TSTP Solution File: GRP601-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP601-1 : 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 : n029.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 0.13s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP601-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % 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 : n029.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 : Mon Aug 28 23:20:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.13/0.41
% 0.13/0.41 % SZS status Unsatisfiable
% 0.13/0.41
% 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(inverse(double_divide(X, inverse(double_divide(Y, double_divide(X, Z))))), Z)) = Y.
% 0.21/0.43
% 0.21/0.43 Lemma 3: multiply(X, multiply(multiply(double_divide(Y, X), Z), Y)) = Z.
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(X, multiply(multiply(double_divide(Y, X), Z), Y))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 multiply(X, multiply(inverse(double_divide(Z, double_divide(Y, X))), Y))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 multiply(X, inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.43 inverse(double_divide(inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))), X))
% 0.21/0.43 = { by axiom 2 (single_axiom) }
% 0.21/0.43 Z
% 0.21/0.43
% 0.21/0.43 Lemma 4: multiply(double_divide(X, Y), multiply(Y, multiply(Z, X))) = Z.
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(double_divide(X, Y), multiply(Y, multiply(Z, X)))
% 0.21/0.43 = { by lemma 3 R->L }
% 0.21/0.43 multiply(double_divide(X, Y), multiply(Y, multiply(multiply(double_divide(X, Y), multiply(multiply(double_divide(W, double_divide(X, Y)), Z), W)), X)))
% 0.21/0.43 = { by lemma 3 }
% 0.21/0.43 multiply(double_divide(X, Y), multiply(multiply(double_divide(W, double_divide(X, Y)), Z), W))
% 0.21/0.43 = { by lemma 3 }
% 0.21/0.43 Z
% 0.21/0.43
% 0.21/0.43 Lemma 5: multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, Y)) = double_divide(Z, X).
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, Y))
% 0.21/0.43 = { by lemma 4 R->L }
% 0.21/0.43 multiply(double_divide(multiply(X, multiply(Y, Z)), W), multiply(W, multiply(double_divide(Z, X), multiply(X, multiply(Y, Z)))))
% 0.21/0.43 = { by lemma 4 }
% 0.21/0.43 double_divide(Z, X)
% 0.21/0.43
% 0.21/0.43 Lemma 6: double_divide(X, multiply(double_divide(multiply(Y, X), Z), Y)) = Z.
% 0.21/0.43 Proof:
% 0.21/0.43 double_divide(X, multiply(double_divide(multiply(Y, X), Z), Y))
% 0.21/0.43 = { by lemma 5 R->L }
% 0.21/0.43 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))
% 0.21/0.43 = { by lemma 4 R->L }
% 0.21/0.43 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)))))
% 0.21/0.43 = { by lemma 4 }
% 0.21/0.43 Z
% 0.21/0.43
% 0.21/0.43 Lemma 7: multiply(double_divide(X, multiply(Y, Z)), multiply(Z, X)) = inverse(Y).
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(double_divide(X, multiply(Y, Z)), multiply(Z, X))
% 0.21/0.43 = { by axiom 1 (multiply) }
% 0.21/0.44 inverse(double_divide(multiply(Z, X), double_divide(X, multiply(Y, Z))))
% 0.21/0.44 = { by lemma 5 R->L }
% 0.21/0.44 inverse(double_divide(multiply(Z, X), multiply(double_divide(multiply(multiply(Y, Z), multiply(Z, X)), Y), multiply(Y, Z))))
% 0.21/0.44 = { by lemma 6 }
% 0.21/0.44 inverse(Y)
% 0.21/0.44
% 0.21/0.44 Lemma 8: multiply(double_divide(X, double_divide(X, multiply(Y, Z))), inverse(Y)) = Z.
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(double_divide(X, double_divide(X, multiply(Y, Z))), inverse(Y))
% 0.21/0.44 = { by lemma 7 R->L }
% 0.21/0.44 multiply(double_divide(X, double_divide(X, multiply(Y, Z))), multiply(double_divide(X, multiply(Y, Z)), multiply(Z, X)))
% 0.21/0.44 = { by lemma 4 }
% 0.21/0.44 Z
% 0.21/0.44
% 0.21/0.44 Lemma 9: multiply(double_divide(X, Y), X) = inverse(Y).
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(double_divide(X, Y), X)
% 0.21/0.44 = { by lemma 8 R->L }
% 0.21/0.44 multiply(double_divide(X, multiply(double_divide(X, double_divide(X, multiply(double_divide(multiply(Y, X), Y), Y))), inverse(double_divide(multiply(Y, X), Y)))), X)
% 0.21/0.44 = { by lemma 8 R->L }
% 0.21/0.44 multiply(double_divide(X, multiply(double_divide(X, multiply(double_divide(multiply(inverse(double_divide(multiply(Y, X), Y)), X), double_divide(multiply(inverse(double_divide(multiply(Y, X), Y)), X), multiply(double_divide(multiply(Y, X), Y), double_divide(X, multiply(double_divide(multiply(Y, X), Y), Y))))), inverse(double_divide(multiply(Y, X), Y)))), inverse(double_divide(multiply(Y, X), Y)))), X)
% 0.21/0.44 = { by lemma 6 }
% 0.21/0.44 multiply(double_divide(X, multiply(double_divide(multiply(inverse(double_divide(multiply(Y, X), Y)), X), multiply(double_divide(multiply(Y, X), Y), double_divide(X, multiply(double_divide(multiply(Y, X), Y), Y)))), inverse(double_divide(multiply(Y, X), Y)))), X)
% 0.21/0.44 = { by lemma 6 }
% 0.21/0.44 multiply(multiply(double_divide(multiply(Y, X), Y), double_divide(X, multiply(double_divide(multiply(Y, X), Y), Y))), X)
% 0.21/0.44 = { by lemma 6 }
% 0.21/0.44 multiply(multiply(double_divide(multiply(Y, X), Y), Y), X)
% 0.21/0.44 = { by axiom 1 (multiply) }
% 0.21/0.44 inverse(double_divide(X, multiply(double_divide(multiply(Y, X), Y), Y)))
% 0.21/0.44 = { by lemma 6 }
% 0.21/0.44 inverse(Y)
% 0.21/0.44
% 0.21/0.44 Lemma 10: multiply(multiply(X, Y), inverse(X)) = Y.
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(multiply(X, Y), inverse(X))
% 0.21/0.44 = { by axiom 1 (multiply) }
% 0.21/0.44 inverse(double_divide(inverse(X), multiply(X, Y)))
% 0.21/0.44 = { by lemma 9 R->L }
% 0.21/0.44 multiply(double_divide(inverse(X), double_divide(inverse(X), multiply(X, Y))), inverse(X))
% 0.21/0.44 = { by lemma 8 }
% 0.21/0.44 Y
% 0.21/0.44
% 0.21/0.44 Lemma 11: multiply(inverse(X), Y) = multiply(Y, inverse(X)).
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(inverse(X), Y)
% 0.21/0.44 = { by lemma 10 R->L }
% 0.21/0.44 multiply(multiply(X, multiply(inverse(X), Y)), inverse(X))
% 0.21/0.44 = { by lemma 9 R->L }
% 0.21/0.44 multiply(multiply(X, multiply(multiply(double_divide(Y, X), Y), Y)), inverse(X))
% 0.21/0.44 = { by lemma 3 }
% 0.21/0.44 multiply(Y, inverse(X))
% 0.21/0.44
% 0.21/0.44 Lemma 12: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(multiply(X, inverse(X)), Y)
% 0.21/0.44 = { by lemma 3 R->L }
% 0.21/0.44 multiply(multiply(X, inverse(X)), multiply(inverse(X), multiply(multiply(double_divide(Z, inverse(X)), Y), Z)))
% 0.21/0.44 = { by lemma 7 R->L }
% 0.21/0.44 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)))
% 0.21/0.44 = { by lemma 3 }
% 0.21/0.44 multiply(inverse(X), multiply(multiply(double_divide(Z, inverse(X)), Y), 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_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(inverse(a1), a1)
% 0.21/0.44 = { by lemma 11 }
% 0.21/0.44 multiply(a1, inverse(a1))
% 0.21/0.44 = { by lemma 12 R->L }
% 0.21/0.44 multiply(a1, inverse(multiply(multiply(multiply(b1, inverse(b1)), inverse(multiply(b1, inverse(b1)))), a1)))
% 0.21/0.44 = { by lemma 12 }
% 0.21/0.44 multiply(a1, inverse(multiply(inverse(multiply(b1, inverse(b1))), a1)))
% 0.21/0.44 = { by lemma 9 R->L }
% 0.21/0.44 multiply(a1, multiply(double_divide(X, multiply(inverse(multiply(b1, inverse(b1))), a1)), X))
% 0.21/0.44 = { by axiom 1 (multiply) }
% 0.21/0.44 multiply(a1, inverse(double_divide(X, double_divide(X, multiply(inverse(multiply(b1, inverse(b1))), a1)))))
% 0.21/0.44 = { by lemma 8 R->L }
% 0.21/0.44 multiply(multiply(double_divide(X, double_divide(X, multiply(inverse(multiply(b1, inverse(b1))), a1))), inverse(inverse(multiply(b1, inverse(b1))))), inverse(double_divide(X, double_divide(X, multiply(inverse(multiply(b1, inverse(b1))), a1)))))
% 0.21/0.44 = { by lemma 10 }
% 0.21/0.44 inverse(inverse(multiply(b1, inverse(b1))))
% 0.21/0.44 = { by lemma 9 R->L }
% 0.21/0.44 inverse(multiply(double_divide(Y, multiply(b1, inverse(b1))), Y))
% 0.21/0.44 = { by lemma 9 R->L }
% 0.21/0.44 multiply(double_divide(multiply(multiply(double_divide(Y, multiply(b1, inverse(b1))), Y), Y), multiply(double_divide(Y, multiply(b1, inverse(b1))), Y)), multiply(multiply(double_divide(Y, multiply(b1, inverse(b1))), Y), Y))
% 0.21/0.44 = { by lemma 3 R->L }
% 0.21/0.44 multiply(double_divide(multiply(multiply(double_divide(Y, multiply(b1, inverse(b1))), Y), Y), multiply(double_divide(Y, multiply(b1, inverse(b1))), Y)), multiply(multiply(double_divide(Y, multiply(b1, inverse(b1))), Y), multiply(multiply(b1, inverse(b1)), multiply(multiply(double_divide(Y, multiply(b1, inverse(b1))), Y), Y))))
% 0.21/0.44 = { by lemma 4 }
% 0.21/0.44 multiply(b1, inverse(b1))
% 0.21/0.44 = { by lemma 11 R->L }
% 0.21/0.44 multiply(inverse(b1), b1)
% 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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