%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM474+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 : n009.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 20.49s 7.97s
% Output : CNFRefutation 20.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 43 unt; 0 typ; 2 def)
% Number of atoms : 148 ( 67 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 124 ( 48 ~; 42 |; 25 &)
% ( 2 <=>; 7 =>; 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-2 aty)
% Number of variables : 33 ( 30 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xq > xp > xn > xm > xl > sz10 > sz00 > #skF_5 > #skF_3 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xq,type,
xq: $i ).
tff(xl,type,
xl: $i ).
tff(xr,type,
xr: $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('#skF_5',type,
'#skF_5': $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(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_352,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
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_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(f_372,hypothesis,
( aNaturalNumber0(xp)
& ( xm = sdtasdt0(xl,xp) )
& ( xp = sdtsldt0(xm,xl) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
tff(f_377,hypothesis,
( aNaturalNumber0(xq)
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
& ( xq = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
tff(f_383,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xp,W0) = xq ) )
& sdtlseqdt0(xp,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1395) ).
tff(f_388,hypothesis,
( aNaturalNumber0(xr)
& ( sdtpldt0(xp,xr) = xq )
& ( xr = sdtmndt0(xq,xp) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1422) ).
tff(f_175,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
tff(f_390,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_367,hypothesis,
xl != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).
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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
tff(f_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_103,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
tff(c_121,plain,
aNaturalNumber0(xl),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_127,plain,
aNaturalNumber0('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_1190,plain,
! [W1_96,W0_97] :
( ( sdtasdt0(W1_96,W0_97) = sdtasdt0(W0_97,W1_96) )
| ~ aNaturalNumber0(W1_96)
| ~ aNaturalNumber0(W0_97) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_14503,plain,
! [W0_215] :
( ( sdtasdt0(W0_215,'#skF_3') = sdtasdt0('#skF_3',W0_215) )
| ~ aNaturalNumber0(W0_215) ),
inference(resolution,[status(thm)],[c_127,c_1190]) ).
tff(c_14557,plain,
sdtasdt0(xl,'#skF_3') = sdtasdt0('#skF_3',xl),
inference(resolution,[status(thm)],[c_121,c_14503]) ).
tff(c_141,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_147,plain,
aNaturalNumber0(xq),
inference(cnfTransformation,[status(thm)],[f_377]) ).
tff(c_151,plain,
sdtpldt0(xp,'#skF_5') = xq,
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_149,plain,
sdtlseqdt0(xp,xq),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_153,plain,
aNaturalNumber0('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_155,plain,
sdtmndt0(xq,xp) = xr,
inference(cnfTransformation,[status(thm)],[f_388]) ).
tff(c_11599,plain,
! [W0_202,W2_203] :
( ( sdtmndt0(sdtpldt0(W0_202,W2_203),W0_202) = W2_203 )
| ~ aNaturalNumber0(W2_203)
| ~ sdtlseqdt0(W0_202,sdtpldt0(W0_202,W2_203))
| ~ aNaturalNumber0(sdtpldt0(W0_202,W2_203))
| ~ aNaturalNumber0(W0_202) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_11698,plain,
( ( sdtmndt0(sdtpldt0(xp,'#skF_5'),xp) = '#skF_5' )
| ~ aNaturalNumber0('#skF_5')
| ~ sdtlseqdt0(xp,xq)
| ~ aNaturalNumber0(sdtpldt0(xp,'#skF_5'))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_151,c_11599]) ).
tff(c_11752,plain,
xr = '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_141,c_147,c_151,c_149,c_153,c_155,c_151,c_11698]) ).
tff(c_159,plain,
aNaturalNumber0(xr),
inference(cnfTransformation,[status(thm)],[f_388]) ).
tff(c_1232,plain,
! [W0_97] :
( ( sdtasdt0(xr,W0_97) = sdtasdt0(W0_97,xr) )
| ~ aNaturalNumber0(W0_97) ),
inference(resolution,[status(thm)],[c_159,c_1190]) ).
tff(c_15565,plain,
! [W0_219] :
( ( sdtasdt0(W0_219,'#skF_5') = sdtasdt0('#skF_5',W0_219) )
| ~ aNaturalNumber0(W0_219) ),
inference(demodulation,[status(thm),theory(equality)],[c_11752,c_11752,c_1232]) ).
tff(c_15632,plain,
sdtasdt0(xl,'#skF_5') = sdtasdt0('#skF_5',xl),
inference(resolution,[status(thm)],[c_121,c_15565]) ).
tff(c_125,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,'#skF_3'),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_145,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cnfTransformation,[status(thm)],[f_377]) ).
tff(c_165,plain,
sdtasdt0(xl,xq) = sdtasdt0(xl,'#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_125,c_145]) ).
tff(c_139,plain,
sdtasdt0(xl,xp) = xm,
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_161,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnfTransformation,[status(thm)],[f_390]) ).
tff(c_163,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtpldt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_139,c_139,c_161]) ).
tff(c_164,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtasdt0(xl,xq),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_163]) ).
tff(c_166,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtasdt0(xl,'#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_165,c_164]) ).
tff(c_11770,plain,
sdtpldt0(xm,sdtasdt0(xl,'#skF_5')) != sdtasdt0(xl,'#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_11752,c_166]) ).
tff(c_16188,plain,
sdtpldt0(xm,sdtasdt0('#skF_5',xl)) != sdtasdt0(xl,'#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_15632,c_11770]) ).
tff(c_16627,plain,
sdtpldt0(xm,sdtasdt0('#skF_5',xl)) != sdtasdt0('#skF_3',xl),
inference(demodulation,[status(thm),theory(equality)],[c_14557,c_16188]) ).
tff(c_135,plain,
xl != sz00,
inference(cnfTransformation,[status(thm)],[f_367]) ).
tff(c_119,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_131,plain,
sdtasdt0(xl,'#skF_4') = xm,
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_129,plain,
doDivides0(xl,xm),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_133,plain,
aNaturalNumber0('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_137,plain,
sdtsldt0(xm,xl) = xp,
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_12970,plain,
! [W0_210,W2_211] :
( ( sdtsldt0(sdtasdt0(W0_210,W2_211),W0_210) = W2_211 )
| ~ aNaturalNumber0(W2_211)
| ~ doDivides0(W0_210,sdtasdt0(W0_210,W2_211))
| ( sz00 = W0_210 )
| ~ aNaturalNumber0(sdtasdt0(W0_210,W2_211))
| ~ aNaturalNumber0(W0_210) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_13102,plain,
( ( sdtsldt0(sdtasdt0(xl,'#skF_4'),xl) = '#skF_4' )
| ~ aNaturalNumber0('#skF_4')
| ~ doDivides0(xl,xm)
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xl,'#skF_4'))
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_131,c_12970]) ).
tff(c_13223,plain,
( ( xp = '#skF_4' )
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_131,c_129,c_133,c_137,c_131,c_13102]) ).
tff(c_13224,plain,
xp = '#skF_4',
inference(negUnitSimplification,[status(thm)],[c_135,c_13223]) ).
tff(c_582,plain,
! [W0_87,W1_88] :
( aNaturalNumber0(sdtasdt0(W0_87,W1_88))
| ~ aNaturalNumber0(W1_88)
| ~ aNaturalNumber0(W0_87) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_636,plain,
( aNaturalNumber0(sdtasdt0(xl,'#skF_3'))
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_165,c_582]) ).
tff(c_696,plain,
aNaturalNumber0(sdtasdt0(xl,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_147,c_636]) ).
tff(c_143,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) = xq,
inference(cnfTransformation,[status(thm)],[f_377]) ).
tff(c_162,plain,
sdtsldt0(sdtasdt0(xl,xq),xl) = xq,
inference(demodulation,[status(thm),theory(equality)],[c_145,c_143]) ).
tff(c_167,plain,
sdtsldt0(sdtasdt0(xl,'#skF_3'),xl) = xq,
inference(demodulation,[status(thm),theory(equality)],[c_165,c_162]) ).
tff(c_123,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_168,plain,
doDivides0(xl,sdtasdt0(xl,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_125,c_123]) ).
tff(c_13096,plain,
( ( sdtsldt0(sdtasdt0(xl,'#skF_3'),xl) = '#skF_3' )
| ~ aNaturalNumber0('#skF_3')
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xl,'#skF_3'))
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[c_168,c_12970]) ).
tff(c_13217,plain,
( ( xq = '#skF_3' )
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_696,c_127,c_167,c_13096]) ).
tff(c_13218,plain,
xq = '#skF_3',
inference(negUnitSimplification,[status(thm)],[c_135,c_13217]) ).
tff(c_13247,plain,
sdtpldt0(xp,'#skF_5') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_13218,c_151]) ).
tff(c_13343,plain,
sdtpldt0('#skF_4','#skF_5') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_13224,c_13247]) ).
tff(c_5127,plain,
! [W0_157,W1_158,W2_159] :
( ( sdtpldt0(sdtasdt0(W0_157,W1_158),sdtasdt0(W0_157,W2_159)) = sdtasdt0(W0_157,sdtpldt0(W1_158,W2_159)) )
| ~ aNaturalNumber0(W2_159)
| ~ aNaturalNumber0(W1_158)
| ~ aNaturalNumber0(W0_157) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_5424,plain,
! [W2_159] :
( ( sdtpldt0(xm,sdtasdt0(xl,W2_159)) = sdtasdt0(xl,sdtpldt0(xp,W2_159)) )
| ~ aNaturalNumber0(W2_159)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_139,c_5127]) ).
tff(c_5601,plain,
! [W2_159] :
( ( sdtpldt0(xm,sdtasdt0(xl,W2_159)) = sdtasdt0(xl,sdtpldt0(xp,W2_159)) )
| ~ aNaturalNumber0(W2_159) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_141,c_5424]) ).
tff(c_34000,plain,
! [W2_279] :
( ( sdtpldt0(xm,sdtasdt0(xl,W2_279)) = sdtasdt0(xl,sdtpldt0('#skF_4',W2_279)) )
| ~ aNaturalNumber0(W2_279) ),
inference(demodulation,[status(thm),theory(equality)],[c_13224,c_5601]) ).
tff(c_34068,plain,
( ( sdtpldt0(xm,sdtasdt0('#skF_5',xl)) = sdtasdt0(xl,sdtpldt0('#skF_4','#skF_5')) )
| ~ aNaturalNumber0('#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_15632,c_34000]) ).
tff(c_34130,plain,
sdtpldt0(xm,sdtasdt0('#skF_5',xl)) = sdtasdt0('#skF_3',xl),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_14557,c_13343,c_34068]) ).
tff(c_34132,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16627,c_34130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.31 % Problem : NUM474+2 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.32 % 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
% 0.16/0.53 % Computer : n009.cluster.edu
% 0.16/0.53 % Model : x86_64 x86_64
% 0.16/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.53 % Memory : 8042.1875MB
% 0.16/0.53 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.53 % CPULimit : 300
% 0.16/0.53 % WCLimit : 300
% 0.16/0.53 % DateTime : Tue Apr 8 12:47:42 EDT 2025
% 0.16/0.53 % CPUTime :
% 20.49/7.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.53/7.98
% 20.53/7.98 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------