TSTP Solution File: NUM528+3 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM528+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 : n021.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 10:52:00 EDT 2023
% Result : Theorem 58.26s 42.10s
% Output : CNFRefutation 58.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 50
% Syntax : Number of formulae : 251 ( 105 unt; 24 typ; 4 def)
% Number of atoms : 572 ( 251 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 567 ( 222 ~; 262 |; 50 &)
% ( 4 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 15 >; 13 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-3 aty)
% Number of variables : 107 (; 99 !; 8 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xq > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_6 > #skF_7 > #skF_5 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xq,type,
xq: $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $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_7',type,
'#skF_7': $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(isPrime0,type,
isPrime0: $i > $o ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
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_8',type,
'#skF_8': $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(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_446,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
tff(f_504,hypothesis,
( ( xp != sz10 )
& ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& ( xp = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xp) ) )
=> ( ( W0 = sz10 )
| ( W0 = xp ) ) )
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
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_517,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xn,xn) = sdtasdt0(xp,W0) ) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [W0] :
( aNaturalNumber0(W0)
& ( xn = sdtasdt0(xp,W0) ) )
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
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_87,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
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_93,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
tff(f_151,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
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_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_418,axiom,
! [W0] :
( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ? [W1] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
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_486,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
tff(f_522,hypothesis,
( aNaturalNumber0(xq)
& ( xn = sdtasdt0(xp,xq) )
& ( xq = sdtsldt0(xn,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
tff(f_523,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
tff(f_384,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
tff(f_546,negated_conjecture,
~ ( ( xm != xn )
& ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xn ) )
| sdtlseqdt0(xm,xn) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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_536,hypothesis,
( ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xn,W0) = xm ) )
| sdtlseqdt0(xn,xm) )
=> ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(sdtasdt0(xn,xn),W0) = sdtasdt0(xm,xm) ) )
& sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3152) ).
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(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_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_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(c_145,plain,
xp != sz00,
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_175,plain,
xp != sz10,
inference(cnfTransformation,[status(thm)],[f_504]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_133,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_217,plain,
~ isPrime0(sz10),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_133]) ).
tff(c_151,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_191,plain,
aNaturalNumber0('#skF_8'),
inference(cnfTransformation,[status(thm)],[f_517]) ).
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_2466,plain,
! [W0_146] :
( ( sdtasdt0(sz10,W0_146) = W0_146 )
| ~ aNaturalNumber0(W0_146) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_2495,plain,
sdtasdt0(sz10,'#skF_8') = '#skF_8',
inference(resolution,[status(thm)],[c_191,c_2466]) ).
tff(c_3976,plain,
! [W1_166,W0_167] :
( ( sdtasdt0(W1_166,W0_167) = sdtasdt0(W0_167,W1_166) )
| ~ aNaturalNumber0(W1_166)
| ~ aNaturalNumber0(W0_167) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_124193,plain,
! [W0_1064] :
( ( sdtasdt0(W0_1064,'#skF_8') = sdtasdt0('#skF_8',W0_1064) )
| ~ aNaturalNumber0(W0_1064) ),
inference(resolution,[status(thm)],[c_191,c_3976]) ).
tff(c_124334,plain,
sdtasdt0(xp,'#skF_8') = sdtasdt0('#skF_8',xp),
inference(resolution,[status(thm)],[c_151,c_124193]) ).
tff(c_189,plain,
sdtasdt0(xp,'#skF_8') = sdtasdt0(xn,xn),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_124557,plain,
sdtasdt0(xn,xn) = sdtasdt0('#skF_8',xp),
inference(demodulation,[status(thm),theory(equality)],[c_124334,c_189]) ).
tff(c_4702,plain,
! [W1_174,W0_175] :
( sdtlseqdt0(W1_174,sdtasdt0(W1_174,W0_175))
| ( sz00 = W0_175 )
| ~ aNaturalNumber0(W1_174)
| ~ aNaturalNumber0(W0_175) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_4789,plain,
( sdtlseqdt0(sz10,'#skF_8')
| ( sz00 = '#skF_8' )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_2495,c_4702]) ).
tff(c_4944,plain,
( sdtlseqdt0(sz10,'#skF_8')
| ( sz00 = '#skF_8' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_191,c_8,c_4789]) ).
tff(c_5515,plain,
sz00 = '#skF_8',
inference(splitLeft,[status(thm)],[c_4944]) ).
tff(c_149,plain,
xn != sz00,
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_5620,plain,
xn != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_5515,c_149]) ).
tff(c_155,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_2262,plain,
! [W0_143] :
( ( sdtasdt0(W0_143,sz00) = sz00 )
| ~ aNaturalNumber0(W0_143) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_2295,plain,
sdtasdt0(xp,sz00) = sz00,
inference(resolution,[status(thm)],[c_151,c_2262]) ).
tff(c_5606,plain,
sdtasdt0(xp,'#skF_8') = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_5515,c_5515,c_2295]) ).
tff(c_5804,plain,
sdtasdt0(xn,xn) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_5606,c_189]) ).
tff(c_50,plain,
! [W1_33,W0_32] :
( ( sz00 = W1_33 )
| ( sz00 = W0_32 )
| ( sdtasdt0(W0_32,W1_33) != sz00 )
| ~ aNaturalNumber0(W1_33)
| ~ aNaturalNumber0(W0_32) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_6096,plain,
! [W1_203,W0_204] :
( ( W1_203 = '#skF_8' )
| ( W0_204 = '#skF_8' )
| ( sdtasdt0(W0_204,W1_203) != '#skF_8' )
| ~ aNaturalNumber0(W1_203)
| ~ aNaturalNumber0(W0_204) ),
inference(demodulation,[status(thm),theory(equality)],[c_5515,c_5515,c_5515,c_50]) ).
tff(c_6110,plain,
( ( xn = '#skF_8' )
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_5804,c_6096]) ).
tff(c_6197,plain,
xn = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_155,c_6110]) ).
tff(c_6199,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5620,c_6197]) ).
tff(c_6201,plain,
sz00 != '#skF_8',
inference(splitRight,[status(thm)],[c_4944]) ).
tff(c_107785,plain,
! [W2_951,W0_952,W1_953] :
( ( sdtasdt0(W2_951,W0_952) != sdtasdt0(W1_953,W0_952) )
| ( W2_951 = W1_953 )
| ~ aNaturalNumber0(W2_951)
| ~ aNaturalNumber0(W1_953)
| ( sz00 = W0_952 )
| ~ aNaturalNumber0(W0_952) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_107977,plain,
! [W2_951] :
( ( sdtasdt0(xn,xn) != sdtasdt0(W2_951,'#skF_8') )
| ( xp = W2_951 )
| ~ aNaturalNumber0(W2_951)
| ~ aNaturalNumber0(xp)
| ( sz00 = '#skF_8' )
| ~ aNaturalNumber0('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_189,c_107785]) ).
tff(c_108312,plain,
! [W2_951] :
( ( sdtasdt0(xn,xn) != sdtasdt0(W2_951,'#skF_8') )
| ( xp = W2_951 )
| ~ aNaturalNumber0(W2_951)
| ( sz00 = '#skF_8' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_191,c_151,c_107977]) ).
tff(c_108313,plain,
! [W2_951] :
( ( sdtasdt0(xn,xn) != sdtasdt0(W2_951,'#skF_8') )
| ( xp = W2_951 )
| ~ aNaturalNumber0(W2_951) ),
inference(negUnitSimplification,[status(thm)],[c_6201,c_108312]) ).
tff(c_141753,plain,
! [W2_1111] :
( ( sdtasdt0(W2_1111,'#skF_8') != sdtasdt0('#skF_8',xp) )
| ( xp = W2_1111 )
| ~ aNaturalNumber0(W2_1111) ),
inference(demodulation,[status(thm),theory(equality)],[c_124557,c_108313]) ).
tff(c_141894,plain,
( ( sdtasdt0(sz10,'#skF_8') != sdtasdt0('#skF_8',xp) )
| ( xp = sz10 ) ),
inference(resolution,[status(thm)],[c_8,c_141753]) ).
tff(c_141980,plain,
( ( sdtasdt0('#skF_8',xp) != '#skF_8' )
| ( xp = sz10 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2495,c_141894]) ).
tff(c_141981,plain,
sdtasdt0('#skF_8',xp) != '#skF_8',
inference(negUnitSimplification,[status(thm)],[c_175,c_141980]) ).
tff(c_12,plain,
! [W0_4,W1_5] :
( aNaturalNumber0(sdtasdt0(W0_4,W1_5))
| ~ aNaturalNumber0(W1_5)
| ~ aNaturalNumber0(W0_4) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_124627,plain,
( aNaturalNumber0(sdtasdt0('#skF_8',xp))
| ~ aNaturalNumber0('#skF_8')
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_124334,c_12]) ).
tff(c_124692,plain,
aNaturalNumber0(sdtasdt0('#skF_8',xp)),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_191,c_124627]) ).
tff(c_141,plain,
! [W0_93] :
( aNaturalNumber0('#skF_4'(W0_93))
| ( sz10 = W0_93 )
| ( sz00 = W0_93 )
| ~ aNaturalNumber0(W0_93) ),
inference(cnfTransformation,[status(thm)],[f_418]) ).
tff(c_3679,plain,
! [W0_161] :
( doDivides0('#skF_4'(W0_161),W0_161)
| ( sz10 = W0_161 )
| ( sz00 = W0_161 )
| ~ aNaturalNumber0(W0_161) ),
inference(cnfTransformation,[status(thm)],[f_418]) ).
tff(c_177,plain,
! [W0_105] :
( ~ doDivides0(W0_105,xp)
| ( xp = W0_105 )
| ( sz10 = W0_105 )
| ~ aNaturalNumber0(W0_105) ),
inference(cnfTransformation,[status(thm)],[f_504]) ).
tff(c_3683,plain,
( ( '#skF_4'(xp) = xp )
| ( '#skF_4'(xp) = sz10 )
| ~ aNaturalNumber0('#skF_4'(xp))
| ( xp = sz10 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_3679,c_177]) ).
tff(c_3686,plain,
( ( '#skF_4'(xp) = xp )
| ( '#skF_4'(xp) = sz10 )
| ~ aNaturalNumber0('#skF_4'(xp))
| ( xp = sz10 )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_3683]) ).
tff(c_3687,plain,
( ( '#skF_4'(xp) = xp )
| ( '#skF_4'(xp) = sz10 )
| ~ aNaturalNumber0('#skF_4'(xp)) ),
inference(negUnitSimplification,[status(thm)],[c_145,c_175,c_3686]) ).
tff(c_3688,plain,
~ aNaturalNumber0('#skF_4'(xp)),
inference(splitLeft,[status(thm)],[c_3687]) ).
tff(c_3691,plain,
( ( xp = sz10 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_141,c_3688]) ).
tff(c_3694,plain,
( ( xp = sz10 )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_3691]) ).
tff(c_3696,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_145,c_175,c_3694]) ).
tff(c_3697,plain,
( ( '#skF_4'(xp) = sz10 )
| ( '#skF_4'(xp) = xp ) ),
inference(splitRight,[status(thm)],[c_3687]) ).
tff(c_3755,plain,
'#skF_4'(xp) = xp,
inference(splitLeft,[status(thm)],[c_3697]) ).
tff(c_139,plain,
! [W0_93] :
( doDivides0('#skF_4'(W0_93),W0_93)
| ( sz10 = W0_93 )
| ( sz00 = W0_93 )
| ~ aNaturalNumber0(W0_93) ),
inference(cnfTransformation,[status(thm)],[f_418]) ).
tff(c_3766,plain,
( doDivides0(xp,xp)
| ( xp = sz10 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_3755,c_139]) ).
tff(c_3776,plain,
( doDivides0(xp,xp)
| ( xp = sz10 )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_3766]) ).
tff(c_3777,plain,
doDivides0(xp,xp),
inference(negUnitSimplification,[status(thm)],[c_145,c_175,c_3776]) ).
tff(c_2587,plain,
! [W0_148] :
( ( sdtasdt0(W0_148,sz10) = W0_148 )
| ~ aNaturalNumber0(W0_148) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_2616,plain,
sdtasdt0('#skF_8',sz10) = '#skF_8',
inference(resolution,[status(thm)],[c_191,c_2587]) ).
tff(c_2622,plain,
sdtasdt0(xp,sz10) = xp,
inference(resolution,[status(thm)],[c_151,c_2587]) ).
tff(c_117914,plain,
! [W0_1011,W2_1012] :
( ( sdtsldt0(sdtasdt0(W0_1011,W2_1012),W0_1011) = W2_1012 )
| ~ aNaturalNumber0(W2_1012)
| ~ doDivides0(W0_1011,sdtasdt0(W0_1011,W2_1012))
| ( sz00 = W0_1011 )
| ~ aNaturalNumber0(sdtasdt0(W0_1011,W2_1012))
| ~ aNaturalNumber0(W0_1011) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_118055,plain,
( ( sdtsldt0(sdtasdt0(xp,sz10),xp) = sz10 )
| ~ aNaturalNumber0(sz10)
| ~ doDivides0(xp,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xp,sz10))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_2622,c_117914]) ).
tff(c_118278,plain,
( ( sdtsldt0(xp,xp) = sz10 )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_151,c_2622,c_3777,c_8,c_2622,c_118055]) ).
tff(c_118279,plain,
sdtsldt0(xp,xp) = sz10,
inference(negUnitSimplification,[status(thm)],[c_145,c_118278]) ).
tff(c_2646,plain,
! [W0_149,W1_150] :
( aNaturalNumber0(sdtasdt0(W0_149,W1_150))
| ~ aNaturalNumber0(W1_150)
| ~ aNaturalNumber0(W0_149) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_2694,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0('#skF_8')
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_189,c_2646]) ).
tff(c_2773,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_191,c_2694]) ).
tff(c_171,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnfTransformation,[status(thm)],[f_486]) ).
tff(c_187,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_197,plain,
aNaturalNumber0(xq),
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_199,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xm,xm),
inference(cnfTransformation,[status(thm)],[f_523]) ).
tff(c_3246,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_199,c_12]) ).
tff(c_3252,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_3246]) ).
tff(c_3269,plain,
~ aNaturalNumber0(sdtasdt0(xq,xq)),
inference(splitLeft,[status(thm)],[c_3252]) ).
tff(c_3272,plain,
~ aNaturalNumber0(xq),
inference(resolution,[status(thm)],[c_12,c_3269]) ).
tff(c_3276,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_197,c_3272]) ).
tff(c_3277,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(splitRight,[status(thm)],[c_3252]) ).
tff(c_118037,plain,
( ( sdtsldt0(sdtasdt0(xp,sdtasdt0(xm,xm)),xp) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_171,c_117914]) ).
tff(c_118260,plain,
( ( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_2773,c_171,c_187,c_3277,c_171,c_118037]) ).
tff(c_118261,plain,
sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm),
inference(negUnitSimplification,[status(thm)],[c_145,c_118260]) ).
tff(c_128012,plain,
sdtsldt0(sdtasdt0('#skF_8',xp),xp) = sdtasdt0(xm,xm),
inference(demodulation,[status(thm),theory(equality)],[c_124557,c_118261]) ).
tff(c_121,plain,
! [W2_88,W1_86,W0_85] :
( ( sdtsldt0(sdtasdt0(W2_88,W1_86),W0_85) = sdtasdt0(W2_88,sdtsldt0(W1_86,W0_85)) )
| ~ aNaturalNumber0(W2_88)
| ~ doDivides0(W0_85,W1_86)
| ( sz00 = W0_85 )
| ~ aNaturalNumber0(W1_86)
| ~ aNaturalNumber0(W0_85) ),
inference(cnfTransformation,[status(thm)],[f_384]) ).
tff(c_128019,plain,
( ( sdtasdt0('#skF_8',sdtsldt0(xp,xp)) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0('#skF_8')
| ~ doDivides0(xp,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_128012,c_121]) ).
tff(c_128038,plain,
( ( sdtasdt0(xm,xm) = '#skF_8' )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_151,c_3777,c_191,c_2616,c_118279,c_128019]) ).
tff(c_128039,plain,
sdtasdt0(xm,xm) = '#skF_8',
inference(negUnitSimplification,[status(thm)],[c_145,c_128038]) ).
tff(c_213,plain,
( ~ sdtlseqdt0(xm,xn)
| ( xn = xm ) ),
inference(cnfTransformation,[status(thm)],[f_546]) ).
tff(c_220,plain,
~ sdtlseqdt0(xm,xn),
inference(splitLeft,[status(thm)],[c_213]) ).
tff(c_153,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_2209,plain,
! [W1_140,W0_141] :
( sdtlseqdt0(W1_140,W0_141)
| sdtlseqdt0(W0_141,W1_140)
| ~ aNaturalNumber0(W1_140)
| ~ aNaturalNumber0(W0_141) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_209,plain,
( ~ sdtlseqdt0(xn,xm)
| aNaturalNumber0('#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_536]) ).
tff(c_235,plain,
~ sdtlseqdt0(xn,xm),
inference(splitLeft,[status(thm)],[c_209]) ).
tff(c_2212,plain,
( sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_2209,c_235]) ).
tff(c_2220,plain,
sdtlseqdt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_155,c_2212]) ).
tff(c_2222,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_220,c_2220]) ).
tff(c_2224,plain,
sdtlseqdt0(xn,xm),
inference(splitRight,[status(thm)],[c_209]) ).
tff(c_201,plain,
( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(cnfTransformation,[status(thm)],[f_536]) ).
tff(c_4617,plain,
sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_2224,c_201]) ).
tff(c_126541,plain,
sdtlseqdt0(sdtasdt0('#skF_8',xp),sdtasdt0(xm,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_124557,c_4617]) ).
tff(c_149555,plain,
sdtlseqdt0(sdtasdt0('#skF_8',xp),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_128039,c_126541]) ).
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_149564,plain,
( ( sdtasdt0('#skF_8',xp) = '#skF_8' )
| ~ sdtlseqdt0('#skF_8',sdtasdt0('#skF_8',xp))
| ~ aNaturalNumber0(sdtasdt0('#skF_8',xp))
| ~ aNaturalNumber0('#skF_8') ),
inference(resolution,[status(thm)],[c_149555,c_66]) ).
tff(c_149577,plain,
( ( sdtasdt0('#skF_8',xp) = '#skF_8' )
| ~ sdtlseqdt0('#skF_8',sdtasdt0('#skF_8',xp)) ),
inference(demodulation,[status(thm),theory(equality)],[c_191,c_124692,c_149564]) ).
tff(c_149578,plain,
~ sdtlseqdt0('#skF_8',sdtasdt0('#skF_8',xp)),
inference(negUnitSimplification,[status(thm)],[c_141981,c_149577]) ).
tff(c_149585,plain,
( ( xp = sz00 )
| ~ aNaturalNumber0('#skF_8')
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_95,c_149578]) ).
tff(c_149594,plain,
xp = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_151,c_191,c_149585]) ).
tff(c_149596,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_145,c_149594]) ).
tff(c_149597,plain,
'#skF_4'(xp) = sz10,
inference(splitRight,[status(thm)],[c_3697]) ).
tff(c_137,plain,
! [W0_93] :
( isPrime0('#skF_4'(W0_93))
| ( sz10 = W0_93 )
| ( sz00 = W0_93 )
| ~ aNaturalNumber0(W0_93) ),
inference(cnfTransformation,[status(thm)],[f_418]) ).
tff(c_149612,plain,
( isPrime0(sz10)
| ( xp = sz10 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_149597,c_137]) ).
tff(c_149622,plain,
( isPrime0(sz10)
| ( xp = sz10 )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_149612]) ).
tff(c_149624,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_145,c_175,c_217,c_149622]) ).
tff(c_149625,plain,
xn = xm,
inference(splitRight,[status(thm)],[c_213]) ).
tff(c_149626,plain,
sdtlseqdt0(xm,xn),
inference(splitRight,[status(thm)],[c_213]) ).
tff(c_149635,plain,
sdtlseqdt0(xm,xm),
inference(demodulation,[status(thm),theory(equality)],[c_149625,c_149626]) ).
tff(c_149655,plain,
aNaturalNumber0('#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_149635,c_149625,c_209]) ).
tff(c_149697,plain,
! [W0_1136] :
( ( sdtasdt0(sz10,W0_1136) = W0_1136 )
| ~ aNaturalNumber0(W0_1136) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_149722,plain,
sdtasdt0(sz10,'#skF_9') = '#skF_9',
inference(resolution,[status(thm)],[c_149655,c_149697]) ).
tff(c_151094,plain,
! [W1_1162,W0_1163] :
( sdtlseqdt0(W1_1162,sdtasdt0(W1_1162,W0_1163))
| ( sz00 = W0_1163 )
| ~ aNaturalNumber0(W1_1162)
| ~ aNaturalNumber0(W0_1163) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_151118,plain,
( sdtlseqdt0(sz10,'#skF_9')
| ( sz00 = '#skF_9' )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0('#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_149722,c_151094]) ).
tff(c_151225,plain,
( sdtlseqdt0(sz10,'#skF_9')
| ( sz00 = '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_149655,c_8,c_151118]) ).
tff(c_152632,plain,
sz00 = '#skF_9',
inference(splitLeft,[status(thm)],[c_151225]) ).
tff(c_149723,plain,
sdtasdt0(sz10,'#skF_8') = '#skF_8',
inference(resolution,[status(thm)],[c_191,c_149697]) ).
tff(c_151115,plain,
( sdtlseqdt0(sz10,'#skF_8')
| ( sz00 = '#skF_8' )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_149723,c_151094]) ).
tff(c_151223,plain,
( sdtlseqdt0(sz10,'#skF_8')
| ( sz00 = '#skF_8' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_191,c_8,c_151115]) ).
tff(c_151687,plain,
sz00 = '#skF_8',
inference(splitLeft,[status(thm)],[c_151223]) ).
tff(c_147,plain,
xm != sz00,
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_151747,plain,
xm != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_151687,c_147]) ).
tff(c_149656,plain,
! [W0_1135] :
( ( sdtasdt0(W0_1135,sz00) = sz00 )
| ~ aNaturalNumber0(W0_1135) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_149685,plain,
sdtasdt0(xp,sz00) = sz00,
inference(resolution,[status(thm)],[c_151,c_149656]) ).
tff(c_151708,plain,
sdtasdt0(xp,'#skF_8') = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_151687,c_151687,c_149685]) ).
tff(c_149938,plain,
sdtasdt0(xp,'#skF_8') = sdtasdt0(xm,xm),
inference(demodulation,[status(thm),theory(equality)],[c_149625,c_149625,c_189]) ).
tff(c_152166,plain,
sdtasdt0(xm,xm) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_151708,c_149938]) ).
tff(c_152033,plain,
! [W1_33,W0_32] :
( ( W1_33 = '#skF_8' )
| ( W0_32 = '#skF_8' )
| ( sdtasdt0(W0_32,W1_33) != '#skF_8' )
| ~ aNaturalNumber0(W1_33)
| ~ aNaturalNumber0(W0_32) ),
inference(demodulation,[status(thm),theory(equality)],[c_151687,c_151687,c_151687,c_50]) ).
tff(c_152577,plain,
( ( xm = '#skF_8' )
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_152166,c_152033]) ).
tff(c_152587,plain,
xm = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_153,c_152577]) ).
tff(c_152589,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_151747,c_152587]) ).
tff(c_152591,plain,
sz00 != '#skF_8',
inference(splitRight,[status(thm)],[c_151223]) ).
tff(c_152823,plain,
'#skF_9' != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_152632,c_152591]) ).
tff(c_152879,plain,
xp != '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_152632,c_145]) ).
tff(c_150910,plain,
! [W1_1159,W0_1160] :
( ( sdtasdt0(W1_1159,W0_1160) = sdtasdt0(W0_1160,W1_1159) )
| ~ aNaturalNumber0(W1_1159)
| ~ aNaturalNumber0(W0_1160) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_164805,plain,
! [W0_1327] :
( ( sdtasdt0(xp,W0_1327) = sdtasdt0(W0_1327,xp) )
| ~ aNaturalNumber0(W0_1327) ),
inference(resolution,[status(thm)],[c_151,c_150910]) ).
tff(c_164887,plain,
sdtasdt0(xp,'#skF_8') = sdtasdt0('#skF_8',xp),
inference(resolution,[status(thm)],[c_191,c_164805]) ).
tff(c_164950,plain,
( aNaturalNumber0(sdtasdt0('#skF_8',xp))
| ~ aNaturalNumber0('#skF_8')
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_164887,c_12]) ).
tff(c_165004,plain,
aNaturalNumber0(sdtasdt0('#skF_8',xp)),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_191,c_164950]) ).
tff(c_164895,plain,
sdtasdt0(xm,xm) = sdtasdt0('#skF_8',xp),
inference(demodulation,[status(thm),theory(equality)],[c_164887,c_149938]) ).
tff(c_149976,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xm,xm),
inference(demodulation,[status(thm),theory(equality)],[c_149625,c_149625,c_171]) ).
tff(c_165229,plain,
sdtasdt0(xp,sdtasdt0('#skF_8',xp)) = sdtasdt0('#skF_8',xp),
inference(demodulation,[status(thm),theory(equality)],[c_164895,c_164895,c_149976]) ).
tff(c_149652,plain,
doDivides0(xp,sdtasdt0(xm,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_149625,c_149625,c_187]) ).
tff(c_165230,plain,
doDivides0(xp,sdtasdt0('#skF_8',xp)),
inference(demodulation,[status(thm),theory(equality)],[c_164895,c_149652]) ).
tff(c_150014,plain,
! [W0_1141,W1_1142] :
( aNaturalNumber0(sdtasdt0(W0_1141,W1_1142))
| ~ aNaturalNumber0(W1_1142)
| ~ aNaturalNumber0(W0_1141) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_150068,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0('#skF_8')
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_149938,c_150014]) ).
tff(c_150143,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_191,c_150068]) ).
tff(c_107,plain,
! [W0_70,W2_73] :
( ( sdtsldt0(sdtasdt0(W0_70,W2_73),W0_70) = W2_73 )
| ~ aNaturalNumber0(W2_73)
| ~ doDivides0(W0_70,sdtasdt0(W0_70,W2_73))
| ( sz00 = W0_70 )
| ~ aNaturalNumber0(sdtasdt0(W0_70,W2_73))
| ~ aNaturalNumber0(W0_70) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_161790,plain,
! [W0_1301,W2_1302] :
( ( sdtsldt0(sdtasdt0(W0_1301,W2_1302),W0_1301) = W2_1302 )
| ~ aNaturalNumber0(W2_1302)
| ~ doDivides0(W0_1301,sdtasdt0(W0_1301,W2_1302))
| ( W0_1301 = '#skF_9' )
| ~ aNaturalNumber0(sdtasdt0(W0_1301,W2_1302))
| ~ aNaturalNumber0(W0_1301) ),
inference(demodulation,[status(thm),theory(equality)],[c_152632,c_107]) ).
tff(c_161874,plain,
( ( sdtsldt0(sdtasdt0(xp,'#skF_8'),xp) = '#skF_8' )
| ~ aNaturalNumber0('#skF_8')
| ~ doDivides0(xp,sdtasdt0(xm,xm))
| ( xp = '#skF_9' )
| ~ aNaturalNumber0(sdtasdt0(xp,'#skF_8'))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_149938,c_161790]) ).
tff(c_161973,plain,
( ( sdtsldt0(sdtasdt0(xm,xm),xp) = '#skF_8' )
| ( xp = '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_150143,c_149938,c_149652,c_191,c_149938,c_161874]) ).
tff(c_161974,plain,
sdtsldt0(sdtasdt0(xm,xm),xp) = '#skF_8',
inference(negUnitSimplification,[status(thm)],[c_152879,c_161973]) ).
tff(c_165218,plain,
sdtsldt0(sdtasdt0('#skF_8',xp),xp) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_164895,c_161974]) ).
tff(c_161789,plain,
! [W0_70,W2_73] :
( ( sdtsldt0(sdtasdt0(W0_70,W2_73),W0_70) = W2_73 )
| ~ aNaturalNumber0(W2_73)
| ~ doDivides0(W0_70,sdtasdt0(W0_70,W2_73))
| ( W0_70 = '#skF_9' )
| ~ aNaturalNumber0(sdtasdt0(W0_70,W2_73))
| ~ aNaturalNumber0(W0_70) ),
inference(demodulation,[status(thm),theory(equality)],[c_152632,c_107]) ).
tff(c_169488,plain,
( ( sdtsldt0(sdtasdt0(xp,sdtasdt0('#skF_8',xp)),xp) = sdtasdt0('#skF_8',xp) )
| ~ aNaturalNumber0(sdtasdt0('#skF_8',xp))
| ~ doDivides0(xp,sdtasdt0('#skF_8',xp))
| ( xp = '#skF_9' )
| ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0('#skF_8',xp)))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_165229,c_161789]) ).
tff(c_169543,plain,
( ( sdtasdt0('#skF_8',xp) = '#skF_8' )
| ( xp = '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_165004,c_165229,c_165230,c_165004,c_165218,c_165229,c_169488]) ).
tff(c_169544,plain,
sdtasdt0('#skF_8',xp) = '#skF_8',
inference(negUnitSimplification,[status(thm)],[c_152879,c_169543]) ).
tff(c_149742,plain,
! [W0_1137] :
( ( sdtasdt0(W0_1137,sz10) = W0_1137 )
| ~ aNaturalNumber0(W0_1137) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_149768,plain,
sdtasdt0('#skF_8',sz10) = '#skF_8',
inference(resolution,[status(thm)],[c_191,c_149742]) ).
tff(c_153833,plain,
! [W0_1216,W2_1217] :
( doDivides0(W0_1216,sdtasdt0(W0_1216,W2_1217))
| ~ aNaturalNumber0(W2_1217)
| ~ aNaturalNumber0(sdtasdt0(W0_1216,W2_1217))
| ~ aNaturalNumber0(W0_1216) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_153878,plain,
( doDivides0('#skF_8','#skF_8')
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0('#skF_8',sz10))
| ~ aNaturalNumber0('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_149768,c_153833]) ).
tff(c_153947,plain,
doDivides0('#skF_8','#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_191,c_191,c_149768,c_8,c_153878]) ).
tff(c_161859,plain,
( ( sdtsldt0(sdtasdt0('#skF_8',sz10),'#skF_8') = sz10 )
| ~ aNaturalNumber0(sz10)
| ~ doDivides0('#skF_8','#skF_8')
| ( '#skF_9' = '#skF_8' )
| ~ aNaturalNumber0(sdtasdt0('#skF_8',sz10))
| ~ aNaturalNumber0('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_149768,c_161790]) ).
tff(c_161958,plain,
( ( sdtsldt0('#skF_8','#skF_8') = sz10 )
| ( '#skF_9' = '#skF_8' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_191,c_191,c_149768,c_153947,c_8,c_149768,c_161859]) ).
tff(c_161959,plain,
sdtsldt0('#skF_8','#skF_8') = sz10,
inference(negUnitSimplification,[status(thm)],[c_152823,c_161958]) ).
tff(c_169630,plain,
( ( sdtsldt0(sdtasdt0('#skF_8',xp),'#skF_8') = xp )
| ~ aNaturalNumber0(xp)
| ~ doDivides0('#skF_8','#skF_8')
| ( '#skF_9' = '#skF_8' )
| ~ aNaturalNumber0(sdtasdt0('#skF_8',xp))
| ~ aNaturalNumber0('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_169544,c_161789]) ).
tff(c_169685,plain,
( ( xp = sz10 )
| ( '#skF_9' = '#skF_8' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_191,c_191,c_169544,c_153947,c_151,c_161959,c_169544,c_169630]) ).
tff(c_169687,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_152823,c_175,c_169685]) ).
tff(c_169689,plain,
sz00 != '#skF_9',
inference(splitRight,[status(thm)],[c_151225]) ).
tff(c_236924,plain,
! [W0_2139,W2_2140] :
( ( sdtsldt0(sdtasdt0(W0_2139,W2_2140),W0_2139) = W2_2140 )
| ~ aNaturalNumber0(W2_2140)
| ~ doDivides0(W0_2139,sdtasdt0(W0_2139,W2_2140))
| ( sz00 = W0_2139 )
| ~ aNaturalNumber0(sdtasdt0(W0_2139,W2_2140))
| ~ aNaturalNumber0(W0_2139) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_237026,plain,
( ( sdtsldt0(sdtasdt0(xp,'#skF_8'),xp) = '#skF_8' )
| ~ aNaturalNumber0('#skF_8')
| ~ doDivides0(xp,sdtasdt0(xm,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xp,'#skF_8'))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_149938,c_236924]) ).
tff(c_237149,plain,
( ( sdtsldt0(sdtasdt0(xm,xm),xp) = '#skF_8' )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_150143,c_149938,c_149652,c_191,c_149938,c_237026]) ).
tff(c_237150,plain,
sdtsldt0(sdtasdt0(xm,xm),xp) = '#skF_8',
inference(negUnitSimplification,[status(thm)],[c_145,c_237149]) ).
tff(c_237008,plain,
( ( sdtsldt0(sdtasdt0(xp,sdtasdt0(xm,xm)),xp) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ doDivides0(xp,sdtasdt0(xm,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_149976,c_236924]) ).
tff(c_237131,plain,
( ( sdtsldt0(sdtasdt0(xm,xm),xp) = sdtasdt0(xm,xm) )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_150143,c_149976,c_149652,c_150143,c_149976,c_237008]) ).
tff(c_237132,plain,
sdtsldt0(sdtasdt0(xm,xm),xp) = sdtasdt0(xm,xm),
inference(negUnitSimplification,[status(thm)],[c_145,c_237131]) ).
tff(c_239068,plain,
sdtasdt0(xm,xm) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_237150,c_237132]) ).
tff(c_205,plain,
( ~ sdtlseqdt0(xn,xm)
| ( sdtpldt0(sdtasdt0(xn,xn),'#skF_9') = sdtasdt0(xm,xm) ) ),
inference(cnfTransformation,[status(thm)],[f_536]) ).
tff(c_151304,plain,
sdtpldt0(sdtasdt0(xm,xm),'#skF_9') = sdtasdt0(xm,xm),
inference(demodulation,[status(thm),theory(equality)],[c_149625,c_149625,c_149635,c_149625,c_205]) ).
tff(c_239080,plain,
sdtpldt0('#skF_8','#skF_9') = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_239068,c_239068,c_151304]) ).
tff(c_6,plain,
sz10 != sz00,
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_151121,plain,
( sdtlseqdt0('#skF_8','#skF_8')
| ( sz10 = sz00 )
| ~ aNaturalNumber0('#skF_8')
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_149768,c_151094]) ).
tff(c_151227,plain,
( sdtlseqdt0('#skF_8','#skF_8')
| ( sz10 = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_191,c_151121]) ).
tff(c_151228,plain,
sdtlseqdt0('#skF_8','#skF_8'),
inference(negUnitSimplification,[status(thm)],[c_6,c_151227]) ).
tff(c_149795,plain,
! [W0_1138] :
( ( sdtpldt0(W0_1138,sz00) = W0_1138 )
| ~ aNaturalNumber0(W0_1138) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_149821,plain,
sdtpldt0('#skF_8',sz00) = '#skF_8',
inference(resolution,[status(thm)],[c_191,c_149795]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_235302,plain,
! [W0_2128,W2_2129] :
( ( sdtmndt0(sdtpldt0(W0_2128,W2_2129),W0_2128) = W2_2129 )
| ~ aNaturalNumber0(W2_2129)
| ~ sdtlseqdt0(W0_2128,sdtpldt0(W0_2128,W2_2129))
| ~ aNaturalNumber0(sdtpldt0(W0_2128,W2_2129))
| ~ aNaturalNumber0(W0_2128) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_235372,plain,
( ( sdtmndt0(sdtpldt0('#skF_8',sz00),'#skF_8') = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0('#skF_8','#skF_8')
| ~ aNaturalNumber0(sdtpldt0('#skF_8',sz00))
| ~ aNaturalNumber0('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_149821,c_235302]) ).
tff(c_235429,plain,
sdtmndt0('#skF_8','#skF_8') = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_191,c_191,c_149821,c_151228,c_4,c_149821,c_235372]) ).
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_239276,plain,
( ( sdtmndt0(sdtpldt0('#skF_8','#skF_9'),'#skF_8') = '#skF_9' )
| ~ aNaturalNumber0('#skF_9')
| ~ sdtlseqdt0('#skF_8','#skF_8')
| ~ aNaturalNumber0(sdtpldt0('#skF_8','#skF_9'))
| ~ aNaturalNumber0('#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_239080,c_58]) ).
tff(c_239319,plain,
sz00 = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_191,c_191,c_239080,c_151228,c_149655,c_235429,c_239080,c_239276]) ).
tff(c_239321,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_169689,c_239319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM528+3 : 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
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 15:13:21 EDT 2023
% 0.14/0.35 % CPUTime :
% 58.26/42.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 58.26/42.14
% 58.26/42.14 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 58.35/42.19
% 58.35/42.19 Inference rules
% 58.35/42.19 ----------------------
% 58.35/42.19 #Ref : 85
% 58.35/42.19 #Sup : 48887
% 58.35/42.19 #Fact : 12
% 58.35/42.19 #Define : 0
% 58.35/42.19 #Split : 159
% 58.35/42.19 #Chain : 0
% 58.35/42.19 #Close : 0
% 58.35/42.19
% 58.35/42.19 Ordering : KBO
% 58.35/42.19
% 58.35/42.19 Simplification rules
% 58.35/42.19 ----------------------
% 58.35/42.19 #Subsume : 4805
% 58.35/42.19 #Demod : 101176
% 58.35/42.19 #Tautology : 15880
% 58.35/42.19 #SimpNegUnit : 8933
% 58.35/42.19 #BackRed : 5416
% 58.35/42.19
% 58.35/42.19 #Partial instantiations: 0
% 58.35/42.19 #Strategies tried : 1
% 58.35/42.19
% 58.35/42.19 Timing (in seconds)
% 58.35/42.19 ----------------------
% 58.35/42.19 Preprocessing : 0.73
% 58.35/42.19 Parsing : 0.36
% 58.35/42.19 CNF conversion : 0.06
% 58.35/42.19 Main loop : 40.34
% 58.35/42.19 Inferencing : 5.28
% 58.35/42.19 Reduction : 24.81
% 58.35/42.19 Demodulation : 21.28
% 58.35/42.19 BG Simplification : 0.38
% 58.35/42.19 Subsumption : 7.83
% 58.35/42.19 Abstraction : 0.56
% 58.35/42.19 MUC search : 0.00
% 58.35/42.19 Cooper : 0.00
% 58.35/42.19 Total : 41.18
% 58.35/42.19 Index Insertion : 0.00
% 58.35/42.19 Index Deletion : 0.00
% 58.35/42.19 Index Matching : 0.00
% 58.35/42.19 BG Taut test : 0.00
%------------------------------------------------------------------------------