TSTP Solution File: NUM537+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM537+2 : 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 : n010.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 10:52:01 EDT 2023

% Result   : Theorem 6.72s 2.61s
% Output   : CNFRefutation 7.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   81 (  34 unt;  19 typ;   2 def)
%            Number of atoms       :  159 (  20 equ)
%            Maximal formula atoms :   26 (   2 avg)
%            Number of connectives :  165 (  68   ~;  60   |;  19   &)
%                                         (   8 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   27 (  14   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-3 aty)
%            Number of variables   :   36 (;  36   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > sdtpldt0 > sdtmndt0 > #nlpp > xx > xS > slcrc0 > #skF_6 > #skF_1 > #skF_4 > #skF_7 > #skF_5 > #skF_8 > #skF_3 > #skF_2

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(aSet0,type,
    aSet0: $i > $o ).

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

tff(sdtmndt0,type,
    sdtmndt0: ( $i * $i ) > $i ).

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

tff(aElement0,type,
    aElement0: $i > $o ).

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

tff('#skF_4',type,
    '#skF_4': ( $i * $i * $i ) > $i ).

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

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

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

tff(aSubsetOf0,type,
    aSubsetOf0: ( $i * $i ) > $o ).

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

tff(isCountable0,type,
    isCountable0: $i > $o ).

tff(aElementOf0,type,
    aElementOf0: ( $i * $i ) > $o ).

tff('#skF_8',type,
    '#skF_8': $i ).

tff(slcrc0,type,
    slcrc0: $i ).

tff(isFinite0,type,
    isFinite0: $i > $o ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i * $i ) > $i ).

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

tff(f_228,negated_conjecture,
    ~ ( ( ( aSet0(sdtpldt0(xS,xx))
          & ! [W0] :
              ( aElementOf0(W0,sdtpldt0(xS,xx))
            <=> ( aElement0(W0)
                & ( aElementOf0(W0,xS)
                  | ( W0 = xx ) ) ) ) )
       => ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
            & ! [W0] :
                ( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
              <=> ( aElement0(W0)
                  & aElementOf0(W0,sdtpldt0(xS,xx))
                  & ( W0 != xx ) ) ) )
         => ( ! [W0] :
                ( aElementOf0(W0,xS)
               => aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
            | aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) )
      & ( ( aSet0(sdtpldt0(xS,xx))
          & ! [W0] :
              ( aElementOf0(W0,sdtpldt0(xS,xx))
            <=> ( aElement0(W0)
                & ( aElementOf0(W0,xS)
                  | ( W0 = xx ) ) ) ) )
       => ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
            & ! [W0] :
                ( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
              <=> ( aElement0(W0)
                  & aElementOf0(W0,sdtpldt0(xS,xx))
                  & ( W0 != xx ) ) ) )
         => ( ! [W0] :
                ( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
               => aElementOf0(W0,xS) )
            | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_166,hypothesis,
    ( aElement0(xx)
    & aSet0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679) ).

tff(f_156,definition,
    ! [W0,W1] :
      ( ( aSet0(W0)
        & aElement0(W1) )
     => ! [W2] :
          ( ( W2 = sdtmndt0(W0,W1) )
        <=> ( aSet0(W2)
            & ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( aElement0(W3)
                  & aElementOf0(W3,W0)
                  & ( W3 != W1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).

tff(f_137,definition,
    ! [W0,W1] :
      ( ( aSet0(W0)
        & aElement0(W1) )
     => ! [W2] :
          ( ( W2 = sdtpldt0(W0,W1) )
        <=> ( aSet0(W2)
            & ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( aElement0(W3)
                  & ( aElementOf0(W3,W0)
                    | ( W3 = W1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).

tff(f_39,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => aElement0(W1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

tff(f_168,hypothesis,
    ~ aElementOf0(xx,xS),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679_02) ).

tff(c_132,plain,
    ( aElementOf0('#skF_7',xS)
    | ~ aElementOf0('#skF_8',xS) ),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_486,plain,
    ~ aElementOf0('#skF_8',xS),
    inference(splitLeft,[status(thm)],[c_132]) ).

tff(c_96,plain,
    aSet0(xS),
    inference(cnfTransformation,[status(thm)],[f_166]) ).

tff(c_98,plain,
    aElement0(xx),
    inference(cnfTransformation,[status(thm)],[f_166]) ).

tff(c_424,plain,
    aSet0(sdtpldt0(xS,xx)),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_158,plain,
    ( aElementOf0('#skF_7',xS)
    | aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_534,plain,
    aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(splitLeft,[status(thm)],[c_158]) ).

tff(c_627,plain,
    ! [W3_94,W0_95,W1_96] :
      ( aElementOf0(W3_94,W0_95)
      | ~ aElementOf0(W3_94,sdtmndt0(W0_95,W1_96))
      | ~ aElement0(W1_96)
      | ~ aSet0(W0_95) ),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_630,plain,
    ( aElementOf0('#skF_8',sdtpldt0(xS,xx))
    | ~ aElement0(xx)
    | ~ aSet0(sdtpldt0(xS,xx)) ),
    inference(resolution,[status(thm)],[c_534,c_627]) ).

tff(c_637,plain,
    aElementOf0('#skF_8',sdtpldt0(xS,xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_424,c_98,c_630]) ).

tff(c_784,plain,
    ! [W3_111,W1_112,W0_113] :
      ( ( W3_111 = W1_112 )
      | aElementOf0(W3_111,W0_113)
      | ~ aElementOf0(W3_111,sdtpldt0(W0_113,W1_112))
      | ~ aElement0(W1_112)
      | ~ aSet0(W0_113) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_795,plain,
    ( ( xx = '#skF_8' )
    | aElementOf0('#skF_8',xS)
    | ~ aElement0(xx)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_637,c_784]) ).

tff(c_813,plain,
    ( ( xx = '#skF_8' )
    | aElementOf0('#skF_8',xS) ),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_98,c_795]) ).

tff(c_814,plain,
    xx = '#skF_8',
    inference(negUnitSimplification,[status(thm)],[c_486,c_813]) ).

tff(c_192,plain,
    ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_832,plain,
    ~ aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,'#skF_8'),'#skF_8')),
    inference(demodulation,[status(thm),theory(equality)],[c_814,c_814,c_814,c_192]) ).

tff(c_830,plain,
    aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,'#skF_8'),'#skF_8')),
    inference(demodulation,[status(thm),theory(equality)],[c_814,c_814,c_534]) ).

tff(c_906,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_832,c_830]) ).

tff(c_908,plain,
    ~ aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(splitRight,[status(thm)],[c_158]) ).

tff(c_907,plain,
    aElementOf0('#skF_7',xS),
    inference(splitRight,[status(thm)],[c_158]) ).

tff(c_6,plain,
    ! [W1_5,W0_3] :
      ( aElement0(W1_5)
      | ~ aElementOf0(W1_5,W0_3)
      | ~ aSet0(W0_3) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_911,plain,
    ( aElement0('#skF_7')
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_907,c_6]) ).

tff(c_914,plain,
    aElement0('#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_911]) ).

tff(c_48,plain,
    ! [W3_43,W0_33,W1_34] :
      ( ~ aElementOf0(W3_43,W0_33)
      | aElementOf0(W3_43,sdtpldt0(W0_33,W1_34))
      | ~ aElement0(W3_43)
      | ~ aElement0(W1_34)
      | ~ aSet0(W0_33) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_1323,plain,
    ! [W3_160,W0_161,W1_162] :
      ( aElementOf0(W3_160,sdtmndt0(W0_161,W1_162))
      | ( W3_160 = W1_162 )
      | ~ aElementOf0(W3_160,W0_161)
      | ~ aElement0(W3_160)
      | ~ aElement0(W1_162)
      | ~ aSet0(W0_161) ),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_338,plain,
    ! [W0_60] :
      ( ~ aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx))
      | aElement0(W0_60)
      | ~ aElementOf0(W0_60,sdtpldt0(xS,xx)) ),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_1104,plain,
    ~ aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(splitLeft,[status(thm)],[c_338]) ).

tff(c_1330,plain,
    ( ( xx = '#skF_7' )
    | ~ aElementOf0('#skF_7',sdtpldt0(xS,xx))
    | ~ aElement0('#skF_7')
    | ~ aElement0(xx)
    | ~ aSet0(sdtpldt0(xS,xx)) ),
    inference(resolution,[status(thm)],[c_1323,c_1104]) ).

tff(c_1361,plain,
    ( ( xx = '#skF_7' )
    | ~ aElementOf0('#skF_7',sdtpldt0(xS,xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_424,c_98,c_914,c_1330]) ).

tff(c_1376,plain,
    ~ aElementOf0('#skF_7',sdtpldt0(xS,xx)),
    inference(splitLeft,[status(thm)],[c_1361]) ).

tff(c_1379,plain,
    ( ~ aElementOf0('#skF_7',xS)
    | ~ aElement0('#skF_7')
    | ~ aElement0(xx)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_48,c_1376]) ).

tff(c_1383,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_98,c_914,c_907,c_1379]) ).

tff(c_1384,plain,
    xx = '#skF_7',
    inference(splitRight,[status(thm)],[c_1361]) ).

tff(c_100,plain,
    ~ aElementOf0(xx,xS),
    inference(cnfTransformation,[status(thm)],[f_168]) ).

tff(c_1402,plain,
    ~ aElementOf0('#skF_7',xS),
    inference(demodulation,[status(thm),theory(equality)],[c_1384,c_100]) ).

tff(c_1406,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_907,c_1402]) ).

tff(c_1408,plain,
    aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(splitRight,[status(thm)],[c_338]) ).

tff(c_156,plain,
    ( ~ aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx))
    | aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_1559,plain,
    aElementOf0('#skF_8',sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_1408,c_156]) ).

tff(c_1560,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_908,c_1559]) ).

tff(c_1561,plain,
    aElementOf0('#skF_7',xS),
    inference(splitRight,[status(thm)],[c_132]) ).

tff(c_1570,plain,
    ! [W1_171,W0_172] :
      ( aElement0(W1_171)
      | ~ aElementOf0(W1_171,W0_172)
      | ~ aSet0(W0_172) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_1579,plain,
    ( aElement0('#skF_7')
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_1561,c_1570]) ).

tff(c_1588,plain,
    aElement0('#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_1579]) ).

tff(c_3075,plain,
    ! [W3_257,W0_258,W1_259] :
      ( aElementOf0(W3_257,sdtmndt0(W0_258,W1_259))
      | ( W3_257 = W1_259 )
      | ~ aElementOf0(W3_257,W0_258)
      | ~ aElement0(W3_257)
      | ~ aElement0(W1_259)
      | ~ aSet0(W0_258) ),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_1562,plain,
    aElementOf0('#skF_8',xS),
    inference(splitRight,[status(thm)],[c_132]) ).

tff(c_130,plain,
    ( ~ aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx))
    | ~ aElementOf0('#skF_8',xS) ),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_1624,plain,
    ~ aElementOf0('#skF_7',sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_1562,c_130]) ).

tff(c_3098,plain,
    ( ( xx = '#skF_7' )
    | ~ aElementOf0('#skF_7',sdtpldt0(xS,xx))
    | ~ aElement0('#skF_7')
    | ~ aElement0(xx)
    | ~ aSet0(sdtpldt0(xS,xx)) ),
    inference(resolution,[status(thm)],[c_3075,c_1624]) ).

tff(c_3121,plain,
    ( ( xx = '#skF_7' )
    | ~ aElementOf0('#skF_7',sdtpldt0(xS,xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_424,c_98,c_1588,c_3098]) ).

tff(c_3129,plain,
    ~ aElementOf0('#skF_7',sdtpldt0(xS,xx)),
    inference(splitLeft,[status(thm)],[c_3121]) ).

tff(c_3132,plain,
    ( ~ aElementOf0('#skF_7',xS)
    | ~ aElement0('#skF_7')
    | ~ aElement0(xx)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_48,c_3129]) ).

tff(c_3139,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_98,c_1588,c_1561,c_3132]) ).

tff(c_3140,plain,
    xx = '#skF_7',
    inference(splitRight,[status(thm)],[c_3121]) ).

tff(c_3166,plain,
    ~ aElementOf0('#skF_7',xS),
    inference(demodulation,[status(thm),theory(equality)],[c_3140,c_100]) ).

tff(c_3170,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1561,c_3166]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM537+2 : 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 : n010.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 14:31:28 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 6.72/2.61  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.72/2.62  
% 6.72/2.62  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.05/2.65  
% 7.05/2.65  Inference rules
% 7.05/2.65  ----------------------
% 7.05/2.65  #Ref     : 0
% 7.05/2.65  #Sup     : 441
% 7.05/2.65  #Fact    : 0
% 7.05/2.65  #Define  : 0
% 7.05/2.65  #Split   : 24
% 7.05/2.65  #Chain   : 0
% 7.05/2.65  #Close   : 0
% 7.05/2.65  
% 7.05/2.65  Ordering : KBO
% 7.05/2.65  
% 7.05/2.65  Simplification rules
% 7.05/2.65  ----------------------
% 7.05/2.65  #Subsume      : 219
% 7.05/2.65  #Demod        : 713
% 7.05/2.65  #Tautology    : 248
% 7.05/2.65  #SimpNegUnit  : 32
% 7.05/2.65  #BackRed      : 123
% 7.05/2.65  
% 7.05/2.65  #Partial instantiations: 0
% 7.05/2.65  #Strategies tried      : 1
% 7.05/2.65  
% 7.05/2.65  Timing (in seconds)
% 7.05/2.65  ----------------------
% 7.05/2.65  Preprocessing        : 0.69
% 7.05/2.65  Parsing              : 0.32
% 7.05/2.65  CNF conversion       : 0.06
% 7.05/2.65  Main loop            : 0.81
% 7.05/2.65  Inferencing          : 0.25
% 7.05/2.65  Reduction            : 0.27
% 7.05/2.65  Demodulation         : 0.19
% 7.05/2.66  BG Simplification    : 0.07
% 7.05/2.66  Subsumption          : 0.19
% 7.05/2.66  Abstraction          : 0.04
% 7.05/2.66  MUC search           : 0.00
% 7.05/2.66  Cooper               : 0.00
% 7.05/2.66  Total                : 1.55
% 7.05/2.66  Index Insertion      : 0.00
% 7.05/2.66  Index Deletion       : 0.00
% 7.05/2.66  Index Matching       : 0.00
% 7.05/2.66  BG Taut test         : 0.00
%------------------------------------------------------------------------------