TSTP Solution File: NUM498+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM498+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 : 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 10:51:53 EDT 2023

% Result   : Theorem 10.17s 3.41s
% Output   : CNFRefutation 10.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   36
% Syntax   : Number of formulae    :  152 (  74 unt;  19 typ;   3 def)
%            Number of atoms       :  277 ( 112 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  237 (  93   ~; 102   |;  23   &)
%                                         (   3 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 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   :   50 (;  49   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > 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(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_464,negated_conjecture,
    ~ ( ( ( xk = sz00 )
        | ( xk = sz10 ) )
     => ( doDivides0(xp,xn)
        | doDivides0(xp,xm) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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

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_93,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( sdtasdt0(W0,sz00) = sz00 )
        & ( sz00 = sdtasdt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).

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_442,hypothesis,
    ( isPrime0(xp)
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).

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_455,hypothesis,
    ( ( xn != xp )
    & sdtlseqdt0(xn,xp)
    & ( xm != xp )
    & sdtlseqdt0(xm,xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).

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

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

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_456,hypothesis,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).

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_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(c_169,plain,
    ~ doDivides0(xp,xm),
    inference(cnfTransformation,[status(thm)],[f_464]) ).

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

tff(c_4101,plain,
    ! [W0_180] :
      ( ( sdtasdt0(sz10,W0_180) = W0_180 )
      | ~ aNaturalNumber0(W0_180) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_4120,plain,
    sdtasdt0(sz10,xm) = xm,
    inference(resolution,[status(thm)],[c_145,c_4101]) ).

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

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

tff(c_3931,plain,
    ! [W0_175] :
      ( ( sdtasdt0(sz00,W0_175) = sz00 )
      | ~ aNaturalNumber0(W0_175) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_3949,plain,
    sdtasdt0(sz00,xm) = sz00,
    inference(resolution,[status(thm)],[c_145,c_3931]) ).

tff(c_4119,plain,
    sdtasdt0(sz10,xn) = xn,
    inference(resolution,[status(thm)],[c_147,c_4101]) ).

tff(c_4830,plain,
    ! [W1_202,W0_203] :
      ( sdtlseqdt0(W1_202,sdtasdt0(W1_202,W0_203))
      | ( sz00 = W0_203 )
      | ~ aNaturalNumber0(W1_202)
      | ~ aNaturalNumber0(W0_203) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_4848,plain,
    ( sdtlseqdt0(sz10,xn)
    | ( xn = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_4119,c_4830]) ).

tff(c_4902,plain,
    ( sdtlseqdt0(sz10,xn)
    | ( xn = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_8,c_4848]) ).

tff(c_5058,plain,
    xn = sz00,
    inference(splitLeft,[status(thm)],[c_4902]) ).

tff(c_151,plain,
    doDivides0(xp,sdtasdt0(xn,xm)),
    inference(cnfTransformation,[status(thm)],[f_442]) ).

tff(c_5080,plain,
    doDivides0(xp,sdtasdt0(sz00,xm)),
    inference(demodulation,[status(thm),theory(equality)],[c_5058,c_151]) ).

tff(c_5106,plain,
    doDivides0(xp,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_3949,c_5080]) ).

tff(c_171,plain,
    ~ doDivides0(xp,xn),
    inference(cnfTransformation,[status(thm)],[f_464]) ).

tff(c_5083,plain,
    ~ doDivides0(xp,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_5058,c_171]) ).

tff(c_5160,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5106,c_5083]) ).

tff(c_5161,plain,
    sdtlseqdt0(sz10,xn),
    inference(splitRight,[status(thm)],[c_4902]) ).

tff(c_5795,plain,
    ! [W0_222,W1_223] :
      ( iLess0(W0_222,W1_223)
      | ~ sdtlseqdt0(W0_222,W1_223)
      | ( W1_223 = W0_222 )
      | ~ aNaturalNumber0(W1_223)
      | ~ aNaturalNumber0(W0_222) ),
    inference(cnfTransformation,[status(thm)],[f_296]) ).

tff(c_5804,plain,
    ( iLess0(sz10,xn)
    | ( xn = sz10 )
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sz10) ),
    inference(resolution,[status(thm)],[c_5161,c_5795]) ).

tff(c_5850,plain,
    ( iLess0(sz10,xn)
    | ( xn = sz10 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_147,c_5804]) ).

tff(c_5890,plain,
    xn = sz10,
    inference(splitLeft,[status(thm)],[c_5850]) ).

tff(c_6086,plain,
    doDivides0(xp,sdtasdt0(sz10,xm)),
    inference(demodulation,[status(thm),theory(equality)],[c_5890,c_151]) ).

tff(c_6106,plain,
    doDivides0(xp,xm),
    inference(demodulation,[status(thm),theory(equality)],[c_4120,c_6086]) ).

tff(c_6108,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_169,c_6106]) ).

tff(c_6110,plain,
    xn != sz10,
    inference(splitRight,[status(thm)],[c_5850]) ).

tff(c_165,plain,
    xp != xn,
    inference(cnfTransformation,[status(thm)],[f_455]) ).

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

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

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_177,plain,
    ~ isPrime0(sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).

tff(c_4123,plain,
    sdtasdt0(sz10,xp) = xp,
    inference(resolution,[status(thm)],[c_143,c_4101]) ).

tff(c_4857,plain,
    ( sdtlseqdt0(sz10,xp)
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_4123,c_4830]) ).

tff(c_4908,plain,
    ( sdtlseqdt0(sz10,xp)
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_4857]) ).

tff(c_4979,plain,
    xp = sz00,
    inference(splitLeft,[status(thm)],[c_4908]) ).

tff(c_5001,plain,
    isPrime0(sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_4979,c_153]) ).

tff(c_5016,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_177,c_5001]) ).

tff(c_5018,plain,
    xp != sz00,
    inference(splitRight,[status(thm)],[c_4908]) ).

tff(c_4570,plain,
    ! [W1_196,W0_197] :
      ( ( sdtasdt0(W1_196,W0_197) = sdtasdt0(W0_197,W1_196) )
      | ~ aNaturalNumber0(W1_196)
      | ~ aNaturalNumber0(W0_197) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_5723,plain,
    ! [W0_221] :
      ( ( sdtasdt0(xm,W0_221) = sdtasdt0(W0_221,xm) )
      | ~ aNaturalNumber0(W0_221) ),
    inference(resolution,[status(thm)],[c_145,c_4570]) ).

tff(c_5789,plain,
    sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
    inference(resolution,[status(thm)],[c_147,c_5723]) ).

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_6481,plain,
    ( aNaturalNumber0(sdtasdt0(xm,xn))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_5789,c_12]) ).

tff(c_6491,plain,
    aNaturalNumber0(sdtasdt0(xm,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_6481]) ).

tff(c_6472,plain,
    doDivides0(xp,sdtasdt0(xm,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_5789,c_151]) ).

tff(c_3985,plain,
    ! [W0_177] :
      ( ( sdtasdt0(W0_177,sz10) = W0_177 )
      | ~ aNaturalNumber0(W0_177) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_4005,plain,
    sdtasdt0(xp,sz10) = xp,
    inference(resolution,[status(thm)],[c_143,c_3985]) ).

tff(c_326,plain,
    ! [W0_103] :
      ( ( sdtasdt0(sz10,W0_103) = W0_103 )
      | ~ aNaturalNumber0(W0_103) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_347,plain,
    sdtasdt0(sz10,xp) = xp,
    inference(resolution,[status(thm)],[c_143,c_326]) ).

tff(c_1565,plain,
    ! [W1_132,W0_133] :
      ( sdtlseqdt0(W1_132,sdtasdt0(W1_132,W0_133))
      | ( sz00 = W0_133 )
      | ~ aNaturalNumber0(W1_132)
      | ~ aNaturalNumber0(W0_133) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_1610,plain,
    ( sdtlseqdt0(sz10,xp)
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_347,c_1565]) ).

tff(c_1673,plain,
    ( sdtlseqdt0(sz10,xp)
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_1610]) ).

tff(c_1895,plain,
    xp = sz00,
    inference(splitLeft,[status(thm)],[c_1673]) ).

tff(c_1924,plain,
    isPrime0(sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_1895,c_153]) ).

tff(c_1945,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_177,c_1924]) ).

tff(c_1947,plain,
    xp != sz00,
    inference(splitRight,[status(thm)],[c_1673]) ).

tff(c_343,plain,
    sdtasdt0(sz10,xn) = xn,
    inference(resolution,[status(thm)],[c_147,c_326]) ).

tff(c_1595,plain,
    ( sdtlseqdt0(sz10,xn)
    | ( xn = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_343,c_1565]) ).

tff(c_1663,plain,
    ( sdtlseqdt0(sz10,xn)
    | ( xn = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_8,c_1595]) ).

tff(c_2007,plain,
    xn = sz00,
    inference(splitLeft,[status(thm)],[c_1663]) ).

tff(c_2037,plain,
    ~ doDivides0(xp,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_2007,c_171]) ).

tff(c_293,plain,
    ! [W0_102] :
      ( ( sdtasdt0(W0_102,sz00) = sz00 )
      | ~ aNaturalNumber0(W0_102) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_311,plain,
    sdtasdt0(xm,sz00) = sz00,
    inference(resolution,[status(thm)],[c_145,c_293]) ).

tff(c_622,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_685,plain,
    ! [W0_115] :
      ( ( sdtasdt0(xn,W0_115) = sdtasdt0(W0_115,xn) )
      | ~ aNaturalNumber0(W0_115) ),
    inference(resolution,[status(thm)],[c_147,c_622]) ).

tff(c_717,plain,
    sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
    inference(resolution,[status(thm)],[c_145,c_685]) ).

tff(c_722,plain,
    doDivides0(xp,sdtasdt0(xm,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_717,c_151]) ).

tff(c_2025,plain,
    doDivides0(xp,sdtasdt0(xm,sz00)),
    inference(demodulation,[status(thm),theory(equality)],[c_2007,c_722]) ).

tff(c_2056,plain,
    doDivides0(xp,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_311,c_2025]) ).

tff(c_2082,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2037,c_2056]) ).

tff(c_2084,plain,
    xn != sz00,
    inference(splitRight,[status(thm)],[c_1663]) ).

tff(c_368,plain,
    ! [W0_104] :
      ( ( sdtasdt0(sz00,W0_104) = sz00 )
      | ~ aNaturalNumber0(W0_104) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_385,plain,
    sdtasdt0(sz00,xn) = sz00,
    inference(resolution,[status(thm)],[c_147,c_368]) ).

tff(c_344,plain,
    sdtasdt0(sz10,xm) = xm,
    inference(resolution,[status(thm)],[c_145,c_326]) ).

tff(c_1604,plain,
    ( sdtlseqdt0(sz10,xm)
    | ( xm = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_344,c_1565]) ).

tff(c_1669,plain,
    ( sdtlseqdt0(sz10,xm)
    | ( xm = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_8,c_1604]) ).

tff(c_1780,plain,
    xm = sz00,
    inference(splitLeft,[status(thm)],[c_1669]) ).

tff(c_1852,plain,
    doDivides0(xp,sdtasdt0(sz00,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_1780,c_722]) ).

tff(c_1877,plain,
    doDivides0(xp,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_385,c_1852]) ).

tff(c_1861,plain,
    ~ doDivides0(xp,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_1780,c_169]) ).

tff(c_1892,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1877,c_1861]) ).

tff(c_1894,plain,
    xm != sz00,
    inference(splitRight,[status(thm)],[c_1669]) ).

tff(c_2323,plain,
    ! [W1_143,W0_144] :
      ( ( sz00 = W1_143 )
      | ( sz00 = W0_144 )
      | ( sdtasdt0(W0_144,W1_143) != sz00 )
      | ~ aNaturalNumber0(W1_143)
      | ~ aNaturalNumber0(W0_144) ),
    inference(cnfTransformation,[status(thm)],[f_151]) ).

tff(c_2353,plain,
    ( ( xm = sz00 )
    | ( xn = sz00 )
    | ( sdtasdt0(xm,xn) != sz00 )
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_717,c_2323]) ).

tff(c_2447,plain,
    ( ( xm = sz00 )
    | ( xn = sz00 )
    | ( sdtasdt0(xm,xn) != sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_2353]) ).

tff(c_2448,plain,
    sdtasdt0(xm,xn) != sz00,
    inference(negUnitSimplification,[status(thm)],[c_2084,c_1894,c_2447]) ).

tff(c_726,plain,
    ( aNaturalNumber0(sdtasdt0(xm,xn))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_717,c_12]) ).

tff(c_730,plain,
    aNaturalNumber0(sdtasdt0(xm,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_726]) ).

tff(c_313,plain,
    sdtasdt0(xp,sz00) = sz00,
    inference(resolution,[status(thm)],[c_143,c_293]) ).

tff(c_173,plain,
    ( ( xk = sz10 )
    | ( xk = sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_464]) ).

tff(c_178,plain,
    xk = sz00,
    inference(splitLeft,[status(thm)],[c_173]) ).

tff(c_167,plain,
    sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
    inference(cnfTransformation,[status(thm)],[f_456]) ).

tff(c_250,plain,
    sdtsldt0(sdtasdt0(xn,xm),xp) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_178,c_167]) ).

tff(c_721,plain,
    sdtsldt0(sdtasdt0(xm,xn),xp) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_717,c_250]) ).

tff(c_3896,plain,
    ! [W0_172,W1_173] :
      ( ( sdtasdt0(W0_172,sdtsldt0(W1_173,W0_172)) = W1_173 )
      | ~ doDivides0(W0_172,W1_173)
      | ( sz00 = W0_172 )
      | ~ aNaturalNumber0(W1_173)
      | ~ aNaturalNumber0(W0_172) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_3916,plain,
    ( ( sdtasdt0(xp,sz00) = sdtasdt0(xm,xn) )
    | ~ doDivides0(xp,sdtasdt0(xm,xn))
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sdtasdt0(xm,xn))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_721,c_3896]) ).

tff(c_3920,plain,
    ( ( sdtasdt0(xm,xn) = sz00 )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_730,c_722,c_313,c_3916]) ).

tff(c_3922,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1947,c_2448,c_3920]) ).

tff(c_3923,plain,
    xk = sz10,
    inference(splitRight,[status(thm)],[c_173]) ).

tff(c_4136,plain,
    sdtsldt0(sdtasdt0(xn,xm),xp) = sz10,
    inference(demodulation,[status(thm),theory(equality)],[c_3923,c_167]) ).

tff(c_6471,plain,
    sdtsldt0(sdtasdt0(xm,xn),xp) = sz10,
    inference(demodulation,[status(thm),theory(equality)],[c_5789,c_4136]) ).

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_7996,plain,
    ( ( sdtasdt0(xp,sz10) = sdtasdt0(xm,xn) )
    | ~ doDivides0(xp,sdtasdt0(xm,xn))
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sdtasdt0(xm,xn))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_6471,c_109]) ).

tff(c_8003,plain,
    ( ( sdtasdt0(xm,xn) = xp )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_6491,c_6472,c_4005,c_7996]) ).

tff(c_8004,plain,
    sdtasdt0(xm,xn) = xp,
    inference(negUnitSimplification,[status(thm)],[c_5018,c_8003]) ).

tff(c_6699,plain,
    ! [W0_234,W2_235] :
      ( doDivides0(W0_234,sdtasdt0(W0_234,W2_235))
      | ~ aNaturalNumber0(W2_235)
      | ~ aNaturalNumber0(sdtasdt0(W0_234,W2_235))
      | ~ aNaturalNumber0(W0_234) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_6705,plain,
    ( doDivides0(xn,sdtasdt0(xm,xn))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_5789,c_6699]) ).

tff(c_6785,plain,
    doDivides0(xn,sdtasdt0(xm,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_6491,c_5789,c_145,c_6705]) ).

tff(c_8010,plain,
    doDivides0(xn,xp),
    inference(demodulation,[status(thm),theory(equality)],[c_8004,c_6785]) ).

tff(c_131,plain,
    ! [W1_92,W0_89] :
      ( ( W1_92 = W0_89 )
      | ( sz10 = W1_92 )
      | ~ doDivides0(W1_92,W0_89)
      | ~ aNaturalNumber0(W1_92)
      | ~ isPrime0(W0_89)
      | ~ aNaturalNumber0(W0_89) ),
    inference(cnfTransformation,[status(thm)],[f_403]) ).

tff(c_8048,plain,
    ( ( xp = xn )
    | ( xn = sz10 )
    | ~ aNaturalNumber0(xn)
    | ~ isPrime0(xp)
    | ~ aNaturalNumber0(xp) ),
    inference(resolution,[status(thm)],[c_8010,c_131]) ).

tff(c_8054,plain,
    ( ( xp = xn )
    | ( xn = sz10 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_153,c_147,c_8048]) ).

tff(c_8056,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6110,c_165,c_8054]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : NUM498+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34  % Computer : n023.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 15:36:37 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 10.17/3.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.35/3.42  
% 10.35/3.42  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.50/3.46  
% 10.50/3.46  Inference rules
% 10.50/3.46  ----------------------
% 10.50/3.46  #Ref     : 4
% 10.50/3.46  #Sup     : 1642
% 10.50/3.46  #Fact    : 4
% 10.50/3.46  #Define  : 0
% 10.50/3.46  #Split   : 17
% 10.50/3.46  #Chain   : 0
% 10.50/3.46  #Close   : 0
% 10.50/3.46  
% 10.50/3.46  Ordering : KBO
% 10.50/3.46  
% 10.50/3.46  Simplification rules
% 10.50/3.46  ----------------------
% 10.50/3.46  #Subsume      : 102
% 10.50/3.46  #Demod        : 2592
% 10.50/3.46  #Tautology    : 787
% 10.50/3.46  #SimpNegUnit  : 214
% 10.50/3.46  #BackRed      : 393
% 10.50/3.46  
% 10.50/3.46  #Partial instantiations: 0
% 10.50/3.46  #Strategies tried      : 1
% 10.50/3.46  
% 10.50/3.46  Timing (in seconds)
% 10.50/3.46  ----------------------
% 10.50/3.47  Preprocessing        : 0.68
% 10.50/3.47  Parsing              : 0.34
% 10.50/3.47  CNF conversion       : 0.05
% 10.50/3.47  Main loop            : 1.63
% 10.50/3.47  Inferencing          : 0.50
% 10.50/3.47  Reduction            : 0.63
% 10.50/3.47  Demodulation         : 0.47
% 10.50/3.47  BG Simplification    : 0.07
% 10.50/3.47  Subsumption          : 0.31
% 10.50/3.47  Abstraction          : 0.06
% 10.50/3.47  MUC search           : 0.00
% 10.50/3.47  Cooper               : 0.00
% 10.50/3.47  Total                : 2.39
% 10.50/3.47  Index Insertion      : 0.00
% 10.50/3.47  Index Deletion       : 0.00
% 10.50/3.47  Index Matching       : 0.00
% 10.50/3.47  BG Taut test         : 0.00
%------------------------------------------------------------------------------