TSTP Solution File: SET789+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET789+4 : TPTP v8.1.2. Released v3.2.0.
% 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 : n016.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 10:57:01 EDT 2023

% Result   : Theorem 6.25s 2.51s
% Output   : CNFRefutation 6.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   53 (   9 unt;  32 typ;   0 def)
%            Number of atoms       :   60 (   6 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :   63 (  24   ~;  20   |;   9   &)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   77 (  28   >;  49   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  12 usr;   1 prp; 0-4 aty)
%            Number of functors    :   20 (  20 usr;   4 con; 0-4 aty)
%            Number of variables   :   34 (;  34   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ least_upper_bound > greatest_lower_bound > upper_bound > min > max > lower_bound > least > greatest > apply > total_order > order > member > #nlpp > #skF_13 > #skF_6 > #skF_20 > #skF_18 > #skF_17 > #skF_12 > #skF_19 > #skF_3 > #skF_15 > #skF_16 > #skF_8 > #skF_11 > #skF_9 > #skF_14 > #skF_2 > #skF_7 > #skF_1 > #skF_5 > #skF_4 > #skF_10

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_13',type,
    '#skF_13': ( $i * $i * $i ) > $i ).

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

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

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

tff('#skF_20',type,
    '#skF_20': $i ).

tff('#skF_18',type,
    '#skF_18': $i ).

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

tff('#skF_17',type,
    '#skF_17': $i ).

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

tff('#skF_12',type,
    '#skF_12': ( $i * $i * $i ) > $i ).

tff('#skF_19',type,
    '#skF_19': $i ).

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

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

tff('#skF_15',type,
    '#skF_15': ( $i * $i * $i * $i ) > $i ).

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

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

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

tff('#skF_16',type,
    '#skF_16': ( $i * $i * $i * $i ) > $i ).

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

tff('#skF_11',type,
    '#skF_11': ( $i * $i * $i ) > $i ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i * $i ) > $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

tff('#skF_10',type,
    '#skF_10': ( $i * $i * $i ) > $i ).

tff(f_185,negated_conjecture,
    ~ ! [R,E,M] :
        ( ( order(R,E)
          & greatest(M,R,E) )
       => ! [X] :
            ( greatest(X,R,E)
           => ( M = X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV1) ).

tff(f_116,axiom,
    ! [R,E,M] :
      ( greatest(M,R,E)
    <=> ( member(M,E)
        & ! [X] :
            ( member(X,E)
           => apply(R,X,M) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',greatest) ).

tff(f_80,axiom,
    ! [R,E] :
      ( order(R,E)
    <=> ( ! [X] :
            ( member(X,E)
           => apply(R,X,X) )
        & ! [X,Y] :
            ( ( member(X,E)
              & member(Y,E) )
           => ( ( apply(R,X,Y)
                & apply(R,Y,X) )
             => ( X = Y ) ) )
        & ! [X,Y,Z] :
            ( ( member(X,E)
              & member(Y,E)
              & member(Z,E) )
           => ( ( apply(R,X,Y)
                & apply(R,Y,Z) )
             => apply(R,X,Z) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',order) ).

tff(c_216,plain,
    greatest('#skF_19','#skF_17','#skF_18'),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_220,plain,
    ! [M_82,E_83,R_84] :
      ( member(M_82,E_83)
      | ~ greatest(M_82,R_84,E_83) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_228,plain,
    member('#skF_19','#skF_18'),
    inference(resolution,[status(thm)],[c_216,c_220]) ).

tff(c_214,plain,
    greatest('#skF_20','#skF_17','#skF_18'),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_227,plain,
    member('#skF_20','#skF_18'),
    inference(resolution,[status(thm)],[c_214,c_220]) ).

tff(c_218,plain,
    order('#skF_17','#skF_18'),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_212,plain,
    '#skF_20' != '#skF_19',
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_253,plain,
    ! [R_121,X_122,M_123,E_124] :
      ( apply(R_121,X_122,M_123)
      | ~ member(X_122,E_124)
      | ~ greatest(M_123,R_121,E_124) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_266,plain,
    ! [R_125,M_126] :
      ( apply(R_125,'#skF_19',M_126)
      | ~ greatest(M_126,R_125,'#skF_18') ),
    inference(resolution,[status(thm)],[c_228,c_253]) ).

tff(c_273,plain,
    apply('#skF_17','#skF_19','#skF_20'),
    inference(resolution,[status(thm)],[c_214,c_266]) ).

tff(c_275,plain,
    ! [R_127,M_128] :
      ( apply(R_127,'#skF_20',M_128)
      | ~ greatest(M_128,R_127,'#skF_18') ),
    inference(resolution,[status(thm)],[c_227,c_253]) ).

tff(c_283,plain,
    apply('#skF_17','#skF_20','#skF_19'),
    inference(resolution,[status(thm)],[c_216,c_275]) ).

tff(c_1593,plain,
    ! [Y_421,X_422,R_423,E_424] :
      ( ( Y_421 = X_422 )
      | ~ apply(R_423,Y_421,X_422)
      | ~ apply(R_423,X_422,Y_421)
      | ~ member(Y_421,E_424)
      | ~ member(X_422,E_424)
      | ~ order(R_423,E_424) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_1663,plain,
    ! [E_424] :
      ( ( '#skF_20' = '#skF_19' )
      | ~ apply('#skF_17','#skF_19','#skF_20')
      | ~ member('#skF_20',E_424)
      | ~ member('#skF_19',E_424)
      | ~ order('#skF_17',E_424) ),
    inference(resolution,[status(thm)],[c_283,c_1593]) ).

tff(c_1720,plain,
    ! [E_424] :
      ( ( '#skF_20' = '#skF_19' )
      | ~ member('#skF_20',E_424)
      | ~ member('#skF_19',E_424)
      | ~ order('#skF_17',E_424) ),
    inference(demodulation,[status(thm),theory(equality)],[c_273,c_1663]) ).

tff(c_1738,plain,
    ! [E_425] :
      ( ~ member('#skF_20',E_425)
      | ~ member('#skF_19',E_425)
      | ~ order('#skF_17',E_425) ),
    inference(negUnitSimplification,[status(thm)],[c_212,c_1720]) ).

tff(c_1741,plain,
    ( ~ member('#skF_20','#skF_18')
    | ~ member('#skF_19','#skF_18') ),
    inference(resolution,[status(thm)],[c_218,c_1738]) ).

tff(c_1745,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_228,c_227,c_1741]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET789+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % 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 : n016.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 17:25:52 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 6.25/2.51  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.25/2.52  
% 6.25/2.52  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.34/2.55  
% 6.34/2.55  Inference rules
% 6.34/2.55  ----------------------
% 6.34/2.55  #Ref     : 0
% 6.34/2.55  #Sup     : 371
% 6.34/2.55  #Fact    : 4
% 6.34/2.55  #Define  : 0
% 6.34/2.55  #Split   : 0
% 6.34/2.55  #Chain   : 0
% 6.34/2.55  #Close   : 0
% 6.34/2.55  
% 6.34/2.55  Ordering : KBO
% 6.34/2.55  
% 6.34/2.55  Simplification rules
% 6.34/2.55  ----------------------
% 6.34/2.55  #Subsume      : 12
% 6.34/2.55  #Demod        : 21
% 6.34/2.55  #Tautology    : 38
% 6.34/2.55  #SimpNegUnit  : 14
% 6.34/2.55  #BackRed      : 0
% 6.34/2.55  
% 6.34/2.55  #Partial instantiations: 0
% 6.34/2.55  #Strategies tried      : 1
% 6.34/2.55  
% 6.34/2.55  Timing (in seconds)
% 6.34/2.55  ----------------------
% 6.34/2.55  Preprocessing        : 0.64
% 6.34/2.55  Parsing              : 0.28
% 6.34/2.56  CNF conversion       : 0.07
% 6.34/2.56  Main loop            : 0.79
% 6.34/2.56  Inferencing          : 0.31
% 6.34/2.56  Reduction            : 0.18
% 6.34/2.56  Demodulation         : 0.12
% 6.34/2.56  BG Simplification    : 0.06
% 6.34/2.56  Subsumption          : 0.19
% 6.34/2.56  Abstraction          : 0.03
% 6.34/2.56  MUC search           : 0.00
% 6.34/2.56  Cooper               : 0.00
% 6.34/2.56  Total                : 1.48
% 6.34/2.56  Index Insertion      : 0.00
% 6.34/2.56  Index Deletion       : 0.00
% 6.34/2.56  Index Matching       : 0.00
% 6.34/2.56  BG Taut test         : 0.00
%------------------------------------------------------------------------------