TSTP Solution File: NUM525+3 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM525+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/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 : n003.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 19.30s 7.44s
% Output   : CNFRefutation 19.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   63 (  22 unt;  23 typ;   1 def)
%            Number of atoms       :   88 (  43 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   83 (  35   ~;  25   |;  18   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   28 (  15   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-3 aty)
%            Number of variables   :   22 (;  20   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xq > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_6 > #skF_7 > #skF_5 > #skF_8 > #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('#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_7',type,
    '#skF_7': $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_8',type,
    '#skF_8': $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(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_517,hypothesis,
    ( ? [W0] :
        ( aNaturalNumber0(W0)
        & ( sdtasdt0(xn,xn) = sdtasdt0(xp,W0) ) )
    & doDivides0(xp,sdtasdt0(xn,xn))
    & ? [W0] :
        ( aNaturalNumber0(W0)
        & ( xn = sdtasdt0(xp,W0) ) )
    & doDivides0(xp,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).

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_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_522,hypothesis,
    ( aNaturalNumber0(xq)
    & ( xn = sdtasdt0(xp,xq) )
    & ( 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_486,hypothesis,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).

tff(f_524,negated_conjecture,
    sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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

tff(c_191,plain,
    aNaturalNumber0('#skF_8'),
    inference(cnfTransformation,[status(thm)],[f_517]) ).

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

tff(c_957,plain,
    ! [W1_123,W0_124] :
      ( ( sdtasdt0(W1_123,W0_124) = sdtasdt0(W0_124,W1_123) )
      | ~ aNaturalNumber0(W1_123)
      | ~ aNaturalNumber0(W0_124) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_994,plain,
    ! [W0_125] :
      ( ( sdtasdt0(xp,W0_125) = sdtasdt0(W0_125,xp) )
      | ~ aNaturalNumber0(W0_125) ),
    inference(resolution,[status(thm)],[c_151,c_957]) ).

tff(c_1045,plain,
    sdtasdt0(xp,'#skF_8') = sdtasdt0('#skF_8',xp),
    inference(resolution,[status(thm)],[c_191,c_994]) ).

tff(c_189,plain,
    sdtasdt0(xp,'#skF_8') = sdtasdt0(xn,xn),
    inference(cnfTransformation,[status(thm)],[f_517]) ).

tff(c_1189,plain,
    sdtasdt0(xn,xn) = sdtasdt0('#skF_8',xp),
    inference(demodulation,[status(thm),theory(equality)],[c_1045,c_189]) ).

tff(c_185,plain,
    aNaturalNumber0('#skF_7'),
    inference(cnfTransformation,[status(thm)],[f_517]) ).

tff(c_183,plain,
    sdtasdt0(xp,'#skF_7') = xn,
    inference(cnfTransformation,[status(thm)],[f_517]) ).

tff(c_18598,plain,
    ! [W0_406,W1_407,W2_408] :
      ( ( sdtasdt0(sdtasdt0(W0_406,W1_407),W2_408) = sdtasdt0(W0_406,sdtasdt0(W1_407,W2_408)) )
      | ~ aNaturalNumber0(W2_408)
      | ~ aNaturalNumber0(W1_407)
      | ~ aNaturalNumber0(W0_406) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_18763,plain,
    ! [W2_408] :
      ( ( sdtasdt0(xp,sdtasdt0('#skF_7',W2_408)) = sdtasdt0(xn,W2_408) )
      | ~ aNaturalNumber0(W2_408)
      | ~ aNaturalNumber0('#skF_7')
      | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_183,c_18598]) ).

tff(c_18844,plain,
    ! [W2_408] :
      ( ( sdtasdt0(xp,sdtasdt0('#skF_7',W2_408)) = sdtasdt0(xn,W2_408) )
      | ~ aNaturalNumber0(W2_408) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_185,c_18763]) ).

tff(c_28761,plain,
    ! [W0_496] :
      ( ( sdtasdt0(xn,W0_496) = sdtasdt0(W0_496,xn) )
      | ~ aNaturalNumber0(W0_496) ),
    inference(resolution,[status(thm)],[c_155,c_957]) ).

tff(c_28880,plain,
    sdtasdt0(xn,'#skF_7') = sdtasdt0('#skF_7',xn),
    inference(resolution,[status(thm)],[c_185,c_28761]) ).

tff(c_36027,plain,
    ! [W2_513] :
      ( ( sdtasdt0(xp,sdtasdt0('#skF_7',W2_513)) = sdtasdt0(xn,W2_513) )
      | ~ aNaturalNumber0(W2_513) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_185,c_18763]) ).

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

tff(c_181,plain,
    doDivides0(xp,xn),
    inference(cnfTransformation,[status(thm)],[f_517]) ).

tff(c_193,plain,
    sdtsldt0(xn,xp) = xq,
    inference(cnfTransformation,[status(thm)],[f_522]) ).

tff(c_25031,plain,
    ! [W0_463,W2_464] :
      ( ( sdtsldt0(sdtasdt0(W0_463,W2_464),W0_463) = W2_464 )
      | ~ aNaturalNumber0(W2_464)
      | ~ doDivides0(W0_463,sdtasdt0(W0_463,W2_464))
      | ( sz00 = W0_463 )
      | ~ aNaturalNumber0(sdtasdt0(W0_463,W2_464))
      | ~ aNaturalNumber0(W0_463) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_25145,plain,
    ( ( sdtsldt0(sdtasdt0(xp,'#skF_7'),xp) = '#skF_7' )
    | ~ aNaturalNumber0('#skF_7')
    | ~ doDivides0(xp,xn)
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sdtasdt0(xp,'#skF_7'))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_183,c_25031]) ).

tff(c_25250,plain,
    ( ( xq = '#skF_7' )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_155,c_183,c_181,c_185,c_193,c_183,c_25145]) ).

tff(c_25251,plain,
    xq = '#skF_7',
    inference(negUnitSimplification,[status(thm)],[c_145,c_25250]) ).

tff(c_171,plain,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    inference(cnfTransformation,[status(thm)],[f_486]) ).

tff(c_199,plain,
    sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xp,sdtasdt0(xm,xm)),
    inference(cnfTransformation,[status(thm)],[f_524]) ).

tff(c_200,plain,
    sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xn,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_171,c_199]) ).

tff(c_1308,plain,
    sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0('#skF_8',xp),
    inference(demodulation,[status(thm),theory(equality)],[c_1189,c_200]) ).

tff(c_25296,plain,
    sdtasdt0(xp,sdtasdt0(xp,sdtasdt0('#skF_7','#skF_7'))) != sdtasdt0('#skF_8',xp),
    inference(demodulation,[status(thm),theory(equality)],[c_25251,c_25251,c_1308]) ).

tff(c_36048,plain,
    ( ( sdtasdt0(xp,sdtasdt0(xn,'#skF_7')) != sdtasdt0('#skF_8',xp) )
    | ~ aNaturalNumber0('#skF_7') ),
    inference(superposition,[status(thm),theory(equality)],[c_36027,c_25296]) ).

tff(c_36141,plain,
    sdtasdt0(xp,sdtasdt0('#skF_7',xn)) != sdtasdt0('#skF_8',xp),
    inference(demodulation,[status(thm),theory(equality)],[c_185,c_28880,c_36048]) ).

tff(c_36206,plain,
    ( ( sdtasdt0(xn,xn) != sdtasdt0('#skF_8',xp) )
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_18844,c_36141]) ).

tff(c_36209,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_155,c_1189,c_36206]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : NUM525+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15  % 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
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 14:37:38 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 19.30/7.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.30/7.45  
% 19.30/7.45  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.30/7.48  
% 19.30/7.48  Inference rules
% 19.30/7.48  ----------------------
% 19.30/7.48  #Ref     : 19
% 19.30/7.48  #Sup     : 7410
% 19.30/7.48  #Fact    : 2
% 19.30/7.48  #Define  : 0
% 19.30/7.48  #Split   : 43
% 19.30/7.48  #Chain   : 0
% 19.30/7.48  #Close   : 0
% 19.30/7.48  
% 19.30/7.48  Ordering : KBO
% 19.30/7.48  
% 19.30/7.48  Simplification rules
% 19.30/7.48  ----------------------
% 19.30/7.48  #Subsume      : 346
% 19.30/7.48  #Demod        : 13506
% 19.30/7.48  #Tautology    : 2649
% 19.30/7.48  #SimpNegUnit  : 1591
% 19.30/7.48  #BackRed      : 1077
% 19.30/7.48  
% 19.30/7.48  #Partial instantiations: 0
% 19.30/7.48  #Strategies tried      : 1
% 19.30/7.48  
% 19.30/7.48  Timing (in seconds)
% 19.30/7.48  ----------------------
% 19.30/7.48  Preprocessing        : 0.68
% 19.30/7.48  Parsing              : 0.34
% 19.30/7.48  CNF conversion       : 0.05
% 19.30/7.48  Main loop            : 5.71
% 19.30/7.48  Inferencing          : 1.15
% 19.30/7.48  Reduction            : 2.92
% 19.30/7.48  Demodulation         : 2.39
% 19.30/7.48  BG Simplification    : 0.13
% 19.30/7.48  Subsumption          : 1.10
% 19.30/7.48  Abstraction          : 0.13
% 19.30/7.48  MUC search           : 0.00
% 19.30/7.48  Cooper               : 0.00
% 19.30/7.48  Total                : 6.45
% 19.30/7.48  Index Insertion      : 0.00
% 19.30/7.48  Index Deletion       : 0.00
% 19.30/7.48  Index Matching       : 0.00
% 19.30/7.48  BG Taut test         : 0.00
%------------------------------------------------------------------------------