TSTP Solution File: NUM525+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM525+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 : n022.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 10:51:59 EDT 2023

% Result   : Theorem 164.53s 136.67s
% Output   : CNFRefutation 164.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   66 (  22 unt;  19 typ;   1 def)
%            Number of atoms       :  130 (  45 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  143 (  60   ~;  61   |;  14   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   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    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :   31 (;  31   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(xq,type,
    xq: $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_446,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp)
    & ( xn != sz00 )
    & ( xm != sz00 )
    & ( xp != sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).

tff(f_473,hypothesis,
    ( doDivides0(xp,sdtasdt0(xn,xn))
    & doDivides0(xp,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).

tff(f_474,hypothesis,
    xq = sdtsldt0(xn,xp),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).

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_469,hypothesis,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).

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_384,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( ( W0 != sz00 )
          & doDivides0(W0,W1) )
       => ! [W2] :
            ( aNaturalNumber0(W2)
           => ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).

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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).

tff(f_476,negated_conjecture,
    sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(c_145,plain,
    xp != sz00,
    inference(cnfTransformation,[status(thm)],[f_446]) ).

tff(c_151,plain,
    aNaturalNumber0(xp),
    inference(cnfTransformation,[status(thm)],[f_446]) ).

tff(c_155,plain,
    aNaturalNumber0(xn),
    inference(cnfTransformation,[status(thm)],[f_446]) ).

tff(c_163,plain,
    doDivides0(xp,xn),
    inference(cnfTransformation,[status(thm)],[f_473]) ).

tff(c_167,plain,
    sdtsldt0(xn,xp) = xq,
    inference(cnfTransformation,[status(thm)],[f_474]) ).

tff(c_7232,plain,
    ! [W1_238,W0_239] :
      ( aNaturalNumber0(sdtsldt0(W1_238,W0_239))
      | ~ doDivides0(W0_239,W1_238)
      | ( sz00 = W0_239 )
      | ~ aNaturalNumber0(W1_238)
      | ~ aNaturalNumber0(W0_239) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_7266,plain,
    ( aNaturalNumber0(xq)
    | ~ doDivides0(xp,xn)
    | ( xp = sz00 )
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_167,c_7232]) ).

tff(c_7279,plain,
    ( aNaturalNumber0(xq)
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_155,c_163,c_7266]) ).

tff(c_7280,plain,
    aNaturalNumber0(xq),
    inference(negUnitSimplification,[status(thm)],[c_145,c_7279]) ).

tff(c_159,plain,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    inference(cnfTransformation,[status(thm)],[f_469]) ).

tff(c_153,plain,
    aNaturalNumber0(xm),
    inference(cnfTransformation,[status(thm)],[f_446]) ).

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_500,plain,
    ( aNaturalNumber0(sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_159,c_12]) ).

tff(c_504,plain,
    ( aNaturalNumber0(sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_500]) ).

tff(c_595,plain,
    ~ aNaturalNumber0(sdtasdt0(xm,xm)),
    inference(splitLeft,[status(thm)],[c_504]) ).

tff(c_599,plain,
    ~ aNaturalNumber0(xm),
    inference(resolution,[status(thm)],[c_12,c_595]) ).

tff(c_603,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_153,c_599]) ).

tff(c_604,plain,
    aNaturalNumber0(sdtasdt0(xn,xn)),
    inference(splitRight,[status(thm)],[c_504]) ).

tff(c_165,plain,
    doDivides0(xp,sdtasdt0(xn,xn)),
    inference(cnfTransformation,[status(thm)],[f_473]) ).

tff(c_605,plain,
    aNaturalNumber0(sdtasdt0(xm,xm)),
    inference(splitRight,[status(thm)],[c_504]) ).

tff(c_15404,plain,
    ! [W0_314,W2_315] :
      ( ( sdtsldt0(sdtasdt0(W0_314,W2_315),W0_314) = W2_315 )
      | ~ aNaturalNumber0(W2_315)
      | ~ doDivides0(W0_314,sdtasdt0(W0_314,W2_315))
      | ( sz00 = W0_314 )
      | ~ aNaturalNumber0(sdtasdt0(W0_314,W2_315))
      | ~ aNaturalNumber0(W0_314) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_15515,plain,
    ( ( sdtsldt0(sdtasdt0(xp,sdtasdt0(xm,xm)),xp) = sdtasdt0(xm,xm) )
    | ~ aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ doDivides0(xp,sdtasdt0(xn,xn))
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_159,c_15404]) ).

tff(c_15652,plain,
    ( ( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_604,c_159,c_165,c_605,c_159,c_15515]) ).

tff(c_15653,plain,
    sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm),
    inference(negUnitSimplification,[status(thm)],[c_145,c_15652]) ).

tff(c_121,plain,
    ! [W2_88,W1_86,W0_85] :
      ( ( sdtsldt0(sdtasdt0(W2_88,W1_86),W0_85) = sdtasdt0(W2_88,sdtsldt0(W1_86,W0_85)) )
      | ~ aNaturalNumber0(W2_88)
      | ~ doDivides0(W0_85,W1_86)
      | ( sz00 = W0_85 )
      | ~ aNaturalNumber0(W1_86)
      | ~ aNaturalNumber0(W0_85) ),
    inference(cnfTransformation,[status(thm)],[f_384]) ).

tff(c_16071,plain,
    ( ( sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(xm,xm) )
    | ~ aNaturalNumber0(xn)
    | ~ doDivides0(xp,xn)
    | ( xp = sz00 )
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_15653,c_121]) ).

tff(c_16084,plain,
    ( ( sdtasdt0(xn,xq) = sdtasdt0(xm,xm) )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_155,c_163,c_155,c_167,c_16071]) ).

tff(c_16085,plain,
    sdtasdt0(xn,xq) = sdtasdt0(xm,xm),
    inference(negUnitSimplification,[status(thm)],[c_145,c_16084]) ).

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_10106,plain,
    ! [W0_274,W1_275,W2_276] :
      ( ( sdtasdt0(sdtasdt0(W0_274,W1_275),W2_276) = sdtasdt0(W0_274,sdtasdt0(W1_275,W2_276)) )
      | ~ aNaturalNumber0(W2_276)
      | ~ aNaturalNumber0(W1_275)
      | ~ aNaturalNumber0(W0_274) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_118848,plain,
    ! [W0_742,W1_743,W2_744] :
      ( ( sdtasdt0(W0_742,sdtasdt0(sdtsldt0(W1_743,W0_742),W2_744)) = sdtasdt0(W1_743,W2_744) )
      | ~ aNaturalNumber0(W2_744)
      | ~ aNaturalNumber0(sdtsldt0(W1_743,W0_742))
      | ~ aNaturalNumber0(W0_742)
      | ~ doDivides0(W0_742,W1_743)
      | ( sz00 = W0_742 )
      | ~ aNaturalNumber0(W1_743)
      | ~ aNaturalNumber0(W0_742) ),
    inference(superposition,[status(thm),theory(equality)],[c_109,c_10106]) ).

tff(c_119321,plain,
    ! [W2_744] :
      ( ( sdtasdt0(xp,sdtasdt0(xq,W2_744)) = sdtasdt0(xn,W2_744) )
      | ~ aNaturalNumber0(W2_744)
      | ~ aNaturalNumber0(sdtsldt0(xn,xp))
      | ~ aNaturalNumber0(xp)
      | ~ doDivides0(xp,xn)
      | ( xp = sz00 )
      | ~ aNaturalNumber0(xn)
      | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_167,c_118848]) ).

tff(c_119551,plain,
    ! [W2_744] :
      ( ( sdtasdt0(xp,sdtasdt0(xq,W2_744)) = sdtasdt0(xn,W2_744) )
      | ~ aNaturalNumber0(W2_744)
      | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_155,c_163,c_151,c_7280,c_167,c_119321]) ).

tff(c_215656,plain,
    ! [W2_981] :
      ( ( sdtasdt0(xp,sdtasdt0(xq,W2_981)) = sdtasdt0(xn,W2_981) )
      | ~ aNaturalNumber0(W2_981) ),
    inference(negUnitSimplification,[status(thm)],[c_145,c_119551]) ).

tff(c_169,plain,
    sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xp,sdtasdt0(xm,xm)),
    inference(cnfTransformation,[status(thm)],[f_476]) ).

tff(c_170,plain,
    sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xn,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_159,c_169]) ).

tff(c_215932,plain,
    ( ( sdtasdt0(xp,sdtasdt0(xn,xq)) != sdtasdt0(xn,xn) )
    | ~ aNaturalNumber0(xq) ),
    inference(superposition,[status(thm),theory(equality)],[c_215656,c_170]) ).

tff(c_216202,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_7280,c_159,c_16085,c_215932]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM525+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
% 0.18/0.35  % Computer : n022.cluster.edu
% 0.18/0.35  % Model    : x86_64 x86_64
% 0.18/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35  % Memory   : 8042.1875MB
% 0.18/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35  % CPULimit : 300
% 0.18/0.35  % WCLimit  : 300
% 0.18/0.35  % DateTime : Thu Aug  3 15:13:03 EDT 2023
% 0.18/0.35  % CPUTime  : 
% 164.53/136.67  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 164.53/136.68  
% 164.53/136.68  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 164.67/136.71  
% 164.67/136.71  Inference rules
% 164.67/136.71  ----------------------
% 164.67/136.71  #Ref     : 13
% 164.67/136.71  #Sup     : 45921
% 164.67/136.71  #Fact    : 14
% 164.67/136.71  #Define  : 0
% 164.67/136.71  #Split   : 58
% 164.67/136.71  #Chain   : 0
% 164.67/136.71  #Close   : 0
% 164.67/136.71  
% 164.67/136.71  Ordering : KBO
% 164.67/136.71  
% 164.67/136.71  Simplification rules
% 164.67/136.71  ----------------------
% 164.67/136.71  #Subsume      : 4782
% 164.67/136.71  #Demod        : 101211
% 164.67/136.71  #Tautology    : 10704
% 164.67/136.71  #SimpNegUnit  : 8494
% 164.67/136.71  #BackRed      : 844
% 164.67/136.71  
% 164.67/136.71  #Partial instantiations: 0
% 164.67/136.71  #Strategies tried      : 1
% 164.67/136.71  
% 164.67/136.71  Timing (in seconds)
% 164.67/136.71  ----------------------
% 164.67/136.71  Preprocessing        : 0.68
% 164.67/136.71  Parsing              : 0.34
% 164.67/136.72  CNF conversion       : 0.05
% 164.67/136.72  Main loop            : 134.98
% 164.67/136.72  Inferencing          : 7.87
% 164.67/136.72  Reduction            : 94.20
% 164.67/136.72  Demodulation         : 80.90
% 164.67/136.72  BG Simplification    : 0.54
% 164.67/136.72  Subsumption          : 27.64
% 164.67/136.72  Abstraction          : 0.85
% 164.67/136.72  MUC search           : 0.00
% 164.67/136.72  Cooper               : 0.00
% 164.67/136.72  Total                : 135.71
% 164.67/136.72  Index Insertion      : 0.00
% 164.67/136.72  Index Deletion       : 0.00
% 164.67/136.72  Index Matching       : 0.00
% 164.67/136.72  BG Taut test         : 0.00
%------------------------------------------------------------------------------