TSTP Solution File: NUM496+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM496+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 10:51:53 EDT 2023

% Result   : Theorem 179.46s 152.81s
% Output   : CNFRefutation 179.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   46
% Syntax   : Number of formulae    :  145 (  55 unt;  29 typ;   2 def)
%            Number of atoms       :  281 ( 106 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  286 ( 121   ~; 117   |;  30   &)
%                                         (   2 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   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    :   24 (  24 usr;  12 con; 0-3 aty)
%            Number of variables   :   72 (;  65   !;   7   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_11 > #skF_6 > #skF_10 > #skF_14 > #skF_13 > #skF_5 > #skF_9 > #skF_7 > #skF_3 > #skF_2 > #skF_8 > #skF_1 > #skF_12

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(xr,type,
    xr: $i ).

tff(sdtasdt0,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff('#skF_4',type,
    '#skF_4': $i > $i ).

tff('#skF_11',type,
    '#skF_11': $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i * $i ) > $i ).

tff(sz10,type,
    sz10: $i ).

tff(sdtmndt0,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff(sdtlseqdt0,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(sz00,type,
    sz00: $i ).

tff('#skF_10',type,
    '#skF_10': $i ).

tff(sdtpldt0,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(isPrime0,type,
    isPrime0: $i > $o ).

tff('#skF_14',type,
    '#skF_14': $i ).

tff(aNaturalNumber0,type,
    aNaturalNumber0: $i > $o ).

tff('#skF_13',type,
    '#skF_13': $i ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i * $i ) > $i ).

tff(doDivides0,type,
    doDivides0: ( $i * $i ) > $o ).

tff('#skF_9',type,
    '#skF_9': $i ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i * $i ) > $i ).

tff('#skF_3',type,
    '#skF_3': $i > $i ).

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

tff(xp,type,
    xp: $i ).

tff(iLess0,type,
    iLess0: ( $i * $i ) > $o ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i * $i ) > $i ).

tff(xm,type,
    xm: $i ).

tff(sdtsldt0,type,
    sdtsldt0: ( $i * $i ) > $i ).

tff(xn,type,
    xn: $i ).

tff('#skF_1',type,
    '#skF_1': ( $i * $i ) > $i ).

tff('#skF_12',type,
    '#skF_12': $i ).

tff(f_522,hypothesis,
    ( ( xr != xn )
    & ? [W0] :
        ( aNaturalNumber0(W0)
        & ( sdtpldt0(xr,W0) = xn ) )
    & sdtlseqdt0(xr,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1894) ).

tff(f_555,negated_conjecture,
    ~ ( ? [W0] :
          ( aNaturalNumber0(W0)
          & ( xn = sdtasdt0(xp,W0) ) )
      | doDivides0(xp,xn)
      | ? [W0] :
          ( aNaturalNumber0(W0)
          & ( xm = sdtasdt0(xp,W0) ) )
      | doDivides0(xp,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_541,hypothesis,
    ( ( ? [W0] :
          ( aNaturalNumber0(W0)
          & ( xr = sdtasdt0(xp,W0) ) )
      & doDivides0(xp,xr) )
    | ( ? [W0] :
          ( aNaturalNumber0(W0)
          & ( xm = sdtasdt0(xp,W0) ) )
      & doDivides0(xp,xm) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2027) ).

tff(f_73,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).

tff(f_423,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).

tff(f_508,hypothesis,
    ( ? [W0] :
        ( aNaturalNumber0(W0)
        & ( sdtpldt0(xp,W0) = xn ) )
    & sdtlseqdt0(xp,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).

tff(f_513,hypothesis,
    ( aNaturalNumber0(xr)
    & ( sdtpldt0(xp,xr) = xn )
    & ( xr = sdtmndt0(xn,xp) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).

tff(f_175,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtlseqdt0(W0,W1)
       => ! [W2] :
            ( ( W2 = sdtmndt0(W1,W0) )
          <=> ( aNaturalNumber0(W2)
              & ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).

tff(f_278,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( W0 != sz00 )
       => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).

tff(f_67,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( sdtpldt0(W0,sz00) = W0 )
        & ( W0 = sdtpldt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).

tff(f_93,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( sdtasdt0(W0,sz00) = sz00 )
        & ( sz00 = sdtasdt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).

tff(f_87,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( sdtasdt0(W0,sz10) = W0 )
        & ( W0 = sdtasdt0(sz10,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).

tff(f_35,axiom,
    ( aNaturalNumber0(sz10)
    & ( sz10 != sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).

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/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).

tff(f_53,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

tff(f_307,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( doDivides0(W0,W1)
      <=> ? [W2] :
            ( aNaturalNumber0(W2)
            & ( W1 = sdtasdt0(W0,W2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).

tff(f_347,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( ( doDivides0(W0,W1)
          & doDivides0(W0,W2) )
       => doDivides0(W0,sdtpldt0(W1,W2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivSum) ).

tff(c_433,plain,
    aNaturalNumber0('#skF_11'),
    inference(cnfTransformation,[status(thm)],[f_522]) ).

tff(c_461,plain,
    ~ doDivides0(xp,xm),
    inference(cnfTransformation,[status(thm)],[f_555]) ).

tff(c_447,plain,
    ( aNaturalNumber0('#skF_13')
    | doDivides0(xp,xm) ),
    inference(cnfTransformation,[status(thm)],[f_541]) ).

tff(c_468,plain,
    aNaturalNumber0('#skF_13'),
    inference(negUnitSimplification,[status(thm)],[c_461,c_447]) ).

tff(c_3517,plain,
    ! [W1_145,W0_146] :
      ( ( sdtasdt0(W1_145,W0_146) = sdtasdt0(W0_146,W1_145) )
      | ~ aNaturalNumber0(W1_145)
      | ~ aNaturalNumber0(W0_146) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_83849,plain,
    ! [W0_807] :
      ( ( sdtasdt0(W0_807,'#skF_13') = sdtasdt0('#skF_13',W0_807) )
      | ~ aNaturalNumber0(W0_807) ),
    inference(resolution,[status(thm)],[c_468,c_3517]) ).

tff(c_83958,plain,
    sdtasdt0('#skF_11','#skF_13') = sdtasdt0('#skF_13','#skF_11'),
    inference(resolution,[status(thm)],[c_433,c_83849]) ).

tff(c_143,plain,
    aNaturalNumber0(xp),
    inference(cnfTransformation,[status(thm)],[f_423]) ).

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

tff(c_419,plain,
    sdtpldt0(xp,'#skF_10') = xn,
    inference(cnfTransformation,[status(thm)],[f_508]) ).

tff(c_417,plain,
    sdtlseqdt0(xp,xn),
    inference(cnfTransformation,[status(thm)],[f_508]) ).

tff(c_421,plain,
    aNaturalNumber0('#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_508]) ).

tff(c_423,plain,
    sdtmndt0(xn,xp) = xr,
    inference(cnfTransformation,[status(thm)],[f_513]) ).

tff(c_115558,plain,
    ! [W0_1054,W2_1055] :
      ( ( sdtmndt0(sdtpldt0(W0_1054,W2_1055),W0_1054) = W2_1055 )
      | ~ aNaturalNumber0(W2_1055)
      | ~ sdtlseqdt0(W0_1054,sdtpldt0(W0_1054,W2_1055))
      | ~ aNaturalNumber0(sdtpldt0(W0_1054,W2_1055))
      | ~ aNaturalNumber0(W0_1054) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_115712,plain,
    ( ( sdtmndt0(sdtpldt0(xp,'#skF_10'),xp) = '#skF_10' )
    | ~ aNaturalNumber0('#skF_10')
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(sdtpldt0(xp,'#skF_10'))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_419,c_115558]) ).

tff(c_115801,plain,
    xr = '#skF_10',
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_419,c_417,c_421,c_423,c_419,c_115712]) ).

tff(c_445,plain,
    ( ( sdtasdt0(xp,'#skF_13') = xr )
    | doDivides0(xp,xm) ),
    inference(cnfTransformation,[status(thm)],[f_541]) ).

tff(c_471,plain,
    sdtasdt0(xp,'#skF_13') = xr,
    inference(negUnitSimplification,[status(thm)],[c_461,c_445]) ).

tff(c_3954,plain,
    ! [W1_153,W0_154] :
      ( sdtlseqdt0(W1_153,sdtasdt0(W1_153,W0_154))
      | ( sz00 = W0_154 )
      | ~ aNaturalNumber0(W1_153)
      | ~ aNaturalNumber0(W0_154) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_4143,plain,
    ( sdtlseqdt0(xp,xr)
    | ( sz00 = '#skF_13' )
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0('#skF_13') ),
    inference(superposition,[status(thm),theory(equality)],[c_471,c_3954]) ).

tff(c_4314,plain,
    ( sdtlseqdt0(xp,xr)
    | ( sz00 = '#skF_13' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_468,c_143,c_4143]) ).

tff(c_4426,plain,
    sz00 = '#skF_13',
    inference(splitLeft,[status(thm)],[c_4314]) ).

tff(c_909,plain,
    ! [W0_118] :
      ( ( sdtpldt0(sz00,W0_118) = W0_118 )
      | ~ aNaturalNumber0(W0_118) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_945,plain,
    sdtpldt0(sz00,'#skF_11') = '#skF_11',
    inference(resolution,[status(thm)],[c_433,c_909]) ).

tff(c_4473,plain,
    sdtpldt0('#skF_13','#skF_11') = '#skF_11',
    inference(demodulation,[status(thm),theory(equality)],[c_4426,c_945]) ).

tff(c_640,plain,
    ! [W0_115] :
      ( ( sdtasdt0(W0_115,sz00) = sz00 )
      | ~ aNaturalNumber0(W0_115) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_679,plain,
    sdtasdt0(xp,sz00) = sz00,
    inference(resolution,[status(thm)],[c_143,c_640]) ).

tff(c_4505,plain,
    sdtasdt0(xp,'#skF_13') = '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_4426,c_4426,c_679]) ).

tff(c_5173,plain,
    xr = '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_4505,c_471]) ).

tff(c_431,plain,
    sdtpldt0(xr,'#skF_11') = xn,
    inference(cnfTransformation,[status(thm)],[f_522]) ).

tff(c_5313,plain,
    sdtpldt0('#skF_13','#skF_11') = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_5173,c_431]) ).

tff(c_5328,plain,
    xn = '#skF_11',
    inference(demodulation,[status(thm),theory(equality)],[c_4473,c_5313]) ).

tff(c_990,plain,
    ! [W0_119] :
      ( ( sdtasdt0(W0_119,sz10) = W0_119 )
      | ~ aNaturalNumber0(W0_119) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_1030,plain,
    sdtasdt0(xp,sz10) = xp,
    inference(resolution,[status(thm)],[c_143,c_990]) ).

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

tff(c_502,plain,
    ! [W0_111] :
      ( ( sdtasdt0(xp,W0_111) != xn )
      | ~ aNaturalNumber0(W0_111) ),
    inference(cnfTransformation,[status(thm)],[f_555]) ).

tff(c_537,plain,
    sdtasdt0(xp,sz10) != xn,
    inference(resolution,[status(thm)],[c_8,c_502]) ).

tff(c_1069,plain,
    xp != xn,
    inference(demodulation,[status(thm),theory(equality)],[c_1030,c_537]) ).

tff(c_5364,plain,
    xp != '#skF_11',
    inference(demodulation,[status(thm),theory(equality)],[c_5328,c_1069]) ).

tff(c_5379,plain,
    sdtlseqdt0(xp,'#skF_11'),
    inference(demodulation,[status(thm),theory(equality)],[c_5328,c_417]) ).

tff(c_765,plain,
    ! [W0_116] :
      ( ( sdtpldt0(W0_116,sz00) = W0_116 )
      | ~ aNaturalNumber0(W0_116) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_804,plain,
    sdtpldt0(xp,sz00) = xp,
    inference(resolution,[status(thm)],[c_143,c_765]) ).

tff(c_4476,plain,
    sdtpldt0(xp,'#skF_13') = xp,
    inference(demodulation,[status(thm),theory(equality)],[c_4426,c_804]) ).

tff(c_5314,plain,
    sdtmndt0(xn,xp) = '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_5173,c_423]) ).

tff(c_6933,plain,
    sdtmndt0('#skF_11',xp) = '#skF_13',
    inference(demodulation,[status(thm),theory(equality)],[c_5328,c_5314]) ).

tff(c_60,plain,
    ! [W0_39,W1_40] :
      ( ( sdtpldt0(W0_39,sdtmndt0(W1_40,W0_39)) = W1_40 )
      | ~ sdtlseqdt0(W0_39,W1_40)
      | ~ aNaturalNumber0(W1_40)
      | ~ aNaturalNumber0(W0_39) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_6940,plain,
    ( ( sdtpldt0(xp,'#skF_13') = '#skF_11' )
    | ~ sdtlseqdt0(xp,'#skF_11')
    | ~ aNaturalNumber0('#skF_11')
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_6933,c_60]) ).

tff(c_6949,plain,
    xp = '#skF_11',
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_433,c_5379,c_4476,c_6940]) ).

tff(c_6951,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5364,c_6949]) ).

tff(c_6953,plain,
    sz00 != '#skF_13',
    inference(splitRight,[status(thm)],[c_4314]) ).

tff(c_110952,plain,
    ! [W2_1033,W0_1034,W1_1035] :
      ( ( sdtasdt0(W2_1033,W0_1034) != sdtasdt0(W1_1035,W0_1034) )
      | ( W2_1033 = W1_1035 )
      | ~ aNaturalNumber0(W2_1033)
      | ~ aNaturalNumber0(W1_1035)
      | ( sz00 = W0_1034 )
      | ~ aNaturalNumber0(W0_1034) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_111218,plain,
    ! [W1_1035] :
      ( ( sdtasdt0(W1_1035,'#skF_13') != xr )
      | ( xp = W1_1035 )
      | ~ aNaturalNumber0(xp)
      | ~ aNaturalNumber0(W1_1035)
      | ( sz00 = '#skF_13' )
      | ~ aNaturalNumber0('#skF_13') ),
    inference(superposition,[status(thm),theory(equality)],[c_471,c_110952]) ).

tff(c_111600,plain,
    ! [W1_1035] :
      ( ( sdtasdt0(W1_1035,'#skF_13') != xr )
      | ( xp = W1_1035 )
      | ~ aNaturalNumber0(W1_1035)
      | ( sz00 = '#skF_13' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_468,c_143,c_111218]) ).

tff(c_111601,plain,
    ! [W1_1035] :
      ( ( sdtasdt0(W1_1035,'#skF_13') != xr )
      | ( xp = W1_1035 )
      | ~ aNaturalNumber0(W1_1035) ),
    inference(negUnitSimplification,[status(thm)],[c_6953,c_111600]) ).

tff(c_167623,plain,
    ! [W1_1341] :
      ( ( sdtasdt0(W1_1341,'#skF_13') != '#skF_10' )
      | ( xp = W1_1341 )
      | ~ aNaturalNumber0(W1_1341) ),
    inference(demodulation,[status(thm),theory(equality)],[c_115801,c_111601]) ).

tff(c_167743,plain,
    ( ( sdtasdt0('#skF_11','#skF_13') != '#skF_10' )
    | ( xp = '#skF_11' ) ),
    inference(resolution,[status(thm)],[c_433,c_167623]) ).

tff(c_167822,plain,
    ( ( sdtasdt0('#skF_13','#skF_11') != '#skF_10' )
    | ( xp = '#skF_11' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_83958,c_167743]) ).

tff(c_168870,plain,
    sdtasdt0('#skF_13','#skF_11') != '#skF_10',
    inference(splitLeft,[status(thm)],[c_167822]) ).

tff(c_427,plain,
    aNaturalNumber0(xr),
    inference(cnfTransformation,[status(thm)],[f_513]) ).

tff(c_2531,plain,
    ! [W1_136,W0_137] :
      ( ( sdtpldt0(W1_136,W0_137) = sdtpldt0(W0_137,W1_136) )
      | ~ aNaturalNumber0(W1_136)
      | ~ aNaturalNumber0(W0_137) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_2573,plain,
    ! [W0_137] :
      ( ( sdtpldt0(xr,W0_137) = sdtpldt0(W0_137,xr) )
      | ~ aNaturalNumber0(W0_137) ),
    inference(resolution,[status(thm)],[c_427,c_2531]) ).

tff(c_221044,plain,
    ! [W0_1497] :
      ( ( sdtpldt0(W0_1497,'#skF_10') = sdtpldt0('#skF_10',W0_1497) )
      | ~ aNaturalNumber0(W0_1497) ),
    inference(demodulation,[status(thm),theory(equality)],[c_115801,c_115801,c_2573]) ).

tff(c_221206,plain,
    sdtpldt0(xp,'#skF_10') = sdtpldt0('#skF_10',xp),
    inference(resolution,[status(thm)],[c_143,c_221044]) ).

tff(c_221279,plain,
    sdtpldt0('#skF_10',xp) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_419,c_221206]) ).

tff(c_429,plain,
    sdtlseqdt0(xr,xn),
    inference(cnfTransformation,[status(thm)],[f_522]) ).

tff(c_115868,plain,
    sdtlseqdt0('#skF_10',xn),
    inference(demodulation,[status(thm),theory(equality)],[c_115801,c_429]) ).

tff(c_115709,plain,
    ( ( sdtmndt0(sdtpldt0(xr,'#skF_11'),xr) = '#skF_11' )
    | ~ aNaturalNumber0('#skF_11')
    | ~ sdtlseqdt0(xr,xn)
    | ~ aNaturalNumber0(sdtpldt0(xr,'#skF_11'))
    | ~ aNaturalNumber0(xr) ),
    inference(superposition,[status(thm),theory(equality)],[c_431,c_115558]) ).

tff(c_115799,plain,
    sdtmndt0(xn,xr) = '#skF_11',
    inference(demodulation,[status(thm),theory(equality)],[c_427,c_147,c_431,c_429,c_433,c_431,c_115709]) ).

tff(c_118451,plain,
    sdtmndt0(xn,'#skF_10') = '#skF_11',
    inference(demodulation,[status(thm),theory(equality)],[c_115801,c_115799]) ).

tff(c_58,plain,
    ! [W0_39,W2_42] :
      ( ( sdtmndt0(sdtpldt0(W0_39,W2_42),W0_39) = W2_42 )
      | ~ aNaturalNumber0(W2_42)
      | ~ sdtlseqdt0(W0_39,sdtpldt0(W0_39,W2_42))
      | ~ aNaturalNumber0(sdtpldt0(W0_39,W2_42))
      | ~ aNaturalNumber0(W0_39) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_221444,plain,
    ( ( sdtmndt0(sdtpldt0('#skF_10',xp),'#skF_10') = xp )
    | ~ aNaturalNumber0(xp)
    | ~ sdtlseqdt0('#skF_10',xn)
    | ~ aNaturalNumber0(sdtpldt0('#skF_10',xp))
    | ~ aNaturalNumber0('#skF_10') ),
    inference(superposition,[status(thm),theory(equality)],[c_221279,c_58]) ).

tff(c_221621,plain,
    xp = '#skF_11',
    inference(demodulation,[status(thm),theory(equality)],[c_421,c_147,c_221279,c_115868,c_143,c_118451,c_221279,c_221444]) ).

tff(c_83921,plain,
    sdtasdt0(xp,'#skF_13') = sdtasdt0('#skF_13',xp),
    inference(resolution,[status(thm)],[c_143,c_83849]) ).

tff(c_83963,plain,
    sdtasdt0('#skF_13',xp) = xr,
    inference(demodulation,[status(thm),theory(equality)],[c_471,c_83921]) ).

tff(c_115821,plain,
    sdtasdt0('#skF_13',xp) = '#skF_10',
    inference(demodulation,[status(thm),theory(equality)],[c_115801,c_83963]) ).

tff(c_222008,plain,
    sdtasdt0('#skF_13','#skF_11') = '#skF_10',
    inference(demodulation,[status(thm),theory(equality)],[c_221621,c_115821]) ).

tff(c_222141,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_168870,c_222008]) ).

tff(c_222142,plain,
    xp = '#skF_11',
    inference(splitRight,[status(thm)],[c_167822]) ).

tff(c_443,plain,
    ( doDivides0(xp,xr)
    | doDivides0(xp,xm) ),
    inference(cnfTransformation,[status(thm)],[f_541]) ).

tff(c_474,plain,
    doDivides0(xp,xr),
    inference(negUnitSimplification,[status(thm)],[c_461,c_443]) ).

tff(c_115869,plain,
    doDivides0(xp,'#skF_10'),
    inference(demodulation,[status(thm),theory(equality)],[c_115801,c_474]) ).

tff(c_222380,plain,
    doDivides0('#skF_11','#skF_10'),
    inference(demodulation,[status(thm),theory(equality)],[c_222142,c_115869]) ).

tff(c_1026,plain,
    sdtasdt0('#skF_11',sz10) = '#skF_11',
    inference(resolution,[status(thm)],[c_433,c_990]) ).

tff(c_83533,plain,
    ! [W0_805,W2_806] :
      ( doDivides0(W0_805,sdtasdt0(W0_805,W2_806))
      | ~ aNaturalNumber0(W2_806)
      | ~ aNaturalNumber0(sdtasdt0(W0_805,W2_806))
      | ~ aNaturalNumber0(W0_805) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_83611,plain,
    ( doDivides0('#skF_11','#skF_11')
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(sdtasdt0('#skF_11',sz10))
    | ~ aNaturalNumber0('#skF_11') ),
    inference(superposition,[status(thm),theory(equality)],[c_1026,c_83533]) ).

tff(c_83774,plain,
    doDivides0('#skF_11','#skF_11'),
    inference(demodulation,[status(thm),theory(equality)],[c_433,c_433,c_1026,c_8,c_83611]) ).

tff(c_111671,plain,
    ! [W0_1036,W1_1037,W2_1038] :
      ( doDivides0(W0_1036,sdtpldt0(W1_1037,W2_1038))
      | ~ doDivides0(W0_1036,W2_1038)
      | ~ doDivides0(W0_1036,W1_1037)
      | ~ aNaturalNumber0(W2_1038)
      | ~ aNaturalNumber0(W1_1037)
      | ~ aNaturalNumber0(W0_1036) ),
    inference(cnfTransformation,[status(thm)],[f_347]) ).

tff(c_111799,plain,
    ! [W0_1036] :
      ( doDivides0(W0_1036,xn)
      | ~ doDivides0(W0_1036,'#skF_11')
      | ~ doDivides0(W0_1036,xr)
      | ~ aNaturalNumber0('#skF_11')
      | ~ aNaturalNumber0(xr)
      | ~ aNaturalNumber0(W0_1036) ),
    inference(superposition,[status(thm),theory(equality)],[c_431,c_111671]) ).

tff(c_111883,plain,
    ! [W0_1036] :
      ( doDivides0(W0_1036,xn)
      | ~ doDivides0(W0_1036,'#skF_11')
      | ~ doDivides0(W0_1036,xr)
      | ~ aNaturalNumber0(W0_1036) ),
    inference(demodulation,[status(thm),theory(equality)],[c_427,c_433,c_111799]) ).

tff(c_300383,plain,
    ! [W0_1762] :
      ( doDivides0(W0_1762,xn)
      | ~ doDivides0(W0_1762,'#skF_11')
      | ~ doDivides0(W0_1762,'#skF_10')
      | ~ aNaturalNumber0(W0_1762) ),
    inference(demodulation,[status(thm),theory(equality)],[c_115801,c_111883]) ).

tff(c_84823,plain,
    ! [W0_823,W1_824] :
      ( ( sdtasdt0(W0_823,'#skF_2'(W0_823,W1_824)) = W1_824 )
      | ~ doDivides0(W0_823,W1_824)
      | ~ aNaturalNumber0(W1_824)
      | ~ aNaturalNumber0(W0_823) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_3648,plain,
    ! [W0_149,W1_150] :
      ( aNaturalNumber0('#skF_2'(W0_149,W1_150))
      | ~ doDivides0(W0_149,W1_150)
      | ~ aNaturalNumber0(W1_150)
      | ~ aNaturalNumber0(W0_149) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_467,plain,
    ! [W0_109] :
      ( ( sdtasdt0(xp,W0_109) != xn )
      | ~ aNaturalNumber0(W0_109) ),
    inference(cnfTransformation,[status(thm)],[f_555]) ).

tff(c_3690,plain,
    ! [W0_149,W1_150] :
      ( ( sdtasdt0(xp,'#skF_2'(W0_149,W1_150)) != xn )
      | ~ doDivides0(W0_149,W1_150)
      | ~ aNaturalNumber0(W1_150)
      | ~ aNaturalNumber0(W0_149) ),
    inference(resolution,[status(thm)],[c_3648,c_467]) ).

tff(c_84833,plain,
    ! [W1_824] :
      ( ( xn != W1_824 )
      | ~ doDivides0(xp,W1_824)
      | ~ aNaturalNumber0(W1_824)
      | ~ aNaturalNumber0(xp)
      | ~ doDivides0(xp,W1_824)
      | ~ aNaturalNumber0(W1_824)
      | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_84823,c_3690]) ).

tff(c_84859,plain,
    ! [W1_824] :
      ( ( xn != W1_824 )
      | ~ doDivides0(xp,W1_824)
      | ~ aNaturalNumber0(W1_824) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_143,c_84833]) ).

tff(c_222287,plain,
    ! [W1_824] :
      ( ( xn != W1_824 )
      | ~ doDivides0('#skF_11',W1_824)
      | ~ aNaturalNumber0(W1_824) ),
    inference(demodulation,[status(thm),theory(equality)],[c_222142,c_84859]) ).

tff(c_300406,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ doDivides0('#skF_11','#skF_11')
    | ~ doDivides0('#skF_11','#skF_10')
    | ~ aNaturalNumber0('#skF_11') ),
    inference(resolution,[status(thm)],[c_300383,c_222287]) ).

tff(c_300436,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_433,c_222380,c_83774,c_147,c_300406]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM496+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36  % Computer : n007.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 14:16:53 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 179.46/152.81  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 179.46/152.83  
% 179.46/152.83  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 179.69/152.87  
% 179.69/152.87  Inference rules
% 179.69/152.87  ----------------------
% 179.69/152.87  #Ref     : 130
% 179.69/152.87  #Sup     : 63835
% 179.69/152.87  #Fact    : 2
% 179.69/152.87  #Define  : 0
% 179.69/152.87  #Split   : 71
% 179.69/152.87  #Chain   : 0
% 179.69/152.87  #Close   : 0
% 179.69/152.87  
% 179.69/152.87  Ordering : KBO
% 179.69/152.87  
% 179.69/152.87  Simplification rules
% 179.69/152.87  ----------------------
% 179.69/152.87  #Subsume      : 5990
% 179.69/152.87  #Demod        : 132556
% 179.69/152.87  #Tautology    : 13966
% 179.69/152.87  #SimpNegUnit  : 16999
% 179.69/152.87  #BackRed      : 3917
% 179.69/152.87  
% 179.69/152.87  #Partial instantiations: 0
% 179.69/152.87  #Strategies tried      : 1
% 179.69/152.87  
% 179.69/152.87  Timing (in seconds)
% 179.69/152.87  ----------------------
% 179.69/152.87  Preprocessing        : 0.80
% 179.69/152.87  Parsing              : 0.36
% 179.69/152.87  CNF conversion       : 0.07
% 179.69/152.87  Main loop            : 150.98
% 179.69/152.87  Inferencing          : 7.37
% 179.69/152.87  Reduction            : 104.88
% 179.69/152.88  Demodulation         : 90.82
% 179.69/152.88  BG Simplification    : 0.73
% 179.69/152.88  Subsumption          : 32.36
% 179.69/152.88  Abstraction          : 1.27
% 179.69/152.88  MUC search           : 0.00
% 179.69/152.88  Cooper               : 0.00
% 179.69/152.88  Total                : 151.85
% 179.69/152.88  Index Insertion      : 0.00
% 179.69/152.88  Index Deletion       : 0.00
% 179.69/152.88  Index Matching       : 0.00
% 179.69/152.88  BG Taut test         : 0.00
%------------------------------------------------------------------------------