TSTP Solution File: SET794+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET794+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/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 : n032.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 33.15s 19.62s
% Output   : CNFRefutation 33.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   70 (  12 unt;  31 typ;   0 def)
%            Number of atoms       :  107 (   9 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  112 (  44   ~;  53   |;   6   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   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    :   19 (  19 usr;   3 con; 0-4 aty)
%            Number of variables   :   70 (;  70   !;   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_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_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_182,negated_conjecture,
    ~ ! [R,E,M] :
        ( ( total_order(R,E)
          & min(M,R,E) )
       => least(M,R,E) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV6) ).

tff(f_147,axiom,
    ! [R,E,M] :
      ( min(M,R,E)
    <=> ( member(M,E)
        & ! [X] :
            ( ( member(X,E)
              & apply(R,X,M) )
           => ( M = X ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',min) ).

tff(f_93,axiom,
    ! [R,E] :
      ( total_order(R,E)
    <=> ( order(R,E)
        & ! [X,Y] :
            ( ( member(X,E)
              & member(Y,E) )
           => ( apply(R,X,Y)
              | apply(R,Y,X) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',total_order) ).

tff(f_107,axiom,
    ! [R,E,M] :
      ( lower_bound(M,R,E)
    <=> ! [X] :
          ( member(X,E)
         => apply(R,M,X) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',lower_bound) ).

tff(f_125,axiom,
    ! [R,E,M] :
      ( least(M,R,E)
    <=> ( member(M,E)
        & ! [X] :
            ( member(X,E)
           => apply(R,M,X) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least) ).

tff(c_216,plain,
    total_order('#skF_17','#skF_18'),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_214,plain,
    min('#skF_19','#skF_17','#skF_18'),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_225,plain,
    ! [M_90,E_91,R_92] :
      ( member(M_90,E_91)
      | ~ min(M_90,R_92,E_91) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_229,plain,
    member('#skF_19','#skF_18'),
    inference(resolution,[status(thm)],[c_214,c_225]) ).

tff(c_586,plain,
    ! [R_246,Y_247,X_248,E_249] :
      ( apply(R_246,Y_247,X_248)
      | apply(R_246,X_248,Y_247)
      | ~ member(Y_247,E_249)
      | ~ member(X_248,E_249)
      | ~ total_order(R_246,E_249) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_613,plain,
    ! [R_246,X_248] :
      ( apply(R_246,'#skF_19',X_248)
      | apply(R_246,X_248,'#skF_19')
      | ~ member(X_248,'#skF_18')
      | ~ total_order(R_246,'#skF_18') ),
    inference(resolution,[status(thm)],[c_229,c_586]) ).

tff(c_625,plain,
    ! [R_246] :
      ( ~ member('#skF_19','#skF_18')
      | ~ total_order(R_246,'#skF_18')
      | apply(R_246,'#skF_19','#skF_19') ),
    inference(factorization,[status(thm),theory(equality)],[c_613]) ).

tff(c_628,plain,
    ! [R_246] :
      ( ~ total_order(R_246,'#skF_18')
      | apply(R_246,'#skF_19','#skF_19') ),
    inference(demodulation,[status(thm),theory(equality)],[c_229,c_625]) ).

tff(c_212,plain,
    ~ least('#skF_19','#skF_17','#skF_18'),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_150,plain,
    ! [R_35,E_36,M_37] :
      ( member('#skF_10'(R_35,E_36,M_37),E_36)
      | lower_bound(M_37,R_35,E_36) ),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_632,plain,
    ! [R_250,X_251] :
      ( apply(R_250,'#skF_19',X_251)
      | apply(R_250,X_251,'#skF_19')
      | ~ member(X_251,'#skF_18')
      | ~ total_order(R_250,'#skF_18') ),
    inference(resolution,[status(thm)],[c_229,c_586]) ).

tff(c_178,plain,
    ! [X_64,M_61,R_59,E_60] :
      ( ( X_64 = M_61 )
      | ~ apply(R_59,X_64,M_61)
      | ~ member(X_64,E_60)
      | ~ min(M_61,R_59,E_60) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_1105,plain,
    ! [X_347,E_348,R_349] :
      ( ( X_347 = '#skF_19' )
      | ~ member(X_347,E_348)
      | ~ min('#skF_19',R_349,E_348)
      | apply(R_349,'#skF_19',X_347)
      | ~ member(X_347,'#skF_18')
      | ~ total_order(R_349,'#skF_18') ),
    inference(resolution,[status(thm)],[c_632,c_178]) ).

tff(c_74947,plain,
    ! [R_4809,E_4810,M_4811,R_4812] :
      ( ( '#skF_10'(R_4809,E_4810,M_4811) = '#skF_19' )
      | ~ min('#skF_19',R_4812,E_4810)
      | apply(R_4812,'#skF_19','#skF_10'(R_4809,E_4810,M_4811))
      | ~ member('#skF_10'(R_4809,E_4810,M_4811),'#skF_18')
      | ~ total_order(R_4812,'#skF_18')
      | lower_bound(M_4811,R_4809,E_4810) ),
    inference(resolution,[status(thm)],[c_150,c_1105]) ).

tff(c_148,plain,
    ! [R_35,M_37,E_36] :
      ( ~ apply(R_35,M_37,'#skF_10'(R_35,E_36,M_37))
      | lower_bound(M_37,R_35,E_36) ),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_74974,plain,
    ! [R_4813,E_4814] :
      ( ( '#skF_10'(R_4813,E_4814,'#skF_19') = '#skF_19' )
      | ~ min('#skF_19',R_4813,E_4814)
      | ~ member('#skF_10'(R_4813,E_4814,'#skF_19'),'#skF_18')
      | ~ total_order(R_4813,'#skF_18')
      | lower_bound('#skF_19',R_4813,E_4814) ),
    inference(resolution,[status(thm)],[c_74947,c_148]) ).

tff(c_75050,plain,
    ! [R_4818] :
      ( ( '#skF_10'(R_4818,'#skF_18','#skF_19') = '#skF_19' )
      | ~ min('#skF_19',R_4818,'#skF_18')
      | ~ total_order(R_4818,'#skF_18')
      | lower_bound('#skF_19',R_4818,'#skF_18') ),
    inference(resolution,[status(thm)],[c_150,c_74974]) ).

tff(c_75065,plain,
    ( ( '#skF_10'('#skF_17','#skF_18','#skF_19') = '#skF_19' )
    | ~ total_order('#skF_17','#skF_18')
    | lower_bound('#skF_19','#skF_17','#skF_18') ),
    inference(resolution,[status(thm)],[c_214,c_75050]) ).

tff(c_75077,plain,
    ( ( '#skF_10'('#skF_17','#skF_18','#skF_19') = '#skF_19' )
    | lower_bound('#skF_19','#skF_17','#skF_18') ),
    inference(demodulation,[status(thm),theory(equality)],[c_216,c_75065]) ).

tff(c_75078,plain,
    lower_bound('#skF_19','#skF_17','#skF_18'),
    inference(splitLeft,[status(thm)],[c_75077]) ).

tff(c_393,plain,
    ! [R_176,E_177,M_178] :
      ( member('#skF_12'(R_176,E_177,M_178),E_177)
      | least(M_178,R_176,E_177)
      | ~ member(M_178,E_177) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_146,plain,
    ! [R_35,M_37,X_40,E_36] :
      ( apply(R_35,M_37,X_40)
      | ~ member(X_40,E_36)
      | ~ lower_bound(M_37,R_35,E_36) ),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_1486,plain,
    ! [M_403,E_402,M_405,R_404,R_401] :
      ( apply(R_404,M_405,'#skF_12'(R_401,E_402,M_403))
      | ~ lower_bound(M_405,R_404,E_402)
      | least(M_403,R_401,E_402)
      | ~ member(M_403,E_402) ),
    inference(resolution,[status(thm)],[c_393,c_146]) ).

tff(c_164,plain,
    ! [R_47,M_49,E_48] :
      ( ~ apply(R_47,M_49,'#skF_12'(R_47,E_48,M_49))
      | least(M_49,R_47,E_48)
      | ~ member(M_49,E_48) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_1506,plain,
    ! [M_403,R_401,E_402] :
      ( ~ lower_bound(M_403,R_401,E_402)
      | least(M_403,R_401,E_402)
      | ~ member(M_403,E_402) ),
    inference(resolution,[status(thm)],[c_1486,c_164]) ).

tff(c_75110,plain,
    ( least('#skF_19','#skF_17','#skF_18')
    | ~ member('#skF_19','#skF_18') ),
    inference(resolution,[status(thm)],[c_75078,c_1506]) ).

tff(c_75162,plain,
    least('#skF_19','#skF_17','#skF_18'),
    inference(demodulation,[status(thm),theory(equality)],[c_229,c_75110]) ).

tff(c_75164,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_212,c_75162]) ).

tff(c_75166,plain,
    ~ lower_bound('#skF_19','#skF_17','#skF_18'),
    inference(splitRight,[status(thm)],[c_75077]) ).

tff(c_75165,plain,
    '#skF_10'('#skF_17','#skF_18','#skF_19') = '#skF_19',
    inference(splitRight,[status(thm)],[c_75077]) ).

tff(c_75285,plain,
    ( ~ apply('#skF_17','#skF_19','#skF_19')
    | lower_bound('#skF_19','#skF_17','#skF_18') ),
    inference(superposition,[status(thm),theory(equality)],[c_75165,c_148]) ).

tff(c_75382,plain,
    ~ apply('#skF_17','#skF_19','#skF_19'),
    inference(negUnitSimplification,[status(thm)],[c_75166,c_75285]) ).

tff(c_75581,plain,
    ~ total_order('#skF_17','#skF_18'),
    inference(resolution,[status(thm)],[c_628,c_75382]) ).

tff(c_75603,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_216,c_75581]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET794+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11  % 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
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu Aug  3 17:07:06 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 33.15/19.62  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.15/19.63  
% 33.15/19.63  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 33.15/19.66  
% 33.15/19.66  Inference rules
% 33.15/19.66  ----------------------
% 33.15/19.66  #Ref     : 0
% 33.15/19.66  #Sup     : 20055
% 33.15/19.66  #Fact    : 184
% 33.15/19.66  #Define  : 0
% 33.15/19.66  #Split   : 5
% 33.15/19.66  #Chain   : 0
% 33.15/19.66  #Close   : 0
% 33.15/19.66  
% 33.15/19.66  Ordering : KBO
% 33.15/19.66  
% 33.15/19.66  Simplification rules
% 33.15/19.66  ----------------------
% 33.15/19.66  #Subsume      : 1714
% 33.15/19.66  #Demod        : 275
% 33.15/19.66  #Tautology    : 692
% 33.15/19.66  #SimpNegUnit  : 46
% 33.15/19.66  #BackRed      : 0
% 33.15/19.66  
% 33.15/19.66  #Partial instantiations: 0
% 33.15/19.66  #Strategies tried      : 1
% 33.15/19.66  
% 33.15/19.66  Timing (in seconds)
% 33.15/19.66  ----------------------
% 33.15/19.66  Preprocessing        : 0.58
% 33.15/19.66  Parsing              : 0.27
% 33.15/19.66  CNF conversion       : 0.06
% 33.15/19.66  Main loop            : 18.16
% 33.15/19.66  Inferencing          : 5.25
% 33.15/19.66  Reduction            : 3.11
% 33.15/19.66  Demodulation         : 1.99
% 33.15/19.66  BG Simplification    : 0.29
% 33.15/19.66  Subsumption          : 8.10
% 33.15/19.66  Abstraction          : 0.50
% 33.15/19.66  MUC search           : 0.00
% 33.15/19.66  Cooper               : 0.00
% 33.15/19.66  Total                : 18.79
% 33.15/19.66  Index Insertion      : 0.00
% 33.15/19.66  Index Deletion       : 0.00
% 33.15/19.66  Index Matching       : 0.00
% 33.15/19.66  BG Taut test         : 0.00
%------------------------------------------------------------------------------