TSTP Solution File: COM013+4 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : COM013+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 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 : Tue Aug 22 10:35:18 EDT 2023
% Result : Theorem 5.67s 2.34s
% Output : CNFRefutation 5.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 33
% Syntax : Number of formulae : 74 ( 10 unt; 27 typ; 2 def)
% Number of atoms : 198 ( 6 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 259 ( 108 ~; 110 |; 27 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 25 >; 19 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 2 con; 0-4 aty)
% Number of variables : 68 (; 60 !; 8 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtmndtplgtdt0 > sdtmndtasgtdt0 > aReductOfIn0 > aNormalFormOfIn0 > iLess0 > isTerminating0 > isLocallyConfluent0 > isConfluent0 > aRewritingSystem0 > aElement0 > #nlpp > xR > #skF_9 > #skF_7 > #skF_5 > #skF_16 > #skF_1 > #skF_4 > #skF_12 > #skF_8 > #skF_15 > #skF_10 > #skF_2 > #skF_13 > #skF_6 > #skF_3 > #skF_11 > #skF_14
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(sdtmndtplgtdt0,type,
sdtmndtplgtdt0: ( $i * $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff('#skF_16',type,
'#skF_16': $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(aReductOfIn0,type,
aReductOfIn0: ( $i * $i * $i ) > $o ).
tff(aElement0,type,
aElement0: $i > $o ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(isTerminating0,type,
isTerminating0: $i > $o ).
tff(aNormalFormOfIn0,type,
aNormalFormOfIn0: ( $i * $i * $i ) > $o ).
tff(xR,type,
xR: $i ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff(aRewritingSystem0,type,
aRewritingSystem0: $i > $o ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff(isConfluent0,type,
isConfluent0: $i > $o ).
tff(isLocallyConfluent0,type,
isLocallyConfluent0: $i > $o ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff(sdtmndtasgtdt0,type,
sdtmndtasgtdt0: ( $i * $i * $i ) > $o ).
tff(f_264,negated_conjecture,
~ ! [W0] :
( aElement0(W0)
=> ( ! [W1] :
( aElement0(W1)
=> ( iLess0(W1,W0)
=> ? [W2] :
( aElement0(W2)
& ( ( W1 = W2 )
| ( ( aReductOfIn0(W2,W1,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W1,xR)
& sdtmndtplgtdt0(W3,xR,W2) ) )
& sdtmndtplgtdt0(W1,xR,W2) ) )
& sdtmndtasgtdt0(W1,xR,W2)
& ~ ? [W3] : aReductOfIn0(W3,W2,xR)
& aNormalFormOfIn0(W2,W1,xR) ) ) )
=> ? [W1] :
( ( aElement0(W1)
& ( ( W0 = W1 )
| aReductOfIn0(W1,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1)
| sdtmndtasgtdt0(W0,xR,W1) )
& ~ ? [W2] : aReductOfIn0(W2,W1,xR) )
| aNormalFormOfIn0(W1,W0,xR) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_208,hypothesis,
( aRewritingSystem0(xR)
& ! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( aReductOfIn0(W1,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1) )
=> iLess0(W1,W0) ) )
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__587) ).
tff(f_42,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aRewritingSystem0(W1) )
=> ! [W2] :
( aReductOfIn0(W2,W0,W1)
=> aElement0(W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).
tff(f_75,definition,
! [W0,W1,W2] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2) )
=> ( sdtmndtplgtdt0(W0,W1,W2)
<=> ( aReductOfIn0(W2,W0,W1)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W0,W1)
& sdtmndtplgtdt0(W3,W1,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCDef) ).
tff(f_101,definition,
! [W0,W1,W2] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2) )
=> ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( ( W0 = W2 )
| sdtmndtplgtdt0(W0,W1,W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRDef) ).
tff(f_115,axiom,
! [W0,W1,W2,W3] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2)
& aElement0(W3) )
=> ( ( sdtmndtasgtdt0(W0,W1,W2)
& sdtmndtasgtdt0(W2,W1,W3) )
=> sdtmndtasgtdt0(W0,W1,W3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRTrans) ).
tff(c_98,plain,
aElement0('#skF_13'),
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_88,plain,
aRewritingSystem0(xR),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_108,plain,
( aReductOfIn0('#skF_16'('#skF_13'),'#skF_13',xR)
| ~ aElement0('#skF_13') ),
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_126,plain,
aReductOfIn0('#skF_16'('#skF_13'),'#skF_13',xR),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_108]) ).
tff(c_139,plain,
! [W2_127,W0_128,W1_129] :
( aElement0(W2_127)
| ~ aReductOfIn0(W2_127,W0_128,W1_129)
| ~ aRewritingSystem0(W1_129)
| ~ aElement0(W0_128) ),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_142,plain,
( aElement0('#skF_16'('#skF_13'))
| ~ aRewritingSystem0(xR)
| ~ aElement0('#skF_13') ),
inference(resolution,[status(thm)],[c_126,c_139]) ).
tff(c_145,plain,
aElement0('#skF_16'('#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_88,c_142]) ).
tff(c_360,plain,
! [W2_177,W0_178,W1_179] :
( ~ aReductOfIn0(W2_177,W0_178,W1_179)
| sdtmndtplgtdt0(W0_178,W1_179,W2_177)
| ~ aElement0(W2_177)
| ~ aRewritingSystem0(W1_179)
| ~ aElement0(W0_178) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_26,plain,
! [W0_22,W1_23,W2_24] :
( ~ sdtmndtplgtdt0(W0_22,W1_23,W2_24)
| sdtmndtasgtdt0(W0_22,W1_23,W2_24)
| ~ aElement0(W2_24)
| ~ aRewritingSystem0(W1_23)
| ~ aElement0(W0_22) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_374,plain,
! [W0_178,W1_179,W2_177] :
( sdtmndtasgtdt0(W0_178,W1_179,W2_177)
| ~ aReductOfIn0(W2_177,W0_178,W1_179)
| ~ aElement0(W2_177)
| ~ aRewritingSystem0(W1_179)
| ~ aElement0(W0_178) ),
inference(resolution,[status(thm)],[c_360,c_26]) ).
tff(c_176,plain,
! [W1_142,W0_143] :
( ~ aReductOfIn0(W1_142,W0_143,xR)
| iLess0(W1_142,W0_143)
| ~ aElement0(W1_142)
| ~ aElement0(W0_143) ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_187,plain,
( iLess0('#skF_16'('#skF_13'),'#skF_13')
| ~ aElement0('#skF_16'('#skF_13'))
| ~ aElement0('#skF_13') ),
inference(resolution,[status(thm)],[c_126,c_176]) ).
tff(c_196,plain,
iLess0('#skF_16'('#skF_13'),'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_145,c_187]) ).
tff(c_116,plain,
! [W1_101] :
( aElement0('#skF_14'(W1_101))
| ~ iLess0(W1_101,'#skF_13')
| ~ aElement0(W1_101) ),
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_124,plain,
! [W1_101] :
( aElement0('#skF_15'(W1_101))
| aReductOfIn0('#skF_14'(W1_101),W1_101,xR)
| ( '#skF_14'(W1_101) = W1_101 )
| ~ iLess0(W1_101,'#skF_13')
| ~ aElement0(W1_101) ),
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_14,plain,
! [W2_14,W0_12,W1_13] :
( ~ aReductOfIn0(W2_14,W0_12,W1_13)
| sdtmndtplgtdt0(W0_12,W1_13,W2_14)
| ~ aElement0(W2_14)
| ~ aRewritingSystem0(W1_13)
| ~ aElement0(W0_12) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_394,plain,
! [W2_182,W1_183] :
( ~ sdtmndtplgtdt0(W2_182,xR,W1_183)
| ~ aReductOfIn0(W2_182,'#skF_13',xR)
| ~ aElement0(W2_182)
| aReductOfIn0('#skF_16'(W1_183),W1_183,xR)
| ~ aElement0(W1_183) ),
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_397,plain,
! [W0_12,W2_14] :
( ~ aReductOfIn0(W0_12,'#skF_13',xR)
| aReductOfIn0('#skF_16'(W2_14),W2_14,xR)
| ~ aReductOfIn0(W2_14,W0_12,xR)
| ~ aElement0(W2_14)
| ~ aRewritingSystem0(xR)
| ~ aElement0(W0_12) ),
inference(resolution,[status(thm)],[c_14,c_394]) ).
tff(c_820,plain,
! [W0_227,W2_228] :
( ~ aReductOfIn0(W0_227,'#skF_13',xR)
| aReductOfIn0('#skF_16'(W2_228),W2_228,xR)
| ~ aReductOfIn0(W2_228,W0_227,xR)
| ~ aElement0(W2_228)
| ~ aElement0(W0_227) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_397]) ).
tff(c_837,plain,
! [W2_228] :
( aReductOfIn0('#skF_16'(W2_228),W2_228,xR)
| ~ aReductOfIn0(W2_228,'#skF_16'('#skF_13'),xR)
| ~ aElement0(W2_228)
| ~ aElement0('#skF_16'('#skF_13')) ),
inference(resolution,[status(thm)],[c_126,c_820]) ).
tff(c_876,plain,
! [W2_233] :
( aReductOfIn0('#skF_16'(W2_233),W2_233,xR)
| ~ aReductOfIn0(W2_233,'#skF_16'('#skF_13'),xR)
| ~ aElement0(W2_233) ),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_837]) ).
tff(c_112,plain,
! [W3_109,W1_101] :
( ~ aReductOfIn0(W3_109,'#skF_14'(W1_101),xR)
| ~ iLess0(W1_101,'#skF_13')
| ~ aElement0(W1_101) ),
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_962,plain,
! [W1_235] :
( ~ iLess0(W1_235,'#skF_13')
| ~ aElement0(W1_235)
| ~ aReductOfIn0('#skF_14'(W1_235),'#skF_16'('#skF_13'),xR)
| ~ aElement0('#skF_14'(W1_235)) ),
inference(resolution,[status(thm)],[c_876,c_112]) ).
tff(c_966,plain,
( ~ aElement0('#skF_14'('#skF_16'('#skF_13')))
| aElement0('#skF_15'('#skF_16'('#skF_13')))
| ( '#skF_14'('#skF_16'('#skF_13')) = '#skF_16'('#skF_13') )
| ~ iLess0('#skF_16'('#skF_13'),'#skF_13')
| ~ aElement0('#skF_16'('#skF_13')) ),
inference(resolution,[status(thm)],[c_124,c_962]) ).
tff(c_969,plain,
( ~ aElement0('#skF_14'('#skF_16'('#skF_13')))
| aElement0('#skF_15'('#skF_16'('#skF_13')))
| ( '#skF_14'('#skF_16'('#skF_13')) = '#skF_16'('#skF_13') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_196,c_966]) ).
tff(c_977,plain,
~ aElement0('#skF_14'('#skF_16'('#skF_13'))),
inference(splitLeft,[status(thm)],[c_969]) ).
tff(c_1004,plain,
( ~ iLess0('#skF_16'('#skF_13'),'#skF_13')
| ~ aElement0('#skF_16'('#skF_13')) ),
inference(resolution,[status(thm)],[c_116,c_977]) ).
tff(c_1008,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_145,c_196,c_1004]) ).
tff(c_1010,plain,
aElement0('#skF_14'('#skF_16'('#skF_13'))),
inference(splitRight,[status(thm)],[c_969]) ).
tff(c_114,plain,
! [W1_101] :
( sdtmndtasgtdt0(W1_101,xR,'#skF_14'(W1_101))
| ~ iLess0(W1_101,'#skF_13')
| ~ aElement0(W1_101) ),
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_1146,plain,
! [W0_257,W1_258,W3_259,W2_260] :
( sdtmndtasgtdt0(W0_257,W1_258,W3_259)
| ~ sdtmndtasgtdt0(W2_260,W1_258,W3_259)
| ~ sdtmndtasgtdt0(W0_257,W1_258,W2_260)
| ~ aElement0(W3_259)
| ~ aElement0(W2_260)
| ~ aRewritingSystem0(W1_258)
| ~ aElement0(W0_257) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_1158,plain,
! [W0_257,W1_101] :
( sdtmndtasgtdt0(W0_257,xR,'#skF_14'(W1_101))
| ~ sdtmndtasgtdt0(W0_257,xR,W1_101)
| ~ aElement0('#skF_14'(W1_101))
| ~ aRewritingSystem0(xR)
| ~ aElement0(W0_257)
| ~ iLess0(W1_101,'#skF_13')
| ~ aElement0(W1_101) ),
inference(resolution,[status(thm)],[c_114,c_1146]) ).
tff(c_1737,plain,
! [W0_293,W1_294] :
( sdtmndtasgtdt0(W0_293,xR,'#skF_14'(W1_294))
| ~ sdtmndtasgtdt0(W0_293,xR,W1_294)
| ~ aElement0('#skF_14'(W1_294))
| ~ aElement0(W0_293)
| ~ iLess0(W1_294,'#skF_13')
| ~ aElement0(W1_294) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_1158]) ).
tff(c_197,plain,
! [W1_144] :
( ~ sdtmndtasgtdt0('#skF_13',xR,W1_144)
| aReductOfIn0('#skF_16'(W1_144),W1_144,xR)
| ~ aElement0(W1_144) ),
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_209,plain,
! [W1_101] :
( ~ iLess0(W1_101,'#skF_13')
| ~ aElement0(W1_101)
| ~ sdtmndtasgtdt0('#skF_13',xR,'#skF_14'(W1_101))
| ~ aElement0('#skF_14'(W1_101)) ),
inference(resolution,[status(thm)],[c_197,c_112]) ).
tff(c_1771,plain,
! [W1_294] :
( ~ sdtmndtasgtdt0('#skF_13',xR,W1_294)
| ~ aElement0('#skF_14'(W1_294))
| ~ aElement0('#skF_13')
| ~ iLess0(W1_294,'#skF_13')
| ~ aElement0(W1_294) ),
inference(resolution,[status(thm)],[c_1737,c_209]) ).
tff(c_1798,plain,
! [W1_295] :
( ~ sdtmndtasgtdt0('#skF_13',xR,W1_295)
| ~ aElement0('#skF_14'(W1_295))
| ~ iLess0(W1_295,'#skF_13')
| ~ aElement0(W1_295) ),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_1771]) ).
tff(c_1801,plain,
( ~ sdtmndtasgtdt0('#skF_13',xR,'#skF_16'('#skF_13'))
| ~ iLess0('#skF_16'('#skF_13'),'#skF_13')
| ~ aElement0('#skF_16'('#skF_13')) ),
inference(resolution,[status(thm)],[c_1010,c_1798]) ).
tff(c_1807,plain,
~ sdtmndtasgtdt0('#skF_13',xR,'#skF_16'('#skF_13')),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_196,c_1801]) ).
tff(c_1811,plain,
( ~ aReductOfIn0('#skF_16'('#skF_13'),'#skF_13',xR)
| ~ aElement0('#skF_16'('#skF_13'))
| ~ aRewritingSystem0(xR)
| ~ aElement0('#skF_13') ),
inference(resolution,[status(thm)],[c_374,c_1807]) ).
tff(c_1818,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_88,c_145,c_126,c_1811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM013+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 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 : Thu Aug 3 23:55:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.67/2.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.67/2.34
% 5.67/2.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.67/2.37
% 5.67/2.37 Inference rules
% 5.67/2.37 ----------------------
% 5.67/2.37 #Ref : 0
% 5.67/2.37 #Sup : 301
% 5.67/2.37 #Fact : 0
% 5.67/2.37 #Define : 0
% 5.67/2.37 #Split : 6
% 5.67/2.37 #Chain : 0
% 5.67/2.37 #Close : 0
% 5.67/2.37
% 5.67/2.37 Ordering : KBO
% 5.67/2.37
% 5.67/2.37 Simplification rules
% 5.67/2.37 ----------------------
% 5.67/2.37 #Subsume : 57
% 5.67/2.37 #Demod : 311
% 5.67/2.37 #Tautology : 44
% 5.67/2.37 #SimpNegUnit : 4
% 5.67/2.37 #BackRed : 1
% 5.67/2.37
% 5.67/2.37 #Partial instantiations: 0
% 5.67/2.37 #Strategies tried : 1
% 5.67/2.37
% 5.67/2.37 Timing (in seconds)
% 5.67/2.37 ----------------------
% 5.90/2.38 Preprocessing : 0.57
% 5.90/2.38 Parsing : 0.30
% 5.90/2.38 CNF conversion : 0.05
% 5.90/2.38 Main loop : 0.70
% 5.90/2.38 Inferencing : 0.27
% 5.90/2.38 Reduction : 0.19
% 5.90/2.38 Demodulation : 0.13
% 5.90/2.38 BG Simplification : 0.04
% 5.90/2.38 Subsumption : 0.15
% 5.90/2.38 Abstraction : 0.03
% 5.90/2.38 MUC search : 0.00
% 5.90/2.38 Cooper : 0.00
% 5.90/2.38 Total : 1.32
% 5.90/2.38 Index Insertion : 0.00
% 5.90/2.38 Index Deletion : 0.00
% 5.90/2.38 Index Matching : 0.00
% 5.90/2.38 BG Taut test : 0.00
%------------------------------------------------------------------------------