TSTP Solution File: SET766+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% 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 : n021.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 10:56:59 EDT 2023

% Result   : Theorem 7.84s 2.95s
% Output   : CNFRefutation 7.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   54 (   6 unt;  41 typ;   0 def)
%            Number of atoms       :   35 (   0 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :   33 (  11   ~;   6   |;   8   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   73 (  37   >;  36   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   33 (  33 usr;   4 con; 0-3 aty)
%            Number of variables   :   23 (;  23   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ apply > subset > pre_order > partition > member > equivalence > equal_set > disjoint > equivalence_class > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_11 > #skF_6 > #skF_17 > #skF_20 > #skF_3 > #skF_13 > #skF_14 > #skF_12 > #skF_18 > #skF_19 > #skF_8 > #skF_21 > #skF_22 > #skF_2 > #skF_23 > #skF_7 > #skF_1 > #skF_16 > #skF_9 > #skF_5 > #skF_15 > #skF_4 > #skF_10

%Foreground sorts:

%Background operators:

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

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

tff(power_set,type,
    power_set: $i > $i ).

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

tff(product,type,
    product: $i > $i ).

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

tff(singleton,type,
    singleton: $i > $i ).

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

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

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

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

tff(sum,type,
    sum: $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_21',type,
    '#skF_21': $i ).

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

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

tff('#skF_22',type,
    '#skF_22': $i ).

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

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

tff('#skF_23',type,
    '#skF_23': $i ).

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

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

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

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

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

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

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

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

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

tff(f_237,negated_conjecture,
    ~ ! [E,R,A] :
        ( ( equivalence(R,E)
          & member(A,E) )
       => member(A,equivalence_class(A,E,R)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII02) ).

tff(f_202,axiom,
    ! [A,R] :
      ( equivalence(R,A)
    <=> ( ! [X] :
            ( member(X,A)
           => apply(R,X,X) )
        & ! [X,Y] :
            ( ( member(X,A)
              & member(Y,A) )
           => ( apply(R,X,Y)
             => apply(R,Y,X) ) )
        & ! [X,Y,Z] :
            ( ( member(X,A)
              & member(Y,A)
              & member(Z,A) )
           => ( ( apply(R,X,Y)
                & apply(R,Y,Z) )
             => apply(R,X,Z) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',equivalence) ).

tff(f_208,axiom,
    ! [R,E,A,X] :
      ( member(X,equivalence_class(A,E,R))
    <=> ( member(X,E)
        & apply(R,A,X) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',equivalence_class) ).

tff(c_254,plain,
    equivalence('#skF_22','#skF_21'),
    inference(cnfTransformation,[status(thm)],[f_237]) ).

tff(c_252,plain,
    member('#skF_23','#skF_21'),
    inference(cnfTransformation,[status(thm)],[f_237]) ).

tff(c_1536,plain,
    ! [R_289,X_290,A_291] :
      ( apply(R_289,X_290,X_290)
      | ~ member(X_290,A_291)
      | ~ equivalence(R_289,A_291) ),
    inference(cnfTransformation,[status(thm)],[f_202]) ).

tff(c_1587,plain,
    ! [R_289] :
      ( apply(R_289,'#skF_23','#skF_23')
      | ~ equivalence(R_289,'#skF_21') ),
    inference(resolution,[status(thm)],[c_252,c_1536]) ).

tff(c_3553,plain,
    ! [X_393,A_394,E_395,R_396] :
      ( member(X_393,equivalence_class(A_394,E_395,R_396))
      | ~ apply(R_396,A_394,X_393)
      | ~ member(X_393,E_395) ),
    inference(cnfTransformation,[status(thm)],[f_208]) ).

tff(c_250,plain,
    ~ member('#skF_23',equivalence_class('#skF_23','#skF_21','#skF_22')),
    inference(cnfTransformation,[status(thm)],[f_237]) ).

tff(c_3595,plain,
    ( ~ apply('#skF_22','#skF_23','#skF_23')
    | ~ member('#skF_23','#skF_21') ),
    inference(resolution,[status(thm)],[c_3553,c_250]) ).

tff(c_3613,plain,
    ~ apply('#skF_22','#skF_23','#skF_23'),
    inference(demodulation,[status(thm),theory(equality)],[c_252,c_3595]) ).

tff(c_3619,plain,
    ~ equivalence('#skF_22','#skF_21'),
    inference(resolution,[status(thm)],[c_1587,c_3613]) ).

tff(c_3624,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_254,c_3619]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13  % 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
% 0.14/0.34  % Computer : n021.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 16:28:06 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 7.84/2.95  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.84/2.96  
% 7.84/2.96  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.84/2.98  
% 7.84/2.98  Inference rules
% 7.84/2.98  ----------------------
% 7.84/2.98  #Ref     : 0
% 7.84/2.98  #Sup     : 777
% 7.84/2.98  #Fact    : 0
% 7.84/2.98  #Define  : 0
% 7.84/2.98  #Split   : 3
% 7.84/2.98  #Chain   : 0
% 7.84/2.98  #Close   : 0
% 7.84/2.98  
% 7.84/2.98  Ordering : KBO
% 7.84/2.98  
% 7.84/2.98  Simplification rules
% 7.84/2.98  ----------------------
% 7.99/2.98  #Subsume      : 66
% 7.99/2.98  #Demod        : 76
% 7.99/2.98  #Tautology    : 89
% 7.99/2.98  #SimpNegUnit  : 5
% 7.99/2.98  #BackRed      : 0
% 7.99/2.98  
% 7.99/2.98  #Partial instantiations: 0
% 7.99/2.98  #Strategies tried      : 1
% 7.99/2.98  
% 7.99/2.98  Timing (in seconds)
% 7.99/2.98  ----------------------
% 7.99/2.99  Preprocessing        : 0.66
% 7.99/2.99  Parsing              : 0.30
% 7.99/2.99  CNF conversion       : 0.06
% 7.99/2.99  Main loop            : 1.18
% 7.99/2.99  Inferencing          : 0.41
% 7.99/2.99  Reduction            : 0.33
% 7.99/2.99  Demodulation         : 0.21
% 7.99/2.99  BG Simplification    : 0.06
% 7.99/2.99  Subsumption          : 0.29
% 7.99/2.99  Abstraction          : 0.04
% 7.99/2.99  MUC search           : 0.00
% 7.99/2.99  Cooper               : 0.00
% 7.99/2.99  Total                : 1.90
% 7.99/2.99  Index Insertion      : 0.00
% 7.99/2.99  Index Deletion       : 0.00
% 7.99/2.99  Index Matching       : 0.00
% 7.99/2.99  BG Taut test         : 0.00
%------------------------------------------------------------------------------