TSTP Solution File: NUM496+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM496+3 : 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 : n007.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 10:51:53 EDT 2023
% Result : Theorem 179.46s 152.81s
% Output : CNFRefutation 179.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 46
% Syntax : Number of formulae : 145 ( 55 unt; 29 typ; 2 def)
% Number of atoms : 281 ( 106 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 286 ( 121 ~; 117 |; 30 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 17 >; 17 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 12 con; 0-3 aty)
% Number of variables : 72 (; 65 !; 7 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_11 > #skF_6 > #skF_10 > #skF_14 > #skF_13 > #skF_5 > #skF_9 > #skF_7 > #skF_3 > #skF_2 > #skF_8 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xr,type,
xr: $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz00,type,
sz00: $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(isPrime0,type,
isPrime0: $i > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(xp,type,
xp: $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff(xm,type,
xm: $i ).
tff(sdtsldt0,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xn,type,
xn: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_522,hypothesis,
( ( xr != xn )
& ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xr,W0) = xn ) )
& sdtlseqdt0(xr,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1894) ).
tff(f_555,negated_conjecture,
~ ( ? [W0] :
( aNaturalNumber0(W0)
& ( xn = sdtasdt0(xp,W0) ) )
| doDivides0(xp,xn)
| ? [W0] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xp,W0) ) )
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_541,hypothesis,
( ( ? [W0] :
( aNaturalNumber0(W0)
& ( xr = sdtasdt0(xp,W0) ) )
& doDivides0(xp,xr) )
| ( ? [W0] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xp,W0) ) )
& doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2027) ).
tff(f_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(f_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(f_508,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xp,W0) = xn ) )
& sdtlseqdt0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
tff(f_513,hypothesis,
( aNaturalNumber0(xr)
& ( sdtpldt0(xp,xr) = xn )
& ( xr = sdtmndt0(xn,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
tff(f_175,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
tff(f_278,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00 )
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
tff(f_67,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
tff(f_93,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
tff(f_87,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
tff(f_131,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1,W2] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
tff(f_53,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
tff(f_307,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
tff(f_347,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W0,W2) )
=> doDivides0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivSum) ).
tff(c_433,plain,
aNaturalNumber0('#skF_11'),
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_461,plain,
~ doDivides0(xp,xm),
inference(cnfTransformation,[status(thm)],[f_555]) ).
tff(c_447,plain,
( aNaturalNumber0('#skF_13')
| doDivides0(xp,xm) ),
inference(cnfTransformation,[status(thm)],[f_541]) ).
tff(c_468,plain,
aNaturalNumber0('#skF_13'),
inference(negUnitSimplification,[status(thm)],[c_461,c_447]) ).
tff(c_3517,plain,
! [W1_145,W0_146] :
( ( sdtasdt0(W1_145,W0_146) = sdtasdt0(W0_146,W1_145) )
| ~ aNaturalNumber0(W1_145)
| ~ aNaturalNumber0(W0_146) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_83849,plain,
! [W0_807] :
( ( sdtasdt0(W0_807,'#skF_13') = sdtasdt0('#skF_13',W0_807) )
| ~ aNaturalNumber0(W0_807) ),
inference(resolution,[status(thm)],[c_468,c_3517]) ).
tff(c_83958,plain,
sdtasdt0('#skF_11','#skF_13') = sdtasdt0('#skF_13','#skF_11'),
inference(resolution,[status(thm)],[c_433,c_83849]) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_419,plain,
sdtpldt0(xp,'#skF_10') = xn,
inference(cnfTransformation,[status(thm)],[f_508]) ).
tff(c_417,plain,
sdtlseqdt0(xp,xn),
inference(cnfTransformation,[status(thm)],[f_508]) ).
tff(c_421,plain,
aNaturalNumber0('#skF_10'),
inference(cnfTransformation,[status(thm)],[f_508]) ).
tff(c_423,plain,
sdtmndt0(xn,xp) = xr,
inference(cnfTransformation,[status(thm)],[f_513]) ).
tff(c_115558,plain,
! [W0_1054,W2_1055] :
( ( sdtmndt0(sdtpldt0(W0_1054,W2_1055),W0_1054) = W2_1055 )
| ~ aNaturalNumber0(W2_1055)
| ~ sdtlseqdt0(W0_1054,sdtpldt0(W0_1054,W2_1055))
| ~ aNaturalNumber0(sdtpldt0(W0_1054,W2_1055))
| ~ aNaturalNumber0(W0_1054) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_115712,plain,
( ( sdtmndt0(sdtpldt0(xp,'#skF_10'),xp) = '#skF_10' )
| ~ aNaturalNumber0('#skF_10')
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(sdtpldt0(xp,'#skF_10'))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_419,c_115558]) ).
tff(c_115801,plain,
xr = '#skF_10',
inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_419,c_417,c_421,c_423,c_419,c_115712]) ).
tff(c_445,plain,
( ( sdtasdt0(xp,'#skF_13') = xr )
| doDivides0(xp,xm) ),
inference(cnfTransformation,[status(thm)],[f_541]) ).
tff(c_471,plain,
sdtasdt0(xp,'#skF_13') = xr,
inference(negUnitSimplification,[status(thm)],[c_461,c_445]) ).
tff(c_3954,plain,
! [W1_153,W0_154] :
( sdtlseqdt0(W1_153,sdtasdt0(W1_153,W0_154))
| ( sz00 = W0_154 )
| ~ aNaturalNumber0(W1_153)
| ~ aNaturalNumber0(W0_154) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_4143,plain,
( sdtlseqdt0(xp,xr)
| ( sz00 = '#skF_13' )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0('#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_471,c_3954]) ).
tff(c_4314,plain,
( sdtlseqdt0(xp,xr)
| ( sz00 = '#skF_13' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_468,c_143,c_4143]) ).
tff(c_4426,plain,
sz00 = '#skF_13',
inference(splitLeft,[status(thm)],[c_4314]) ).
tff(c_909,plain,
! [W0_118] :
( ( sdtpldt0(sz00,W0_118) = W0_118 )
| ~ aNaturalNumber0(W0_118) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_945,plain,
sdtpldt0(sz00,'#skF_11') = '#skF_11',
inference(resolution,[status(thm)],[c_433,c_909]) ).
tff(c_4473,plain,
sdtpldt0('#skF_13','#skF_11') = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_4426,c_945]) ).
tff(c_640,plain,
! [W0_115] :
( ( sdtasdt0(W0_115,sz00) = sz00 )
| ~ aNaturalNumber0(W0_115) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_679,plain,
sdtasdt0(xp,sz00) = sz00,
inference(resolution,[status(thm)],[c_143,c_640]) ).
tff(c_4505,plain,
sdtasdt0(xp,'#skF_13') = '#skF_13',
inference(demodulation,[status(thm),theory(equality)],[c_4426,c_4426,c_679]) ).
tff(c_5173,plain,
xr = '#skF_13',
inference(demodulation,[status(thm),theory(equality)],[c_4505,c_471]) ).
tff(c_431,plain,
sdtpldt0(xr,'#skF_11') = xn,
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_5313,plain,
sdtpldt0('#skF_13','#skF_11') = xn,
inference(demodulation,[status(thm),theory(equality)],[c_5173,c_431]) ).
tff(c_5328,plain,
xn = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_4473,c_5313]) ).
tff(c_990,plain,
! [W0_119] :
( ( sdtasdt0(W0_119,sz10) = W0_119 )
| ~ aNaturalNumber0(W0_119) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_1030,plain,
sdtasdt0(xp,sz10) = xp,
inference(resolution,[status(thm)],[c_143,c_990]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_502,plain,
! [W0_111] :
( ( sdtasdt0(xp,W0_111) != xn )
| ~ aNaturalNumber0(W0_111) ),
inference(cnfTransformation,[status(thm)],[f_555]) ).
tff(c_537,plain,
sdtasdt0(xp,sz10) != xn,
inference(resolution,[status(thm)],[c_8,c_502]) ).
tff(c_1069,plain,
xp != xn,
inference(demodulation,[status(thm),theory(equality)],[c_1030,c_537]) ).
tff(c_5364,plain,
xp != '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_5328,c_1069]) ).
tff(c_5379,plain,
sdtlseqdt0(xp,'#skF_11'),
inference(demodulation,[status(thm),theory(equality)],[c_5328,c_417]) ).
tff(c_765,plain,
! [W0_116] :
( ( sdtpldt0(W0_116,sz00) = W0_116 )
| ~ aNaturalNumber0(W0_116) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_804,plain,
sdtpldt0(xp,sz00) = xp,
inference(resolution,[status(thm)],[c_143,c_765]) ).
tff(c_4476,plain,
sdtpldt0(xp,'#skF_13') = xp,
inference(demodulation,[status(thm),theory(equality)],[c_4426,c_804]) ).
tff(c_5314,plain,
sdtmndt0(xn,xp) = '#skF_13',
inference(demodulation,[status(thm),theory(equality)],[c_5173,c_423]) ).
tff(c_6933,plain,
sdtmndt0('#skF_11',xp) = '#skF_13',
inference(demodulation,[status(thm),theory(equality)],[c_5328,c_5314]) ).
tff(c_60,plain,
! [W0_39,W1_40] :
( ( sdtpldt0(W0_39,sdtmndt0(W1_40,W0_39)) = W1_40 )
| ~ sdtlseqdt0(W0_39,W1_40)
| ~ aNaturalNumber0(W1_40)
| ~ aNaturalNumber0(W0_39) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_6940,plain,
( ( sdtpldt0(xp,'#skF_13') = '#skF_11' )
| ~ sdtlseqdt0(xp,'#skF_11')
| ~ aNaturalNumber0('#skF_11')
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_6933,c_60]) ).
tff(c_6949,plain,
xp = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_143,c_433,c_5379,c_4476,c_6940]) ).
tff(c_6951,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5364,c_6949]) ).
tff(c_6953,plain,
sz00 != '#skF_13',
inference(splitRight,[status(thm)],[c_4314]) ).
tff(c_110952,plain,
! [W2_1033,W0_1034,W1_1035] :
( ( sdtasdt0(W2_1033,W0_1034) != sdtasdt0(W1_1035,W0_1034) )
| ( W2_1033 = W1_1035 )
| ~ aNaturalNumber0(W2_1033)
| ~ aNaturalNumber0(W1_1035)
| ( sz00 = W0_1034 )
| ~ aNaturalNumber0(W0_1034) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_111218,plain,
! [W1_1035] :
( ( sdtasdt0(W1_1035,'#skF_13') != xr )
| ( xp = W1_1035 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(W1_1035)
| ( sz00 = '#skF_13' )
| ~ aNaturalNumber0('#skF_13') ),
inference(superposition,[status(thm),theory(equality)],[c_471,c_110952]) ).
tff(c_111600,plain,
! [W1_1035] :
( ( sdtasdt0(W1_1035,'#skF_13') != xr )
| ( xp = W1_1035 )
| ~ aNaturalNumber0(W1_1035)
| ( sz00 = '#skF_13' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_468,c_143,c_111218]) ).
tff(c_111601,plain,
! [W1_1035] :
( ( sdtasdt0(W1_1035,'#skF_13') != xr )
| ( xp = W1_1035 )
| ~ aNaturalNumber0(W1_1035) ),
inference(negUnitSimplification,[status(thm)],[c_6953,c_111600]) ).
tff(c_167623,plain,
! [W1_1341] :
( ( sdtasdt0(W1_1341,'#skF_13') != '#skF_10' )
| ( xp = W1_1341 )
| ~ aNaturalNumber0(W1_1341) ),
inference(demodulation,[status(thm),theory(equality)],[c_115801,c_111601]) ).
tff(c_167743,plain,
( ( sdtasdt0('#skF_11','#skF_13') != '#skF_10' )
| ( xp = '#skF_11' ) ),
inference(resolution,[status(thm)],[c_433,c_167623]) ).
tff(c_167822,plain,
( ( sdtasdt0('#skF_13','#skF_11') != '#skF_10' )
| ( xp = '#skF_11' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_83958,c_167743]) ).
tff(c_168870,plain,
sdtasdt0('#skF_13','#skF_11') != '#skF_10',
inference(splitLeft,[status(thm)],[c_167822]) ).
tff(c_427,plain,
aNaturalNumber0(xr),
inference(cnfTransformation,[status(thm)],[f_513]) ).
tff(c_2531,plain,
! [W1_136,W0_137] :
( ( sdtpldt0(W1_136,W0_137) = sdtpldt0(W0_137,W1_136) )
| ~ aNaturalNumber0(W1_136)
| ~ aNaturalNumber0(W0_137) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_2573,plain,
! [W0_137] :
( ( sdtpldt0(xr,W0_137) = sdtpldt0(W0_137,xr) )
| ~ aNaturalNumber0(W0_137) ),
inference(resolution,[status(thm)],[c_427,c_2531]) ).
tff(c_221044,plain,
! [W0_1497] :
( ( sdtpldt0(W0_1497,'#skF_10') = sdtpldt0('#skF_10',W0_1497) )
| ~ aNaturalNumber0(W0_1497) ),
inference(demodulation,[status(thm),theory(equality)],[c_115801,c_115801,c_2573]) ).
tff(c_221206,plain,
sdtpldt0(xp,'#skF_10') = sdtpldt0('#skF_10',xp),
inference(resolution,[status(thm)],[c_143,c_221044]) ).
tff(c_221279,plain,
sdtpldt0('#skF_10',xp) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_419,c_221206]) ).
tff(c_429,plain,
sdtlseqdt0(xr,xn),
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_115868,plain,
sdtlseqdt0('#skF_10',xn),
inference(demodulation,[status(thm),theory(equality)],[c_115801,c_429]) ).
tff(c_115709,plain,
( ( sdtmndt0(sdtpldt0(xr,'#skF_11'),xr) = '#skF_11' )
| ~ aNaturalNumber0('#skF_11')
| ~ sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(sdtpldt0(xr,'#skF_11'))
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_431,c_115558]) ).
tff(c_115799,plain,
sdtmndt0(xn,xr) = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_427,c_147,c_431,c_429,c_433,c_431,c_115709]) ).
tff(c_118451,plain,
sdtmndt0(xn,'#skF_10') = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_115801,c_115799]) ).
tff(c_58,plain,
! [W0_39,W2_42] :
( ( sdtmndt0(sdtpldt0(W0_39,W2_42),W0_39) = W2_42 )
| ~ aNaturalNumber0(W2_42)
| ~ sdtlseqdt0(W0_39,sdtpldt0(W0_39,W2_42))
| ~ aNaturalNumber0(sdtpldt0(W0_39,W2_42))
| ~ aNaturalNumber0(W0_39) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_221444,plain,
( ( sdtmndt0(sdtpldt0('#skF_10',xp),'#skF_10') = xp )
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0('#skF_10',xn)
| ~ aNaturalNumber0(sdtpldt0('#skF_10',xp))
| ~ aNaturalNumber0('#skF_10') ),
inference(superposition,[status(thm),theory(equality)],[c_221279,c_58]) ).
tff(c_221621,plain,
xp = '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_421,c_147,c_221279,c_115868,c_143,c_118451,c_221279,c_221444]) ).
tff(c_83921,plain,
sdtasdt0(xp,'#skF_13') = sdtasdt0('#skF_13',xp),
inference(resolution,[status(thm)],[c_143,c_83849]) ).
tff(c_83963,plain,
sdtasdt0('#skF_13',xp) = xr,
inference(demodulation,[status(thm),theory(equality)],[c_471,c_83921]) ).
tff(c_115821,plain,
sdtasdt0('#skF_13',xp) = '#skF_10',
inference(demodulation,[status(thm),theory(equality)],[c_115801,c_83963]) ).
tff(c_222008,plain,
sdtasdt0('#skF_13','#skF_11') = '#skF_10',
inference(demodulation,[status(thm),theory(equality)],[c_221621,c_115821]) ).
tff(c_222141,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_168870,c_222008]) ).
tff(c_222142,plain,
xp = '#skF_11',
inference(splitRight,[status(thm)],[c_167822]) ).
tff(c_443,plain,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
inference(cnfTransformation,[status(thm)],[f_541]) ).
tff(c_474,plain,
doDivides0(xp,xr),
inference(negUnitSimplification,[status(thm)],[c_461,c_443]) ).
tff(c_115869,plain,
doDivides0(xp,'#skF_10'),
inference(demodulation,[status(thm),theory(equality)],[c_115801,c_474]) ).
tff(c_222380,plain,
doDivides0('#skF_11','#skF_10'),
inference(demodulation,[status(thm),theory(equality)],[c_222142,c_115869]) ).
tff(c_1026,plain,
sdtasdt0('#skF_11',sz10) = '#skF_11',
inference(resolution,[status(thm)],[c_433,c_990]) ).
tff(c_83533,plain,
! [W0_805,W2_806] :
( doDivides0(W0_805,sdtasdt0(W0_805,W2_806))
| ~ aNaturalNumber0(W2_806)
| ~ aNaturalNumber0(sdtasdt0(W0_805,W2_806))
| ~ aNaturalNumber0(W0_805) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_83611,plain,
( doDivides0('#skF_11','#skF_11')
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0('#skF_11',sz10))
| ~ aNaturalNumber0('#skF_11') ),
inference(superposition,[status(thm),theory(equality)],[c_1026,c_83533]) ).
tff(c_83774,plain,
doDivides0('#skF_11','#skF_11'),
inference(demodulation,[status(thm),theory(equality)],[c_433,c_433,c_1026,c_8,c_83611]) ).
tff(c_111671,plain,
! [W0_1036,W1_1037,W2_1038] :
( doDivides0(W0_1036,sdtpldt0(W1_1037,W2_1038))
| ~ doDivides0(W0_1036,W2_1038)
| ~ doDivides0(W0_1036,W1_1037)
| ~ aNaturalNumber0(W2_1038)
| ~ aNaturalNumber0(W1_1037)
| ~ aNaturalNumber0(W0_1036) ),
inference(cnfTransformation,[status(thm)],[f_347]) ).
tff(c_111799,plain,
! [W0_1036] :
( doDivides0(W0_1036,xn)
| ~ doDivides0(W0_1036,'#skF_11')
| ~ doDivides0(W0_1036,xr)
| ~ aNaturalNumber0('#skF_11')
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(W0_1036) ),
inference(superposition,[status(thm),theory(equality)],[c_431,c_111671]) ).
tff(c_111883,plain,
! [W0_1036] :
( doDivides0(W0_1036,xn)
| ~ doDivides0(W0_1036,'#skF_11')
| ~ doDivides0(W0_1036,xr)
| ~ aNaturalNumber0(W0_1036) ),
inference(demodulation,[status(thm),theory(equality)],[c_427,c_433,c_111799]) ).
tff(c_300383,plain,
! [W0_1762] :
( doDivides0(W0_1762,xn)
| ~ doDivides0(W0_1762,'#skF_11')
| ~ doDivides0(W0_1762,'#skF_10')
| ~ aNaturalNumber0(W0_1762) ),
inference(demodulation,[status(thm),theory(equality)],[c_115801,c_111883]) ).
tff(c_84823,plain,
! [W0_823,W1_824] :
( ( sdtasdt0(W0_823,'#skF_2'(W0_823,W1_824)) = W1_824 )
| ~ doDivides0(W0_823,W1_824)
| ~ aNaturalNumber0(W1_824)
| ~ aNaturalNumber0(W0_823) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_3648,plain,
! [W0_149,W1_150] :
( aNaturalNumber0('#skF_2'(W0_149,W1_150))
| ~ doDivides0(W0_149,W1_150)
| ~ aNaturalNumber0(W1_150)
| ~ aNaturalNumber0(W0_149) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_467,plain,
! [W0_109] :
( ( sdtasdt0(xp,W0_109) != xn )
| ~ aNaturalNumber0(W0_109) ),
inference(cnfTransformation,[status(thm)],[f_555]) ).
tff(c_3690,plain,
! [W0_149,W1_150] :
( ( sdtasdt0(xp,'#skF_2'(W0_149,W1_150)) != xn )
| ~ doDivides0(W0_149,W1_150)
| ~ aNaturalNumber0(W1_150)
| ~ aNaturalNumber0(W0_149) ),
inference(resolution,[status(thm)],[c_3648,c_467]) ).
tff(c_84833,plain,
! [W1_824] :
( ( xn != W1_824 )
| ~ doDivides0(xp,W1_824)
| ~ aNaturalNumber0(W1_824)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,W1_824)
| ~ aNaturalNumber0(W1_824)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_84823,c_3690]) ).
tff(c_84859,plain,
! [W1_824] :
( ( xn != W1_824 )
| ~ doDivides0(xp,W1_824)
| ~ aNaturalNumber0(W1_824) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_143,c_84833]) ).
tff(c_222287,plain,
! [W1_824] :
( ( xn != W1_824 )
| ~ doDivides0('#skF_11',W1_824)
| ~ aNaturalNumber0(W1_824) ),
inference(demodulation,[status(thm),theory(equality)],[c_222142,c_84859]) ).
tff(c_300406,plain,
( ~ aNaturalNumber0(xn)
| ~ doDivides0('#skF_11','#skF_11')
| ~ doDivides0('#skF_11','#skF_10')
| ~ aNaturalNumber0('#skF_11') ),
inference(resolution,[status(thm)],[c_300383,c_222287]) ).
tff(c_300436,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_433,c_222380,c_83774,c_147,c_300406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM496+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % 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
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 14:16:53 EDT 2023
% 0.14/0.36 % CPUTime :
% 179.46/152.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 179.46/152.83
% 179.46/152.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 179.69/152.87
% 179.69/152.87 Inference rules
% 179.69/152.87 ----------------------
% 179.69/152.87 #Ref : 130
% 179.69/152.87 #Sup : 63835
% 179.69/152.87 #Fact : 2
% 179.69/152.87 #Define : 0
% 179.69/152.87 #Split : 71
% 179.69/152.87 #Chain : 0
% 179.69/152.87 #Close : 0
% 179.69/152.87
% 179.69/152.87 Ordering : KBO
% 179.69/152.87
% 179.69/152.87 Simplification rules
% 179.69/152.87 ----------------------
% 179.69/152.87 #Subsume : 5990
% 179.69/152.87 #Demod : 132556
% 179.69/152.87 #Tautology : 13966
% 179.69/152.87 #SimpNegUnit : 16999
% 179.69/152.87 #BackRed : 3917
% 179.69/152.87
% 179.69/152.87 #Partial instantiations: 0
% 179.69/152.87 #Strategies tried : 1
% 179.69/152.87
% 179.69/152.87 Timing (in seconds)
% 179.69/152.87 ----------------------
% 179.69/152.87 Preprocessing : 0.80
% 179.69/152.87 Parsing : 0.36
% 179.69/152.87 CNF conversion : 0.07
% 179.69/152.87 Main loop : 150.98
% 179.69/152.87 Inferencing : 7.37
% 179.69/152.87 Reduction : 104.88
% 179.69/152.88 Demodulation : 90.82
% 179.69/152.88 BG Simplification : 0.73
% 179.69/152.88 Subsumption : 32.36
% 179.69/152.88 Abstraction : 1.27
% 179.69/152.88 MUC search : 0.00
% 179.69/152.88 Cooper : 0.00
% 179.69/152.88 Total : 151.85
% 179.69/152.88 Index Insertion : 0.00
% 179.69/152.88 Index Deletion : 0.00
% 179.69/152.88 Index Matching : 0.00
% 179.69/152.88 BG Taut test : 0.00
%------------------------------------------------------------------------------