TSTP Solution File: NUM514+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM514+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 : n004.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 10:51:57 EDT 2023
% Result : Theorem 14.81s 4.48s
% Output : CNFRefutation 15.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 97 ( 42 unt; 20 typ; 3 def)
% Number of atoms : 162 ( 41 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 145 ( 60 ~; 49 |; 21 &)
% ( 3 <=>; 12 =>; 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 : 31 (; 30 !; 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_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_470,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
tff(f_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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_477,hypothesis,
( ( xk != xp )
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2377) ).
tff(f_296,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
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_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
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_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_489,hypothesis,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2613) ).
tff(f_491,negated_conjecture,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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_212,plain,
~ isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).
tff(c_181,plain,
aNaturalNumber0(xr),
inference(cnfTransformation,[status(thm)],[f_470]) ).
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_218,plain,
! [W0_99] :
( ( sdtasdt0(sz10,W0_99) = W0_99 )
| ~ aNaturalNumber0(W0_99) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_237,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_218]) ).
tff(c_1961,plain,
! [W1_136,W0_137] :
( sdtlseqdt0(W1_136,sdtasdt0(W1_136,W0_137))
| ( sz00 = W0_137 )
| ~ aNaturalNumber0(W1_136)
| ~ aNaturalNumber0(W0_137) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_2081,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_237,c_1961]) ).
tff(c_2184,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_2081]) ).
tff(c_5782,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_2184]) ).
tff(c_153,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_5829,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_5782,c_153]) ).
tff(c_5869,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_212,c_5829]) ).
tff(c_5871,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_2184]) ).
tff(c_189,plain,
xp != xk,
inference(cnfTransformation,[status(thm)],[f_477]) ).
tff(c_187,plain,
sdtlseqdt0(xk,xp),
inference(cnfTransformation,[status(thm)],[f_477]) ).
tff(c_2549,plain,
! [W0_142,W1_143] :
( iLess0(W0_142,W1_143)
| ~ sdtlseqdt0(W0_142,W1_143)
| ( W1_143 = W0_142 )
| ~ aNaturalNumber0(W1_143)
| ~ aNaturalNumber0(W0_142) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_2597,plain,
( iLess0(xk,xp)
| ( xp = xk )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_187,c_2549]) ).
tff(c_2647,plain,
( iLess0(xk,xp)
| ( xp = xk )
| ~ aNaturalNumber0(xk) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_2597]) ).
tff(c_2648,plain,
( iLess0(xk,xp)
| ~ aNaturalNumber0(xk) ),
inference(negUnitSimplification,[status(thm)],[c_189,c_2647]) ).
tff(c_2649,plain,
~ aNaturalNumber0(xk),
inference(splitLeft,[status(thm)],[c_2648]) ).
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_1161,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_1807,plain,
! [W0_135] :
( ( sdtasdt0(xn,W0_135) = sdtasdt0(W0_135,xn) )
| ~ aNaturalNumber0(W0_135) ),
inference(resolution,[status(thm)],[c_147,c_1161]) ).
tff(c_1891,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_145,c_1807]) ).
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_1955,plain,
( aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_1891,c_12]) ).
tff(c_1959,plain,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_1955]) ).
tff(c_151,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_1951,plain,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_1891,c_151]) ).
tff(c_167,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_1949,plain,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_1891,c_167]) ).
tff(c_111,plain,
! [W1_71,W0_70] :
( aNaturalNumber0(sdtsldt0(W1_71,W0_70))
| ~ doDivides0(W0_70,W1_71)
| ( sz00 = W0_70 )
| ~ aNaturalNumber0(W1_71)
| ~ aNaturalNumber0(W0_70) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_12595,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sdtasdt0(xm,xn))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_1949,c_111]) ).
tff(c_12608,plain,
( aNaturalNumber0(xk)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_1959,c_1951,c_12595]) ).
tff(c_12610,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5871,c_2649,c_12608]) ).
tff(c_12612,plain,
aNaturalNumber0(xk),
inference(splitRight,[status(thm)],[c_2648]) ).
tff(c_179,plain,
doDivides0(xr,xk),
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_13868,plain,
! [W0_295,W2_296] :
( doDivides0(W0_295,sdtasdt0(W0_295,W2_296))
| ~ aNaturalNumber0(W2_296)
| ~ aNaturalNumber0(sdtasdt0(W0_295,W2_296))
| ~ aNaturalNumber0(W0_295) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_203,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(cnfTransformation,[status(thm)],[f_489]) ).
tff(c_205,plain,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnfTransformation,[status(thm)],[f_491]) ).
tff(c_206,plain,
~ doDivides0(xp,sdtasdt0(xp,sdtsldt0(xk,xr))),
inference(demodulation,[status(thm),theory(equality)],[c_203,c_205]) ).
tff(c_13874,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(sdtasdt0(xp,sdtsldt0(xk,xr)))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_13868,c_206]) ).
tff(c_14013,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(sdtasdt0(xp,sdtsldt0(xk,xr))) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_13874]) ).
tff(c_14300,plain,
~ aNaturalNumber0(sdtasdt0(xp,sdtsldt0(xk,xr))),
inference(splitLeft,[status(thm)],[c_14013]) ).
tff(c_14500,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_12,c_14300]) ).
tff(c_14503,plain,
~ aNaturalNumber0(sdtsldt0(xk,xr)),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_14500]) ).
tff(c_14572,plain,
( ~ doDivides0(xr,xk)
| ( xr = sz00 )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[c_111,c_14503]) ).
tff(c_14575,plain,
xr = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_181,c_12612,c_179,c_14572]) ).
tff(c_177,plain,
isPrime0(xr),
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_14615,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_14575,c_177]) ).
tff(c_14647,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_212,c_14615]) ).
tff(c_14648,plain,
~ aNaturalNumber0(sdtsldt0(xk,xr)),
inference(splitRight,[status(thm)],[c_14013]) ).
tff(c_14848,plain,
( ~ doDivides0(xr,xk)
| ( xr = sz00 )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[c_111,c_14648]) ).
tff(c_14851,plain,
xr = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_181,c_12612,c_179,c_14848]) ).
tff(c_14890,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_14851,c_177]) ).
tff(c_14921,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_212,c_14890]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM514+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/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
% 0.17/0.34 % Computer : n004.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Thu Aug 3 14:52:41 EDT 2023
% 0.17/0.34 % CPUTime :
% 14.81/4.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.81/4.49
% 14.81/4.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.05/4.52
% 15.05/4.52 Inference rules
% 15.05/4.52 ----------------------
% 15.05/4.52 #Ref : 15
% 15.05/4.52 #Sup : 2949
% 15.05/4.52 #Fact : 2
% 15.05/4.52 #Define : 0
% 15.05/4.52 #Split : 30
% 15.05/4.52 #Chain : 0
% 15.05/4.52 #Close : 0
% 15.05/4.52
% 15.05/4.52 Ordering : KBO
% 15.05/4.52
% 15.05/4.52 Simplification rules
% 15.05/4.52 ----------------------
% 15.05/4.52 #Subsume : 111
% 15.05/4.52 #Demod : 6280
% 15.05/4.52 #Tautology : 1163
% 15.05/4.52 #SimpNegUnit : 498
% 15.05/4.52 #BackRed : 680
% 15.05/4.52
% 15.05/4.52 #Partial instantiations: 0
% 15.05/4.52 #Strategies tried : 1
% 15.05/4.52
% 15.05/4.52 Timing (in seconds)
% 15.05/4.52 ----------------------
% 15.05/4.53 Preprocessing : 0.71
% 15.05/4.53 Parsing : 0.36
% 15.05/4.53 CNF conversion : 0.06
% 15.05/4.53 Main loop : 2.75
% 15.05/4.53 Inferencing : 0.65
% 15.05/4.53 Reduction : 1.32
% 15.05/4.53 Demodulation : 1.07
% 15.05/4.53 BG Simplification : 0.09
% 15.05/4.53 Subsumption : 0.51
% 15.05/4.53 Abstraction : 0.08
% 15.05/4.53 MUC search : 0.00
% 15.05/4.53 Cooper : 0.00
% 15.05/4.53 Total : 3.52
% 15.05/4.53 Index Insertion : 0.00
% 15.05/4.53 Index Deletion : 0.00
% 15.05/4.53 Index Matching : 0.00
% 15.05/4.53 BG Taut test : 0.00
%------------------------------------------------------------------------------