TSTP Solution File: NUM505+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM505+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 : 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 10:51:55 EDT 2023

% Result   : Theorem 8.66s 3.09s
% Output   : CNFRefutation 9.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   70 (  26 unt;  20 typ;   2 def)
%            Number of atoms       :  109 (  27 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   99 (  40   ~;  31   |;  16   &)
%                                         (   2 <=>;  10  =>;   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    :   15 (  15 usr;   7 con; 0-2 aty)
%            Number of variables   :   21 (;  21   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > 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(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_423,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).

tff(f_47,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => aNaturalNumber0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).

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_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_481,negated_conjecture,
    ~ ( ~ sdtlseqdt0(xp,xk)
     => ( ( xk != xp )
        & sdtlseqdt0(xk,xp) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

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

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

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

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_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_193,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_270,plain,
    ! [W0_101] :
      ( ( sdtasdt0(sz10,W0_101) = W0_101 )
      | ~ aNaturalNumber0(W0_101) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_292,plain,
    sdtasdt0(sz10,xp) = xp,
    inference(resolution,[status(thm)],[c_143,c_270]) ).

tff(c_1256,plain,
    ! [W1_126,W0_127] :
      ( sdtlseqdt0(W1_126,sdtasdt0(W1_126,W0_127))
      | ( sz00 = W0_127 )
      | ~ aNaturalNumber0(W1_126)
      | ~ aNaturalNumber0(W0_127) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_1313,plain,
    ( sdtlseqdt0(sz10,xp)
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_292,c_1256]) ).

tff(c_1381,plain,
    ( sdtlseqdt0(sz10,xp)
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_1313]) ).

tff(c_3810,plain,
    xp = sz00,
    inference(splitLeft,[status(thm)],[c_1381]) ).

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

tff(c_3832,plain,
    isPrime0(sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_3810,c_153]) ).

tff(c_3845,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_193,c_3832]) ).

tff(c_3847,plain,
    xp != sz00,
    inference(splitRight,[status(thm)],[c_1381]) ).

tff(c_187,plain,
    ( ~ sdtlseqdt0(xk,xp)
    | ( xp = xk ) ),
    inference(cnfTransformation,[status(thm)],[f_481]) ).

tff(c_194,plain,
    ~ sdtlseqdt0(xk,xp),
    inference(splitLeft,[status(thm)],[c_187]) ).

tff(c_1135,plain,
    ! [W1_122,W0_123] :
      ( sdtlseqdt0(W1_122,W0_123)
      | sdtlseqdt0(W0_123,W1_122)
      | ~ aNaturalNumber0(W1_122)
      | ~ aNaturalNumber0(W0_123) ),
    inference(cnfTransformation,[status(thm)],[f_212]) ).

tff(c_189,plain,
    ~ sdtlseqdt0(xp,xk),
    inference(cnfTransformation,[status(thm)],[f_481]) ).

tff(c_1145,plain,
    ( sdtlseqdt0(xk,xp)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xk) ),
    inference(resolution,[status(thm)],[c_1135,c_189]) ).

tff(c_1164,plain,
    ( sdtlseqdt0(xk,xp)
    | ~ aNaturalNumber0(xk) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_1145]) ).

tff(c_1165,plain,
    ~ aNaturalNumber0(xk),
    inference(negUnitSimplification,[status(thm)],[c_194,c_1164]) ).

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

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

tff(c_4851,plain,
    ! [W1_202,W0_203] :
      ( aNaturalNumber0(sdtsldt0(W1_202,W0_203))
      | ~ doDivides0(W0_203,W1_202)
      | ( sz00 = W0_203 )
      | ~ aNaturalNumber0(W1_202)
      | ~ aNaturalNumber0(W0_203) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_4885,plain,
    ( aNaturalNumber0(xk)
    | ~ doDivides0(xp,sdtasdt0(xn,xm))
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_167,c_4851]) ).

tff(c_4898,plain,
    ( aNaturalNumber0(xk)
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_151,c_4885]) ).

tff(c_4899,plain,
    ~ aNaturalNumber0(sdtasdt0(xn,xm)),
    inference(negUnitSimplification,[status(thm)],[c_3847,c_1165,c_4898]) ).

tff(c_4902,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(resolution,[status(thm)],[c_12,c_4899]) ).

tff(c_4906,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_4902]) ).

tff(c_4907,plain,
    xp = xk,
    inference(splitRight,[status(thm)],[c_187]) ).

tff(c_4910,plain,
    ~ sdtlseqdt0(xk,xk),
    inference(demodulation,[status(thm),theory(equality)],[c_4907,c_189]) ).

tff(c_4908,plain,
    sdtlseqdt0(xk,xp),
    inference(splitRight,[status(thm)],[c_187]) ).

tff(c_4919,plain,
    sdtlseqdt0(xk,xk),
    inference(demodulation,[status(thm),theory(equality)],[c_4907,c_4908]) ).

tff(c_4920,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4910,c_4919]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : NUM505+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % 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
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 14:49:07 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 8.66/3.09  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.66/3.10  
% 8.66/3.10  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.04/3.16  
% 9.04/3.16  Inference rules
% 9.04/3.16  ----------------------
% 9.04/3.16  #Ref     : 0
% 9.04/3.16  #Sup     : 914
% 9.04/3.16  #Fact    : 2
% 9.04/3.16  #Define  : 0
% 9.04/3.16  #Split   : 17
% 9.04/3.16  #Chain   : 0
% 9.04/3.16  #Close   : 0
% 9.04/3.16  
% 9.04/3.16  Ordering : KBO
% 9.04/3.16  
% 9.04/3.16  Simplification rules
% 9.04/3.16  ----------------------
% 9.04/3.16  #Subsume      : 90
% 9.04/3.16  #Demod        : 1510
% 9.04/3.16  #Tautology    : 591
% 9.04/3.16  #SimpNegUnit  : 177
% 9.04/3.16  #BackRed      : 281
% 9.04/3.16  
% 9.04/3.16  #Partial instantiations: 0
% 9.04/3.16  #Strategies tried      : 1
% 9.04/3.16  
% 9.04/3.16  Timing (in seconds)
% 9.04/3.16  ----------------------
% 9.04/3.16  Preprocessing        : 0.70
% 9.04/3.16  Parsing              : 0.36
% 9.04/3.16  CNF conversion       : 0.05
% 9.04/3.16  Main loop            : 1.25
% 9.04/3.16  Inferencing          : 0.39
% 9.04/3.16  Reduction            : 0.46
% 9.04/3.16  Demodulation         : 0.33
% 9.04/3.16  BG Simplification    : 0.06
% 9.04/3.16  Subsumption          : 0.25
% 9.04/3.16  Abstraction          : 0.05
% 9.04/3.16  MUC search           : 0.00
% 9.04/3.17  Cooper               : 0.00
% 9.04/3.17  Total                : 2.04
% 9.04/3.17  Index Insertion      : 0.00
% 9.04/3.17  Index Deletion       : 0.00
% 9.04/3.17  Index Matching       : 0.00
% 9.04/3.17  BG Taut test         : 0.00
%------------------------------------------------------------------------------