TSTP Solution File: NUM481+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM481+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 : n014.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 10:51:50 EDT 2023
% Result : Theorem 24.09s 13.06s
% Output : CNFRefutation 24.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 28
% Syntax : Number of formulae : 127 ( 36 unt; 19 typ; 2 def)
% Number of atoms : 346 ( 152 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 376 ( 138 ~; 184 |; 35 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 16 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 56 (; 49 !; 7 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > sz10 > sz00 > #skF_7 > #skF_5 > #skF_8 > #skF_4 > #skF_3 > #skF_2 > #skF_1 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $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_8',type,
'#skF_8': $i > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(isPrime0,type,
isPrime0: $i > $o ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff(sdtsldt0,type,
sdtsldt0: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_487,negated_conjecture,
~ ! [W0] :
( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ( ! [W1] :
( ( aNaturalNumber0(W1)
& ( W1 != sz00 )
& ( W1 != sz10 ) )
=> ( iLess0(W1,W0)
=> ? [W2] :
( aNaturalNumber0(W2)
& ? [W3] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1)
& ( W2 != sz00 )
& ( W2 != sz10 )
& ! [W3] :
( ( aNaturalNumber0(W3)
& ( ? [W4] :
( aNaturalNumber0(W4)
& ( W2 = sdtasdt0(W3,W4) ) )
| doDivides0(W3,W2) ) )
=> ( ( W3 = sz10 )
| ( W3 = W2 ) ) )
& isPrime0(W2) ) ) )
=> ? [W1] :
( aNaturalNumber0(W1)
& ( ? [W2] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
| doDivides0(W1,W0) )
& ( ( ( W1 != sz00 )
& ( W1 != sz10 )
& ! [W2] :
( ( aNaturalNumber0(W2)
& ? [W3] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
& doDivides0(W2,W1) )
=> ( ( W2 = sz10 )
| ( W2 = W1 ) ) ) )
| isPrime0(W1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
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_93,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
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_403,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
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_296,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
tff(f_335,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W1,W2) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
tff(c_139,plain,
sz00 != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_137,plain,
sz10 != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_141,plain,
aNaturalNumber0('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_340,plain,
! [W0_154] :
( ( sdtasdt0(W0_154,sz10) = W0_154 )
| ~ aNaturalNumber0(W0_154) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_354,plain,
sdtasdt0('#skF_4',sz10) = '#skF_4',
inference(resolution,[status(thm)],[c_141,c_340]) ).
tff(c_4336,plain,
! [W1_228,W2_229] :
( ( sdtasdt0(W1_228,W2_229) != '#skF_4' )
| ~ aNaturalNumber0(W2_229)
| aNaturalNumber0('#skF_8'(W1_228))
| ( sz10 = W1_228 )
| ( sz00 = W1_228 )
| ~ aNaturalNumber0(W1_228) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_4376,plain,
( ~ aNaturalNumber0(sz10)
| aNaturalNumber0('#skF_8'('#skF_4'))
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_354,c_4336]) ).
tff(c_4448,plain,
( aNaturalNumber0('#skF_8'('#skF_4'))
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_8,c_4376]) ).
tff(c_4449,plain,
aNaturalNumber0('#skF_8'('#skF_4')),
inference(negUnitSimplification,[status(thm)],[c_139,c_137,c_4448]) ).
tff(c_30,plain,
! [W0_18] :
( ( sdtasdt0(sz00,W0_18) = sz00 )
| ~ aNaturalNumber0(W0_18) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_4525,plain,
sdtasdt0(sz00,'#skF_8'('#skF_4')) = sz00,
inference(resolution,[status(thm)],[c_4449,c_30]) ).
tff(c_2340,plain,
! [W1_204] :
( ~ doDivides0(W1_204,'#skF_4')
| doDivides0('#skF_7'(W1_204),W1_204)
| ( sz10 = W1_204 )
| ( sz00 = W1_204 )
| ~ aNaturalNumber0(W1_204) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_143,plain,
! [W1_138] :
( ~ doDivides0(W1_138,'#skF_4')
| ~ isPrime0(W1_138)
| ~ aNaturalNumber0(W1_138) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_2352,plain,
( ~ isPrime0('#skF_7'('#skF_4'))
| ~ aNaturalNumber0('#skF_7'('#skF_4'))
| ~ doDivides0('#skF_4','#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_2340,c_143]) ).
tff(c_2363,plain,
( ~ isPrime0('#skF_7'('#skF_4'))
| ~ aNaturalNumber0('#skF_7'('#skF_4'))
| ~ doDivides0('#skF_4','#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_2352]) ).
tff(c_2364,plain,
( ~ isPrime0('#skF_7'('#skF_4'))
| ~ aNaturalNumber0('#skF_7'('#skF_4'))
| ~ doDivides0('#skF_4','#skF_4') ),
inference(negUnitSimplification,[status(thm)],[c_139,c_137,c_2363]) ).
tff(c_2365,plain,
~ doDivides0('#skF_4','#skF_4'),
inference(splitLeft,[status(thm)],[c_2364]) ).
tff(c_3703,plain,
! [W0_220,W2_221] :
( doDivides0(W0_220,sdtasdt0(W0_220,W2_221))
| ~ aNaturalNumber0(W2_221)
| ~ aNaturalNumber0(sdtasdt0(W0_220,W2_221))
| ~ aNaturalNumber0(W0_220) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_3754,plain,
( doDivides0('#skF_4','#skF_4')
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0('#skF_4',sz10))
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_354,c_3703]) ).
tff(c_3807,plain,
doDivides0('#skF_4','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_141,c_354,c_8,c_3754]) ).
tff(c_3809,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2365,c_3807]) ).
tff(c_3811,plain,
doDivides0('#skF_4','#skF_4'),
inference(splitRight,[status(thm)],[c_2364]) ).
tff(c_167,plain,
! [W1_138] :
( ~ doDivides0(W1_138,'#skF_4')
| aNaturalNumber0('#skF_7'(W1_138))
| ( sz10 = W1_138 )
| ( sz00 = W1_138 )
| ~ aNaturalNumber0(W1_138) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_151,plain,
! [W1_138] :
( ~ doDivides0(W1_138,'#skF_4')
| ( '#skF_7'(W1_138) != sz10 )
| ( sz10 = W1_138 )
| ( sz00 = W1_138 )
| ~ aNaturalNumber0(W1_138) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_3814,plain,
( ( '#skF_7'('#skF_4') != sz10 )
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_3811,c_151]) ).
tff(c_3823,plain,
( ( '#skF_7'('#skF_4') != sz10 )
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_3814]) ).
tff(c_3824,plain,
'#skF_7'('#skF_4') != sz10,
inference(negUnitSimplification,[status(thm)],[c_139,c_137,c_3823]) ).
tff(c_125,plain,
! [W0_89] :
( ( '#skF_3'(W0_89) != sz10 )
| isPrime0(W0_89)
| ( sz10 = W0_89 )
| ( sz00 = W0_89 )
| ~ aNaturalNumber0(W0_89) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_3810,plain,
( ~ aNaturalNumber0('#skF_7'('#skF_4'))
| ~ isPrime0('#skF_7'('#skF_4')) ),
inference(splitRight,[status(thm)],[c_2364]) ).
tff(c_3857,plain,
~ isPrime0('#skF_7'('#skF_4')),
inference(splitLeft,[status(thm)],[c_3810]) ).
tff(c_3860,plain,
( ( '#skF_3'('#skF_7'('#skF_4')) != sz10 )
| ( '#skF_7'('#skF_4') = sz10 )
| ( '#skF_7'('#skF_4') = sz00 )
| ~ aNaturalNumber0('#skF_7'('#skF_4')) ),
inference(resolution,[status(thm)],[c_125,c_3857]) ).
tff(c_3866,plain,
( ( '#skF_3'('#skF_7'('#skF_4')) != sz10 )
| ( '#skF_7'('#skF_4') = sz00 )
| ~ aNaturalNumber0('#skF_7'('#skF_4')) ),
inference(negUnitSimplification,[status(thm)],[c_3824,c_3860]) ).
tff(c_3871,plain,
~ aNaturalNumber0('#skF_7'('#skF_4')),
inference(splitLeft,[status(thm)],[c_3866]) ).
tff(c_3899,plain,
( ~ doDivides0('#skF_4','#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_167,c_3871]) ).
tff(c_3902,plain,
( ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_3811,c_3899]) ).
tff(c_3904,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_139,c_137,c_3902]) ).
tff(c_3906,plain,
aNaturalNumber0('#skF_7'('#skF_4')),
inference(splitRight,[status(thm)],[c_3866]) ).
tff(c_26,plain,
! [W0_17] :
( ( sdtasdt0(sz10,W0_17) = W0_17 )
| ~ aNaturalNumber0(W0_17) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_3957,plain,
sdtasdt0(sz10,'#skF_7'('#skF_4')) = '#skF_7'('#skF_4'),
inference(resolution,[status(thm)],[c_3906,c_26]) ).
tff(c_95,plain,
! [W1_60,W0_59] :
( sdtlseqdt0(W1_60,sdtasdt0(W1_60,W0_59))
| ( sz00 = W0_59 )
| ~ aNaturalNumber0(W1_60)
| ~ aNaturalNumber0(W0_59) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_4178,plain,
( sdtlseqdt0(sz10,'#skF_7'('#skF_4'))
| ( '#skF_7'('#skF_4') = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0('#skF_7'('#skF_4')) ),
inference(superposition,[status(thm),theory(equality)],[c_3957,c_95]) ).
tff(c_4196,plain,
( sdtlseqdt0(sz10,'#skF_7'('#skF_4'))
| ( '#skF_7'('#skF_4') = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3906,c_8,c_4178]) ).
tff(c_4921,plain,
'#skF_7'('#skF_4') = sz00,
inference(splitLeft,[status(thm)],[c_4196]) ).
tff(c_5887,plain,
! [W1_248] :
( ~ doDivides0(W1_248,'#skF_4')
| ( sdtasdt0('#skF_7'(W1_248),'#skF_8'(W1_248)) = W1_248 )
| ( sz10 = W1_248 )
| ( sz00 = W1_248 )
| ~ aNaturalNumber0(W1_248) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_5920,plain,
( ~ doDivides0('#skF_4','#skF_4')
| ( sdtasdt0(sz00,'#skF_8'('#skF_4')) = '#skF_4' )
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_4921,c_5887]) ).
tff(c_5924,plain,
( ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_4525,c_3811,c_5920]) ).
tff(c_5926,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_139,c_137,c_5924]) ).
tff(c_5928,plain,
'#skF_7'('#skF_4') != sz00,
inference(splitRight,[status(thm)],[c_4196]) ).
tff(c_147,plain,
! [W1_138] :
( ~ doDivides0(W1_138,'#skF_4')
| ( '#skF_7'(W1_138) != W1_138 )
| ( sz10 = W1_138 )
| ( sz00 = W1_138 )
| ~ aNaturalNumber0(W1_138) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_3817,plain,
( ( '#skF_7'('#skF_4') != '#skF_4' )
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_3811,c_147]) ).
tff(c_3827,plain,
( ( '#skF_7'('#skF_4') != '#skF_4' )
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_3817]) ).
tff(c_3828,plain,
'#skF_7'('#skF_4') != '#skF_4',
inference(negUnitSimplification,[status(thm)],[c_139,c_137,c_3827]) ).
tff(c_32,plain,
! [W0_18] :
( ( sdtasdt0(W0_18,sz00) = sz00 )
| ~ aNaturalNumber0(W0_18) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_3960,plain,
sdtasdt0('#skF_7'('#skF_4'),sz00) = sz00,
inference(resolution,[status(thm)],[c_3906,c_32]) ).
tff(c_4523,plain,
sdtasdt0(sz10,'#skF_8'('#skF_4')) = '#skF_8'('#skF_4'),
inference(resolution,[status(thm)],[c_4449,c_26]) ).
tff(c_4843,plain,
( sdtlseqdt0(sz10,'#skF_8'('#skF_4'))
| ( '#skF_8'('#skF_4') = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0('#skF_8'('#skF_4')) ),
inference(superposition,[status(thm),theory(equality)],[c_4523,c_95]) ).
tff(c_4870,plain,
( sdtlseqdt0(sz10,'#skF_8'('#skF_4'))
| ( '#skF_8'('#skF_4') = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4449,c_8,c_4843]) ).
tff(c_5954,plain,
'#skF_8'('#skF_4') = sz00,
inference(splitLeft,[status(thm)],[c_4870]) ).
tff(c_6522,plain,
! [W1_254] :
( ~ doDivides0(W1_254,'#skF_4')
| ( sdtasdt0('#skF_7'(W1_254),'#skF_8'(W1_254)) = W1_254 )
| ( sz10 = W1_254 )
| ( sz00 = W1_254 )
| ~ aNaturalNumber0(W1_254) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_6553,plain,
( ~ doDivides0('#skF_4','#skF_4')
| ( sdtasdt0('#skF_7'('#skF_4'),sz00) = '#skF_4' )
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_5954,c_6522]) ).
tff(c_6557,plain,
( ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_3960,c_3811,c_6553]) ).
tff(c_6559,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_139,c_137,c_6557]) ).
tff(c_6561,plain,
'#skF_8'('#skF_4') != sz00,
inference(splitRight,[status(thm)],[c_4870]) ).
tff(c_28845,plain,
! [W1_431,W2_432] :
( ( sdtasdt0(W1_431,W2_432) != '#skF_4' )
| ~ aNaturalNumber0(W2_432)
| ( sdtasdt0('#skF_7'(W1_431),'#skF_8'(W1_431)) = W1_431 )
| ( sz10 = W1_431 )
| ( sz00 = W1_431 )
| ~ aNaturalNumber0(W1_431) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_28913,plain,
( ~ aNaturalNumber0(sz10)
| ( sdtasdt0('#skF_7'('#skF_4'),'#skF_8'('#skF_4')) = '#skF_4' )
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_354,c_28845]) ).
tff(c_29020,plain,
( ( sdtasdt0('#skF_7'('#skF_4'),'#skF_8'('#skF_4')) = '#skF_4' )
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_8,c_28913]) ).
tff(c_29021,plain,
sdtasdt0('#skF_7'('#skF_4'),'#skF_8'('#skF_4')) = '#skF_4',
inference(negUnitSimplification,[status(thm)],[c_139,c_137,c_29020]) ).
tff(c_29731,plain,
( sdtlseqdt0('#skF_7'('#skF_4'),'#skF_4')
| ( '#skF_8'('#skF_4') = sz00 )
| ~ aNaturalNumber0('#skF_7'('#skF_4'))
| ~ aNaturalNumber0('#skF_8'('#skF_4')) ),
inference(superposition,[status(thm),theory(equality)],[c_29021,c_95]) ).
tff(c_29785,plain,
( sdtlseqdt0('#skF_7'('#skF_4'),'#skF_4')
| ( '#skF_8'('#skF_4') = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4449,c_3906,c_29731]) ).
tff(c_29786,plain,
sdtlseqdt0('#skF_7'('#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_6561,c_29785]) ).
tff(c_99,plain,
! [W0_63,W1_64] :
( iLess0(W0_63,W1_64)
| ~ sdtlseqdt0(W0_63,W1_64)
| ( W1_64 = W0_63 )
| ~ aNaturalNumber0(W1_64)
| ~ aNaturalNumber0(W0_63) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_29911,plain,
( iLess0('#skF_7'('#skF_4'),'#skF_4')
| ( '#skF_7'('#skF_4') = '#skF_4' )
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0('#skF_7'('#skF_4')) ),
inference(resolution,[status(thm)],[c_29786,c_99]) ).
tff(c_29916,plain,
( iLess0('#skF_7'('#skF_4'),'#skF_4')
| ( '#skF_7'('#skF_4') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3906,c_141,c_29911]) ).
tff(c_29917,plain,
iLess0('#skF_7'('#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_3828,c_29916]) ).
tff(c_171,plain,
! [W1_121] :
( isPrime0('#skF_5'(W1_121))
| ~ iLess0(W1_121,'#skF_4')
| ( sz10 = W1_121 )
| ( sz00 = W1_121 )
| ~ aNaturalNumber0(W1_121) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_183,plain,
! [W1_121] :
( aNaturalNumber0('#skF_5'(W1_121))
| ~ iLess0(W1_121,'#skF_4')
| ( sz10 = W1_121 )
| ( sz00 = W1_121 )
| ~ aNaturalNumber0(W1_121) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_177,plain,
! [W1_121] :
( doDivides0('#skF_5'(W1_121),W1_121)
| ~ iLess0(W1_121,'#skF_4')
| ( sz10 = W1_121 )
| ( sz00 = W1_121 )
| ~ aNaturalNumber0(W1_121) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_28384,plain,
! [W1_427,W2_428] :
( ( sdtasdt0(W1_427,W2_428) != '#skF_4' )
| ~ aNaturalNumber0(W2_428)
| doDivides0('#skF_7'(W1_427),W1_427)
| ( sz10 = W1_427 )
| ( sz00 = W1_427 )
| ~ aNaturalNumber0(W1_427) ),
inference(cnfTransformation,[status(thm)],[f_487]) ).
tff(c_28452,plain,
( ~ aNaturalNumber0(sz10)
| doDivides0('#skF_7'('#skF_4'),'#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_354,c_28384]) ).
tff(c_28559,plain,
( doDivides0('#skF_7'('#skF_4'),'#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_8,c_28452]) ).
tff(c_28560,plain,
doDivides0('#skF_7'('#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_139,c_137,c_28559]) ).
tff(c_31050,plain,
! [W0_457,W2_458,W1_459] :
( doDivides0(W0_457,W2_458)
| ~ doDivides0(W1_459,W2_458)
| ~ doDivides0(W0_457,W1_459)
| ~ aNaturalNumber0(W2_458)
| ~ aNaturalNumber0(W1_459)
| ~ aNaturalNumber0(W0_457) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_31104,plain,
! [W0_457] :
( doDivides0(W0_457,'#skF_4')
| ~ doDivides0(W0_457,'#skF_7'('#skF_4'))
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0('#skF_7'('#skF_4'))
| ~ aNaturalNumber0(W0_457) ),
inference(resolution,[status(thm)],[c_28560,c_31050]) ).
tff(c_59924,plain,
! [W0_644] :
( doDivides0(W0_644,'#skF_4')
| ~ doDivides0(W0_644,'#skF_7'('#skF_4'))
| ~ aNaturalNumber0(W0_644) ),
inference(demodulation,[status(thm),theory(equality)],[c_3906,c_141,c_31104]) ).
tff(c_59941,plain,
( doDivides0('#skF_5'('#skF_7'('#skF_4')),'#skF_4')
| ~ aNaturalNumber0('#skF_5'('#skF_7'('#skF_4')))
| ~ iLess0('#skF_7'('#skF_4'),'#skF_4')
| ( '#skF_7'('#skF_4') = sz10 )
| ( '#skF_7'('#skF_4') = sz00 )
| ~ aNaturalNumber0('#skF_7'('#skF_4')) ),
inference(resolution,[status(thm)],[c_177,c_59924]) ).
tff(c_59961,plain,
( doDivides0('#skF_5'('#skF_7'('#skF_4')),'#skF_4')
| ~ aNaturalNumber0('#skF_5'('#skF_7'('#skF_4')))
| ( '#skF_7'('#skF_4') = sz10 )
| ( '#skF_7'('#skF_4') = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3906,c_29917,c_59941]) ).
tff(c_59962,plain,
( doDivides0('#skF_5'('#skF_7'('#skF_4')),'#skF_4')
| ~ aNaturalNumber0('#skF_5'('#skF_7'('#skF_4'))) ),
inference(negUnitSimplification,[status(thm)],[c_5928,c_3824,c_59961]) ).
tff(c_60644,plain,
~ aNaturalNumber0('#skF_5'('#skF_7'('#skF_4'))),
inference(splitLeft,[status(thm)],[c_59962]) ).
tff(c_60647,plain,
( ~ iLess0('#skF_7'('#skF_4'),'#skF_4')
| ( '#skF_7'('#skF_4') = sz10 )
| ( '#skF_7'('#skF_4') = sz00 )
| ~ aNaturalNumber0('#skF_7'('#skF_4')) ),
inference(resolution,[status(thm)],[c_183,c_60644]) ).
tff(c_60650,plain,
( ( '#skF_7'('#skF_4') = sz10 )
| ( '#skF_7'('#skF_4') = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3906,c_29917,c_60647]) ).
tff(c_60652,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5928,c_3824,c_60650]) ).
tff(c_60654,plain,
aNaturalNumber0('#skF_5'('#skF_7'('#skF_4'))),
inference(splitRight,[status(thm)],[c_59962]) ).
tff(c_60653,plain,
doDivides0('#skF_5'('#skF_7'('#skF_4')),'#skF_4'),
inference(splitRight,[status(thm)],[c_59962]) ).
tff(c_60843,plain,
( ~ isPrime0('#skF_5'('#skF_7'('#skF_4')))
| ~ aNaturalNumber0('#skF_5'('#skF_7'('#skF_4'))) ),
inference(resolution,[status(thm)],[c_60653,c_143]) ).
tff(c_60869,plain,
~ isPrime0('#skF_5'('#skF_7'('#skF_4'))),
inference(demodulation,[status(thm),theory(equality)],[c_60654,c_60843]) ).
tff(c_60872,plain,
( ~ iLess0('#skF_7'('#skF_4'),'#skF_4')
| ( '#skF_7'('#skF_4') = sz10 )
| ( '#skF_7'('#skF_4') = sz00 )
| ~ aNaturalNumber0('#skF_7'('#skF_4')) ),
inference(resolution,[status(thm)],[c_171,c_60869]) ).
tff(c_60881,plain,
( ( '#skF_7'('#skF_4') = sz10 )
| ( '#skF_7'('#skF_4') = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3906,c_29917,c_60872]) ).
tff(c_60883,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5928,c_3824,c_60881]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM481+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
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 14:20:33 EDT 2023
% 0.13/0.35 % CPUTime :
% 24.09/13.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.09/13.07
% 24.09/13.07 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.18/13.11
% 24.18/13.11 Inference rules
% 24.18/13.11 ----------------------
% 24.18/13.11 #Ref : 8
% 24.18/13.11 #Sup : 12290
% 24.18/13.11 #Fact : 8
% 24.18/13.11 #Define : 0
% 24.18/13.11 #Split : 30
% 24.18/13.11 #Chain : 0
% 24.18/13.11 #Close : 0
% 24.18/13.11
% 24.18/13.11 Ordering : KBO
% 24.18/13.11
% 24.18/13.11 Simplification rules
% 24.18/13.11 ----------------------
% 24.18/13.11 #Subsume : 2163
% 24.18/13.11 #Demod : 19205
% 24.18/13.11 #Tautology : 4026
% 24.18/13.11 #SimpNegUnit : 3053
% 24.18/13.11 #BackRed : 106
% 24.18/13.11
% 24.18/13.11 #Partial instantiations: 0
% 24.18/13.11 #Strategies tried : 1
% 24.18/13.11
% 24.18/13.11 Timing (in seconds)
% 24.18/13.11 ----------------------
% 24.18/13.12 Preprocessing : 0.69
% 24.18/13.12 Parsing : 0.35
% 24.18/13.12 CNF conversion : 0.05
% 24.18/13.12 Main loop : 11.22
% 24.18/13.12 Inferencing : 1.78
% 24.18/13.12 Reduction : 6.22
% 24.18/13.12 Demodulation : 4.92
% 24.18/13.12 BG Simplification : 0.13
% 24.18/13.12 Subsumption : 2.63
% 24.18/13.12 Abstraction : 0.22
% 24.18/13.12 MUC search : 0.00
% 24.18/13.12 Cooper : 0.00
% 24.18/13.12 Total : 11.98
% 24.18/13.12 Index Insertion : 0.00
% 24.18/13.12 Index Deletion : 0.00
% 24.18/13.12 Index Matching : 0.00
% 24.18/13.12 BG Taut test : 0.00
%------------------------------------------------------------------------------