TSTP Solution File: NUM510+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM510+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 : n016.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 10:51:56 EDT 2023
% Result : Theorem 25.25s 12.29s
% Output : CNFRefutation 25.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 44
% Syntax : Number of formulae : 209 ( 89 unt; 20 typ; 3 def)
% Number of atoms : 440 ( 164 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 423 ( 172 ~; 193 |; 33 &)
% ( 3 <=>; 22 =>; 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 : 81 (; 80 !; 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_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
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_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
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_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_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(f_442,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
tff(f_465,hypothesis,
( ( xk != sz00 )
& ( xk != sz10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).
tff(f_477,hypothesis,
( ( xk != xp )
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2377) ).
tff(f_93,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
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_151,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
tff(f_481,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
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_455,hypothesis,
( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
tff(f_212,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
tff(f_486,negated_conjecture,
~ ( ( sdtsldt0(xn,xr) != xn )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_370,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( doDivides0(W0,W1)
& ( W1 != sz00 ) )
=> sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
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_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_131,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1,W2] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_133,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_198,plain,
~ isPrime0(sz10),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_133]) ).
tff(c_181,plain,
aNaturalNumber0(xr),
inference(cnfTransformation,[status(thm)],[f_470]) ).
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_200,plain,
~ isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).
tff(c_58503,plain,
! [W0_612] :
( ( sdtasdt0(sz10,W0_612) = W0_612 )
| ~ aNaturalNumber0(W0_612) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_58522,plain,
sdtasdt0(sz10,xr) = xr,
inference(resolution,[status(thm)],[c_181,c_58503]) ).
tff(c_59829,plain,
! [W1_643,W0_644] :
( sdtlseqdt0(W1_643,sdtasdt0(W1_643,W0_644))
| ( sz00 = W0_644 )
| ~ aNaturalNumber0(W1_643)
| ~ aNaturalNumber0(W0_644) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_59865,plain,
( sdtlseqdt0(sz10,xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_58522,c_59829]) ).
tff(c_59945,plain,
( sdtlseqdt0(sz10,xr)
| ( xr = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_181,c_8,c_59865]) ).
tff(c_62364,plain,
xr = sz00,
inference(splitLeft,[status(thm)],[c_59945]) ).
tff(c_177,plain,
isPrime0(xr),
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_62394,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_62364,c_177]) ).
tff(c_62419,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_200,c_62394]) ).
tff(c_62420,plain,
sdtlseqdt0(sz10,xr),
inference(splitRight,[status(thm)],[c_59945]) ).
tff(c_64377,plain,
! [W0_743,W1_744] :
( iLess0(W0_743,W1_744)
| ~ sdtlseqdt0(W0_743,W1_744)
| ( W1_744 = W0_743 )
| ~ aNaturalNumber0(W1_744)
| ~ aNaturalNumber0(W0_743) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_64386,plain,
( iLess0(sz10,xr)
| ( xr = sz10 )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[c_62420,c_64377]) ).
tff(c_64443,plain,
( iLess0(sz10,xr)
| ( xr = sz10 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_181,c_64386]) ).
tff(c_68731,plain,
xr = sz10,
inference(splitLeft,[status(thm)],[c_64443]) ).
tff(c_68873,plain,
isPrime0(sz10),
inference(demodulation,[status(thm),theory(equality)],[c_68731,c_177]) ).
tff(c_68907,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_198,c_68873]) ).
tff(c_68909,plain,
xr != sz10,
inference(splitRight,[status(thm)],[c_64443]) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_58429,plain,
! [W0_610] :
( ( sdtasdt0(W0_610,sz10) = W0_610 )
| ~ aNaturalNumber0(W0_610) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_58450,plain,
sdtasdt0(xn,sz10) = xn,
inference(resolution,[status(thm)],[c_147,c_58429]) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_58527,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_58503]) ).
tff(c_59895,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_58527,c_59829]) ).
tff(c_59968,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_59895]) ).
tff(c_62468,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_59968]) ).
tff(c_153,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_62493,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_62468,c_153]) ).
tff(c_62511,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_200,c_62493]) ).
tff(c_62513,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_59968]) ).
tff(c_175,plain,
xk != sz00,
inference(cnfTransformation,[status(thm)],[f_465]) ).
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_62515,plain,
! [W0_704,W1_705] :
( iLess0(W0_704,W1_705)
| ~ sdtlseqdt0(W0_704,W1_705)
| ( W1_705 = W0_704 )
| ~ aNaturalNumber0(W1_705)
| ~ aNaturalNumber0(W0_704) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_62566,plain,
( iLess0(xk,xp)
| ( xp = xk )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_187,c_62515]) ).
tff(c_62620,plain,
( iLess0(xk,xp)
| ( xp = xk )
| ~ aNaturalNumber0(xk) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_62566]) ).
tff(c_62621,plain,
( iLess0(xk,xp)
| ~ aNaturalNumber0(xk) ),
inference(negUnitSimplification,[status(thm)],[c_189,c_62620]) ).
tff(c_62787,plain,
~ aNaturalNumber0(xk),
inference(splitLeft,[status(thm)],[c_62621]) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_58625,plain,
! [W0_615] :
( ( sdtasdt0(sz00,W0_615) = sz00 )
| ~ aNaturalNumber0(W0_615) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_58645,plain,
sdtasdt0(sz00,xm) = sz00,
inference(resolution,[status(thm)],[c_145,c_58625]) ).
tff(c_58524,plain,
sdtasdt0(sz10,xn) = xn,
inference(resolution,[status(thm)],[c_147,c_58503]) ).
tff(c_59892,plain,
( sdtlseqdt0(sz10,xn)
| ( xn = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_58524,c_59829]) ).
tff(c_59966,plain,
( sdtlseqdt0(sz10,xn)
| ( xn = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_8,c_59892]) ).
tff(c_62514,plain,
xn = sz00,
inference(splitLeft,[status(thm)],[c_59966]) ).
tff(c_151,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_62641,plain,
doDivides0(xp,sdtasdt0(sz00,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_62514,c_151]) ).
tff(c_62664,plain,
doDivides0(xp,sz00),
inference(demodulation,[status(thm),theory(equality)],[c_58645,c_62641]) ).
tff(c_167,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_62639,plain,
sdtsldt0(sdtasdt0(sz00,xm),xp) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_62514,c_167]) ).
tff(c_62662,plain,
sdtsldt0(sz00,xp) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_58645,c_62639]) ).
tff(c_62948,plain,
! [W1_712,W0_713] :
( aNaturalNumber0(sdtsldt0(W1_712,W0_713))
| ~ doDivides0(W0_713,W1_712)
| ( sz00 = W0_713 )
| ~ aNaturalNumber0(W1_712)
| ~ aNaturalNumber0(W0_713) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_62982,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sz00)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_62662,c_62948]) ).
tff(c_62998,plain,
( aNaturalNumber0(xk)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_4,c_62664,c_62982]) ).
tff(c_63000,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62513,c_62787,c_62998]) ).
tff(c_63002,plain,
aNaturalNumber0(xk),
inference(splitRight,[status(thm)],[c_62621]) ).
tff(c_64322,plain,
! [W0_741,W1_742] :
( ( sdtasdt0(W0_741,sdtsldt0(W1_742,W0_741)) = W1_742 )
| ~ doDivides0(W0_741,W1_742)
| ( sz00 = W0_741 )
| ~ aNaturalNumber0(W1_742)
| ~ aNaturalNumber0(W0_741) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_64342,plain,
( ( sdtasdt0(xp,xk) = sz00 )
| ~ doDivides0(xp,sz00)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_62662,c_64322]) ).
tff(c_64349,plain,
( ( sdtasdt0(xp,xk) = sz00 )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_4,c_62664,c_64342]) ).
tff(c_64350,plain,
sdtasdt0(xp,xk) = sz00,
inference(negUnitSimplification,[status(thm)],[c_62513,c_64349]) ).
tff(c_50,plain,
! [W1_33,W0_32] :
( ( sz00 = W1_33 )
| ( sz00 = W0_32 )
| ( sdtasdt0(W0_32,W1_33) != sz00 )
| ~ aNaturalNumber0(W1_33)
| ~ aNaturalNumber0(W0_32) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_64359,plain,
( ( xk = sz00 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_64350,c_50]) ).
tff(c_64372,plain,
( ( xk = sz00 )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_63002,c_64359]) ).
tff(c_64374,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62513,c_175,c_64372]) ).
tff(c_64376,plain,
xn != sz00,
inference(splitRight,[status(thm)],[c_59966]) ).
tff(c_62421,plain,
xr != sz00,
inference(splitRight,[status(thm)],[c_59945]) ).
tff(c_193,plain,
doDivides0(xr,xn),
inference(cnfTransformation,[status(thm)],[f_481]) ).
tff(c_59044,plain,
! [W1_627,W0_628] :
( ( sdtasdt0(W1_627,W0_628) = sdtasdt0(W0_628,W1_627) )
| ~ aNaturalNumber0(W1_627)
| ~ aNaturalNumber0(W0_628) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_59072,plain,
! [W0_629] :
( ( sdtasdt0(xr,W0_629) = sdtasdt0(W0_629,xr) )
| ~ aNaturalNumber0(W0_629) ),
inference(resolution,[status(thm)],[c_181,c_59044]) ).
tff(c_59106,plain,
sdtasdt0(xr,xn) = sdtasdt0(xn,xr),
inference(resolution,[status(thm)],[c_147,c_59072]) ).
tff(c_331,plain,
! [W0_102] :
( ( sdtasdt0(sz10,W0_102) = W0_102 )
| ~ aNaturalNumber0(W0_102) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_350,plain,
sdtasdt0(sz10,xr) = xr,
inference(resolution,[status(thm)],[c_181,c_331]) ).
tff(c_3682,plain,
! [W1_164,W0_165] :
( sdtlseqdt0(W1_164,sdtasdt0(W1_164,W0_165))
| ( sz00 = W0_165 )
| ~ aNaturalNumber0(W1_164)
| ~ aNaturalNumber0(W0_165) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_3763,plain,
( sdtlseqdt0(sz10,xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_350,c_3682]) ).
tff(c_3879,plain,
( sdtlseqdt0(sz10,xr)
| ( xr = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_181,c_8,c_3763]) ).
tff(c_18597,plain,
xr = sz00,
inference(splitLeft,[status(thm)],[c_3879]) ).
tff(c_18656,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_18597,c_177]) ).
tff(c_18698,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_200,c_18656]) ).
tff(c_18700,plain,
xr != sz00,
inference(splitRight,[status(thm)],[c_3879]) ).
tff(c_352,plain,
sdtasdt0(sz10,xn) = xn,
inference(resolution,[status(thm)],[c_147,c_331]) ).
tff(c_3769,plain,
( sdtlseqdt0(sz10,xn)
| ( xn = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_352,c_3682]) ).
tff(c_3883,plain,
( sdtlseqdt0(sz10,xn)
| ( xn = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_8,c_3769]) ).
tff(c_4004,plain,
xn = sz00,
inference(splitLeft,[status(thm)],[c_3883]) ).
tff(c_165,plain,
xp != xn,
inference(cnfTransformation,[status(thm)],[f_455]) ).
tff(c_4037,plain,
xp != sz00,
inference(demodulation,[status(thm),theory(equality)],[c_4004,c_165]) ).
tff(c_8782,plain,
! [W0_226,W1_227] :
( iLess0(W0_226,W1_227)
| ~ sdtlseqdt0(W0_226,W1_227)
| ( W1_227 = W0_226 )
| ~ aNaturalNumber0(W1_227)
| ~ aNaturalNumber0(W0_226) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_8836,plain,
( iLess0(xk,xp)
| ( xp = xk )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_187,c_8782]) ).
tff(c_8893,plain,
( iLess0(xk,xp)
| ( xp = xk )
| ~ aNaturalNumber0(xk) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8836]) ).
tff(c_8894,plain,
( iLess0(xk,xp)
| ~ aNaturalNumber0(xk) ),
inference(negUnitSimplification,[status(thm)],[c_189,c_8893]) ).
tff(c_8902,plain,
~ aNaturalNumber0(xk),
inference(splitLeft,[status(thm)],[c_8894]) ).
tff(c_203,plain,
! [W0_99] :
( ( sdtasdt0(W0_99,sz00) = sz00 )
| ~ aNaturalNumber0(W0_99) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_223,plain,
sdtasdt0(xm,sz00) = sz00,
inference(resolution,[status(thm)],[c_145,c_203]) ).
tff(c_2920,plain,
! [W1_154,W0_155] :
( ( sdtasdt0(W1_154,W0_155) = sdtasdt0(W0_155,W1_154) )
| ~ aNaturalNumber0(W1_154)
| ~ aNaturalNumber0(W0_155) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_3539,plain,
! [W0_163] :
( ( sdtasdt0(xm,W0_163) = sdtasdt0(W0_163,xm) )
| ~ aNaturalNumber0(W0_163) ),
inference(resolution,[status(thm)],[c_145,c_2920]) ).
tff(c_3618,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_147,c_3539]) ).
tff(c_3625,plain,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_3618,c_151]) ).
tff(c_4005,plain,
doDivides0(xp,sdtasdt0(xm,sz00)),
inference(demodulation,[status(thm),theory(equality)],[c_4004,c_3625]) ).
tff(c_4039,plain,
doDivides0(xp,sz00),
inference(demodulation,[status(thm),theory(equality)],[c_223,c_4005]) ).
tff(c_3624,plain,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_3618,c_167]) ).
tff(c_8391,plain,
sdtsldt0(sz00,xp) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_223,c_4004,c_3624]) ).
tff(c_10123,plain,
! [W1_243,W0_244] :
( aNaturalNumber0(sdtsldt0(W1_243,W0_244))
| ~ doDivides0(W0_244,W1_243)
| ( sz00 = W0_244 )
| ~ aNaturalNumber0(W1_243)
| ~ aNaturalNumber0(W0_244) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_10163,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sz00)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_8391,c_10123]) ).
tff(c_10178,plain,
( aNaturalNumber0(xk)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_4,c_4039,c_10163]) ).
tff(c_10180,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4037,c_8902,c_10178]) ).
tff(c_10182,plain,
aNaturalNumber0(xk),
inference(splitRight,[status(thm)],[c_8894]) ).
tff(c_12532,plain,
! [W0_273,W1_274] :
( ( sdtasdt0(W0_273,sdtsldt0(W1_274,W0_273)) = W1_274 )
| ~ doDivides0(W0_273,W1_274)
| ( sz00 = W0_273 )
| ~ aNaturalNumber0(W1_274)
| ~ aNaturalNumber0(W0_273) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_12555,plain,
( ( sdtasdt0(xp,xk) = sz00 )
| ~ doDivides0(xp,sz00)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_8391,c_12532]) ).
tff(c_12562,plain,
( ( sdtasdt0(xp,xk) = sz00 )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_4,c_4039,c_12555]) ).
tff(c_12563,plain,
sdtasdt0(xp,xk) = sz00,
inference(negUnitSimplification,[status(thm)],[c_4037,c_12562]) ).
tff(c_12615,plain,
( ( xk = sz00 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_12563,c_50]) ).
tff(c_12628,plain,
( ( xk = sz00 )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_10182,c_12615]) ).
tff(c_12630,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4037,c_175,c_12628]) ).
tff(c_12632,plain,
xn != sz00,
inference(splitRight,[status(thm)],[c_3883]) ).
tff(c_1742,plain,
! [W1_134,W0_135] :
( sdtlseqdt0(W1_134,sdtasdt0(W1_134,W0_135))
| ( sz00 = W0_135 )
| ~ aNaturalNumber0(W1_134)
| ~ aNaturalNumber0(W0_135) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_1811,plain,
( sdtlseqdt0(sz10,xr)
| ( xr = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_350,c_1742]) ).
tff(c_1917,plain,
( sdtlseqdt0(sz10,xr)
| ( xr = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_181,c_8,c_1811]) ).
tff(c_2713,plain,
xr = sz00,
inference(splitLeft,[status(thm)],[c_1917]) ).
tff(c_2756,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_2713,c_177]) ).
tff(c_2792,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_200,c_2756]) ).
tff(c_2794,plain,
xr != sz00,
inference(splitRight,[status(thm)],[c_1917]) ).
tff(c_2823,plain,
! [W1_152,W0_153] :
( aNaturalNumber0(sdtsldt0(W1_152,W0_153))
| ~ doDivides0(W0_153,W1_152)
| ( sz00 = W0_153 )
| ~ aNaturalNumber0(W1_152)
| ~ aNaturalNumber0(W0_153) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_1066,plain,
! [W1_120,W0_121] :
( sdtlseqdt0(W1_120,W0_121)
| sdtlseqdt0(W0_121,W1_120)
| ~ aNaturalNumber0(W1_120)
| ~ aNaturalNumber0(W0_121) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_195,plain,
( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ( sdtsldt0(xn,xr) = xn ) ),
inference(cnfTransformation,[status(thm)],[f_486]) ).
tff(c_201,plain,
~ sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(splitLeft,[status(thm)],[c_195]) ).
tff(c_1075,plain,
( sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_1066,c_201]) ).
tff(c_1093,plain,
( sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_1075]) ).
tff(c_1135,plain,
~ aNaturalNumber0(sdtsldt0(xn,xr)),
inference(splitLeft,[status(thm)],[c_1093]) ).
tff(c_2834,plain,
( ~ doDivides0(xr,xn)
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[c_2823,c_1135]) ).
tff(c_2866,plain,
xr = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_181,c_147,c_193,c_2834]) ).
tff(c_2868,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2794,c_2866]) ).
tff(c_2870,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(splitRight,[status(thm)],[c_1093]) ).
tff(c_21497,plain,
! [W0_388,W1_389] :
( sdtlseqdt0(W0_388,W1_389)
| ( sz00 = W1_389 )
| ~ doDivides0(W0_388,W1_389)
| ~ aNaturalNumber0(W1_389)
| ~ aNaturalNumber0(W0_388) ),
inference(cnfTransformation,[status(thm)],[f_370]) ).
tff(c_21514,plain,
( ( xn = sz00 )
| ~ doDivides0(sdtsldt0(xn,xr),xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(resolution,[status(thm)],[c_21497,c_201]) ).
tff(c_21534,plain,
( ( xn = sz00 )
| ~ doDivides0(sdtsldt0(xn,xr),xn) ),
inference(demodulation,[status(thm),theory(equality)],[c_2870,c_147,c_21514]) ).
tff(c_21535,plain,
~ doDivides0(sdtsldt0(xn,xr),xn),
inference(negUnitSimplification,[status(thm)],[c_12632,c_21534]) ).
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_3203,plain,
! [W0_160] :
( ( sdtasdt0(xr,W0_160) = sdtasdt0(W0_160,xr) )
| ~ aNaturalNumber0(W0_160) ),
inference(resolution,[status(thm)],[c_181,c_2920]) ).
tff(c_3254,plain,
sdtasdt0(sdtsldt0(xn,xr),xr) = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(resolution,[status(thm)],[c_2870,c_3203]) ).
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_18589,plain,
( aNaturalNumber0(sdtasdt0(xr,sdtsldt0(xn,xr)))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm),theory(equality)],[c_3254,c_12]) ).
tff(c_18595,plain,
aNaturalNumber0(sdtasdt0(xr,sdtsldt0(xn,xr))),
inference(demodulation,[status(thm),theory(equality)],[c_2870,c_181,c_18589]) ).
tff(c_44917,plain,
! [W0_527,W2_528] :
( doDivides0(W0_527,sdtasdt0(W0_527,W2_528))
| ~ aNaturalNumber0(W2_528)
| ~ aNaturalNumber0(sdtasdt0(W0_527,W2_528))
| ~ aNaturalNumber0(W0_527) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_44944,plain,
( doDivides0(sdtsldt0(xn,xr),sdtasdt0(xr,sdtsldt0(xn,xr)))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm),theory(equality)],[c_3254,c_44917]) ).
tff(c_45091,plain,
doDivides0(sdtsldt0(xn,xr),sdtasdt0(xr,sdtsldt0(xn,xr))),
inference(demodulation,[status(thm),theory(equality)],[c_2870,c_18595,c_3254,c_181,c_44944]) ).
tff(c_58406,plain,
( doDivides0(sdtsldt0(xn,xr),xn)
| ~ doDivides0(xr,xn)
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_109,c_45091]) ).
tff(c_58414,plain,
( doDivides0(sdtsldt0(xn,xr),xn)
| ( xr = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_181,c_147,c_193,c_58406]) ).
tff(c_58416,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18700,c_21535,c_58414]) ).
tff(c_58417,plain,
sdtsldt0(xn,xr) = xn,
inference(splitRight,[status(thm)],[c_195]) ).
tff(c_66715,plain,
! [W0_788,W1_789] :
( ( sdtasdt0(W0_788,sdtsldt0(W1_789,W0_788)) = W1_789 )
| ~ doDivides0(W0_788,W1_789)
| ( sz00 = W0_788 )
| ~ aNaturalNumber0(W1_789)
| ~ aNaturalNumber0(W0_788) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_66738,plain,
( ( sdtasdt0(xr,xn) = xn )
| ~ doDivides0(xr,xn)
| ( xr = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_58417,c_66715]) ).
tff(c_66745,plain,
( ( sdtasdt0(xn,xr) = xn )
| ( xr = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_181,c_147,c_193,c_59106,c_66738]) ).
tff(c_66746,plain,
sdtasdt0(xn,xr) = xn,
inference(negUnitSimplification,[status(thm)],[c_62421,c_66745]) ).
tff(c_67511,plain,
! [W0_797,W2_798,W1_799] :
( ( sdtasdt0(W0_797,W2_798) != sdtasdt0(W0_797,W1_799) )
| ( W2_798 = W1_799 )
| ~ aNaturalNumber0(W2_798)
| ~ aNaturalNumber0(W1_799)
| ( sz00 = W0_797 )
| ~ aNaturalNumber0(W0_797) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_67517,plain,
! [W1_799] :
( ( sdtasdt0(xn,W1_799) != xn )
| ( xr = W1_799 )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(W1_799)
| ( xn = sz00 )
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_66746,c_67511]) ).
tff(c_67655,plain,
! [W1_799] :
( ( sdtasdt0(xn,W1_799) != xn )
| ( xr = W1_799 )
| ~ aNaturalNumber0(W1_799)
| ( xn = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_181,c_67517]) ).
tff(c_69089,plain,
! [W1_815] :
( ( sdtasdt0(xn,W1_815) != xn )
| ( xr = W1_815 )
| ~ aNaturalNumber0(W1_815) ),
inference(negUnitSimplification,[status(thm)],[c_64376,c_67655]) ).
tff(c_69152,plain,
( ( sdtasdt0(xn,sz10) != xn )
| ( xr = sz10 ) ),
inference(resolution,[status(thm)],[c_8,c_69089]) ).
tff(c_69182,plain,
xr = sz10,
inference(demodulation,[status(thm),theory(equality)],[c_58450,c_69152]) ).
tff(c_69184,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_68909,c_69182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM510+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 : n016.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 15:09:52 EDT 2023
% 0.14/0.36 % CPUTime :
% 25.25/12.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.25/12.32
% 25.25/12.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.87/12.36
% 25.87/12.36 Inference rules
% 25.87/12.36 ----------------------
% 25.87/12.36 #Ref : 25
% 25.87/12.36 #Sup : 13828
% 25.87/12.36 #Fact : 4
% 25.87/12.36 #Define : 0
% 25.87/12.36 #Split : 135
% 25.87/12.36 #Chain : 0
% 25.87/12.36 #Close : 0
% 25.87/12.36
% 25.87/12.36 Ordering : KBO
% 25.87/12.36
% 25.87/12.36 Simplification rules
% 25.87/12.36 ----------------------
% 25.87/12.36 #Subsume : 641
% 25.87/12.36 #Demod : 25714
% 25.87/12.36 #Tautology : 5417
% 25.87/12.36 #SimpNegUnit : 2398
% 25.87/12.36 #BackRed : 2636
% 25.87/12.36
% 25.87/12.36 #Partial instantiations: 0
% 25.87/12.36 #Strategies tried : 1
% 25.87/12.36
% 25.87/12.36 Timing (in seconds)
% 25.87/12.36 ----------------------
% 25.87/12.37 Preprocessing : 0.71
% 25.87/12.37 Parsing : 0.36
% 25.87/12.37 CNF conversion : 0.06
% 25.87/12.37 Main loop : 10.53
% 25.87/12.37 Inferencing : 1.96
% 25.87/12.37 Reduction : 5.81
% 25.87/12.37 Demodulation : 4.80
% 25.87/12.37 BG Simplification : 0.15
% 25.87/12.37 Subsumption : 2.04
% 25.87/12.37 Abstraction : 0.20
% 25.87/12.37 MUC search : 0.00
% 25.87/12.37 Cooper : 0.00
% 25.87/12.37 Total : 11.33
% 25.87/12.37 Index Insertion : 0.00
% 25.87/12.37 Index Deletion : 0.00
% 25.87/12.37 Index Matching : 0.00
% 25.87/12.37 BG Taut test : 0.00
%------------------------------------------------------------------------------