TSTP Solution File: NUM494+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM494+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 : n001.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 58.99s 44.44s
% Output : CNFRefutation 59.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 37
% Syntax : Number of formulae : 163 ( 70 unt; 19 typ; 3 def)
% Number of atoms : 327 ( 94 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 346 ( 163 ~; 142 |; 23 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 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 : 82 (; 81 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
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_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_443,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
tff(f_444,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
tff(f_175,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
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_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_454,negated_conjecture,
~ ( ( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) )
& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(f_61,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
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(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_169,plain,
~ isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).
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_19166,plain,
! [W0_308] :
( ( sdtasdt0(sz10,W0_308) = W0_308 )
| ~ aNaturalNumber0(W0_308) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_19183,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_19166]) ).
tff(c_21852,plain,
! [W1_355,W0_356] :
( sdtlseqdt0(W1_355,sdtasdt0(W1_355,W0_356))
| ( sz00 = W0_356 )
| ~ aNaturalNumber0(W1_355)
| ~ aNaturalNumber0(W0_356) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_21972,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_19183,c_21852]) ).
tff(c_22082,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_21972]) ).
tff(c_31712,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_22082]) ).
tff(c_153,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_31755,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_31712,c_153]) ).
tff(c_31789,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_169,c_31755]) ).
tff(c_31791,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_22082]) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_155,plain,
sdtlseqdt0(xp,xn),
inference(cnfTransformation,[status(thm)],[f_443]) ).
tff(c_157,plain,
sdtmndt0(xn,xp) = xr,
inference(cnfTransformation,[status(thm)],[f_444]) ).
tff(c_22106,plain,
! [W1_357,W0_358] :
( aNaturalNumber0(sdtmndt0(W1_357,W0_358))
| ~ sdtlseqdt0(W0_358,W1_357)
| ~ aNaturalNumber0(W1_357)
| ~ aNaturalNumber0(W0_358) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_22152,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_22106]) ).
tff(c_22169,plain,
aNaturalNumber0(xr),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_22152]) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_19609,plain,
! [W1_321,W0_322] :
( ( sdtpldt0(W1_321,W0_322) = sdtpldt0(W0_322,W1_321) )
| ~ aNaturalNumber0(W1_321)
| ~ aNaturalNumber0(W0_322) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_19629,plain,
! [W0_322] :
( ( sdtpldt0(xm,W0_322) = sdtpldt0(W0_322,xm) )
| ~ aNaturalNumber0(W0_322) ),
inference(resolution,[status(thm)],[c_145,c_19609]) ).
tff(c_22220,plain,
sdtpldt0(xr,xm) = sdtpldt0(xm,xr),
inference(resolution,[status(thm)],[c_22169,c_19629]) ).
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_609,plain,
! [W1_112,W0_113] :
( ( sdtpldt0(W1_112,W0_113) = sdtpldt0(W0_113,W1_112) )
| ~ aNaturalNumber0(W1_112)
| ~ aNaturalNumber0(W0_113) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_634,plain,
! [W0_114] :
( ( sdtpldt0(xm,W0_114) = sdtpldt0(W0_114,xm) )
| ~ aNaturalNumber0(W0_114) ),
inference(resolution,[status(thm)],[c_145,c_609]) ).
tff(c_668,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(resolution,[status(thm)],[c_147,c_634]) ).
tff(c_784,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_668,c_10]) ).
tff(c_788,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_784]) ).
tff(c_914,plain,
! [W1_119,W0_120] :
( sdtlseqdt0(W1_119,W0_120)
| sdtlseqdt0(W0_120,W1_119)
| ~ aNaturalNumber0(W1_119)
| ~ aNaturalNumber0(W0_120) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_165,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(cnfTransformation,[status(thm)],[f_454]) ).
tff(c_170,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(splitLeft,[status(thm)],[c_165]) ).
tff(c_780,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xm,xn),xp)),
inference(demodulation,[status(thm),theory(equality)],[c_668,c_170]) ).
tff(c_922,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xn),xp),sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
inference(resolution,[status(thm)],[c_914,c_780]) ).
tff(c_950,plain,
~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)),
inference(splitLeft,[status(thm)],[c_922]) ).
tff(c_953,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(resolution,[status(thm)],[c_10,c_950]) ).
tff(c_956,plain,
~ aNaturalNumber0(sdtpldt0(xr,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_953]) ).
tff(c_959,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[c_10,c_956]) ).
tff(c_962,plain,
~ aNaturalNumber0(xr),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_959]) ).
tff(c_1218,plain,
! [W1_125,W0_126] :
( aNaturalNumber0(sdtmndt0(W1_125,W0_126))
| ~ sdtlseqdt0(W0_126,W1_125)
| ~ aNaturalNumber0(W1_125)
| ~ aNaturalNumber0(W0_126) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_1249,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_1218]) ).
tff(c_1261,plain,
aNaturalNumber0(xr),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_1249]) ).
tff(c_1263,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_962,c_1261]) ).
tff(c_1265,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)),
inference(splitRight,[status(thm)],[c_922]) ).
tff(c_921,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xn),xp),sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)) ),
inference(resolution,[status(thm)],[c_914,c_780]) ).
tff(c_1466,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xn),xp),sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)) ),
inference(demodulation,[status(thm),theory(equality)],[c_1265,c_921]) ).
tff(c_1467,plain,
~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)),
inference(splitLeft,[status(thm)],[c_1466]) ).
tff(c_1471,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolution,[status(thm)],[c_10,c_1467]) ).
tff(c_1475,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_788,c_143,c_1471]) ).
tff(c_1477,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)),
inference(splitRight,[status(thm)],[c_1466]) ).
tff(c_52,plain,
! [W0_34,W2_38] :
( sdtlseqdt0(W0_34,sdtpldt0(W0_34,W2_38))
| ~ aNaturalNumber0(W2_38)
| ~ aNaturalNumber0(sdtpldt0(W0_34,W2_38))
| ~ aNaturalNumber0(W0_34) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_13778,plain,
! [W0_267,W1_268] :
( ( sdtpldt0(W0_267,sdtmndt0(W1_268,W0_267)) = W1_268 )
| ~ sdtlseqdt0(W0_267,W1_268)
| ~ aNaturalNumber0(W1_268)
| ~ aNaturalNumber0(W0_267) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_13797,plain,
( ( sdtpldt0(xp,xr) = xn )
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_13778]) ).
tff(c_13801,plain,
sdtpldt0(xp,xr) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_13797]) ).
tff(c_7705,plain,
! [W1_200,W0_201] :
( aNaturalNumber0(sdtmndt0(W1_200,W0_201))
| ~ sdtlseqdt0(W0_201,W1_200)
| ~ aNaturalNumber0(W1_200)
| ~ aNaturalNumber0(W0_201) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_7751,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_7705]) ).
tff(c_7768,plain,
aNaturalNumber0(xr),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_7751]) ).
tff(c_18092,plain,
! [W0_301] :
( ( sdtpldt0(xp,W0_301) = sdtpldt0(W0_301,xp) )
| ~ aNaturalNumber0(W0_301) ),
inference(resolution,[status(thm)],[c_143,c_609]) ).
tff(c_18125,plain,
sdtpldt0(xr,xp) = sdtpldt0(xp,xr),
inference(resolution,[status(thm)],[c_7768,c_18092]) ).
tff(c_18203,plain,
sdtpldt0(xr,xp) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_13801,c_18125]) ).
tff(c_17401,plain,
! [W0_297,W1_298,W2_299] :
( ( sdtpldt0(sdtpldt0(W0_297,W1_298),W2_299) = sdtpldt0(W0_297,sdtpldt0(W1_298,W2_299)) )
| ~ aNaturalNumber0(W2_299)
| ~ aNaturalNumber0(W1_298)
| ~ aNaturalNumber0(W0_297) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_629,plain,
! [W0_113] :
( ( sdtpldt0(xm,W0_113) = sdtpldt0(W0_113,xm) )
| ~ aNaturalNumber0(W0_113) ),
inference(resolution,[status(thm)],[c_145,c_609]) ).
tff(c_7819,plain,
sdtpldt0(xr,xm) = sdtpldt0(xm,xr),
inference(resolution,[status(thm)],[c_7768,c_629]) ).
tff(c_11997,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(sdtpldt0(xm,xn),xp)),
inference(demodulation,[status(thm),theory(equality)],[c_7819,c_780]) ).
tff(c_17512,plain,
( ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(sdtpldt0(xm,xn),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_17401,c_11997]) ).
tff(c_17702,plain,
~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(sdtpldt0(xm,xn),xp)),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_7768,c_143,c_17512]) ).
tff(c_19141,plain,
~ sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(sdtpldt0(xm,xn),xp)),
inference(demodulation,[status(thm),theory(equality)],[c_18203,c_17702]) ).
tff(c_19147,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp))
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolution,[status(thm)],[c_52,c_19141]) ).
tff(c_19158,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_788,c_1477,c_143,c_19147]) ).
tff(c_19159,plain,
sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp),
inference(splitRight,[status(thm)],[c_165]) ).
tff(c_19507,plain,
! [W0_316,W1_317] :
( aNaturalNumber0(sdtpldt0(W0_316,W1_317))
| ~ aNaturalNumber0(W1_317)
| ~ aNaturalNumber0(W0_316) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_19555,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(superposition,[status(thm),theory(equality)],[c_19159,c_19507]) ).
tff(c_19581,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_19555]) ).
tff(c_19709,plain,
~ aNaturalNumber0(sdtpldt0(xr,xm)),
inference(splitLeft,[status(thm)],[c_19581]) ).
tff(c_19712,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[c_10,c_19709]) ).
tff(c_19715,plain,
~ aNaturalNumber0(xr),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_19712]) ).
tff(c_20431,plain,
! [W1_337,W0_338] :
( aNaturalNumber0(sdtmndt0(W1_337,W0_338))
| ~ sdtlseqdt0(W0_338,W1_337)
| ~ aNaturalNumber0(W1_337)
| ~ aNaturalNumber0(W0_338) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_20465,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_20431]) ).
tff(c_20478,plain,
aNaturalNumber0(xr),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_20465]) ).
tff(c_20480,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_19715,c_20478]) ).
tff(c_20482,plain,
aNaturalNumber0(sdtpldt0(xr,xm)),
inference(splitRight,[status(thm)],[c_19581]) ).
tff(c_20,plain,
! [W0_11] :
( ( sdtpldt0(W0_11,sz00) = W0_11 )
| ~ aNaturalNumber0(W0_11) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_20511,plain,
sdtpldt0(sdtpldt0(xr,xm),sz00) = sdtpldt0(xr,xm),
inference(resolution,[status(thm)],[c_20482,c_20]) ).
tff(c_56082,plain,
sdtpldt0(sdtpldt0(xm,xr),sz00) = sdtpldt0(xm,xr),
inference(demodulation,[status(thm),theory(equality)],[c_22220,c_22220,c_20511]) ).
tff(c_58007,plain,
! [W0_792,W1_793] :
( ( sdtpldt0(W0_792,sdtmndt0(W1_793,W0_792)) = W1_793 )
| ~ sdtlseqdt0(W0_792,W1_793)
| ~ aNaturalNumber0(W1_793)
| ~ aNaturalNumber0(W0_792) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_58023,plain,
( ( sdtpldt0(xp,xr) = xn )
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_58007]) ).
tff(c_58027,plain,
sdtpldt0(xp,xr) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_58023]) ).
tff(c_19630,plain,
! [W0_322] :
( ( sdtpldt0(xp,W0_322) = sdtpldt0(W0_322,xp) )
| ~ aNaturalNumber0(W0_322) ),
inference(resolution,[status(thm)],[c_143,c_19609]) ).
tff(c_22215,plain,
sdtpldt0(xr,xp) = sdtpldt0(xp,xr),
inference(resolution,[status(thm)],[c_22169,c_19630]) ).
tff(c_58056,plain,
sdtpldt0(xr,xp) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_58027,c_22215]) ).
tff(c_60470,plain,
! [W0_817,W1_818,W2_819] :
( ( sdtpldt0(sdtpldt0(W0_817,W1_818),W2_819) = sdtpldt0(W0_817,sdtpldt0(W1_818,W2_819)) )
| ~ aNaturalNumber0(W2_819)
| ~ aNaturalNumber0(W1_818)
| ~ aNaturalNumber0(W0_817) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_19634,plain,
! [W0_323] :
( ( sdtpldt0(xm,W0_323) = sdtpldt0(W0_323,xm) )
| ~ aNaturalNumber0(W0_323) ),
inference(resolution,[status(thm)],[c_145,c_19609]) ).
tff(c_19668,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(resolution,[status(thm)],[c_147,c_19634]) ).
tff(c_20596,plain,
sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xm,xn),xp),
inference(demodulation,[status(thm),theory(equality)],[c_19668,c_19159]) ).
tff(c_56083,plain,
sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(sdtpldt0(xm,xn),xp),
inference(demodulation,[status(thm),theory(equality)],[c_22220,c_20596]) ).
tff(c_21498,plain,
! [W0_351] :
( ( sdtpldt0(xp,W0_351) = sdtpldt0(W0_351,xp) )
| ~ aNaturalNumber0(W0_351) ),
inference(resolution,[status(thm)],[c_143,c_19609]) ).
tff(c_21561,plain,
sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xp,sdtpldt0(xr,xm)),
inference(resolution,[status(thm)],[c_20482,c_21498]) ).
tff(c_56395,plain,
sdtpldt0(sdtpldt0(xm,xn),xp) = sdtpldt0(xp,sdtpldt0(xm,xr)),
inference(demodulation,[status(thm),theory(equality)],[c_56083,c_22220,c_22220,c_21561]) ).
tff(c_56396,plain,
sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(xp,sdtpldt0(xm,xr)),
inference(demodulation,[status(thm),theory(equality)],[c_56395,c_56083]) ).
tff(c_60526,plain,
( ( sdtpldt0(xp,sdtpldt0(xm,xr)) = sdtpldt0(xm,sdtpldt0(xr,xp)) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_60470,c_56396]) ).
tff(c_60706,plain,
sdtpldt0(xp,sdtpldt0(xm,xr)) = sdtpldt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_22169,c_143,c_58056,c_60526]) ).
tff(c_56086,plain,
aNaturalNumber0(sdtpldt0(xm,xr)),
inference(demodulation,[status(thm),theory(equality)],[c_22220,c_20482]) ).
tff(c_58537,plain,
! [W0_799,W2_800,W1_801] :
( ( sdtpldt0(W0_799,W2_800) != sdtpldt0(W0_799,W1_801) )
| ( W2_800 = W1_801 )
| ~ aNaturalNumber0(W2_800)
| ~ aNaturalNumber0(W1_801)
| ~ aNaturalNumber0(W0_799) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_58579,plain,
! [W1_801] :
( ( sdtpldt0(sdtpldt0(xm,xr),W1_801) != sdtpldt0(xp,sdtpldt0(xm,xr)) )
| ( xp = W1_801 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(W1_801)
| ~ aNaturalNumber0(sdtpldt0(xm,xr)) ),
inference(superposition,[status(thm),theory(equality)],[c_56396,c_58537]) ).
tff(c_58695,plain,
! [W1_801] :
( ( sdtpldt0(sdtpldt0(xm,xr),W1_801) != sdtpldt0(xp,sdtpldt0(xm,xr)) )
| ( xp = W1_801 )
| ~ aNaturalNumber0(W1_801) ),
inference(demodulation,[status(thm),theory(equality)],[c_56086,c_143,c_58579]) ).
tff(c_78111,plain,
! [W1_903] :
( ( sdtpldt0(sdtpldt0(xm,xr),W1_903) != sdtpldt0(xm,xn) )
| ( xp = W1_903 )
| ~ aNaturalNumber0(W1_903) ),
inference(demodulation,[status(thm),theory(equality)],[c_60706,c_58695]) ).
tff(c_78127,plain,
( ( sdtpldt0(xm,xr) != sdtpldt0(xm,xn) )
| ( xp = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm),theory(equality)],[c_56082,c_78111]) ).
tff(c_78155,plain,
( ( sdtpldt0(xm,xr) != sdtpldt0(xm,xn) )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_78127]) ).
tff(c_78156,plain,
sdtpldt0(xm,xr) != sdtpldt0(xm,xn),
inference(negUnitSimplification,[status(thm)],[c_31791,c_78155]) ).
tff(c_20600,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_19668,c_10]) ).
tff(c_20604,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_20600]) ).
tff(c_64939,plain,
sdtpldt0(sdtpldt0(xm,xn),xp) = sdtpldt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_60706,c_56395]) ).
tff(c_20481,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(splitRight,[status(thm)],[c_19581]) ).
tff(c_20594,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)),
inference(demodulation,[status(thm),theory(equality)],[c_19668,c_20481]) ).
tff(c_21558,plain,
sdtpldt0(sdtpldt0(sdtpldt0(xm,xn),xp),xp) = sdtpldt0(xp,sdtpldt0(sdtpldt0(xm,xn),xp)),
inference(resolution,[status(thm)],[c_20594,c_21498]) ).
tff(c_90076,plain,
sdtpldt0(xp,sdtpldt0(xm,xn)) = sdtpldt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_64939,c_64939,c_64939,c_21558]) ).
tff(c_64937,plain,
sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_60706,c_56396]) ).
tff(c_38,plain,
! [W2_24,W0_22,W1_23] :
( ( sdtpldt0(W2_24,W0_22) != sdtpldt0(W1_23,W0_22) )
| ( W2_24 = W1_23 )
| ~ aNaturalNumber0(W2_24)
| ~ aNaturalNumber0(W1_23)
| ~ aNaturalNumber0(W0_22) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_159483,plain,
! [W2_1251,W2_1252,W0_1253,W1_1254] :
( ( sdtpldt0(W2_1251,W2_1252) != sdtpldt0(W0_1253,sdtpldt0(W1_1254,W2_1252)) )
| ( sdtpldt0(W0_1253,W1_1254) = W2_1251 )
| ~ aNaturalNumber0(W2_1251)
| ~ aNaturalNumber0(sdtpldt0(W0_1253,W1_1254))
| ~ aNaturalNumber0(W2_1252)
| ~ aNaturalNumber0(W2_1252)
| ~ aNaturalNumber0(W1_1254)
| ~ aNaturalNumber0(W0_1253) ),
inference(superposition,[status(thm),theory(equality)],[c_60470,c_38]) ).
tff(c_159776,plain,
! [W0_1253,W1_1254] :
( ( sdtpldt0(W0_1253,sdtpldt0(W1_1254,xp)) != sdtpldt0(xm,xn) )
| ( sdtpldt0(xm,xr) = sdtpldt0(W0_1253,W1_1254) )
| ~ aNaturalNumber0(sdtpldt0(xm,xr))
| ~ aNaturalNumber0(sdtpldt0(W0_1253,W1_1254))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(W1_1254)
| ~ aNaturalNumber0(W0_1253) ),
inference(superposition,[status(thm),theory(equality)],[c_64937,c_159483]) ).
tff(c_160352,plain,
! [W0_1257,W1_1258] :
( ( sdtpldt0(W0_1257,sdtpldt0(W1_1258,xp)) != sdtpldt0(xm,xn) )
| ( sdtpldt0(xm,xr) = sdtpldt0(W0_1257,W1_1258) )
| ~ aNaturalNumber0(sdtpldt0(W0_1257,W1_1258))
| ~ aNaturalNumber0(W1_1258)
| ~ aNaturalNumber0(W0_1257) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_143,c_56086,c_159776]) ).
tff(c_160532,plain,
( ( sdtpldt0(xp,sdtpldt0(sdtpldt0(xm,xn),xp)) != sdtpldt0(xm,xn) )
| ( sdtpldt0(xp,sdtpldt0(xm,xn)) = sdtpldt0(xm,xr) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_90076,c_160352]) ).
tff(c_160816,plain,
sdtpldt0(xm,xr) = sdtpldt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_20604,c_20604,c_90076,c_90076,c_64939,c_160532]) ).
tff(c_160818,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_78156,c_160816]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM494+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % 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
% 0.18/0.37 % Computer : n001.cluster.edu
% 0.18/0.37 % Model : x86_64 x86_64
% 0.18/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.37 % Memory : 8042.1875MB
% 0.18/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.37 % CPULimit : 300
% 0.18/0.37 % WCLimit : 300
% 0.18/0.37 % DateTime : Thu Aug 3 15:22:55 EDT 2023
% 0.18/0.37 % CPUTime :
% 58.99/44.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.99/44.46
% 58.99/44.46 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 59.23/44.50
% 59.23/44.50 Inference rules
% 59.23/44.50 ----------------------
% 59.23/44.50 #Ref : 26
% 59.23/44.51 #Sup : 33071
% 59.23/44.51 #Fact : 12
% 59.23/44.51 #Define : 0
% 59.23/44.51 #Split : 132
% 59.23/44.51 #Chain : 0
% 59.23/44.51 #Close : 0
% 59.23/44.51
% 59.23/44.51 Ordering : KBO
% 59.23/44.51
% 59.23/44.51 Simplification rules
% 59.23/44.51 ----------------------
% 59.23/44.51 #Subsume : 3889
% 59.23/44.51 #Demod : 58735
% 59.23/44.51 #Tautology : 10476
% 59.23/44.51 #SimpNegUnit : 6112
% 59.23/44.51 #BackRed : 2661
% 59.23/44.51
% 59.23/44.51 #Partial instantiations: 0
% 59.23/44.51 #Strategies tried : 1
% 59.23/44.51
% 59.23/44.51 Timing (in seconds)
% 59.23/44.51 ----------------------
% 59.23/44.51 Preprocessing : 0.69
% 59.23/44.51 Parsing : 0.35
% 59.23/44.51 CNF conversion : 0.05
% 59.23/44.51 Main loop : 42.69
% 59.23/44.51 Inferencing : 4.40
% 59.23/44.51 Reduction : 26.63
% 59.23/44.51 Demodulation : 21.77
% 59.23/44.51 BG Simplification : 0.27
% 59.23/44.51 Subsumption : 9.48
% 59.23/44.51 Abstraction : 0.43
% 59.23/44.51 MUC search : 0.00
% 59.23/44.51 Cooper : 0.00
% 59.23/44.51 Total : 43.47
% 59.23/44.51 Index Insertion : 0.00
% 59.23/44.51 Index Deletion : 0.00
% 59.23/44.51 Index Matching : 0.00
% 59.23/44.51 BG Taut test : 0.00
%------------------------------------------------------------------------------