TSTP Solution File: SET056+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET056+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : n015.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 10:55:43 EDT 2023

% Result   : Theorem 5.03s 2.28s
% Output   : CNFRefutation 5.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   57 (   5 unt;  40 typ;   0 def)
%            Number of atoms       :   35 (   5 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   31 (  13   ~;  12   |;   3   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   47 (  31   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   35 (  35 usr;   9 con; 0-3 aty)
%            Number of variables   :   21 (;  19   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subclass > member > disjoint > inductive > function > restrict > unordered_pair > union > ordered_pair > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > second > rotate > range_of > power_class > inverse > flip > first > domain_of > complement > universal_class > successor_relation > null_class > identity_relation > element_relation > #skF_4 > #skF_7 > #skF_3 > #skF_2 > #skF_9 > #skF_8 > #skF_1 > #skF_5 > #skF_6

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(null_class,type,
    null_class: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_391,negated_conjecture,
    ~ ! [X,Y] :
        ( ( X = Y )
        | ? [U] :
            ( member(U,X)
            & ~ member(U,Y) )
        | ? [W] :
            ( member(W,Y)
            & ~ member(W,X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality1) ).

tff(f_68,axiom,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( member(U,X)
         => member(U,Y) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_defn) ).

tff(f_79,axiom,
    ! [X,Y] :
      ( ( X = Y )
    <=> ( subclass(X,Y)
        & subclass(Y,X) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',extensionality) ).

tff(c_184,plain,
    '#skF_9' != '#skF_8',
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_695,plain,
    ! [X_205,Y_206] :
      ( member('#skF_1'(X_205,Y_206),X_205)
      | subclass(X_205,Y_206) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_182,plain,
    ! [U_97] :
      ( member(U_97,'#skF_9')
      | ~ member(U_97,'#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_565,plain,
    ! [X_188,Y_189] :
      ( ~ member('#skF_1'(X_188,Y_189),Y_189)
      | subclass(X_188,Y_189) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_580,plain,
    ! [X_188] :
      ( subclass(X_188,'#skF_9')
      | ~ member('#skF_1'(X_188,'#skF_9'),'#skF_8') ),
    inference(resolution,[status(thm)],[c_182,c_565]) ).

tff(c_757,plain,
    subclass('#skF_8','#skF_9'),
    inference(resolution,[status(thm)],[c_695,c_580]) ).

tff(c_10,plain,
    ! [Y_8,X_7] :
      ( ( Y_8 = X_7 )
      | ~ subclass(Y_8,X_7)
      | ~ subclass(X_7,Y_8) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_782,plain,
    ( ( '#skF_9' = '#skF_8' )
    | ~ subclass('#skF_9','#skF_8') ),
    inference(resolution,[status(thm)],[c_757,c_10]) ).

tff(c_785,plain,
    ~ subclass('#skF_9','#skF_8'),
    inference(negUnitSimplification,[status(thm)],[c_184,c_782]) ).

tff(c_180,plain,
    ! [W_98] :
      ( member(W_98,'#skF_8')
      | ~ member(W_98,'#skF_9') ),
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_928,plain,
    ! [Y_228] :
      ( member('#skF_1'('#skF_9',Y_228),'#skF_8')
      | subclass('#skF_9',Y_228) ),
    inference(resolution,[status(thm)],[c_695,c_180]) ).

tff(c_4,plain,
    ! [X_1,Y_2] :
      ( ~ member('#skF_1'(X_1,Y_2),Y_2)
      | subclass(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_936,plain,
    subclass('#skF_9','#skF_8'),
    inference(resolution,[status(thm)],[c_928,c_4]) ).

tff(c_942,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_785,c_785,c_936]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : SET056+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.14/0.14  % 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
% 0.14/0.36  % Computer : n015.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 17:03:29 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 5.03/2.28  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.03/2.28  
% 5.03/2.28  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.03/2.31  
% 5.03/2.31  Inference rules
% 5.03/2.31  ----------------------
% 5.03/2.31  #Ref     : 0
% 5.03/2.31  #Sup     : 143
% 5.03/2.31  #Fact    : 0
% 5.03/2.31  #Define  : 0
% 5.03/2.31  #Split   : 7
% 5.03/2.31  #Chain   : 0
% 5.03/2.31  #Close   : 0
% 5.03/2.31  
% 5.03/2.31  Ordering : KBO
% 5.03/2.31  
% 5.03/2.31  Simplification rules
% 5.03/2.31  ----------------------
% 5.03/2.31  #Subsume      : 21
% 5.03/2.31  #Demod        : 14
% 5.03/2.31  #Tautology    : 29
% 5.03/2.31  #SimpNegUnit  : 4
% 5.03/2.31  #BackRed      : 7
% 5.03/2.31  
% 5.03/2.31  #Partial instantiations: 0
% 5.03/2.31  #Strategies tried      : 1
% 5.03/2.31  
% 5.03/2.31  Timing (in seconds)
% 5.03/2.31  ----------------------
% 5.03/2.31  Preprocessing        : 0.65
% 5.03/2.31  Parsing              : 0.34
% 5.03/2.31  CNF conversion       : 0.05
% 5.03/2.31  Main loop            : 0.51
% 5.03/2.31  Inferencing          : 0.18
% 5.03/2.31  Reduction            : 0.15
% 5.03/2.31  Demodulation         : 0.10
% 5.03/2.31  BG Simplification    : 0.04
% 5.03/2.31  Subsumption          : 0.12
% 5.03/2.31  Abstraction          : 0.02
% 5.03/2.31  MUC search           : 0.00
% 5.03/2.31  Cooper               : 0.00
% 5.03/2.31  Total                : 1.21
% 5.03/2.31  Index Insertion      : 0.00
% 5.03/2.31  Index Deletion       : 0.00
% 5.03/2.31  Index Matching       : 0.00
% 5.03/2.31  BG Taut test         : 0.00
%------------------------------------------------------------------------------