%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM476+2 : 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 : n014.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 07:56:03 PM UTC 2025
% Result : Theorem 5.33s 2.25s
% Output : CNFRefutation 5.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 43 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 50 ( 14 ~; 9 |; 23 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 2 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-2 aty)
% Number of variables : 14 ( 7 !; 7 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > xl > sz10 > sz00 > #skF_7 > #skF_5 > #skF_6 > #skF_3 > #skF_8 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xl,type,
xl: $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('#skF_7',type,
'#skF_7': $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $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_352,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
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_407,negated_conjecture,
~ ( ( ( xl != sz00 )
=> ? [W0] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xl,W0) )
& ( W0 = sdtsldt0(xm,xl) )
& ? [W1] :
( aNaturalNumber0(W1)
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,W1) )
& ( W1 = sdtsldt0(sdtpldt0(xm,xn),xl) )
& ? [W2] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) )
& sdtlseqdt0(W0,W1)
& ? [W2] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 )
& ( W2 = sdtmndt0(W1,W0) )
& ( sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn) )
& ( xn = sdtasdt0(xl,W2) ) ) ) ) )
=> ( ? [W0] :
( aNaturalNumber0(W0)
& ( xn = sdtasdt0(xl,W0) ) )
| doDivides0(xl,xn) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_365,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xl,W0) ) )
& doDivides0(xl,xm)
& ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,W0) ) )
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).
tff(f_67,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
tff(c_117,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_243,plain,
! [W0_90] :
( ( sdtasdt0(sz00,W0_90) = sz00 )
| ~ aNaturalNumber0(W0_90) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_263,plain,
sdtasdt0(sz00,xn) = sz00,
inference(resolution,[status(thm)],[c_117,c_243]) ).
tff(c_159,plain,
( aNaturalNumber0('#skF_6')
| ( xl = sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_407]) ).
tff(c_169,plain,
xl = sz00,
inference(splitLeft,[status(thm)],[c_159]) ).
tff(c_137,plain,
! [W0_87] :
( ( sdtasdt0(xl,W0_87) != xn )
| ~ aNaturalNumber0(W0_87) ),
inference(cnfTransformation,[status(thm)],[f_407]) ).
tff(c_318,plain,
! [W0_91] :
( ( sdtasdt0(sz00,W0_91) != xn )
| ~ aNaturalNumber0(W0_91) ),
inference(demodulation,[status(thm),theory(equality)],[c_169,c_137]) ).
tff(c_321,plain,
sdtasdt0(sz00,xn) != xn,
inference(resolution,[status(thm)],[c_117,c_318]) ).
tff(c_335,plain,
xn != sz00,
inference(demodulation,[status(thm),theory(equality)],[c_263,c_321]) ).
tff(c_133,plain,
aNaturalNumber0('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_267,plain,
sdtasdt0(sz00,'#skF_4') = sz00,
inference(resolution,[status(thm)],[c_133,c_243]) ).
tff(c_131,plain,
sdtasdt0(xl,'#skF_4') = xm,
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_178,plain,
sdtasdt0(sz00,'#skF_4') = xm,
inference(demodulation,[status(thm),theory(equality)],[c_169,c_131]) ).
tff(c_292,plain,
xm = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_267,c_178]) ).
tff(c_127,plain,
aNaturalNumber0('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_266,plain,
sdtasdt0(sz00,'#skF_3') = sz00,
inference(resolution,[status(thm)],[c_127,c_243]) ).
tff(c_125,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,'#skF_3'),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_230,plain,
sdtpldt0(xm,xn) = sdtasdt0(sz00,'#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_169,c_125]) ).
tff(c_273,plain,
sdtpldt0(xm,xn) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_266,c_230]) ).
tff(c_310,plain,
sdtpldt0(sz00,xn) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_292,c_273]) ).
tff(c_457,plain,
! [W0_95] :
( ( sdtpldt0(sz00,W0_95) = W0_95 )
| ~ aNaturalNumber0(W0_95) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_460,plain,
sdtpldt0(sz00,xn) = xn,
inference(resolution,[status(thm)],[c_117,c_457]) ).
tff(c_474,plain,
xn = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_310,c_460]) ).
tff(c_476,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_335,c_474]) ).
tff(c_478,plain,
xl != sz00,
inference(splitRight,[status(thm)],[c_159]) ).
tff(c_147,plain,
( aNaturalNumber0('#skF_8')
| ( xl = sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_407]) ).
tff(c_481,plain,
aNaturalNumber0('#skF_8'),
inference(negUnitSimplification,[status(thm)],[c_478,c_147]) ).
tff(c_705,plain,
! [W0_100] :
( ( sdtasdt0(xl,W0_100) != xn )
| ~ aNaturalNumber0(W0_100) ),
inference(cnfTransformation,[status(thm)],[f_407]) ).
tff(c_739,plain,
sdtasdt0(xl,'#skF_8') != xn,
inference(resolution,[status(thm)],[c_481,c_705]) ).
tff(c_139,plain,
( ( sdtasdt0(xl,'#skF_8') = xn )
| ( xl = sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_407]) ).
tff(c_788,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_478,c_739,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM476+2 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.13 % 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
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 12:48:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 5.33/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.33/2.26
% 5.33/2.26 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------