TSTP Solution File: SET792+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET792+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 : n009.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 20.13s 9.61s
% Output   : CNFRefutation 20.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   55 (   7 unt;  31 typ;   0 def)
%            Number of atoms       :   85 (  11 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :   97 (  36   ~;  39   |;  11   &)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 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   :   58 (;  58   !;   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] :
        ( ( order(R,E)
          & least(M,R,E) )
       => min(M,R,E) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV4) ).

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(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_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/sandbox2/benchmark/Axioms/SET006+3.ax',order) ).

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

tff(c_220,plain,
    ! [M_87,E_88,R_89] :
      ( member(M_87,E_88)
      | ~ least(M_87,R_89,E_88) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_224,plain,
    member('#skF_19','#skF_18'),
    inference(resolution,[status(thm)],[c_214,c_220]) ).

tff(c_325,plain,
    ! [R_153,E_154,M_155] :
      ( ( '#skF_14'(R_153,E_154,M_155) != M_155 )
      | min(M_155,R_153,E_154)
      | ~ member(M_155,E_154) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

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

tff(c_331,plain,
    ( ( '#skF_14'('#skF_17','#skF_18','#skF_19') != '#skF_19' )
    | ~ member('#skF_19','#skF_18') ),
    inference(resolution,[status(thm)],[c_325,c_212]) ).

tff(c_335,plain,
    '#skF_14'('#skF_17','#skF_18','#skF_19') != '#skF_19',
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_331]) ).

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

tff(c_186,plain,
    ! [R_59,E_60,M_61] :
      ( member('#skF_14'(R_59,E_60,M_61),E_60)
      | min(M_61,R_59,E_60)
      | ~ member(M_61,E_60) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_341,plain,
    ! [R_159,E_160,M_161] :
      ( member('#skF_14'(R_159,E_160,M_161),E_160)
      | min(M_161,R_159,E_160)
      | ~ member(M_161,E_160) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_160,plain,
    ! [R_47,M_49,X_52,E_48] :
      ( apply(R_47,M_49,X_52)
      | ~ member(X_52,E_48)
      | ~ least(M_49,R_47,E_48) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_352,plain,
    ! [R_47,R_159,M_161,M_49,E_160] :
      ( apply(R_47,M_49,'#skF_14'(R_159,E_160,M_161))
      | ~ least(M_49,R_47,E_160)
      | min(M_161,R_159,E_160)
      | ~ member(M_161,E_160) ),
    inference(resolution,[status(thm)],[c_341,c_160]) ).

tff(c_184,plain,
    ! [R_59,E_60,M_61] :
      ( apply(R_59,'#skF_14'(R_59,E_60,M_61),M_61)
      | min(M_61,R_59,E_60)
      | ~ member(M_61,E_60) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_1745,plain,
    ! [Y_469,X_470,R_471,E_472] :
      ( ( Y_469 = X_470 )
      | ~ apply(R_471,Y_469,X_470)
      | ~ apply(R_471,X_470,Y_469)
      | ~ member(Y_469,E_472)
      | ~ member(X_470,E_472)
      | ~ order(R_471,E_472) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_39029,plain,
    ! [R_2907,E_2908,M_2909,E_2910] :
      ( ( '#skF_14'(R_2907,E_2908,M_2909) = M_2909 )
      | ~ apply(R_2907,M_2909,'#skF_14'(R_2907,E_2908,M_2909))
      | ~ member('#skF_14'(R_2907,E_2908,M_2909),E_2910)
      | ~ member(M_2909,E_2910)
      | ~ order(R_2907,E_2910)
      | min(M_2909,R_2907,E_2908)
      | ~ member(M_2909,E_2908) ),
    inference(resolution,[status(thm)],[c_184,c_1745]) ).

tff(c_40472,plain,
    ! [R_2932,E_2933,M_2934,E_2935] :
      ( ( '#skF_14'(R_2932,E_2933,M_2934) = M_2934 )
      | ~ member('#skF_14'(R_2932,E_2933,M_2934),E_2935)
      | ~ member(M_2934,E_2935)
      | ~ order(R_2932,E_2935)
      | ~ least(M_2934,R_2932,E_2933)
      | min(M_2934,R_2932,E_2933)
      | ~ member(M_2934,E_2933) ),
    inference(resolution,[status(thm)],[c_352,c_39029]) ).

tff(c_40477,plain,
    ! [R_2936,E_2937,M_2938] :
      ( ( '#skF_14'(R_2936,E_2937,M_2938) = M_2938 )
      | ~ order(R_2936,E_2937)
      | ~ least(M_2938,R_2936,E_2937)
      | min(M_2938,R_2936,E_2937)
      | ~ member(M_2938,E_2937) ),
    inference(resolution,[status(thm)],[c_186,c_40472]) ).

tff(c_40622,plain,
    ( ( '#skF_14'('#skF_17','#skF_18','#skF_19') = '#skF_19' )
    | ~ order('#skF_17','#skF_18')
    | ~ least('#skF_19','#skF_17','#skF_18')
    | ~ member('#skF_19','#skF_18') ),
    inference(resolution,[status(thm)],[c_40477,c_212]) ).

tff(c_40670,plain,
    '#skF_14'('#skF_17','#skF_18','#skF_19') = '#skF_19',
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_214,c_216,c_40622]) ).

tff(c_40672,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_335,c_40670]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET792+4 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 16:18:54 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 20.13/9.61  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.36/9.61  
% 20.36/9.62  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.46/9.64  
% 20.46/9.64  Inference rules
% 20.46/9.64  ----------------------
% 20.46/9.64  #Ref     : 0
% 20.46/9.64  #Sup     : 11346
% 20.46/9.64  #Fact    : 94
% 20.46/9.64  #Define  : 0
% 20.46/9.64  #Split   : 2
% 20.46/9.64  #Chain   : 0
% 20.46/9.64  #Close   : 0
% 20.46/9.64  
% 20.46/9.64  Ordering : KBO
% 20.46/9.64  
% 20.46/9.64  Simplification rules
% 20.46/9.64  ----------------------
% 20.46/9.64  #Subsume      : 708
% 20.46/9.64  #Demod        : 77
% 20.46/9.64  #Tautology    : 228
% 20.46/9.64  #SimpNegUnit  : 1
% 20.46/9.64  #BackRed      : 0
% 20.46/9.64  
% 20.46/9.64  #Partial instantiations: 0
% 20.46/9.64  #Strategies tried      : 1
% 20.46/9.64  
% 20.46/9.64  Timing (in seconds)
% 20.46/9.64  ----------------------
% 20.46/9.65  Preprocessing        : 0.59
% 20.46/9.65  Parsing              : 0.28
% 20.46/9.65  CNF conversion       : 0.06
% 20.46/9.65  Main loop            : 7.98
% 20.46/9.65  Inferencing          : 2.29
% 20.46/9.65  Reduction            : 1.26
% 20.46/9.65  Demodulation         : 0.75
% 20.46/9.65  BG Simplification    : 0.19
% 20.46/9.65  Subsumption          : 3.68
% 20.46/9.65  Abstraction          : 0.29
% 20.46/9.65  MUC search           : 0.00
% 20.46/9.65  Cooper               : 0.00
% 20.46/9.65  Total                : 8.63
% 20.46/9.65  Index Insertion      : 0.00
% 20.46/9.65  Index Deletion       : 0.00
% 20.46/9.65  Index Matching       : 0.00
% 20.46/9.65  BG Taut test         : 0.00
%------------------------------------------------------------------------------