TSTP Solution File: NUM524+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM524+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 : n027.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 22.67s 10.45s
% Output   : CNFRefutation 22.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   80 (  28 unt;  23 typ;   1 def)
%            Number of atoms       :  141 (  59 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  141 (  57   ~;  54   |;  21   &)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   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   :   32 (;  30   !;   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_47,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => aNaturalNumber0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

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_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_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_524,negated_conjecture,
    sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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

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_185,plain,
    aNaturalNumber0('#skF_7'),
    inference(cnfTransformation,[status(thm)],[f_517]) ).

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_181,plain,
    doDivides0(xp,xn),
    inference(cnfTransformation,[status(thm)],[f_517]) ).

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

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

tff(c_21223,plain,
    ! [W0_367,W2_368] :
      ( ( sdtsldt0(sdtasdt0(W0_367,W2_368),W0_367) = W2_368 )
      | ~ aNaturalNumber0(W2_368)
      | ~ doDivides0(W0_367,sdtasdt0(W0_367,W2_368))
      | ( sz00 = W0_367 )
      | ~ aNaturalNumber0(sdtasdt0(W0_367,W2_368))
      | ~ aNaturalNumber0(W0_367) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_21379,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_21223]) ).

tff(c_21522,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_21379]) ).

tff(c_21523,plain,
    xq = '#skF_7',
    inference(negUnitSimplification,[status(thm)],[c_145,c_21522]) ).

tff(c_21554,plain,
    sdtsldt0(xn,xp) = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_21523,c_193]) ).

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

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

tff(c_636,plain,
    ! [W0_117,W1_118] :
      ( aNaturalNumber0(sdtasdt0(W0_117,W1_118))
      | ~ aNaturalNumber0(W1_118)
      | ~ aNaturalNumber0(W0_117) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_678,plain,
    ( aNaturalNumber0(sdtasdt0(xn,xn))
    | ~ aNaturalNumber0('#skF_8')
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_189,c_636]) ).

tff(c_754,plain,
    aNaturalNumber0(sdtasdt0(xn,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_191,c_678]) ).

tff(c_187,plain,
    doDivides0(xp,sdtasdt0(xn,xn)),
    inference(cnfTransformation,[status(thm)],[f_517]) ).

tff(c_21328,plain,
    ( ( sdtsldt0(sdtasdt0(xp,'#skF_8'),xp) = '#skF_8' )
    | ~ aNaturalNumber0('#skF_8')
    | ~ doDivides0(xp,sdtasdt0(xn,xn))
    | ( xp = sz00 )
    | ~ aNaturalNumber0(sdtasdt0(xp,'#skF_8'))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_189,c_21223]) ).

tff(c_21471,plain,
    ( ( sdtsldt0(sdtasdt0(xn,xn),xp) = '#skF_8' )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_754,c_189,c_187,c_191,c_189,c_21328]) ).

tff(c_21472,plain,
    sdtsldt0(sdtasdt0(xn,xn),xp) = '#skF_8',
    inference(negUnitSimplification,[status(thm)],[c_145,c_21471]) ).

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_22580,plain,
    ( ( sdtasdt0(xn,sdtsldt0(xn,xp)) = '#skF_8' )
    | ~ aNaturalNumber0(xn)
    | ~ doDivides0(xp,xn)
    | ( xp = sz00 )
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_21472,c_121]) ).

tff(c_22593,plain,
    ( ( sdtasdt0(xn,'#skF_7') = '#skF_8' )
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_155,c_181,c_155,c_21554,c_22580]) ).

tff(c_22594,plain,
    sdtasdt0(xn,'#skF_7') = '#skF_8',
    inference(negUnitSimplification,[status(thm)],[c_145,c_22593]) ).

tff(c_12055,plain,
    ! [W0_289,W1_290,W2_291] :
      ( ( sdtasdt0(sdtasdt0(W0_289,W1_290),W2_291) = sdtasdt0(W0_289,sdtasdt0(W1_290,W2_291)) )
      | ~ aNaturalNumber0(W2_291)
      | ~ aNaturalNumber0(W1_290)
      | ~ aNaturalNumber0(W0_289) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_12282,plain,
    ! [W2_291] :
      ( ( sdtasdt0(xp,sdtasdt0('#skF_7',W2_291)) = sdtasdt0(xn,W2_291) )
      | ~ aNaturalNumber0(W2_291)
      | ~ aNaturalNumber0('#skF_7')
      | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_183,c_12055]) ).

tff(c_35127,plain,
    ! [W2_417] :
      ( ( sdtasdt0(xp,sdtasdt0('#skF_7',W2_417)) = sdtasdt0(xn,W2_417) )
      | ~ aNaturalNumber0(W2_417) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_185,c_12282]) ).

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

tff(c_21556,plain,
    sdtasdt0(xp,sdtasdt0('#skF_7','#skF_7')) != sdtasdt0(xm,xm),
    inference(demodulation,[status(thm),theory(equality)],[c_21523,c_21523,c_199]) ).

tff(c_35145,plain,
    ( ( sdtasdt0(xn,'#skF_7') != sdtasdt0(xm,xm) )
    | ~ aNaturalNumber0('#skF_7') ),
    inference(superposition,[status(thm),theory(equality)],[c_35127,c_21556]) ).

tff(c_35239,plain,
    sdtasdt0(xm,xm) != '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_185,c_22594,c_35145]) ).

tff(c_965,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_25664,plain,
    ! [W0_399] :
      ( ( sdtasdt0(xp,W0_399) = sdtasdt0(W0_399,xp) )
      | ~ aNaturalNumber0(W0_399) ),
    inference(resolution,[status(thm)],[c_151,c_965]) ).

tff(c_25809,plain,
    sdtasdt0(xp,'#skF_8') = sdtasdt0('#skF_8',xp),
    inference(resolution,[status(thm)],[c_191,c_25664]) ).

tff(c_26008,plain,
    sdtasdt0(xn,xn) = sdtasdt0('#skF_8',xp),
    inference(demodulation,[status(thm),theory(equality)],[c_25809,c_189]) ).

tff(c_26211,plain,
    sdtsldt0(sdtasdt0('#skF_8',xp),xp) = '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_26008,c_21472]) ).

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

tff(c_21316,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_171,c_21223]) ).

tff(c_21459,plain,
    ( ( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
    | ~ aNaturalNumber0(sdtasdt0(xm,xm))
    | ( xp = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_754,c_171,c_187,c_171,c_21316]) ).

tff(c_21460,plain,
    ( ( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
    | ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
    inference(negUnitSimplification,[status(thm)],[c_145,c_21459]) ).

tff(c_44737,plain,
    ( ( sdtasdt0(xm,xm) = '#skF_8' )
    | ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26211,c_26008,c_21460]) ).

tff(c_44738,plain,
    ~ aNaturalNumber0(sdtasdt0(xm,xm)),
    inference(negUnitSimplification,[status(thm)],[c_35239,c_44737]) ).

tff(c_44741,plain,
    ~ aNaturalNumber0(xm),
    inference(resolution,[status(thm)],[c_12,c_44738]) ).

tff(c_44745,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_153,c_44741]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM524+3 : 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
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 15:03:09 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 22.67/10.45  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.67/10.46  
% 22.67/10.46  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.73/10.49  
% 22.73/10.49  Inference rules
% 22.73/10.49  ----------------------
% 22.73/10.49  #Ref     : 16
% 22.73/10.49  #Sup     : 9056
% 22.73/10.49  #Fact    : 2
% 22.73/10.49  #Define  : 0
% 22.73/10.49  #Split   : 34
% 22.73/10.49  #Chain   : 0
% 22.73/10.49  #Close   : 0
% 22.73/10.49  
% 22.73/10.49  Ordering : KBO
% 22.73/10.49  
% 22.73/10.49  Simplification rules
% 22.73/10.49  ----------------------
% 22.73/10.49  #Subsume      : 504
% 22.73/10.49  #Demod        : 16265
% 22.73/10.49  #Tautology    : 3199
% 22.73/10.49  #SimpNegUnit  : 1923
% 22.73/10.49  #BackRed      : 960
% 22.73/10.49  
% 22.73/10.49  #Partial instantiations: 0
% 22.73/10.49  #Strategies tried      : 1
% 22.73/10.49  
% 22.73/10.49  Timing (in seconds)
% 22.73/10.49  ----------------------
% 22.73/10.49  Preprocessing        : 0.70
% 22.73/10.49  Parsing              : 0.35
% 22.73/10.49  CNF conversion       : 0.05
% 22.73/10.49  Main loop            : 8.66
% 22.73/10.49  Inferencing          : 1.45
% 22.73/10.49  Reduction            : 4.88
% 22.73/10.49  Demodulation         : 4.03
% 22.73/10.49  BG Simplification    : 0.12
% 22.73/10.49  Subsumption          : 1.70
% 22.73/10.49  Abstraction          : 0.15
% 22.73/10.49  MUC search           : 0.00
% 22.73/10.49  Cooper               : 0.00
% 22.73/10.49  Total                : 9.42
% 22.73/10.49  Index Insertion      : 0.00
% 22.73/10.49  Index Deletion       : 0.00
% 22.73/10.49  Index Matching       : 0.00
% 22.73/10.49  BG Taut test         : 0.00
%------------------------------------------------------------------------------