TSTP Solution File: NUM500+3 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM500+3 : 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 : n018.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 10:51:54 EDT 2023

% Result   : Theorem 8.78s 3.03s
% Output   : CNFRefutation 8.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   50 (   7 unt;  28 typ;   0 def)
%            Number of atoms       :   67 (  32 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :   71 (  26   ~;  28   |;  15   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   36 (  19   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;   9 con; 0-3 aty)
%            Number of variables   :   10 (;   6   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_11 > #skF_6 > #skF_10 > #skF_5 > #skF_9 > #skF_7 > #skF_13 > #skF_3 > #skF_2 > #skF_8 > #skF_12 > #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('#skF_11',type,
    '#skF_11': $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $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('#skF_10',type,
    '#skF_10': $i ).

tff(sdtpldt0,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(isPrime0,type,
    isPrime0: $i > $o ).

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

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

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

tff('#skF_9',type,
    '#skF_9': $i ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i * $i ) > $i ).

tff('#skF_13',type,
    '#skF_13': $i > $i ).

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('#skF_8',type,
    '#skF_8': ( $i * $i * $i ) > $i ).

tff(xm,type,
    xm: $i ).

tff('#skF_12',type,
    '#skF_12': $i > $i ).

tff(sdtsldt0,type,
    sdtsldt0: ( $i * $i ) > $i ).

tff(xn,type,
    xn: $i ).

tff('#skF_1',type,
    '#skF_1': ( $i * $i ) > $i ).

tff(f_549,hypothesis,
    ( ( xk != sz00 )
    & ( xk != sz10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).

tff(f_540,hypothesis,
    ( aNaturalNumber0(xk)
    & ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
    & ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).

tff(f_418,axiom,
    ! [W0] :
      ( ( aNaturalNumber0(W0)
        & ( W0 != sz00 )
        & ( W0 != sz10 ) )
     => ? [W1] :
          ( aNaturalNumber0(W1)
          & doDivides0(W1,W0)
          & isPrime0(W1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).

tff(f_581,negated_conjecture,
    ~ ? [W0] :
        ( aNaturalNumber0(W0)
        & ( ? [W1] :
              ( aNaturalNumber0(W1)
              & ( xk = sdtasdt0(W0,W1) ) )
          | doDivides0(W0,xk) )
        & ( ( ( W0 != sz00 )
            & ( W0 != sz10 )
            & ! [W1] :
                ( ( aNaturalNumber0(W1)
                  & ? [W2] :
                      ( aNaturalNumber0(W2)
                      & ( W0 = sdtasdt0(W1,W2) ) )
                  & doDivides0(W1,W0) )
               => ( ( W1 = sz10 )
                  | ( W1 = W0 ) ) ) )
          | isPrime0(W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(c_453,plain,
    xk != sz00,
    inference(cnfTransformation,[status(thm)],[f_549]) ).

tff(c_451,plain,
    xk != sz10,
    inference(cnfTransformation,[status(thm)],[f_549]) ).

tff(c_445,plain,
    aNaturalNumber0(xk),
    inference(cnfTransformation,[status(thm)],[f_540]) ).

tff(c_137,plain,
    ! [W0_93] :
      ( isPrime0('#skF_4'(W0_93))
      | ( sz10 = W0_93 )
      | ( sz00 = W0_93 )
      | ~ aNaturalNumber0(W0_93) ),
    inference(cnfTransformation,[status(thm)],[f_418]) ).

tff(c_141,plain,
    ! [W0_93] :
      ( aNaturalNumber0('#skF_4'(W0_93))
      | ( sz10 = W0_93 )
      | ( sz00 = W0_93 )
      | ~ aNaturalNumber0(W0_93) ),
    inference(cnfTransformation,[status(thm)],[f_418]) ).

tff(c_3535,plain,
    ! [W0_160] :
      ( doDivides0('#skF_4'(W0_160),W0_160)
      | ( sz10 = W0_160 )
      | ( sz00 = W0_160 )
      | ~ aNaturalNumber0(W0_160) ),
    inference(cnfTransformation,[status(thm)],[f_418]) ).

tff(c_455,plain,
    ! [W0_111] :
      ( ~ doDivides0(W0_111,xk)
      | ~ isPrime0(W0_111)
      | ~ aNaturalNumber0(W0_111) ),
    inference(cnfTransformation,[status(thm)],[f_581]) ).

tff(c_3551,plain,
    ( ~ isPrime0('#skF_4'(xk))
    | ~ aNaturalNumber0('#skF_4'(xk))
    | ( xk = sz10 )
    | ( xk = sz00 )
    | ~ aNaturalNumber0(xk) ),
    inference(resolution,[status(thm)],[c_3535,c_455]) ).

tff(c_3566,plain,
    ( ~ isPrime0('#skF_4'(xk))
    | ~ aNaturalNumber0('#skF_4'(xk))
    | ( xk = sz10 )
    | ( xk = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_445,c_3551]) ).

tff(c_3567,plain,
    ( ~ isPrime0('#skF_4'(xk))
    | ~ aNaturalNumber0('#skF_4'(xk)) ),
    inference(negUnitSimplification,[status(thm)],[c_453,c_451,c_3566]) ).

tff(c_3568,plain,
    ~ aNaturalNumber0('#skF_4'(xk)),
    inference(splitLeft,[status(thm)],[c_3567]) ).

tff(c_3571,plain,
    ( ( xk = sz10 )
    | ( xk = sz00 )
    | ~ aNaturalNumber0(xk) ),
    inference(resolution,[status(thm)],[c_141,c_3568]) ).

tff(c_3574,plain,
    ( ( xk = sz10 )
    | ( xk = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_445,c_3571]) ).

tff(c_3576,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_453,c_451,c_3574]) ).

tff(c_3577,plain,
    ~ isPrime0('#skF_4'(xk)),
    inference(splitRight,[status(thm)],[c_3567]) ).

tff(c_3581,plain,
    ( ( xk = sz10 )
    | ( xk = sz00 )
    | ~ aNaturalNumber0(xk) ),
    inference(resolution,[status(thm)],[c_137,c_3577]) ).

tff(c_3584,plain,
    ( ( xk = sz10 )
    | ( xk = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_445,c_3581]) ).

tff(c_3586,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_453,c_451,c_3584]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : NUM500+3 : 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
% 0.15/0.37  % Computer : n018.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 15:12:50 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 8.78/3.03  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.96/3.03  
% 8.96/3.03  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.99/3.06  
% 8.99/3.06  Inference rules
% 8.99/3.06  ----------------------
% 8.99/3.06  #Ref     : 0
% 8.99/3.06  #Sup     : 730
% 8.99/3.06  #Fact    : 0
% 8.99/3.06  #Define  : 0
% 8.99/3.06  #Split   : 9
% 8.99/3.06  #Chain   : 0
% 8.99/3.06  #Close   : 0
% 8.99/3.06  
% 8.99/3.06  Ordering : KBO
% 8.99/3.06  
% 8.99/3.06  Simplification rules
% 8.99/3.06  ----------------------
% 8.99/3.06  #Subsume      : 247
% 8.99/3.06  #Demod        : 930
% 8.99/3.06  #Tautology    : 275
% 8.99/3.06  #SimpNegUnit  : 222
% 8.99/3.06  #BackRed      : 16
% 8.99/3.06  
% 8.99/3.06  #Partial instantiations: 0
% 8.99/3.06  #Strategies tried      : 1
% 8.99/3.06  
% 8.99/3.06  Timing (in seconds)
% 8.99/3.06  ----------------------
% 8.99/3.06  Preprocessing        : 0.80
% 8.99/3.06  Parsing              : 0.36
% 8.99/3.06  CNF conversion       : 0.07
% 8.99/3.06  Main loop            : 1.19
% 8.99/3.06  Inferencing          : 0.24
% 8.99/3.06  Reduction            : 0.45
% 8.99/3.06  Demodulation         : 0.32
% 8.99/3.06  BG Simplification    : 0.08
% 8.99/3.06  Subsumption          : 0.38
% 8.99/3.06  Abstraction          : 0.05
% 8.99/3.06  MUC search           : 0.00
% 8.99/3.07  Cooper               : 0.00
% 8.99/3.07  Total                : 2.04
% 8.99/3.07  Index Insertion      : 0.00
% 8.99/3.07  Index Deletion       : 0.00
% 8.99/3.07  Index Matching       : 0.00
% 8.99/3.07  BG Taut test         : 0.00
%------------------------------------------------------------------------------