TSTP Solution File: GRP606-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP606-1 : 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 : n009.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 01:19:05 EDT 2023
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP606-1 : TPTP v8.1.2. Released v2.6.0.
% 0.04/0.13 % 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 : n009.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 02:21:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.41
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.20/0.42 Axiom 2 (single_axiom): double_divide(inverse(double_divide(X, inverse(double_divide(inverse(Y), double_divide(X, Z))))), Z) = Y.
% 0.20/0.42
% 0.20/0.42 Lemma 3: double_divide(multiply(multiply(double_divide(X, Y), inverse(Z)), X), Y) = Z.
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(multiply(multiply(double_divide(X, Y), inverse(Z)), X), Y)
% 0.20/0.42 = { by axiom 1 (multiply) }
% 0.20/0.42 double_divide(multiply(inverse(double_divide(inverse(Z), double_divide(X, Y))), X), Y)
% 0.20/0.42 = { by axiom 1 (multiply) }
% 0.20/0.42 double_divide(inverse(double_divide(X, inverse(double_divide(inverse(Z), double_divide(X, Y))))), Y)
% 0.20/0.42 = { by axiom 2 (single_axiom) }
% 0.20/0.42 Z
% 0.20/0.42
% 0.20/0.42 Lemma 4: multiply(X, multiply(multiply(double_divide(Y, X), inverse(Z)), Y)) = inverse(Z).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, multiply(multiply(double_divide(Y, X), inverse(Z)), Y))
% 0.20/0.42 = { by axiom 1 (multiply) }
% 0.20/0.42 inverse(double_divide(multiply(multiply(double_divide(Y, X), inverse(Z)), Y), X))
% 0.20/0.42 = { by lemma 3 }
% 0.20/0.42 inverse(Z)
% 0.20/0.42
% 0.20/0.42 Lemma 5: multiply(X, multiply(multiply(double_divide(Y, X), multiply(Z, W)), Y)) = multiply(Z, W).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(X, multiply(multiply(double_divide(Y, X), multiply(Z, W)), Y))
% 0.20/0.42 = { by axiom 1 (multiply) }
% 0.20/0.42 multiply(X, multiply(multiply(double_divide(Y, X), inverse(double_divide(W, Z))), Y))
% 0.20/0.42 = { by lemma 4 }
% 0.20/0.42 inverse(double_divide(W, Z))
% 0.20/0.42 = { by axiom 1 (multiply) R->L }
% 0.20/0.42 multiply(Z, W)
% 0.20/0.42
% 0.20/0.42 Lemma 6: double_divide(multiply(multiply(double_divide(X, Y), multiply(Z, W)), X), Y) = double_divide(W, Z).
% 0.20/0.42 Proof:
% 0.20/0.42 double_divide(multiply(multiply(double_divide(X, Y), multiply(Z, W)), X), Y)
% 0.20/0.42 = { by axiom 1 (multiply) }
% 0.20/0.42 double_divide(multiply(multiply(double_divide(X, Y), inverse(double_divide(W, Z))), X), Y)
% 0.20/0.42 = { by lemma 3 }
% 0.20/0.42 double_divide(W, Z)
% 0.20/0.42
% 0.20/0.42 Lemma 7: multiply(multiply(double_divide(X, double_divide(Y, Z)), inverse(W)), X) = multiply(Z, multiply(inverse(W), Y)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(multiply(double_divide(X, double_divide(Y, Z)), inverse(W)), X)
% 0.20/0.42 = { by axiom 1 (multiply) }
% 0.20/0.42 inverse(double_divide(X, multiply(double_divide(X, double_divide(Y, Z)), inverse(W))))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 inverse(double_divide(multiply(multiply(double_divide(Y, Z), multiply(multiply(double_divide(X, double_divide(Y, Z)), inverse(W)), X)), Y), Z))
% 0.20/0.42 = { by lemma 4 }
% 0.20/0.42 inverse(double_divide(multiply(inverse(W), Y), Z))
% 0.20/0.42 = { by axiom 1 (multiply) R->L }
% 0.20/0.42 multiply(Z, multiply(inverse(W), Y))
% 0.20/0.42
% 0.20/0.42 Lemma 8: multiply(multiply(X, multiply(Y, Z)), multiply(W, multiply(inverse(X), V))) = multiply(W, multiply(multiply(Y, Z), V)).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(multiply(X, multiply(Y, Z)), multiply(W, multiply(inverse(X), V)))
% 0.20/0.42 = { by axiom 1 (multiply) }
% 0.20/0.42 multiply(multiply(X, inverse(double_divide(Z, Y))), multiply(W, multiply(inverse(X), V)))
% 0.20/0.42 = { by lemma 7 R->L }
% 0.20/0.43 multiply(multiply(X, inverse(double_divide(Z, Y))), multiply(multiply(double_divide(U, double_divide(V, W)), inverse(X)), U))
% 0.20/0.43 = { by lemma 3 R->L }
% 0.20/0.43 multiply(multiply(double_divide(multiply(multiply(double_divide(U, double_divide(V, W)), inverse(X)), U), double_divide(V, W)), inverse(double_divide(Z, Y))), multiply(multiply(double_divide(U, double_divide(V, W)), inverse(X)), U))
% 0.20/0.43 = { by lemma 7 }
% 0.20/0.43 multiply(W, multiply(inverse(double_divide(Z, Y)), V))
% 0.20/0.43 = { by axiom 1 (multiply) R->L }
% 0.20/0.43 multiply(W, multiply(multiply(Y, Z), V))
% 0.20/0.43
% 0.20/0.43 Lemma 9: multiply(inverse(Y), multiply(inverse(X), Z)) = multiply(inverse(X), multiply(inverse(Y), Z)).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(inverse(Y), multiply(inverse(X), Z))
% 0.20/0.43 = { by lemma 4 R->L }
% 0.20/0.43 multiply(multiply(W, multiply(multiply(double_divide(V, W), inverse(Y)), V)), multiply(inverse(X), Z))
% 0.20/0.43 = { by lemma 5 R->L }
% 0.20/0.43 multiply(multiply(W, multiply(multiply(double_divide(V, W), inverse(Y)), V)), multiply(multiply(U, T), multiply(multiply(double_divide(S, multiply(U, T)), multiply(inverse(X), Z)), S)))
% 0.20/0.43 = { by lemma 8 R->L }
% 0.20/0.43 multiply(multiply(X2, multiply(U, T)), multiply(multiply(W, multiply(multiply(double_divide(V, W), inverse(Y)), V)), multiply(inverse(X2), multiply(multiply(double_divide(S, multiply(U, T)), multiply(inverse(X), Z)), S))))
% 0.20/0.43 = { by lemma 8 R->L }
% 0.20/0.43 multiply(multiply(X, multiply(W, multiply(multiply(double_divide(V, W), inverse(Y)), V))), multiply(multiply(X2, multiply(U, T)), multiply(inverse(X), multiply(inverse(X2), multiply(multiply(double_divide(S, multiply(U, T)), multiply(inverse(X), Z)), S)))))
% 0.20/0.43 = { by lemma 8 }
% 0.20/0.43 multiply(multiply(X, multiply(W, multiply(multiply(double_divide(V, W), inverse(Y)), V))), multiply(inverse(X), multiply(multiply(U, T), multiply(multiply(double_divide(S, multiply(U, T)), multiply(inverse(X), Z)), S))))
% 0.20/0.43 = { by lemma 5 }
% 0.20/0.43 multiply(multiply(X, multiply(W, multiply(multiply(double_divide(V, W), inverse(Y)), V))), multiply(inverse(X), multiply(inverse(X), Z)))
% 0.20/0.43 = { by lemma 8 }
% 0.20/0.43 multiply(inverse(X), multiply(multiply(W, multiply(multiply(double_divide(V, W), inverse(Y)), V)), Z))
% 0.20/0.43 = { by lemma 4 }
% 0.20/0.43 multiply(inverse(X), multiply(inverse(Y), Z))
% 0.20/0.43
% 0.20/0.43 Lemma 10: multiply(X, multiply(inverse(Y), inverse(X))) = inverse(Y).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, multiply(inverse(Y), inverse(X)))
% 0.20/0.43 = { by axiom 1 (multiply) }
% 0.20/0.43 inverse(double_divide(multiply(inverse(Y), inverse(X)), X))
% 0.20/0.43 = { by lemma 4 R->L }
% 0.20/0.43 inverse(double_divide(multiply(inverse(Y), multiply(inverse(Z), multiply(multiply(double_divide(W, inverse(Z)), inverse(X)), W))), X))
% 0.20/0.43 = { by lemma 3 R->L }
% 0.20/0.43 inverse(double_divide(multiply(inverse(Y), multiply(inverse(Z), multiply(multiply(double_divide(W, inverse(Z)), inverse(X)), W))), double_divide(multiply(multiply(double_divide(W, inverse(Z)), inverse(X)), W), inverse(Z))))
% 0.20/0.43 = { by lemma 9 }
% 0.20/0.43 inverse(double_divide(multiply(inverse(Z), multiply(inverse(Y), multiply(multiply(double_divide(W, inverse(Z)), inverse(X)), W))), double_divide(multiply(multiply(double_divide(W, inverse(Z)), inverse(X)), W), inverse(Z))))
% 0.20/0.43 = { by lemma 7 R->L }
% 0.20/0.43 inverse(double_divide(multiply(multiply(double_divide(V, double_divide(multiply(multiply(double_divide(W, inverse(Z)), inverse(X)), W), inverse(Z))), inverse(Y)), V), double_divide(multiply(multiply(double_divide(W, inverse(Z)), inverse(X)), W), inverse(Z))))
% 0.20/0.43 = { by lemma 3 }
% 0.20/0.43 inverse(Y)
% 0.20/0.43
% 0.20/0.43 Lemma 11: multiply(inverse(X), multiply(Y, inverse(Y))) = inverse(X).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(inverse(X), multiply(Y, inverse(Y)))
% 0.20/0.43 = { by axiom 1 (multiply) }
% 0.20/0.43 multiply(inverse(X), inverse(double_divide(inverse(Y), Y)))
% 0.20/0.43 = { by lemma 5 R->L }
% 0.20/0.43 multiply(Y, multiply(multiply(double_divide(inverse(Y), Y), multiply(inverse(X), inverse(double_divide(inverse(Y), Y)))), inverse(Y)))
% 0.20/0.43 = { by lemma 10 }
% 0.20/0.43 multiply(Y, multiply(inverse(X), inverse(Y)))
% 0.20/0.43 = { by lemma 10 }
% 0.20/0.43 inverse(X)
% 0.20/0.43
% 0.20/0.43 Lemma 12: multiply(X, multiply(inverse(X), inverse(Y))) = inverse(Y).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(X, multiply(inverse(X), inverse(Y)))
% 0.20/0.43 = { by lemma 11 R->L }
% 0.20/0.43 multiply(X, multiply(inverse(X), multiply(inverse(Y), multiply(Z, inverse(Z)))))
% 0.20/0.43 = { by lemma 9 R->L }
% 0.20/0.43 multiply(X, multiply(inverse(Y), multiply(inverse(X), multiply(Z, inverse(Z)))))
% 0.20/0.43 = { by lemma 11 }
% 0.20/0.43 multiply(X, multiply(inverse(Y), inverse(X)))
% 0.20/0.43 = { by lemma 10 }
% 0.20/0.43 inverse(Y)
% 0.20/0.43
% 0.20/0.43 Lemma 13: inverse(inverse(X)) = X.
% 0.20/0.43 Proof:
% 0.20/0.43 inverse(inverse(X))
% 0.20/0.43 = { by lemma 4 R->L }
% 0.20/0.43 inverse(multiply(Y, multiply(multiply(double_divide(Z, Y), inverse(X)), Z)))
% 0.20/0.43 = { by lemma 3 R->L }
% 0.20/0.43 double_divide(multiply(multiply(double_divide(W, V), inverse(inverse(multiply(Y, multiply(multiply(double_divide(Z, Y), inverse(X)), Z))))), W), V)
% 0.20/0.43 = { by lemma 12 R->L }
% 0.20/0.43 double_divide(multiply(multiply(double_divide(W, V), multiply(multiply(Y, multiply(multiply(double_divide(Z, Y), inverse(X)), Z)), multiply(inverse(multiply(Y, multiply(multiply(double_divide(Z, Y), inverse(X)), Z))), inverse(inverse(multiply(Y, multiply(multiply(double_divide(Z, Y), inverse(X)), Z))))))), W), V)
% 0.20/0.43 = { by axiom 1 (multiply) }
% 0.20/0.43 double_divide(multiply(multiply(double_divide(W, V), multiply(inverse(double_divide(multiply(multiply(double_divide(Z, Y), inverse(X)), Z), Y)), multiply(inverse(multiply(Y, multiply(multiply(double_divide(Z, Y), inverse(X)), Z))), inverse(inverse(multiply(Y, multiply(multiply(double_divide(Z, Y), inverse(X)), Z))))))), W), V)
% 0.20/0.43 = { by lemma 11 }
% 0.20/0.43 double_divide(multiply(multiply(double_divide(W, V), inverse(double_divide(multiply(multiply(double_divide(Z, Y), inverse(X)), Z), Y))), W), V)
% 0.20/0.43 = { by axiom 1 (multiply) R->L }
% 0.20/0.43 double_divide(multiply(multiply(double_divide(W, V), multiply(Y, multiply(multiply(double_divide(Z, Y), inverse(X)), Z))), W), V)
% 0.20/0.43 = { by lemma 6 }
% 0.20/0.43 double_divide(multiply(multiply(double_divide(Z, Y), inverse(X)), Z), Y)
% 0.20/0.43 = { by lemma 3 }
% 0.20/0.43 X
% 0.20/0.43
% 0.20/0.43 Lemma 14: multiply(Y, X) = multiply(X, Y).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(Y, X)
% 0.20/0.43 = { by lemma 13 R->L }
% 0.20/0.43 multiply(Y, inverse(inverse(X)))
% 0.20/0.43 = { by lemma 10 R->L }
% 0.20/0.43 multiply(Y, multiply(inverse(Y), multiply(inverse(inverse(X)), inverse(inverse(Y)))))
% 0.20/0.43 = { by lemma 13 }
% 0.20/0.43 multiply(Y, multiply(inverse(Y), multiply(X, inverse(inverse(Y)))))
% 0.20/0.43 = { by lemma 13 R->L }
% 0.20/0.43 multiply(Y, multiply(inverse(Y), inverse(inverse(multiply(X, inverse(inverse(Y)))))))
% 0.20/0.43 = { by lemma 12 }
% 0.20/0.43 inverse(inverse(multiply(X, inverse(inverse(Y)))))
% 0.20/0.43 = { by lemma 13 }
% 0.20/0.43 multiply(X, inverse(inverse(Y)))
% 0.20/0.43 = { by lemma 13 }
% 0.20/0.43 multiply(X, Y)
% 0.20/0.43
% 0.20/0.43 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(multiply(inverse(b2), b2), a2)
% 0.20/0.43 = { by lemma 14 R->L }
% 0.20/0.43 multiply(a2, multiply(inverse(b2), b2))
% 0.20/0.43 = { by lemma 14 R->L }
% 0.20/0.43 multiply(a2, multiply(b2, inverse(b2)))
% 0.20/0.43 = { by lemma 13 R->L }
% 0.20/0.43 multiply(inverse(inverse(a2)), multiply(b2, inverse(b2)))
% 0.20/0.43 = { by lemma 11 }
% 0.20/0.43 inverse(inverse(a2))
% 0.20/0.43 = { by lemma 13 }
% 0.20/0.43 a2
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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