TSTP Solution File: SET095+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET095+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/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 : n019.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 10:55:56 EDT 2023

% Result   : Theorem 11.65s 4.05s
% Output   : CNFRefutation 11.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   56 (   7 unt;  40 typ;   0 def)
%            Number of atoms       :   30 (  10 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   20 (   6   ~;   9   |;   1   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   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 (;  21   !;   0   ?;   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_380,negated_conjecture,
    ~ ! [X,Y] :
        ( member(X,Y)
       => subclass(singleton(X),Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_singletons2) ).

tff(f_67,axiom,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( member(U,X)
         => member(U,Y) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',subclass_defn) ).

tff(f_100,axiom,
    ! [X] : ( singleton(X) = unordered_pair(X,X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).

tff(f_87,axiom,
    ! [U,X,Y] :
      ( member(U,unordered_pair(X,Y))
    <=> ( member(U,universal_class)
        & ( ( U = X )
          | ( U = Y ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).

tff(c_180,plain,
    ~ subclass(singleton('#skF_8'),'#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_380]) ).

tff(c_182,plain,
    member('#skF_8','#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_380]) ).

tff(c_6,plain,
    ! [X_1,Y_2] :
      ( member('#skF_1'(X_1,Y_2),X_1)
      | subclass(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_26,plain,
    ! [X_14] : ( unordered_pair(X_14,X_14) = singleton(X_14) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_1283,plain,
    ! [Y_231,U_232,X_233] :
      ( ( Y_231 = U_232 )
      | ( X_233 = U_232 )
      | ~ member(U_232,unordered_pair(X_233,Y_231)) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_1433,plain,
    ! [X_248,U_249] :
      ( ( X_248 = U_249 )
      | ( X_248 = U_249 )
      | ~ member(U_249,singleton(X_248)) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_1283]) ).

tff(c_9978,plain,
    ! [X_698,Y_699] :
      ( ( '#skF_1'(singleton(X_698),Y_699) = X_698 )
      | subclass(singleton(X_698),Y_699) ),
    inference(resolution,[status(thm)],[c_6,c_1433]) ).

tff(c_10007,plain,
    '#skF_1'(singleton('#skF_8'),'#skF_9') = '#skF_8',
    inference(resolution,[status(thm)],[c_9978,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_67]) ).

tff(c_10014,plain,
    ( ~ member('#skF_8','#skF_9')
    | subclass(singleton('#skF_8'),'#skF_9') ),
    inference(superposition,[status(thm),theory(equality)],[c_10007,c_4]) ).

tff(c_10019,plain,
    subclass(singleton('#skF_8'),'#skF_9'),
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_10014]) ).

tff(c_10021,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_180,c_10019]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET095+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.14  % 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
% 0.14/0.36  % Computer : n019.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 16:36:01 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 11.65/4.05  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.65/4.05  
% 11.65/4.05  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.65/4.11  
% 11.65/4.11  Inference rules
% 11.65/4.11  ----------------------
% 11.65/4.11  #Ref     : 0
% 11.65/4.11  #Sup     : 2099
% 11.65/4.11  #Fact    : 0
% 11.65/4.11  #Define  : 0
% 11.65/4.11  #Split   : 64
% 11.65/4.11  #Chain   : 0
% 11.65/4.11  #Close   : 0
% 11.65/4.11  
% 11.65/4.11  Ordering : KBO
% 11.65/4.11  
% 11.65/4.11  Simplification rules
% 11.65/4.11  ----------------------
% 11.65/4.11  #Subsume      : 496
% 11.65/4.11  #Demod        : 621
% 11.65/4.11  #Tautology    : 233
% 11.65/4.11  #SimpNegUnit  : 39
% 11.65/4.11  #BackRed      : 212
% 11.65/4.11  
% 11.65/4.11  #Partial instantiations: 0
% 11.65/4.11  #Strategies tried      : 1
% 11.65/4.11  
% 11.65/4.11  Timing (in seconds)
% 11.65/4.11  ----------------------
% 11.65/4.11  Preprocessing        : 0.66
% 11.65/4.11  Parsing              : 0.34
% 11.65/4.11  CNF conversion       : 0.05
% 11.65/4.11  Main loop            : 2.22
% 11.65/4.11  Inferencing          : 0.67
% 11.65/4.11  Reduction            : 0.72
% 11.65/4.11  Demodulation         : 0.46
% 11.65/4.11  BG Simplification    : 0.06
% 11.65/4.11  Subsumption          : 0.57
% 11.65/4.11  Abstraction          : 0.06
% 11.65/4.11  MUC search           : 0.00
% 11.65/4.11  Cooper               : 0.00
% 11.65/4.11  Total                : 2.95
% 11.65/4.12  Index Insertion      : 0.00
% 11.65/4.12  Index Deletion       : 0.00
% 11.65/4.12  Index Matching       : 0.00
% 11.65/4.12  BG Taut test         : 0.00
%------------------------------------------------------------------------------