%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM483+3 : 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/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 : n002.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 07:56:05 PM UTC 2025
% Result : Theorem 19.18s 7.50s
% Output : CNFRefutation 19.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 192 ( 75 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 198 ( 72 ~; 82 |; 31 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 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 : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 34 !; 7 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xk > sz10 > sz00 > #skF_9 > #skF_5 > #skF_4 > #skF_8 > #skF_7 > #skF_6 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff(xk,type,
xk: $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(sz10,type,
sz10: $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz00,type,
sz00: $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff('#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_6',type,
'#skF_6': $i ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
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_467,hypothesis,
~ ( ! [W0] :
( ( aNaturalNumber0(W0)
& ? [W1] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) )
& doDivides0(W0,xk) )
=> ( ( W0 = sz10 )
| ( W0 = xk ) ) )
| isPrime0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1725) ).
tff(f_499,negated_conjecture,
~ ? [W0] :
( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xk) )
& ( ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1] :
( ( aNaturalNumber0(W1)
& ? [W2] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) )
| isPrime0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(f_404,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
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_451,hypothesis,
( ( xk != sz00 )
& ( xk != sz10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716_04) ).
tff(f_296,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
tff(f_446,hypothesis,
! [W0] :
( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ( iLess0(W0,xk)
=> ? [W1] :
( aNaturalNumber0(W1)
& ? [W2] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0)
& ( W1 != sz00 )
& ( W1 != sz10 )
& ! [W2] :
( ( aNaturalNumber0(W2)
& ( ? [W3] :
( aNaturalNumber0(W3)
& ( W1 = sdtasdt0(W2,W3) ) )
| doDivides0(W2,W1) ) )
=> ( ( W2 = sz10 )
| ( W2 = W1 ) ) )
& isPrime0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1700) ).
tff(f_335,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W1,W2) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
tff(c_163,plain,
xk != '#skF_6',
inference(cnfTransformation,[status(thm)],[f_467]) ).
tff(c_165,plain,
sz10 != '#skF_6',
inference(cnfTransformation,[status(thm)],[f_467]) ).
tff(c_173,plain,
aNaturalNumber0('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_467]) ).
tff(c_171,plain,
aNaturalNumber0('#skF_7'),
inference(cnfTransformation,[status(thm)],[f_467]) ).
tff(c_169,plain,
sdtasdt0('#skF_6','#skF_7') = xk,
inference(cnfTransformation,[status(thm)],[f_467]) ).
tff(c_1195,plain,
! [W0_147,W1_148] :
( ( sdtasdt0(W0_147,W1_148) != xk )
| ~ aNaturalNumber0(W1_148)
| aNaturalNumber0('#skF_9'(W0_147))
| ( sz10 = W0_147 )
| ( sz00 = W0_147 )
| ~ aNaturalNumber0(W0_147) ),
inference(cnfTransformation,[status(thm)],[f_499]) ).
tff(c_1243,plain,
( ~ aNaturalNumber0('#skF_7')
| aNaturalNumber0('#skF_9'('#skF_6'))
| ( sz10 = '#skF_6' )
| ( sz00 = '#skF_6' )
| ~ aNaturalNumber0('#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_169,c_1195]) ).
tff(c_1315,plain,
( aNaturalNumber0('#skF_9'('#skF_6'))
| ( sz10 = '#skF_6' )
| ( sz00 = '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_173,c_171,c_1243]) ).
tff(c_1316,plain,
( aNaturalNumber0('#skF_9'('#skF_6'))
| ( sz00 = '#skF_6' ) ),
inference(negUnitSimplification,[status(thm)],[c_165,c_1315]) ).
tff(c_1359,plain,
sz00 = '#skF_6',
inference(splitLeft,[status(thm)],[c_1316]) ).
tff(c_526,plain,
! [W0_130] :
( ( sdtasdt0(W0_130,sz00) = sz00 )
| ~ aNaturalNumber0(W0_130) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_555,plain,
sdtasdt0('#skF_7',sz00) = sz00,
inference(resolution,[status(thm)],[c_171,c_526]) ).
tff(c_1370,plain,
sdtasdt0('#skF_7','#skF_6') = '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_1359,c_1359,c_555]) ).
tff(c_771,plain,
! [W1_137,W0_138] :
( ( sdtasdt0(W1_137,W0_138) = sdtasdt0(W0_138,W1_137) )
| ~ aNaturalNumber0(W1_137)
| ~ aNaturalNumber0(W0_138) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1131,plain,
! [W0_146] :
( ( sdtasdt0(W0_146,'#skF_6') = sdtasdt0('#skF_6',W0_146) )
| ~ aNaturalNumber0(W0_146) ),
inference(resolution,[status(thm)],[c_173,c_771]) ).
tff(c_1161,plain,
sdtasdt0('#skF_7','#skF_6') = sdtasdt0('#skF_6','#skF_7'),
inference(resolution,[status(thm)],[c_171,c_1131]) ).
tff(c_1178,plain,
sdtasdt0('#skF_7','#skF_6') = xk,
inference(demodulation,[status(thm),theory(equality)],[c_169,c_1161]) ).
tff(c_1418,plain,
xk = '#skF_6',
inference(demodulation,[status(thm),theory(equality)],[c_1370,c_1178]) ).
tff(c_1420,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_163,c_1418]) ).
tff(c_1422,plain,
sz00 != '#skF_6',
inference(splitRight,[status(thm)],[c_1316]) ).
tff(c_137,plain,
aNaturalNumber0(xk),
inference(cnfTransformation,[status(thm)],[f_404]) ).
tff(c_2520,plain,
! [W1_163,W0_164] :
( sdtlseqdt0(W1_163,sdtasdt0(W1_163,W0_164))
| ( sz00 = W0_164 )
| ~ aNaturalNumber0(W1_163)
| ~ aNaturalNumber0(W0_164) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_2628,plain,
( sdtlseqdt0('#skF_6',xk)
| ( sz00 = '#skF_7' )
| ~ aNaturalNumber0('#skF_6')
| ~ aNaturalNumber0('#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_169,c_2520]) ).
tff(c_2722,plain,
( sdtlseqdt0('#skF_6',xk)
| ( sz00 = '#skF_7' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_171,c_173,c_2628]) ).
tff(c_3149,plain,
sz00 = '#skF_7',
inference(splitLeft,[status(thm)],[c_2722]) ).
tff(c_159,plain,
xk != sz00,
inference(cnfTransformation,[status(thm)],[f_451]) ).
tff(c_3206,plain,
xk != '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_3149,c_159]) ).
tff(c_556,plain,
sdtasdt0('#skF_6',sz00) = sz00,
inference(resolution,[status(thm)],[c_173,c_526]) ).
tff(c_3181,plain,
sdtasdt0('#skF_6','#skF_7') = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_3149,c_3149,c_556]) ).
tff(c_3278,plain,
xk = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_3181,c_169]) ).
tff(c_3280,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3206,c_3278]) ).
tff(c_3281,plain,
sdtlseqdt0('#skF_6',xk),
inference(splitRight,[status(thm)],[c_2722]) ).
tff(c_6014,plain,
! [W0_201,W1_202] :
( iLess0(W0_201,W1_202)
| ~ sdtlseqdt0(W0_201,W1_202)
| ( W1_202 = W0_201 )
| ~ aNaturalNumber0(W1_202)
| ~ aNaturalNumber0(W0_201) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_6053,plain,
( iLess0('#skF_6',xk)
| ( xk = '#skF_6' )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0('#skF_6') ),
inference(resolution,[status(thm)],[c_3281,c_6014]) ).
tff(c_6138,plain,
( iLess0('#skF_6',xk)
| ( xk = '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_173,c_137,c_6053]) ).
tff(c_6139,plain,
iLess0('#skF_6',xk),
inference(negUnitSimplification,[status(thm)],[c_163,c_6138]) ).
tff(c_139,plain,
! [W0_93] :
( isPrime0('#skF_4'(W0_93))
| ~ iLess0(W0_93,xk)
| ( sz10 = W0_93 )
| ( sz00 = W0_93 )
| ~ aNaturalNumber0(W0_93) ),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_151,plain,
! [W0_93] :
( aNaturalNumber0('#skF_4'(W0_93))
| ~ iLess0(W0_93,xk)
| ( sz10 = W0_93 )
| ( sz00 = W0_93 )
| ~ aNaturalNumber0(W0_93) ),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_145,plain,
! [W0_93] :
( doDivides0('#skF_4'(W0_93),W0_93)
| ~ iLess0(W0_93,xk)
| ( sz10 = W0_93 )
| ( sz00 = W0_93 )
| ~ aNaturalNumber0(W0_93) ),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_167,plain,
doDivides0('#skF_6',xk),
inference(cnfTransformation,[status(thm)],[f_467]) ).
tff(c_27294,plain,
! [W0_385,W2_386,W1_387] :
( doDivides0(W0_385,W2_386)
| ~ doDivides0(W1_387,W2_386)
| ~ doDivides0(W0_385,W1_387)
| ~ aNaturalNumber0(W2_386)
| ~ aNaturalNumber0(W1_387)
| ~ aNaturalNumber0(W0_385) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_27370,plain,
! [W0_385] :
( doDivides0(W0_385,xk)
| ~ doDivides0(W0_385,'#skF_6')
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0('#skF_6')
| ~ aNaturalNumber0(W0_385) ),
inference(resolution,[status(thm)],[c_167,c_27294]) ).
tff(c_32076,plain,
! [W0_425] :
( doDivides0(W0_425,xk)
| ~ doDivides0(W0_425,'#skF_6')
| ~ aNaturalNumber0(W0_425) ),
inference(demodulation,[status(thm),theory(equality)],[c_173,c_137,c_27370]) ).
tff(c_175,plain,
! [W0_111] :
( ~ doDivides0(W0_111,xk)
| ~ isPrime0(W0_111)
| ~ aNaturalNumber0(W0_111) ),
inference(cnfTransformation,[status(thm)],[f_499]) ).
tff(c_32262,plain,
! [W0_429] :
( ~ isPrime0(W0_429)
| ~ doDivides0(W0_429,'#skF_6')
| ~ aNaturalNumber0(W0_429) ),
inference(resolution,[status(thm)],[c_32076,c_175]) ).
tff(c_32269,plain,
( ~ isPrime0('#skF_4'('#skF_6'))
| ~ aNaturalNumber0('#skF_4'('#skF_6'))
| ~ iLess0('#skF_6',xk)
| ( sz10 = '#skF_6' )
| ( sz00 = '#skF_6' )
| ~ aNaturalNumber0('#skF_6') ),
inference(resolution,[status(thm)],[c_145,c_32262]) ).
tff(c_32289,plain,
( ~ isPrime0('#skF_4'('#skF_6'))
| ~ aNaturalNumber0('#skF_4'('#skF_6'))
| ( sz10 = '#skF_6' )
| ( sz00 = '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_173,c_6139,c_32269]) ).
tff(c_32290,plain,
( ~ isPrime0('#skF_4'('#skF_6'))
| ~ aNaturalNumber0('#skF_4'('#skF_6')) ),
inference(negUnitSimplification,[status(thm)],[c_1422,c_165,c_32289]) ).
tff(c_32305,plain,
~ aNaturalNumber0('#skF_4'('#skF_6')),
inference(splitLeft,[status(thm)],[c_32290]) ).
tff(c_32308,plain,
( ~ iLess0('#skF_6',xk)
| ( sz10 = '#skF_6' )
| ( sz00 = '#skF_6' )
| ~ aNaturalNumber0('#skF_6') ),
inference(resolution,[status(thm)],[c_151,c_32305]) ).
tff(c_32311,plain,
( ( sz10 = '#skF_6' )
| ( sz00 = '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_173,c_6139,c_32308]) ).
tff(c_32313,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1422,c_165,c_32311]) ).
tff(c_32314,plain,
~ isPrime0('#skF_4'('#skF_6')),
inference(splitRight,[status(thm)],[c_32290]) ).
tff(c_32365,plain,
( ~ iLess0('#skF_6',xk)
| ( sz10 = '#skF_6' )
| ( sz00 = '#skF_6' )
| ~ aNaturalNumber0('#skF_6') ),
inference(resolution,[status(thm)],[c_139,c_32314]) ).
tff(c_32374,plain,
( ( sz10 = '#skF_6' )
| ( sz00 = '#skF_6' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_173,c_6139,c_32365]) ).
tff(c_32376,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1422,c_165,c_32374]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM483+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.13 % 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
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 12:51:48 EDT 2025
% 0.13/0.34 % CPUTime :
% 19.18/7.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.18/7.51
% 19.18/7.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------