TSTP Solution File: NUM507+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM507+3 : 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 : n007.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 : Timeout 288.62s 249.57s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 53
% Syntax : Number of formulae : 171 ( 65 unt; 31 typ; 2 def)
% Number of atoms : 339 ( 104 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 341 ( 142 ~; 119 |; 56 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 17 >; 17 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 14 con; 0-3 aty)
% Number of variables : 84 (; 75 !; 9 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_11 > #skF_6 > #skF_15 > #skF_10 > #skF_14 > #skF_13 > #skF_5 > #skF_9 > #skF_7 > #skF_3 > #skF_2 > #skF_8 > #skF_1 > #skF_12
%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('#skF_11',type,
'#skF_11': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz00,type,
sz00: $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(isPrime0,type,
isPrime0: $i > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
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('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
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('#skF_12',type,
'#skF_12': $i ).
tff(f_599,hypothesis,
( ( xk != xp )
& ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xk,W0) = xp ) )
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2377) ).
tff(f_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(f_540,hypothesis,
( aNaturalNumber0(xk)
& ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
& ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
tff(f_189,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
tff(f_579,hypothesis,
( aNaturalNumber0(xr)
& ? [W0] :
( aNaturalNumber0(W0)
& ( xk = sdtasdt0(xr,W0) ) )
& doDivides0(xr,xk)
& ( xr != sz00 )
& ( xr != sz10 )
& ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& ( xr = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xr) ) )
=> ( ( W0 = sz10 )
| ( W0 = xr ) ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
tff(f_41,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
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_502,hypothesis,
( ( xp != sz00 )
& ( xp != sz10 )
& ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& ( xp = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xp) ) )
=> ( ( W0 = sz10 )
| ( W0 = xp ) ) )
& isPrime0(xp)
& ? [W0] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xn,xm) = sdtasdt0(xp,W0) ) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
tff(f_590,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xr,W0) = xk ) )
& ? [W0] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xn,xm) = sdtasdt0(xr,W0) ) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
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_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_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_549,hypothesis,
( ( xk != sz00 )
& ( xk != sz10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).
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_201,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
tff(f_53,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
tff(f_234,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
tff(f_609,negated_conjecture,
~ ( ( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) )
& ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),W0) = sdtpldt0(sdtpldt0(xn,xm),xp) ) )
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
tff(f_67,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
tff(f_115,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
tff(f_162,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
tff(c_489,plain,
xp != xk,
inference(cnfTransformation,[status(thm)],[f_599]) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_445,plain,
aNaturalNumber0(xk),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_483,plain,
sdtlseqdt0(xk,xp),
inference(cnfTransformation,[status(thm)],[f_599]) ).
tff(c_374154,plain,
! [W1_1802,W0_1803] :
( ( W1_1802 = W0_1803 )
| ~ sdtlseqdt0(W1_1802,W0_1803)
| ~ sdtlseqdt0(W0_1803,W1_1802)
| ~ aNaturalNumber0(W1_1802)
| ~ aNaturalNumber0(W0_1803) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_374198,plain,
( ( xp = xk )
| ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_483,c_374154]) ).
tff(c_374280,plain,
( ( xp = xk )
| ~ sdtlseqdt0(xp,xk) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_445,c_374198]) ).
tff(c_374281,plain,
~ sdtlseqdt0(xp,xk),
inference(negUnitSimplification,[status(thm)],[c_489,c_374280]) ).
tff(c_467,plain,
aNaturalNumber0(xr),
inference(cnfTransformation,[status(thm)],[f_579]) ).
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_10,plain,
! [W0_2,W1_3] :
( aNaturalNumber0(sdtpldt0(W0_2,W1_3))
| ~ aNaturalNumber0(W1_3)
| ~ aNaturalNumber0(W0_2) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_366882,plain,
! [W1_1719] :
( sdtlseqdt0(W1_1719,W1_1719)
| ~ aNaturalNumber0(W1_1719) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_411,plain,
xp != sz00,
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_477,plain,
aNaturalNumber0('#skF_13'),
inference(cnfTransformation,[status(thm)],[f_590]) ).
tff(c_475,plain,
sdtasdt0(xr,'#skF_13') = sdtasdt0(xn,xm),
inference(cnfTransformation,[status(thm)],[f_590]) ).
tff(c_1152,plain,
! [W0_125,W1_126] :
( aNaturalNumber0(sdtasdt0(W0_125,W1_126))
| ~ aNaturalNumber0(W1_126)
| ~ aNaturalNumber0(W0_125) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_1248,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0('#skF_13')
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_475,c_1152]) ).
tff(c_1307,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_477,c_1248]) ).
tff(c_403,plain,
sdtasdt0(xp,'#skF_9') = sdtasdt0(xn,xm),
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_401,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_405,plain,
aNaturalNumber0('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_502]) ).
tff(c_441,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_130590,plain,
! [W0_1229,W2_1230] :
( ( sdtsldt0(sdtasdt0(W0_1229,W2_1230),W0_1229) = W2_1230 )
| ~ aNaturalNumber0(W2_1230)
| ~ doDivides0(W0_1229,sdtasdt0(W0_1229,W2_1230))
| ( sz00 = W0_1229 )
| ~ aNaturalNumber0(sdtasdt0(W0_1229,W2_1230))
| ~ aNaturalNumber0(W0_1229) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_130776,plain,
( ( sdtsldt0(sdtasdt0(xp,'#skF_9'),xp) = '#skF_9' )
| ~ aNaturalNumber0('#skF_9')
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xp,'#skF_9'))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_403,c_130590]) ).
tff(c_130962,plain,
( ( xk = '#skF_9' )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_1307,c_403,c_401,c_405,c_441,c_403,c_130776]) ).
tff(c_130963,plain,
xk = '#skF_9',
inference(negUnitSimplification,[status(thm)],[c_411,c_130962]) ).
tff(c_465,plain,
aNaturalNumber0('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_463,plain,
sdtasdt0(xr,'#skF_12') = xk,
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_4591,plain,
! [W1_166,W0_167] :
( sdtlseqdt0(W1_166,sdtasdt0(W1_166,W0_167))
| ( sz00 = W0_167 )
| ~ aNaturalNumber0(W1_166)
| ~ aNaturalNumber0(W0_167) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_4765,plain,
( sdtlseqdt0(xr,xk)
| ( sz00 = '#skF_12' )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0('#skF_12') ),
inference(superposition,[status(thm),theory(equality)],[c_463,c_4591]) ).
tff(c_4917,plain,
( sdtlseqdt0(xr,xk)
| ( sz00 = '#skF_12' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_465,c_467,c_4765]) ).
tff(c_88919,plain,
sz00 = '#skF_12',
inference(splitLeft,[status(thm)],[c_4917]) ).
tff(c_453,plain,
xk != sz00,
inference(cnfTransformation,[status(thm)],[f_549]) ).
tff(c_88996,plain,
xk != '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_88919,c_453]) ).
tff(c_1034,plain,
! [W0_124] :
( ( sdtasdt0(W0_124,sz00) = sz00 )
| ~ aNaturalNumber0(W0_124) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_1078,plain,
sdtasdt0(xr,sz00) = sz00,
inference(resolution,[status(thm)],[c_467,c_1034]) ).
tff(c_88953,plain,
sdtasdt0(xr,'#skF_12') = '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_88919,c_88919,c_1078]) ).
tff(c_91145,plain,
xk = '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_88953,c_463]) ).
tff(c_91147,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_88996,c_91145]) ).
tff(c_91148,plain,
sdtlseqdt0(xr,xk),
inference(splitRight,[status(thm)],[c_4917]) ).
tff(c_131007,plain,
sdtlseqdt0(xr,'#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_130963,c_91148]) ).
tff(c_120750,plain,
! [W0_1176,W2_1177,W1_1178] :
( sdtlseqdt0(W0_1176,W2_1177)
| ~ sdtlseqdt0(W1_1178,W2_1177)
| ~ sdtlseqdt0(W0_1176,W1_1178)
| ~ aNaturalNumber0(W2_1177)
| ~ aNaturalNumber0(W1_1178)
| ~ aNaturalNumber0(W0_1176) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_120840,plain,
! [W0_1176] :
( sdtlseqdt0(W0_1176,xp)
| ~ sdtlseqdt0(W0_1176,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(W0_1176) ),
inference(resolution,[status(thm)],[c_483,c_120750]) ).
tff(c_120967,plain,
! [W0_1176] :
( sdtlseqdt0(W0_1176,xp)
| ~ sdtlseqdt0(W0_1176,xk)
| ~ aNaturalNumber0(W0_1176) ),
inference(demodulation,[status(thm),theory(equality)],[c_445,c_143,c_120840]) ).
tff(c_366758,plain,
! [W0_1718] :
( sdtlseqdt0(W0_1718,xp)
| ~ sdtlseqdt0(W0_1718,'#skF_9')
| ~ aNaturalNumber0(W0_1718) ),
inference(demodulation,[status(thm),theory(equality)],[c_130963,c_120967]) ).
tff(c_1688,plain,
! [W1_134,W0_135] :
( ( sdtpldt0(W1_134,W0_135) = sdtpldt0(W0_135,W1_134) )
| ~ aNaturalNumber0(W1_134)
| ~ aNaturalNumber0(W0_135) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_3816,plain,
! [W0_161] :
( ( sdtpldt0(xm,W0_161) = sdtpldt0(W0_161,xm) )
| ~ aNaturalNumber0(W0_161) ),
inference(resolution,[status(thm)],[c_145,c_1688]) ).
tff(c_3896,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(resolution,[status(thm)],[c_147,c_3816]) ).
tff(c_4265,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_3896,c_10]) ).
tff(c_4273,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_4265]) ).
tff(c_126862,plain,
! [W2_1212,W0_1213,W1_1214] :
( sdtlseqdt0(sdtpldt0(W2_1212,W0_1213),sdtpldt0(W2_1212,W1_1214))
| ~ aNaturalNumber0(W2_1212)
| ~ sdtlseqdt0(W0_1213,W1_1214)
| ( W1_1214 = W0_1213 )
| ~ aNaturalNumber0(W1_1214)
| ~ aNaturalNumber0(W0_1213) ),
inference(cnfTransformation,[status(thm)],[f_234]) ).
tff(c_491,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(cnfTransformation,[status(thm)],[f_609]) ).
tff(c_498,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(splitLeft,[status(thm)],[c_491]) ).
tff(c_4257,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xn),xr),sdtpldt0(sdtpldt0(xm,xn),xp)),
inference(demodulation,[status(thm),theory(equality)],[c_3896,c_3896,c_498]) ).
tff(c_126872,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xr,xp)
| ( xr = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[c_126862,c_4257]) ).
tff(c_127196,plain,
( ~ sdtlseqdt0(xr,xp)
| ( xr = xp ) ),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_143,c_4273,c_126872]) ).
tff(c_127488,plain,
~ sdtlseqdt0(xr,xp),
inference(splitLeft,[status(thm)],[c_127196]) ).
tff(c_366768,plain,
( ~ sdtlseqdt0(xr,'#skF_9')
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[c_366758,c_127488]) ).
tff(c_366785,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_467,c_131007,c_366768]) ).
tff(c_366786,plain,
xr = xp,
inference(splitRight,[status(thm)],[c_127196]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_1875,plain,
! [W1_139,W0_140] :
( sdtlseqdt0(W1_139,W0_140)
| sdtlseqdt0(W0_140,W1_139)
| ~ aNaturalNumber0(W1_139)
| ~ aNaturalNumber0(W0_140) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_1907,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(resolution,[status(thm)],[c_1875,c_498]) ).
tff(c_2748,plain,
~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)),
inference(splitLeft,[status(thm)],[c_1907]) ).
tff(c_3154,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[status(thm)],[c_10,c_2748]) ).
tff(c_3157,plain,
~ aNaturalNumber0(sdtpldt0(xn,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_3154]) ).
tff(c_3253,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_10,c_3157]) ).
tff(c_3257,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_3253]) ).
tff(c_3259,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)),
inference(splitRight,[status(thm)],[c_1907]) ).
tff(c_20,plain,
! [W0_11] :
( ( sdtpldt0(W0_11,sz00) = W0_11 )
| ~ aNaturalNumber0(W0_11) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_3292,plain,
sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),sz00) = sdtpldt0(sdtpldt0(xn,xm),xr),
inference(resolution,[status(thm)],[c_3259,c_20]) ).
tff(c_118314,plain,
sdtpldt0(sdtpldt0(sdtpldt0(xm,xn),xr),sz00) = sdtpldt0(sdtpldt0(xm,xn),xr),
inference(demodulation,[status(thm),theory(equality)],[c_3896,c_3896,c_3292]) ).
tff(c_493,plain,
! [W0_114] :
( ( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),W0_114) != sdtpldt0(sdtpldt0(xn,xm),xp) )
| ~ aNaturalNumber0(W0_114)
| ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(cnfTransformation,[status(thm)],[f_609]) ).
tff(c_499,plain,
! [W0_114] :
( ( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),W0_114) != sdtpldt0(sdtpldt0(xn,xm),xp) )
| ~ aNaturalNumber0(W0_114) ),
inference(splitLeft,[status(thm)],[c_493]) ).
tff(c_4256,plain,
! [W0_114] :
( ( sdtpldt0(sdtpldt0(sdtpldt0(xm,xn),xr),W0_114) != sdtpldt0(sdtpldt0(xm,xn),xp) )
| ~ aNaturalNumber0(W0_114) ),
inference(demodulation,[status(thm),theory(equality)],[c_3896,c_3896,c_499]) ).
tff(c_118318,plain,
( ( sdtpldt0(sdtpldt0(xm,xn),xr) != sdtpldt0(sdtpldt0(xm,xn),xp) )
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm),theory(equality)],[c_118314,c_4256]) ).
tff(c_118329,plain,
sdtpldt0(sdtpldt0(xm,xn),xr) != sdtpldt0(sdtpldt0(xm,xn),xp),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_118318]) ).
tff(c_366855,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_366786,c_118329]) ).
tff(c_366856,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp),
inference(splitRight,[status(thm)],[c_493]) ).
tff(c_366861,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(demodulation,[status(thm),theory(equality)],[c_366856,c_498]) ).
tff(c_366886,plain,
~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(resolution,[status(thm)],[c_366882,c_366861]) ).
tff(c_367525,plain,
! [W0_1728,W1_1729] :
( aNaturalNumber0(sdtpldt0(W0_1728,W1_1729))
| ~ aNaturalNumber0(W1_1729)
| ~ aNaturalNumber0(W0_1728) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_367609,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(superposition,[status(thm),theory(equality)],[c_366856,c_367525]) ).
tff(c_367658,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_367609]) ).
tff(c_367659,plain,
~ aNaturalNumber0(sdtpldt0(xn,xm)),
inference(negUnitSimplification,[status(thm)],[c_366886,c_367658]) ).
tff(c_367675,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_10,c_367659]) ).
tff(c_367679,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_367675]) ).
tff(c_367680,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp),
inference(splitRight,[status(thm)],[c_491]) ).
tff(c_370391,plain,
! [W0_1766,W1_1767] :
( aNaturalNumber0(sdtpldt0(W0_1766,W1_1767))
| ~ aNaturalNumber0(W1_1767)
| ~ aNaturalNumber0(W0_1766) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_370475,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(superposition,[status(thm),theory(equality)],[c_367680,c_370391]) ).
tff(c_370523,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_370475]) ).
tff(c_370715,plain,
~ aNaturalNumber0(sdtpldt0(xn,xm)),
inference(splitLeft,[status(thm)],[c_370523]) ).
tff(c_370771,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_10,c_370715]) ).
tff(c_370775,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_370771]) ).
tff(c_370777,plain,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(splitRight,[status(thm)],[c_370523]) ).
tff(c_371833,plain,
! [W1_1783,W0_1784] :
( ( sdtpldt0(W1_1783,W0_1784) = sdtpldt0(W0_1784,W1_1783) )
| ~ aNaturalNumber0(W1_1783)
| ~ aNaturalNumber0(W0_1784) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_372889,plain,
! [W0_1792] :
( ( sdtpldt0(sdtpldt0(xn,xm),W0_1792) = sdtpldt0(W0_1792,sdtpldt0(xn,xm)) )
| ~ aNaturalNumber0(W0_1792) ),
inference(resolution,[status(thm)],[c_370777,c_371833]) ).
tff(c_372969,plain,
( ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xr,sdtpldt0(xn,xm)) )
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_367680,c_372889]) ).
tff(c_373023,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xr,sdtpldt0(xn,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_372969]) ).
tff(c_371879,plain,
! [W0_1784] :
( ( sdtpldt0(sdtpldt0(xn,xm),W0_1784) = sdtpldt0(W0_1784,sdtpldt0(xn,xm)) )
| ~ aNaturalNumber0(W0_1784) ),
inference(resolution,[status(thm)],[c_370777,c_371833]) ).
tff(c_373141,plain,
( ( sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) )
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_373023,c_371879]) ).
tff(c_373155,plain,
sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_373141]) ).
tff(c_375386,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xp,sdtpldt0(xn,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_373155,c_373023]) ).
tff(c_373137,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(xr,sdtpldt0(xn,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_373023,c_367680]) ).
tff(c_375385,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(xp,sdtpldt0(xn,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_373155,c_373137]) ).
tff(c_377090,plain,
! [W0_1831,W2_1832,W1_1833] :
( ( sdtpldt0(W0_1831,W2_1832) != sdtpldt0(W0_1831,W1_1833) )
| ( W2_1832 = W1_1833 )
| ~ aNaturalNumber0(W2_1832)
| ~ aNaturalNumber0(W1_1833)
| ~ aNaturalNumber0(W0_1831) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_377098,plain,
! [W2_1832] :
( ( sdtpldt0(sdtpldt0(xn,xm),W2_1832) != sdtpldt0(xp,sdtpldt0(xn,xm)) )
| ( xr = W2_1832 )
| ~ aNaturalNumber0(W2_1832)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(superposition,[status(thm),theory(equality)],[c_375385,c_377090]) ).
tff(c_377770,plain,
! [W2_1837] :
( ( sdtpldt0(sdtpldt0(xn,xm),W2_1837) != sdtpldt0(xp,sdtpldt0(xn,xm)) )
| ( xr = W2_1837 )
| ~ aNaturalNumber0(W2_1837) ),
inference(demodulation,[status(thm),theory(equality)],[c_370777,c_467,c_377098]) ).
tff(c_377773,plain,
( ( xr = xp )
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_375386,c_377770]) ).
tff(c_377793,plain,
xr = xp,
inference(demodulation,[status(thm),theory(equality)],[c_143,c_377773]) ).
tff(c_479,plain,
sdtpldt0(xr,'#skF_14') = xk,
inference(cnfTransformation,[status(thm)],[f_590]) ).
tff(c_481,plain,
aNaturalNumber0('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_590]) ).
tff(c_376088,plain,
! [W0_1821,W2_1822] :
( sdtlseqdt0(W0_1821,sdtpldt0(W0_1821,W2_1822))
| ~ aNaturalNumber0(W2_1822)
| ~ aNaturalNumber0(sdtpldt0(W0_1821,W2_1822))
| ~ aNaturalNumber0(W0_1821) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_376228,plain,
( sdtlseqdt0(xr,xk)
| ~ aNaturalNumber0('#skF_14')
| ~ aNaturalNumber0(sdtpldt0(xr,'#skF_14'))
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_479,c_376088]) ).
tff(c_376322,plain,
sdtlseqdt0(xr,xk),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_445,c_479,c_481,c_376228]) ).
tff(c_377809,plain,
sdtlseqdt0(xp,xk),
inference(demodulation,[status(thm),theory(equality)],[c_377793,c_376322]) ).
tff(c_377842,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_374281,c_377809]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM507+3 : 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
% 0.18/0.34 % Computer : n007.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 3 14:46:53 EDT 2023
% 0.18/0.35 % CPUTime :
% 288.62/249.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 288.62/249.59
% 288.62/249.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 288.76/249.63
% 288.76/249.63 Inference rules
% 288.76/249.63 ----------------------
% 288.76/249.63 #Ref : 118
% 288.76/249.63 #Sup : 81151
% 288.76/249.63 #Fact : 6
% 288.76/249.63 #Define : 0
% 288.76/249.63 #Split : 184
% 288.76/249.63 #Chain : 0
% 288.76/249.63 #Close : 0
% 288.76/249.63
% 288.76/249.63 Ordering : KBO
% 288.76/249.63
% 288.76/249.63 Simplification rules
% 288.76/249.63 ----------------------
% 288.76/249.63 #Subsume : 3530
% 288.76/249.63 #Demod : 164894
% 288.76/249.63 #Tautology : 20651
% 288.76/249.63 #SimpNegUnit : 21351
% 288.76/249.63 #BackRed : 6197
% 288.76/249.63
% 288.76/249.63 #Partial instantiations: 0
% 288.76/249.63 #Strategies tried : 1
% 288.76/249.63
% 288.76/249.63 Timing (in seconds)
% 288.76/249.63 ----------------------
% 288.76/249.63 Preprocessing : 0.89
% 288.76/249.63 Parsing : 0.39
% 288.76/249.63 CNF conversion : 0.07
% 288.76/249.63 Main loop : 247.68
% 288.76/249.63 Inferencing : 8.79
% 288.76/249.63 Reduction : 184.97
% 288.76/249.63 Demodulation : 167.76
% 288.76/249.63 BG Simplification : 0.97
% 288.76/249.63 Subsumption : 44.86
% 288.76/249.63 Abstraction : 1.68
% 288.76/249.63 MUC search : 0.00
% 288.76/249.63 Cooper : 0.00
% 288.76/249.63 Total : 248.63
% 288.76/249.63 Index Insertion : 0.00
% 288.76/249.63 Index Deletion : 0.00
% 288.76/249.63 Index Matching : 0.00
% 288.76/249.63 BG Taut test : 0.00
%------------------------------------------------------------------------------