TSTP Solution File: NUM483+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------