%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM479+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 : 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 07:56:04 PM UTC 2025
% Result : Theorem 77.04s 59.06s
% Output : CNFRefutation 77.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 49 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 96 ( 42 ~; 36 |; 10 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 27 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > xl > sz10 > sz00 > #skF_3 > #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_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_383,hypothesis,
aNaturalNumber0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1553) ).
tff(f_382,hypothesis,
( ( xl != sz00 )
& ? [W0] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xl,W0) ) )
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524_04) ).
tff(f_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(f_393,negated_conjecture,
~ ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) )
=> ( ( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))
& ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ) )
=> ( sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_373,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524) ).
tff(f_131,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1,W2] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
tff(f_81,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
tff(c_133,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_129,plain,
aNaturalNumber0('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_1030,plain,
! [W1_103,W0_104] :
( ( sdtasdt0(W1_103,W0_104) = sdtasdt0(W0_104,W1_103) )
| ~ aNaturalNumber0(W1_103)
| ~ aNaturalNumber0(W0_104) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_78246,plain,
! [W0_1303] :
( ( sdtasdt0(W0_1303,'#skF_3') = sdtasdt0('#skF_3',W0_1303) )
| ~ aNaturalNumber0(W0_1303) ),
inference(resolution,[status(thm)],[c_129,c_1030]) ).
tff(c_78343,plain,
sdtasdt0(xn,'#skF_3') = sdtasdt0('#skF_3',xn),
inference(resolution,[status(thm)],[c_133,c_78246]) ).
tff(c_141,plain,
sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
inference(cnfTransformation,[status(thm)],[f_393]) ).
tff(c_143,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnfTransformation,[status(thm)],[f_393]) ).
tff(c_131,plain,
xl != sz00,
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_123,plain,
aNaturalNumber0(xl),
inference(cnfTransformation,[status(thm)],[f_373]) ).
tff(c_127,plain,
sdtasdt0(xl,'#skF_3') = xm,
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_80182,plain,
! [W0_1313,W2_1314,W1_1315] :
( ( sdtasdt0(W0_1313,W2_1314) != sdtasdt0(W0_1313,W1_1315) )
| ( W2_1314 = W1_1315 )
| ~ aNaturalNumber0(W2_1314)
| ~ aNaturalNumber0(W1_1315)
| ( sz00 = W0_1313 )
| ~ aNaturalNumber0(W0_1313) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_80440,plain,
! [W1_1315] :
( ( sdtasdt0(xl,W1_1315) != xm )
| ( W1_1315 = '#skF_3' )
| ~ aNaturalNumber0('#skF_3')
| ~ aNaturalNumber0(W1_1315)
| ( xl = sz00 )
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_80182]) ).
tff(c_80786,plain,
! [W1_1315] :
( ( sdtasdt0(xl,W1_1315) != xm )
| ( W1_1315 = '#skF_3' )
| ~ aNaturalNumber0(W1_1315)
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_123,c_129,c_80440]) ).
tff(c_84696,plain,
! [W1_1338] :
( ( sdtasdt0(xl,W1_1338) != xm )
| ( W1_1338 = '#skF_3' )
| ~ aNaturalNumber0(W1_1338) ),
inference(negUnitSimplification,[status(thm)],[c_131,c_80786]) ).
tff(c_84780,plain,
( ( sdtasdt0(xl,sdtsldt0(xm,xl)) != xm )
| ( sdtsldt0(xm,xl) = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_143,c_84696]) ).
tff(c_84829,plain,
sdtsldt0(xm,xl) = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_141,c_84780]) ).
tff(c_79806,plain,
! [W0_1312] :
( ( sdtasdt0(xn,W0_1312) = sdtasdt0(W0_1312,xn) )
| ~ aNaturalNumber0(W0_1312) ),
inference(resolution,[status(thm)],[c_133,c_1030]) ).
tff(c_79900,plain,
sdtasdt0(sdtsldt0(xm,xl),xn) = sdtasdt0(xn,sdtsldt0(xm,xl)),
inference(resolution,[status(thm)],[c_143,c_79806]) ).
tff(c_78603,plain,
! [W0_1306,W1_1307,W2_1308] :
( ( sdtasdt0(sdtasdt0(W0_1306,W1_1307),W2_1308) = sdtasdt0(W0_1306,sdtasdt0(W1_1307,W2_1308)) )
| ~ aNaturalNumber0(W2_1308)
| ~ aNaturalNumber0(W1_1307)
| ~ aNaturalNumber0(W0_1306) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_78847,plain,
! [W2_1308] :
( ( sdtasdt0(xl,sdtasdt0(sdtsldt0(xm,xl),W2_1308)) = sdtasdt0(xm,W2_1308) )
| ~ aNaturalNumber0(W2_1308)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_141,c_78603]) ).
tff(c_83991,plain,
! [W2_1334] :
( ( sdtasdt0(xl,sdtasdt0(sdtsldt0(xm,xl),W2_1334)) = sdtasdt0(xm,W2_1334) )
| ~ aNaturalNumber0(W2_1334) ),
inference(demodulation,[status(thm),theory(equality)],[c_123,c_143,c_78847]) ).
tff(c_84028,plain,
( ( sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_79900,c_83991]) ).
tff(c_84080,plain,
sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) = sdtasdt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_133,c_84028]) ).
tff(c_112384,plain,
sdtasdt0(xl,sdtasdt0('#skF_3',xn)) = sdtasdt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_78343,c_84829,c_84080]) ).
tff(c_24,plain,
! [W0_14,W1_15,W2_16] :
( ( sdtasdt0(sdtasdt0(W0_14,W1_15),W2_16) = sdtasdt0(W0_14,sdtasdt0(W1_15,W2_16)) )
| ~ aNaturalNumber0(W2_16)
| ~ aNaturalNumber0(W1_15)
| ~ aNaturalNumber0(W0_14) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_121,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_373]) ).
tff(c_1277,plain,
! [W0_109] :
( ( sdtasdt0(xm,W0_109) = sdtasdt0(W0_109,xm) )
| ~ aNaturalNumber0(W0_109) ),
inference(resolution,[status(thm)],[c_121,c_1030]) ).
tff(c_1324,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_133,c_1277]) ).
tff(c_137,plain,
sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) = sdtasdt0(xn,xm),
inference(cnfTransformation,[status(thm)],[f_393]) ).
tff(c_135,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnfTransformation,[status(thm)],[f_393]) ).
tff(c_144,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xn,xm),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_135]) ).
tff(c_1452,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_1324,c_144]) ).
tff(c_84849,plain,
sdtasdt0(sdtasdt0(xl,xn),'#skF_3') != sdtasdt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_84829,c_1452]) ).
tff(c_97183,plain,
( ( sdtasdt0(xl,sdtasdt0(xn,'#skF_3')) != sdtasdt0(xm,xn) )
| ~ aNaturalNumber0('#skF_3')
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_84849]) ).
tff(c_97185,plain,
sdtasdt0(xl,sdtasdt0('#skF_3',xn)) != sdtasdt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_123,c_133,c_129,c_78343,c_97183]) ).
tff(c_200646,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_112384,c_97185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.39 % Problem : NUM479+2 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.40 % 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
% 0.15/0.62 % Computer : n002.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8042.1875MB
% 0.15/0.62 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Tue Apr 8 12:51:17 EDT 2025
% 0.15/0.63 % CPUTime :
% 77.04/59.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 77.04/59.07
% 77.04/59.07 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------