TSTP Solution File: NUM523+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM523+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 : n031.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 10:51:58 EDT 2023

% Result   : Theorem 13.93s 4.46s
% Output   : CNFRefutation 14.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   50 (  19 unt;  18 typ;   1 def)
%            Number of atoms       :   71 (   6 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   68 (  29   ~;  22   |;  12   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   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    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :   15 (;  14   !;   1   ?;   0   :)

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

%Foreground sorts:

%Background operators:

%Foreground operators:
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_474,negated_conjecture,
    ~ ( doDivides0(xp,sdtasdt0(xn,xn))
      & doDivides0(xp,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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

tff(f_307,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( doDivides0(W0,W1)
      <=> ? [W2] :
            ( aNaturalNumber0(W2)
            & ( W1 = sdtasdt0(W0,W2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).

tff(f_470,hypothesis,
    isPrime0(xp),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).

tff(f_432,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( ( isPrime0(W2)
          & doDivides0(W2,sdtasdt0(W0,W1)) )
       => ( doDivides0(W2,W0)
          | doDivides0(W2,W1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPDP) ).

tff(c_163,plain,
    ( ~ doDivides0(xp,xn)
    | ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
    inference(cnfTransformation,[status(thm)],[f_474]) ).

tff(c_168,plain,
    ~ doDivides0(xp,sdtasdt0(xn,xn)),
    inference(splitLeft,[status(thm)],[c_163]) ).

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

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_159,plain,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    inference(cnfTransformation,[status(thm)],[f_469]) ).

tff(c_579,plain,
    ( aNaturalNumber0(sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_159,c_12]) ).

tff(c_583,plain,
    ( aNaturalNumber0(sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_579]) ).

tff(c_585,plain,
    ~ aNaturalNumber0(sdtasdt0(xm,xm)),
    inference(splitLeft,[status(thm)],[c_583]) ).

tff(c_588,plain,
    ~ aNaturalNumber0(xm),
    inference(resolution,[status(thm)],[c_12,c_585]) ).

tff(c_592,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_153,c_588]) ).

tff(c_593,plain,
    aNaturalNumber0(sdtasdt0(xn,xn)),
    inference(splitRight,[status(thm)],[c_583]) ).

tff(c_594,plain,
    aNaturalNumber0(sdtasdt0(xm,xm)),
    inference(splitRight,[status(thm)],[c_583]) ).

tff(c_4153,plain,
    ! [W0_184,W2_185] :
      ( doDivides0(W0_184,sdtasdt0(W0_184,W2_185))
      | ~ aNaturalNumber0(W2_185)
      | ~ aNaturalNumber0(sdtasdt0(W0_184,W2_185))
      | ~ aNaturalNumber0(W0_184) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_4225,plain,
    ( doDivides0(xp,sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[status(thm),theory(equality)],[c_159,c_4153]) ).

tff(c_4321,plain,
    doDivides0(xp,sdtasdt0(xn,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_151,c_593,c_159,c_594,c_4225]) ).

tff(c_4323,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_168,c_4321]) ).

tff(c_4324,plain,
    ~ doDivides0(xp,xn),
    inference(splitRight,[status(thm)],[c_163]) ).

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

tff(c_161,plain,
    isPrime0(xp),
    inference(cnfTransformation,[status(thm)],[f_470]) ).

tff(c_4325,plain,
    doDivides0(xp,sdtasdt0(xn,xn)),
    inference(splitRight,[status(thm)],[c_163]) ).

tff(c_15511,plain,
    ! [W2_342,W1_343,W0_344] :
      ( doDivides0(W2_342,W1_343)
      | doDivides0(W2_342,W0_344)
      | ~ doDivides0(W2_342,sdtasdt0(W0_344,W1_343))
      | ~ isPrime0(W2_342)
      | ~ aNaturalNumber0(W2_342)
      | ~ aNaturalNumber0(W1_343)
      | ~ aNaturalNumber0(W0_344) ),
    inference(cnfTransformation,[status(thm)],[f_432]) ).

tff(c_15702,plain,
    ( doDivides0(xp,xn)
    | ~ isPrime0(xp)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(resolution,[status(thm)],[c_4325,c_15511]) ).

tff(c_15831,plain,
    doDivides0(xp,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_155,c_151,c_161,c_15702]) ).

tff(c_15833,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4324,c_15831]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : NUM523+1 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.14  % 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
% 0.15/0.36  % Computer : n031.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 15:19:44 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 13.93/4.46  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.93/4.46  
% 13.93/4.46  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.08/4.49  
% 14.08/4.49  Inference rules
% 14.08/4.49  ----------------------
% 14.08/4.49  #Ref     : 7
% 14.08/4.49  #Sup     : 3327
% 14.08/4.49  #Fact    : 4
% 14.08/4.49  #Define  : 0
% 14.08/4.49  #Split   : 20
% 14.08/4.49  #Chain   : 0
% 14.08/4.49  #Close   : 0
% 14.08/4.49  
% 14.08/4.49  Ordering : KBO
% 14.08/4.49  
% 14.08/4.49  Simplification rules
% 14.08/4.49  ----------------------
% 14.08/4.49  #Subsume      : 184
% 14.08/4.49  #Demod        : 5212
% 14.08/4.49  #Tautology    : 1258
% 14.08/4.49  #SimpNegUnit  : 455
% 14.08/4.49  #BackRed      : 391
% 14.08/4.49  
% 14.08/4.49  #Partial instantiations: 0
% 14.08/4.49  #Strategies tried      : 1
% 14.08/4.49  
% 14.08/4.49  Timing (in seconds)
% 14.08/4.49  ----------------------
% 14.08/4.49  Preprocessing        : 0.67
% 14.08/4.49  Parsing              : 0.34
% 14.08/4.49  CNF conversion       : 0.05
% 14.08/4.49  Main loop            : 2.63
% 14.08/4.49  Inferencing          : 0.67
% 14.08/4.49  Reduction            : 1.19
% 14.08/4.49  Demodulation         : 0.93
% 14.08/4.49  BG Simplification    : 0.08
% 14.08/4.49  Subsumption          : 0.52
% 14.08/4.49  Abstraction          : 0.08
% 14.08/4.49  MUC search           : 0.00
% 14.08/4.49  Cooper               : 0.00
% 14.08/4.49  Total                : 3.34
% 14.08/4.49  Index Insertion      : 0.00
% 14.08/4.49  Index Deletion       : 0.00
% 14.08/4.49  Index Matching       : 0.00
% 14.08/4.49  BG Taut test         : 0.00
%------------------------------------------------------------------------------