TSTP Solution File: NUM503+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM503+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 : n025.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 10:51:55 EDT 2023

% Result   : Theorem 248.62s 211.93s
% Output   : CNFRefutation 248.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   56
% Syntax   : Number of formulae    :  204 (  86 unt;  31 typ;   2 def)
%            Number of atoms       :  443 ( 183 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  448 ( 178   ~; 177   |;  67   &)
%                                         (   2 <=>;  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    :   26 (  26 usr;  14 con; 0-3 aty)
%            Number of variables   :   94 (;  81   !;  13   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_11 > #skF_6 > #skF_15 > #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(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_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(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_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/sandbox2/benchmark/theBenchmark.p',m__2287) ).

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

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_31,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

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_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/sandbox2/benchmark/theBenchmark.p',m__1860) ).

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_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_47,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => aNaturalNumber0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

tff(f_370,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( doDivides0(W0,W1)
          & ( W1 != sz00 ) )
       => sdtlseqdt0(W0,W1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).

tff(f_540,hypothesis,
    ( aNaturalNumber0(xk)
    & ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
    & ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).

tff(f_616,negated_conjecture,
    ~ ( ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm) )
      & ( ? [W0] :
            ( aNaturalNumber0(W0)
            & ( sdtpldt0(sdtasdt0(xn,xm),W0) = sdtasdt0(xp,xm) ) )
        | sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) )
      & ( sdtasdt0(xp,xm) != sdtasdt0(xp,xk) )
      & ( ? [W0] :
            ( aNaturalNumber0(W0)
            & ( sdtpldt0(sdtasdt0(xp,xm),W0) = sdtasdt0(xp,xk) ) )
        | sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_258,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( ( ( W0 != sz00 )
          & ( W1 != W2 )
          & sdtlseqdt0(W1,W2) )
       => ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
          & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
          & ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
          & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).

tff(f_151,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( sdtasdt0(W0,W1) = sz00 )
       => ( ( W0 = sz00 )
          | ( W1 = sz00 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).

tff(f_516,hypothesis,
    ~ ( ? [W0] :
          ( aNaturalNumber0(W0)
          & ( sdtpldt0(xp,W0) = xm ) )
      | sdtlseqdt0(xp,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).

tff(f_549,hypothesis,
    ( ( xk != sz00 )
    & ( xk != sz10 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).

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/sandbox2/benchmark/theBenchmark.p',m__2342) ).

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/sandbox2/benchmark/theBenchmark.p',m__2362) ).

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

tff(f_596,hypothesis,
    ( ? [W0] :
        ( aNaturalNumber0(W0)
        & ( sdtpldt0(xp,W0) = xk ) )
    & sdtlseqdt0(xp,xk) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2389) ).

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

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_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(c_439,plain,
    xp != xn,
    inference(cnfTransformation,[status(thm)],[f_535]) ).

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

tff(c_429,plain,
    aNaturalNumber0('#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_535]) ).

tff(c_327785,plain,
    ! [W0_1564] :
      ( ( sdtpldt0(sz00,W0_1564) = W0_1564 )
      | ~ aNaturalNumber0(W0_1564) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_327838,plain,
    sdtpldt0(sz00,'#skF_10') = '#skF_10',
    inference(resolution,[status(thm)],[c_429,c_327785]) ).

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

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

tff(c_292051,plain,
    ! [W0_1261] :
      ( ( sdtasdt0(W0_1261,sz00) = sz00 )
      | ~ aNaturalNumber0(W0_1261) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_292101,plain,
    sdtasdt0(xn,sz00) = sz00,
    inference(resolution,[status(thm)],[c_147,c_292051]) ).

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

tff(c_292097,plain,
    sdtasdt0(xp,sz00) = sz00,
    inference(resolution,[status(thm)],[c_143,c_292051]) ).

tff(c_297213,plain,
    ! [W0_1327,W2_1328] :
      ( doDivides0(W0_1327,sdtasdt0(W0_1327,W2_1328))
      | ~ aNaturalNumber0(W2_1328)
      | ~ aNaturalNumber0(sdtasdt0(W0_1327,W2_1328))
      | ~ aNaturalNumber0(W0_1327) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_297237,plain,
    ( doDivides0(xp,sz00)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sdtasdt0(xp,sz00))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_292097,c_297213]) ).

tff(c_297403,plain,
    doDivides0(xp,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_4,c_292097,c_4,c_297237]) ).

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

tff(c_291834,plain,
    ! [W0_1258] :
      ( ( sdtasdt0(W0_1258,sz10) = W0_1258 )
      | ~ aNaturalNumber0(W0_1258) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_291885,plain,
    sdtasdt0(sz00,sz10) = sz00,
    inference(resolution,[status(thm)],[c_4,c_291834]) ).

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

tff(c_297345,plain,
    ( doDivides0(sz00,sz00)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(sdtasdt0(sz00,sz10))
    | ~ aNaturalNumber0(sz00) ),
    inference(superposition,[status(thm),theory(equality)],[c_291885,c_297213]) ).

tff(c_297475,plain,
    doDivides0(sz00,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_291885,c_8,c_297345]) ).

tff(c_291667,plain,
    ! [W0_1255] :
      ( ( sdtasdt0(sz10,W0_1255) = W0_1255 )
      | ~ aNaturalNumber0(W0_1255) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_291717,plain,
    sdtasdt0(sz10,xm) = xm,
    inference(resolution,[status(thm)],[c_145,c_291667]) ).

tff(c_294308,plain,
    ! [W1_1292,W0_1293] :
      ( sdtlseqdt0(W1_1292,sdtasdt0(W1_1292,W0_1293))
      | ( sz00 = W0_1293 )
      | ~ aNaturalNumber0(W1_1292)
      | ~ aNaturalNumber0(W0_1293) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_294329,plain,
    ( sdtlseqdt0(sz10,xm)
    | ( xm = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_291717,c_294308]) ).

tff(c_294501,plain,
    ( sdtlseqdt0(sz10,xm)
    | ( xm = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_8,c_294329]) ).

tff(c_311075,plain,
    xm = sz00,
    inference(splitLeft,[status(thm)],[c_294501]) ).

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_405,plain,
    aNaturalNumber0('#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_502]) ).

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

tff(c_292399,plain,
    ! [W0_1265,W1_1266] :
      ( aNaturalNumber0(sdtasdt0(W0_1265,W1_1266))
      | ~ aNaturalNumber0(W1_1266)
      | ~ aNaturalNumber0(W0_1265) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_292477,plain,
    ( aNaturalNumber0(sdtasdt0(xn,xm))
    | ~ aNaturalNumber0('#skF_9')
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_403,c_292399]) ).

tff(c_292602,plain,
    aNaturalNumber0(sdtasdt0(xn,xm)),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_405,c_292477]) ).

tff(c_295640,plain,
    ! [W0_1304,W1_1305] :
      ( sdtlseqdt0(W0_1304,W1_1305)
      | ( sz00 = W1_1305 )
      | ~ doDivides0(W0_1304,W1_1305)
      | ~ aNaturalNumber0(W1_1305)
      | ~ aNaturalNumber0(W0_1304) ),
    inference(cnfTransformation,[status(thm)],[f_370]) ).

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

tff(c_493,plain,
    ! [W0_115] :
      ( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
      | ( sdtpldt0(sdtasdt0(xp,xm),W0_115) != sdtasdt0(xp,xk) )
      | ~ aNaturalNumber0(W0_115)
      | ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
      | ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ) ),
    inference(cnfTransformation,[status(thm)],[f_616]) ).

tff(c_498,plain,
    ! [W0_115] :
      ( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
      | ( sdtpldt0(sdtasdt0(xp,xm),W0_115) != sdtasdt0(xn,xm) )
      | ~ aNaturalNumber0(W0_115)
      | ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) )
      | ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_443,c_443,c_493]) ).

tff(c_291366,plain,
    ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
    inference(splitLeft,[status(thm)],[c_498]) ).

tff(c_295657,plain,
    ( ( sdtasdt0(xp,xm) = sz00 )
    | ~ doDivides0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(resolution,[status(thm)],[c_295640,c_291366]) ).

tff(c_295680,plain,
    ( ( sdtasdt0(xp,xm) = sz00 )
    | ~ doDivides0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_292602,c_295657]) ).

tff(c_295687,plain,
    ~ aNaturalNumber0(sdtasdt0(xp,xm)),
    inference(splitLeft,[status(thm)],[c_295680]) ).

tff(c_295690,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xp) ),
    inference(resolution,[status(thm)],[c_12,c_295687]) ).

tff(c_295694,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_145,c_295690]) ).

tff(c_295695,plain,
    ( ~ doDivides0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | ( sdtasdt0(xp,xm) = sz00 ) ),
    inference(splitRight,[status(thm)],[c_295680]) ).

tff(c_297582,plain,
    ~ doDivides0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
    inference(splitLeft,[status(thm)],[c_295695]) ).

tff(c_311077,plain,
    ~ doDivides0(sdtasdt0(xn,sz00),sdtasdt0(xp,sz00)),
    inference(demodulation,[status(thm),theory(equality)],[c_311075,c_311075,c_297582]) ).

tff(c_311144,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_297475,c_292101,c_292097,c_311077]) ).

tff(c_311146,plain,
    xm != sz00,
    inference(splitRight,[status(thm)],[c_294501]) ).

tff(c_433,plain,
    sdtlseqdt0(xn,xp),
    inference(cnfTransformation,[status(thm)],[f_535]) ).

tff(c_324706,plain,
    ! [W1_1528,W0_1529,W2_1530] :
      ( sdtlseqdt0(sdtasdt0(W1_1528,W0_1529),sdtasdt0(W2_1530,W0_1529))
      | ~ sdtlseqdt0(W1_1528,W2_1530)
      | ( W2_1530 = W1_1528 )
      | ( sz00 = W0_1529 )
      | ~ aNaturalNumber0(W2_1530)
      | ~ aNaturalNumber0(W1_1528)
      | ~ aNaturalNumber0(W0_1529) ),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_324720,plain,
    ( ~ sdtlseqdt0(xn,xp)
    | ( xp = xn )
    | ( xm = sz00 )
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(resolution,[status(thm)],[c_324706,c_291366]) ).

tff(c_325120,plain,
    ( ( xp = xn )
    | ( xm = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_147,c_143,c_433,c_324720]) ).

tff(c_325122,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_311146,c_439,c_325120]) ).

tff(c_325123,plain,
    sdtasdt0(xp,xm) = sz00,
    inference(splitRight,[status(thm)],[c_295695]) ).

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_325516,plain,
    ( ( xm = sz00 )
    | ( xp = sz00 )
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_325123,c_50]) ).

tff(c_325535,plain,
    ( ( xm = sz00 )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_145,c_325516]) ).

tff(c_325536,plain,
    xm = sz00,
    inference(negUnitSimplification,[status(thm)],[c_411,c_325535]) ).

tff(c_421,plain,
    ~ sdtlseqdt0(xp,xm),
    inference(cnfTransformation,[status(thm)],[f_516]) ).

tff(c_295663,plain,
    ( ( xm = sz00 )
    | ~ doDivides0(xp,xm)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xp) ),
    inference(resolution,[status(thm)],[c_295640,c_421]) ).

tff(c_295686,plain,
    ( ( xm = sz00 )
    | ~ doDivides0(xp,xm) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_145,c_295663]) ).

tff(c_296947,plain,
    ~ doDivides0(xp,xm),
    inference(splitLeft,[status(thm)],[c_295686]) ).

tff(c_325546,plain,
    ~ doDivides0(xp,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_325536,c_296947]) ).

tff(c_325596,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_297403,c_325546]) ).

tff(c_325597,plain,
    xm = sz00,
    inference(splitRight,[status(thm)],[c_295686]) ).

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

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

tff(c_294654,plain,
    ! [W1_1295,W0_1296] :
      ( ( sz00 = W1_1295 )
      | ( sz00 = W0_1296 )
      | ( sdtasdt0(W0_1296,W1_1295) != sz00 )
      | ~ aNaturalNumber0(W1_1295)
      | ~ aNaturalNumber0(W0_1296) ),
    inference(cnfTransformation,[status(thm)],[f_151]) ).

tff(c_294690,plain,
    ( ( xk = sz00 )
    | ( xp = sz00 )
    | ( sdtasdt0(xn,xm) != sz00 )
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_443,c_294654]) ).

tff(c_294842,plain,
    ( ( xk = sz00 )
    | ( xp = sz00 )
    | ( sdtasdt0(xn,xm) != sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_445,c_294690]) ).

tff(c_294843,plain,
    sdtasdt0(xn,xm) != sz00,
    inference(negUnitSimplification,[status(thm)],[c_411,c_453,c_294842]) ).

tff(c_325601,plain,
    sdtasdt0(xn,sz00) != sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_325597,c_294843]) ).

tff(c_325651,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_292101,c_325601]) ).

tff(c_325653,plain,
    sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
    inference(splitRight,[status(thm)],[c_498]) ).

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_475,plain,
    sdtasdt0(xr,'#skF_13') = sdtasdt0(xn,xm),
    inference(cnfTransformation,[status(thm)],[f_590]) ).

tff(c_3062,plain,
    ! [W0_157,W1_158] :
      ( aNaturalNumber0(sdtasdt0(W0_157,W1_158))
      | ~ aNaturalNumber0(W1_158)
      | ~ aNaturalNumber0(W0_157) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_3161,plain,
    ( aNaturalNumber0(sdtasdt0(xn,xm))
    | ~ aNaturalNumber0('#skF_13')
    | ~ aNaturalNumber0(xr) ),
    inference(superposition,[status(thm),theory(equality)],[c_475,c_3062]) ).

tff(c_3243,plain,
    aNaturalNumber0(sdtasdt0(xn,xm)),
    inference(demodulation,[status(thm),theory(equality)],[c_467,c_477,c_3161]) ).

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

tff(c_441,plain,
    sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
    inference(cnfTransformation,[status(thm)],[f_540]) ).

tff(c_49716,plain,
    ! [W0_575,W2_576] :
      ( ( sdtsldt0(sdtasdt0(W0_575,W2_576),W0_575) = W2_576 )
      | ~ aNaturalNumber0(W2_576)
      | ~ doDivides0(W0_575,sdtasdt0(W0_575,W2_576))
      | ( sz00 = W0_575 )
      | ~ aNaturalNumber0(sdtasdt0(W0_575,W2_576))
      | ~ aNaturalNumber0(W0_575) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_49797,plain,
    ( ( sdtsldt0(sdtasdt0(xp,'#skF_9'),xp) = '#skF_9' )
    | ~ aNaturalNumber0('#skF_9')
    | ~ doDivides0(xp,sdtasdt0(xn,xm))
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sdtasdt0(xp,'#skF_9'))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_403,c_49716]) ).

tff(c_49895,plain,
    ( ( xk = '#skF_9' )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_3243,c_403,c_401,c_405,c_441,c_403,c_49797]) ).

tff(c_49896,plain,
    xk = '#skF_9',
    inference(negUnitSimplification,[status(thm)],[c_411,c_49895]) ).

tff(c_485,plain,
    sdtpldt0(xp,'#skF_15') = xk,
    inference(cnfTransformation,[status(thm)],[f_596]) ).

tff(c_487,plain,
    aNaturalNumber0('#skF_15'),
    inference(cnfTransformation,[status(thm)],[f_596]) ).

tff(c_2200,plain,
    ! [W0_146] :
      ( ( sdtpldt0(xp,W0_146) != xm )
      | ~ aNaturalNumber0(W0_146) ),
    inference(cnfTransformation,[status(thm)],[f_516]) ).

tff(c_2242,plain,
    sdtpldt0(xp,'#skF_15') != xm,
    inference(resolution,[status(thm)],[c_487,c_2200]) ).

tff(c_2257,plain,
    xm != xk,
    inference(demodulation,[status(thm),theory(equality)],[c_485,c_2242]) ).

tff(c_49963,plain,
    xm != '#skF_9',
    inference(demodulation,[status(thm),theory(equality)],[c_49896,c_2257]) ).

tff(c_425,plain,
    sdtlseqdt0(xm,xp),
    inference(cnfTransformation,[status(thm)],[f_535]) ).

tff(c_483,plain,
    sdtlseqdt0(xp,xk),
    inference(cnfTransformation,[status(thm)],[f_596]) ).

tff(c_19445,plain,
    ! [W0_362,W2_363,W1_364] :
      ( sdtlseqdt0(W0_362,W2_363)
      | ~ sdtlseqdt0(W1_364,W2_363)
      | ~ sdtlseqdt0(W0_362,W1_364)
      | ~ aNaturalNumber0(W2_363)
      | ~ aNaturalNumber0(W1_364)
      | ~ aNaturalNumber0(W0_362) ),
    inference(cnfTransformation,[status(thm)],[f_201]) ).

tff(c_19545,plain,
    ! [W0_362] :
      ( sdtlseqdt0(W0_362,xk)
      | ~ sdtlseqdt0(W0_362,xp)
      | ~ aNaturalNumber0(xk)
      | ~ aNaturalNumber0(xp)
      | ~ aNaturalNumber0(W0_362) ),
    inference(resolution,[status(thm)],[c_483,c_19445]) ).

tff(c_19687,plain,
    ! [W0_362] :
      ( sdtlseqdt0(W0_362,xk)
      | ~ sdtlseqdt0(W0_362,xp)
      | ~ aNaturalNumber0(W0_362) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_445,c_19545]) ).

tff(c_265184,plain,
    ! [W0_1220] :
      ( sdtlseqdt0(W0_1220,'#skF_9')
      | ~ sdtlseqdt0(W0_1220,xp)
      | ~ aNaturalNumber0(W0_1220) ),
    inference(demodulation,[status(thm),theory(equality)],[c_49896,c_19687]) ).

tff(c_265218,plain,
    ( sdtlseqdt0(xm,'#skF_9')
    | ~ aNaturalNumber0(xm) ),
    inference(resolution,[status(thm)],[c_425,c_265184]) ).

tff(c_265252,plain,
    sdtlseqdt0(xm,'#skF_9'),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_265218]) ).

tff(c_82,plain,
    ! [W1_56,W0_55,W2_57] :
      ( sdtlseqdt0(sdtasdt0(W1_56,W0_55),sdtasdt0(W2_57,W0_55))
      | ~ sdtlseqdt0(W1_56,W2_57)
      | ( W2_57 = W1_56 )
      | ( sz00 = W0_55 )
      | ~ aNaturalNumber0(W2_57)
      | ~ aNaturalNumber0(W1_56)
      | ~ aNaturalNumber0(W0_55) ),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_3646,plain,
    ! [W1_169,W0_170] :
      ( ( sdtasdt0(W1_169,W0_170) = sdtasdt0(W0_170,W1_169) )
      | ~ aNaturalNumber0(W1_169)
      | ~ aNaturalNumber0(W0_170) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_265342,plain,
    ! [W0_1221] :
      ( ( sdtasdt0(xp,W0_1221) = sdtasdt0(W0_1221,xp) )
      | ~ aNaturalNumber0(W0_1221) ),
    inference(resolution,[status(thm)],[c_143,c_3646]) ).

tff(c_265732,plain,
    sdtasdt0(xp,'#skF_9') = sdtasdt0('#skF_9',xp),
    inference(resolution,[status(thm)],[c_405,c_265342]) ).

tff(c_159605,plain,
    ! [W0_1039] :
      ( ( sdtasdt0(xr,W0_1039) = sdtasdt0(W0_1039,xr) )
      | ~ aNaturalNumber0(W0_1039) ),
    inference(resolution,[status(thm)],[c_467,c_3646]) ).

tff(c_159891,plain,
    sdtasdt0(xr,'#skF_13') = sdtasdt0('#skF_13',xr),
    inference(resolution,[status(thm)],[c_477,c_159605]) ).

tff(c_170597,plain,
    sdtasdt0(xn,xm) = sdtasdt0('#skF_13',xr),
    inference(demodulation,[status(thm),theory(equality)],[c_159891,c_475]) ).

tff(c_173276,plain,
    sdtasdt0(xp,'#skF_9') = sdtasdt0('#skF_13',xr),
    inference(demodulation,[status(thm),theory(equality)],[c_170597,c_403]) ).

tff(c_271318,plain,
    sdtasdt0('#skF_13',xr) = sdtasdt0('#skF_9',xp),
    inference(demodulation,[status(thm),theory(equality)],[c_265732,c_173276]) ).

tff(c_265739,plain,
    sdtasdt0(xp,xm) = sdtasdt0(xm,xp),
    inference(resolution,[status(thm)],[c_145,c_265342]) ).

tff(c_491,plain,
    ! [W0_114] :
      ( ( sdtpldt0(sdtasdt0(xn,xm),W0_114) != sdtasdt0(xp,xm) )
      | ~ aNaturalNumber0(W0_114)
      | ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
      | ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
      | ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ) ),
    inference(cnfTransformation,[status(thm)],[f_616]) ).

tff(c_499,plain,
    ! [W0_114] :
      ( ( sdtpldt0(sdtasdt0(xn,xm),W0_114) != sdtasdt0(xp,xm) )
      | ~ aNaturalNumber0(W0_114)
      | ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
      | ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) )
      | ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_443,c_443,c_491]) ).

tff(c_2177,plain,
    ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)),
    inference(splitLeft,[status(thm)],[c_499]) ).

tff(c_173279,plain,
    ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0('#skF_13',xr)),
    inference(demodulation,[status(thm),theory(equality)],[c_170597,c_2177]) ).

tff(c_268118,plain,
    ~ sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0('#skF_13',xr)),
    inference(demodulation,[status(thm),theory(equality)],[c_265739,c_173279]) ).

tff(c_290488,plain,
    ~ sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0('#skF_9',xp)),
    inference(demodulation,[status(thm),theory(equality)],[c_271318,c_268118]) ).

tff(c_291204,plain,
    ( ~ sdtlseqdt0(xm,'#skF_9')
    | ( xm = '#skF_9' )
    | ( xp = sz00 )
    | ~ aNaturalNumber0('#skF_9')
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xp) ),
    inference(resolution,[status(thm)],[c_82,c_290488]) ).

tff(c_291216,plain,
    ( ( xm = '#skF_9' )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_145,c_405,c_265252,c_291204]) ).

tff(c_291218,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_411,c_49963,c_291216]) ).

tff(c_291220,plain,
    sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)),
    inference(splitRight,[status(thm)],[c_499]) ).

tff(c_489,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
    | ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ) ),
    inference(cnfTransformation,[status(thm)],[f_616]) ).

tff(c_497,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
    | ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) )
    | ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_443,c_443,c_489]) ).

tff(c_504,plain,
    ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)),
    inference(splitLeft,[status(thm)],[c_497]) ).

tff(c_291363,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_291220,c_504]) ).

tff(c_291364,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    | ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) )
    | ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) ) ),
    inference(splitRight,[status(thm)],[c_497]) ).

tff(c_327604,plain,
    sdtasdt0(xp,xm) = sdtasdt0(xn,xm),
    inference(demodulation,[status(thm),theory(equality)],[c_325653,c_291364]) ).

tff(c_330770,plain,
    ! [W1_1598,W0_1599] :
      ( sdtlseqdt0(W1_1598,sdtasdt0(W1_1598,W0_1599))
      | ( sz00 = W0_1599 )
      | ~ aNaturalNumber0(W1_1598)
      | ~ aNaturalNumber0(W0_1599) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_330932,plain,
    ( sdtlseqdt0(xp,sdtasdt0(xn,xm))
    | ( xm = sz00 )
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_327604,c_330770]) ).

tff(c_331098,plain,
    ( sdtlseqdt0(xp,sdtasdt0(xn,xm))
    | ( xm = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_143,c_330932]) ).

tff(c_331123,plain,
    xm = sz00,
    inference(splitLeft,[status(thm)],[c_331098]) ).

tff(c_427,plain,
    sdtpldt0(xm,'#skF_10') = xp,
    inference(cnfTransformation,[status(thm)],[f_535]) ).

tff(c_331171,plain,
    sdtpldt0(sz00,'#skF_10') = xp,
    inference(demodulation,[status(thm),theory(equality)],[c_331123,c_427]) ).

tff(c_331210,plain,
    xp = '#skF_10',
    inference(demodulation,[status(thm),theory(equality)],[c_327838,c_331171]) ).

tff(c_331247,plain,
    sz00 != '#skF_10',
    inference(demodulation,[status(thm),theory(equality)],[c_331210,c_411]) ).

tff(c_327461,plain,
    ! [W0_1560] :
      ( ( sdtasdt0(W0_1560,sz00) = sz00 )
      | ~ aNaturalNumber0(W0_1560) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_327510,plain,
    sdtasdt0(xn,sz00) = sz00,
    inference(resolution,[status(thm)],[c_147,c_327461]) ).

tff(c_331146,plain,
    sdtasdt0(xp,xk) = sdtasdt0(xn,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_331123,c_443]) ).

tff(c_331197,plain,
    sdtasdt0(xp,xk) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_327510,c_331146]) ).

tff(c_332452,plain,
    sdtasdt0('#skF_10',xk) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_331210,c_331197]) ).

tff(c_332455,plain,
    ( ( xk = sz00 )
    | ( sz00 = '#skF_10' )
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0('#skF_10') ),
    inference(superposition,[status(thm),theory(equality)],[c_332452,c_50]) ).

tff(c_332468,plain,
    ( ( xk = sz00 )
    | ( sz00 = '#skF_10' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_429,c_445,c_332455]) ).

tff(c_332470,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_331247,c_453,c_332468]) ).

tff(c_332472,plain,
    xm != sz00,
    inference(splitRight,[status(thm)],[c_331098]) ).

tff(c_377798,plain,
    ! [W2_2045,W0_2046,W1_2047] :
      ( ( sdtasdt0(W2_2045,W0_2046) != sdtasdt0(W1_2047,W0_2046) )
      | ( W2_2045 = W1_2047 )
      | ~ aNaturalNumber0(W2_2045)
      | ~ aNaturalNumber0(W1_2047)
      | ( sz00 = W0_2046 )
      | ~ aNaturalNumber0(W0_2046) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_378028,plain,
    ! [W1_2047] :
      ( ( sdtasdt0(xn,xm) != sdtasdt0(W1_2047,xm) )
      | ( xp = W1_2047 )
      | ~ aNaturalNumber0(xp)
      | ~ aNaturalNumber0(W1_2047)
      | ( xm = sz00 )
      | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_327604,c_377798]) ).

tff(c_378376,plain,
    ! [W1_2047] :
      ( ( sdtasdt0(xn,xm) != sdtasdt0(W1_2047,xm) )
      | ( xp = W1_2047 )
      | ~ aNaturalNumber0(W1_2047)
      | ( xm = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_143,c_378028]) ).

tff(c_378433,plain,
    ! [W1_2048] :
      ( ( sdtasdt0(xn,xm) != sdtasdt0(W1_2048,xm) )
      | ( xp = W1_2048 )
      | ~ aNaturalNumber0(W1_2048) ),
    inference(negUnitSimplification,[status(thm)],[c_332472,c_378376]) ).

tff(c_378526,plain,
    xp = xn,
    inference(resolution,[status(thm)],[c_147,c_378433]) ).

tff(c_378590,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_439,c_378526]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM503+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
% 0.15/0.35  % Computer : n025.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 14:51:34 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 248.62/211.93  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 248.70/211.95  
% 248.70/211.95  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 248.94/212.00  
% 248.94/212.00  Inference rules
% 248.94/212.00  ----------------------
% 248.94/212.00  #Ref     : 121
% 248.94/212.00  #Sup     : 80854
% 248.94/212.00  #Fact    : 8
% 248.94/212.00  #Define  : 0
% 248.94/212.00  #Split   : 236
% 248.94/212.00  #Chain   : 0
% 248.94/212.00  #Close   : 0
% 248.94/212.00  
% 248.94/212.00  Ordering : KBO
% 248.94/212.00  
% 248.94/212.00  Simplification rules
% 248.94/212.00  ----------------------
% 248.94/212.00  #Subsume      : 3413
% 248.94/212.00  #Demod        : 163232
% 248.94/212.00  #Tautology    : 19343
% 248.94/212.00  #SimpNegUnit  : 20790
% 248.94/212.00  #BackRed      : 7873
% 248.94/212.00  
% 248.94/212.00  #Partial instantiations: 0
% 248.94/212.00  #Strategies tried      : 1
% 248.94/212.00  
% 248.94/212.00  Timing (in seconds)
% 248.94/212.00  ----------------------
% 248.94/212.00  Preprocessing        : 0.82
% 248.94/212.00  Parsing              : 0.37
% 248.94/212.00  CNF conversion       : 0.07
% 248.94/212.00  Main loop            : 210.08
% 248.94/212.00  Inferencing          : 7.87
% 248.94/212.00  Reduction            : 153.38
% 248.94/212.00  Demodulation         : 138.56
% 248.94/212.00  BG Simplification    : 0.94
% 248.94/212.00  Subsumption          : 39.03
% 248.94/212.00  Abstraction          : 1.52
% 249.10/212.00  MUC search           : 0.00
% 249.10/212.00  Cooper               : 0.00
% 249.10/212.00  Total                : 210.98
% 249.10/212.00  Index Insertion      : 0.00
% 249.10/212.00  Index Deletion       : 0.00
% 249.10/212.00  Index Matching       : 0.00
% 249.10/212.00  BG Taut test         : 0.00
%------------------------------------------------------------------------------