TSTP Solution File: NUM537+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM537+2 : 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/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 : n010.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 10:52:01 EDT 2023
% Result : Theorem 6.72s 2.61s
% Output : CNFRefutation 7.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 25
% Syntax : Number of formulae : 81 ( 34 unt; 19 typ; 2 def)
% Number of atoms : 159 ( 20 equ)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 165 ( 68 ~; 60 |; 19 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 14 >; 13 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 36 (; 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > sdtpldt0 > sdtmndt0 > #nlpp > xx > xS > slcrc0 > #skF_6 > #skF_1 > #skF_4 > #skF_7 > #skF_5 > #skF_8 > #skF_3 > #skF_2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(aSet0,type,
aSet0: $i > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff(xS,type,
xS: $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xx,type,
xx: $i ).
tff(aSubsetOf0,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(isCountable0,type,
isCountable0: $i > $o ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(slcrc0,type,
slcrc0: $i ).
tff(isFinite0,type,
isFinite0: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(f_228,negated_conjecture,
~ ( ( ( aSet0(sdtpldt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xS,xx))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xS)
| ( W0 = xx ) ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtpldt0(xS,xx))
& ( W0 != xx ) ) ) )
=> ( ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) )
& ( ( aSet0(sdtpldt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xS,xx))
<=> ( aElement0(W0)
& ( aElementOf0(W0,xS)
| ( W0 = xx ) ) ) ) )
=> ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( aElement0(W0)
& aElementOf0(W0,sdtpldt0(xS,xx))
& ( W0 != xx ) ) ) )
=> ( ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(W0,xS) )
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_166,hypothesis,
( aElement0(xx)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679) ).
tff(f_156,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
tff(f_137,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2] :
( ( W2 = sdtpldt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& ( aElementOf0(W3,W0)
| ( W3 = W1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
tff(f_39,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(f_168,hypothesis,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679_02) ).
tff(c_132,plain,
( aElementOf0('#skF_7',xS)
| ~ aElementOf0('#skF_8',xS) ),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_486,plain,
~ aElementOf0('#skF_8',xS),
inference(splitLeft,[status(thm)],[c_132]) ).
tff(c_96,plain,
aSet0(xS),
inference(cnfTransformation,[status(thm)],[f_166]) ).
tff(c_98,plain,
aElement0(xx),
inference(cnfTransformation,[status(thm)],[f_166]) ).
tff(c_424,plain,
aSet0(sdtpldt0(xS,xx)),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_158,plain,
( aElementOf0('#skF_7',xS)
| aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_534,plain,
aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(splitLeft,[status(thm)],[c_158]) ).
tff(c_627,plain,
! [W3_94,W0_95,W1_96] :
( aElementOf0(W3_94,W0_95)
| ~ aElementOf0(W3_94,sdtmndt0(W0_95,W1_96))
| ~ aElement0(W1_96)
| ~ aSet0(W0_95) ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_630,plain,
( aElementOf0('#skF_8',sdtpldt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[c_534,c_627]) ).
tff(c_637,plain,
aElementOf0('#skF_8',sdtpldt0(xS,xx)),
inference(demodulation,[status(thm),theory(equality)],[c_424,c_98,c_630]) ).
tff(c_784,plain,
! [W3_111,W1_112,W0_113] :
( ( W3_111 = W1_112 )
| aElementOf0(W3_111,W0_113)
| ~ aElementOf0(W3_111,sdtpldt0(W0_113,W1_112))
| ~ aElement0(W1_112)
| ~ aSet0(W0_113) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_795,plain,
( ( xx = '#skF_8' )
| aElementOf0('#skF_8',xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_637,c_784]) ).
tff(c_813,plain,
( ( xx = '#skF_8' )
| aElementOf0('#skF_8',xS) ),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_98,c_795]) ).
tff(c_814,plain,
xx = '#skF_8',
inference(negUnitSimplification,[status(thm)],[c_486,c_813]) ).
tff(c_192,plain,
~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_832,plain,
~ aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,'#skF_8'),'#skF_8')),
inference(demodulation,[status(thm),theory(equality)],[c_814,c_814,c_814,c_192]) ).
tff(c_830,plain,
aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,'#skF_8'),'#skF_8')),
inference(demodulation,[status(thm),theory(equality)],[c_814,c_814,c_534]) ).
tff(c_906,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_832,c_830]) ).
tff(c_908,plain,
~ aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(splitRight,[status(thm)],[c_158]) ).
tff(c_907,plain,
aElementOf0('#skF_7',xS),
inference(splitRight,[status(thm)],[c_158]) ).
tff(c_6,plain,
! [W1_5,W0_3] :
( aElement0(W1_5)
| ~ aElementOf0(W1_5,W0_3)
| ~ aSet0(W0_3) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_911,plain,
( aElement0('#skF_7')
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_907,c_6]) ).
tff(c_914,plain,
aElement0('#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_911]) ).
tff(c_48,plain,
! [W3_43,W0_33,W1_34] :
( ~ aElementOf0(W3_43,W0_33)
| aElementOf0(W3_43,sdtpldt0(W0_33,W1_34))
| ~ aElement0(W3_43)
| ~ aElement0(W1_34)
| ~ aSet0(W0_33) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_1323,plain,
! [W3_160,W0_161,W1_162] :
( aElementOf0(W3_160,sdtmndt0(W0_161,W1_162))
| ( W3_160 = W1_162 )
| ~ aElementOf0(W3_160,W0_161)
| ~ aElement0(W3_160)
| ~ aElement0(W1_162)
| ~ aSet0(W0_161) ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_338,plain,
! [W0_60] :
( ~ aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx))
| aElement0(W0_60)
| ~ aElementOf0(W0_60,sdtpldt0(xS,xx)) ),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_1104,plain,
~ aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(splitLeft,[status(thm)],[c_338]) ).
tff(c_1330,plain,
( ( xx = '#skF_7' )
| ~ aElementOf0('#skF_7',sdtpldt0(xS,xx))
| ~ aElement0('#skF_7')
| ~ aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[c_1323,c_1104]) ).
tff(c_1361,plain,
( ( xx = '#skF_7' )
| ~ aElementOf0('#skF_7',sdtpldt0(xS,xx)) ),
inference(demodulation,[status(thm),theory(equality)],[c_424,c_98,c_914,c_1330]) ).
tff(c_1376,plain,
~ aElementOf0('#skF_7',sdtpldt0(xS,xx)),
inference(splitLeft,[status(thm)],[c_1361]) ).
tff(c_1379,plain,
( ~ aElementOf0('#skF_7',xS)
| ~ aElement0('#skF_7')
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_48,c_1376]) ).
tff(c_1383,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_96,c_98,c_914,c_907,c_1379]) ).
tff(c_1384,plain,
xx = '#skF_7',
inference(splitRight,[status(thm)],[c_1361]) ).
tff(c_100,plain,
~ aElementOf0(xx,xS),
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_1402,plain,
~ aElementOf0('#skF_7',xS),
inference(demodulation,[status(thm),theory(equality)],[c_1384,c_100]) ).
tff(c_1406,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_907,c_1402]) ).
tff(c_1408,plain,
aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(splitRight,[status(thm)],[c_338]) ).
tff(c_156,plain,
( ~ aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_1559,plain,
aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(demodulation,[status(thm),theory(equality)],[c_1408,c_156]) ).
tff(c_1560,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_908,c_1559]) ).
tff(c_1561,plain,
aElementOf0('#skF_7',xS),
inference(splitRight,[status(thm)],[c_132]) ).
tff(c_1570,plain,
! [W1_171,W0_172] :
( aElement0(W1_171)
| ~ aElementOf0(W1_171,W0_172)
| ~ aSet0(W0_172) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_1579,plain,
( aElement0('#skF_7')
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_1561,c_1570]) ).
tff(c_1588,plain,
aElement0('#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_96,c_1579]) ).
tff(c_3075,plain,
! [W3_257,W0_258,W1_259] :
( aElementOf0(W3_257,sdtmndt0(W0_258,W1_259))
| ( W3_257 = W1_259 )
| ~ aElementOf0(W3_257,W0_258)
| ~ aElement0(W3_257)
| ~ aElement0(W1_259)
| ~ aSet0(W0_258) ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_1562,plain,
aElementOf0('#skF_8',xS),
inference(splitRight,[status(thm)],[c_132]) ).
tff(c_130,plain,
( ~ aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElementOf0('#skF_8',xS) ),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_1624,plain,
~ aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(demodulation,[status(thm),theory(equality)],[c_1562,c_130]) ).
tff(c_3098,plain,
( ( xx = '#skF_7' )
| ~ aElementOf0('#skF_7',sdtpldt0(xS,xx))
| ~ aElement0('#skF_7')
| ~ aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[c_3075,c_1624]) ).
tff(c_3121,plain,
( ( xx = '#skF_7' )
| ~ aElementOf0('#skF_7',sdtpldt0(xS,xx)) ),
inference(demodulation,[status(thm),theory(equality)],[c_424,c_98,c_1588,c_3098]) ).
tff(c_3129,plain,
~ aElementOf0('#skF_7',sdtpldt0(xS,xx)),
inference(splitLeft,[status(thm)],[c_3121]) ).
tff(c_3132,plain,
( ~ aElementOf0('#skF_7',xS)
| ~ aElement0('#skF_7')
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_48,c_3129]) ).
tff(c_3139,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_96,c_98,c_1588,c_1561,c_3132]) ).
tff(c_3140,plain,
xx = '#skF_7',
inference(splitRight,[status(thm)],[c_3121]) ).
tff(c_3166,plain,
~ aElementOf0('#skF_7',xS),
inference(demodulation,[status(thm),theory(equality)],[c_3140,c_100]) ).
tff(c_3170,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1561,c_3166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM537+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n010.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 14:31:28 EDT 2023
% 0.13/0.35 % CPUTime :
% 6.72/2.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.72/2.62
% 6.72/2.62 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.05/2.65
% 7.05/2.65 Inference rules
% 7.05/2.65 ----------------------
% 7.05/2.65 #Ref : 0
% 7.05/2.65 #Sup : 441
% 7.05/2.65 #Fact : 0
% 7.05/2.65 #Define : 0
% 7.05/2.65 #Split : 24
% 7.05/2.65 #Chain : 0
% 7.05/2.65 #Close : 0
% 7.05/2.65
% 7.05/2.65 Ordering : KBO
% 7.05/2.65
% 7.05/2.65 Simplification rules
% 7.05/2.65 ----------------------
% 7.05/2.65 #Subsume : 219
% 7.05/2.65 #Demod : 713
% 7.05/2.65 #Tautology : 248
% 7.05/2.65 #SimpNegUnit : 32
% 7.05/2.65 #BackRed : 123
% 7.05/2.65
% 7.05/2.65 #Partial instantiations: 0
% 7.05/2.65 #Strategies tried : 1
% 7.05/2.65
% 7.05/2.65 Timing (in seconds)
% 7.05/2.65 ----------------------
% 7.05/2.65 Preprocessing : 0.69
% 7.05/2.65 Parsing : 0.32
% 7.05/2.65 CNF conversion : 0.06
% 7.05/2.65 Main loop : 0.81
% 7.05/2.65 Inferencing : 0.25
% 7.05/2.65 Reduction : 0.27
% 7.05/2.65 Demodulation : 0.19
% 7.05/2.66 BG Simplification : 0.07
% 7.05/2.66 Subsumption : 0.19
% 7.05/2.66 Abstraction : 0.04
% 7.05/2.66 MUC search : 0.00
% 7.05/2.66 Cooper : 0.00
% 7.05/2.66 Total : 1.55
% 7.05/2.66 Index Insertion : 0.00
% 7.05/2.66 Index Deletion : 0.00
% 7.05/2.66 Index Matching : 0.00
% 7.05/2.66 BG Taut test : 0.00
%------------------------------------------------------------------------------