TSTP Solution File: GRP609-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP609-1 : 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 : n027.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 01:19:06 EDT 2023
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% 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 : GRP609-1 : 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
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 02:57:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.41 Command-line arguments: --no-flatten-goal
% 0.19/0.41
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.19/0.43 Axiom 2 (single_axiom): inverse(double_divide(inverse(double_divide(inverse(double_divide(X, Y)), Z)), double_divide(X, Z))) = Y.
% 0.19/0.44
% 0.19/0.44 Lemma 3: multiply(double_divide(X, Y), multiply(Y, multiply(Z, X))) = Z.
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(double_divide(X, Y), multiply(Y, multiply(Z, X)))
% 0.19/0.44 = { by axiom 1 (multiply) }
% 0.19/0.44 multiply(double_divide(X, Y), multiply(Y, inverse(double_divide(X, Z))))
% 0.19/0.44 = { by axiom 1 (multiply) }
% 0.19/0.44 multiply(double_divide(X, Y), inverse(double_divide(inverse(double_divide(X, Z)), Y)))
% 0.19/0.44 = { by axiom 1 (multiply) }
% 0.19/0.44 inverse(double_divide(inverse(double_divide(inverse(double_divide(X, Z)), Y)), double_divide(X, Y)))
% 0.19/0.44 = { by axiom 2 (single_axiom) }
% 0.19/0.44 Z
% 0.19/0.44
% 0.19/0.44 Lemma 4: multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X) = Z.
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X)
% 0.19/0.44 = { by lemma 3 R->L }
% 0.19/0.44 multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), multiply(double_divide(Y, Z), multiply(Z, multiply(X, Y))))
% 0.19/0.44 = { by lemma 3 }
% 0.19/0.44 Z
% 0.19/0.44
% 0.19/0.44 Lemma 5: double_divide(multiply(X, Y), double_divide(Y, Z)) = multiply(double_divide(X, W), multiply(W, Z)).
% 0.19/0.44 Proof:
% 0.19/0.44 double_divide(multiply(X, Y), double_divide(Y, Z))
% 0.19/0.44 = { by lemma 3 R->L }
% 0.19/0.44 multiply(double_divide(X, W), multiply(W, multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X)))
% 0.19/0.44 = { by lemma 4 }
% 0.19/0.44 multiply(double_divide(X, W), multiply(W, Z))
% 0.19/0.44
% 0.19/0.44 Lemma 6: multiply(double_divide(X, multiply(Y, Z)), multiply(Z, X)) = inverse(Y).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(double_divide(X, multiply(Y, Z)), multiply(Z, X))
% 0.19/0.44 = { by axiom 1 (multiply) }
% 0.19/0.44 inverse(double_divide(multiply(Z, X), double_divide(X, multiply(Y, Z))))
% 0.19/0.44 = { by lemma 5 }
% 0.19/0.44 inverse(multiply(double_divide(Z, W), multiply(W, multiply(Y, Z))))
% 0.19/0.44 = { by lemma 3 }
% 0.19/0.44 inverse(Y)
% 0.19/0.44
% 0.19/0.44 Lemma 7: multiply(double_divide(X, double_divide(X, multiply(Y, Z))), inverse(Y)) = Z.
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(double_divide(X, double_divide(X, multiply(Y, Z))), inverse(Y))
% 0.19/0.44 = { by lemma 6 R->L }
% 0.19/0.44 multiply(double_divide(X, double_divide(X, multiply(Y, Z))), multiply(double_divide(X, multiply(Y, Z)), multiply(Z, X)))
% 0.19/0.44 = { by lemma 3 }
% 0.19/0.44 Z
% 0.19/0.44
% 0.19/0.44 Lemma 8: multiply(double_divide(W, Y), multiply(Z, W)) = multiply(double_divide(X, Y), multiply(Z, X)).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(double_divide(W, Y), multiply(Z, W))
% 0.19/0.44 = { by axiom 1 (multiply) }
% 0.19/0.44 inverse(double_divide(multiply(Z, W), double_divide(W, Y)))
% 0.19/0.44 = { by lemma 5 }
% 0.19/0.44 inverse(multiply(double_divide(Z, V), multiply(V, Y)))
% 0.19/0.44 = { by lemma 5 R->L }
% 0.19/0.44 inverse(double_divide(multiply(Z, X), double_divide(X, Y)))
% 0.19/0.44 = { by axiom 1 (multiply) R->L }
% 0.19/0.44 multiply(double_divide(X, Y), multiply(Z, X))
% 0.19/0.44
% 0.19/0.44 Lemma 9: multiply(multiply(double_divide(X, Y), multiply(Y, Z)), X) = Z.
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(multiply(double_divide(X, Y), multiply(Y, Z)), X)
% 0.19/0.44 = { by lemma 5 R->L }
% 0.19/0.44 multiply(double_divide(multiply(X, W), double_divide(W, Z)), X)
% 0.19/0.44 = { by lemma 4 }
% 0.19/0.44 Z
% 0.19/0.44
% 0.19/0.44 Lemma 10: multiply(multiply(double_divide(X, Y), multiply(Y, X)), Z) = Z.
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(multiply(double_divide(X, Y), multiply(Y, X)), Z)
% 0.19/0.44 = { by lemma 8 }
% 0.19/0.44 multiply(multiply(double_divide(Z, Y), multiply(Y, Z)), Z)
% 0.19/0.44 = { by lemma 9 }
% 0.19/0.44 Z
% 0.19/0.44
% 0.19/0.44 Lemma 11: multiply(double_divide(X, double_divide(X, Y)), multiply(Z, W)) = multiply(Z, multiply(Y, W)).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(double_divide(X, double_divide(X, Y)), multiply(Z, W))
% 0.19/0.44 = { by axiom 1 (multiply) }
% 0.19/0.44 multiply(double_divide(X, double_divide(X, Y)), inverse(double_divide(W, Z)))
% 0.19/0.44 = { by lemma 3 R->L }
% 0.19/0.44 multiply(double_divide(X, double_divide(X, multiply(double_divide(W, Z), multiply(Z, multiply(Y, W))))), inverse(double_divide(W, Z)))
% 0.19/0.44 = { by lemma 7 }
% 0.19/0.44 multiply(Z, multiply(Y, W))
% 0.19/0.44
% 0.19/0.44 Lemma 12: multiply(double_divide(X, double_divide(X, Y)), Z) = multiply(Y, Z).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(double_divide(X, double_divide(X, Y)), Z)
% 0.19/0.44 = { by lemma 10 R->L }
% 0.19/0.44 multiply(double_divide(X, double_divide(X, Y)), multiply(multiply(double_divide(W, V), multiply(V, W)), Z))
% 0.19/0.44 = { by lemma 11 }
% 0.19/0.44 multiply(multiply(double_divide(W, V), multiply(V, W)), multiply(Y, Z))
% 0.19/0.44 = { by lemma 10 }
% 0.19/0.44 multiply(Y, Z)
% 0.19/0.44
% 0.19/0.44 Lemma 13: multiply(multiply(double_divide(X, Y), X), multiply(Y, Z)) = Z.
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(multiply(double_divide(X, Y), X), multiply(Y, Z))
% 0.19/0.44 = { by lemma 10 R->L }
% 0.19/0.44 multiply(multiply(double_divide(X, Y), multiply(multiply(double_divide(W, V), multiply(V, W)), X)), multiply(Y, Z))
% 0.19/0.44 = { by lemma 8 }
% 0.19/0.44 multiply(multiply(double_divide(multiply(Y, Z), Y), multiply(multiply(double_divide(W, V), multiply(V, W)), multiply(Y, Z))), multiply(Y, Z))
% 0.19/0.44 = { by lemma 10 }
% 0.19/0.44 multiply(multiply(double_divide(multiply(Y, Z), Y), multiply(Y, Z)), multiply(Y, Z))
% 0.19/0.44 = { by lemma 9 }
% 0.19/0.44 Z
% 0.19/0.44
% 0.19/0.44 Lemma 14: multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, Y)) = double_divide(Z, X).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, Y))
% 0.19/0.44 = { by lemma 3 R->L }
% 0.19/0.44 multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, multiply(double_divide(Z, X), multiply(X, multiply(Y, Z)))))
% 0.19/0.44 = { by lemma 3 }
% 0.19/0.44 double_divide(Z, X)
% 0.19/0.44
% 0.19/0.44 Lemma 15: double_divide(X, multiply(double_divide(Y, Z), Y)) = multiply(double_divide(X, W), multiply(W, Z)).
% 0.19/0.44 Proof:
% 0.19/0.44 double_divide(X, multiply(double_divide(Y, Z), Y))
% 0.19/0.44 = { by lemma 14 R->L }
% 0.19/0.44 multiply(double_divide(multiply(multiply(double_divide(Y, Z), Y), multiply(Z, X)), W), multiply(W, Z))
% 0.19/0.44 = { by lemma 13 }
% 0.19/0.44 multiply(double_divide(X, W), multiply(W, Z))
% 0.19/0.44
% 0.19/0.44 Lemma 16: multiply(Y, X) = multiply(X, Y).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(Y, X)
% 0.19/0.44 = { by lemma 7 R->L }
% 0.19/0.44 multiply(double_divide(U, double_divide(U, multiply(multiply(double_divide(multiply(Y, Z), Y), multiply(Y, Z)), multiply(Y, X)))), inverse(multiply(double_divide(multiply(Y, Z), Y), multiply(Y, Z))))
% 0.19/0.44 = { by lemma 12 }
% 0.19/0.44 multiply(multiply(multiply(double_divide(multiply(Y, Z), Y), multiply(Y, Z)), multiply(Y, X)), inverse(multiply(double_divide(multiply(Y, Z), Y), multiply(Y, Z))))
% 0.19/0.45 = { by lemma 13 }
% 0.19/0.45 multiply(X, inverse(multiply(double_divide(multiply(Y, Z), Y), multiply(Y, Z))))
% 0.19/0.45 = { by lemma 10 R->L }
% 0.19/0.45 multiply(X, multiply(multiply(double_divide(Z, V), multiply(V, Z)), inverse(multiply(double_divide(multiply(Y, Z), Y), multiply(Y, Z)))))
% 0.19/0.45 = { by lemma 15 R->L }
% 0.19/0.45 multiply(X, multiply(double_divide(Z, multiply(double_divide(W, Z), W)), inverse(multiply(double_divide(multiply(Y, Z), Y), multiply(Y, Z)))))
% 0.19/0.45 = { by lemma 15 R->L }
% 0.19/0.45 multiply(X, multiply(double_divide(Z, multiply(double_divide(W, Z), W)), inverse(double_divide(multiply(Y, Z), multiply(double_divide(W, Z), W)))))
% 0.19/0.45 = { by axiom 1 (multiply) R->L }
% 0.19/0.45 multiply(X, multiply(double_divide(Z, multiply(double_divide(W, Z), W)), multiply(multiply(double_divide(W, Z), W), multiply(Y, Z))))
% 0.19/0.45 = { by lemma 3 }
% 0.19/0.45 multiply(X, Y)
% 0.19/0.45
% 0.19/0.45 Lemma 17: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.19/0.45 Proof:
% 0.19/0.45 multiply(multiply(X, inverse(X)), Y)
% 0.19/0.45 = { by lemma 12 R->L }
% 0.19/0.45 multiply(double_divide(Z, double_divide(Z, multiply(X, inverse(X)))), Y)
% 0.19/0.45 = { by lemma 14 R->L }
% 0.19/0.45 multiply(multiply(double_divide(multiply(double_divide(Z, multiply(X, inverse(X))), multiply(inverse(X), Z)), W), multiply(W, inverse(X))), Y)
% 0.19/0.45 = { by lemma 6 }
% 0.19/0.45 multiply(multiply(double_divide(inverse(X), W), multiply(W, inverse(X))), Y)
% 0.19/0.45 = { by lemma 10 }
% 0.19/0.45 Y
% 0.19/0.45
% 0.19/0.45 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.45 Proof:
% 0.19/0.45 multiply(inverse(a1), a1)
% 0.19/0.45 = { by lemma 16 R->L }
% 0.19/0.45 multiply(a1, inverse(a1))
% 0.19/0.45 = { by lemma 17 R->L }
% 0.19/0.45 multiply(a1, multiply(multiply(b1, inverse(b1)), inverse(a1)))
% 0.19/0.45 = { by lemma 11 R->L }
% 0.19/0.45 multiply(double_divide(X, double_divide(X, multiply(b1, inverse(b1)))), multiply(a1, inverse(a1)))
% 0.19/0.45 = { by lemma 17 R->L }
% 0.19/0.45 multiply(double_divide(multiply(multiply(a1, inverse(a1)), X), double_divide(X, multiply(b1, inverse(b1)))), multiply(a1, inverse(a1)))
% 0.19/0.45 = { by lemma 4 }
% 0.19/0.45 multiply(b1, inverse(b1))
% 0.19/0.45 = { by lemma 16 }
% 0.19/0.45 multiply(inverse(b1), b1)
% 0.19/0.45 % SZS output end Proof
% 0.19/0.45
% 0.19/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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