TSTP Solution File: NUM501+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM501+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 : n013.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 10:51:54 EDT 2023
% Result : Theorem 177.25s 147.14s
% Output : CNFRefutation 177.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 37
% Syntax : Number of formulae : 78 ( 25 unt; 28 typ; 1 def)
% Number of atoms : 125 ( 48 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 117 ( 42 ~; 38 |; 29 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 17 >; 17 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 11 con; 0-3 aty)
% Number of variables : 35 (; 30 !; 5 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_11 > #skF_6 > #skF_10 > #skF_5 > #skF_9 > #skF_7 > #skF_3 > #skF_2 > #skF_8 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $i ).
tff(xr,type,
xr: $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_11',type,
'#skF_11': $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_10',type,
'#skF_10': $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_9',type,
'#skF_9': $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $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('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
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('#skF_12',type,
'#skF_12': $i ).
tff(f_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(f_502,hypothesis,
( ( xp != sz00 )
& ( xp != sz10 )
& ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& ( xp = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xp) ) )
=> ( ( W0 = sz10 )
| ( W0 = xp ) ) )
& isPrime0(xp)
& ? [W0] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xn,xm) = sdtasdt0(xp,W0) ) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
tff(f_540,hypothesis,
( aNaturalNumber0(xk)
& ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
& ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
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_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_579,hypothesis,
( aNaturalNumber0(xr)
& ? [W0] :
( aNaturalNumber0(W0)
& ( xk = sdtasdt0(xr,W0) ) )
& doDivides0(xr,xk)
& ( xr != sz00 )
& ( xr != sz10 )
& ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& ( xr = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xr) ) )
=> ( ( W0 = sz10 )
| ( W0 = xr ) ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
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_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(f_586,negated_conjecture,
~ ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xn,xm) = sdtasdt0(xr,W0) ) )
| doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_411,plain,
xp != sz00,
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_445,plain,
aNaturalNumber0(xk),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_443,plain,
sdtasdt0(xp,xk) = sdtasdt0(xn,xm),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_1101,plain,
! [W0_125,W1_126] :
( aNaturalNumber0(sdtasdt0(W0_125,W1_126))
| ~ aNaturalNumber0(W1_126)
| ~ aNaturalNumber0(W0_125) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_1221,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_443,c_1101]) ).
tff(c_1295,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_445,c_1221]) ).
tff(c_403,plain,
sdtasdt0(xp,'#skF_9') = sdtasdt0(xn,xm),
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_401,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_405,plain,
aNaturalNumber0('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_441,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_167163,plain,
! [W0_1489,W2_1490] :
( ( sdtsldt0(sdtasdt0(W0_1489,W2_1490),W0_1489) = W2_1490 )
| ~ aNaturalNumber0(W2_1490)
| ~ doDivides0(W0_1489,sdtasdt0(W0_1489,W2_1490))
| ( sz00 = W0_1489 )
| ~ aNaturalNumber0(sdtasdt0(W0_1489,W2_1490))
| ~ aNaturalNumber0(W0_1489) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_167340,plain,
( ( sdtsldt0(sdtasdt0(xp,'#skF_9'),xp) = '#skF_9' )
| ~ aNaturalNumber0('#skF_9')
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xp,'#skF_9'))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_403,c_167163]) ).
tff(c_167511,plain,
( ( xk = '#skF_9' )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_1295,c_403,c_401,c_405,c_441,c_403,c_167340]) ).
tff(c_167512,plain,
xk = '#skF_9',
inference(negUnitSimplification,[status(thm)],[c_411,c_167511]) ).
tff(c_467,plain,
aNaturalNumber0(xr),
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_465,plain,
aNaturalNumber0('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_463,plain,
sdtasdt0(xr,'#skF_12') = xk,
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_159919,plain,
! [W0_1437,W1_1438,W2_1439] :
( ( sdtasdt0(sdtasdt0(W0_1437,W1_1438),W2_1439) = sdtasdt0(W0_1437,sdtasdt0(W1_1438,W2_1439)) )
| ~ aNaturalNumber0(W2_1439)
| ~ aNaturalNumber0(W1_1438)
| ~ aNaturalNumber0(W0_1437) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_160113,plain,
! [W2_1439] :
( ( sdtasdt0(xr,sdtasdt0('#skF_12',W2_1439)) = sdtasdt0(xk,W2_1439) )
| ~ aNaturalNumber0(W2_1439)
| ~ aNaturalNumber0('#skF_12')
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_463,c_159919]) ).
tff(c_160207,plain,
! [W2_1439] :
( ( sdtasdt0(xr,sdtasdt0('#skF_12',W2_1439)) = sdtasdt0(xk,W2_1439) )
| ~ aNaturalNumber0(W2_1439) ),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_465,c_160113]) ).
tff(c_292525,plain,
! [W2_2004] :
( ( sdtasdt0(xr,sdtasdt0('#skF_12',W2_2004)) = sdtasdt0('#skF_9',W2_2004) )
| ~ aNaturalNumber0(W2_2004) ),
inference(demodulation,[status(thm),theory(equality)],[c_167512,c_160207]) ).
tff(c_2709,plain,
! [W1_149,W0_150] :
( ( sdtasdt0(W1_149,W0_150) = sdtasdt0(W0_150,W1_149) )
| ~ aNaturalNumber0(W1_149)
| ~ aNaturalNumber0(W0_150) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_200400,plain,
! [W0_1676] :
( ( sdtasdt0(xp,W0_1676) = sdtasdt0(W0_1676,xp) )
| ~ aNaturalNumber0(W0_1676) ),
inference(resolution,[status(thm)],[c_143,c_2709]) ).
tff(c_200583,plain,
sdtasdt0(xp,'#skF_9') = sdtasdt0('#skF_9',xp),
inference(resolution,[status(thm)],[c_405,c_200400]) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_177458,plain,
! [W0_1570] :
( ( sdtasdt0(xn,W0_1570) = sdtasdt0(W0_1570,xn) )
| ~ aNaturalNumber0(W0_1570) ),
inference(resolution,[status(thm)],[c_147,c_2709]) ).
tff(c_177568,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_145,c_177458]) ).
tff(c_179080,plain,
sdtasdt0(xp,'#skF_9') = sdtasdt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_177568,c_403]) ).
tff(c_202087,plain,
sdtasdt0(xm,xn) = sdtasdt0('#skF_9',xp),
inference(demodulation,[status(thm),theory(equality)],[c_200583,c_179080]) ).
tff(c_200572,plain,
sdtasdt0(xp,'#skF_12') = sdtasdt0('#skF_12',xp),
inference(resolution,[status(thm)],[c_465,c_200400]) ).
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_200642,plain,
( aNaturalNumber0(sdtasdt0('#skF_12',xp))
| ~ aNaturalNumber0('#skF_12')
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_200572,c_12]) ).
tff(c_200698,plain,
aNaturalNumber0(sdtasdt0('#skF_12',xp)),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_465,c_200642]) ).
tff(c_475,plain,
! [W0_114] :
( ( sdtasdt0(xr,W0_114) != sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(W0_114) ),
inference(cnfTransformation,[status(thm)],[f_586]) ).
tff(c_179083,plain,
! [W0_114] :
( ( sdtasdt0(xr,W0_114) != sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(W0_114) ),
inference(demodulation,[status(thm),theory(equality)],[c_177568,c_475]) ).
tff(c_200977,plain,
sdtasdt0(xr,sdtasdt0('#skF_12',xp)) != sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_200698,c_179083]) ).
tff(c_221589,plain,
sdtasdt0(xr,sdtasdt0('#skF_12',xp)) != sdtasdt0('#skF_9',xp),
inference(demodulation,[status(thm),theory(equality)],[c_202087,c_200977]) ).
tff(c_292714,plain,
~ aNaturalNumber0(xp),
inference(superposition,[status(thm),theory(equality)],[c_292525,c_221589]) ).
tff(c_293051,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_143,c_292714]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM501+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % 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
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 15:19:03 EDT 2023
% 0.14/0.36 % CPUTime :
% 177.25/147.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 177.25/147.15
% 177.25/147.15 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 177.33/147.18
% 177.33/147.18 Inference rules
% 177.33/147.18 ----------------------
% 177.33/147.18 #Ref : 156
% 177.33/147.18 #Sup : 62570
% 177.33/147.18 #Fact : 2
% 177.33/147.18 #Define : 0
% 177.33/147.18 #Split : 88
% 177.33/147.18 #Chain : 0
% 177.33/147.18 #Close : 0
% 177.33/147.18
% 177.33/147.18 Ordering : KBO
% 177.33/147.18
% 177.33/147.18 Simplification rules
% 177.33/147.18 ----------------------
% 177.33/147.18 #Subsume : 4302
% 177.33/147.18 #Demod : 128399
% 177.33/147.18 #Tautology : 13958
% 177.33/147.18 #SimpNegUnit : 18652
% 177.33/147.18 #BackRed : 3220
% 177.33/147.18
% 177.33/147.18 #Partial instantiations: 0
% 177.33/147.18 #Strategies tried : 1
% 177.33/147.18
% 177.33/147.18 Timing (in seconds)
% 177.33/147.18 ----------------------
% 177.33/147.18 Preprocessing : 0.79
% 177.33/147.18 Parsing : 0.36
% 177.33/147.18 CNF conversion : 0.07
% 177.33/147.18 Main loop : 145.25
% 177.33/147.18 Inferencing : 6.74
% 177.33/147.18 Reduction : 97.98
% 177.33/147.18 Demodulation : 84.22
% 177.33/147.18 BG Simplification : 0.81
% 177.33/147.18 Subsumption : 32.89
% 177.33/147.18 Abstraction : 1.30
% 177.33/147.18 MUC search : 0.00
% 177.33/147.18 Cooper : 0.00
% 177.33/147.18 Total : 146.09
% 177.33/147.18 Index Insertion : 0.00
% 177.33/147.18 Index Deletion : 0.00
% 177.33/147.18 Index Matching : 0.00
% 177.33/147.18 BG Taut test : 0.00
%------------------------------------------------------------------------------