TSTP Solution File: NUM493+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM493+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/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 : n032.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 10:51:52 EDT 2023

% Result   : Timeout 296.22s 250.55s
% Output   : None 
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  121 (  37 unt;  19 typ;   2 def)
%            Number of atoms       :  326 (  70 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  395 ( 171   ~; 178   |;  26   &)
%                                         (   2 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   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    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :   91 (;  90   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_3 > #skF_2 > #skF_1

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

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

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(f_448,hypothesis,
    ( ( xr != xn )
    & sdtlseqdt0(xr,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1894) ).

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

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_443,hypothesis,
    sdtlseqdt0(xp,xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).

tff(f_444,hypothesis,
    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_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/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).

tff(f_41,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => aNaturalNumber0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

tff(f_162,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtlseqdt0(W0,W1)
      <=> ? [W2] :
            ( aNaturalNumber0(W2)
            & ( sdtpldt0(W0,W2) = W1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).

tff(f_453,negated_conjecture,
    ~ ( doDivides0(xp,xr)
      | doDivides0(xp,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_31,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

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_61,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).

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_449,hypothesis,
    doDivides0(xp,sdtasdt0(xr,xm)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1913) ).

tff(f_296,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( ( W0 != W1 )
          & sdtlseqdt0(W0,W1) )
       => iLess0(W0,W1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).

tff(f_442,hypothesis,
    ( isPrime0(xp)
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).

tff(f_439,hypothesis,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( ( isPrime0(W2)
          & doDivides0(W2,sdtasdt0(W0,W1)) )
       => ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
         => ( doDivides0(W2,W0)
            | doDivides0(W2,W1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).

tff(f_234,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( ( W0 != W1 )
          & sdtlseqdt0(W0,W1) )
       => ! [W2] :
            ( aNaturalNumber0(W2)
           => ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
              & sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
              & ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
              & sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).

tff(c_161,plain,
    xr != xn,
    inference(cnfTransformation,[status(thm)],[f_448]) ).

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

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

tff(c_635,plain,
    ! [W1_114,W0_115] :
      ( ( sdtpldt0(W1_114,W0_115) = sdtpldt0(W0_115,W1_114) )
      | ~ aNaturalNumber0(W1_114)
      | ~ aNaturalNumber0(W0_115) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_1081,plain,
    ! [W0_126] :
      ( ( sdtpldt0(xp,W0_126) = sdtpldt0(W0_126,xp) )
      | ~ aNaturalNumber0(W0_126) ),
    inference(resolution,[status(thm)],[c_143,c_635]) ).

tff(c_1121,plain,
    sdtpldt0(xp,xn) = sdtpldt0(xn,xp),
    inference(resolution,[status(thm)],[c_147,c_1081]) ).

tff(c_155,plain,
    sdtlseqdt0(xp,xn),
    inference(cnfTransformation,[status(thm)],[f_443]) ).

tff(c_157,plain,
    sdtmndt0(xn,xp) = xr,
    inference(cnfTransformation,[status(thm)],[f_444]) ).

tff(c_1647,plain,
    ! [W1_134,W0_135] :
      ( aNaturalNumber0(sdtmndt0(W1_134,W0_135))
      | ~ sdtlseqdt0(W0_135,W1_134)
      | ~ aNaturalNumber0(W1_134)
      | ~ aNaturalNumber0(W0_135) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_1684,plain,
    ( aNaturalNumber0(xr)
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_157,c_1647]) ).

tff(c_1698,plain,
    aNaturalNumber0(xr),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_1684]) ).

tff(c_3887,plain,
    ! [W0_176,W1_177] :
      ( ( sdtpldt0(W0_176,sdtmndt0(W1_177,W0_176)) = W1_177 )
      | ~ sdtlseqdt0(W0_176,W1_177)
      | ~ aNaturalNumber0(W1_177)
      | ~ aNaturalNumber0(W0_176) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_3906,plain,
    ( ( sdtpldt0(xp,xr) = xn )
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_157,c_3887]) ).

tff(c_3910,plain,
    sdtpldt0(xp,xr) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_3906]) ).

tff(c_40,plain,
    ! [W0_22,W2_24,W1_23] :
      ( ( sdtpldt0(W0_22,W2_24) != sdtpldt0(W0_22,W1_23) )
      | ( W2_24 = W1_23 )
      | ~ aNaturalNumber0(W2_24)
      | ~ aNaturalNumber0(W1_23)
      | ~ aNaturalNumber0(W0_22) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_4333,plain,
    ! [W1_23] :
      ( ( sdtpldt0(xp,W1_23) != xn )
      | ( xr = W1_23 )
      | ~ aNaturalNumber0(xr)
      | ~ aNaturalNumber0(W1_23)
      | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_3910,c_40]) ).

tff(c_27551,plain,
    ! [W1_327] :
      ( ( sdtpldt0(xp,W1_327) != xn )
      | ( xr = W1_327 )
      | ~ aNaturalNumber0(W1_327) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_1698,c_4333]) ).

tff(c_27629,plain,
    ( ( sdtpldt0(xp,xn) != xn )
    | ( xr = xn ) ),
    inference(resolution,[status(thm)],[c_147,c_27551]) ).

tff(c_27671,plain,
    ( ( sdtpldt0(xn,xp) != xn )
    | ( xr = xn ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1121,c_27629]) ).

tff(c_27672,plain,
    sdtpldt0(xn,xp) != xn,
    inference(negUnitSimplification,[status(thm)],[c_161,c_27671]) ).

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

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_1135,plain,
    ( aNaturalNumber0(sdtpldt0(xn,xp))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_1121,c_10]) ).

tff(c_1143,plain,
    aNaturalNumber0(sdtpldt0(xn,xp)),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_1135]) ).

tff(c_12231,plain,
    ! [W0_245] :
      ( ( sdtpldt0(xn,W0_245) = sdtpldt0(W0_245,xn) )
      | ~ aNaturalNumber0(W0_245) ),
    inference(resolution,[status(thm)],[c_147,c_635]) ).

tff(c_12329,plain,
    sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
    inference(resolution,[status(thm)],[c_145,c_12231]) ).

tff(c_12522,plain,
    ( aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_12329,c_10]) ).

tff(c_12558,plain,
    aNaturalNumber0(sdtpldt0(xm,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_12522]) ).

tff(c_52,plain,
    ! [W0_34,W2_38] :
      ( sdtlseqdt0(W0_34,sdtpldt0(W0_34,W2_38))
      | ~ aNaturalNumber0(W2_38)
      | ~ aNaturalNumber0(sdtpldt0(W0_34,W2_38))
      | ~ aNaturalNumber0(W0_34) ),
    inference(cnfTransformation,[status(thm)],[f_162]) ).

tff(c_8038,plain,
    ! [W0_225,W2_226] :
      ( ( sdtmndt0(sdtpldt0(W0_225,W2_226),W0_225) = W2_226 )
      | ~ aNaturalNumber0(W2_226)
      | ~ sdtlseqdt0(W0_225,sdtpldt0(W0_225,W2_226))
      | ~ aNaturalNumber0(sdtpldt0(W0_225,W2_226))
      | ~ aNaturalNumber0(W0_225) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_28801,plain,
    ! [W0_335,W2_336] :
      ( ( sdtmndt0(sdtpldt0(W0_335,W2_336),W0_335) = W2_336 )
      | ~ aNaturalNumber0(W2_336)
      | ~ aNaturalNumber0(sdtpldt0(W0_335,W2_336))
      | ~ aNaturalNumber0(W0_335) ),
    inference(resolution,[status(thm)],[c_52,c_8038]) ).

tff(c_28829,plain,
    ( ( sdtmndt0(sdtpldt0(xm,xn),xm) = xn )
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(resolution,[status(thm)],[c_12558,c_28801]) ).

tff(c_28927,plain,
    sdtmndt0(sdtpldt0(xm,xn),xm) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_147,c_28829]) ).

tff(c_165,plain,
    ~ doDivides0(xp,xm),
    inference(cnfTransformation,[status(thm)],[f_453]) ).

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

tff(c_315,plain,
    ! [W0_103] :
      ( ( sdtpldt0(sz00,W0_103) = W0_103 )
      | ~ aNaturalNumber0(W0_103) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_331,plain,
    sdtpldt0(sz00,xn) = xn,
    inference(resolution,[status(thm)],[c_147,c_315]) ).

tff(c_18,plain,
    ! [W0_11] :
      ( ( sdtpldt0(sz00,W0_11) = W0_11 )
      | ~ aNaturalNumber0(W0_11) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_1186,plain,
    sdtpldt0(sz00,sdtpldt0(xn,xp)) = sdtpldt0(xn,xp),
    inference(resolution,[status(thm)],[c_1143,c_18]) ).

tff(c_5623,plain,
    ! [W0_201,W1_202,W2_203] :
      ( ( sdtpldt0(sdtpldt0(W0_201,W1_202),W2_203) = sdtpldt0(W0_201,sdtpldt0(W1_202,W2_203)) )
      | ~ aNaturalNumber0(W2_203)
      | ~ aNaturalNumber0(W1_202)
      | ~ aNaturalNumber0(W0_201) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_92839,plain,
    ! [W0_621,W1_622,W2_623] :
      ( sdtlseqdt0(sdtpldt0(W0_621,W1_622),sdtpldt0(W0_621,sdtpldt0(W1_622,W2_623)))
      | ~ aNaturalNumber0(W2_623)
      | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(W0_621,W1_622),W2_623))
      | ~ aNaturalNumber0(sdtpldt0(W0_621,W1_622))
      | ~ aNaturalNumber0(W2_623)
      | ~ aNaturalNumber0(W1_622)
      | ~ aNaturalNumber0(W0_621) ),
    inference(superposition,[status(thm),theory(equality)],[c_5623,c_52]) ).

tff(c_93107,plain,
    ( sdtlseqdt0(sdtpldt0(sz00,xn),sdtpldt0(xn,xp))
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sz00,xn),xp))
    | ~ aNaturalNumber0(sdtpldt0(sz00,xn))
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sz00) ),
    inference(superposition,[status(thm),theory(equality)],[c_1186,c_92839]) ).

tff(c_93608,plain,
    sdtlseqdt0(xn,sdtpldt0(xn,xp)),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_147,c_143,c_147,c_331,c_1143,c_331,c_143,c_331,c_93107]) ).

tff(c_16,plain,
    ! [W0_8,W1_9,W2_10] :
      ( ( sdtpldt0(sdtpldt0(W0_8,W1_9),W2_10) = sdtpldt0(W0_8,sdtpldt0(W1_9,W2_10)) )
      | ~ aNaturalNumber0(W2_10)
      | ~ aNaturalNumber0(W1_9)
      | ~ aNaturalNumber0(W0_8) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_610,plain,
    ! [W1_112,W0_113] :
      ( ( sdtasdt0(W1_112,W0_113) = sdtasdt0(W0_113,W1_112) )
      | ~ aNaturalNumber0(W1_112)
      | ~ aNaturalNumber0(W0_113) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_13725,plain,
    ! [W0_248] :
      ( ( sdtasdt0(xm,W0_248) = sdtasdt0(W0_248,xm) )
      | ~ aNaturalNumber0(W0_248) ),
    inference(resolution,[status(thm)],[c_145,c_610]) ).

tff(c_13820,plain,
    sdtasdt0(xr,xm) = sdtasdt0(xm,xr),
    inference(resolution,[status(thm)],[c_1698,c_13725]) ).

tff(c_163,plain,
    doDivides0(xp,sdtasdt0(xr,xm)),
    inference(cnfTransformation,[status(thm)],[f_449]) ).

tff(c_13843,plain,
    doDivides0(xp,sdtasdt0(xm,xr)),
    inference(demodulation,[status(thm),theory(equality)],[c_13820,c_163]) ).

tff(c_3610,plain,
    ! [W0_170,W2_171] :
      ( sdtlseqdt0(W0_170,sdtpldt0(W0_170,W2_171))
      | ~ aNaturalNumber0(W2_171)
      | ~ aNaturalNumber0(sdtpldt0(W0_170,W2_171))
      | ~ aNaturalNumber0(W0_170) ),
    inference(cnfTransformation,[status(thm)],[f_162]) ).

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_3658,plain,
    ! [W0_170,W2_171] :
      ( iLess0(W0_170,sdtpldt0(W0_170,W2_171))
      | ( sdtpldt0(W0_170,W2_171) = W0_170 )
      | ~ aNaturalNumber0(W2_171)
      | ~ aNaturalNumber0(sdtpldt0(W0_170,W2_171))
      | ~ aNaturalNumber0(W0_170) ),
    inference(resolution,[status(thm)],[c_3610,c_99]) ).

tff(c_167,plain,
    ~ doDivides0(xp,xr),
    inference(cnfTransformation,[status(thm)],[f_453]) ).

tff(c_153,plain,
    isPrime0(xp),
    inference(cnfTransformation,[status(thm)],[f_442]) ).

tff(c_657,plain,
    ! [W0_115] :
      ( ( sdtpldt0(xp,W0_115) = sdtpldt0(W0_115,xp) )
      | ~ aNaturalNumber0(W0_115) ),
    inference(resolution,[status(thm)],[c_143,c_635]) ).

tff(c_1733,plain,
    sdtpldt0(xr,xp) = sdtpldt0(xp,xr),
    inference(resolution,[status(thm)],[c_1698,c_657]) ).

tff(c_7108,plain,
    sdtpldt0(xr,xp) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_3910,c_1733]) ).

tff(c_9872,plain,
    ! [W2_238,W1_239,W0_240] :
      ( doDivides0(W2_238,W1_239)
      | doDivides0(W2_238,W0_240)
      | ~ iLess0(sdtpldt0(sdtpldt0(W0_240,W1_239),W2_238),sdtpldt0(sdtpldt0(xn,xm),xp))
      | ~ doDivides0(W2_238,sdtasdt0(W0_240,W1_239))
      | ~ isPrime0(W2_238)
      | ~ aNaturalNumber0(W2_238)
      | ~ aNaturalNumber0(W1_239)
      | ~ aNaturalNumber0(W0_240) ),
    inference(cnfTransformation,[status(thm)],[f_439]) ).

tff(c_9887,plain,
    ! [W2_10,W1_9,W0_8] :
      ( doDivides0(W2_10,W1_9)
      | doDivides0(W2_10,W0_8)
      | ~ iLess0(sdtpldt0(W0_8,sdtpldt0(W1_9,W2_10)),sdtpldt0(sdtpldt0(xn,xm),xp))
      | ~ doDivides0(W2_10,sdtasdt0(W0_8,W1_9))
      | ~ isPrime0(W2_10)
      | ~ aNaturalNumber0(W2_10)
      | ~ aNaturalNumber0(W1_9)
      | ~ aNaturalNumber0(W0_8)
      | ~ aNaturalNumber0(W2_10)
      | ~ aNaturalNumber0(W1_9)
      | ~ aNaturalNumber0(W0_8) ),
    inference(superposition,[status(thm),theory(equality)],[c_16,c_9872]) ).

tff(c_271588,plain,
    ! [W2_1013,W1_1014,W0_1015] :
      ( doDivides0(W2_1013,W1_1014)
      | doDivides0(W2_1013,W0_1015)
      | ~ iLess0(sdtpldt0(W0_1015,sdtpldt0(W1_1014,W2_1013)),sdtpldt0(sdtpldt0(xm,xn),xp))
      | ~ doDivides0(W2_1013,sdtasdt0(W0_1015,W1_1014))
      | ~ isPrime0(W2_1013)
      | ~ aNaturalNumber0(W2_1013)
      | ~ aNaturalNumber0(W1_1014)
      | ~ aNaturalNumber0(W0_1015)
      | ~ aNaturalNumber0(W2_1013)
      | ~ aNaturalNumber0(W1_1014)
      | ~ aNaturalNumber0(W0_1015) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12329,c_9887]) ).

tff(c_272029,plain,
    ! [W0_1015] :
      ( doDivides0(xp,xr)
      | doDivides0(xp,W0_1015)
      | ~ iLess0(sdtpldt0(W0_1015,xn),sdtpldt0(sdtpldt0(xm,xn),xp))
      | ~ doDivides0(xp,sdtasdt0(W0_1015,xr))
      | ~ isPrime0(xp)
      | ~ aNaturalNumber0(xp)
      | ~ aNaturalNumber0(xr)
      | ~ aNaturalNumber0(W0_1015)
      | ~ aNaturalNumber0(xp)
      | ~ aNaturalNumber0(xr)
      | ~ aNaturalNumber0(W0_1015) ),
    inference(superposition,[status(thm),theory(equality)],[c_7108,c_271588]) ).

tff(c_272285,plain,
    ! [W0_1015] :
      ( doDivides0(xp,xr)
      | doDivides0(xp,W0_1015)
      | ~ iLess0(sdtpldt0(W0_1015,xn),sdtpldt0(sdtpldt0(xm,xn),xp))
      | ~ doDivides0(xp,sdtasdt0(W0_1015,xr))
      | ~ aNaturalNumber0(W0_1015) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1698,c_143,c_1698,c_143,c_153,c_272029]) ).

tff(c_272342,plain,
    ! [W0_1016] :
      ( doDivides0(xp,W0_1016)
      | ~ iLess0(sdtpldt0(W0_1016,xn),sdtpldt0(sdtpldt0(xm,xn),xp))
      | ~ doDivides0(xp,sdtasdt0(W0_1016,xr))
      | ~ aNaturalNumber0(W0_1016) ),
    inference(negUnitSimplification,[status(thm)],[c_167,c_272285]) ).

tff(c_272397,plain,
    ( doDivides0(xp,xm)
    | ~ doDivides0(xp,sdtasdt0(xm,xr))
    | ~ aNaturalNumber0(xm)
    | ( sdtpldt0(sdtpldt0(xm,xn),xp) = sdtpldt0(xm,xn) )
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp))
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(resolution,[status(thm)],[c_3658,c_272342]) ).

tff(c_272462,plain,
    ( doDivides0(xp,xm)
    | ( sdtpldt0(sdtpldt0(xm,xn),xp) = sdtpldt0(xm,xn) )
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12558,c_143,c_145,c_13843,c_272397]) ).

tff(c_272463,plain,
    ( ( sdtpldt0(sdtpldt0(xm,xn),xp) = sdtpldt0(xm,xn) )
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)) ),
    inference(negUnitSimplification,[status(thm)],[c_165,c_272462]) ).

tff(c_277068,plain,
    ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)),
    inference(splitLeft,[status(thm)],[c_272463]) ).

tff(c_277077,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(resolution,[status(thm)],[c_10,c_277068]) ).

tff(c_277085,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_12558,c_143,c_277077]) ).

tff(c_277087,plain,
    aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)),
    inference(splitRight,[status(thm)],[c_272463]) ).

tff(c_277313,plain,
    ( aNaturalNumber0(sdtpldt0(xm,sdtpldt0(xn,xp)))
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_16,c_277087]) ).

tff(c_277403,plain,
    aNaturalNumber0(sdtpldt0(xm,sdtpldt0(xn,xp))),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_147,c_143,c_277313]) ).

tff(c_7175,plain,
    ! [W2_219,W0_220,W1_221] :
      ( sdtlseqdt0(sdtpldt0(W2_219,W0_220),sdtpldt0(W2_219,W1_221))
      | ~ aNaturalNumber0(W2_219)
      | ~ sdtlseqdt0(W0_220,W1_221)
      | ( W1_221 = W0_220 )
      | ~ aNaturalNumber0(W1_221)
      | ~ aNaturalNumber0(W0_220) ),
    inference(cnfTransformation,[status(thm)],[f_234]) ).

tff(c_7304,plain,
    ! [W2_219,W0_220,W1_221] :
      ( iLess0(sdtpldt0(W2_219,W0_220),sdtpldt0(W2_219,W1_221))
      | ( sdtpldt0(W2_219,W1_221) = sdtpldt0(W2_219,W0_220) )
      | ~ aNaturalNumber0(sdtpldt0(W2_219,W1_221))
      | ~ aNaturalNumber0(sdtpldt0(W2_219,W0_220))
      | ~ aNaturalNumber0(W2_219)
      | ~ sdtlseqdt0(W0_220,W1_221)
      | ( W1_221 = W0_220 )
      | ~ aNaturalNumber0(W1_221)
      | ~ aNaturalNumber0(W0_220) ),
    inference(resolution,[status(thm)],[c_7175,c_99]) ).

tff(c_272425,plain,
    ! [W0_1016] :
      ( doDivides0(xp,W0_1016)
      | ~ iLess0(sdtpldt0(W0_1016,xn),sdtpldt0(xm,sdtpldt0(xn,xp)))
      | ~ doDivides0(xp,sdtasdt0(W0_1016,xr))
      | ~ aNaturalNumber0(W0_1016)
      | ~ aNaturalNumber0(xp)
      | ~ aNaturalNumber0(xn)
      | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_16,c_272342]) ).

tff(c_362568,plain,
    ! [W0_1124] :
      ( doDivides0(xp,W0_1124)
      | ~ iLess0(sdtpldt0(W0_1124,xn),sdtpldt0(xm,sdtpldt0(xn,xp)))
      | ~ doDivides0(xp,sdtasdt0(W0_1124,xr))
      | ~ aNaturalNumber0(W0_1124) ),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_147,c_143,c_272425]) ).

tff(c_362586,plain,
    ( doDivides0(xp,xm)
    | ~ doDivides0(xp,sdtasdt0(xm,xr))
    | ( sdtpldt0(xm,sdtpldt0(xn,xp)) = sdtpldt0(xm,xn) )
    | ~ aNaturalNumber0(sdtpldt0(xm,sdtpldt0(xn,xp)))
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xm)
    | ~ sdtlseqdt0(xn,sdtpldt0(xn,xp))
    | ( sdtpldt0(xn,xp) = xn )
    | ~ aNaturalNumber0(sdtpldt0(xn,xp))
    | ~ aNaturalNumber0(xn) ),
    inference(resolution,[status(thm)],[c_7304,c_362568]) ).

tff(c_362665,plain,
    ( doDivides0(xp,xm)
    | ( sdtpldt0(xm,sdtpldt0(xn,xp)) = sdtpldt0(xm,xn) )
    | ( sdtpldt0(xn,xp) = xn ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_1143,c_93608,c_145,c_12558,c_277403,c_13843,c_362586]) ).

tff(c_362666,plain,
    sdtpldt0(xm,sdtpldt0(xn,xp)) = sdtpldt0(xm,xn),
    inference(negUnitSimplification,[status(thm)],[c_27672,c_165,c_362665]) ).

tff(c_28975,plain,
    ! [W0_2,W1_3] :
      ( ( sdtmndt0(sdtpldt0(W0_2,W1_3),W0_2) = W1_3 )
      | ~ aNaturalNumber0(W1_3)
      | ~ aNaturalNumber0(W0_2) ),
    inference(resolution,[status(thm)],[c_10,c_28801]) ).

tff(c_364082,plain,
    ( ( sdtmndt0(sdtpldt0(xm,xn),xm) = sdtpldt0(xn,xp) )
    | ~ aNaturalNumber0(sdtpldt0(xn,xp))
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_362666,c_28975]) ).

tff(c_364343,plain,
    sdtpldt0(xn,xp) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_1143,c_28927,c_364082]) ).

tff(c_364345,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_27672,c_364343]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : NUM493+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % 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
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu Aug  3 15:25:51 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 296.22/250.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 296.22/250.57  
% 296.22/250.57  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 296.22/250.61  
% 296.22/250.61  Inference rules
% 296.22/250.61  ----------------------
% 296.22/250.61  #Ref     : 9
% 296.22/250.61  #Sup     : 76947
% 296.22/250.61  #Fact    : 14
% 296.22/250.61  #Define  : 0
% 296.22/250.61  #Split   : 55
% 296.22/250.61  #Chain   : 0
% 296.22/250.61  #Close   : 0
% 296.22/250.61  
% 296.22/250.61  Ordering : KBO
% 296.22/250.61  
% 296.22/250.61  Simplification rules
% 296.22/250.61  ----------------------
% 296.22/250.61  #Subsume      : 8286
% 296.22/250.61  #Demod        : 153721
% 296.22/250.61  #Tautology    : 15583
% 296.22/250.61  #SimpNegUnit  : 10868
% 296.22/250.61  #BackRed      : 607
% 296.22/250.61  
% 296.22/250.61  #Partial instantiations: 0
% 296.22/250.61  #Strategies tried      : 1
% 296.22/250.61  
% 296.22/250.61  Timing (in seconds)
% 296.22/250.61  ----------------------
% 296.22/250.61  Preprocessing        : 0.68
% 296.22/250.61  Parsing              : 0.34
% 296.22/250.61  CNF conversion       : 0.05
% 296.22/250.61  Main loop            : 248.86
% 296.22/250.61  Inferencing          : 11.42
% 296.22/250.61  Reduction            : 166.78
% 296.22/250.61  Demodulation         : 143.46
% 296.22/250.61  BG Simplification    : 0.84
% 296.22/250.61  Subsumption          : 55.66
% 296.22/250.61  Abstraction          : 1.40
% 296.22/250.61  MUC search           : 0.00
% 296.22/250.61  Cooper               : 0.00
% 296.22/250.61  Total                : 249.60
% 296.22/250.61  Index Insertion      : 0.00
% 296.22/250.61  Index Deletion       : 0.00
% 296.22/250.61  Index Matching       : 0.00
% 296.22/250.61  BG Taut test         : 0.00
%------------------------------------------------------------------------------