TSTP Solution File: NUM501+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM501+1 : 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/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 : Tue Aug 22 10:51:54 EDT 2023
% Result : Theorem 29.72s 17.51s
% Output : CNFRefutation 29.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 35
% Syntax : Number of formulae : 88 ( 34 unt; 20 typ; 3 def)
% Number of atoms : 160 ( 38 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 153 ( 61 ~; 56 |; 21 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 13 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 39 (; 38 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%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(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(isPrime0,type,
isPrime0: $i > $o ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
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_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
tff(f_403,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
tff(f_87,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
tff(f_278,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00 )
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
tff(f_442,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
tff(f_456,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
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_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(f_470,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
tff(f_307,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
tff(f_335,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W1,W2) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
tff(f_472,negated_conjecture,
~ doDivides0(xr,sdtasdt0(xn,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
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_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_135,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_187,plain,
~ isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_359,plain,
! [W0_103] :
( ( sdtasdt0(sz10,W0_103) = W0_103 )
| ~ aNaturalNumber0(W0_103) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_380,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_359]) ).
tff(c_1662,plain,
! [W1_132,W0_133] :
( sdtlseqdt0(W1_132,sdtasdt0(W1_132,W0_133))
| ( sz00 = W0_133 )
| ~ aNaturalNumber0(W1_132)
| ~ aNaturalNumber0(W0_133) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_1698,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_380,c_1662]) ).
tff(c_1781,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_1698]) ).
tff(c_1889,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_1781]) ).
tff(c_153,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_1912,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_1889,c_153]) ).
tff(c_1930,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_187,c_1912]) ).
tff(c_1932,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_1781]) ).
tff(c_151,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_167,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_3873,plain,
! [W1_172,W0_173] :
( aNaturalNumber0(sdtsldt0(W1_172,W0_173))
| ~ doDivides0(W0_173,W1_172)
| ( sz00 = W0_173 )
| ~ aNaturalNumber0(W1_172)
| ~ aNaturalNumber0(W0_173) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_3907,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_3873]) ).
tff(c_3920,plain,
( aNaturalNumber0(xk)
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_151,c_3907]) ).
tff(c_3921,plain,
( aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(negUnitSimplification,[status(thm)],[c_1932,c_3920]) ).
tff(c_6523,plain,
~ aNaturalNumber0(sdtasdt0(xn,xm)),
inference(splitLeft,[status(thm)],[c_3921]) ).
tff(c_6526,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_12,c_6523]) ).
tff(c_6530,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_6526]) ).
tff(c_6531,plain,
aNaturalNumber0(xk),
inference(splitRight,[status(thm)],[c_3921]) ).
tff(c_1078,plain,
! [W1_121,W0_122] :
( ( sdtasdt0(W1_121,W0_122) = sdtasdt0(W0_122,W1_121) )
| ~ aNaturalNumber0(W1_121)
| ~ aNaturalNumber0(W0_122) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_12957,plain,
! [W0_247] :
( ( sdtasdt0(xp,W0_247) = sdtasdt0(W0_247,xp) )
| ~ aNaturalNumber0(W0_247) ),
inference(resolution,[status(thm)],[c_143,c_1078]) ).
tff(c_13068,plain,
sdtasdt0(xp,xk) = sdtasdt0(xk,xp),
inference(resolution,[status(thm)],[c_6531,c_12957]) ).
tff(c_14556,plain,
( aNaturalNumber0(sdtasdt0(xk,xp))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_13068,c_12]) ).
tff(c_14607,plain,
aNaturalNumber0(sdtasdt0(xk,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_6531,c_14556]) ).
tff(c_181,plain,
aNaturalNumber0(xr),
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_179,plain,
doDivides0(xr,xk),
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_101,plain,
! [W0_65,W2_69] :
( doDivides0(W0_65,sdtasdt0(W0_65,W2_69))
| ~ aNaturalNumber0(W2_69)
| ~ aNaturalNumber0(sdtasdt0(W0_65,W2_69))
| ~ aNaturalNumber0(W0_65) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_4659,plain,
! [W0_189,W2_190,W1_191] :
( doDivides0(W0_189,W2_190)
| ~ doDivides0(W1_191,W2_190)
| ~ doDivides0(W0_189,W1_191)
| ~ aNaturalNumber0(W2_190)
| ~ aNaturalNumber0(W1_191)
| ~ aNaturalNumber0(W0_189) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_60489,plain,
! [W0_432,W0_433,W2_434] :
( doDivides0(W0_432,sdtasdt0(W0_433,W2_434))
| ~ doDivides0(W0_432,W0_433)
| ~ aNaturalNumber0(W0_432)
| ~ aNaturalNumber0(W2_434)
| ~ aNaturalNumber0(sdtasdt0(W0_433,W2_434))
| ~ aNaturalNumber0(W0_433) ),
inference(resolution,[status(thm)],[c_101,c_4659]) ).
tff(c_13476,plain,
! [W0_248] :
( ( sdtasdt0(xm,W0_248) = sdtasdt0(W0_248,xm) )
| ~ aNaturalNumber0(W0_248) ),
inference(resolution,[status(thm)],[c_145,c_1078]) ).
tff(c_13618,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_147,c_13476]) ).
tff(c_6532,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(splitRight,[status(thm)],[c_3921]) ).
tff(c_13909,plain,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_13618,c_6532]) ).
tff(c_13911,plain,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_13618,c_151]) ).
tff(c_13910,plain,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_13618,c_167]) ).
tff(c_109,plain,
! [W0_70,W1_71] :
( ( sdtasdt0(W0_70,sdtsldt0(W1_71,W0_70)) = W1_71 )
| ~ doDivides0(W0_70,W1_71)
| ( sz00 = W0_70 )
| ~ aNaturalNumber0(W1_71)
| ~ aNaturalNumber0(W0_70) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_14709,plain,
( ( sdtasdt0(xp,xk) = sdtasdt0(xm,xn) )
| ~ doDivides0(xp,sdtasdt0(xm,xn))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_13910,c_109]) ).
tff(c_14722,plain,
( ( sdtasdt0(xm,xn) = sdtasdt0(xk,xp) )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_13909,c_13911,c_13068,c_14709]) ).
tff(c_14723,plain,
sdtasdt0(xm,xn) = sdtasdt0(xk,xp),
inference(negUnitSimplification,[status(thm)],[c_1932,c_14722]) ).
tff(c_183,plain,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnfTransformation,[status(thm)],[f_472]) ).
tff(c_13912,plain,
~ doDivides0(xr,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_13618,c_183]) ).
tff(c_15265,plain,
~ doDivides0(xr,sdtasdt0(xk,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_14723,c_13912]) ).
tff(c_60496,plain,
( ~ doDivides0(xr,xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xk,xp))
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_60489,c_15265]) ).
tff(c_60913,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6531,c_14607,c_143,c_181,c_179,c_60496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM501+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % 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
% 0.14/0.36 % Computer : n002.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 15:31:46 EDT 2023
% 0.14/0.36 % CPUTime :
% 29.72/17.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.81/17.52
% 29.81/17.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.81/17.55
% 29.81/17.55 Inference rules
% 29.81/17.56 ----------------------
% 29.81/17.56 #Ref : 5
% 29.81/17.56 #Sup : 12518
% 29.81/17.56 #Fact : 2
% 29.81/17.56 #Define : 0
% 29.81/17.56 #Split : 24
% 29.81/17.56 #Chain : 0
% 29.81/17.56 #Close : 0
% 29.81/17.56
% 29.81/17.56 Ordering : KBO
% 29.81/17.56
% 29.81/17.56 Simplification rules
% 29.81/17.56 ----------------------
% 29.81/17.56 #Subsume : 1441
% 29.81/17.56 #Demod : 22968
% 29.81/17.56 #Tautology : 4557
% 29.81/17.56 #SimpNegUnit : 2398
% 29.81/17.56 #BackRed : 388
% 29.81/17.56
% 29.81/17.56 #Partial instantiations: 0
% 29.81/17.56 #Strategies tried : 1
% 29.81/17.56
% 29.81/17.56 Timing (in seconds)
% 29.81/17.56 ----------------------
% 29.81/17.56 Preprocessing : 0.71
% 29.81/17.56 Parsing : 0.37
% 29.81/17.56 CNF conversion : 0.05
% 29.81/17.56 Main loop : 15.77
% 29.81/17.56 Inferencing : 2.04
% 29.81/17.56 Reduction : 9.83
% 29.81/17.56 Demodulation : 8.18
% 29.81/17.56 BG Simplification : 0.14
% 29.81/17.56 Subsumption : 3.11
% 29.81/17.56 Abstraction : 0.20
% 29.81/17.56 MUC search : 0.00
% 29.81/17.56 Cooper : 0.00
% 29.81/17.56 Total : 16.54
% 29.81/17.56 Index Insertion : 0.00
% 29.81/17.56 Index Deletion : 0.00
% 29.81/17.56 Index Matching : 0.00
% 29.81/17.56 BG Taut test : 0.00
%------------------------------------------------------------------------------