%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM469+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 : n003.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 07:56:02 PM UTC 2025
% Result : Theorem 8.19s 2.97s
% Output : CNFRefutation 8.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 38 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 52 ( 19 ~; 14 |; 15 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 16 ( 13 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > xl > sz10 > sz00 > #skF_3 > #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(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
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_353,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xl,W0) ) )
& doDivides0(xl,xm)
& ? [W0] :
( aNaturalNumber0(W0)
& ( xn = sdtasdt0(xl,W0) ) )
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
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_365,hypothesis,
( ( xl != sz00 )
=> ( aNaturalNumber0(sdtsldt0(xm,xl))
& ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
& aNaturalNumber0(sdtsldt0(xn,xl))
& ( xn = sdtasdt0(xl,sdtsldt0(xn,xl)) )
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1298) ).
tff(f_340,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
tff(f_372,negated_conjecture,
~ ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,W0) ) )
| doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(f_41,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(c_125,plain,
aNaturalNumber0('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_301,plain,
! [W0_82] :
( ( sdtasdt0(sz00,W0_82) = sz00 )
| ~ aNaturalNumber0(W0_82) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_324,plain,
sdtasdt0(sz00,'#skF_3') = sz00,
inference(resolution,[status(thm)],[c_125,c_301]) ).
tff(c_137,plain,
( aNaturalNumber0(sdtsldt0(xn,xl))
| ( xl = sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_268,plain,
xl = sz00,
inference(splitLeft,[status(thm)],[c_137]) ).
tff(c_123,plain,
sdtasdt0(xl,'#skF_3') = xn,
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_270,plain,
sdtasdt0(sz00,'#skF_3') = xn,
inference(demodulation,[status(thm),theory(equality)],[c_268,c_123]) ).
tff(c_353,plain,
xn = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_324,c_270]) ).
tff(c_131,plain,
aNaturalNumber0('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_325,plain,
sdtasdt0(sz00,'#skF_4') = sz00,
inference(resolution,[status(thm)],[c_131,c_301]) ).
tff(c_129,plain,
sdtasdt0(xl,'#skF_4') = xm,
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_271,plain,
sdtasdt0(sz00,'#skF_4') = xm,
inference(demodulation,[status(thm),theory(equality)],[c_268,c_129]) ).
tff(c_335,plain,
xm = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_325,c_271]) ).
tff(c_119,plain,
aNaturalNumber0(xl),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_184,plain,
! [W0_80] :
( ( sdtasdt0(W0_80,sz00) = sz00 )
| ~ aNaturalNumber0(W0_80) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_208,plain,
sdtasdt0(xl,sz00) = sz00,
inference(resolution,[status(thm)],[c_119,c_184]) ).
tff(c_326,plain,
sdtasdt0(sz00,sz00) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_268,c_208]) ).
tff(c_225,plain,
! [W0_81] :
( ( sdtpldt0(xm,xn) != sdtasdt0(xl,W0_81) )
| ~ aNaturalNumber0(W0_81) ),
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_249,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,xl),
inference(resolution,[status(thm)],[c_119,c_225]) ).
tff(c_399,plain,
sdtpldt0(sz00,sz00) != sz00,
inference(demodulation,[status(thm),theory(equality)],[c_353,c_335,c_326,c_268,c_268,c_249]) ).
tff(c_115,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_358,plain,
! [W0_83] :
( ( sdtpldt0(sz00,W0_83) = W0_83 )
| ~ aNaturalNumber0(W0_83) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_376,plain,
sdtpldt0(sz00,xn) = xn,
inference(resolution,[status(thm)],[c_115,c_358]) ).
tff(c_404,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_353,c_353,c_376]) ).
tff(c_405,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_399,c_404]) ).
tff(c_407,plain,
xl != sz00,
inference(splitRight,[status(thm)],[c_137]) ).
tff(c_141,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| ( xl = sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_551,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(negUnitSimplification,[status(thm)],[c_407,c_141]) ).
tff(c_406,plain,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(splitRight,[status(thm)],[c_137]) ).
tff(c_133,plain,
( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn) )
| ( xl = sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_5647,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn),
inference(negUnitSimplification,[status(thm)],[c_407,c_133]) ).
tff(c_703,plain,
! [W0_88,W1_89] :
( aNaturalNumber0(sdtpldt0(W0_88,W1_89))
| ~ aNaturalNumber0(W1_89)
| ~ aNaturalNumber0(W0_88) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_145,plain,
! [W0_77] :
( ( sdtpldt0(xm,xn) != sdtasdt0(xl,W0_77) )
| ~ aNaturalNumber0(W0_77) ),
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_765,plain,
! [W0_88,W1_89] :
( ( sdtasdt0(xl,sdtpldt0(W0_88,W1_89)) != sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(W1_89)
| ~ aNaturalNumber0(W0_88) ),
inference(resolution,[status(thm)],[c_703,c_145]) ).
tff(c_5654,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(superposition,[status(thm),theory(equality)],[c_5647,c_765]) ).
tff(c_5674,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_551,c_406,c_5654]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : NUM469+2 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.15 % 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 : n003.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 12:45:03 EDT 2025
% 0.13/0.37 % CPUTime :
% 8.19/2.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.19/2.98
% 8.19/2.98 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------