TSTP Solution File: NUM476+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM476+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 : n029.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 10:51:49 EDT 2023

% Result   : Theorem 14.45s 4.77s
% Output   : CNFRefutation 14.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   32
% Syntax   : Number of formulae    :  106 (  38 unt;  18 typ;   3 def)
%            Number of atoms       :  220 (  59 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  221 (  89   ~;  90   |;  24   &)
%                                         (   3 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  10   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   8 con; 0-2 aty)
%            Number of variables   :   53 (;  49   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > xl > sz10 > sz00 > #skF_5 > #skF_3 > #skF_4 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(xl,type,
    xl: $i ).

tff(sdtasdt0,type,
    sdtasdt0: ( $i * $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('#skF_5',type,
    '#skF_5': $i ).

tff(aNaturalNumber0,type,
    aNaturalNumber0: $i > $o ).

tff('#skF_3',type,
    '#skF_3': $i ).

tff(doDivides0,type,
    doDivides0: ( $i * $i ) > $o ).

tff('#skF_4',type,
    '#skF_4': $i ).

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $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_375,negated_conjecture,
    ~ ( ( ( xl != sz00 )
       => ? [W0] :
            ( ( W0 = sdtsldt0(xm,xl) )
            & ? [W1] :
                ( ( W1 = sdtsldt0(sdtpldt0(xm,xn),xl) )
                & sdtlseqdt0(W0,W1)
                & ? [W2] :
                    ( ( W2 = sdtmndt0(W1,W0) )
                    & ( sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn) )
                    & ( xn = sdtasdt0(xl,W2) ) ) ) ) )
     => doDivides0(xl,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_352,hypothesis,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).

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_35,axiom,
    ( aNaturalNumber0(sz10)
    & ( sz10 != sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).

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_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_355,hypothesis,
    ( doDivides0(xl,xm)
    & doDivides0(xl,sdtpldt0(xm,xn)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).

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

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_307,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( doDivides0(W0,W1)
      <=> ? [W2] :
            ( aNaturalNumber0(W2)
            & ( W1 = sdtasdt0(W0,W2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).

tff(f_335,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( ( doDivides0(W0,W1)
          & doDivides0(W1,W2) )
       => doDivides0(W0,W2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).

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

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_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(c_127,plain,
    ~ doDivides0(xl,xn),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_121,plain,
    aNaturalNumber0(xl),
    inference(cnfTransformation,[status(thm)],[f_352]) ).

tff(c_117,plain,
    aNaturalNumber0(xn),
    inference(cnfTransformation,[status(thm)],[f_352]) ).

tff(c_135,plain,
    ( sdtlseqdt0('#skF_3','#skF_4')
    | ( xl = sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_140,plain,
    xl = sz00,
    inference(splitLeft,[status(thm)],[c_135]) ).

tff(c_142,plain,
    ~ doDivides0(sz00,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_140,c_127]) ).

tff(c_153,plain,
    ! [W0_85] :
      ( ( sdtpldt0(sz00,W0_85) = W0_85 )
      | ~ aNaturalNumber0(W0_85) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_168,plain,
    sdtpldt0(sz00,xn) = xn,
    inference(resolution,[status(thm)],[c_117,c_153]) ).

tff(c_119,plain,
    aNaturalNumber0(xm),
    inference(cnfTransformation,[status(thm)],[f_352]) ).

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

tff(c_274,plain,
    ! [W0_89] :
      ( ( sdtasdt0(sz10,W0_89) = W0_89 )
      | ~ aNaturalNumber0(W0_89) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_291,plain,
    sdtasdt0(sz10,xm) = xm,
    inference(resolution,[status(thm)],[c_119,c_274]) ).

tff(c_902,plain,
    ! [W1_110,W0_111] :
      ( sdtlseqdt0(W1_110,sdtasdt0(W1_110,W0_111))
      | ( sz00 = W0_111 )
      | ~ aNaturalNumber0(W1_110)
      | ~ aNaturalNumber0(W0_111) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_923,plain,
    ( sdtlseqdt0(sz10,xm)
    | ( xm = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_291,c_902]) ).

tff(c_970,plain,
    ( sdtlseqdt0(sz10,xm)
    | ( xm = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_8,c_923]) ).

tff(c_1138,plain,
    xm = sz00,
    inference(splitLeft,[status(thm)],[c_970]) ).

tff(c_123,plain,
    doDivides0(xl,sdtpldt0(xm,xn)),
    inference(cnfTransformation,[status(thm)],[f_355]) ).

tff(c_151,plain,
    doDivides0(sz00,sdtpldt0(xm,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_140,c_123]) ).

tff(c_1157,plain,
    doDivides0(sz00,sdtpldt0(sz00,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_1138,c_151]) ).

tff(c_1177,plain,
    doDivides0(sz00,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_1157]) ).

tff(c_1179,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_142,c_1177]) ).

tff(c_1181,plain,
    xm != sz00,
    inference(splitRight,[status(thm)],[c_970]) ).

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

tff(c_252,plain,
    ! [W0_88] :
      ( ( sdtasdt0(sz00,W0_88) = sz00 )
      | ~ aNaturalNumber0(W0_88) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_269,plain,
    sdtasdt0(sz00,xm) = sz00,
    inference(resolution,[status(thm)],[c_119,c_252]) ).

tff(c_2366,plain,
    ! [W0_143,W2_144] :
      ( doDivides0(W0_143,sdtasdt0(W0_143,W2_144))
      | ~ aNaturalNumber0(W2_144)
      | ~ aNaturalNumber0(sdtasdt0(W0_143,W2_144))
      | ~ aNaturalNumber0(W0_143) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_2408,plain,
    ( doDivides0(sz00,sz00)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sdtasdt0(sz00,xm))
    | ~ aNaturalNumber0(sz00) ),
    inference(superposition,[status(thm),theory(equality)],[c_269,c_2366]) ).

tff(c_2452,plain,
    doDivides0(sz00,sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_269,c_119,c_2408]) ).

tff(c_125,plain,
    doDivides0(xl,xm),
    inference(cnfTransformation,[status(thm)],[f_355]) ).

tff(c_143,plain,
    doDivides0(sz00,xm),
    inference(demodulation,[status(thm),theory(equality)],[c_140,c_125]) ).

tff(c_2924,plain,
    ! [W0_159,W2_160,W1_161] :
      ( doDivides0(W0_159,W2_160)
      | ~ doDivides0(W1_161,W2_160)
      | ~ doDivides0(W0_159,W1_161)
      | ~ aNaturalNumber0(W2_160)
      | ~ aNaturalNumber0(W1_161)
      | ~ aNaturalNumber0(W0_159) ),
    inference(cnfTransformation,[status(thm)],[f_335]) ).

tff(c_2952,plain,
    ! [W0_159] :
      ( doDivides0(W0_159,xm)
      | ~ doDivides0(W0_159,sz00)
      | ~ aNaturalNumber0(xm)
      | ~ aNaturalNumber0(sz00)
      | ~ aNaturalNumber0(W0_159) ),
    inference(resolution,[status(thm)],[c_143,c_2924]) ).

tff(c_2992,plain,
    ! [W0_159] :
      ( doDivides0(W0_159,xm)
      | ~ doDivides0(W0_159,sz00)
      | ~ aNaturalNumber0(W0_159) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_119,c_2952]) ).

tff(c_1090,plain,
    ! [W0_114,W1_115] :
      ( aNaturalNumber0('#skF_2'(W0_114,W1_115))
      | ~ doDivides0(W0_114,W1_115)
      | ~ aNaturalNumber0(W1_115)
      | ~ aNaturalNumber0(W0_114) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_30,plain,
    ! [W0_18] :
      ( ( sdtasdt0(sz00,W0_18) = sz00 )
      | ~ aNaturalNumber0(W0_18) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_13509,plain,
    ! [W0_269,W1_270] :
      ( ( sdtasdt0(sz00,'#skF_2'(W0_269,W1_270)) = sz00 )
      | ~ doDivides0(W0_269,W1_270)
      | ~ aNaturalNumber0(W1_270)
      | ~ aNaturalNumber0(W0_269) ),
    inference(resolution,[status(thm)],[c_1090,c_30]) ).

tff(c_103,plain,
    ! [W0_65,W1_66] :
      ( ( sdtasdt0(W0_65,'#skF_2'(W0_65,W1_66)) = W1_66 )
      | ~ doDivides0(W0_65,W1_66)
      | ~ aNaturalNumber0(W1_66)
      | ~ aNaturalNumber0(W0_65) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_13575,plain,
    ! [W1_270] :
      ( ( sz00 = W1_270 )
      | ~ doDivides0(sz00,W1_270)
      | ~ aNaturalNumber0(W1_270)
      | ~ aNaturalNumber0(sz00)
      | ~ doDivides0(sz00,W1_270)
      | ~ aNaturalNumber0(W1_270)
      | ~ aNaturalNumber0(sz00) ),
    inference(superposition,[status(thm),theory(equality)],[c_13509,c_103]) ).

tff(c_13652,plain,
    ! [W1_271] :
      ( ( sz00 = W1_271 )
      | ~ doDivides0(sz00,W1_271)
      | ~ aNaturalNumber0(W1_271) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_13575]) ).

tff(c_13660,plain,
    ( ( xm = sz00 )
    | ~ aNaturalNumber0(xm)
    | ~ doDivides0(sz00,sz00)
    | ~ aNaturalNumber0(sz00) ),
    inference(resolution,[status(thm)],[c_2992,c_13652]) ).

tff(c_13679,plain,
    xm = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_2452,c_119,c_13660]) ).

tff(c_13681,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1181,c_13679]) ).

tff(c_13683,plain,
    xl != sz00,
    inference(splitRight,[status(thm)],[c_135]) ).

tff(c_129,plain,
    ( ( sdtasdt0(xl,'#skF_5') = xn )
    | ( xl = sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_13690,plain,
    sdtasdt0(xl,'#skF_5') = xn,
    inference(negUnitSimplification,[status(thm)],[c_13683,c_129]) ).

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_13682,plain,
    sdtlseqdt0('#skF_3','#skF_4'),
    inference(splitRight,[status(thm)],[c_135]) ).

tff(c_133,plain,
    ( ( sdtmndt0('#skF_4','#skF_3') = '#skF_5' )
    | ( xl = sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_13695,plain,
    sdtmndt0('#skF_4','#skF_3') = '#skF_5',
    inference(negUnitSimplification,[status(thm)],[c_13683,c_133]) ).

tff(c_14475,plain,
    ! [W1_297,W0_298] :
      ( aNaturalNumber0(sdtmndt0(W1_297,W0_298))
      | ~ sdtlseqdt0(W0_298,W1_297)
      | ~ aNaturalNumber0(W1_297)
      | ~ aNaturalNumber0(W0_298) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_14509,plain,
    ( aNaturalNumber0('#skF_5')
    | ~ sdtlseqdt0('#skF_3','#skF_4')
    | ~ aNaturalNumber0('#skF_4')
    | ~ aNaturalNumber0('#skF_3') ),
    inference(superposition,[status(thm),theory(equality)],[c_13695,c_14475]) ).

tff(c_14522,plain,
    ( aNaturalNumber0('#skF_5')
    | ~ aNaturalNumber0('#skF_4')
    | ~ aNaturalNumber0('#skF_3') ),
    inference(demodulation,[status(thm),theory(equality)],[c_13682,c_14509]) ).

tff(c_14523,plain,
    ~ aNaturalNumber0('#skF_3'),
    inference(splitLeft,[status(thm)],[c_14522]) ).

tff(c_139,plain,
    ( ( sdtsldt0(xm,xl) = '#skF_3' )
    | ( xl = sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_13684,plain,
    sdtsldt0(xm,xl) = '#skF_3',
    inference(negUnitSimplification,[status(thm)],[c_13683,c_139]) ).

tff(c_16529,plain,
    ! [W1_331,W0_332] :
      ( aNaturalNumber0(sdtsldt0(W1_331,W0_332))
      | ~ doDivides0(W0_332,W1_331)
      | ( sz00 = W0_332 )
      | ~ aNaturalNumber0(W1_331)
      | ~ aNaturalNumber0(W0_332) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_16569,plain,
    ( aNaturalNumber0('#skF_3')
    | ~ doDivides0(xl,xm)
    | ( xl = sz00 )
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_13684,c_16529]) ).

tff(c_16586,plain,
    ( aNaturalNumber0('#skF_3')
    | ( xl = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_125,c_16569]) ).

tff(c_16588,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_13683,c_14523,c_16586]) ).

tff(c_16589,plain,
    ( ~ aNaturalNumber0('#skF_4')
    | aNaturalNumber0('#skF_5') ),
    inference(splitRight,[status(thm)],[c_14522]) ).

tff(c_16633,plain,
    ~ aNaturalNumber0('#skF_4'),
    inference(splitLeft,[status(thm)],[c_16589]) ).

tff(c_137,plain,
    ( ( sdtsldt0(sdtpldt0(xm,xn),xl) = '#skF_4' )
    | ( xl = sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_375]) ).

tff(c_13754,plain,
    sdtsldt0(sdtpldt0(xm,xn),xl) = '#skF_4',
    inference(negUnitSimplification,[status(thm)],[c_13683,c_137]) ).

tff(c_18805,plain,
    ! [W1_367,W0_368] :
      ( aNaturalNumber0(sdtsldt0(W1_367,W0_368))
      | ~ doDivides0(W0_368,W1_367)
      | ( sz00 = W0_368 )
      | ~ aNaturalNumber0(W1_367)
      | ~ aNaturalNumber0(W0_368) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_18845,plain,
    ( aNaturalNumber0('#skF_4')
    | ~ doDivides0(xl,sdtpldt0(xm,xn))
    | ( xl = sz00 )
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_13754,c_18805]) ).

tff(c_18863,plain,
    ( aNaturalNumber0('#skF_4')
    | ( xl = sz00 )
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_123,c_18845]) ).

tff(c_18864,plain,
    ~ aNaturalNumber0(sdtpldt0(xm,xn)),
    inference(negUnitSimplification,[status(thm)],[c_13683,c_16633,c_18863]) ).

tff(c_18870,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(resolution,[status(thm)],[c_10,c_18864]) ).

tff(c_18874,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_117,c_18870]) ).

tff(c_18875,plain,
    aNaturalNumber0('#skF_5'),
    inference(splitRight,[status(thm)],[c_16589]) ).

tff(c_23387,plain,
    ! [W0_429,W2_430] :
      ( doDivides0(W0_429,sdtasdt0(W0_429,W2_430))
      | ~ aNaturalNumber0(W2_430)
      | ~ aNaturalNumber0(sdtasdt0(W0_429,W2_430))
      | ~ aNaturalNumber0(W0_429) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_23420,plain,
    ( doDivides0(xl,xn)
    | ~ aNaturalNumber0('#skF_5')
    | ~ aNaturalNumber0(sdtasdt0(xl,'#skF_5'))
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_13690,c_23387]) ).

tff(c_23442,plain,
    doDivides0(xl,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_117,c_13690,c_18875,c_23420]) ).

tff(c_23444,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_127,c_23442]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM476+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % 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 : n029.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 14:48:37 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 14.45/4.77  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.63/4.79  
% 14.63/4.79  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.63/4.82  
% 14.63/4.82  Inference rules
% 14.63/4.82  ----------------------
% 14.63/4.82  #Ref     : 4
% 14.63/4.82  #Sup     : 4720
% 14.63/4.82  #Fact    : 4
% 14.63/4.82  #Define  : 0
% 14.63/4.82  #Split   : 66
% 14.63/4.82  #Chain   : 0
% 14.63/4.82  #Close   : 0
% 14.63/4.82  
% 14.63/4.82  Ordering : KBO
% 14.63/4.82  
% 14.63/4.82  Simplification rules
% 14.63/4.82  ----------------------
% 14.63/4.82  #Subsume      : 427
% 14.63/4.82  #Demod        : 8419
% 14.63/4.82  #Tautology    : 2314
% 14.63/4.82  #SimpNegUnit  : 806
% 14.63/4.82  #BackRed      : 1083
% 14.63/4.82  
% 14.63/4.82  #Partial instantiations: 0
% 14.63/4.82  #Strategies tried      : 1
% 14.63/4.82  
% 14.63/4.82  Timing (in seconds)
% 14.63/4.82  ----------------------
% 14.63/4.82  Preprocessing        : 0.68
% 14.63/4.82  Parsing              : 0.35
% 14.63/4.82  CNF conversion       : 0.05
% 14.63/4.82  Main loop            : 3.06
% 14.63/4.82  Inferencing          : 0.81
% 14.63/4.82  Reduction            : 1.32
% 14.63/4.82  Demodulation         : 0.98
% 14.63/4.82  BG Simplification    : 0.09
% 14.63/4.82  Subsumption          : 0.62
% 14.63/4.82  Abstraction          : 0.09
% 14.63/4.82  MUC search           : 0.00
% 14.63/4.82  Cooper               : 0.00
% 14.63/4.82  Total                : 3.81
% 14.63/4.82  Index Insertion      : 0.00
% 14.63/4.82  Index Deletion       : 0.00
% 14.63/4.82  Index Matching       : 0.00
% 14.63/4.82  BG Taut test         : 0.00
%------------------------------------------------------------------------------