TSTP Solution File: NUM510+3 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM510+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 : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 10:51:56 EDT 2023

% Result   : Theorem 66.16s 47.95s
% Output   : CNFRefutation 66.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   58
% Syntax   : Number of formulae    :  218 ( 100 unt;  34 typ;   3 def)
%            Number of atoms       :  425 ( 208 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  398 ( 157   ~; 153   |;  61   &)
%                                         (   3 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    3 (   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    :   29 (  29 usr;  17 con; 0-3 aty)
%            Number of variables   :   89 (;  77   !;  12   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_18 > #skF_17 > #skF_11 > #skF_6 > #skF_15 > #skF_10 > #skF_16 > #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_18',type,
    '#skF_18': $i ).

tff('#skF_17',type,
    '#skF_17': $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('#skF_16',type,
    '#skF_16': $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_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_423,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).

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_35,axiom,
    ( aNaturalNumber0(sz10)
    & ( sz10 != sz00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).

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_93,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( sdtasdt0(W0,sz00) = sz00 )
        & ( sz00 = sdtasdt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).

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_31,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).

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_618,hypothesis,
    ( ? [W0] :
        ( aNaturalNumber0(W0)
        & ( xn = sdtasdt0(xr,W0) ) )
    & doDivides0(xr,xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).

tff(f_636,negated_conjecture,
    ~ ( ~ ( aNaturalNumber0(sdtsldt0(xn,xr))
          & ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
          & ( sdtsldt0(xn,xr) = xn ) )
      & ( ( aNaturalNumber0(sdtsldt0(xn,xr))
          & ( xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ) )
       => ( ? [W0] :
              ( aNaturalNumber0(W0)
              & ( sdtpldt0(sdtsldt0(xn,xr),W0) = xn ) )
          | sdtlseqdt0(sdtsldt0(xn,xr),xn) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_131,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( W0 != sz00 )
       => ! [W1,W2] :
            ( ( aNaturalNumber0(W1)
              & aNaturalNumber0(W2) )
           => ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
                | ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
             => ( W1 = W2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).

tff(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_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_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_151,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( sdtasdt0(W0,W1) = sz00 )
       => ( ( W0 = sz00 )
          | ( W1 = sz00 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).

tff(f_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_73,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).

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_535,hypothesis,
    ( ( xn != xp )
    & ? [W0] :
        ( aNaturalNumber0(W0)
        & ( sdtpldt0(xn,W0) = xp ) )
    & sdtlseqdt0(xn,xp)
    & ( xm != xp )
    & ? [W0] :
        ( aNaturalNumber0(W0)
        & ( sdtpldt0(xm,W0) = xp ) )
    & sdtlseqdt0(xm,xp) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).

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_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_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_549,hypothesis,
    ( ( xk != sz00 )
    & ( xk != sz10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).

tff(c_457,plain,
    xr != sz10,
    inference(cnfTransformation,[status(thm)],[f_579]) ).

tff(c_147,plain,
    aNaturalNumber0(xn),
    inference(cnfTransformation,[status(thm)],[f_423]) ).

tff(c_167858,plain,
    ! [W0_1421] :
      ( ( sdtasdt0(sz10,W0_1421) = W0_1421 )
      | ~ aNaturalNumber0(W0_1421) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_167915,plain,
    sdtasdt0(sz10,xn) = xn,
    inference(resolution,[status(thm)],[c_147,c_167858]) ).

tff(c_8,plain,
    aNaturalNumber0(sz10),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_459,plain,
    xr != sz00,
    inference(cnfTransformation,[status(thm)],[f_579]) ).

tff(c_467,plain,
    aNaturalNumber0(xr),
    inference(cnfTransformation,[status(thm)],[f_579]) ).

tff(c_477,plain,
    aNaturalNumber0('#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_590]) ).

tff(c_145,plain,
    aNaturalNumber0(xm),
    inference(cnfTransformation,[status(thm)],[f_423]) ).

tff(c_168021,plain,
    ! [W0_1423] :
      ( ( sdtasdt0(sz00,W0_1423) = sz00 )
      | ~ aNaturalNumber0(W0_1423) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_168076,plain,
    sdtasdt0(sz00,xm) = sz00,
    inference(resolution,[status(thm)],[c_145,c_168021]) ).

tff(c_167338,plain,
    ! [W0_1415] :
      ( ( sdtpldt0(W0_1415,sz00) = W0_1415 )
      | ~ aNaturalNumber0(W0_1415) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_167395,plain,
    sdtpldt0(xn,sz00) = xn,
    inference(resolution,[status(thm)],[c_147,c_167338]) ).

tff(c_4,plain,
    aNaturalNumber0(sz00),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_72,plain,
    ! [W1_50] :
      ( sdtlseqdt0(W1_50,W1_50)
      | ~ aNaturalNumber0(W1_50) ),
    inference(cnfTransformation,[status(thm)],[f_212]) ).

tff(c_511,plain,
    sdtasdt0(xr,'#skF_18') = xn,
    inference(cnfTransformation,[status(thm)],[f_618]) ).

tff(c_513,plain,
    aNaturalNumber0('#skF_18'),
    inference(cnfTransformation,[status(thm)],[f_618]) ).

tff(c_537,plain,
    aNaturalNumber0(sdtsldt0(xn,xr)),
    inference(cnfTransformation,[status(thm)],[f_636]) ).

tff(c_529,plain,
    sdtasdt0(xr,sdtsldt0(xn,xr)) = xn,
    inference(cnfTransformation,[status(thm)],[f_636]) ).

tff(c_163194,plain,
    ! [W0_1390,W2_1391,W1_1392] :
      ( ( sdtasdt0(W0_1390,W2_1391) != sdtasdt0(W0_1390,W1_1392) )
      | ( W2_1391 = W1_1392 )
      | ~ aNaturalNumber0(W2_1391)
      | ~ aNaturalNumber0(W1_1392)
      | ( sz00 = W0_1390 )
      | ~ aNaturalNumber0(W0_1390) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_163514,plain,
    ! [W2_1391] :
      ( ( sdtasdt0(xr,W2_1391) != xn )
      | ( sdtsldt0(xn,xr) = W2_1391 )
      | ~ aNaturalNumber0(W2_1391)
      | ~ aNaturalNumber0(sdtsldt0(xn,xr))
      | ( xr = sz00 )
      | ~ aNaturalNumber0(xr) ),
    inference(superposition,[status(thm),theory(equality)],[c_529,c_163194]) ).

tff(c_163973,plain,
    ! [W2_1391] :
      ( ( sdtasdt0(xr,W2_1391) != xn )
      | ( sdtsldt0(xn,xr) = W2_1391 )
      | ~ aNaturalNumber0(W2_1391)
      | ( xr = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_467,c_537,c_163514]) ).

tff(c_164790,plain,
    ! [W2_1399] :
      ( ( sdtasdt0(xr,W2_1399) != xn )
      | ( sdtsldt0(xn,xr) = W2_1399 )
      | ~ aNaturalNumber0(W2_1399) ),
    inference(negUnitSimplification,[status(thm)],[c_459,c_163973]) ).

tff(c_164928,plain,
    ( ( sdtasdt0(xr,'#skF_18') != xn )
    | ( sdtsldt0(xn,xr) = '#skF_18' ) ),
    inference(resolution,[status(thm)],[c_513,c_164790]) ).

tff(c_164987,plain,
    sdtsldt0(xn,xr) = '#skF_18',
    inference(demodulation,[status(thm),theory(equality)],[c_511,c_164928]) ).

tff(c_1189,plain,
    ! [W0_122] :
      ( ( sdtasdt0(sz10,W0_122) = W0_122 )
      | ~ aNaturalNumber0(W0_122) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_1258,plain,
    sdtasdt0(sz10,'#skF_18') = '#skF_18',
    inference(resolution,[status(thm)],[c_513,c_1189]) ).

tff(c_4116,plain,
    ! [W1_155,W0_156] :
      ( sdtlseqdt0(W1_155,sdtasdt0(W1_155,W0_156))
      | ( sz00 = W0_156 )
      | ~ aNaturalNumber0(W1_155)
      | ~ aNaturalNumber0(W0_156) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_4227,plain,
    ( sdtlseqdt0(sz10,'#skF_18')
    | ( sz00 = '#skF_18' )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0('#skF_18') ),
    inference(superposition,[status(thm),theory(equality)],[c_1258,c_4116]) ).

tff(c_4434,plain,
    ( sdtlseqdt0(sz10,'#skF_18')
    | ( sz00 = '#skF_18' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_513,c_8,c_4227]) ).

tff(c_43130,plain,
    sz00 = '#skF_18',
    inference(splitLeft,[status(thm)],[c_4434]) ).

tff(c_43230,plain,
    xr != '#skF_18',
    inference(demodulation,[status(thm),theory(equality)],[c_43130,c_459]) ).

tff(c_1083,plain,
    ! [W0_121] :
      ( ( sdtasdt0(W0_121,sz00) = sz00 )
      | ~ aNaturalNumber0(W0_121) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_1138,plain,
    sdtasdt0(xr,sz00) = sz00,
    inference(resolution,[status(thm)],[c_467,c_1083]) ).

tff(c_43164,plain,
    sdtasdt0(xr,'#skF_18') = '#skF_18',
    inference(demodulation,[status(thm),theory(equality)],[c_43130,c_43130,c_1138]) ).

tff(c_43623,plain,
    xn = '#skF_18',
    inference(demodulation,[status(thm),theory(equality)],[c_43164,c_511]) ).

tff(c_4341,plain,
    ( sdtlseqdt0(xr,xn)
    | ( sdtsldt0(xn,xr) = sz00 )
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
    inference(superposition,[status(thm),theory(equality)],[c_529,c_4116]) ).

tff(c_4533,plain,
    ( sdtlseqdt0(xr,xn)
    | ( sdtsldt0(xn,xr) = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_537,c_467,c_4341]) ).

tff(c_4534,plain,
    sdtsldt0(xn,xr) = sz00,
    inference(splitLeft,[status(thm)],[c_4533]) ).

tff(c_4574,plain,
    sdtasdt0(xr,sz00) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_4534,c_529]) ).

tff(c_4587,plain,
    xn = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_1138,c_4574]) ).

tff(c_655,plain,
    ! [W0_117] :
      ( ( sdtpldt0(W0_117,sz00) = W0_117 )
      | ~ aNaturalNumber0(W0_117) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_719,plain,
    sdtpldt0(sdtsldt0(xn,xr),sz00) = sdtsldt0(xn,xr),
    inference(resolution,[status(thm)],[c_537,c_655]) ).

tff(c_521,plain,
    ! [W0_114] :
      ( ( sdtsldt0(xn,xr) = xn )
      | ( sdtpldt0(sdtsldt0(xn,xr),W0_114) != xn )
      | ~ aNaturalNumber0(W0_114) ),
    inference(cnfTransformation,[status(thm)],[f_636]) ).

tff(c_558,plain,
    ! [W0_114] :
      ( ( sdtpldt0(sdtsldt0(xn,xr),W0_114) != xn )
      | ~ aNaturalNumber0(W0_114) ),
    inference(splitLeft,[status(thm)],[c_521]) ).

tff(c_915,plain,
    ( ( sdtsldt0(xn,xr) != xn )
    | ~ aNaturalNumber0(sz00) ),
    inference(superposition,[status(thm),theory(equality)],[c_719,c_558]) ).

tff(c_919,plain,
    sdtsldt0(xn,xr) != xn,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_915]) ).

tff(c_4567,plain,
    xn != sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_4534,c_919]) ).

tff(c_4753,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4587,c_4567]) ).

tff(c_4754,plain,
    sdtlseqdt0(xr,xn),
    inference(splitRight,[status(thm)],[c_4533]) ).

tff(c_43679,plain,
    sdtlseqdt0(xr,'#skF_18'),
    inference(demodulation,[status(thm),theory(equality)],[c_43623,c_4754]) ).

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_44165,plain,
    ( ( xr = '#skF_18' )
    | ~ sdtlseqdt0('#skF_18',xr)
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0('#skF_18') ),
    inference(resolution,[status(thm)],[c_43679,c_66]) ).

tff(c_44172,plain,
    ( ( xr = '#skF_18' )
    | ~ sdtlseqdt0('#skF_18',xr) ),
    inference(demodulation,[status(thm),theory(equality)],[c_513,c_467,c_44165]) ).

tff(c_44173,plain,
    ~ sdtlseqdt0('#skF_18',xr),
    inference(negUnitSimplification,[status(thm)],[c_43230,c_44172]) ).

tff(c_586,plain,
    ! [W0_116] :
      ( ( sdtpldt0(sz00,W0_116) = W0_116 )
      | ~ aNaturalNumber0(W0_116) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_641,plain,
    sdtpldt0(sz00,xr) = xr,
    inference(resolution,[status(thm)],[c_467,c_586]) ).

tff(c_43202,plain,
    sdtpldt0('#skF_18',xr) = xr,
    inference(demodulation,[status(thm),theory(equality)],[c_43130,c_641]) ).

tff(c_44470,plain,
    ! [W0_483,W2_484] :
      ( sdtlseqdt0(W0_483,sdtpldt0(W0_483,W2_484))
      | ~ aNaturalNumber0(W2_484)
      | ~ aNaturalNumber0(sdtpldt0(W0_483,W2_484))
      | ~ aNaturalNumber0(W0_483) ),
    inference(cnfTransformation,[status(thm)],[f_162]) ).

tff(c_44478,plain,
    ( sdtlseqdt0('#skF_18',xr)
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(sdtpldt0('#skF_18',xr))
    | ~ aNaturalNumber0('#skF_18') ),
    inference(superposition,[status(thm),theory(equality)],[c_43202,c_44470]) ).

tff(c_44554,plain,
    sdtlseqdt0('#skF_18',xr),
    inference(demodulation,[status(thm),theory(equality)],[c_513,c_467,c_43202,c_467,c_44478]) ).

tff(c_44556,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_44173,c_44554]) ).

tff(c_44558,plain,
    sz00 != '#skF_18',
    inference(splitRight,[status(thm)],[c_4434]) ).

tff(c_132521,plain,
    ! [W1_1161,W0_1162] :
      ( ( sz00 = W1_1161 )
      | ( sz00 = W0_1162 )
      | ( sdtasdt0(W0_1162,W1_1161) != sz00 )
      | ~ aNaturalNumber0(W1_1161)
      | ~ aNaturalNumber0(W0_1162) ),
    inference(cnfTransformation,[status(thm)],[f_151]) ).

tff(c_132669,plain,
    ( ( sz00 = '#skF_18' )
    | ( xr = sz00 )
    | ( xn != sz00 )
    | ~ aNaturalNumber0('#skF_18')
    | ~ aNaturalNumber0(xr) ),
    inference(superposition,[status(thm),theory(equality)],[c_511,c_132521]) ).

tff(c_132955,plain,
    ( ( sz00 = '#skF_18' )
    | ( xr = sz00 )
    | ( xn != sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_467,c_513,c_132669]) ).

tff(c_132956,plain,
    xn != sz00,
    inference(negUnitSimplification,[status(thm)],[c_459,c_44558,c_132955]) ).

tff(c_136850,plain,
    ! [W0_1206,W1_1207] :
      ( sdtlseqdt0(W0_1206,W1_1207)
      | ( sz00 = W1_1207 )
      | ~ doDivides0(W0_1206,W1_1207)
      | ~ aNaturalNumber0(W1_1207)
      | ~ aNaturalNumber0(W0_1206) ),
    inference(cnfTransformation,[status(thm)],[f_370]) ).

tff(c_515,plain,
    ( ( sdtsldt0(xn,xr) = xn )
    | ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
    inference(cnfTransformation,[status(thm)],[f_636]) ).

tff(c_557,plain,
    ~ sdtlseqdt0(sdtsldt0(xn,xr),xn),
    inference(splitLeft,[status(thm)],[c_515]) ).

tff(c_136870,plain,
    ( ( xn = sz00 )
    | ~ doDivides0(sdtsldt0(xn,xr),xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
    inference(resolution,[status(thm)],[c_136850,c_557]) ).

tff(c_136897,plain,
    ( ( xn = sz00 )
    | ~ doDivides0(sdtsldt0(xn,xr),xn) ),
    inference(demodulation,[status(thm),theory(equality)],[c_537,c_147,c_136870]) ).

tff(c_136898,plain,
    ~ doDivides0(sdtsldt0(xn,xr),xn),
    inference(negUnitSimplification,[status(thm)],[c_132956,c_136897]) ).

tff(c_165005,plain,
    ~ doDivides0('#skF_18',xn),
    inference(demodulation,[status(thm),theory(equality)],[c_164987,c_136898]) ).

tff(c_2732,plain,
    ! [W1_140,W0_141] :
      ( ( sdtasdt0(W1_140,W0_141) = sdtasdt0(W0_141,W1_140) )
      | ~ aNaturalNumber0(W1_140)
      | ~ aNaturalNumber0(W0_141) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_2806,plain,
    ! [W0_141] :
      ( ( sdtasdt0(sdtsldt0(xn,xr),W0_141) = sdtasdt0(W0_141,sdtsldt0(xn,xr)) )
      | ~ aNaturalNumber0(W0_141) ),
    inference(resolution,[status(thm)],[c_537,c_2732]) ).

tff(c_166958,plain,
    ! [W0_1411] :
      ( ( sdtasdt0(W0_1411,'#skF_18') = sdtasdt0('#skF_18',W0_1411) )
      | ~ aNaturalNumber0(W0_1411) ),
    inference(demodulation,[status(thm),theory(equality)],[c_164987,c_164987,c_2806]) ).

tff(c_167042,plain,
    sdtasdt0(xr,'#skF_18') = sdtasdt0('#skF_18',xr),
    inference(resolution,[status(thm)],[c_467,c_166958]) ).

tff(c_167107,plain,
    sdtasdt0('#skF_18',xr) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_511,c_167042]) ).

tff(c_101,plain,
    ! [W0_65,W2_69] :
      ( doDivides0(W0_65,sdtasdt0(W0_65,W2_69))
      | ~ aNaturalNumber0(W2_69)
      | ~ aNaturalNumber0(sdtasdt0(W0_65,W2_69))
      | ~ aNaturalNumber0(W0_65) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_167143,plain,
    ( doDivides0('#skF_18',xn)
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(sdtasdt0('#skF_18',xr))
    | ~ aNaturalNumber0('#skF_18') ),
    inference(superposition,[status(thm),theory(equality)],[c_167107,c_101]) ).

tff(c_167177,plain,
    doDivides0('#skF_18',xn),
    inference(demodulation,[status(thm),theory(equality)],[c_513,c_147,c_167107,c_467,c_167143]) ).

tff(c_167179,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_165005,c_167177]) ).

tff(c_167180,plain,
    sdtsldt0(xn,xr) = xn,
    inference(splitRight,[status(thm)],[c_521]) ).

tff(c_167219,plain,
    ~ sdtlseqdt0(xn,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_167180,c_557]) ).

tff(c_167222,plain,
    ~ aNaturalNumber0(xn),
    inference(resolution,[status(thm)],[c_72,c_167219]) ).

tff(c_167226,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_167222]) ).

tff(c_167227,plain,
    sdtsldt0(xn,xr) = xn,
    inference(splitRight,[status(thm)],[c_515]) ).

tff(c_167229,plain,
    ! [W0_114] :
      ( ( sdtpldt0(sdtsldt0(xn,xr),W0_114) != xn )
      | ~ aNaturalNumber0(W0_114) ),
    inference(splitLeft,[status(thm)],[c_521]) ).

tff(c_167416,plain,
    ! [W0_1416] :
      ( ( sdtpldt0(xn,W0_1416) != xn )
      | ~ aNaturalNumber0(W0_1416) ),
    inference(demodulation,[status(thm),theory(equality)],[c_167227,c_167229]) ).

tff(c_167478,plain,
    sdtpldt0(xn,sz00) != xn,
    inference(resolution,[status(thm)],[c_4,c_167416]) ).

tff(c_167714,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_167395,c_167478]) ).

tff(c_167715,plain,
    sdtsldt0(xn,xr) = xn,
    inference(splitRight,[status(thm)],[c_521]) ).

tff(c_167716,plain,
    sdtasdt0(xr,xn) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_167715,c_529]) ).

tff(c_169957,plain,
    ! [W1_1454,W0_1455] :
      ( sdtlseqdt0(W1_1454,sdtasdt0(W1_1454,W0_1455))
      | ( sz00 = W0_1455 )
      | ~ aNaturalNumber0(W1_1454)
      | ~ aNaturalNumber0(W0_1455) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_170161,plain,
    ( sdtlseqdt0(xr,xn)
    | ( xn = sz00 )
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_167716,c_169957]) ).

tff(c_170336,plain,
    ( sdtlseqdt0(xr,xn)
    | ( xn = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_467,c_170161]) ).

tff(c_170337,plain,
    xn = sz00,
    inference(splitLeft,[status(thm)],[c_170336]) ).

tff(c_475,plain,
    sdtasdt0(xr,'#skF_13') = sdtasdt0(xn,xm),
    inference(cnfTransformation,[status(thm)],[f_590]) ).

tff(c_170365,plain,
    sdtasdt0(xr,'#skF_13') = sdtasdt0(sz00,xm),
    inference(demodulation,[status(thm),theory(equality)],[c_170337,c_475]) ).

tff(c_170391,plain,
    sdtasdt0(xr,'#skF_13') = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_168076,c_170365]) ).

tff(c_50,plain,
    ! [W1_33,W0_32] :
      ( ( sz00 = W1_33 )
      | ( sz00 = W0_32 )
      | ( sdtasdt0(W0_32,W1_33) != sz00 )
      | ~ aNaturalNumber0(W1_33)
      | ~ aNaturalNumber0(W0_32) ),
    inference(cnfTransformation,[status(thm)],[f_151]) ).

tff(c_176856,plain,
    ( ( sz00 = '#skF_13' )
    | ( xr = sz00 )
    | ~ aNaturalNumber0('#skF_13')
    | ~ aNaturalNumber0(xr) ),
    inference(superposition,[status(thm),theory(equality)],[c_170391,c_50]) ).

tff(c_176890,plain,
    ( ( sz00 = '#skF_13' )
    | ( xr = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_467,c_477,c_176856]) ).

tff(c_176891,plain,
    sz00 = '#skF_13',
    inference(negUnitSimplification,[status(thm)],[c_459,c_176890]) ).

tff(c_437,plain,
    aNaturalNumber0('#skF_11'),
    inference(cnfTransformation,[status(thm)],[f_535]) ).

tff(c_167935,plain,
    ! [W0_1422] :
      ( ( sdtpldt0(sz00,W0_1422) = W0_1422 )
      | ~ aNaturalNumber0(W0_1422) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_167994,plain,
    sdtpldt0(sz00,'#skF_11') = '#skF_11',
    inference(resolution,[status(thm)],[c_437,c_167935]) ).

tff(c_435,plain,
    sdtpldt0(xn,'#skF_11') = xp,
    inference(cnfTransformation,[status(thm)],[f_535]) ).

tff(c_170370,plain,
    sdtpldt0(sz00,'#skF_11') = xp,
    inference(demodulation,[status(thm),theory(equality)],[c_170337,c_435]) ).

tff(c_170395,plain,
    xp = '#skF_11',
    inference(demodulation,[status(thm),theory(equality)],[c_167994,c_170370]) ).

tff(c_411,plain,
    xp != sz00,
    inference(cnfTransformation,[status(thm)],[f_502]) ).

tff(c_170432,plain,
    sz00 != '#skF_11',
    inference(demodulation,[status(thm),theory(equality)],[c_170395,c_411]) ).

tff(c_177575,plain,
    '#skF_11' != '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_176891,c_170432]) ).

tff(c_403,plain,
    sdtasdt0(xp,'#skF_9') = sdtasdt0(xn,xm),
    inference(cnfTransformation,[status(thm)],[f_502]) ).

tff(c_170357,plain,
    sdtasdt0(xp,'#skF_9') = sdtasdt0(sz00,xm),
    inference(demodulation,[status(thm),theory(equality)],[c_170337,c_403]) ).

tff(c_170387,plain,
    sdtasdt0(xp,'#skF_9') = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_168076,c_170357]) ).

tff(c_180489,plain,
    sdtasdt0('#skF_11','#skF_9') = '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_176891,c_170395,c_170387]) ).

tff(c_401,plain,
    doDivides0(xp,sdtasdt0(xn,xm)),
    inference(cnfTransformation,[status(thm)],[f_502]) ).

tff(c_170367,plain,
    doDivides0(xp,sdtasdt0(sz00,xm)),
    inference(demodulation,[status(thm),theory(equality)],[c_170337,c_401]) ).

tff(c_170393,plain,
    doDivides0(xp,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_168076,c_170367]) ).

tff(c_170487,plain,
    doDivides0('#skF_11',sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_170395,c_170393]) ).

tff(c_177569,plain,
    doDivides0('#skF_11','#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_176891,c_170487]) ).

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_170366,plain,
    sdtsldt0(sdtasdt0(sz00,xm),xp) = xk,
    inference(demodulation,[status(thm),theory(equality)],[c_170337,c_441]) ).

tff(c_170392,plain,
    sdtsldt0(sz00,xp) = xk,
    inference(demodulation,[status(thm),theory(equality)],[c_168076,c_170366]) ).

tff(c_180355,plain,
    sdtsldt0('#skF_13','#skF_11') = xk,
    inference(demodulation,[status(thm),theory(equality)],[c_176891,c_170395,c_170392]) ).

tff(c_107,plain,
    ! [W0_70,W2_73] :
      ( ( sdtsldt0(sdtasdt0(W0_70,W2_73),W0_70) = W2_73 )
      | ~ aNaturalNumber0(W2_73)
      | ~ doDivides0(W0_70,sdtasdt0(W0_70,W2_73))
      | ( sz00 = W0_70 )
      | ~ aNaturalNumber0(sdtasdt0(W0_70,W2_73))
      | ~ aNaturalNumber0(W0_70) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_178713,plain,
    ! [W0_70,W2_73] :
      ( ( sdtsldt0(sdtasdt0(W0_70,W2_73),W0_70) = W2_73 )
      | ~ aNaturalNumber0(W2_73)
      | ~ doDivides0(W0_70,sdtasdt0(W0_70,W2_73))
      | ( W0_70 = '#skF_13' )
      | ~ aNaturalNumber0(sdtasdt0(W0_70,W2_73))
      | ~ aNaturalNumber0(W0_70) ),
    inference(demodulation,[status(thm),theory(equality)],[c_176891,c_107]) ).

tff(c_180505,plain,
    ( ( sdtsldt0(sdtasdt0('#skF_11','#skF_9'),'#skF_11') = '#skF_9' )
    | ~ aNaturalNumber0('#skF_9')
    | ~ doDivides0('#skF_11','#skF_13')
    | ( '#skF_11' = '#skF_13' )
    | ~ aNaturalNumber0(sdtasdt0('#skF_11','#skF_9'))
    | ~ aNaturalNumber0('#skF_11') ),
    inference(superposition,[status(thm),theory(equality)],[c_180489,c_178713]) ).

tff(c_180561,plain,
    ( ( xk = '#skF_9' )
    | ( '#skF_11' = '#skF_13' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_437,c_477,c_180489,c_177569,c_405,c_180355,c_180489,c_180505]) ).

tff(c_180562,plain,
    xk = '#skF_9',
    inference(negUnitSimplification,[status(thm)],[c_177575,c_180561]) ).

tff(c_453,plain,
    xk != sz00,
    inference(cnfTransformation,[status(thm)],[f_549]) ).

tff(c_177647,plain,
    xk != '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_176891,c_453]) ).

tff(c_180606,plain,
    '#skF_13' != '#skF_9',
    inference(demodulation,[status(thm),theory(equality)],[c_180562,c_177647]) ).

tff(c_168319,plain,
    ! [W0_1426] :
      ( ( sdtasdt0(W0_1426,sz00) = sz00 )
      | ~ aNaturalNumber0(W0_1426) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_168379,plain,
    sdtasdt0('#skF_11',sz00) = sz00,
    inference(resolution,[status(thm)],[c_437,c_168319]) ).

tff(c_177612,plain,
    sdtasdt0('#skF_11','#skF_13') = '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_176891,c_176891,c_168379]) ).

tff(c_186333,plain,
    ( ( sdtsldt0(sdtasdt0('#skF_11','#skF_13'),'#skF_11') = '#skF_13' )
    | ~ aNaturalNumber0('#skF_13')
    | ~ doDivides0('#skF_11','#skF_13')
    | ( '#skF_11' = '#skF_13' )
    | ~ aNaturalNumber0(sdtasdt0('#skF_11','#skF_13'))
    | ~ aNaturalNumber0('#skF_11') ),
    inference(superposition,[status(thm),theory(equality)],[c_177612,c_178713]) ).

tff(c_186409,plain,
    ( ( sdtsldt0('#skF_13','#skF_11') = '#skF_13' )
    | ( '#skF_11' = '#skF_13' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_437,c_477,c_177612,c_177569,c_477,c_177612,c_186333]) ).

tff(c_186410,plain,
    sdtsldt0('#skF_13','#skF_11') = '#skF_13',
    inference(negUnitSimplification,[status(thm)],[c_177575,c_186409]) ).

tff(c_443,plain,
    sdtasdt0(xp,xk) = sdtasdt0(xn,xm),
    inference(cnfTransformation,[status(thm)],[f_540]) ).

tff(c_170363,plain,
    sdtasdt0(xp,xk) = sdtasdt0(sz00,xm),
    inference(demodulation,[status(thm),theory(equality)],[c_170337,c_443]) ).

tff(c_170389,plain,
    sdtasdt0(xp,xk) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_168076,c_170363]) ).

tff(c_180032,plain,
    sdtasdt0('#skF_11',xk) = '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_176891,c_170395,c_170389]) ).

tff(c_445,plain,
    aNaturalNumber0(xk),
    inference(cnfTransformation,[status(thm)],[f_540]) ).

tff(c_180044,plain,
    ( ( sdtsldt0(sdtasdt0('#skF_11',xk),'#skF_11') = xk )
    | ~ aNaturalNumber0(xk)
    | ~ doDivides0('#skF_11','#skF_13')
    | ( '#skF_11' = '#skF_13' )
    | ~ aNaturalNumber0(sdtasdt0('#skF_11',xk))
    | ~ aNaturalNumber0('#skF_11') ),
    inference(superposition,[status(thm),theory(equality)],[c_180032,c_178713]) ).

tff(c_180096,plain,
    ( ( sdtsldt0('#skF_13','#skF_11') = xk )
    | ( '#skF_11' = '#skF_13' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_437,c_477,c_180032,c_177569,c_445,c_180032,c_180044]) ).

tff(c_180097,plain,
    sdtsldt0('#skF_13','#skF_11') = xk,
    inference(negUnitSimplification,[status(thm)],[c_177575,c_180096]) ).

tff(c_190885,plain,
    '#skF_13' = '#skF_9',
    inference(demodulation,[status(thm),theory(equality)],[c_186410,c_180562,c_180097]) ).

tff(c_190886,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_180606,c_190885]) ).

tff(c_190888,plain,
    xn != sz00,
    inference(splitRight,[status(thm)],[c_170336]) ).

tff(c_234305,plain,
    ! [W2_2113,W0_2114,W1_2115] :
      ( ( sdtasdt0(W2_2113,W0_2114) != sdtasdt0(W1_2115,W0_2114) )
      | ( W2_2113 = W1_2115 )
      | ~ aNaturalNumber0(W2_2113)
      | ~ aNaturalNumber0(W1_2115)
      | ( sz00 = W0_2114 )
      | ~ aNaturalNumber0(W0_2114) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_234591,plain,
    ! [W1_2115] :
      ( ( sdtasdt0(W1_2115,xn) != xn )
      | ( xr = W1_2115 )
      | ~ aNaturalNumber0(xr)
      | ~ aNaturalNumber0(W1_2115)
      | ( xn = sz00 )
      | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_167716,c_234305]) ).

tff(c_234977,plain,
    ! [W1_2115] :
      ( ( sdtasdt0(W1_2115,xn) != xn )
      | ( xr = W1_2115 )
      | ~ aNaturalNumber0(W1_2115)
      | ( xn = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_467,c_234591]) ).

tff(c_235001,plain,
    ! [W1_2116] :
      ( ( sdtasdt0(W1_2116,xn) != xn )
      | ( xr = W1_2116 )
      | ~ aNaturalNumber0(W1_2116) ),
    inference(negUnitSimplification,[status(thm)],[c_190888,c_234977]) ).

tff(c_235052,plain,
    ( ( sdtasdt0(sz10,xn) != xn )
    | ( xr = sz10 ) ),
    inference(resolution,[status(thm)],[c_8,c_235001]) ).

tff(c_235098,plain,
    xr = sz10,
    inference(demodulation,[status(thm),theory(equality)],[c_167915,c_235052]) ).

tff(c_235100,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_457,c_235098]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : NUM510+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35  % Computer : n012.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 14:56:52 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 66.16/47.95  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.16/47.98  
% 66.16/47.98  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 66.16/48.03  
% 66.16/48.03  Inference rules
% 66.16/48.03  ----------------------
% 66.16/48.03  #Ref     : 109
% 66.16/48.03  #Sup     : 49189
% 66.16/48.03  #Fact    : 4
% 66.16/48.03  #Define  : 0
% 66.16/48.03  #Split   : 129
% 66.16/48.03  #Chain   : 0
% 66.16/48.03  #Close   : 0
% 66.16/48.03  
% 66.16/48.03  Ordering : KBO
% 66.16/48.03  
% 66.16/48.03  Simplification rules
% 66.16/48.03  ----------------------
% 66.16/48.03  #Subsume      : 3144
% 66.16/48.03  #Demod        : 99181
% 66.16/48.03  #Tautology    : 14297
% 66.16/48.03  #SimpNegUnit  : 8467
% 66.16/48.03  #BackRed      : 4898
% 66.16/48.03  
% 66.16/48.03  #Partial instantiations: 0
% 66.16/48.03  #Strategies tried      : 1
% 66.16/48.03  
% 66.16/48.03  Timing (in seconds)
% 66.16/48.03  ----------------------
% 66.16/48.03  Preprocessing        : 0.92
% 66.16/48.03  Parsing              : 0.38
% 66.16/48.03  CNF conversion       : 0.10
% 66.16/48.03  Main loop            : 46.00
% 66.16/48.03  Inferencing          : 6.18
% 66.16/48.03  Reduction            : 28.57
% 66.16/48.03  Demodulation         : 24.55
% 66.16/48.03  BG Simplification    : 0.42
% 66.16/48.04  Subsumption          : 8.57
% 66.16/48.04  Abstraction          : 0.59
% 66.16/48.04  MUC search           : 0.00
% 66.16/48.04  Cooper               : 0.00
% 66.16/48.04  Total                : 47.02
% 66.16/48.04  Index Insertion      : 0.00
% 66.16/48.04  Index Deletion       : 0.00
% 66.16/48.04  Index Matching       : 0.00
% 66.16/48.04  BG Taut test         : 0.00
%------------------------------------------------------------------------------