TSTP Solution File: NUM518+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM518+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n023.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 10:51:57 EDT 2023

% Result   : Theorem 107.80s 90.00s
% Output   : CNFRefutation 107.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  102 (  33 unt;  20 typ;   3 def)
%            Number of atoms       :  236 (  56 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  260 ( 106   ~; 109   |;  26   &)
%                                         (   3 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  13   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   7 con; 0-2 aty)
%            Number of variables   :   64 (;  63   !;   1   ?;   0   :)

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

%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(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_493,negated_conjecture,
    ~ ( doDivides0(xp,xn)
      | doDivides0(xp,xm) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

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

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

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

tff(f_403,definition,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( isPrime0(W0)
      <=> ( ( W0 != sz00 )
          & ( W0 != sz10 )
          & ! [W1] :
              ( ( aNaturalNumber0(W1)
                & doDivides0(W1,W0) )
             => ( ( W1 = sz10 )
                | ( W1 = W0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).

tff(f_470,hypothesis,
    ( aNaturalNumber0(xr)
    & doDivides0(xr,xk)
    & isPrime0(xr) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).

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

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

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

tff(f_481,hypothesis,
    doDivides0(xr,xn),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).

tff(f_323,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( ( W0 != sz00 )
          & doDivides0(W0,W1) )
       => ! [W2] :
            ( ( W2 = sdtsldt0(W1,W0) )
          <=> ( aNaturalNumber0(W2)
              & ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).

tff(f_489,hypothesis,
    ( doDivides0(xp,sdtsldt0(xn,xr))
    | doDivides0(xp,xm) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2645) ).

tff(f_81,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).

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

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

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

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/sandbox/benchmark/theBenchmark.p',mDivSum) ).

tff(f_335,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( ( doDivides0(W0,W1)
          & doDivides0(W1,W2) )
       => doDivides0(W0,W2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).

tff(c_205,plain,
    ~ doDivides0(xp,xn),
    inference(cnfTransformation,[status(thm)],[f_493]) ).

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

tff(c_408,plain,
    ! [W0_104] :
      ( ( sdtpldt0(W0_104,sz00) = W0_104 )
      | ~ aNaturalNumber0(W0_104) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_427,plain,
    sdtpldt0(xn,sz00) = xn,
    inference(resolution,[status(thm)],[c_147,c_408]) ).

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

tff(c_135,plain,
    ( ~ isPrime0(sz00)
    | ~ aNaturalNumber0(sz00) ),
    inference(cnfTransformation,[status(thm)],[f_403]) ).

tff(c_211,plain,
    ~ isPrime0(sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).

tff(c_181,plain,
    aNaturalNumber0(xr),
    inference(cnfTransformation,[status(thm)],[f_470]) ).

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

tff(c_328,plain,
    ! [W0_102] :
      ( ( sdtasdt0(sz10,W0_102) = W0_102 )
      | ~ aNaturalNumber0(W0_102) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_348,plain,
    sdtasdt0(sz10,xr) = xr,
    inference(resolution,[status(thm)],[c_181,c_328]) ).

tff(c_1689,plain,
    ! [W1_131,W0_132] :
      ( sdtlseqdt0(W1_131,sdtasdt0(W1_131,W0_132))
      | ( sz00 = W0_132 )
      | ~ aNaturalNumber0(W1_131)
      | ~ aNaturalNumber0(W0_132) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_1770,plain,
    ( sdtlseqdt0(sz10,xr)
    | ( xr = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xr) ),
    inference(superposition,[status(thm),theory(equality)],[c_348,c_1689]) ).

tff(c_1861,plain,
    ( sdtlseqdt0(sz10,xr)
    | ( xr = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_181,c_8,c_1770]) ).

tff(c_2254,plain,
    xr = sz00,
    inference(splitLeft,[status(thm)],[c_1861]) ).

tff(c_177,plain,
    isPrime0(xr),
    inference(cnfTransformation,[status(thm)],[f_470]) ).

tff(c_2281,plain,
    isPrime0(sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_2254,c_177]) ).

tff(c_2301,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_211,c_2281]) ).

tff(c_2303,plain,
    xr != sz00,
    inference(splitRight,[status(thm)],[c_1861]) ).

tff(c_193,plain,
    doDivides0(xr,xn),
    inference(cnfTransformation,[status(thm)],[f_481]) ).

tff(c_111,plain,
    ! [W1_71,W0_70] :
      ( aNaturalNumber0(sdtsldt0(W1_71,W0_70))
      | ~ doDivides0(W0_70,W1_71)
      | ( sz00 = W0_70 )
      | ~ aNaturalNumber0(W1_71)
      | ~ aNaturalNumber0(W0_70) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

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

tff(c_203,plain,
    ~ doDivides0(xp,xm),
    inference(cnfTransformation,[status(thm)],[f_493]) ).

tff(c_201,plain,
    ( doDivides0(xp,xm)
    | doDivides0(xp,sdtsldt0(xn,xr)) ),
    inference(cnfTransformation,[status(thm)],[f_489]) ).

tff(c_206,plain,
    doDivides0(xp,sdtsldt0(xn,xr)),
    inference(negUnitSimplification,[status(thm)],[c_203,c_201]) ).

tff(c_101287,plain,
    ! [W1_624,W0_625] :
      ( ( W1_624 = W0_625 )
      | ( sz10 = W1_624 )
      | ~ doDivides0(W1_624,W0_625)
      | ~ aNaturalNumber0(W1_624)
      | ~ isPrime0(W0_625)
      | ~ aNaturalNumber0(W0_625) ),
    inference(cnfTransformation,[status(thm)],[f_403]) ).

tff(c_101323,plain,
    ( ( sdtsldt0(xn,xr) = xp )
    | ( xp = sz10 )
    | ~ aNaturalNumber0(xp)
    | ~ isPrime0(sdtsldt0(xn,xr))
    | ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
    inference(resolution,[status(thm)],[c_206,c_101287]) ).

tff(c_101364,plain,
    ( ( sdtsldt0(xn,xr) = xp )
    | ( xp = sz10 )
    | ~ isPrime0(sdtsldt0(xn,xr))
    | ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_101323]) ).

tff(c_101381,plain,
    ~ aNaturalNumber0(sdtsldt0(xn,xr)),
    inference(splitLeft,[status(thm)],[c_101364]) ).

tff(c_101476,plain,
    ( ~ doDivides0(xr,xn)
    | ( xr = sz00 )
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xr) ),
    inference(resolution,[status(thm)],[c_111,c_101381]) ).

tff(c_101479,plain,
    xr = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_181,c_147,c_193,c_101476]) ).

tff(c_101481,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2303,c_101479]) ).

tff(c_101483,plain,
    aNaturalNumber0(sdtsldt0(xn,xr)),
    inference(splitRight,[status(thm)],[c_101364]) ).

tff(c_365,plain,
    ! [W0_103] :
      ( ( sdtasdt0(W0_103,sz10) = W0_103 )
      | ~ aNaturalNumber0(W0_103) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_384,plain,
    sdtasdt0(xn,sz10) = xn,
    inference(resolution,[status(thm)],[c_147,c_365]) ).

tff(c_28,plain,
    ! [W0_17] :
      ( ( sdtasdt0(W0_17,sz10) = W0_17 )
      | ~ aNaturalNumber0(W0_17) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_101617,plain,
    sdtasdt0(sdtsldt0(xn,xr),sz10) = sdtsldt0(xn,xr),
    inference(resolution,[status(thm)],[c_101483,c_28]) ).

tff(c_109,plain,
    ! [W0_70,W1_71] :
      ( ( sdtasdt0(W0_70,sdtsldt0(W1_71,W0_70)) = W1_71 )
      | ~ doDivides0(W0_70,W1_71)
      | ( sz00 = W0_70 )
      | ~ aNaturalNumber0(W1_71)
      | ~ aNaturalNumber0(W0_70) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_102920,plain,
    ! [W0_648,W1_649,W2_650] :
      ( ( sdtasdt0(sdtasdt0(W0_648,W1_649),W2_650) = sdtasdt0(W0_648,sdtasdt0(W1_649,W2_650)) )
      | ~ aNaturalNumber0(W2_650)
      | ~ aNaturalNumber0(W1_649)
      | ~ aNaturalNumber0(W0_648) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_219646,plain,
    ! [W0_1149,W1_1150,W2_1151] :
      ( ( sdtasdt0(W0_1149,sdtasdt0(sdtsldt0(W1_1150,W0_1149),W2_1151)) = sdtasdt0(W1_1150,W2_1151) )
      | ~ aNaturalNumber0(W2_1151)
      | ~ aNaturalNumber0(sdtsldt0(W1_1150,W0_1149))
      | ~ aNaturalNumber0(W0_1149)
      | ~ doDivides0(W0_1149,W1_1150)
      | ( sz00 = W0_1149 )
      | ~ aNaturalNumber0(W1_1150)
      | ~ aNaturalNumber0(W0_1149) ),
    inference(superposition,[status(thm),theory(equality)],[c_109,c_102920]) ).

tff(c_220153,plain,
    ( ( sdtasdt0(xr,sdtsldt0(xn,xr)) = sdtasdt0(xn,sz10) )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(sdtsldt0(xn,xr))
    | ~ aNaturalNumber0(xr)
    | ~ doDivides0(xr,xn)
    | ( xr = sz00 )
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xr) ),
    inference(superposition,[status(thm),theory(equality)],[c_101617,c_219646]) ).

tff(c_220423,plain,
    ( ( sdtasdt0(xr,sdtsldt0(xn,xr)) = xn )
    | ( xr = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_181,c_147,c_193,c_181,c_101483,c_8,c_384,c_220153]) ).

tff(c_220424,plain,
    sdtasdt0(xr,sdtsldt0(xn,xr)) = xn,
    inference(negUnitSimplification,[status(thm)],[c_2303,c_220423]) ).

tff(c_728,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_114014,plain,
    ! [W0_708] :
      ( ( sdtasdt0(xr,W0_708) = sdtasdt0(W0_708,xr) )
      | ~ aNaturalNumber0(W0_708) ),
    inference(resolution,[status(thm)],[c_181,c_728]) ).

tff(c_114141,plain,
    sdtasdt0(sdtsldt0(xn,xr),xr) = sdtasdt0(xr,sdtsldt0(xn,xr)),
    inference(resolution,[status(thm)],[c_101483,c_114014]) ).

tff(c_220443,plain,
    sdtasdt0(sdtsldt0(xn,xr),xr) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_220424,c_114141]) ).

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

tff(c_220879,plain,
    ( doDivides0(sdtsldt0(xn,xr),xn)
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xr))
    | ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
    inference(superposition,[status(thm),theory(equality)],[c_220443,c_101]) ).

tff(c_221016,plain,
    doDivides0(sdtsldt0(xn,xr),xn),
    inference(demodulation,[status(thm),theory(equality)],[c_101483,c_147,c_220443,c_181,c_220879]) ).

tff(c_32,plain,
    ! [W0_18] :
      ( ( sdtasdt0(W0_18,sz00) = sz00 )
      | ~ aNaturalNumber0(W0_18) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_101621,plain,
    sdtasdt0(sdtsldt0(xn,xr),sz00) = sz00,
    inference(resolution,[status(thm)],[c_101483,c_32]) ).

tff(c_102170,plain,
    ( doDivides0(sdtsldt0(xn,xr),sz00)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),sz00))
    | ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
    inference(superposition,[status(thm),theory(equality)],[c_101621,c_101]) ).

tff(c_102182,plain,
    doDivides0(sdtsldt0(xn,xr),sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_101483,c_4,c_101621,c_4,c_102170]) ).

tff(c_104976,plain,
    ! [W0_660,W1_661,W2_662] :
      ( doDivides0(W0_660,sdtpldt0(W1_661,W2_662))
      | ~ doDivides0(W0_660,W2_662)
      | ~ doDivides0(W0_660,W1_661)
      | ~ aNaturalNumber0(W2_662)
      | ~ aNaturalNumber0(W1_661)
      | ~ aNaturalNumber0(W0_660) ),
    inference(cnfTransformation,[status(thm)],[f_347]) ).

tff(c_113,plain,
    ! [W0_74,W2_76,W1_75] :
      ( doDivides0(W0_74,W2_76)
      | ~ doDivides0(W1_75,W2_76)
      | ~ doDivides0(W0_74,W1_75)
      | ~ aNaturalNumber0(W2_76)
      | ~ aNaturalNumber0(W1_75)
      | ~ aNaturalNumber0(W0_74) ),
    inference(cnfTransformation,[status(thm)],[f_335]) ).

tff(c_205347,plain,
    ! [W0_1057,W1_1058,W2_1059,W0_1060] :
      ( doDivides0(W0_1057,sdtpldt0(W1_1058,W2_1059))
      | ~ doDivides0(W0_1057,W0_1060)
      | ~ aNaturalNumber0(sdtpldt0(W1_1058,W2_1059))
      | ~ aNaturalNumber0(W0_1057)
      | ~ doDivides0(W0_1060,W2_1059)
      | ~ doDivides0(W0_1060,W1_1058)
      | ~ aNaturalNumber0(W2_1059)
      | ~ aNaturalNumber0(W1_1058)
      | ~ aNaturalNumber0(W0_1060) ),
    inference(resolution,[status(thm)],[c_104976,c_113]) ).

tff(c_205515,plain,
    ! [W1_1058,W2_1059] :
      ( doDivides0(xp,sdtpldt0(W1_1058,W2_1059))
      | ~ aNaturalNumber0(sdtpldt0(W1_1058,W2_1059))
      | ~ aNaturalNumber0(xp)
      | ~ doDivides0(sdtsldt0(xn,xr),W2_1059)
      | ~ doDivides0(sdtsldt0(xn,xr),W1_1058)
      | ~ aNaturalNumber0(W2_1059)
      | ~ aNaturalNumber0(W1_1058)
      | ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
    inference(resolution,[status(thm)],[c_206,c_205347]) ).

tff(c_206108,plain,
    ! [W1_1062,W2_1063] :
      ( doDivides0(xp,sdtpldt0(W1_1062,W2_1063))
      | ~ aNaturalNumber0(sdtpldt0(W1_1062,W2_1063))
      | ~ doDivides0(sdtsldt0(xn,xr),W2_1063)
      | ~ doDivides0(sdtsldt0(xn,xr),W1_1062)
      | ~ aNaturalNumber0(W2_1063)
      | ~ aNaturalNumber0(W1_1062) ),
    inference(demodulation,[status(thm),theory(equality)],[c_101483,c_143,c_205515]) ).

tff(c_206127,plain,
    ! [W1_1062] :
      ( doDivides0(xp,sdtpldt0(W1_1062,sz00))
      | ~ aNaturalNumber0(sdtpldt0(W1_1062,sz00))
      | ~ doDivides0(sdtsldt0(xn,xr),W1_1062)
      | ~ aNaturalNumber0(sz00)
      | ~ aNaturalNumber0(W1_1062) ),
    inference(resolution,[status(thm)],[c_102182,c_206108]) ).

tff(c_206151,plain,
    ! [W1_1062] :
      ( doDivides0(xp,sdtpldt0(W1_1062,sz00))
      | ~ aNaturalNumber0(sdtpldt0(W1_1062,sz00))
      | ~ doDivides0(sdtsldt0(xn,xr),W1_1062)
      | ~ aNaturalNumber0(W1_1062) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_206127]) ).

tff(c_221035,plain,
    ( doDivides0(xp,sdtpldt0(xn,sz00))
    | ~ aNaturalNumber0(sdtpldt0(xn,sz00))
    | ~ aNaturalNumber0(xn) ),
    inference(resolution,[status(thm)],[c_221016,c_206151]) ).

tff(c_221055,plain,
    doDivides0(xp,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_147,c_427,c_427,c_221035]) ).

tff(c_221057,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_205,c_221055]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM518+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 15:08:07 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 107.80/90.00  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 107.80/90.01  
% 107.80/90.01  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 107.82/90.05  
% 107.82/90.05  Inference rules
% 107.82/90.05  ----------------------
% 107.82/90.05  #Ref     : 16
% 107.82/90.05  #Sup     : 45815
% 107.82/90.05  #Fact    : 2
% 107.82/90.05  #Define  : 0
% 107.82/90.05  #Split   : 96
% 107.82/90.05  #Chain   : 0
% 107.82/90.05  #Close   : 0
% 107.82/90.05  
% 107.82/90.05  Ordering : KBO
% 107.82/90.05  
% 107.82/90.05  Simplification rules
% 107.82/90.05  ----------------------
% 107.82/90.05  #Subsume      : 7383
% 107.82/90.05  #Demod        : 89969
% 107.82/90.05  #Tautology    : 13696
% 107.82/90.05  #SimpNegUnit  : 8451
% 107.82/90.05  #BackRed      : 1770
% 107.82/90.05  
% 107.82/90.05  #Partial instantiations: 0
% 107.82/90.05  #Strategies tried      : 1
% 107.82/90.05  
% 107.82/90.05  Timing (in seconds)
% 107.82/90.05  ----------------------
% 108.06/90.06  Preprocessing        : 0.71
% 108.06/90.06  Parsing              : 0.36
% 108.06/90.06  CNF conversion       : 0.05
% 108.06/90.06  Main loop            : 88.25
% 108.06/90.06  Inferencing          : 7.45
% 108.06/90.06  Reduction            : 58.28
% 108.06/90.06  Demodulation         : 48.53
% 108.06/90.06  BG Simplification    : 0.35
% 108.06/90.06  Subsumption          : 18.29
% 108.06/90.06  Abstraction          : 0.65
% 108.06/90.06  MUC search           : 0.00
% 108.06/90.06  Cooper               : 0.00
% 108.06/90.06  Total                : 89.04
% 108.06/90.06  Index Insertion      : 0.00
% 108.06/90.06  Index Deletion       : 0.00
% 108.06/90.06  Index Matching       : 0.00
% 108.06/90.06  BG Taut test         : 0.00
%------------------------------------------------------------------------------