20/0.45 = { by lemma 3 }
% 0.20/0.45 multiply(b, a)
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45
% 0.20/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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