%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM500+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/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 : n018.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 07:56:09 PM UTC 2025
% Result : Theorem 8.85s 3.03s
% Output : CNFRefutation 8.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 29 unt; 0 typ; 2 def)
% Number of atoms : 147 ( 50 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 136 ( 53 ~; 50 |; 21 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 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 : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 27 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $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(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_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_465,hypothesis,
( ( xk != sz00 )
& ( xk != sz10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
tff(f_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
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_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
tff(f_87,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
tff(f_278,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00 )
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
tff(f_442,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
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_472,negated_conjecture,
~ ? [W0] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_456,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
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(c_175,plain,
xk != sz00,
inference(cnfTransformation,[status(thm)],[f_465]) ).
tff(c_173,plain,
xk != sz10,
inference(cnfTransformation,[status(thm)],[f_465]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_135,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_181,plain,
~ isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_372,plain,
! [W0_106] :
( ( sdtasdt0(sz10,W0_106) = W0_106 )
| ~ aNaturalNumber0(W0_106) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_394,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_372]) ).
tff(c_1630,plain,
! [W1_135,W0_136] :
( sdtlseqdt0(W1_135,sdtasdt0(W1_135,W0_136))
| ( sz00 = W0_136 )
| ~ aNaturalNumber0(W1_135)
| ~ aNaturalNumber0(W0_136) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_1663,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_394,c_1630]) ).
tff(c_1730,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_1663]) ).
tff(c_1829,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_1730]) ).
tff(c_153,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_1914,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_1829,c_153]) ).
tff(c_1937,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_181,c_1914]) ).
tff(c_1939,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_1730]) ).
tff(c_818,plain,
! [W0_120] :
( doDivides0('#skF_4'(W0_120),W0_120)
| ( sz10 = W0_120 )
| ( sz00 = W0_120 )
| ~ aNaturalNumber0(W0_120) ),
inference(cnfTransformation,[status(thm)],[f_418]) ).
tff(c_177,plain,
! [W0_98] :
( ~ isPrime0(W0_98)
| ~ doDivides0(W0_98,xk)
| ~ aNaturalNumber0(W0_98) ),
inference(cnfTransformation,[status(thm)],[f_472]) ).
tff(c_822,plain,
( ~ isPrime0('#skF_4'(xk))
| ~ aNaturalNumber0('#skF_4'(xk))
| ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_818,c_177]) ).
tff(c_825,plain,
( ~ isPrime0('#skF_4'(xk))
| ~ aNaturalNumber0('#skF_4'(xk))
| ~ aNaturalNumber0(xk) ),
inference(negUnitSimplification,[status(thm)],[c_175,c_173,c_822]) ).
tff(c_874,plain,
~ aNaturalNumber0(xk),
inference(splitLeft,[status(thm)],[c_825]) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_621,plain,
! [W1_114,W0_115] :
( ( sdtasdt0(W1_114,W0_115) = sdtasdt0(W0_115,W1_114) )
| ~ aNaturalNumber0(W1_114)
| ~ aNaturalNumber0(W0_115) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_727,plain,
! [W0_119] :
( ( sdtasdt0(xn,W0_119) = sdtasdt0(W0_119,xn) )
| ~ aNaturalNumber0(W0_119) ),
inference(resolution,[status(thm)],[c_147,c_621]) ).
tff(c_759,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_145,c_727]) ).
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_768,plain,
( aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_759,c_12]) ).
tff(c_772,plain,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_768]) ).
tff(c_151,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_764,plain,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_759,c_151]) ).
tff(c_167,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_763,plain,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_759,c_167]) ).
tff(c_6234,plain,
! [W1_231,W0_232] :
( aNaturalNumber0(sdtsldt0(W1_231,W0_232))
| ~ doDivides0(W0_232,W1_231)
| ( sz00 = W0_232 )
| ~ aNaturalNumber0(W1_231)
| ~ aNaturalNumber0(W0_232) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_6283,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sdtasdt0(xm,xn))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_763,c_6234]) ).
tff(c_6301,plain,
( aNaturalNumber0(xk)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_772,c_764,c_6283]) ).
tff(c_6303,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1939,c_874,c_6301]) ).
tff(c_6305,plain,
aNaturalNumber0(xk),
inference(splitRight,[status(thm)],[c_825]) ).
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_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_6304,plain,
( ~ aNaturalNumber0('#skF_4'(xk))
| ~ isPrime0('#skF_4'(xk)) ),
inference(splitRight,[status(thm)],[c_825]) ).
tff(c_6363,plain,
~ isPrime0('#skF_4'(xk)),
inference(splitLeft,[status(thm)],[c_6304]) ).
tff(c_6366,plain,
( ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_137,c_6363]) ).
tff(c_6369,plain,
( ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6305,c_6366]) ).
tff(c_6371,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_175,c_173,c_6369]) ).
tff(c_6372,plain,
~ aNaturalNumber0('#skF_4'(xk)),
inference(splitRight,[status(thm)],[c_6304]) ).
tff(c_6376,plain,
( ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_141,c_6372]) ).
tff(c_6379,plain,
( ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6305,c_6376]) ).
tff(c_6381,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_175,c_173,c_6379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : NUM500+1 : TPTP v9.0.0. Released v4.0.0.
% 0.13/0.13 % 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 : n018.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 13:02:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 8.85/3.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.85/3.04
% 8.85/3.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------