%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM481+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/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 : Wed Apr 9 07:56:04 PM UTC 2025
% Result : Theorem 181.68s 153.80s
% Output : CNFRefutation 181.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 24
% Syntax : Number of formulae : 258 ( 82 unt; 0 typ; 3 def)
% Number of atoms : 824 ( 230 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 950 ( 384 ~; 473 |; 52 &)
% ( 3 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 178 ( 174 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > sz10 > sz00 > #skF_5 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
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(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(f_437,negated_conjecture,
~ ! [W0] :
( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ( ! [W1] :
( ( aNaturalNumber0(W1)
& ( W1 != sz00 )
& ( W1 != sz10 ) )
=> ( iLess0(W1,W0)
=> ? [W2] :
( aNaturalNumber0(W2)
& doDivides0(W2,W1)
& isPrime0(W2) ) ) )
=> ? [W1] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
tff(f_53,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
tff(f_41,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(f_370,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( doDivides0(W0,W1)
& ( W1 != sz00 ) )
=> sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
tff(f_87,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
tff(f_189,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
tff(f_141,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtpldt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
tff(f_296,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
tff(f_162,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
tff(f_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
tff(f_93,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
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/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
tff(f_359,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W0,sdtpldt0(W1,W2)) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
tff(f_212,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
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/sandbox/benchmark/theBenchmark.p',mLETran) ).
tff(f_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(f_81,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
tff(f_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
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/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
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/sandbox/benchmark/theBenchmark.p',mMonMul) ).
tff(c_141,plain,
sz00 != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_139,plain,
sz10 != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_143,plain,
aNaturalNumber0('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_437]) ).
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_433,plain,
! [W1_115,W0_116] :
( ( sdtpldt0(W1_115,W0_116) = sdtpldt0(W0_116,W1_115) )
| ~ aNaturalNumber0(W1_115)
| ~ aNaturalNumber0(W0_116) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_467,plain,
! [W0_119] :
( ( sdtpldt0(sz10,W0_119) = sdtpldt0(W0_119,sz10) )
| ~ aNaturalNumber0(W0_119) ),
inference(resolution,[status(thm)],[c_8,c_433]) ).
tff(c_493,plain,
sdtpldt0(sz10,'#skF_4') = sdtpldt0('#skF_4',sz10),
inference(resolution,[status(thm)],[c_143,c_467]) ).
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_497,plain,
( aNaturalNumber0(sdtpldt0('#skF_4',sz10))
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_493,c_10]) ).
tff(c_501,plain,
aNaturalNumber0(sdtpldt0('#skF_4',sz10)),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_143,c_497]) ).
tff(c_119,plain,
! [W0_83,W1_84] :
( sdtlseqdt0(W0_83,W1_84)
| ( sz00 = W1_84 )
| ~ doDivides0(W0_83,W1_84)
| ~ aNaturalNumber0(W1_84)
| ~ aNaturalNumber0(W0_83) ),
inference(cnfTransformation,[status(thm)],[f_370]) ).
tff(c_244,plain,
! [W0_106] :
( ( sdtasdt0(sz10,W0_106) = W0_106 )
| ~ aNaturalNumber0(W0_106) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_262,plain,
sdtasdt0(sz10,'#skF_4') = '#skF_4',
inference(resolution,[status(thm)],[c_143,c_244]) ).
tff(c_1912,plain,
! [W1_150,W0_151] :
( sdtlseqdt0(W1_150,sdtasdt0(W1_150,W0_151))
| ( sz00 = W0_151 )
| ~ aNaturalNumber0(W1_150)
| ~ aNaturalNumber0(W0_151) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_1972,plain,
( sdtlseqdt0(sz10,'#skF_4')
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_262,c_1912]) ).
tff(c_2045,plain,
( sdtlseqdt0(sz10,'#skF_4')
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_1972]) ).
tff(c_2046,plain,
sdtlseqdt0(sz10,'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_141,c_2045]) ).
tff(c_2650,plain,
! [W1_163,W0_164] :
( ( W1_163 = W0_164 )
| ~ sdtlseqdt0(W1_163,W0_164)
| ~ sdtlseqdt0(W0_164,W1_163)
| ~ aNaturalNumber0(W1_163)
| ~ aNaturalNumber0(W0_164) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_2658,plain,
( ( sz10 = '#skF_4' )
| ~ sdtlseqdt0('#skF_4',sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_2046,c_2650]) ).
tff(c_2682,plain,
( ( sz10 = '#skF_4' )
| ~ sdtlseqdt0('#skF_4',sz10) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_2658]) ).
tff(c_2683,plain,
~ sdtlseqdt0('#skF_4',sz10),
inference(negUnitSimplification,[status(thm)],[c_139,c_2682]) ).
tff(c_634,plain,
! [W0_123,W1_124] :
( ( sz00 = W0_123 )
| ( sdtpldt0(W0_123,W1_124) != sz00 )
| ~ aNaturalNumber0(W1_124)
| ~ aNaturalNumber0(W0_123) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_638,plain,
( ( sz10 = sz00 )
| ( sdtpldt0('#skF_4',sz10) != sz00 )
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_493,c_634]) ).
tff(c_652,plain,
( ( sz10 = sz00 )
| ( sdtpldt0('#skF_4',sz10) != sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_143,c_638]) ).
tff(c_653,plain,
sdtpldt0('#skF_4',sz10) != sz00,
inference(negUnitSimplification,[status(thm)],[c_6,c_652]) ).
tff(c_26,plain,
! [W0_17] :
( ( sdtasdt0(sz10,W0_17) = W0_17 )
| ~ aNaturalNumber0(W0_17) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_530,plain,
sdtasdt0(sz10,sdtpldt0('#skF_4',sz10)) = sdtpldt0('#skF_4',sz10),
inference(resolution,[status(thm)],[c_501,c_26]) ).
tff(c_1957,plain,
( sdtlseqdt0(sz10,sdtpldt0('#skF_4',sz10))
| ( sdtpldt0('#skF_4',sz10) = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtpldt0('#skF_4',sz10)) ),
inference(superposition,[status(thm),theory(equality)],[c_530,c_1912]) ).
tff(c_2030,plain,
( sdtlseqdt0(sz10,sdtpldt0('#skF_4',sz10))
| ( sdtpldt0('#skF_4',sz10) = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_501,c_8,c_1957]) ).
tff(c_2031,plain,
sdtlseqdt0(sz10,sdtpldt0('#skF_4',sz10)),
inference(negUnitSimplification,[status(thm)],[c_653,c_2030]) ).
tff(c_2143,plain,
! [W0_157,W1_158] :
( iLess0(W0_157,W1_158)
| ~ sdtlseqdt0(W0_157,W1_158)
| ( W1_158 = W0_157 )
| ~ aNaturalNumber0(W1_158)
| ~ aNaturalNumber0(W0_157) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_2152,plain,
( iLess0(sz10,sdtpldt0('#skF_4',sz10))
| ( sdtpldt0('#skF_4',sz10) = sz10 )
| ~ aNaturalNumber0(sdtpldt0('#skF_4',sz10))
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[c_2031,c_2143]) ).
tff(c_2190,plain,
( iLess0(sz10,sdtpldt0('#skF_4',sz10))
| ( sdtpldt0('#skF_4',sz10) = sz10 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_501,c_2152]) ).
tff(c_2220,plain,
sdtpldt0('#skF_4',sz10) = sz10,
inference(splitLeft,[status(thm)],[c_2190]) ).
tff(c_4302,plain,
! [W0_199,W2_200] :
( sdtlseqdt0(W0_199,sdtpldt0(W0_199,W2_200))
| ~ aNaturalNumber0(W2_200)
| ~ aNaturalNumber0(sdtpldt0(W0_199,W2_200))
| ~ aNaturalNumber0(W0_199) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_4343,plain,
( sdtlseqdt0('#skF_4',sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtpldt0('#skF_4',sz10))
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_2220,c_4302]) ).
tff(c_4385,plain,
sdtlseqdt0('#skF_4',sz10),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_2220,c_8,c_4343]) ).
tff(c_4387,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2683,c_4385]) ).
tff(c_4389,plain,
sdtpldt0('#skF_4',sz10) != sz10,
inference(splitRight,[status(thm)],[c_2190]) ).
tff(c_5337,plain,
! [W1_218,W0_219] :
( ( W1_218 = W0_219 )
| ~ sdtlseqdt0(W1_218,W0_219)
| ~ sdtlseqdt0(W0_219,W1_218)
| ~ aNaturalNumber0(W1_218)
| ~ aNaturalNumber0(W0_219) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_5343,plain,
( ( sdtpldt0('#skF_4',sz10) = sz10 )
| ~ sdtlseqdt0(sdtpldt0('#skF_4',sz10),sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtpldt0('#skF_4',sz10)) ),
inference(resolution,[status(thm)],[c_2031,c_5337]) ).
tff(c_5371,plain,
( ( sdtpldt0('#skF_4',sz10) = sz10 )
| ~ sdtlseqdt0(sdtpldt0('#skF_4',sz10),sz10) ),
inference(demodulation,[status(thm),theory(equality)],[c_501,c_8,c_5343]) ).
tff(c_5372,plain,
~ sdtlseqdt0(sdtpldt0('#skF_4',sz10),sz10),
inference(negUnitSimplification,[status(thm)],[c_4389,c_5371]) ).
tff(c_5573,plain,
( ( sz10 = sz00 )
| ~ doDivides0(sdtpldt0('#skF_4',sz10),sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtpldt0('#skF_4',sz10)) ),
inference(resolution,[status(thm)],[c_119,c_5372]) ).
tff(c_5582,plain,
( ( sz10 = sz00 )
| ~ doDivides0(sdtpldt0('#skF_4',sz10),sz10) ),
inference(demodulation,[status(thm),theory(equality)],[c_501,c_8,c_5573]) ).
tff(c_5583,plain,
~ doDivides0(sdtpldt0('#skF_4',sz10),sz10),
inference(negUnitSimplification,[status(thm)],[c_6,c_5582]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_32,plain,
! [W0_18] :
( ( sdtasdt0(W0_18,sz00) = sz00 )
| ~ aNaturalNumber0(W0_18) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_531,plain,
sdtasdt0(sdtpldt0('#skF_4',sz10),sz00) = sz00,
inference(resolution,[status(thm)],[c_501,c_32]) ).
tff(c_5807,plain,
! [W0_224,W2_225] :
( doDivides0(W0_224,sdtasdt0(W0_224,W2_225))
| ~ aNaturalNumber0(W2_225)
| ~ aNaturalNumber0(sdtasdt0(W0_224,W2_225))
| ~ aNaturalNumber0(W0_224) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_5861,plain,
( doDivides0(sdtpldt0('#skF_4',sz10),sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtasdt0(sdtpldt0('#skF_4',sz10),sz00))
| ~ aNaturalNumber0(sdtpldt0('#skF_4',sz10)) ),
inference(superposition,[status(thm),theory(equality)],[c_531,c_5807]) ).
tff(c_5924,plain,
doDivides0(sdtpldt0('#skF_4',sz10),sz00),
inference(demodulation,[status(thm),theory(equality)],[c_501,c_4,c_531,c_4,c_5861]) ).
tff(c_129,plain,
! [W0_89] :
( aNaturalNumber0('#skF_3'(W0_89))
| isPrime0(W0_89)
| ( sz10 = W0_89 )
| ( sz00 = W0_89 )
| ~ aNaturalNumber0(W0_89) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_4550,plain,
! [W0_203] :
( doDivides0('#skF_3'(W0_203),W0_203)
| isPrime0(W0_203)
| ( sz10 = W0_203 )
| ( sz00 = W0_203 )
| ~ aNaturalNumber0(W0_203) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_137,plain,
! [W1_99] :
( ~ isPrime0(W1_99)
| ~ doDivides0(W1_99,'#skF_4')
| ~ aNaturalNumber0(W1_99) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_4554,plain,
( ~ isPrime0('#skF_3'('#skF_4'))
| ~ aNaturalNumber0('#skF_3'('#skF_4'))
| isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_4550,c_137]) ).
tff(c_4557,plain,
( ~ isPrime0('#skF_3'('#skF_4'))
| ~ aNaturalNumber0('#skF_3'('#skF_4'))
| isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_4554]) ).
tff(c_4558,plain,
( ~ isPrime0('#skF_3'('#skF_4'))
| ~ aNaturalNumber0('#skF_3'('#skF_4'))
| isPrime0('#skF_4') ),
inference(negUnitSimplification,[status(thm)],[c_141,c_139,c_4557]) ).
tff(c_4559,plain,
~ aNaturalNumber0('#skF_3'('#skF_4')),
inference(splitLeft,[status(thm)],[c_4558]) ).
tff(c_4562,plain,
( isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_129,c_4559]) ).
tff(c_4565,plain,
( isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_4562]) ).
tff(c_4566,plain,
isPrime0('#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_141,c_139,c_4565]) ).
tff(c_181,plain,
! [W0_103] :
( ( sdtasdt0(W0_103,sz10) = W0_103 )
| ~ aNaturalNumber0(W0_103) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_193,plain,
sdtasdt0('#skF_4',sz10) = '#skF_4',
inference(resolution,[status(thm)],[c_143,c_181]) ).
tff(c_5127,plain,
! [W0_215,W2_216] :
( doDivides0(W0_215,sdtasdt0(W0_215,W2_216))
| ~ aNaturalNumber0(W2_216)
| ~ aNaturalNumber0(sdtasdt0(W0_215,W2_216))
| ~ aNaturalNumber0(W0_215) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_5202,plain,
( doDivides0('#skF_4','#skF_4')
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0('#skF_4',sz10))
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_193,c_5127]) ).
tff(c_5258,plain,
doDivides0('#skF_4','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_143,c_193,c_8,c_5202]) ).
tff(c_5330,plain,
( ~ isPrime0('#skF_4')
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_5258,c_137]) ).
tff(c_5334,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_143,c_4566,c_5330]) ).
tff(c_5336,plain,
aNaturalNumber0('#skF_3'('#skF_4')),
inference(splitRight,[status(thm)],[c_4558]) ).
tff(c_5450,plain,
sdtasdt0(sz10,'#skF_3'('#skF_4')) = '#skF_3'('#skF_4'),
inference(resolution,[status(thm)],[c_5336,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_5749,plain,
( sdtlseqdt0(sz10,'#skF_3'('#skF_4'))
| ( '#skF_3'('#skF_4') = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0('#skF_3'('#skF_4')) ),
inference(superposition,[status(thm),theory(equality)],[c_5450,c_95]) ).
tff(c_5765,plain,
( sdtlseqdt0(sz10,'#skF_3'('#skF_4'))
| ( '#skF_3'('#skF_4') = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_8,c_5749]) ).
tff(c_5773,plain,
'#skF_3'('#skF_4') = sz00,
inference(splitLeft,[status(thm)],[c_5765]) ).
tff(c_127,plain,
! [W0_89] :
( doDivides0('#skF_3'(W0_89),W0_89)
| isPrime0(W0_89)
| ( sz10 = W0_89 )
| ( sz00 = W0_89 )
| ~ aNaturalNumber0(W0_89) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_5794,plain,
( doDivides0(sz00,'#skF_4')
| isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_5773,c_127]) ).
tff(c_5801,plain,
( doDivides0(sz00,'#skF_4')
| isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_5794]) ).
tff(c_5802,plain,
( doDivides0(sz00,'#skF_4')
| isPrime0('#skF_4') ),
inference(negUnitSimplification,[status(thm)],[c_141,c_139,c_5801]) ).
tff(c_5949,plain,
isPrime0('#skF_4'),
inference(splitLeft,[status(thm)],[c_5802]) ).
tff(c_5882,plain,
( doDivides0('#skF_4','#skF_4')
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0('#skF_4',sz10))
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_193,c_5807]) ).
tff(c_5938,plain,
doDivides0('#skF_4','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_143,c_193,c_8,c_5882]) ).
tff(c_5952,plain,
( ~ isPrime0('#skF_4')
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_5938,c_137]) ).
tff(c_5956,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_143,c_5949,c_5952]) ).
tff(c_5957,plain,
doDivides0(sz00,'#skF_4'),
inference(splitRight,[status(thm)],[c_5802]) ).
tff(c_8384,plain,
! [W0_270,W2_271,W1_272] :
( doDivides0(W0_270,W2_271)
| ~ doDivides0(W1_272,W2_271)
| ~ doDivides0(W0_270,W1_272)
| ~ aNaturalNumber0(W2_271)
| ~ aNaturalNumber0(W1_272)
| ~ aNaturalNumber0(W0_270) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_8400,plain,
! [W0_270] :
( doDivides0(W0_270,'#skF_4')
| ~ doDivides0(W0_270,sz00)
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(W0_270) ),
inference(resolution,[status(thm)],[c_5957,c_8384]) ).
tff(c_8824,plain,
! [W0_286] :
( doDivides0(W0_286,'#skF_4')
| ~ doDivides0(W0_286,sz00)
| ~ aNaturalNumber0(W0_286) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_143,c_8400]) ).
tff(c_8839,plain,
( doDivides0(sdtpldt0('#skF_4',sz10),'#skF_4')
| ~ aNaturalNumber0(sdtpldt0('#skF_4',sz10)) ),
inference(resolution,[status(thm)],[c_5924,c_8824]) ).
tff(c_8869,plain,
doDivides0(sdtpldt0('#skF_4',sz10),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_501,c_8839]) ).
tff(c_28,plain,
! [W0_17] :
( ( sdtasdt0(W0_17,sz10) = W0_17 )
| ~ aNaturalNumber0(W0_17) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_532,plain,
sdtasdt0(sdtpldt0('#skF_4',sz10),sz10) = sdtpldt0('#skF_4',sz10),
inference(resolution,[status(thm)],[c_501,c_28]) ).
tff(c_5858,plain,
( doDivides0(sdtpldt0('#skF_4',sz10),sdtpldt0('#skF_4',sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0(sdtpldt0('#skF_4',sz10),sz10))
| ~ aNaturalNumber0(sdtpldt0('#skF_4',sz10)) ),
inference(superposition,[status(thm),theory(equality)],[c_532,c_5807]) ).
tff(c_5922,plain,
doDivides0(sdtpldt0('#skF_4',sz10),sdtpldt0('#skF_4',sz10)),
inference(demodulation,[status(thm),theory(equality)],[c_501,c_501,c_532,c_8,c_5858]) ).
tff(c_10804,plain,
! [W0_310,W2_311,W1_312] :
( doDivides0(W0_310,W2_311)
| ~ doDivides0(W0_310,sdtpldt0(W1_312,W2_311))
| ~ doDivides0(W0_310,W1_312)
| ~ aNaturalNumber0(W2_311)
| ~ aNaturalNumber0(W1_312)
| ~ aNaturalNumber0(W0_310) ),
inference(cnfTransformation,[status(thm)],[f_359]) ).
tff(c_10831,plain,
( doDivides0(sdtpldt0('#skF_4',sz10),sz10)
| ~ doDivides0(sdtpldt0('#skF_4',sz10),'#skF_4')
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0(sdtpldt0('#skF_4',sz10)) ),
inference(resolution,[status(thm)],[c_5922,c_10804]) ).
tff(c_10896,plain,
doDivides0(sdtpldt0('#skF_4',sz10),sz10),
inference(demodulation,[status(thm),theory(equality)],[c_501,c_143,c_8,c_8869,c_10831]) ).
tff(c_10898,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5583,c_10896]) ).
tff(c_10900,plain,
'#skF_3'('#skF_4') != sz00,
inference(splitRight,[status(thm)],[c_5765]) ).
tff(c_191,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(resolution,[status(thm)],[c_8,c_181]) ).
tff(c_1990,plain,
( sdtlseqdt0(sz10,sz10)
| ( sz10 = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_191,c_1912]) ).
tff(c_2063,plain,
( sdtlseqdt0(sz10,sz10)
| ( sz10 = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_8,c_1990]) ).
tff(c_2064,plain,
sdtlseqdt0(sz10,sz10),
inference(negUnitSimplification,[status(thm)],[c_6,c_2063]) ).
tff(c_10899,plain,
sdtlseqdt0(sz10,'#skF_3'('#skF_4')),
inference(splitRight,[status(thm)],[c_5765]) ).
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_10905,plain,
( iLess0(sz10,'#skF_3'('#skF_4'))
| ( '#skF_3'('#skF_4') = sz10 )
| ~ aNaturalNumber0('#skF_3'('#skF_4'))
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[c_10899,c_99]) ).
tff(c_10911,plain,
( iLess0(sz10,'#skF_3'('#skF_4'))
| ( '#skF_3'('#skF_4') = sz10 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_5336,c_10905]) ).
tff(c_10965,plain,
'#skF_3'('#skF_4') = sz10,
inference(splitLeft,[status(thm)],[c_10911]) ).
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_10902,plain,
( ( '#skF_3'('#skF_4') = sz10 )
| ~ sdtlseqdt0('#skF_3'('#skF_4'),sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0('#skF_3'('#skF_4')) ),
inference(resolution,[status(thm)],[c_10899,c_66]) ).
tff(c_10908,plain,
( ( '#skF_3'('#skF_4') = sz10 )
| ~ sdtlseqdt0('#skF_3'('#skF_4'),sz10) ),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_8,c_10902]) ).
tff(c_10912,plain,
~ sdtlseqdt0('#skF_3'('#skF_4'),sz10),
inference(splitLeft,[status(thm)],[c_10908]) ).
tff(c_10967,plain,
~ sdtlseqdt0(sz10,sz10),
inference(demodulation,[status(thm),theory(equality)],[c_10965,c_10912]) ).
tff(c_10981,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2064,c_10967]) ).
tff(c_10983,plain,
'#skF_3'('#skF_4') != sz10,
inference(splitRight,[status(thm)],[c_10911]) ).
tff(c_123,plain,
! [W0_89] :
( ( '#skF_3'(W0_89) != W0_89 )
| isPrime0(W0_89)
| ( sz10 = W0_89 )
| ( sz00 = W0_89 )
| ~ aNaturalNumber0(W0_89) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_11997,plain,
! [W0_327,W2_328] :
( doDivides0(W0_327,sdtasdt0(W0_327,W2_328))
| ~ aNaturalNumber0(W2_328)
| ~ aNaturalNumber0(sdtasdt0(W0_327,W2_328))
| ~ aNaturalNumber0(W0_327) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_12114,plain,
( doDivides0('#skF_4','#skF_4')
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0('#skF_4',sz10))
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_193,c_11997]) ).
tff(c_12195,plain,
doDivides0('#skF_4','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_143,c_193,c_8,c_12114]) ).
tff(c_12294,plain,
( ~ isPrime0('#skF_4')
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_12195,c_137]) ).
tff(c_12302,plain,
~ isPrime0('#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_12294]) ).
tff(c_12470,plain,
( ( '#skF_3'('#skF_4') != '#skF_4' )
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_123,c_12302]) ).
tff(c_12476,plain,
( ( '#skF_3'('#skF_4') != '#skF_4' )
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_12470]) ).
tff(c_12477,plain,
'#skF_3'('#skF_4') != '#skF_4',
inference(negUnitSimplification,[status(thm)],[c_141,c_139,c_12476]) ).
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_2212,plain,
! [W1_50,W0_49] :
( iLess0(W1_50,W0_49)
| ( W1_50 = W0_49 )
| sdtlseqdt0(W0_49,W1_50)
| ~ aNaturalNumber0(W1_50)
| ~ aNaturalNumber0(W0_49) ),
inference(resolution,[status(thm)],[c_70,c_2143]) ).
tff(c_5452,plain,
sdtasdt0('#skF_3'('#skF_4'),sz10) = '#skF_3'('#skF_4'),
inference(resolution,[status(thm)],[c_5336,c_28]) ).
tff(c_12033,plain,
( doDivides0('#skF_3'('#skF_4'),'#skF_3'('#skF_4'))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0('#skF_3'('#skF_4'),sz10))
| ~ aNaturalNumber0('#skF_3'('#skF_4')) ),
inference(superposition,[status(thm),theory(equality)],[c_5452,c_11997]) ).
tff(c_12141,plain,
doDivides0('#skF_3'('#skF_4'),'#skF_3'('#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_5336,c_5452,c_8,c_12033]) ).
tff(c_13301,plain,
! [W0_348,W2_349,W1_350] :
( doDivides0(W0_348,W2_349)
| ~ doDivides0(W1_350,W2_349)
| ~ doDivides0(W0_348,W1_350)
| ~ aNaturalNumber0(W2_349)
| ~ aNaturalNumber0(W1_350)
| ~ aNaturalNumber0(W0_348) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_96840,plain,
! [W0_831,W0_832] :
( doDivides0(W0_831,W0_832)
| ~ doDivides0(W0_831,'#skF_3'(W0_832))
| ~ aNaturalNumber0('#skF_3'(W0_832))
| ~ aNaturalNumber0(W0_831)
| isPrime0(W0_832)
| ( sz10 = W0_832 )
| ( sz00 = W0_832 )
| ~ aNaturalNumber0(W0_832) ),
inference(resolution,[status(thm)],[c_127,c_13301]) ).
tff(c_96852,plain,
( doDivides0('#skF_3'('#skF_4'),'#skF_4')
| ~ aNaturalNumber0('#skF_3'('#skF_4'))
| isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_12141,c_96840]) ).
tff(c_96878,plain,
( doDivides0('#skF_3'('#skF_4'),'#skF_4')
| isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_5336,c_96852]) ).
tff(c_96879,plain,
doDivides0('#skF_3'('#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_141,c_139,c_12302,c_96878]) ).
tff(c_1984,plain,
( sdtlseqdt0('#skF_4','#skF_4')
| ( sz10 = sz00 )
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_193,c_1912]) ).
tff(c_2057,plain,
( sdtlseqdt0('#skF_4','#skF_4')
| ( sz10 = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_143,c_1984]) ).
tff(c_2058,plain,
sdtlseqdt0('#skF_4','#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_6,c_2057]) ).
tff(c_12745,plain,
! [W0_337,W2_338,W1_339] :
( sdtlseqdt0(W0_337,W2_338)
| ~ sdtlseqdt0(W1_339,W2_338)
| ~ sdtlseqdt0(W0_337,W1_339)
| ~ aNaturalNumber0(W2_338)
| ~ aNaturalNumber0(W1_339)
| ~ aNaturalNumber0(W0_337) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_51254,plain,
! [W0_641,W0_642,W1_643] :
( sdtlseqdt0(W0_641,W0_642)
| ~ sdtlseqdt0(W0_641,W1_643)
| ~ aNaturalNumber0(W0_641)
| sdtlseqdt0(W0_642,W1_643)
| ~ aNaturalNumber0(W1_643)
| ~ aNaturalNumber0(W0_642) ),
inference(resolution,[status(thm)],[c_70,c_12745]) ).
tff(c_51376,plain,
! [W0_642] :
( sdtlseqdt0('#skF_4',W0_642)
| sdtlseqdt0(W0_642,'#skF_4')
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0(W0_642) ),
inference(resolution,[status(thm)],[c_2058,c_51254]) ).
tff(c_51700,plain,
! [W0_645] :
( sdtlseqdt0('#skF_4',W0_645)
| sdtlseqdt0(W0_645,'#skF_4')
| ~ aNaturalNumber0(W0_645) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_51376]) ).
tff(c_5364,plain,
! [W1_84,W0_83] :
( ( W1_84 = W0_83 )
| ~ sdtlseqdt0(W1_84,W0_83)
| ( sz00 = W1_84 )
| ~ doDivides0(W0_83,W1_84)
| ~ aNaturalNumber0(W1_84)
| ~ aNaturalNumber0(W0_83) ),
inference(resolution,[status(thm)],[c_119,c_5337]) ).
tff(c_51706,plain,
! [W0_645] :
( ( W0_645 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ doDivides0(W0_645,'#skF_4')
| ~ aNaturalNumber0('#skF_4')
| sdtlseqdt0(W0_645,'#skF_4')
| ~ aNaturalNumber0(W0_645) ),
inference(resolution,[status(thm)],[c_51700,c_5364]) ).
tff(c_51751,plain,
! [W0_645] :
( ( W0_645 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ doDivides0(W0_645,'#skF_4')
| sdtlseqdt0(W0_645,'#skF_4')
| ~ aNaturalNumber0(W0_645) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_51706]) ).
tff(c_51752,plain,
! [W0_645] :
( ( W0_645 = '#skF_4' )
| ~ doDivides0(W0_645,'#skF_4')
| sdtlseqdt0(W0_645,'#skF_4')
| ~ aNaturalNumber0(W0_645) ),
inference(negUnitSimplification,[status(thm)],[c_141,c_51751]) ).
tff(c_700,plain,
! [W1_125,W0_126] :
( ( sdtasdt0(W1_125,W0_126) = sdtasdt0(W0_126,W1_125) )
| ~ aNaturalNumber0(W1_125)
| ~ aNaturalNumber0(W0_126) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_721,plain,
! [W0_126] :
( ( sdtasdt0(W0_126,'#skF_4') = sdtasdt0('#skF_4',W0_126) )
| ~ aNaturalNumber0(W0_126) ),
inference(resolution,[status(thm)],[c_143,c_700]) ).
tff(c_5440,plain,
sdtasdt0('#skF_3'('#skF_4'),'#skF_4') = sdtasdt0('#skF_4','#skF_3'('#skF_4')),
inference(resolution,[status(thm)],[c_5336,c_721]) ).
tff(c_14432,plain,
! [W0_362,W1_363,W2_364] :
( ( sdtasdt0(sdtasdt0(W0_362,W1_363),W2_364) = sdtasdt0(W0_362,sdtasdt0(W1_363,W2_364)) )
| ~ aNaturalNumber0(W2_364)
| ~ aNaturalNumber0(W1_363)
| ~ aNaturalNumber0(W0_362) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
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_72622,plain,
! [W0_749,W1_750,W2_751] :
( aNaturalNumber0(sdtasdt0(W0_749,sdtasdt0(W1_750,W2_751)))
| ~ aNaturalNumber0(W2_751)
| ~ aNaturalNumber0(sdtasdt0(W0_749,W1_750))
| ~ aNaturalNumber0(W2_751)
| ~ aNaturalNumber0(W1_750)
| ~ aNaturalNumber0(W0_749) ),
inference(superposition,[status(thm),theory(equality)],[c_14432,c_12]) ).
tff(c_73181,plain,
! [W0_749] :
( aNaturalNumber0(sdtasdt0(W0_749,'#skF_4'))
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0(sdtasdt0(W0_749,sz10))
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(W0_749) ),
inference(superposition,[status(thm),theory(equality)],[c_262,c_72622]) ).
tff(c_83475,plain,
! [W0_790] :
( aNaturalNumber0(sdtasdt0(W0_790,'#skF_4'))
| ~ aNaturalNumber0(sdtasdt0(W0_790,sz10))
| ~ aNaturalNumber0(W0_790) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_143,c_143,c_73181]) ).
tff(c_83577,plain,
( aNaturalNumber0(sdtasdt0('#skF_4','#skF_4'))
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_193,c_83475]) ).
tff(c_83627,plain,
aNaturalNumber0(sdtasdt0('#skF_4','#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_143,c_83577]) ).
tff(c_83816,plain,
sdtasdt0(sz10,sdtasdt0('#skF_4','#skF_4')) = sdtasdt0('#skF_4','#skF_4'),
inference(resolution,[status(thm)],[c_83627,c_26]) ).
tff(c_42,plain,
! [W2_29,W0_25,W1_28] :
( ( sdtasdt0(W2_29,W0_25) != sdtasdt0(W1_28,W0_25) )
| ( W2_29 = W1_28 )
| ~ aNaturalNumber0(W2_29)
| ~ aNaturalNumber0(W1_28)
| ( sz00 = W0_25 )
| ~ aNaturalNumber0(W0_25) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_148026,plain,
! [W2_1043,W2_1044,W0_1045,W1_1046] :
( ( sdtasdt0(W2_1043,W2_1044) != sdtasdt0(W0_1045,sdtasdt0(W1_1046,W2_1044)) )
| ( sdtasdt0(W0_1045,W1_1046) = W2_1043 )
| ~ aNaturalNumber0(W2_1043)
| ~ aNaturalNumber0(sdtasdt0(W0_1045,W1_1046))
| ( sz00 = W2_1044 )
| ~ aNaturalNumber0(W2_1044)
| ~ aNaturalNumber0(W2_1044)
| ~ aNaturalNumber0(W1_1046)
| ~ aNaturalNumber0(W0_1045) ),
inference(superposition,[status(thm),theory(equality)],[c_14432,c_42]) ).
tff(c_148158,plain,
! [W2_1043] :
( ( sdtasdt0(W2_1043,'#skF_4') != sdtasdt0('#skF_4','#skF_4') )
| ( sdtasdt0(sz10,'#skF_4') = W2_1043 )
| ~ aNaturalNumber0(W2_1043)
| ~ aNaturalNumber0(sdtasdt0(sz10,'#skF_4'))
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_83816,c_148026]) ).
tff(c_148812,plain,
! [W2_1043] :
( ( sdtasdt0(W2_1043,'#skF_4') != sdtasdt0('#skF_4','#skF_4') )
| ( W2_1043 = '#skF_4' )
| ~ aNaturalNumber0(W2_1043)
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_143,c_143,c_143,c_143,c_262,c_262,c_148158]) ).
tff(c_151181,plain,
! [W2_1051] :
( ( sdtasdt0(W2_1051,'#skF_4') != sdtasdt0('#skF_4','#skF_4') )
| ( W2_1051 = '#skF_4' )
| ~ aNaturalNumber0(W2_1051) ),
inference(negUnitSimplification,[status(thm)],[c_141,c_148812]) ).
tff(c_151352,plain,
( ( sdtasdt0('#skF_3'('#skF_4'),'#skF_4') != sdtasdt0('#skF_4','#skF_4') )
| ( '#skF_3'('#skF_4') = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_5336,c_151181]) ).
tff(c_151475,plain,
( ( sdtasdt0('#skF_4','#skF_3'('#skF_4')) != sdtasdt0('#skF_4','#skF_4') )
| ( '#skF_3'('#skF_4') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5440,c_151352]) ).
tff(c_151476,plain,
sdtasdt0('#skF_4','#skF_3'('#skF_4')) != sdtasdt0('#skF_4','#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_12477,c_151475]) ).
tff(c_11021,plain,
( aNaturalNumber0(sdtasdt0('#skF_4','#skF_3'('#skF_4')))
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0('#skF_3'('#skF_4')) ),
inference(superposition,[status(thm),theory(equality)],[c_5440,c_12]) ).
tff(c_11035,plain,
aNaturalNumber0(sdtasdt0('#skF_4','#skF_3'('#skF_4'))),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_143,c_11021]) ).
tff(c_19152,plain,
! [W1_416,W0_417,W2_418] :
( sdtlseqdt0(sdtasdt0(W1_416,W0_417),sdtasdt0(W2_418,W0_417))
| ~ sdtlseqdt0(W1_416,W2_418)
| ( W2_418 = W1_416 )
| ( sz00 = W0_417 )
| ~ aNaturalNumber0(W2_418)
| ~ aNaturalNumber0(W1_416)
| ~ aNaturalNumber0(W0_417) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_19228,plain,
! [W2_418] :
( sdtlseqdt0(sdtasdt0('#skF_4','#skF_3'('#skF_4')),sdtasdt0(W2_418,'#skF_4'))
| ~ sdtlseqdt0('#skF_3'('#skF_4'),W2_418)
| ( W2_418 = '#skF_3'('#skF_4') )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0(W2_418)
| ~ aNaturalNumber0('#skF_3'('#skF_4'))
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_5440,c_19152]) ).
tff(c_19482,plain,
! [W2_418] :
( sdtlseqdt0(sdtasdt0('#skF_4','#skF_3'('#skF_4')),sdtasdt0(W2_418,'#skF_4'))
| ~ sdtlseqdt0('#skF_3'('#skF_4'),W2_418)
| ( W2_418 = '#skF_3'('#skF_4') )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0(W2_418) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_5336,c_19228]) ).
tff(c_19483,plain,
! [W2_418] :
( sdtlseqdt0(sdtasdt0('#skF_4','#skF_3'('#skF_4')),sdtasdt0(W2_418,'#skF_4'))
| ~ sdtlseqdt0('#skF_3'('#skF_4'),W2_418)
| ( W2_418 = '#skF_3'('#skF_4') )
| ~ aNaturalNumber0(W2_418) ),
inference(negUnitSimplification,[status(thm)],[c_141,c_19482]) ).
tff(c_18475,plain,
! [W0_410,W1_411,W2_412] :
( sdtlseqdt0(sdtasdt0(W0_410,W1_411),sdtasdt0(W0_410,W2_412))
| ~ sdtlseqdt0(W1_411,W2_412)
| ( W2_412 = W1_411 )
| ( sz00 = W0_410 )
| ~ aNaturalNumber0(W2_412)
| ~ aNaturalNumber0(W1_411)
| ~ aNaturalNumber0(W0_410) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_280595,plain,
! [W0_1352,W2_1353,W1_1354] :
( ( sdtasdt0(W0_1352,W2_1353) = sdtasdt0(W0_1352,W1_1354) )
| ~ sdtlseqdt0(sdtasdt0(W0_1352,W2_1353),sdtasdt0(W0_1352,W1_1354))
| ~ aNaturalNumber0(sdtasdt0(W0_1352,W1_1354))
| ~ aNaturalNumber0(sdtasdt0(W0_1352,W2_1353))
| ~ sdtlseqdt0(W1_1354,W2_1353)
| ( W2_1353 = W1_1354 )
| ( sz00 = W0_1352 )
| ~ aNaturalNumber0(W2_1353)
| ~ aNaturalNumber0(W1_1354)
| ~ aNaturalNumber0(W0_1352) ),
inference(resolution,[status(thm)],[c_18475,c_66]) ).
tff(c_281555,plain,
( ( sdtasdt0('#skF_4','#skF_3'('#skF_4')) = sdtasdt0('#skF_4','#skF_4') )
| ~ aNaturalNumber0(sdtasdt0('#skF_4','#skF_4'))
| ~ aNaturalNumber0(sdtasdt0('#skF_4','#skF_3'('#skF_4')))
| ~ sdtlseqdt0('#skF_4','#skF_3'('#skF_4'))
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_3'('#skF_4'))
| ~ sdtlseqdt0('#skF_3'('#skF_4'),'#skF_4')
| ( '#skF_3'('#skF_4') = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_19483,c_280595]) ).
tff(c_282752,plain,
( ( sdtasdt0('#skF_4','#skF_3'('#skF_4')) = sdtasdt0('#skF_4','#skF_4') )
| ~ sdtlseqdt0('#skF_4','#skF_3'('#skF_4'))
| ( sz00 = '#skF_4' )
| ~ sdtlseqdt0('#skF_3'('#skF_4'),'#skF_4')
| ( '#skF_3'('#skF_4') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_5336,c_11035,c_83627,c_281555]) ).
tff(c_282753,plain,
( ~ sdtlseqdt0('#skF_4','#skF_3'('#skF_4'))
| ~ sdtlseqdt0('#skF_3'('#skF_4'),'#skF_4') ),
inference(negUnitSimplification,[status(thm)],[c_12477,c_141,c_151476,c_282752]) ).
tff(c_283216,plain,
~ sdtlseqdt0('#skF_3'('#skF_4'),'#skF_4'),
inference(splitLeft,[status(thm)],[c_282753]) ).
tff(c_283222,plain,
( ( '#skF_3'('#skF_4') = '#skF_4' )
| ~ doDivides0('#skF_3'('#skF_4'),'#skF_4')
| ~ aNaturalNumber0('#skF_3'('#skF_4')) ),
inference(resolution,[status(thm)],[c_51752,c_283216]) ).
tff(c_283255,plain,
'#skF_3'('#skF_4') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_96879,c_283222]) ).
tff(c_283257,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12477,c_283255]) ).
tff(c_283258,plain,
~ sdtlseqdt0('#skF_4','#skF_3'('#skF_4')),
inference(splitRight,[status(thm)],[c_282753]) ).
tff(c_283281,plain,
( iLess0('#skF_3'('#skF_4'),'#skF_4')
| ( '#skF_3'('#skF_4') = '#skF_4' )
| ~ aNaturalNumber0('#skF_3'('#skF_4'))
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_2212,c_283258]) ).
tff(c_283308,plain,
( iLess0('#skF_3'('#skF_4'),'#skF_4')
| ( '#skF_3'('#skF_4') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_5336,c_283281]) ).
tff(c_283309,plain,
iLess0('#skF_3'('#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_12477,c_283308]) ).
tff(c_145,plain,
! [W1_97] :
( isPrime0('#skF_5'(W1_97))
| ~ iLess0(W1_97,'#skF_4')
| ( sz10 = W1_97 )
| ( sz00 = W1_97 )
| ~ aNaturalNumber0(W1_97) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_149,plain,
! [W1_97] :
( aNaturalNumber0('#skF_5'(W1_97))
| ~ iLess0(W1_97,'#skF_4')
| ( sz10 = W1_97 )
| ( sz00 = W1_97 )
| ~ aNaturalNumber0(W1_97) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_147,plain,
! [W1_97] :
( doDivides0('#skF_5'(W1_97),W1_97)
| ~ iLess0(W1_97,'#skF_4')
| ( sz10 = W1_97 )
| ( sz00 = W1_97 )
| ~ aNaturalNumber0(W1_97) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_283259,plain,
sdtlseqdt0('#skF_3'('#skF_4'),'#skF_4'),
inference(splitRight,[status(thm)],[c_282753]) ).
tff(c_68,plain,
! [W0_46,W2_48,W1_47] :
( sdtlseqdt0(W0_46,W2_48)
| ~ sdtlseqdt0(W1_47,W2_48)
| ~ sdtlseqdt0(W0_46,W1_47)
| ~ aNaturalNumber0(W2_48)
| ~ aNaturalNumber0(W1_47)
| ~ aNaturalNumber0(W0_46) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_283322,plain,
! [W0_46] :
( sdtlseqdt0(W0_46,'#skF_4')
| ~ sdtlseqdt0(W0_46,'#skF_3'('#skF_4'))
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0('#skF_3'('#skF_4'))
| ~ aNaturalNumber0(W0_46) ),
inference(resolution,[status(thm)],[c_283259,c_68]) ).
tff(c_283470,plain,
! [W0_1356] :
( sdtlseqdt0(W0_1356,'#skF_4')
| ~ sdtlseqdt0(W0_1356,'#skF_3'('#skF_4'))
| ~ aNaturalNumber0(W0_1356) ),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_143,c_283322]) ).
tff(c_283575,plain,
! [W0_83] :
( sdtlseqdt0(W0_83,'#skF_4')
| ( '#skF_3'('#skF_4') = sz00 )
| ~ doDivides0(W0_83,'#skF_3'('#skF_4'))
| ~ aNaturalNumber0('#skF_3'('#skF_4'))
| ~ aNaturalNumber0(W0_83) ),
inference(resolution,[status(thm)],[c_119,c_283470]) ).
tff(c_283664,plain,
! [W0_83] :
( sdtlseqdt0(W0_83,'#skF_4')
| ( '#skF_3'('#skF_4') = sz00 )
| ~ doDivides0(W0_83,'#skF_3'('#skF_4'))
| ~ aNaturalNumber0(W0_83) ),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_283575]) ).
tff(c_286052,plain,
! [W0_1360] :
( sdtlseqdt0(W0_1360,'#skF_4')
| ~ doDivides0(W0_1360,'#skF_3'('#skF_4'))
| ~ aNaturalNumber0(W0_1360) ),
inference(negUnitSimplification,[status(thm)],[c_10900,c_283664]) ).
tff(c_286072,plain,
( sdtlseqdt0('#skF_5'('#skF_3'('#skF_4')),'#skF_4')
| ~ aNaturalNumber0('#skF_5'('#skF_3'('#skF_4')))
| ~ iLess0('#skF_3'('#skF_4'),'#skF_4')
| ( '#skF_3'('#skF_4') = sz10 )
| ( '#skF_3'('#skF_4') = sz00 )
| ~ aNaturalNumber0('#skF_3'('#skF_4')) ),
inference(resolution,[status(thm)],[c_147,c_286052]) ).
tff(c_286089,plain,
( sdtlseqdt0('#skF_5'('#skF_3'('#skF_4')),'#skF_4')
| ~ aNaturalNumber0('#skF_5'('#skF_3'('#skF_4')))
| ( '#skF_3'('#skF_4') = sz10 )
| ( '#skF_3'('#skF_4') = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_283309,c_286072]) ).
tff(c_286090,plain,
( sdtlseqdt0('#skF_5'('#skF_3'('#skF_4')),'#skF_4')
| ~ aNaturalNumber0('#skF_5'('#skF_3'('#skF_4'))) ),
inference(negUnitSimplification,[status(thm)],[c_10900,c_10983,c_286089]) ).
tff(c_286742,plain,
~ aNaturalNumber0('#skF_5'('#skF_3'('#skF_4'))),
inference(splitLeft,[status(thm)],[c_286090]) ).
tff(c_286745,plain,
( ~ iLess0('#skF_3'('#skF_4'),'#skF_4')
| ( '#skF_3'('#skF_4') = sz10 )
| ( '#skF_3'('#skF_4') = sz00 )
| ~ aNaturalNumber0('#skF_3'('#skF_4')) ),
inference(resolution,[status(thm)],[c_149,c_286742]) ).
tff(c_286748,plain,
( ( '#skF_3'('#skF_4') = sz10 )
| ( '#skF_3'('#skF_4') = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_283309,c_286745]) ).
tff(c_286750,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10900,c_10983,c_286748]) ).
tff(c_286752,plain,
aNaturalNumber0('#skF_5'('#skF_3'('#skF_4'))),
inference(splitRight,[status(thm)],[c_286090]) ).
tff(c_286931,plain,
sdtasdt0('#skF_5'('#skF_3'('#skF_4')),sz10) = '#skF_5'('#skF_3'('#skF_4')),
inference(resolution,[status(thm)],[c_286752,c_28]) ).
tff(c_101,plain,
! [W0_65,W2_69] :
( doDivides0(W0_65,sdtasdt0(W0_65,W2_69))
| ~ aNaturalNumber0(W2_69)
| ~ aNaturalNumber0(sdtasdt0(W0_65,W2_69))
| ~ aNaturalNumber0(W0_65) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_292591,plain,
( doDivides0('#skF_5'('#skF_3'('#skF_4')),'#skF_5'('#skF_3'('#skF_4')))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0('#skF_5'('#skF_3'('#skF_4')),sz10))
| ~ aNaturalNumber0('#skF_5'('#skF_3'('#skF_4'))) ),
inference(superposition,[status(thm),theory(equality)],[c_286931,c_101]) ).
tff(c_292832,plain,
doDivides0('#skF_5'('#skF_3'('#skF_4')),'#skF_5'('#skF_3'('#skF_4'))),
inference(demodulation,[status(thm),theory(equality)],[c_286752,c_286752,c_286931,c_8,c_292591]) ).
tff(c_13405,plain,
! [W0_348,W1_97] :
( doDivides0(W0_348,W1_97)
| ~ doDivides0(W0_348,'#skF_5'(W1_97))
| ~ aNaturalNumber0('#skF_5'(W1_97))
| ~ aNaturalNumber0(W0_348)
| ~ iLess0(W1_97,'#skF_4')
| ( sz10 = W1_97 )
| ( sz00 = W1_97 )
| ~ aNaturalNumber0(W1_97) ),
inference(resolution,[status(thm)],[c_147,c_13301]) ).
tff(c_292867,plain,
( doDivides0('#skF_5'('#skF_3'('#skF_4')),'#skF_3'('#skF_4'))
| ~ aNaturalNumber0('#skF_5'('#skF_3'('#skF_4')))
| ~ iLess0('#skF_3'('#skF_4'),'#skF_4')
| ( '#skF_3'('#skF_4') = sz10 )
| ( '#skF_3'('#skF_4') = sz00 )
| ~ aNaturalNumber0('#skF_3'('#skF_4')) ),
inference(resolution,[status(thm)],[c_292832,c_13405]) ).
tff(c_292878,plain,
( doDivides0('#skF_5'('#skF_3'('#skF_4')),'#skF_3'('#skF_4'))
| ( '#skF_3'('#skF_4') = sz10 )
| ( '#skF_3'('#skF_4') = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_283309,c_286752,c_292867]) ).
tff(c_292879,plain,
doDivides0('#skF_5'('#skF_3'('#skF_4')),'#skF_3'('#skF_4')),
inference(negUnitSimplification,[status(thm)],[c_10900,c_10983,c_292878]) ).
tff(c_13404,plain,
! [W0_348,W0_89] :
( doDivides0(W0_348,W0_89)
| ~ doDivides0(W0_348,'#skF_3'(W0_89))
| ~ aNaturalNumber0('#skF_3'(W0_89))
| ~ aNaturalNumber0(W0_348)
| isPrime0(W0_89)
| ( sz10 = W0_89 )
| ( sz00 = W0_89 )
| ~ aNaturalNumber0(W0_89) ),
inference(resolution,[status(thm)],[c_127,c_13301]) ).
tff(c_292897,plain,
( doDivides0('#skF_5'('#skF_3'('#skF_4')),'#skF_4')
| ~ aNaturalNumber0('#skF_3'('#skF_4'))
| ~ aNaturalNumber0('#skF_5'('#skF_3'('#skF_4')))
| isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_292879,c_13404]) ).
tff(c_292917,plain,
( doDivides0('#skF_5'('#skF_3'('#skF_4')),'#skF_4')
| isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_286752,c_5336,c_292897]) ).
tff(c_292918,plain,
doDivides0('#skF_5'('#skF_3'('#skF_4')),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_141,c_139,c_12302,c_292917]) ).
tff(c_292941,plain,
( ~ isPrime0('#skF_5'('#skF_3'('#skF_4')))
| ~ aNaturalNumber0('#skF_5'('#skF_3'('#skF_4'))) ),
inference(resolution,[status(thm)],[c_292918,c_137]) ).
tff(c_292959,plain,
~ isPrime0('#skF_5'('#skF_3'('#skF_4'))),
inference(demodulation,[status(thm),theory(equality)],[c_286752,c_292941]) ).
tff(c_292968,plain,
( ~ iLess0('#skF_3'('#skF_4'),'#skF_4')
| ( '#skF_3'('#skF_4') = sz10 )
| ( '#skF_3'('#skF_4') = sz00 )
| ~ aNaturalNumber0('#skF_3'('#skF_4')) ),
inference(resolution,[status(thm)],[c_145,c_292959]) ).
tff(c_292977,plain,
( ( '#skF_3'('#skF_4') = sz10 )
| ( '#skF_3'('#skF_4') = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_283309,c_292968]) ).
tff(c_292979,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10900,c_10983,c_292977]) ).
tff(c_292980,plain,
'#skF_3'('#skF_4') = sz10,
inference(splitRight,[status(thm)],[c_10908]) ).
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_293005,plain,
( doDivides0(sz10,'#skF_4')
| isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_292980,c_127]) ).
tff(c_293012,plain,
( doDivides0(sz10,'#skF_4')
| isPrime0('#skF_4')
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_293005]) ).
tff(c_293013,plain,
( doDivides0(sz10,'#skF_4')
| isPrime0('#skF_4') ),
inference(negUnitSimplification,[status(thm)],[c_141,c_139,c_293012]) ).
tff(c_293019,plain,
isPrime0('#skF_4'),
inference(splitLeft,[status(thm)],[c_293013]) ).
tff(c_293020,plain,
! [W0_1365,W2_1366] :
( doDivides0(W0_1365,sdtasdt0(W0_1365,W2_1366))
| ~ aNaturalNumber0(W2_1366)
| ~ aNaturalNumber0(sdtasdt0(W0_1365,W2_1366))
| ~ aNaturalNumber0(W0_1365) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_293095,plain,
( doDivides0('#skF_4','#skF_4')
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0('#skF_4',sz10))
| ~ aNaturalNumber0('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_193,c_293020]) ).
tff(c_293151,plain,
doDivides0('#skF_4','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_143,c_193,c_8,c_293095]) ).
tff(c_293210,plain,
( ~ isPrime0('#skF_4')
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_293151,c_137]) ).
tff(c_293214,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_143,c_293019,c_293210]) ).
tff(c_293216,plain,
~ isPrime0('#skF_4'),
inference(splitRight,[status(thm)],[c_293013]) ).
tff(c_293222,plain,
( ( '#skF_3'('#skF_4') != sz10 )
| ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' )
| ~ aNaturalNumber0('#skF_4') ),
inference(resolution,[status(thm)],[c_125,c_293216]) ).
tff(c_293229,plain,
( ( sz10 = '#skF_4' )
| ( sz00 = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_292980,c_293222]) ).
tff(c_293231,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_141,c_139,c_293229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM481+1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.37 % Computer : n024.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Tue Apr 8 12:50:51 EDT 2025
% 0.13/0.37 % CPUTime :
% 181.68/153.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 181.80/153.84
% 181.80/153.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------