TSTP Solution File: NUM473+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM473+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 : n024.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 10:51:48 EDT 2023
% Result : Theorem 19.63s 8.28s
% Output : CNFRefutation 19.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 41
% Syntax : Number of formulae : 137 ( 54 unt; 20 typ; 2 def)
% Number of atoms : 310 ( 113 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 321 ( 128 ~; 130 |; 40 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 10 >; 9 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 79 (; 75 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xq > xp > xn > xm > xl > sz10 > sz00 > #skF_5 > #skF_3 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xq,type,
xq: $i ).
tff(xl,type,
xl: $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(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(xp,type,
xp: $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
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(f_367,hypothesis,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).
tff(f_352,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
tff(f_365,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xl,W0) ) )
& doDivides0(xl,xm)
& ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,W0) ) )
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
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_383,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) )
& sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1409) ).
tff(f_377,hypothesis,
( aNaturalNumber0(xq)
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
& ( xq = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
tff(f_41,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
tff(f_323,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
tff(f_372,hypothesis,
( aNaturalNumber0(xp)
& ( xm = sdtasdt0(xl,xp) )
& ( xp = sdtsldt0(xm,xl) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
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_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
tff(f_390,negated_conjecture,
~ ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xp,W0) = xq ) )
| sdtlseqdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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_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_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_212,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
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_201,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
tff(f_258,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
tff(f_189,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
tff(c_135,plain,
xl != sz00,
inference(cnfTransformation,[status(thm)],[f_367]) ).
tff(c_121,plain,
aNaturalNumber0(xl),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_127,plain,
aNaturalNumber0('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_1357,plain,
! [W1_98,W0_99] :
( ( sdtasdt0(W1_98,W0_99) = sdtasdt0(W0_99,W1_98) )
| ~ aNaturalNumber0(W1_98)
| ~ aNaturalNumber0(W0_99) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1660,plain,
! [W0_104] :
( ( sdtasdt0(xl,W0_104) = sdtasdt0(W0_104,xl) )
| ~ aNaturalNumber0(W0_104) ),
inference(resolution,[status(thm)],[c_121,c_1357]) ).
tff(c_1715,plain,
sdtasdt0(xl,'#skF_3') = sdtasdt0('#skF_3',xl),
inference(resolution,[status(thm)],[c_127,c_1660]) ).
tff(c_119,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_153,plain,
aNaturalNumber0('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_125,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,'#skF_3'),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_145,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cnfTransformation,[status(thm)],[f_377]) ).
tff(c_162,plain,
sdtasdt0(xl,xq) = sdtasdt0(xl,'#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_125,c_145]) ).
tff(c_151,plain,
sdtpldt0(xm,xn) = sdtpldt0(xm,'#skF_5'),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_159,plain,
sdtpldt0(xm,'#skF_5') = sdtasdt0(xl,xq),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_151]) ).
tff(c_163,plain,
sdtpldt0(xm,'#skF_5') = sdtasdt0(xl,'#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_162,c_159]) ).
tff(c_10,plain,
! [W0_2,W1_3] :
( aNaturalNumber0(sdtpldt0(W0_2,W1_3))
| ~ aNaturalNumber0(W1_3)
| ~ aNaturalNumber0(W0_2) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_704,plain,
( aNaturalNumber0(sdtasdt0(xl,'#skF_3'))
| ~ aNaturalNumber0('#skF_5')
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_163,c_10]) ).
tff(c_708,plain,
aNaturalNumber0(sdtasdt0(xl,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_153,c_704]) ).
tff(c_1768,plain,
aNaturalNumber0(sdtasdt0('#skF_3',xl)),
inference(demodulation,[status(thm),theory(equality)],[c_1715,c_708]) ).
tff(c_123,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_166,plain,
doDivides0(xl,sdtasdt0(xl,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_125,c_123]) ).
tff(c_1774,plain,
doDivides0(xl,sdtasdt0('#skF_3',xl)),
inference(demodulation,[status(thm),theory(equality)],[c_1715,c_166]) ).
tff(c_143,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) = xq,
inference(cnfTransformation,[status(thm)],[f_377]) ).
tff(c_161,plain,
sdtsldt0(sdtasdt0(xl,xq),xl) = xq,
inference(demodulation,[status(thm),theory(equality)],[c_145,c_143]) ).
tff(c_165,plain,
sdtsldt0(sdtasdt0(xl,'#skF_3'),xl) = xq,
inference(demodulation,[status(thm),theory(equality)],[c_162,c_161]) ).
tff(c_1772,plain,
sdtsldt0(sdtasdt0('#skF_3',xl),xl) = xq,
inference(demodulation,[status(thm),theory(equality)],[c_1715,c_165]) ).
tff(c_25832,plain,
! [W0_427,W2_428] :
( ( sdtsldt0(sdtasdt0(W0_427,W2_428),W0_427) = W2_428 )
| ~ aNaturalNumber0(W2_428)
| ~ doDivides0(W0_427,sdtasdt0(W0_427,W2_428))
| ( sz00 = W0_427 )
| ~ aNaturalNumber0(sdtasdt0(W0_427,W2_428))
| ~ aNaturalNumber0(W0_427) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_25907,plain,
( ( sdtsldt0(sdtasdt0(xl,'#skF_3'),xl) = '#skF_3' )
| ~ aNaturalNumber0('#skF_3')
| ~ doDivides0(xl,sdtasdt0('#skF_3',xl))
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xl,'#skF_3'))
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_1715,c_25832]) ).
tff(c_26027,plain,
( ( xq = '#skF_3' )
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_1768,c_1715,c_1774,c_127,c_1772,c_1715,c_25907]) ).
tff(c_26028,plain,
xq = '#skF_3',
inference(negUnitSimplification,[status(thm)],[c_135,c_26027]) ).
tff(c_131,plain,
sdtasdt0(xl,'#skF_4') = xm,
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_129,plain,
doDivides0(xl,xm),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_133,plain,
aNaturalNumber0('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_137,plain,
sdtsldt0(xm,xl) = xp,
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_25961,plain,
( ( sdtsldt0(sdtasdt0(xl,'#skF_4'),xl) = '#skF_4' )
| ~ aNaturalNumber0('#skF_4')
| ~ doDivides0(xl,xm)
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xl,'#skF_4'))
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_131,c_25832]) ).
tff(c_26081,plain,
( ( xp = '#skF_4' )
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_131,c_129,c_133,c_137,c_131,c_25961]) ).
tff(c_26082,plain,
xp = '#skF_4',
inference(negUnitSimplification,[status(thm)],[c_135,c_26081]) ).
tff(c_141,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_225,plain,
! [W0_83] :
( ( sdtpldt0(W0_83,sz00) = W0_83 )
| ~ aNaturalNumber0(W0_83) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_264,plain,
sdtpldt0(xp,sz00) = xp,
inference(resolution,[status(thm)],[c_141,c_225]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_180,plain,
! [W0_82] :
( ( sdtpldt0(xp,W0_82) != xq )
| ~ aNaturalNumber0(W0_82) ),
inference(cnfTransformation,[status(thm)],[f_390]) ).
tff(c_216,plain,
sdtpldt0(xp,sz00) != xq,
inference(resolution,[status(thm)],[c_4,c_180]) ).
tff(c_747,plain,
xq != xp,
inference(demodulation,[status(thm),theory(equality)],[c_264,c_216]) ).
tff(c_26142,plain,
xq != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_26082,c_747]) ).
tff(c_26185,plain,
'#skF_3' != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_26028,c_26142]) ).
tff(c_139,plain,
sdtasdt0(xl,xp) = xm,
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_13807,plain,
! [W0_304,W2_305,W1_306] :
( ( sdtasdt0(W0_304,W2_305) != sdtasdt0(W0_304,W1_306) )
| ( W2_305 = W1_306 )
| ~ aNaturalNumber0(W2_305)
| ~ aNaturalNumber0(W1_306)
| ( sz00 = W0_304 )
| ~ aNaturalNumber0(W0_304) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_13937,plain,
! [W1_306] :
( ( sdtasdt0(xl,W1_306) != xm )
| ( xp = W1_306 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(W1_306)
| ( xl = sz00 )
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_139,c_13807]) ).
tff(c_14121,plain,
! [W1_306] :
( ( sdtasdt0(xl,W1_306) != xm )
| ( xp = W1_306 )
| ~ aNaturalNumber0(W1_306)
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_141,c_13937]) ).
tff(c_14122,plain,
! [W1_306] :
( ( sdtasdt0(xl,W1_306) != xm )
| ( xp = W1_306 )
| ~ aNaturalNumber0(W1_306) ),
inference(negUnitSimplification,[status(thm)],[c_135,c_14121]) ).
tff(c_27568,plain,
! [W1_445] :
( ( sdtasdt0(xl,W1_445) != xm )
| ( W1_445 = '#skF_4' )
| ~ aNaturalNumber0(W1_445) ),
inference(demodulation,[status(thm),theory(equality)],[c_26082,c_14122]) ).
tff(c_27613,plain,
( ( sdtasdt0(xl,'#skF_3') != xm )
| ( '#skF_3' = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_127,c_27568]) ).
tff(c_27639,plain,
( ( sdtasdt0('#skF_3',xl) != xm )
| ( '#skF_3' = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1715,c_27613]) ).
tff(c_27640,plain,
sdtasdt0('#skF_3',xl) != xm,
inference(negUnitSimplification,[status(thm)],[c_26185,c_27639]) ).
tff(c_149,plain,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_158,plain,
sdtlseqdt0(xm,sdtpldt0(xm,'#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_149]) ).
tff(c_160,plain,
sdtlseqdt0(xm,sdtasdt0(xl,xq)),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_158]) ).
tff(c_164,plain,
sdtlseqdt0(xm,sdtasdt0(xl,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_162,c_160]) ).
tff(c_1773,plain,
sdtlseqdt0(xm,sdtasdt0('#skF_3',xl)),
inference(demodulation,[status(thm),theory(equality)],[c_1715,c_164]) ).
tff(c_147,plain,
aNaturalNumber0(xq),
inference(cnfTransformation,[status(thm)],[f_377]) ).
tff(c_6,plain,
sz10 != sz00,
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_404,plain,
! [W0_86] :
( ( sdtasdt0(W0_86,sz10) = W0_86 )
| ~ aNaturalNumber0(W0_86) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_438,plain,
sdtasdt0(xq,sz10) = xq,
inference(resolution,[status(thm)],[c_147,c_404]) ).
tff(c_2234,plain,
! [W1_113,W0_114] :
( sdtlseqdt0(W1_113,sdtasdt0(W1_113,W0_114))
| ( sz00 = W0_114 )
| ~ aNaturalNumber0(W1_113)
| ~ aNaturalNumber0(W0_114) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_2345,plain,
( sdtlseqdt0(xq,xq)
| ( sz10 = sz00 )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_438,c_2234]) ).
tff(c_2484,plain,
( sdtlseqdt0(xq,xq)
| ( sz10 = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_147,c_2345]) ).
tff(c_2485,plain,
sdtlseqdt0(xq,xq),
inference(negUnitSimplification,[status(thm)],[c_6,c_2484]) ).
tff(c_70,plain,
! [W1_50,W0_49] :
( sdtlseqdt0(W1_50,W0_49)
| sdtlseqdt0(W0_49,W1_50)
| ~ aNaturalNumber0(W1_50)
| ~ aNaturalNumber0(W0_49) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_11433,plain,
! [W0_263,W1_264] :
( ( sdtpldt0(W0_263,sdtmndt0(W1_264,W0_263)) = W1_264 )
| ~ sdtlseqdt0(W0_263,W1_264)
| ~ aNaturalNumber0(W1_264)
| ~ aNaturalNumber0(W0_263) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_2517,plain,
! [W1_117,W0_118] :
( aNaturalNumber0(sdtmndt0(W1_117,W0_118))
| ~ sdtlseqdt0(W0_118,W1_117)
| ~ aNaturalNumber0(W1_117)
| ~ aNaturalNumber0(W0_118) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_157,plain,
! [W0_80] :
( ( sdtpldt0(xp,W0_80) != xq )
| ~ aNaturalNumber0(W0_80) ),
inference(cnfTransformation,[status(thm)],[f_390]) ).
tff(c_2555,plain,
! [W1_117,W0_118] :
( ( sdtpldt0(xp,sdtmndt0(W1_117,W0_118)) != xq )
| ~ sdtlseqdt0(W0_118,W1_117)
| ~ aNaturalNumber0(W1_117)
| ~ aNaturalNumber0(W0_118) ),
inference(resolution,[status(thm)],[c_2517,c_157]) ).
tff(c_11440,plain,
! [W1_264] :
( ( xq != W1_264 )
| ~ sdtlseqdt0(xp,W1_264)
| ~ aNaturalNumber0(W1_264)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,W1_264)
| ~ aNaturalNumber0(W1_264)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_11433,c_2555]) ).
tff(c_11727,plain,
! [W1_267] :
( ( xq != W1_267 )
| ~ sdtlseqdt0(xp,W1_267)
| ~ aNaturalNumber0(W1_267) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_141,c_11440]) ).
tff(c_11745,plain,
! [W1_50] :
( ( xq != W1_50 )
| sdtlseqdt0(W1_50,xp)
| ~ aNaturalNumber0(W1_50)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_70,c_11727]) ).
tff(c_11764,plain,
! [W1_50] :
( ( xq != W1_50 )
| sdtlseqdt0(W1_50,xp)
| ~ aNaturalNumber0(W1_50) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_11745]) ).
tff(c_12713,plain,
! [W0_288,W2_289,W1_290] :
( sdtlseqdt0(W0_288,W2_289)
| ~ sdtlseqdt0(W1_290,W2_289)
| ~ sdtlseqdt0(W0_288,W1_290)
| ~ aNaturalNumber0(W2_289)
| ~ aNaturalNumber0(W1_290)
| ~ aNaturalNumber0(W0_288) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_12735,plain,
! [W0_288,W1_50] :
( sdtlseqdt0(W0_288,xp)
| ~ sdtlseqdt0(W0_288,W1_50)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(W0_288)
| ( xq != W1_50 )
| ~ aNaturalNumber0(W1_50) ),
inference(resolution,[status(thm)],[c_11764,c_12713]) ).
tff(c_12896,plain,
! [W0_291,W1_292] :
( sdtlseqdt0(W0_291,xp)
| ~ sdtlseqdt0(W0_291,W1_292)
| ~ aNaturalNumber0(W0_291)
| ( xq != W1_292 )
| ~ aNaturalNumber0(W1_292) ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_12735]) ).
tff(c_12950,plain,
( sdtlseqdt0(xq,xp)
| ~ aNaturalNumber0(xq) ),
inference(resolution,[status(thm)],[c_2485,c_12896]) ).
tff(c_13051,plain,
sdtlseqdt0(xq,xp),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_12950]) ).
tff(c_26118,plain,
sdtlseqdt0(xq,'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_26082,c_13051]) ).
tff(c_26238,plain,
sdtlseqdt0('#skF_3','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_26028,c_26118]) ).
tff(c_25172,plain,
! [W0_420,W1_421,W2_422] :
( sdtlseqdt0(sdtasdt0(W0_420,W1_421),sdtasdt0(W0_420,W2_422))
| ~ sdtlseqdt0(W1_421,W2_422)
| ( W2_422 = W1_421 )
| ( sz00 = W0_420 )
| ~ aNaturalNumber0(W2_422)
| ~ aNaturalNumber0(W1_421)
| ~ aNaturalNumber0(W0_420) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_25439,plain,
! [W1_421] :
( sdtlseqdt0(sdtasdt0(xl,W1_421),xm)
| ~ sdtlseqdt0(W1_421,xp)
| ( xp = W1_421 )
| ( xl = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(W1_421)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_139,c_25172]) ).
tff(c_25682,plain,
! [W1_421] :
( sdtlseqdt0(sdtasdt0(xl,W1_421),xm)
| ~ sdtlseqdt0(W1_421,xp)
| ( xp = W1_421 )
| ( xl = sz00 )
| ~ aNaturalNumber0(W1_421) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_141,c_25439]) ).
tff(c_25683,plain,
! [W1_421] :
( sdtlseqdt0(sdtasdt0(xl,W1_421),xm)
| ~ sdtlseqdt0(W1_421,xp)
| ( xp = W1_421 )
| ~ aNaturalNumber0(W1_421) ),
inference(negUnitSimplification,[status(thm)],[c_135,c_25682]) ).
tff(c_39210,plain,
! [W1_514] :
( sdtlseqdt0(sdtasdt0(xl,W1_514),xm)
| ~ sdtlseqdt0(W1_514,'#skF_4')
| ( W1_514 = '#skF_4' )
| ~ aNaturalNumber0(W1_514) ),
inference(demodulation,[status(thm),theory(equality)],[c_26082,c_26082,c_25683]) ).
tff(c_39234,plain,
( sdtlseqdt0(sdtasdt0('#skF_3',xl),xm)
| ~ sdtlseqdt0('#skF_3','#skF_4')
| ( '#skF_3' = '#skF_4' )
| ~ aNaturalNumber0('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_1715,c_39210]) ).
tff(c_39259,plain,
( sdtlseqdt0(sdtasdt0('#skF_3',xl),xm)
| ( '#skF_3' = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_127,c_26238,c_39234]) ).
tff(c_39260,plain,
sdtlseqdt0(sdtasdt0('#skF_3',xl),xm),
inference(negUnitSimplification,[status(thm)],[c_26185,c_39259]) ).
tff(c_66,plain,
! [W1_45,W0_44] :
( ( W1_45 = W0_44 )
| ~ sdtlseqdt0(W1_45,W0_44)
| ~ sdtlseqdt0(W0_44,W1_45)
| ~ aNaturalNumber0(W1_45)
| ~ aNaturalNumber0(W0_44) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_39273,plain,
( ( sdtasdt0('#skF_3',xl) = xm )
| ~ sdtlseqdt0(xm,sdtasdt0('#skF_3',xl))
| ~ aNaturalNumber0(sdtasdt0('#skF_3',xl))
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_39260,c_66]) ).
tff(c_39283,plain,
sdtasdt0('#skF_3',xl) = xm,
inference(demodulation,[status(thm),theory(equality)],[c_119,c_1768,c_1773,c_39273]) ).
tff(c_39285,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_27640,c_39283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM473+2 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.15 % 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
% 0.14/0.36 % Computer : n024.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 15:00:30 EDT 2023
% 0.14/0.36 % CPUTime :
% 19.63/8.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.63/8.29
% 19.63/8.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.79/8.33
% 19.79/8.33 Inference rules
% 19.79/8.33 ----------------------
% 19.79/8.33 #Ref : 11
% 19.79/8.33 #Sup : 7937
% 19.79/8.33 #Fact : 2
% 19.79/8.33 #Define : 0
% 19.79/8.33 #Split : 29
% 19.79/8.33 #Chain : 0
% 19.79/8.33 #Close : 0
% 19.79/8.33
% 19.79/8.33 Ordering : KBO
% 19.79/8.33
% 19.79/8.33 Simplification rules
% 19.79/8.33 ----------------------
% 19.79/8.33 #Subsume : 1156
% 19.79/8.33 #Demod : 16587
% 19.79/8.33 #Tautology : 2666
% 19.79/8.33 #SimpNegUnit : 1524
% 19.79/8.33 #BackRed : 1110
% 19.79/8.33
% 19.79/8.33 #Partial instantiations: 0
% 19.79/8.33 #Strategies tried : 1
% 19.79/8.33
% 19.79/8.33 Timing (in seconds)
% 19.79/8.33 ----------------------
% 19.79/8.33 Preprocessing : 0.66
% 19.79/8.33 Parsing : 0.33
% 19.79/8.33 CNF conversion : 0.05
% 19.79/8.33 Main loop : 6.58
% 19.79/8.33 Inferencing : 1.22
% 19.79/8.33 Reduction : 3.57
% 19.79/8.33 Demodulation : 2.98
% 19.79/8.33 BG Simplification : 0.10
% 19.79/8.33 Subsumption : 1.21
% 19.79/8.33 Abstraction : 0.12
% 19.79/8.33 MUC search : 0.00
% 19.79/8.33 Cooper : 0.00
% 19.79/8.33 Total : 7.30
% 19.79/8.33 Index Insertion : 0.00
% 19.79/8.33 Index Deletion : 0.00
% 19.79/8.33 Index Matching : 0.00
% 19.79/8.33 BG Taut test : 0.00
%------------------------------------------------------------------------------