TSTP Solution File: NUM494+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM494+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 : n001.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 58.99s 44.44s
% Output   : CNFRefutation 59.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   37
% Syntax   : Number of formulae    :  163 (  70 unt;  19 typ;   3 def)
%            Number of atoms       :  327 (  94 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  346 ( 163   ~; 142   |;  23   &)
%                                         (   3 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 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    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :   82 (;  81   !;   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_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_423,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).

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_442,hypothesis,
    ( isPrime0(xp)
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).

tff(f_443,hypothesis,
    sdtlseqdt0(xp,xn),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).

tff(f_444,hypothesis,
    xr = sdtmndt0(xn,xp),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefDiff) ).

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

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

tff(f_212,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtlseqdt0(W0,W1)
        | ( ( W1 != W0 )
          & sdtlseqdt0(W1,W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).

tff(f_454,negated_conjecture,
    ~ ( ( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) )
      & sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

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

tff(f_61,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).

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

tff(f_115,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
          | ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
       => ( W1 = W2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).

tff(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_169,plain,
    ~ isPrime0(sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).

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

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

tff(c_19166,plain,
    ! [W0_308] :
      ( ( sdtasdt0(sz10,W0_308) = W0_308 )
      | ~ aNaturalNumber0(W0_308) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_19183,plain,
    sdtasdt0(sz10,xp) = xp,
    inference(resolution,[status(thm)],[c_143,c_19166]) ).

tff(c_21852,plain,
    ! [W1_355,W0_356] :
      ( sdtlseqdt0(W1_355,sdtasdt0(W1_355,W0_356))
      | ( sz00 = W0_356 )
      | ~ aNaturalNumber0(W1_355)
      | ~ aNaturalNumber0(W0_356) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_21972,plain,
    ( sdtlseqdt0(sz10,xp)
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_19183,c_21852]) ).

tff(c_22082,plain,
    ( sdtlseqdt0(sz10,xp)
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_21972]) ).

tff(c_31712,plain,
    xp = sz00,
    inference(splitLeft,[status(thm)],[c_22082]) ).

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

tff(c_31755,plain,
    isPrime0(sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_31712,c_153]) ).

tff(c_31789,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_169,c_31755]) ).

tff(c_31791,plain,
    xp != sz00,
    inference(splitRight,[status(thm)],[c_22082]) ).

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

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_22106,plain,
    ! [W1_357,W0_358] :
      ( aNaturalNumber0(sdtmndt0(W1_357,W0_358))
      | ~ sdtlseqdt0(W0_358,W1_357)
      | ~ aNaturalNumber0(W1_357)
      | ~ aNaturalNumber0(W0_358) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_22152,plain,
    ( aNaturalNumber0(xr)
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_157,c_22106]) ).

tff(c_22169,plain,
    aNaturalNumber0(xr),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_22152]) ).

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

tff(c_19609,plain,
    ! [W1_321,W0_322] :
      ( ( sdtpldt0(W1_321,W0_322) = sdtpldt0(W0_322,W1_321) )
      | ~ aNaturalNumber0(W1_321)
      | ~ aNaturalNumber0(W0_322) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_19629,plain,
    ! [W0_322] :
      ( ( sdtpldt0(xm,W0_322) = sdtpldt0(W0_322,xm) )
      | ~ aNaturalNumber0(W0_322) ),
    inference(resolution,[status(thm)],[c_145,c_19609]) ).

tff(c_22220,plain,
    sdtpldt0(xr,xm) = sdtpldt0(xm,xr),
    inference(resolution,[status(thm)],[c_22169,c_19629]) ).

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_609,plain,
    ! [W1_112,W0_113] :
      ( ( sdtpldt0(W1_112,W0_113) = sdtpldt0(W0_113,W1_112) )
      | ~ aNaturalNumber0(W1_112)
      | ~ aNaturalNumber0(W0_113) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_634,plain,
    ! [W0_114] :
      ( ( sdtpldt0(xm,W0_114) = sdtpldt0(W0_114,xm) )
      | ~ aNaturalNumber0(W0_114) ),
    inference(resolution,[status(thm)],[c_145,c_609]) ).

tff(c_668,plain,
    sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
    inference(resolution,[status(thm)],[c_147,c_634]) ).

tff(c_784,plain,
    ( aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_668,c_10]) ).

tff(c_788,plain,
    aNaturalNumber0(sdtpldt0(xm,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_784]) ).

tff(c_914,plain,
    ! [W1_119,W0_120] :
      ( sdtlseqdt0(W1_119,W0_120)
      | sdtlseqdt0(W0_120,W1_119)
      | ~ aNaturalNumber0(W1_119)
      | ~ aNaturalNumber0(W0_120) ),
    inference(cnfTransformation,[status(thm)],[f_212]) ).

tff(c_165,plain,
    ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
    | ( sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
    inference(cnfTransformation,[status(thm)],[f_454]) ).

tff(c_170,plain,
    ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
    inference(splitLeft,[status(thm)],[c_165]) ).

tff(c_780,plain,
    ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xm,xn),xp)),
    inference(demodulation,[status(thm),theory(equality)],[c_668,c_170]) ).

tff(c_922,plain,
    ( sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xn),xp),sdtpldt0(sdtpldt0(xr,xm),xp))
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp))
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
    inference(resolution,[status(thm)],[c_914,c_780]) ).

tff(c_950,plain,
    ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)),
    inference(splitLeft,[status(thm)],[c_922]) ).

tff(c_953,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
    inference(resolution,[status(thm)],[c_10,c_950]) ).

tff(c_956,plain,
    ~ aNaturalNumber0(sdtpldt0(xr,xm)),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_953]) ).

tff(c_959,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xr) ),
    inference(resolution,[status(thm)],[c_10,c_956]) ).

tff(c_962,plain,
    ~ aNaturalNumber0(xr),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_959]) ).

tff(c_1218,plain,
    ! [W1_125,W0_126] :
      ( aNaturalNumber0(sdtmndt0(W1_125,W0_126))
      | ~ sdtlseqdt0(W0_126,W1_125)
      | ~ aNaturalNumber0(W1_125)
      | ~ aNaturalNumber0(W0_126) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_1249,plain,
    ( aNaturalNumber0(xr)
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_157,c_1218]) ).

tff(c_1261,plain,
    aNaturalNumber0(xr),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_1249]) ).

tff(c_1263,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_962,c_1261]) ).

tff(c_1265,plain,
    aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)),
    inference(splitRight,[status(thm)],[c_922]) ).

tff(c_921,plain,
    ( sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xn),xp),sdtpldt0(sdtpldt0(xr,xm),xp))
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)) ),
    inference(resolution,[status(thm)],[c_914,c_780]) ).

tff(c_1466,plain,
    ( sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xn),xp),sdtpldt0(sdtpldt0(xr,xm),xp))
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1265,c_921]) ).

tff(c_1467,plain,
    ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)),
    inference(splitLeft,[status(thm)],[c_1466]) ).

tff(c_1471,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(resolution,[status(thm)],[c_10,c_1467]) ).

tff(c_1475,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_788,c_143,c_1471]) ).

tff(c_1477,plain,
    aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)),
    inference(splitRight,[status(thm)],[c_1466]) ).

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_13778,plain,
    ! [W0_267,W1_268] :
      ( ( sdtpldt0(W0_267,sdtmndt0(W1_268,W0_267)) = W1_268 )
      | ~ sdtlseqdt0(W0_267,W1_268)
      | ~ aNaturalNumber0(W1_268)
      | ~ aNaturalNumber0(W0_267) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_13797,plain,
    ( ( sdtpldt0(xp,xr) = xn )
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_157,c_13778]) ).

tff(c_13801,plain,
    sdtpldt0(xp,xr) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_13797]) ).

tff(c_7705,plain,
    ! [W1_200,W0_201] :
      ( aNaturalNumber0(sdtmndt0(W1_200,W0_201))
      | ~ sdtlseqdt0(W0_201,W1_200)
      | ~ aNaturalNumber0(W1_200)
      | ~ aNaturalNumber0(W0_201) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_7751,plain,
    ( aNaturalNumber0(xr)
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_157,c_7705]) ).

tff(c_7768,plain,
    aNaturalNumber0(xr),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_7751]) ).

tff(c_18092,plain,
    ! [W0_301] :
      ( ( sdtpldt0(xp,W0_301) = sdtpldt0(W0_301,xp) )
      | ~ aNaturalNumber0(W0_301) ),
    inference(resolution,[status(thm)],[c_143,c_609]) ).

tff(c_18125,plain,
    sdtpldt0(xr,xp) = sdtpldt0(xp,xr),
    inference(resolution,[status(thm)],[c_7768,c_18092]) ).

tff(c_18203,plain,
    sdtpldt0(xr,xp) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_13801,c_18125]) ).

tff(c_17401,plain,
    ! [W0_297,W1_298,W2_299] :
      ( ( sdtpldt0(sdtpldt0(W0_297,W1_298),W2_299) = sdtpldt0(W0_297,sdtpldt0(W1_298,W2_299)) )
      | ~ aNaturalNumber0(W2_299)
      | ~ aNaturalNumber0(W1_298)
      | ~ aNaturalNumber0(W0_297) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_629,plain,
    ! [W0_113] :
      ( ( sdtpldt0(xm,W0_113) = sdtpldt0(W0_113,xm) )
      | ~ aNaturalNumber0(W0_113) ),
    inference(resolution,[status(thm)],[c_145,c_609]) ).

tff(c_7819,plain,
    sdtpldt0(xr,xm) = sdtpldt0(xm,xr),
    inference(resolution,[status(thm)],[c_7768,c_629]) ).

tff(c_11997,plain,
    ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(sdtpldt0(xm,xn),xp)),
    inference(demodulation,[status(thm),theory(equality)],[c_7819,c_780]) ).

tff(c_17512,plain,
    ( ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(sdtpldt0(xm,xn),xp))
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_17401,c_11997]) ).

tff(c_17702,plain,
    ~ sdtlseqdt0(sdtpldt0(xm,sdtpldt0(xr,xp)),sdtpldt0(sdtpldt0(xm,xn),xp)),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_7768,c_143,c_17512]) ).

tff(c_19141,plain,
    ~ sdtlseqdt0(sdtpldt0(xm,xn),sdtpldt0(sdtpldt0(xm,xn),xp)),
    inference(demodulation,[status(thm),theory(equality)],[c_18203,c_17702]) ).

tff(c_19147,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp))
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(resolution,[status(thm)],[c_52,c_19141]) ).

tff(c_19158,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_788,c_1477,c_143,c_19147]) ).

tff(c_19159,plain,
    sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp),
    inference(splitRight,[status(thm)],[c_165]) ).

tff(c_19507,plain,
    ! [W0_316,W1_317] :
      ( aNaturalNumber0(sdtpldt0(W0_316,W1_317))
      | ~ aNaturalNumber0(W1_317)
      | ~ aNaturalNumber0(W0_316) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_19555,plain,
    ( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
    inference(superposition,[status(thm),theory(equality)],[c_19159,c_19507]) ).

tff(c_19581,plain,
    ( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ aNaturalNumber0(sdtpldt0(xr,xm)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_19555]) ).

tff(c_19709,plain,
    ~ aNaturalNumber0(sdtpldt0(xr,xm)),
    inference(splitLeft,[status(thm)],[c_19581]) ).

tff(c_19712,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xr) ),
    inference(resolution,[status(thm)],[c_10,c_19709]) ).

tff(c_19715,plain,
    ~ aNaturalNumber0(xr),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_19712]) ).

tff(c_20431,plain,
    ! [W1_337,W0_338] :
      ( aNaturalNumber0(sdtmndt0(W1_337,W0_338))
      | ~ sdtlseqdt0(W0_338,W1_337)
      | ~ aNaturalNumber0(W1_337)
      | ~ aNaturalNumber0(W0_338) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_20465,plain,
    ( aNaturalNumber0(xr)
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_157,c_20431]) ).

tff(c_20478,plain,
    aNaturalNumber0(xr),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_20465]) ).

tff(c_20480,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_19715,c_20478]) ).

tff(c_20482,plain,
    aNaturalNumber0(sdtpldt0(xr,xm)),
    inference(splitRight,[status(thm)],[c_19581]) ).

tff(c_20,plain,
    ! [W0_11] :
      ( ( sdtpldt0(W0_11,sz00) = W0_11 )
      | ~ aNaturalNumber0(W0_11) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_20511,plain,
    sdtpldt0(sdtpldt0(xr,xm),sz00) = sdtpldt0(xr,xm),
    inference(resolution,[status(thm)],[c_20482,c_20]) ).

tff(c_56082,plain,
    sdtpldt0(sdtpldt0(xm,xr),sz00) = sdtpldt0(xm,xr),
    inference(demodulation,[status(thm),theory(equality)],[c_22220,c_22220,c_20511]) ).

tff(c_58007,plain,
    ! [W0_792,W1_793] :
      ( ( sdtpldt0(W0_792,sdtmndt0(W1_793,W0_792)) = W1_793 )
      | ~ sdtlseqdt0(W0_792,W1_793)
      | ~ aNaturalNumber0(W1_793)
      | ~ aNaturalNumber0(W0_792) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_58023,plain,
    ( ( sdtpldt0(xp,xr) = xn )
    | ~ sdtlseqdt0(xp,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_157,c_58007]) ).

tff(c_58027,plain,
    sdtpldt0(xp,xr) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_58023]) ).

tff(c_19630,plain,
    ! [W0_322] :
      ( ( sdtpldt0(xp,W0_322) = sdtpldt0(W0_322,xp) )
      | ~ aNaturalNumber0(W0_322) ),
    inference(resolution,[status(thm)],[c_143,c_19609]) ).

tff(c_22215,plain,
    sdtpldt0(xr,xp) = sdtpldt0(xp,xr),
    inference(resolution,[status(thm)],[c_22169,c_19630]) ).

tff(c_58056,plain,
    sdtpldt0(xr,xp) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_58027,c_22215]) ).

tff(c_60470,plain,
    ! [W0_817,W1_818,W2_819] :
      ( ( sdtpldt0(sdtpldt0(W0_817,W1_818),W2_819) = sdtpldt0(W0_817,sdtpldt0(W1_818,W2_819)) )
      | ~ aNaturalNumber0(W2_819)
      | ~ aNaturalNumber0(W1_818)
      | ~ aNaturalNumber0(W0_817) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_19634,plain,
    ! [W0_323] :
      ( ( sdtpldt0(xm,W0_323) = sdtpldt0(W0_323,xm) )
      | ~ aNaturalNumber0(W0_323) ),
    inference(resolution,[status(thm)],[c_145,c_19609]) ).

tff(c_19668,plain,
    sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
    inference(resolution,[status(thm)],[c_147,c_19634]) ).

tff(c_20596,plain,
    sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xm,xn),xp),
    inference(demodulation,[status(thm),theory(equality)],[c_19668,c_19159]) ).

tff(c_56083,plain,
    sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(sdtpldt0(xm,xn),xp),
    inference(demodulation,[status(thm),theory(equality)],[c_22220,c_20596]) ).

tff(c_21498,plain,
    ! [W0_351] :
      ( ( sdtpldt0(xp,W0_351) = sdtpldt0(W0_351,xp) )
      | ~ aNaturalNumber0(W0_351) ),
    inference(resolution,[status(thm)],[c_143,c_19609]) ).

tff(c_21561,plain,
    sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(xp,sdtpldt0(xr,xm)),
    inference(resolution,[status(thm)],[c_20482,c_21498]) ).

tff(c_56395,plain,
    sdtpldt0(sdtpldt0(xm,xn),xp) = sdtpldt0(xp,sdtpldt0(xm,xr)),
    inference(demodulation,[status(thm),theory(equality)],[c_56083,c_22220,c_22220,c_21561]) ).

tff(c_56396,plain,
    sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(xp,sdtpldt0(xm,xr)),
    inference(demodulation,[status(thm),theory(equality)],[c_56395,c_56083]) ).

tff(c_60526,plain,
    ( ( sdtpldt0(xp,sdtpldt0(xm,xr)) = sdtpldt0(xm,sdtpldt0(xr,xp)) )
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_60470,c_56396]) ).

tff(c_60706,plain,
    sdtpldt0(xp,sdtpldt0(xm,xr)) = sdtpldt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_22169,c_143,c_58056,c_60526]) ).

tff(c_56086,plain,
    aNaturalNumber0(sdtpldt0(xm,xr)),
    inference(demodulation,[status(thm),theory(equality)],[c_22220,c_20482]) ).

tff(c_58537,plain,
    ! [W0_799,W2_800,W1_801] :
      ( ( sdtpldt0(W0_799,W2_800) != sdtpldt0(W0_799,W1_801) )
      | ( W2_800 = W1_801 )
      | ~ aNaturalNumber0(W2_800)
      | ~ aNaturalNumber0(W1_801)
      | ~ aNaturalNumber0(W0_799) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_58579,plain,
    ! [W1_801] :
      ( ( sdtpldt0(sdtpldt0(xm,xr),W1_801) != sdtpldt0(xp,sdtpldt0(xm,xr)) )
      | ( xp = W1_801 )
      | ~ aNaturalNumber0(xp)
      | ~ aNaturalNumber0(W1_801)
      | ~ aNaturalNumber0(sdtpldt0(xm,xr)) ),
    inference(superposition,[status(thm),theory(equality)],[c_56396,c_58537]) ).

tff(c_58695,plain,
    ! [W1_801] :
      ( ( sdtpldt0(sdtpldt0(xm,xr),W1_801) != sdtpldt0(xp,sdtpldt0(xm,xr)) )
      | ( xp = W1_801 )
      | ~ aNaturalNumber0(W1_801) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56086,c_143,c_58579]) ).

tff(c_78111,plain,
    ! [W1_903] :
      ( ( sdtpldt0(sdtpldt0(xm,xr),W1_903) != sdtpldt0(xm,xn) )
      | ( xp = W1_903 )
      | ~ aNaturalNumber0(W1_903) ),
    inference(demodulation,[status(thm),theory(equality)],[c_60706,c_58695]) ).

tff(c_78127,plain,
    ( ( sdtpldt0(xm,xr) != sdtpldt0(xm,xn) )
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sz00) ),
    inference(superposition,[status(thm),theory(equality)],[c_56082,c_78111]) ).

tff(c_78155,plain,
    ( ( sdtpldt0(xm,xr) != sdtpldt0(xm,xn) )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_78127]) ).

tff(c_78156,plain,
    sdtpldt0(xm,xr) != sdtpldt0(xm,xn),
    inference(negUnitSimplification,[status(thm)],[c_31791,c_78155]) ).

tff(c_20600,plain,
    ( aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_19668,c_10]) ).

tff(c_20604,plain,
    aNaturalNumber0(sdtpldt0(xm,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_20600]) ).

tff(c_64939,plain,
    sdtpldt0(sdtpldt0(xm,xn),xp) = sdtpldt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_60706,c_56395]) ).

tff(c_20481,plain,
    aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
    inference(splitRight,[status(thm)],[c_19581]) ).

tff(c_20594,plain,
    aNaturalNumber0(sdtpldt0(sdtpldt0(xm,xn),xp)),
    inference(demodulation,[status(thm),theory(equality)],[c_19668,c_20481]) ).

tff(c_21558,plain,
    sdtpldt0(sdtpldt0(sdtpldt0(xm,xn),xp),xp) = sdtpldt0(xp,sdtpldt0(sdtpldt0(xm,xn),xp)),
    inference(resolution,[status(thm)],[c_20594,c_21498]) ).

tff(c_90076,plain,
    sdtpldt0(xp,sdtpldt0(xm,xn)) = sdtpldt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_64939,c_64939,c_64939,c_21558]) ).

tff(c_64937,plain,
    sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_60706,c_56396]) ).

tff(c_38,plain,
    ! [W2_24,W0_22,W1_23] :
      ( ( sdtpldt0(W2_24,W0_22) != sdtpldt0(W1_23,W0_22) )
      | ( W2_24 = W1_23 )
      | ~ aNaturalNumber0(W2_24)
      | ~ aNaturalNumber0(W1_23)
      | ~ aNaturalNumber0(W0_22) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_159483,plain,
    ! [W2_1251,W2_1252,W0_1253,W1_1254] :
      ( ( sdtpldt0(W2_1251,W2_1252) != sdtpldt0(W0_1253,sdtpldt0(W1_1254,W2_1252)) )
      | ( sdtpldt0(W0_1253,W1_1254) = W2_1251 )
      | ~ aNaturalNumber0(W2_1251)
      | ~ aNaturalNumber0(sdtpldt0(W0_1253,W1_1254))
      | ~ aNaturalNumber0(W2_1252)
      | ~ aNaturalNumber0(W2_1252)
      | ~ aNaturalNumber0(W1_1254)
      | ~ aNaturalNumber0(W0_1253) ),
    inference(superposition,[status(thm),theory(equality)],[c_60470,c_38]) ).

tff(c_159776,plain,
    ! [W0_1253,W1_1254] :
      ( ( sdtpldt0(W0_1253,sdtpldt0(W1_1254,xp)) != sdtpldt0(xm,xn) )
      | ( sdtpldt0(xm,xr) = sdtpldt0(W0_1253,W1_1254) )
      | ~ aNaturalNumber0(sdtpldt0(xm,xr))
      | ~ aNaturalNumber0(sdtpldt0(W0_1253,W1_1254))
      | ~ aNaturalNumber0(xp)
      | ~ aNaturalNumber0(xp)
      | ~ aNaturalNumber0(W1_1254)
      | ~ aNaturalNumber0(W0_1253) ),
    inference(superposition,[status(thm),theory(equality)],[c_64937,c_159483]) ).

tff(c_160352,plain,
    ! [W0_1257,W1_1258] :
      ( ( sdtpldt0(W0_1257,sdtpldt0(W1_1258,xp)) != sdtpldt0(xm,xn) )
      | ( sdtpldt0(xm,xr) = sdtpldt0(W0_1257,W1_1258) )
      | ~ aNaturalNumber0(sdtpldt0(W0_1257,W1_1258))
      | ~ aNaturalNumber0(W1_1258)
      | ~ aNaturalNumber0(W0_1257) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_143,c_56086,c_159776]) ).

tff(c_160532,plain,
    ( ( sdtpldt0(xp,sdtpldt0(sdtpldt0(xm,xn),xp)) != sdtpldt0(xm,xn) )
    | ( sdtpldt0(xp,sdtpldt0(xm,xn)) = sdtpldt0(xm,xr) )
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_90076,c_160352]) ).

tff(c_160816,plain,
    sdtpldt0(xm,xr) = sdtpldt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_20604,c_20604,c_90076,c_90076,c_64939,c_160532]) ).

tff(c_160818,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_78156,c_160816]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : NUM494+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % 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
% 0.18/0.37  % Computer : n001.cluster.edu
% 0.18/0.37  % Model    : x86_64 x86_64
% 0.18/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.37  % Memory   : 8042.1875MB
% 0.18/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.37  % CPULimit : 300
% 0.18/0.37  % WCLimit  : 300
% 0.18/0.37  % DateTime : Thu Aug  3 15:22:55 EDT 2023
% 0.18/0.37  % CPUTime  : 
% 58.99/44.44  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.99/44.46  
% 58.99/44.46  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 59.23/44.50  
% 59.23/44.50  Inference rules
% 59.23/44.50  ----------------------
% 59.23/44.50  #Ref     : 26
% 59.23/44.51  #Sup     : 33071
% 59.23/44.51  #Fact    : 12
% 59.23/44.51  #Define  : 0
% 59.23/44.51  #Split   : 132
% 59.23/44.51  #Chain   : 0
% 59.23/44.51  #Close   : 0
% 59.23/44.51  
% 59.23/44.51  Ordering : KBO
% 59.23/44.51  
% 59.23/44.51  Simplification rules
% 59.23/44.51  ----------------------
% 59.23/44.51  #Subsume      : 3889
% 59.23/44.51  #Demod        : 58735
% 59.23/44.51  #Tautology    : 10476
% 59.23/44.51  #SimpNegUnit  : 6112
% 59.23/44.51  #BackRed      : 2661
% 59.23/44.51  
% 59.23/44.51  #Partial instantiations: 0
% 59.23/44.51  #Strategies tried      : 1
% 59.23/44.51  
% 59.23/44.51  Timing (in seconds)
% 59.23/44.51  ----------------------
% 59.23/44.51  Preprocessing        : 0.69
% 59.23/44.51  Parsing              : 0.35
% 59.23/44.51  CNF conversion       : 0.05
% 59.23/44.51  Main loop            : 42.69
% 59.23/44.51  Inferencing          : 4.40
% 59.23/44.51  Reduction            : 26.63
% 59.23/44.51  Demodulation         : 21.77
% 59.23/44.51  BG Simplification    : 0.27
% 59.23/44.51  Subsumption          : 9.48
% 59.23/44.51  Abstraction          : 0.43
% 59.23/44.51  MUC search           : 0.00
% 59.23/44.51  Cooper               : 0.00
% 59.23/44.51  Total                : 43.47
% 59.23/44.51  Index Insertion      : 0.00
% 59.23/44.51  Index Deletion       : 0.00
% 59.23/44.51  Index Matching       : 0.00
% 59.23/44.51  BG Taut test         : 0.00
%------------------------------------------------------------------------------