TSTP Solution File: NUM483+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM483+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 : n008.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 10:51:50 EDT 2023
% Result : Theorem 43.89s 31.66s
% Output : CNFRefutation 43.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 41
% Syntax : Number of formulae : 189 ( 49 unt; 16 typ; 3 def)
% Number of atoms : 542 ( 153 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 606 ( 237 ~; 299 |; 39 &)
% ( 3 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 129 (; 125 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > 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(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff(sdtsldt0,type,
sdtsldt0: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_426,hypothesis,
( ( xk != sz00 )
& ( xk != sz10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716_04) ).
tff(f_404,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
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_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(f_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
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_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_428,hypothesis,
~ isPrime0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1725) ).
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_435,negated_conjecture,
~ ? [W0] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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_335,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( doDivides0(W0,W1)
& doDivides0(W1,W2) )
=> doDivides0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
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_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(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_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_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_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_421,hypothesis,
! [W0] :
( ( aNaturalNumber0(W0)
& ( W0 != sz00 )
& ( W0 != sz10 ) )
=> ( iLess0(W0,xk)
=> ? [W1] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1700) ).
tff(c_147,plain,
xk != sz00,
inference(cnfTransformation,[status(thm)],[f_426]) ).
tff(c_137,plain,
aNaturalNumber0(xk),
inference(cnfTransformation,[status(thm)],[f_404]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_474,plain,
! [W1_115,W0_116] :
( ( sdtpldt0(W1_115,W0_116) = sdtpldt0(W0_116,W1_115) )
| ~ aNaturalNumber0(W1_115)
| ~ aNaturalNumber0(W0_116) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_514,plain,
! [W0_118] :
( ( sdtpldt0(sz10,W0_118) = sdtpldt0(W0_118,sz10) )
| ~ aNaturalNumber0(W0_118) ),
inference(resolution,[status(thm)],[c_8,c_474]) ).
tff(c_536,plain,
sdtpldt0(xk,sz10) = sdtpldt0(sz10,xk),
inference(resolution,[status(thm)],[c_137,c_514]) ).
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_560,plain,
( aNaturalNumber0(sdtpldt0(sz10,xk))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk) ),
inference(superposition,[status(thm),theory(equality)],[c_536,c_10]) ).
tff(c_570,plain,
aNaturalNumber0(sdtpldt0(sz10,xk)),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_8,c_560]) ).
tff(c_537,plain,
! [W1_119,W0_120] :
( ( sdtasdt0(W1_119,W0_120) = sdtasdt0(W0_120,W1_119) )
| ~ aNaturalNumber0(W1_119)
| ~ aNaturalNumber0(W0_120) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_699,plain,
! [W0_124] :
( ( sdtasdt0(xk,W0_124) = sdtasdt0(W0_124,xk) )
| ~ aNaturalNumber0(W0_124) ),
inference(resolution,[status(thm)],[c_137,c_537]) ).
tff(c_722,plain,
sdtasdt0(sdtpldt0(sz10,xk),xk) = sdtasdt0(xk,sdtpldt0(sz10,xk)),
inference(resolution,[status(thm)],[c_570,c_699]) ).
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_3333,plain,
( aNaturalNumber0(sdtasdt0(xk,sdtpldt0(sz10,xk)))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtpldt0(sz10,xk)) ),
inference(superposition,[status(thm),theory(equality)],[c_722,c_12]) ).
tff(c_3344,plain,
aNaturalNumber0(sdtasdt0(xk,sdtpldt0(sz10,xk))),
inference(demodulation,[status(thm),theory(equality)],[c_570,c_137,c_3333]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_343,plain,
! [W0_106,W1_107] :
( aNaturalNumber0(sdtasdt0(W0_106,W1_107))
| ~ aNaturalNumber0(W1_107)
| ~ aNaturalNumber0(W0_106) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_32,plain,
! [W0_18] :
( ( sdtasdt0(W0_18,sz00) = sz00 )
| ~ aNaturalNumber0(W0_18) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_391,plain,
! [W0_106,W1_107] :
( ( sdtasdt0(sdtasdt0(W0_106,W1_107),sz00) = sz00 )
| ~ aNaturalNumber0(W1_107)
| ~ aNaturalNumber0(W0_106) ),
inference(resolution,[status(thm)],[c_343,c_32]) ).
tff(c_3324,plain,
( ( sdtasdt0(sdtasdt0(xk,sdtpldt0(sz10,xk)),sz00) = sz00 )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtpldt0(sz10,xk)) ),
inference(superposition,[status(thm),theory(equality)],[c_722,c_391]) ).
tff(c_3337,plain,
sdtasdt0(sdtasdt0(xk,sdtpldt0(sz10,xk)),sz00) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_570,c_137,c_3324]) ).
tff(c_4156,plain,
! [W0_178,W2_179] :
( doDivides0(W0_178,sdtasdt0(W0_178,W2_179))
| ~ aNaturalNumber0(W2_179)
| ~ aNaturalNumber0(sdtasdt0(W0_178,W2_179))
| ~ aNaturalNumber0(W0_178) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_4165,plain,
( doDivides0(sdtasdt0(xk,sdtpldt0(sz10,xk)),sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtasdt0(sdtasdt0(xk,sdtpldt0(sz10,xk)),sz00))
| ~ aNaturalNumber0(sdtasdt0(xk,sdtpldt0(sz10,xk))) ),
inference(superposition,[status(thm),theory(equality)],[c_3337,c_4156]) ).
tff(c_4228,plain,
doDivides0(sdtasdt0(xk,sdtpldt0(sz10,xk)),sz00),
inference(demodulation,[status(thm),theory(equality)],[c_3344,c_4,c_3337,c_4,c_4165]) ).
tff(c_4168,plain,
( doDivides0(sdtpldt0(sz10,xk),sdtasdt0(xk,sdtpldt0(sz10,xk)))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(sdtpldt0(sz10,xk),xk))
| ~ aNaturalNumber0(sdtpldt0(sz10,xk)) ),
inference(superposition,[status(thm),theory(equality)],[c_722,c_4156]) ).
tff(c_4230,plain,
doDivides0(sdtpldt0(sz10,xk),sdtasdt0(xk,sdtpldt0(sz10,xk))),
inference(demodulation,[status(thm),theory(equality)],[c_570,c_3344,c_722,c_137,c_4168]) ).
tff(c_145,plain,
xk != sz10,
inference(cnfTransformation,[status(thm)],[f_426]) ).
tff(c_149,plain,
~ isPrime0(xk),
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_129,plain,
! [W0_89] :
( aNaturalNumber0('#skF_3'(W0_89))
| isPrime0(W0_89)
| ( sz10 = W0_89 )
| ( sz00 = W0_89 )
| ~ aNaturalNumber0(W0_89) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_3738,plain,
! [W0_175] :
( doDivides0('#skF_3'(W0_175),W0_175)
| isPrime0(W0_175)
| ( sz10 = W0_175 )
| ( sz00 = W0_175 )
| ~ aNaturalNumber0(W0_175) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_151,plain,
! [W0_95] :
( ~ isPrime0(W0_95)
| ~ doDivides0(W0_95,xk)
| ~ aNaturalNumber0(W0_95) ),
inference(cnfTransformation,[status(thm)],[f_435]) ).
tff(c_3742,plain,
( ~ isPrime0('#skF_3'(xk))
| ~ aNaturalNumber0('#skF_3'(xk))
| isPrime0(xk)
| ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_3738,c_151]) ).
tff(c_3745,plain,
( ~ isPrime0('#skF_3'(xk))
| ~ aNaturalNumber0('#skF_3'(xk))
| isPrime0(xk)
| ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_3742]) ).
tff(c_3746,plain,
( ~ isPrime0('#skF_3'(xk))
| ~ aNaturalNumber0('#skF_3'(xk)) ),
inference(negUnitSimplification,[status(thm)],[c_147,c_145,c_149,c_3745]) ).
tff(c_3747,plain,
~ aNaturalNumber0('#skF_3'(xk)),
inference(splitLeft,[status(thm)],[c_3746]) ).
tff(c_3750,plain,
( isPrime0(xk)
| ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_129,c_3747]) ).
tff(c_3753,plain,
( isPrime0(xk)
| ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_3750]) ).
tff(c_3755,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_147,c_145,c_149,c_3753]) ).
tff(c_3757,plain,
aNaturalNumber0('#skF_3'(xk)),
inference(splitRight,[status(thm)],[c_3746]) ).
tff(c_26,plain,
! [W0_17] :
( ( sdtasdt0(sz10,W0_17) = W0_17 )
| ~ aNaturalNumber0(W0_17) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_3819,plain,
sdtasdt0(sz10,'#skF_3'(xk)) = '#skF_3'(xk),
inference(resolution,[status(thm)],[c_3757,c_26]) ).
tff(c_95,plain,
! [W1_60,W0_59] :
( sdtlseqdt0(W1_60,sdtasdt0(W1_60,W0_59))
| ( sz00 = W0_59 )
| ~ aNaturalNumber0(W1_60)
| ~ aNaturalNumber0(W0_59) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_3933,plain,
( sdtlseqdt0(sz10,'#skF_3'(xk))
| ( '#skF_3'(xk) = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0('#skF_3'(xk)) ),
inference(superposition,[status(thm),theory(equality)],[c_3819,c_95]) ).
tff(c_3947,plain,
( sdtlseqdt0(sz10,'#skF_3'(xk))
| ( '#skF_3'(xk) = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3757,c_8,c_3933]) ).
tff(c_4114,plain,
'#skF_3'(xk) = sz00,
inference(splitLeft,[status(thm)],[c_3947]) ).
tff(c_127,plain,
! [W0_89] :
( doDivides0('#skF_3'(W0_89),W0_89)
| isPrime0(W0_89)
| ( sz10 = W0_89 )
| ( sz00 = W0_89 )
| ~ aNaturalNumber0(W0_89) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_4137,plain,
( doDivides0(sz00,xk)
| isPrime0(xk)
| ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(superposition,[status(thm),theory(equality)],[c_4114,c_127]) ).
tff(c_4144,plain,
( doDivides0(sz00,xk)
| isPrime0(xk)
| ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_4137]) ).
tff(c_4145,plain,
doDivides0(sz00,xk),
inference(negUnitSimplification,[status(thm)],[c_147,c_145,c_149,c_4144]) ).
tff(c_6417,plain,
! [W0_222,W2_223,W1_224] :
( doDivides0(W0_222,W2_223)
| ~ doDivides0(W1_224,W2_223)
| ~ doDivides0(W0_222,W1_224)
| ~ aNaturalNumber0(W2_223)
| ~ aNaturalNumber0(W1_224)
| ~ aNaturalNumber0(W0_222) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_6449,plain,
! [W0_222] :
( doDivides0(W0_222,xk)
| ~ doDivides0(W0_222,sz00)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(W0_222) ),
inference(resolution,[status(thm)],[c_4145,c_6417]) ).
tff(c_6678,plain,
! [W0_229] :
( doDivides0(W0_229,xk)
| ~ doDivides0(W0_229,sz00)
| ~ aNaturalNumber0(W0_229) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_137,c_6449]) ).
tff(c_113,plain,
! [W0_74,W2_76,W1_75] :
( doDivides0(W0_74,W2_76)
| ~ doDivides0(W1_75,W2_76)
| ~ doDivides0(W0_74,W1_75)
| ~ aNaturalNumber0(W2_76)
| ~ aNaturalNumber0(W1_75)
| ~ aNaturalNumber0(W0_74) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_6680,plain,
! [W0_74,W0_229] :
( doDivides0(W0_74,xk)
| ~ doDivides0(W0_74,W0_229)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(W0_74)
| ~ doDivides0(W0_229,sz00)
| ~ aNaturalNumber0(W0_229) ),
inference(resolution,[status(thm)],[c_6678,c_113]) ).
tff(c_9686,plain,
! [W0_276,W0_277] :
( doDivides0(W0_276,xk)
| ~ doDivides0(W0_276,W0_277)
| ~ aNaturalNumber0(W0_276)
| ~ doDivides0(W0_277,sz00)
| ~ aNaturalNumber0(W0_277) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_6680]) ).
tff(c_9696,plain,
( doDivides0(sdtpldt0(sz10,xk),xk)
| ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| ~ doDivides0(sdtasdt0(xk,sdtpldt0(sz10,xk)),sz00)
| ~ aNaturalNumber0(sdtasdt0(xk,sdtpldt0(sz10,xk))) ),
inference(resolution,[status(thm)],[c_4230,c_9686]) ).
tff(c_9737,plain,
doDivides0(sdtpldt0(sz10,xk),xk),
inference(demodulation,[status(thm),theory(equality)],[c_3344,c_4228,c_570,c_9696]) ).
tff(c_119,plain,
! [W0_83,W1_84] :
( sdtlseqdt0(W0_83,W1_84)
| ( sz00 = W1_84 )
| ~ doDivides0(W0_83,W1_84)
| ~ aNaturalNumber0(W1_84)
| ~ aNaturalNumber0(W0_83) ),
inference(cnfTransformation,[status(thm)],[f_370]) ).
tff(c_6,plain,
sz10 != sz00,
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_208,plain,
! [W0_100] :
( ( sdtpldt0(sz00,W0_100) = W0_100 )
| ~ aNaturalNumber0(W0_100) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_221,plain,
sdtpldt0(sz00,xk) = xk,
inference(resolution,[status(thm)],[c_137,c_208]) ).
tff(c_5928,plain,
! [W2_212,W0_213,W1_214] :
( ( sdtpldt0(W2_212,W0_213) != sdtpldt0(W1_214,W0_213) )
| ( W2_212 = W1_214 )
| ~ aNaturalNumber0(W2_212)
| ~ aNaturalNumber0(W1_214)
| ~ aNaturalNumber0(W0_213) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_5966,plain,
! [W1_214] :
( ( sdtpldt0(W1_214,xk) != xk )
| ( sz00 = W1_214 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(W1_214)
| ~ aNaturalNumber0(xk) ),
inference(superposition,[status(thm),theory(equality)],[c_221,c_5928]) ).
tff(c_6034,plain,
! [W1_215] :
( ( sdtpldt0(W1_215,xk) != xk )
| ( sz00 = W1_215 )
| ~ aNaturalNumber0(W1_215) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_4,c_5966]) ).
tff(c_6076,plain,
( ( sdtpldt0(sz10,xk) != xk )
| ( sz10 = sz00 ) ),
inference(resolution,[status(thm)],[c_8,c_6034]) ).
tff(c_6106,plain,
sdtpldt0(sz10,xk) != xk,
inference(negUnitSimplification,[status(thm)],[c_6,c_6076]) ).
tff(c_5565,plain,
! [W0_205,W2_206] :
( sdtlseqdt0(W0_205,sdtpldt0(W0_205,W2_206))
| ~ aNaturalNumber0(W2_206)
| ~ aNaturalNumber0(sdtpldt0(W0_205,W2_206))
| ~ aNaturalNumber0(W0_205) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_5594,plain,
( sdtlseqdt0(xk,sdtpldt0(sz10,xk))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtpldt0(xk,sz10))
| ~ aNaturalNumber0(xk) ),
inference(superposition,[status(thm),theory(equality)],[c_536,c_5565]) ).
tff(c_5625,plain,
sdtlseqdt0(xk,sdtpldt0(sz10,xk)),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_570,c_536,c_8,c_5594]) ).
tff(c_66,plain,
! [W1_45,W0_44] :
( ( W1_45 = W0_44 )
| ~ sdtlseqdt0(W1_45,W0_44)
| ~ sdtlseqdt0(W0_44,W1_45)
| ~ aNaturalNumber0(W1_45)
| ~ aNaturalNumber0(W0_44) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_5766,plain,
( ( sdtpldt0(sz10,xk) = xk )
| ~ sdtlseqdt0(sdtpldt0(sz10,xk),xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtpldt0(sz10,xk)) ),
inference(resolution,[status(thm)],[c_5625,c_66]) ).
tff(c_5772,plain,
( ( sdtpldt0(sz10,xk) = xk )
| ~ sdtlseqdt0(sdtpldt0(sz10,xk),xk) ),
inference(demodulation,[status(thm),theory(equality)],[c_570,c_137,c_5766]) ).
tff(c_12226,plain,
~ sdtlseqdt0(sdtpldt0(sz10,xk),xk),
inference(negUnitSimplification,[status(thm)],[c_6106,c_5772]) ).
tff(c_12238,plain,
( ( xk = sz00 )
| ~ doDivides0(sdtpldt0(sz10,xk),xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtpldt0(sz10,xk)) ),
inference(resolution,[status(thm)],[c_119,c_12226]) ).
tff(c_12257,plain,
xk = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_570,c_137,c_9737,c_12238]) ).
tff(c_12259,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_147,c_12257]) ).
tff(c_12261,plain,
'#skF_3'(xk) != sz00,
inference(splitRight,[status(thm)],[c_3947]) ).
tff(c_914,plain,
! [W0_131] :
( ( '#skF_3'(W0_131) != sz10 )
| isPrime0(W0_131)
| ( sz10 = W0_131 )
| ( sz00 = W0_131 )
| ~ aNaturalNumber0(W0_131) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_923,plain,
( ( '#skF_3'(xk) != sz10 )
| ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_914,c_149]) ).
tff(c_936,plain,
( ( '#skF_3'(xk) != sz10 )
| ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_923]) ).
tff(c_937,plain,
'#skF_3'(xk) != sz10,
inference(negUnitSimplification,[status(thm)],[c_147,c_145,c_936]) ).
tff(c_1148,plain,
! [W0_136] :
( ( '#skF_3'(W0_136) != W0_136 )
| isPrime0(W0_136)
| ( sz10 = W0_136 )
| ( sz00 = W0_136 )
| ~ aNaturalNumber0(W0_136) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_1157,plain,
( ( '#skF_3'(xk) != xk )
| ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_1148,c_149]) ).
tff(c_1170,plain,
( ( '#skF_3'(xk) != xk )
| ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_1157]) ).
tff(c_1171,plain,
'#skF_3'(xk) != xk,
inference(negUnitSimplification,[status(thm)],[c_147,c_145,c_1170]) ).
tff(c_28,plain,
! [W0_17] :
( ( sdtasdt0(W0_17,sz10) = W0_17 )
| ~ aNaturalNumber0(W0_17) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_3818,plain,
sdtasdt0('#skF_3'(xk),sz10) = '#skF_3'(xk),
inference(resolution,[status(thm)],[c_3757,c_28]) ).
tff(c_3896,plain,
( sdtlseqdt0('#skF_3'(xk),'#skF_3'(xk))
| ( sz10 = sz00 )
| ~ aNaturalNumber0('#skF_3'(xk))
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_3818,c_95]) ).
tff(c_3910,plain,
( sdtlseqdt0('#skF_3'(xk),'#skF_3'(xk))
| ( sz10 = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_3757,c_3896]) ).
tff(c_3911,plain,
sdtlseqdt0('#skF_3'(xk),'#skF_3'(xk)),
inference(negUnitSimplification,[status(thm)],[c_6,c_3910]) ).
tff(c_70,plain,
! [W1_50,W0_49] :
( sdtlseqdt0(W1_50,W0_49)
| sdtlseqdt0(W0_49,W1_50)
| ~ aNaturalNumber0(W1_50)
| ~ aNaturalNumber0(W0_49) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_15067,plain,
! [W0_345,W2_346,W1_347] :
( sdtlseqdt0(W0_345,W2_346)
| ~ sdtlseqdt0(W1_347,W2_346)
| ~ sdtlseqdt0(W0_345,W1_347)
| ~ aNaturalNumber0(W2_346)
| ~ aNaturalNumber0(W1_347)
| ~ aNaturalNumber0(W0_345) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_49859,plain,
! [W0_593,W1_594,W0_595] :
( sdtlseqdt0(W0_593,W1_594)
| ~ sdtlseqdt0(W0_593,W0_595)
| ~ aNaturalNumber0(W0_593)
| sdtlseqdt0(W1_594,W0_595)
| ~ aNaturalNumber0(W1_594)
| ~ aNaturalNumber0(W0_595) ),
inference(resolution,[status(thm)],[c_70,c_15067]) ).
tff(c_49937,plain,
! [W1_594] :
( sdtlseqdt0('#skF_3'(xk),W1_594)
| sdtlseqdt0(W1_594,'#skF_3'(xk))
| ~ aNaturalNumber0(W1_594)
| ~ aNaturalNumber0('#skF_3'(xk)) ),
inference(resolution,[status(thm)],[c_3911,c_49859]) ).
tff(c_50064,plain,
! [W1_594] :
( sdtlseqdt0('#skF_3'(xk),W1_594)
| sdtlseqdt0(W1_594,'#skF_3'(xk))
| ~ aNaturalNumber0(W1_594) ),
inference(demodulation,[status(thm),theory(equality)],[c_3757,c_49937]) ).
tff(c_274,plain,
! [W0_103] :
( ( sdtasdt0(W0_103,sz10) = W0_103 )
| ~ aNaturalNumber0(W0_103) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_288,plain,
sdtasdt0(xk,sz10) = xk,
inference(resolution,[status(thm)],[c_137,c_274]) ).
tff(c_731,plain,
! [W1_125,W0_126] :
( sdtlseqdt0(W1_125,sdtasdt0(W1_125,W0_126))
| ( sz00 = W0_126 )
| ~ aNaturalNumber0(W1_125)
| ~ aNaturalNumber0(W0_126) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_740,plain,
( sdtlseqdt0(xk,xk)
| ( sz10 = sz00 )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_288,c_731]) ).
tff(c_769,plain,
( sdtlseqdt0(xk,xk)
| ( sz10 = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_137,c_740]) ).
tff(c_770,plain,
sdtlseqdt0(xk,xk),
inference(negUnitSimplification,[status(thm)],[c_6,c_769]) ).
tff(c_49953,plain,
! [W1_594] :
( sdtlseqdt0(xk,W1_594)
| sdtlseqdt0(W1_594,xk)
| ~ aNaturalNumber0(W1_594)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_770,c_49859]) ).
tff(c_50614,plain,
! [W1_600] :
( sdtlseqdt0(xk,W1_600)
| sdtlseqdt0(W1_600,xk)
| ~ aNaturalNumber0(W1_600) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_49953]) ).
tff(c_99,plain,
! [W0_63,W1_64] :
( iLess0(W0_63,W1_64)
| ~ sdtlseqdt0(W0_63,W1_64)
| ( W1_64 = W0_63 )
| ~ aNaturalNumber0(W1_64)
| ~ aNaturalNumber0(W0_63) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_50670,plain,
! [W1_600] :
( iLess0(W1_600,xk)
| ( xk = W1_600 )
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xk,W1_600)
| ~ aNaturalNumber0(W1_600) ),
inference(resolution,[status(thm)],[c_50614,c_99]) ).
tff(c_51401,plain,
! [W1_609] :
( iLess0(W1_609,xk)
| ( xk = W1_609 )
| sdtlseqdt0(xk,W1_609)
| ~ aNaturalNumber0(W1_609) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_50670]) ).
tff(c_51438,plain,
! [W1_609] :
( ~ sdtlseqdt0(W1_609,xk)
| ~ aNaturalNumber0(xk)
| iLess0(W1_609,xk)
| ( xk = W1_609 )
| ~ aNaturalNumber0(W1_609) ),
inference(resolution,[status(thm)],[c_51401,c_66]) ).
tff(c_71445,plain,
! [W1_705] :
( ~ sdtlseqdt0(W1_705,xk)
| iLess0(W1_705,xk)
| ( xk = W1_705 )
| ~ aNaturalNumber0(W1_705) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_51438]) ).
tff(c_71449,plain,
( iLess0('#skF_3'(xk),xk)
| ( '#skF_3'(xk) = xk )
| ~ aNaturalNumber0('#skF_3'(xk))
| sdtlseqdt0(xk,'#skF_3'(xk))
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_50064,c_71445]) ).
tff(c_71561,plain,
( iLess0('#skF_3'(xk),xk)
| ( '#skF_3'(xk) = xk )
| sdtlseqdt0(xk,'#skF_3'(xk)) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_3757,c_71449]) ).
tff(c_71562,plain,
( iLess0('#skF_3'(xk),xk)
| sdtlseqdt0(xk,'#skF_3'(xk)) ),
inference(negUnitSimplification,[status(thm)],[c_1171,c_71561]) ).
tff(c_71803,plain,
sdtlseqdt0(xk,'#skF_3'(xk)),
inference(splitLeft,[status(thm)],[c_71562]) ).
tff(c_3951,plain,
! [W1_176,W0_177] :
( ( W1_176 = W0_177 )
| ~ sdtlseqdt0(W1_176,W0_177)
| ~ sdtlseqdt0(W0_177,W1_176)
| ~ aNaturalNumber0(W1_176)
| ~ aNaturalNumber0(W0_177) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_3987,plain,
! [W1_84,W0_83] :
( ( W1_84 = W0_83 )
| ~ sdtlseqdt0(W1_84,W0_83)
| ( sz00 = W1_84 )
| ~ doDivides0(W0_83,W1_84)
| ~ aNaturalNumber0(W1_84)
| ~ aNaturalNumber0(W0_83) ),
inference(resolution,[status(thm)],[c_119,c_3951]) ).
tff(c_71818,plain,
( ( '#skF_3'(xk) = xk )
| ( xk = sz00 )
| ~ doDivides0('#skF_3'(xk),xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0('#skF_3'(xk)) ),
inference(resolution,[status(thm)],[c_71803,c_3987]) ).
tff(c_71847,plain,
( ( '#skF_3'(xk) = xk )
| ( xk = sz00 )
| ~ doDivides0('#skF_3'(xk),xk) ),
inference(demodulation,[status(thm),theory(equality)],[c_3757,c_137,c_71818]) ).
tff(c_71848,plain,
~ doDivides0('#skF_3'(xk),xk),
inference(negUnitSimplification,[status(thm)],[c_147,c_1171,c_71847]) ).
tff(c_71865,plain,
( isPrime0(xk)
| ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_127,c_71848]) ).
tff(c_71871,plain,
( isPrime0(xk)
| ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_71865]) ).
tff(c_71873,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_147,c_145,c_149,c_71871]) ).
tff(c_71874,plain,
iLess0('#skF_3'(xk),xk),
inference(splitRight,[status(thm)],[c_71562]) ).
tff(c_139,plain,
! [W0_93] :
( isPrime0('#skF_4'(W0_93))
| ~ iLess0(W0_93,xk)
| ( sz10 = W0_93 )
| ( sz00 = W0_93 )
| ~ aNaturalNumber0(W0_93) ),
inference(cnfTransformation,[status(thm)],[f_421]) ).
tff(c_143,plain,
! [W0_93] :
( aNaturalNumber0('#skF_4'(W0_93))
| ~ iLess0(W0_93,xk)
| ( sz10 = W0_93 )
| ( sz00 = W0_93 )
| ~ aNaturalNumber0(W0_93) ),
inference(cnfTransformation,[status(thm)],[f_421]) ).
tff(c_141,plain,
! [W0_93] :
( doDivides0('#skF_4'(W0_93),W0_93)
| ~ iLess0(W0_93,xk)
| ( sz10 = W0_93 )
| ( sz00 = W0_93 )
| ~ aNaturalNumber0(W0_93) ),
inference(cnfTransformation,[status(thm)],[f_421]) ).
tff(c_12262,plain,
! [W0_306,W2_307] :
( doDivides0(W0_306,sdtasdt0(W0_306,W2_307))
| ~ aNaturalNumber0(W2_307)
| ~ aNaturalNumber0(sdtasdt0(W0_306,W2_307))
| ~ aNaturalNumber0(W0_306) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_12268,plain,
( doDivides0('#skF_3'(xk),'#skF_3'(xk))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0('#skF_3'(xk),sz10))
| ~ aNaturalNumber0('#skF_3'(xk)) ),
inference(superposition,[status(thm),theory(equality)],[c_3818,c_12262]) ).
tff(c_12344,plain,
doDivides0('#skF_3'(xk),'#skF_3'(xk)),
inference(demodulation,[status(thm),theory(equality)],[c_3757,c_3757,c_3818,c_8,c_12268]) ).
tff(c_14856,plain,
! [W0_341,W2_342,W1_343] :
( doDivides0(W0_341,W2_342)
| ~ doDivides0(W1_343,W2_342)
| ~ doDivides0(W0_341,W1_343)
| ~ aNaturalNumber0(W2_342)
| ~ aNaturalNumber0(W1_343)
| ~ aNaturalNumber0(W0_341) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_113008,plain,
! [W0_874,W0_875] :
( doDivides0(W0_874,W0_875)
| ~ doDivides0(W0_874,'#skF_3'(W0_875))
| ~ aNaturalNumber0('#skF_3'(W0_875))
| ~ aNaturalNumber0(W0_874)
| isPrime0(W0_875)
| ( sz10 = W0_875 )
| ( sz00 = W0_875 )
| ~ aNaturalNumber0(W0_875) ),
inference(resolution,[status(thm)],[c_127,c_14856]) ).
tff(c_113024,plain,
( doDivides0('#skF_3'(xk),xk)
| ~ aNaturalNumber0('#skF_3'(xk))
| isPrime0(xk)
| ( xk = sz10 )
| ( xk = sz00 )
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_12344,c_113008]) ).
tff(c_113047,plain,
( doDivides0('#skF_3'(xk),xk)
| isPrime0(xk)
| ( xk = sz10 )
| ( xk = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_3757,c_113024]) ).
tff(c_113048,plain,
doDivides0('#skF_3'(xk),xk),
inference(negUnitSimplification,[status(thm)],[c_147,c_145,c_149,c_113047]) ).
tff(c_113058,plain,
! [W0_74] :
( doDivides0(W0_74,xk)
| ~ doDivides0(W0_74,'#skF_3'(xk))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0('#skF_3'(xk))
| ~ aNaturalNumber0(W0_74) ),
inference(resolution,[status(thm)],[c_113048,c_113]) ).
tff(c_139060,plain,
! [W0_954] :
( doDivides0(W0_954,xk)
| ~ doDivides0(W0_954,'#skF_3'(xk))
| ~ aNaturalNumber0(W0_954) ),
inference(demodulation,[status(thm),theory(equality)],[c_3757,c_137,c_113058]) ).
tff(c_139073,plain,
( doDivides0('#skF_4'('#skF_3'(xk)),xk)
| ~ aNaturalNumber0('#skF_4'('#skF_3'(xk)))
| ~ iLess0('#skF_3'(xk),xk)
| ( '#skF_3'(xk) = sz10 )
| ( '#skF_3'(xk) = sz00 )
| ~ aNaturalNumber0('#skF_3'(xk)) ),
inference(resolution,[status(thm)],[c_141,c_139060]) ).
tff(c_139093,plain,
( doDivides0('#skF_4'('#skF_3'(xk)),xk)
| ~ aNaturalNumber0('#skF_4'('#skF_3'(xk)))
| ( '#skF_3'(xk) = sz10 )
| ( '#skF_3'(xk) = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3757,c_71874,c_139073]) ).
tff(c_139094,plain,
( doDivides0('#skF_4'('#skF_3'(xk)),xk)
| ~ aNaturalNumber0('#skF_4'('#skF_3'(xk))) ),
inference(negUnitSimplification,[status(thm)],[c_12261,c_937,c_139093]) ).
tff(c_139163,plain,
~ aNaturalNumber0('#skF_4'('#skF_3'(xk))),
inference(splitLeft,[status(thm)],[c_139094]) ).
tff(c_139166,plain,
( ~ iLess0('#skF_3'(xk),xk)
| ( '#skF_3'(xk) = sz10 )
| ( '#skF_3'(xk) = sz00 )
| ~ aNaturalNumber0('#skF_3'(xk)) ),
inference(resolution,[status(thm)],[c_143,c_139163]) ).
tff(c_139169,plain,
( ( '#skF_3'(xk) = sz10 )
| ( '#skF_3'(xk) = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3757,c_71874,c_139166]) ).
tff(c_139171,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12261,c_937,c_139169]) ).
tff(c_139173,plain,
aNaturalNumber0('#skF_4'('#skF_3'(xk))),
inference(splitRight,[status(thm)],[c_139094]) ).
tff(c_139172,plain,
doDivides0('#skF_4'('#skF_3'(xk)),xk),
inference(splitRight,[status(thm)],[c_139094]) ).
tff(c_139357,plain,
( ~ isPrime0('#skF_4'('#skF_3'(xk)))
| ~ aNaturalNumber0('#skF_4'('#skF_3'(xk))) ),
inference(resolution,[status(thm)],[c_139172,c_151]) ).
tff(c_139369,plain,
~ isPrime0('#skF_4'('#skF_3'(xk))),
inference(demodulation,[status(thm),theory(equality)],[c_139173,c_139357]) ).
tff(c_139372,plain,
( ~ iLess0('#skF_3'(xk),xk)
| ( '#skF_3'(xk) = sz10 )
| ( '#skF_3'(xk) = sz00 )
| ~ aNaturalNumber0('#skF_3'(xk)) ),
inference(resolution,[status(thm)],[c_139,c_139369]) ).
tff(c_139381,plain,
( ( '#skF_3'(xk) = sz10 )
| ( '#skF_3'(xk) = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3757,c_71874,c_139372]) ).
tff(c_139383,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12261,c_937,c_139381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM483+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
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 14:31:18 EDT 2023
% 0.13/0.35 % CPUTime :
% 43.89/31.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.98/31.69
% 43.98/31.69 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 43.98/31.73
% 43.98/31.73 Inference rules
% 43.98/31.73 ----------------------
% 43.98/31.73 #Ref : 13
% 43.98/31.73 #Sup : 28371
% 43.98/31.73 #Fact : 16
% 43.98/31.73 #Define : 0
% 43.98/31.73 #Split : 19
% 43.98/31.73 #Chain : 0
% 43.98/31.73 #Close : 0
% 43.98/31.73
% 43.98/31.73 Ordering : KBO
% 43.98/31.73
% 43.98/31.73 Simplification rules
% 43.98/31.73 ----------------------
% 43.98/31.73 #Subsume : 6389
% 43.98/31.73 #Demod : 43956
% 43.98/31.73 #Tautology : 9188
% 43.98/31.73 #SimpNegUnit : 4149
% 43.98/31.73 #BackRed : 186
% 43.98/31.73
% 43.98/31.73 #Partial instantiations: 0
% 43.98/31.73 #Strategies tried : 1
% 43.98/31.73
% 43.98/31.73 Timing (in seconds)
% 43.98/31.73 ----------------------
% 43.98/31.74 Preprocessing : 0.67
% 43.98/31.74 Parsing : 0.33
% 43.98/31.74 CNF conversion : 0.05
% 43.98/31.74 Main loop : 30.02
% 43.98/31.74 Inferencing : 3.45
% 43.98/31.74 Reduction : 17.44
% 43.98/31.74 Demodulation : 14.06
% 43.98/31.74 BG Simplification : 0.22
% 43.98/31.74 Subsumption : 7.77
% 43.98/31.74 Abstraction : 0.40
% 43.98/31.74 MUC search : 0.00
% 43.98/31.74 Cooper : 0.00
% 44.23/31.74 Total : 30.78
% 44.23/31.74 Index Insertion : 0.00
% 44.23/31.74 Index Deletion : 0.00
% 44.23/31.74 Index Matching : 0.00
% 44.23/31.74 BG Taut test : 0.00
%------------------------------------------------------------------------------