TSTP Solution File: ALG384-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG384-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n031.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 : Tue Aug 22 10:32:38 EDT 2023
% Result : Unsatisfiable 15.21s 4.74s
% Output : CNFRefutation 15.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 88
% Syntax : Number of formulae : 95 ( 8 unt; 84 typ; 0 def)
% Number of atoms : 16 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 115 ( 76 >; 39 *; 0 +; 0 <<)
% Number of predicates : 46 ( 44 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 8 con; 0-3 aty)
% Number of variables : 4 (; 4 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > class_SEQ_Obanach > class_Ring__and__Field_Osgn__if > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring__abs > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Olordered__ring > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odivision__ring > class_Ring__and__Field_Odivision__by__zero > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Oabs__if > class_RealVector_Oreal__vector > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__algebra__1 > class_RealVector_Oreal__algebra > class_RealVector_Ometric__space > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add__abs > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_Nat_Osemiring__char__0 > class_Int_Onumber__ring > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__cont__1 > c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1 > c_RealVector_OscaleR__class_OscaleR > c_RealVector_Odist__class_Odist > c_HOL_Otimes__class_Otimes > c_HOL_Oinverse__class_Odivide > c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1 > c_Deriv_Osko__Deriv__Xlemma__interval__1__1 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 > c_Transcendental_Oexp > c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1 > c_RealVector_Oof__real > c_RealVector_Onorm__class_Onorm > c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1 > c_RealDef_Oreal > c_NthRoot_Osko__NthRoot__Xrealpow__pos__nth2__1__1 > c_NthRoot_Oroot > c_Nat_Osemiring__1__class_Oof__nat > c_HOL_Osgn__class_Osgn > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > #nlpp > c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1 > c_Transcendental_Oln > c_RealDef_Oreal__of__preal > c_NthRoot_Osqrt > c_HOL_Ozero__class_Ozero > v_c____ > tc_nat > tc_RealDef_Oreal > tc_Complex_Ocomplex > c_Transcendental_Opi > c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1 > c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1 > c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(c_Transcendental_Opi,type,
c_Transcendental_Opi: $i ).
tff(c_Transcendental_Oln,type,
c_Transcendental_Oln: $i > $i ).
tff(class_Ring__and__Field_Opordered__ring__abs,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_RealDef_Oreal,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(c_NthRoot_Osko__NthRoot__Xrealpow__pos__nth2__1__1,type,
c_NthRoot_Osko__NthRoot__Xrealpow__pos__nth2__1__1: ( $i * $i ) > $i ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1,type,
c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1: ( $i * $i ) > $i ).
tff(c_HOL_Oinverse__class_Oinverse,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__semiring,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(class_RealVector_Oreal__vector,type,
class_RealVector_Oreal__vector: $i > $o ).
tff(c_RealVector_OscaleR__class_OscaleR,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
tff(class_RealVector_Oreal__normed__field,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add__abs,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(c_RealDef_Oreal__of__preal,type,
c_RealDef_Oreal__of__preal: $i > $i ).
tff(c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1,type,
c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1: $i ).
tff(class_RealVector_Ometric__space,type,
class_RealVector_Ometric__space: $i > $o ).
tff(class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(c_HOL_Oinverse__class_Odivide,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Odivision__by__zero,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(c_NthRoot_Oroot,type,
c_NthRoot_Oroot: ( $i * $i ) > $i ).
tff(c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(class_SEQ_Obanach,type,
class_SEQ_Obanach: $i > $o ).
tff(class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1,type,
c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1: $i > $i ).
tff(c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1,type,
c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_nat,type,
tc_nat: $i ).
tff(class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(class_RealVector_Oreal__normed__div__algebra,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(c_NthRoot_Osqrt,type,
c_NthRoot_Osqrt: $i > $i ).
tff(class_Ring__and__Field_Oabs__if,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(class_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(class_RealVector_Oreal__algebra,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(class_RealVector_Oreal__algebra__1,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(c_Transcendental_Oexp,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
tff(c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Omult__mono1,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(c_HOL_Osgn__class_Osgn,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1: ( $i * $i * $i ) > $i ).
tff(c_RealVector_Onorm__class_Onorm,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(v_c____,type,
v_c____: $i ).
tff(class_OrderedGroup_Olordered__ab__group__add__abs,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1,type,
c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1: $i ).
tff(class_Ring__and__Field_Olordered__ring,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(class_Ring__and__Field_Osgn__if,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
tff(c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1,type,
c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1,type,
c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1: $i ).
tff(class_Ring__and__Field_Omult__mono,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(c_HOL_Oabs__class_Oabs,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_RealVector_Oof__real,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(class_Ring__and__Field_Odivision__ring,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(c_Deriv_Osko__Deriv__Xlemma__interval__1__1,type,
c_Deriv_Osko__Deriv__Xlemma__interval__1__1: ( $i * $i * $i ) > $i ).
tff(c_RealVector_Odist__class_Odist,type,
c_RealVector_Odist__class_Odist: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__cont__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__cont__1: ( $i * $i * $i ) > $i ).
tff(f_4324,axiom,
v_c____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_4392,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_4235,axiom,
! [T_a,V_x] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal)
| ( V_x = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_4326,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(c_992,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_c____,
inference(cnfTransformation,[status(thm)],[f_4324]) ).
tff(c_1126,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_4392]) ).
tff(c_10530,plain,
! [T_a_1719,V_x_1720] :
( ( c_HOL_Ozero__class_Ozero(T_a_1719) = V_x_1720 )
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_1720,T_a_1719),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a_1719) ),
inference(cnfTransformation,[status(thm)],[f_4235]) ).
tff(c_994,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_4326]) ).
tff(c_10554,plain,
( ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_c____ )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_10530,c_994]) ).
tff(c_10586,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_c____,
inference(demodulation,[status(thm),theory(equality)],[c_1126,c_10554]) ).
tff(c_10588,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_992,c_10586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.15/0.14 % Problem : ALG384-1 : TPTP v8.1.2. Released v4.1.0.
% 0.15/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 20:44:00 EDT 2023
% 0.15/0.37 % CPUTime :
% 15.21/4.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.21/4.75
% 15.21/4.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.21/4.77
% 15.21/4.77 Inference rules
% 15.21/4.77 ----------------------
% 15.21/4.77 #Ref : 5
% 15.21/4.77 #Sup : 1965
% 15.21/4.77 #Fact : 4
% 15.21/4.77 #Define : 0
% 15.21/4.77 #Split : 6
% 15.21/4.77 #Chain : 0
% 15.21/4.77 #Close : 0
% 15.21/4.77
% 15.21/4.77 Ordering : KBO
% 15.21/4.77
% 15.21/4.77 Simplification rules
% 15.21/4.77 ----------------------
% 15.21/4.77 #Subsume : 423
% 15.21/4.77 #Demod : 1442
% 15.21/4.77 #Tautology : 961
% 15.21/4.77 #SimpNegUnit : 60
% 15.21/4.77 #BackRed : 1
% 15.21/4.77
% 15.21/4.77 #Partial instantiations: 0
% 15.21/4.77 #Strategies tried : 1
% 15.21/4.77
% 15.21/4.77 Timing (in seconds)
% 15.21/4.77 ----------------------
% 15.21/4.78 Preprocessing : 1.42
% 15.21/4.78 Parsing : 0.81
% 15.21/4.78 CNF conversion : 0.12
% 15.21/4.78 Main loop : 2.30
% 15.21/4.78 Inferencing : 0.58
% 15.21/4.78 Reduction : 1.00
% 15.21/4.78 Demodulation : 0.71
% 15.21/4.78 BG Simplification : 0.14
% 15.21/4.78 Subsumption : 0.47
% 15.21/4.78 Abstraction : 0.09
% 15.21/4.78 MUC search : 0.00
% 15.21/4.78 Cooper : 0.00
% 15.21/4.78 Total : 3.76
% 15.21/4.78 Index Insertion : 0.00
% 15.21/4.78 Index Deletion : 0.00
% 15.21/4.78 Index Matching : 0.00
% 15.21/4.78 BG Taut test : 0.00
%------------------------------------------------------------------------------