%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM500+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 : n028.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 9.94s 3.22s
% Output : CNFRefutation 9.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 32 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 71 ( 26 ~; 28 |; 15 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 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 : 23 ( 23 usr; 9 con; 0-3 aty)
% Number of variables : 10 ( 6 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_11 > #skF_6 > #skF_10 > #skF_5 > #skF_9 > #skF_7 > #skF_13 > #skF_3 > #skF_2 > #skF_8 > #skF_12 > #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('#skF_11',type,
'#skF_11': $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_10',type,
'#skF_10': $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_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i > $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('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff(xm,type,
xm: $i ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff(sdtsldt0,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xn,type,
xn: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_549,hypothesis,
( ( xk != sz00 )
& ( xk != sz10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
tff(f_540,hypothesis,
( aNaturalNumber0(xk)
& ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
& ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
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_581,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(c_453,plain,
xk != sz00,
inference(cnfTransformation,[status(thm)],[f_549]) ).
tff(c_451,plain,
xk != sz10,
inference(cnfTransformation,[status(thm)],[f_549]) ).
tff(c_445,plain,
aNaturalNumber0(xk),
inference(cnfTransformation,[status(thm)],[f_540]) ).
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_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_3535,plain,
! [W0_160] :
( doDivides0('#skF_4'(W0_160),W0_160)
| ( sz10 = W0_160 )
| ( sz00 = W0_160 )
| ~ aNaturalNumber0(W0_160) ),
inference(cnfTransformation,[status(thm)],[f_418]) ).
tff(c_455,plain,
! [W0_111] :
( ~ doDivides0(W0_111,xk)
| ~ isPrime0(W0_111)
| ~ aNaturalNumber0(W0_111) ),
inference(cnfTransformation,[status(thm)],[f_581]) ).
tff(c_3551,plain,
( ~ isPrime0('#skF_4'(xk))
| ~ aNaturalNumber0('#skF_4'(xk))
| ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_3535,c_455]) ).
tff(c_3566,plain,
( ~ isPrime0('#skF_4'(xk))
| ~ aNaturalNumber0('#skF_4'(xk))
| ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_445,c_3551]) ).
tff(c_3567,plain,
( ~ isPrime0('#skF_4'(xk))
| ~ aNaturalNumber0('#skF_4'(xk)) ),
inference(negUnitSimplification,[status(thm)],[c_453,c_451,c_3566]) ).
tff(c_3568,plain,
~ aNaturalNumber0('#skF_4'(xk)),
inference(splitLeft,[status(thm)],[c_3567]) ).
tff(c_3571,plain,
( ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_141,c_3568]) ).
tff(c_3574,plain,
( ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_445,c_3571]) ).
tff(c_3576,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_453,c_451,c_3574]) ).
tff(c_3577,plain,
~ isPrime0('#skF_4'(xk)),
inference(splitRight,[status(thm)],[c_3567]) ).
tff(c_3581,plain,
( ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_137,c_3577]) ).
tff(c_3584,plain,
( ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_445,c_3581]) ).
tff(c_3586,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_453,c_451,c_3584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : NUM500+3 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.13 % 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
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 13:02:35 EDT 2025
% 0.14/0.34 % CPUTime :
% 9.94/3.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.94/3.22
% 9.94/3.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------