TSTP Solution File: NUM498+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM498+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 : n023.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 10:51:53 EDT 2023
% Result : Theorem 10.17s 3.41s
% Output : CNFRefutation 10.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 36
% Syntax : Number of formulae : 152 ( 74 unt; 19 typ; 3 def)
% Number of atoms : 277 ( 112 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 237 ( 93 ~; 102 |; 23 &)
% ( 3 <=>; 16 =>; 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 : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 50 (; 49 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > 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(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_464,negated_conjecture,
~ ( ( ( xk = sz00 )
| ( xk = sz10 ) )
=> ( doDivides0(xp,xn)
| doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
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_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
tff(f_93,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
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_296,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
tff(f_455,hypothesis,
( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
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_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_151,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
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_307,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
tff(c_169,plain,
~ doDivides0(xp,xm),
inference(cnfTransformation,[status(thm)],[f_464]) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_4101,plain,
! [W0_180] :
( ( sdtasdt0(sz10,W0_180) = W0_180 )
| ~ aNaturalNumber0(W0_180) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_4120,plain,
sdtasdt0(sz10,xm) = xm,
inference(resolution,[status(thm)],[c_145,c_4101]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_3931,plain,
! [W0_175] :
( ( sdtasdt0(sz00,W0_175) = sz00 )
| ~ aNaturalNumber0(W0_175) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_3949,plain,
sdtasdt0(sz00,xm) = sz00,
inference(resolution,[status(thm)],[c_145,c_3931]) ).
tff(c_4119,plain,
sdtasdt0(sz10,xn) = xn,
inference(resolution,[status(thm)],[c_147,c_4101]) ).
tff(c_4830,plain,
! [W1_202,W0_203] :
( sdtlseqdt0(W1_202,sdtasdt0(W1_202,W0_203))
| ( sz00 = W0_203 )
| ~ aNaturalNumber0(W1_202)
| ~ aNaturalNumber0(W0_203) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_4848,plain,
( sdtlseqdt0(sz10,xn)
| ( xn = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_4119,c_4830]) ).
tff(c_4902,plain,
( sdtlseqdt0(sz10,xn)
| ( xn = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_8,c_4848]) ).
tff(c_5058,plain,
xn = sz00,
inference(splitLeft,[status(thm)],[c_4902]) ).
tff(c_151,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_5080,plain,
doDivides0(xp,sdtasdt0(sz00,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_5058,c_151]) ).
tff(c_5106,plain,
doDivides0(xp,sz00),
inference(demodulation,[status(thm),theory(equality)],[c_3949,c_5080]) ).
tff(c_171,plain,
~ doDivides0(xp,xn),
inference(cnfTransformation,[status(thm)],[f_464]) ).
tff(c_5083,plain,
~ doDivides0(xp,sz00),
inference(demodulation,[status(thm),theory(equality)],[c_5058,c_171]) ).
tff(c_5160,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5106,c_5083]) ).
tff(c_5161,plain,
sdtlseqdt0(sz10,xn),
inference(splitRight,[status(thm)],[c_4902]) ).
tff(c_5795,plain,
! [W0_222,W1_223] :
( iLess0(W0_222,W1_223)
| ~ sdtlseqdt0(W0_222,W1_223)
| ( W1_223 = W0_222 )
| ~ aNaturalNumber0(W1_223)
| ~ aNaturalNumber0(W0_222) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_5804,plain,
( iLess0(sz10,xn)
| ( xn = sz10 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[c_5161,c_5795]) ).
tff(c_5850,plain,
( iLess0(sz10,xn)
| ( xn = sz10 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_147,c_5804]) ).
tff(c_5890,plain,
xn = sz10,
inference(splitLeft,[status(thm)],[c_5850]) ).
tff(c_6086,plain,
doDivides0(xp,sdtasdt0(sz10,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_5890,c_151]) ).
tff(c_6106,plain,
doDivides0(xp,xm),
inference(demodulation,[status(thm),theory(equality)],[c_4120,c_6086]) ).
tff(c_6108,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_169,c_6106]) ).
tff(c_6110,plain,
xn != sz10,
inference(splitRight,[status(thm)],[c_5850]) ).
tff(c_165,plain,
xp != xn,
inference(cnfTransformation,[status(thm)],[f_455]) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_153,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_442]) ).
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_177,plain,
~ isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).
tff(c_4123,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_4101]) ).
tff(c_4857,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_4123,c_4830]) ).
tff(c_4908,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_4857]) ).
tff(c_4979,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_4908]) ).
tff(c_5001,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_4979,c_153]) ).
tff(c_5016,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_177,c_5001]) ).
tff(c_5018,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_4908]) ).
tff(c_4570,plain,
! [W1_196,W0_197] :
( ( sdtasdt0(W1_196,W0_197) = sdtasdt0(W0_197,W1_196) )
| ~ aNaturalNumber0(W1_196)
| ~ aNaturalNumber0(W0_197) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_5723,plain,
! [W0_221] :
( ( sdtasdt0(xm,W0_221) = sdtasdt0(W0_221,xm) )
| ~ aNaturalNumber0(W0_221) ),
inference(resolution,[status(thm)],[c_145,c_4570]) ).
tff(c_5789,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_147,c_5723]) ).
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_6481,plain,
( aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_5789,c_12]) ).
tff(c_6491,plain,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_6481]) ).
tff(c_6472,plain,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_5789,c_151]) ).
tff(c_3985,plain,
! [W0_177] :
( ( sdtasdt0(W0_177,sz10) = W0_177 )
| ~ aNaturalNumber0(W0_177) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_4005,plain,
sdtasdt0(xp,sz10) = xp,
inference(resolution,[status(thm)],[c_143,c_3985]) ).
tff(c_326,plain,
! [W0_103] :
( ( sdtasdt0(sz10,W0_103) = W0_103 )
| ~ aNaturalNumber0(W0_103) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_347,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_326]) ).
tff(c_1565,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_1610,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_347,c_1565]) ).
tff(c_1673,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_1610]) ).
tff(c_1895,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_1673]) ).
tff(c_1924,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_1895,c_153]) ).
tff(c_1945,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_177,c_1924]) ).
tff(c_1947,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_1673]) ).
tff(c_343,plain,
sdtasdt0(sz10,xn) = xn,
inference(resolution,[status(thm)],[c_147,c_326]) ).
tff(c_1595,plain,
( sdtlseqdt0(sz10,xn)
| ( xn = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_343,c_1565]) ).
tff(c_1663,plain,
( sdtlseqdt0(sz10,xn)
| ( xn = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_8,c_1595]) ).
tff(c_2007,plain,
xn = sz00,
inference(splitLeft,[status(thm)],[c_1663]) ).
tff(c_2037,plain,
~ doDivides0(xp,sz00),
inference(demodulation,[status(thm),theory(equality)],[c_2007,c_171]) ).
tff(c_293,plain,
! [W0_102] :
( ( sdtasdt0(W0_102,sz00) = sz00 )
| ~ aNaturalNumber0(W0_102) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_311,plain,
sdtasdt0(xm,sz00) = sz00,
inference(resolution,[status(thm)],[c_145,c_293]) ).
tff(c_622,plain,
! [W1_112,W0_113] :
( ( sdtasdt0(W1_112,W0_113) = sdtasdt0(W0_113,W1_112) )
| ~ aNaturalNumber0(W1_112)
| ~ aNaturalNumber0(W0_113) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_685,plain,
! [W0_115] :
( ( sdtasdt0(xn,W0_115) = sdtasdt0(W0_115,xn) )
| ~ aNaturalNumber0(W0_115) ),
inference(resolution,[status(thm)],[c_147,c_622]) ).
tff(c_717,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_145,c_685]) ).
tff(c_722,plain,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_717,c_151]) ).
tff(c_2025,plain,
doDivides0(xp,sdtasdt0(xm,sz00)),
inference(demodulation,[status(thm),theory(equality)],[c_2007,c_722]) ).
tff(c_2056,plain,
doDivides0(xp,sz00),
inference(demodulation,[status(thm),theory(equality)],[c_311,c_2025]) ).
tff(c_2082,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2037,c_2056]) ).
tff(c_2084,plain,
xn != sz00,
inference(splitRight,[status(thm)],[c_1663]) ).
tff(c_368,plain,
! [W0_104] :
( ( sdtasdt0(sz00,W0_104) = sz00 )
| ~ aNaturalNumber0(W0_104) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_385,plain,
sdtasdt0(sz00,xn) = sz00,
inference(resolution,[status(thm)],[c_147,c_368]) ).
tff(c_344,plain,
sdtasdt0(sz10,xm) = xm,
inference(resolution,[status(thm)],[c_145,c_326]) ).
tff(c_1604,plain,
( sdtlseqdt0(sz10,xm)
| ( xm = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_344,c_1565]) ).
tff(c_1669,plain,
( sdtlseqdt0(sz10,xm)
| ( xm = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_8,c_1604]) ).
tff(c_1780,plain,
xm = sz00,
inference(splitLeft,[status(thm)],[c_1669]) ).
tff(c_1852,plain,
doDivides0(xp,sdtasdt0(sz00,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_1780,c_722]) ).
tff(c_1877,plain,
doDivides0(xp,sz00),
inference(demodulation,[status(thm),theory(equality)],[c_385,c_1852]) ).
tff(c_1861,plain,
~ doDivides0(xp,sz00),
inference(demodulation,[status(thm),theory(equality)],[c_1780,c_169]) ).
tff(c_1892,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1877,c_1861]) ).
tff(c_1894,plain,
xm != sz00,
inference(splitRight,[status(thm)],[c_1669]) ).
tff(c_2323,plain,
! [W1_143,W0_144] :
( ( sz00 = W1_143 )
| ( sz00 = W0_144 )
| ( sdtasdt0(W0_144,W1_143) != sz00 )
| ~ aNaturalNumber0(W1_143)
| ~ aNaturalNumber0(W0_144) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_2353,plain,
( ( xm = sz00 )
| ( xn = sz00 )
| ( sdtasdt0(xm,xn) != sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_717,c_2323]) ).
tff(c_2447,plain,
( ( xm = sz00 )
| ( xn = sz00 )
| ( sdtasdt0(xm,xn) != sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_2353]) ).
tff(c_2448,plain,
sdtasdt0(xm,xn) != sz00,
inference(negUnitSimplification,[status(thm)],[c_2084,c_1894,c_2447]) ).
tff(c_726,plain,
( aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_717,c_12]) ).
tff(c_730,plain,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_726]) ).
tff(c_313,plain,
sdtasdt0(xp,sz00) = sz00,
inference(resolution,[status(thm)],[c_143,c_293]) ).
tff(c_173,plain,
( ( xk = sz10 )
| ( xk = sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_464]) ).
tff(c_178,plain,
xk = sz00,
inference(splitLeft,[status(thm)],[c_173]) ).
tff(c_167,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_250,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_178,c_167]) ).
tff(c_721,plain,
sdtsldt0(sdtasdt0(xm,xn),xp) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_717,c_250]) ).
tff(c_3896,plain,
! [W0_172,W1_173] :
( ( sdtasdt0(W0_172,sdtsldt0(W1_173,W0_172)) = W1_173 )
| ~ doDivides0(W0_172,W1_173)
| ( sz00 = W0_172 )
| ~ aNaturalNumber0(W1_173)
| ~ aNaturalNumber0(W0_172) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_3916,plain,
( ( sdtasdt0(xp,sz00) = sdtasdt0(xm,xn) )
| ~ doDivides0(xp,sdtasdt0(xm,xn))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_721,c_3896]) ).
tff(c_3920,plain,
( ( sdtasdt0(xm,xn) = sz00 )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_730,c_722,c_313,c_3916]) ).
tff(c_3922,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1947,c_2448,c_3920]) ).
tff(c_3923,plain,
xk = sz10,
inference(splitRight,[status(thm)],[c_173]) ).
tff(c_4136,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = sz10,
inference(demodulation,[status(thm),theory(equality)],[c_3923,c_167]) ).
tff(c_6471,plain,
sdtsldt0(sdtasdt0(xm,xn),xp) = sz10,
inference(demodulation,[status(thm),theory(equality)],[c_5789,c_4136]) ).
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_7996,plain,
( ( sdtasdt0(xp,sz10) = sdtasdt0(xm,xn) )
| ~ doDivides0(xp,sdtasdt0(xm,xn))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_6471,c_109]) ).
tff(c_8003,plain,
( ( sdtasdt0(xm,xn) = xp )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_6491,c_6472,c_4005,c_7996]) ).
tff(c_8004,plain,
sdtasdt0(xm,xn) = xp,
inference(negUnitSimplification,[status(thm)],[c_5018,c_8003]) ).
tff(c_6699,plain,
! [W0_234,W2_235] :
( doDivides0(W0_234,sdtasdt0(W0_234,W2_235))
| ~ aNaturalNumber0(W2_235)
| ~ aNaturalNumber0(sdtasdt0(W0_234,W2_235))
| ~ aNaturalNumber0(W0_234) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_6705,plain,
( doDivides0(xn,sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_5789,c_6699]) ).
tff(c_6785,plain,
doDivides0(xn,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_6491,c_5789,c_145,c_6705]) ).
tff(c_8010,plain,
doDivides0(xn,xp),
inference(demodulation,[status(thm),theory(equality)],[c_8004,c_6785]) ).
tff(c_131,plain,
! [W1_92,W0_89] :
( ( W1_92 = W0_89 )
| ( sz10 = W1_92 )
| ~ doDivides0(W1_92,W0_89)
| ~ aNaturalNumber0(W1_92)
| ~ isPrime0(W0_89)
| ~ aNaturalNumber0(W0_89) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_8048,plain,
( ( xp = xn )
| ( xn = sz10 )
| ~ aNaturalNumber0(xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_8010,c_131]) ).
tff(c_8054,plain,
( ( xp = xn )
| ( xn = sz10 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_153,c_147,c_8048]) ).
tff(c_8056,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6110,c_165,c_8054]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM498+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % 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
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 15:36:37 EDT 2023
% 0.14/0.34 % CPUTime :
% 10.17/3.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.35/3.42
% 10.35/3.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.50/3.46
% 10.50/3.46 Inference rules
% 10.50/3.46 ----------------------
% 10.50/3.46 #Ref : 4
% 10.50/3.46 #Sup : 1642
% 10.50/3.46 #Fact : 4
% 10.50/3.46 #Define : 0
% 10.50/3.46 #Split : 17
% 10.50/3.46 #Chain : 0
% 10.50/3.46 #Close : 0
% 10.50/3.46
% 10.50/3.46 Ordering : KBO
% 10.50/3.46
% 10.50/3.46 Simplification rules
% 10.50/3.46 ----------------------
% 10.50/3.46 #Subsume : 102
% 10.50/3.46 #Demod : 2592
% 10.50/3.46 #Tautology : 787
% 10.50/3.46 #SimpNegUnit : 214
% 10.50/3.46 #BackRed : 393
% 10.50/3.46
% 10.50/3.46 #Partial instantiations: 0
% 10.50/3.46 #Strategies tried : 1
% 10.50/3.46
% 10.50/3.46 Timing (in seconds)
% 10.50/3.46 ----------------------
% 10.50/3.47 Preprocessing : 0.68
% 10.50/3.47 Parsing : 0.34
% 10.50/3.47 CNF conversion : 0.05
% 10.50/3.47 Main loop : 1.63
% 10.50/3.47 Inferencing : 0.50
% 10.50/3.47 Reduction : 0.63
% 10.50/3.47 Demodulation : 0.47
% 10.50/3.47 BG Simplification : 0.07
% 10.50/3.47 Subsumption : 0.31
% 10.50/3.47 Abstraction : 0.06
% 10.50/3.47 MUC search : 0.00
% 10.50/3.47 Cooper : 0.00
% 10.50/3.47 Total : 2.39
% 10.50/3.47 Index Insertion : 0.00
% 10.50/3.47 Index Deletion : 0.00
% 10.50/3.47 Index Matching : 0.00
% 10.50/3.47 BG Taut test : 0.00
%------------------------------------------------------------------------------