TSTP Solution File: NUM504+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM504+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/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 10:51:55 EDT 2023
% Result : Theorem 15.25s 5.22s
% Output : CNFRefutation 15.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 33
% Syntax : Number of formulae : 93 ( 41 unt; 20 typ; 2 def)
% Number of atoms : 153 ( 48 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 133 ( 53 ~; 48 |; 19 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 29 (; 29 !; 0 ?; 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/sandbox2/benchmark/theBenchmark.p',m__1837) ).
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_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
tff(f_87,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
tff(f_442,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
tff(f_456,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
tff(f_483,hypothesis,
( ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm) )
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ( sdtasdt0(xp,xm) != sdtasdt0(xp,xk) )
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2414) ).
tff(f_189,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_1035,plain,
! [W1_120,W0_121] :
( ( sdtasdt0(W1_120,W0_121) = sdtasdt0(W0_121,W1_120) )
| ~ aNaturalNumber0(W1_120)
| ~ aNaturalNumber0(W0_121) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_11996,plain,
! [W0_259] :
( ( sdtasdt0(xp,W0_259) = sdtasdt0(W0_259,xp) )
| ~ aNaturalNumber0(W0_259) ),
inference(resolution,[status(thm)],[c_143,c_1035]) ).
tff(c_12073,plain,
sdtasdt0(xp,xm) = sdtasdt0(xm,xp),
inference(resolution,[status(thm)],[c_145,c_11996]) ).
tff(c_147,plain,
aNaturalNumber0(xn),
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_201,plain,
~ isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_398,plain,
! [W0_104] :
( ( sdtasdt0(sz10,W0_104) = W0_104 )
| ~ aNaturalNumber0(W0_104) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_423,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_398]) ).
tff(c_1315,plain,
! [W1_128,W0_129] :
( sdtlseqdt0(W1_128,sdtasdt0(W1_128,W0_129))
| ( sz00 = W0_129 )
| ~ aNaturalNumber0(W1_128)
| ~ aNaturalNumber0(W0_129) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_1351,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_423,c_1315]) ).
tff(c_1429,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_1351]) ).
tff(c_3279,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_1429]) ).
tff(c_153,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_3305,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_3279,c_153]) ).
tff(c_3325,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_201,c_3305]) ).
tff(c_3327,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_1429]) ).
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_4320,plain,
! [W1_193,W0_194] :
( aNaturalNumber0(sdtsldt0(W1_193,W0_194))
| ~ doDivides0(W0_194,W1_193)
| ( sz00 = W0_194 )
| ~ aNaturalNumber0(W1_193)
| ~ aNaturalNumber0(W0_194) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_4348,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_4320]) ).
tff(c_4359,plain,
( aNaturalNumber0(xk)
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_151,c_4348]) ).
tff(c_4360,plain,
( aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(negUnitSimplification,[status(thm)],[c_3327,c_4359]) ).
tff(c_6305,plain,
~ aNaturalNumber0(sdtasdt0(xn,xm)),
inference(splitLeft,[status(thm)],[c_4360]) ).
tff(c_6308,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_12,c_6305]) ).
tff(c_6312,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_6308]) ).
tff(c_6313,plain,
aNaturalNumber0(xk),
inference(splitRight,[status(thm)],[c_4360]) ).
tff(c_12056,plain,
sdtasdt0(xp,xk) = sdtasdt0(xk,xp),
inference(resolution,[status(thm)],[c_6313,c_11996]) ).
tff(c_191,plain,
sdtasdt0(xp,xm) != sdtasdt0(xp,xk),
inference(cnfTransformation,[status(thm)],[f_483]) ).
tff(c_12077,plain,
sdtasdt0(xp,xm) != sdtasdt0(xk,xp),
inference(demodulation,[status(thm),theory(equality)],[c_12056,c_191]) ).
tff(c_12484,plain,
sdtasdt0(xm,xp) != sdtasdt0(xk,xp),
inference(demodulation,[status(thm),theory(equality)],[c_12073,c_12077]) ).
tff(c_12539,plain,
( aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_12073,c_12]) ).
tff(c_12590,plain,
aNaturalNumber0(sdtasdt0(xm,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_145,c_12539]) ).
tff(c_12130,plain,
( aNaturalNumber0(sdtasdt0(xk,xp))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_12056,c_12]) ).
tff(c_12181,plain,
aNaturalNumber0(sdtasdt0(xk,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_6313,c_12130]) ).
tff(c_189,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnfTransformation,[status(thm)],[f_483]) ).
tff(c_12076,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xk,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_12056,c_189]) ).
tff(c_18358,plain,
sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xk,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_12073,c_12076]) ).
tff(c_12342,plain,
! [W0_260] :
( ( sdtasdt0(xm,W0_260) = sdtasdt0(W0_260,xm) )
| ~ aNaturalNumber0(W0_260) ),
inference(resolution,[status(thm)],[c_145,c_1035]) ).
tff(c_12418,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_147,c_12342]) ).
tff(c_6314,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(splitRight,[status(thm)],[c_4360]) ).
tff(c_12747,plain,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_12418,c_6314]) ).
tff(c_12749,plain,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_12418,c_151]) ).
tff(c_12748,plain,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_12418,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_13053,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_12748,c_109]) ).
tff(c_13066,plain,
( ( sdtasdt0(xm,xn) = sdtasdt0(xk,xp) )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_12747,c_12749,c_12056,c_13053]) ).
tff(c_13067,plain,
sdtasdt0(xm,xn) = sdtasdt0(xk,xp),
inference(negUnitSimplification,[status(thm)],[c_3327,c_13066]) ).
tff(c_14844,plain,
sdtasdt0(xn,xm) = sdtasdt0(xk,xp),
inference(demodulation,[status(thm),theory(equality)],[c_13067,c_12418]) ).
tff(c_193,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnfTransformation,[status(thm)],[f_483]) ).
tff(c_12485,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_12073,c_193]) ).
tff(c_18377,plain,
sdtlseqdt0(sdtasdt0(xk,xp),sdtasdt0(xm,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_14844,c_12485]) ).
tff(c_66,plain,
! [W1_45,W0_44] :
( ( W1_45 = W0_44 )
| ~ sdtlseqdt0(W1_45,W0_44)
| ~ sdtlseqdt0(W0_44,W1_45)
| ~ aNaturalNumber0(W1_45)
| ~ aNaturalNumber0(W0_44) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_18381,plain,
( ( sdtasdt0(xm,xp) = sdtasdt0(xk,xp) )
| ~ sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xk,xp))
| ~ aNaturalNumber0(sdtasdt0(xk,xp))
| ~ aNaturalNumber0(sdtasdt0(xm,xp)) ),
inference(resolution,[status(thm)],[c_18377,c_66]) ).
tff(c_18390,plain,
sdtasdt0(xm,xp) = sdtasdt0(xk,xp),
inference(demodulation,[status(thm),theory(equality)],[c_12590,c_12181,c_18358,c_18381]) ).
tff(c_18392,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12484,c_18390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM504+1 : 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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 15:21:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 15.25/5.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.25/5.23
% 15.25/5.23 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.42/5.26
% 15.42/5.26 Inference rules
% 15.42/5.26 ----------------------
% 15.42/5.26 #Ref : 6
% 15.42/5.26 #Sup : 3723
% 15.42/5.26 #Fact : 2
% 15.42/5.26 #Define : 0
% 15.42/5.26 #Split : 15
% 15.42/5.26 #Chain : 0
% 15.42/5.26 #Close : 0
% 15.42/5.26
% 15.42/5.26 Ordering : KBO
% 15.42/5.26
% 15.42/5.26 Simplification rules
% 15.42/5.26 ----------------------
% 15.42/5.26 #Subsume : 132
% 15.42/5.26 #Demod : 6784
% 15.42/5.26 #Tautology : 1441
% 15.42/5.26 #SimpNegUnit : 780
% 15.42/5.26 #BackRed : 367
% 15.42/5.26
% 15.42/5.26 #Partial instantiations: 0
% 15.42/5.26 #Strategies tried : 1
% 15.42/5.26
% 15.42/5.26 Timing (in seconds)
% 15.42/5.26 ----------------------
% 15.42/5.26 Preprocessing : 0.68
% 15.42/5.26 Parsing : 0.34
% 15.42/5.26 CNF conversion : 0.05
% 15.42/5.26 Main loop : 3.52
% 15.42/5.26 Inferencing : 0.77
% 15.42/5.26 Reduction : 1.78
% 15.42/5.26 Demodulation : 1.45
% 15.42/5.26 BG Simplification : 0.09
% 15.42/5.26 Subsumption : 0.67
% 15.42/5.26 Abstraction : 0.09
% 15.42/5.26 MUC search : 0.00
% 15.42/5.26 Cooper : 0.00
% 15.42/5.26 Total : 4.25
% 15.42/5.26 Index Insertion : 0.00
% 15.42/5.26 Index Deletion : 0.00
% 15.42/5.26 Index Matching : 0.00
% 15.42/5.26 BG Taut test : 0.00
%------------------------------------------------------------------------------