TSTP Solution File: NUM524+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM524+3 : TPTP v8.1.2. 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 : n027.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 : Tue Aug 22 10:51:59 EDT 2023
% Result : Theorem 22.67s 10.45s
% Output : CNFRefutation 22.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 33
% Syntax : Number of formulae : 80 ( 28 unt; 23 typ; 1 def)
% Number of atoms : 141 ( 59 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 141 ( 57 ~; 54 |; 21 &)
% ( 1 <=>; 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 : 28 ( 15 >; 13 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 32 (; 30 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xq > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_6 > #skF_7 > #skF_5 > #skF_8 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xq,type,
xq: $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $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_7',type,
'#skF_7': $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_8',type,
'#skF_8': $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(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_446,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
tff(f_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_517,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xn,xn) = sdtasdt0(xp,W0) ) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [W0] :
( aNaturalNumber0(W0)
& ( xn = sdtasdt0(xp,W0) ) )
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
tff(f_522,hypothesis,
( aNaturalNumber0(xq)
& ( xn = sdtasdt0(xp,xq) )
& ( xq = sdtsldt0(xn,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
tff(f_384,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
tff(f_524,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(f_486,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
tff(c_153,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_12,plain,
! [W0_4,W1_5] :
( aNaturalNumber0(sdtasdt0(W0_4,W1_5))
| ~ aNaturalNumber0(W1_5)
| ~ aNaturalNumber0(W0_4) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_185,plain,
aNaturalNumber0('#skF_7'),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_145,plain,
xp != sz00,
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_151,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_155,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_181,plain,
doDivides0(xp,xn),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_183,plain,
sdtasdt0(xp,'#skF_7') = xn,
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_193,plain,
sdtsldt0(xn,xp) = xq,
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_21223,plain,
! [W0_367,W2_368] :
( ( sdtsldt0(sdtasdt0(W0_367,W2_368),W0_367) = W2_368 )
| ~ aNaturalNumber0(W2_368)
| ~ doDivides0(W0_367,sdtasdt0(W0_367,W2_368))
| ( sz00 = W0_367 )
| ~ aNaturalNumber0(sdtasdt0(W0_367,W2_368))
| ~ aNaturalNumber0(W0_367) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_21379,plain,
( ( sdtsldt0(sdtasdt0(xp,'#skF_7'),xp) = '#skF_7' )
| ~ aNaturalNumber0('#skF_7')
| ~ doDivides0(xp,xn)
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xp,'#skF_7'))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_183,c_21223]) ).
tff(c_21522,plain,
( ( xq = '#skF_7' )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_155,c_183,c_181,c_185,c_193,c_183,c_21379]) ).
tff(c_21523,plain,
xq = '#skF_7',
inference(negUnitSimplification,[status(thm)],[c_145,c_21522]) ).
tff(c_21554,plain,
sdtsldt0(xn,xp) = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_21523,c_193]) ).
tff(c_191,plain,
aNaturalNumber0('#skF_8'),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_189,plain,
sdtasdt0(xp,'#skF_8') = sdtasdt0(xn,xn),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_636,plain,
! [W0_117,W1_118] :
( aNaturalNumber0(sdtasdt0(W0_117,W1_118))
| ~ aNaturalNumber0(W1_118)
| ~ aNaturalNumber0(W0_117) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_678,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0('#skF_8')
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_189,c_636]) ).
tff(c_754,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_191,c_678]) ).
tff(c_187,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_21328,plain,
( ( sdtsldt0(sdtasdt0(xp,'#skF_8'),xp) = '#skF_8' )
| ~ aNaturalNumber0('#skF_8')
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xp,'#skF_8'))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_189,c_21223]) ).
tff(c_21471,plain,
( ( sdtsldt0(sdtasdt0(xn,xn),xp) = '#skF_8' )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_754,c_189,c_187,c_191,c_189,c_21328]) ).
tff(c_21472,plain,
sdtsldt0(sdtasdt0(xn,xn),xp) = '#skF_8',
inference(negUnitSimplification,[status(thm)],[c_145,c_21471]) ).
tff(c_121,plain,
! [W2_88,W1_86,W0_85] :
( ( sdtsldt0(sdtasdt0(W2_88,W1_86),W0_85) = sdtasdt0(W2_88,sdtsldt0(W1_86,W0_85)) )
| ~ aNaturalNumber0(W2_88)
| ~ doDivides0(W0_85,W1_86)
| ( sz00 = W0_85 )
| ~ aNaturalNumber0(W1_86)
| ~ aNaturalNumber0(W0_85) ),
inference(cnfTransformation,[status(thm)],[f_384]) ).
tff(c_22580,plain,
( ( sdtasdt0(xn,sdtsldt0(xn,xp)) = '#skF_8' )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_21472,c_121]) ).
tff(c_22593,plain,
( ( sdtasdt0(xn,'#skF_7') = '#skF_8' )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_155,c_181,c_155,c_21554,c_22580]) ).
tff(c_22594,plain,
sdtasdt0(xn,'#skF_7') = '#skF_8',
inference(negUnitSimplification,[status(thm)],[c_145,c_22593]) ).
tff(c_12055,plain,
! [W0_289,W1_290,W2_291] :
( ( sdtasdt0(sdtasdt0(W0_289,W1_290),W2_291) = sdtasdt0(W0_289,sdtasdt0(W1_290,W2_291)) )
| ~ aNaturalNumber0(W2_291)
| ~ aNaturalNumber0(W1_290)
| ~ aNaturalNumber0(W0_289) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_12282,plain,
! [W2_291] :
( ( sdtasdt0(xp,sdtasdt0('#skF_7',W2_291)) = sdtasdt0(xn,W2_291) )
| ~ aNaturalNumber0(W2_291)
| ~ aNaturalNumber0('#skF_7')
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_183,c_12055]) ).
tff(c_35127,plain,
! [W2_417] :
( ( sdtasdt0(xp,sdtasdt0('#skF_7',W2_417)) = sdtasdt0(xn,W2_417) )
| ~ aNaturalNumber0(W2_417) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_185,c_12282]) ).
tff(c_199,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) != sdtasdt0(xm,xm),
inference(cnfTransformation,[status(thm)],[f_524]) ).
tff(c_21556,plain,
sdtasdt0(xp,sdtasdt0('#skF_7','#skF_7')) != sdtasdt0(xm,xm),
inference(demodulation,[status(thm),theory(equality)],[c_21523,c_21523,c_199]) ).
tff(c_35145,plain,
( ( sdtasdt0(xn,'#skF_7') != sdtasdt0(xm,xm) )
| ~ aNaturalNumber0('#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_35127,c_21556]) ).
tff(c_35239,plain,
sdtasdt0(xm,xm) != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_185,c_22594,c_35145]) ).
tff(c_965,plain,
! [W1_123,W0_124] :
( ( sdtasdt0(W1_123,W0_124) = sdtasdt0(W0_124,W1_123) )
| ~ aNaturalNumber0(W1_123)
| ~ aNaturalNumber0(W0_124) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_25664,plain,
! [W0_399] :
( ( sdtasdt0(xp,W0_399) = sdtasdt0(W0_399,xp) )
| ~ aNaturalNumber0(W0_399) ),
inference(resolution,[status(thm)],[c_151,c_965]) ).
tff(c_25809,plain,
sdtasdt0(xp,'#skF_8') = sdtasdt0('#skF_8',xp),
inference(resolution,[status(thm)],[c_191,c_25664]) ).
tff(c_26008,plain,
sdtasdt0(xn,xn) = sdtasdt0('#skF_8',xp),
inference(demodulation,[status(thm),theory(equality)],[c_25809,c_189]) ).
tff(c_26211,plain,
sdtsldt0(sdtasdt0('#skF_8',xp),xp) = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_26008,c_21472]) ).
tff(c_171,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnfTransformation,[status(thm)],[f_486]) ).
tff(c_21316,plain,
( ( sdtsldt0(sdtasdt0(xp,sdtasdt0(xm,xm)),xp) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_171,c_21223]) ).
tff(c_21459,plain,
( ( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_754,c_171,c_187,c_171,c_21316]) ).
tff(c_21460,plain,
( ( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(negUnitSimplification,[status(thm)],[c_145,c_21459]) ).
tff(c_44737,plain,
( ( sdtasdt0(xm,xm) = '#skF_8' )
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_26211,c_26008,c_21460]) ).
tff(c_44738,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(negUnitSimplification,[status(thm)],[c_35239,c_44737]) ).
tff(c_44741,plain,
~ aNaturalNumber0(xm),
inference(resolution,[status(thm)],[c_12,c_44738]) ).
tff(c_44745,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_153,c_44741]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM524+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 15:03:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 22.67/10.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.67/10.46
% 22.67/10.46 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.73/10.49
% 22.73/10.49 Inference rules
% 22.73/10.49 ----------------------
% 22.73/10.49 #Ref : 16
% 22.73/10.49 #Sup : 9056
% 22.73/10.49 #Fact : 2
% 22.73/10.49 #Define : 0
% 22.73/10.49 #Split : 34
% 22.73/10.49 #Chain : 0
% 22.73/10.49 #Close : 0
% 22.73/10.49
% 22.73/10.49 Ordering : KBO
% 22.73/10.49
% 22.73/10.49 Simplification rules
% 22.73/10.49 ----------------------
% 22.73/10.49 #Subsume : 504
% 22.73/10.49 #Demod : 16265
% 22.73/10.49 #Tautology : 3199
% 22.73/10.49 #SimpNegUnit : 1923
% 22.73/10.49 #BackRed : 960
% 22.73/10.49
% 22.73/10.49 #Partial instantiations: 0
% 22.73/10.49 #Strategies tried : 1
% 22.73/10.49
% 22.73/10.49 Timing (in seconds)
% 22.73/10.49 ----------------------
% 22.73/10.49 Preprocessing : 0.70
% 22.73/10.49 Parsing : 0.35
% 22.73/10.49 CNF conversion : 0.05
% 22.73/10.49 Main loop : 8.66
% 22.73/10.49 Inferencing : 1.45
% 22.73/10.49 Reduction : 4.88
% 22.73/10.49 Demodulation : 4.03
% 22.73/10.49 BG Simplification : 0.12
% 22.73/10.49 Subsumption : 1.70
% 22.73/10.49 Abstraction : 0.15
% 22.73/10.49 MUC search : 0.00
% 22.73/10.49 Cooper : 0.00
% 22.73/10.49 Total : 9.42
% 22.73/10.49 Index Insertion : 0.00
% 22.73/10.49 Index Deletion : 0.00
% 22.73/10.49 Index Matching : 0.00
% 22.73/10.49 BG Taut test : 0.00
%------------------------------------------------------------------------------