TSTP Solution File: SET168-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET168-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n012.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 10:56:07 EDT 2023

% Result   : Unsatisfiable 100.65s 81.62s
% Output   : CNFRefutation 100.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   67
% Syntax   : Number of formulae    :   83 (  12 unt;  59 typ;   0 def)
%            Number of atoms       :   42 (   2 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   37 (  19   ~;  18   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   72 (  44   >;  28   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   49 (  49 usr;  15 con; 0-3 aty)
%            Number of variables   :   33 (;  33   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ maps > homomorphism > compatible > subclass > member > single_valued_class > operation > one_to_one > inductive > function > restrict > range > not_homomorphism2 > not_homomorphism1 > domain > unordered_pair > union > symmetric_difference > ordered_pair > not_subclass_element > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > single_valued3 > single_valued2 > single_valued1 > second > rotate > regular > range_of > power_class > inverse > flip > first > domain_of > diagonalise > compose_class > complement > cantor > z > y > x > universal_class > successor_relation > subset_relation > singleton_relation > omega > null_class > identity_relation > element_relation > domain_relation > composition_function > choice > application_function

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

tff(single_valued3,type,
    single_valued3: $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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(symmetric_difference,type,
    symmetric_difference: ( $i * $i ) > $i ).

tff(application_function,type,
    application_function: $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(choice,type,
    choice: $i ).

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

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

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

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

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

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

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

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

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

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

tff(single_valued2,type,
    single_valued2: $i > $i ).

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

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

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

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

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

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

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

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

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

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

tff(not_homomorphism2,type,
    not_homomorphism2: ( $i * $i * $i ) > $i ).

tff(single_valued1,type,
    single_valued1: $i > $i ).

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

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

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

tff(not_homomorphism1,type,
    not_homomorphism1: ( $i * $i * $i ) > $i ).

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

tff(f_778,axiom,
    member(x,z),
    file(unknown,unknown) ).

tff(f_80,axiom,
    ! [X] : subclass(X,universal_class),
    file(unknown,unknown) ).

tff(f_66,axiom,
    ! [X,Y,U] :
      ( ~ subclass(X,Y)
      | ~ member(U,X)
      | member(U,Y) ),
    file(unknown,unknown) ).

tff(f_228,axiom,
    ! [X,Y] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
    file(unknown,unknown) ).

tff(f_223,axiom,
    ! [Z,X] :
      ( ~ member(Z,universal_class)
      | member(Z,complement(X))
      | member(Z,X) ),
    file(unknown,unknown) ).

tff(f_200,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    file(unknown,unknown) ).

tff(f_780,axiom,
    ~ member(x,union(y,z)),
    file(unknown,unknown) ).

tff(f_216,axiom,
    ! [Z,X] :
      ( ~ member(Z,complement(X))
      | ~ member(Z,X) ),
    file(unknown,unknown) ).

tff(c_226,plain,
    member(x,z),
    inference(cnfTransformation,[status(thm)],[f_778]) ).

tff(c_8,plain,
    ! [X_8] : subclass(X_8,universal_class),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_960,plain,
    ! [U_341,Y_342,X_343] :
      ( member(U_341,Y_342)
      | ~ member(U_341,X_343)
      | ~ subclass(X_343,Y_342) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_1356,plain,
    ! [Y_373] :
      ( member(x,Y_373)
      | ~ subclass(z,Y_373) ),
    inference(resolution,[status(thm)],[c_226,c_960]) ).

tff(c_1370,plain,
    member(x,universal_class),
    inference(resolution,[status(thm)],[c_8,c_1356]) ).

tff(c_52,plain,
    ! [X_59,Y_60] : ( complement(intersection(complement(X_59),complement(Y_60))) = union(X_59,Y_60) ),
    inference(cnfTransformation,[status(thm)],[f_228]) ).

tff(c_1442,plain,
    ! [Z_380,X_381] :
      ( member(Z_380,X_381)
      | member(Z_380,complement(X_381))
      | ~ member(Z_380,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_285347,plain,
    ! [Z_6960,X_6961,Y_6962] :
      ( member(Z_6960,intersection(complement(X_6961),complement(Y_6962)))
      | member(Z_6960,union(X_6961,Y_6962))
      | ~ member(Z_6960,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_52,c_1442]) ).

tff(c_44,plain,
    ! [Z_49,Y_51,X_50] :
      ( member(Z_49,Y_51)
      | ~ member(Z_49,intersection(X_50,Y_51)) ),
    inference(cnfTransformation,[status(thm)],[f_200]) ).

tff(c_317754,plain,
    ! [Z_7605,Y_7606,X_7607] :
      ( member(Z_7605,complement(Y_7606))
      | member(Z_7605,union(X_7607,Y_7606))
      | ~ member(Z_7605,universal_class) ),
    inference(resolution,[status(thm)],[c_285347,c_44]) ).

tff(c_228,plain,
    ~ member(x,union(y,z)),
    inference(cnfTransformation,[status(thm)],[f_780]) ).

tff(c_317845,plain,
    ( member(x,complement(z))
    | ~ member(x,universal_class) ),
    inference(resolution,[status(thm)],[c_317754,c_228]) ).

tff(c_317931,plain,
    member(x,complement(z)),
    inference(demodulation,[status(thm),theory(equality)],[c_1370,c_317845]) ).

tff(c_48,plain,
    ! [Z_55,X_56] :
      ( ~ member(Z_55,X_56)
      | ~ member(Z_55,complement(X_56)) ),
    inference(cnfTransformation,[status(thm)],[f_216]) ).

tff(c_317952,plain,
    ~ member(x,z),
    inference(resolution,[status(thm)],[c_317931,c_48]) ).

tff(c_317962,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_226,c_317952]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET168-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n012.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 16:05:07 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 100.65/81.62  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 100.65/81.63  
% 100.65/81.63  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 100.73/81.66  
% 100.73/81.66  Inference rules
% 100.73/81.66  ----------------------
% 100.73/81.66  #Ref     : 4
% 100.73/81.66  #Sup     : 84793
% 100.73/81.66  #Fact    : 20
% 100.73/81.66  #Define  : 0
% 100.73/81.66  #Split   : 696
% 100.73/81.66  #Chain   : 0
% 100.73/81.66  #Close   : 0
% 100.73/81.66  
% 100.73/81.66  Ordering : KBO
% 100.73/81.66  
% 100.73/81.66  Simplification rules
% 100.73/81.66  ----------------------
% 100.73/81.66  #Subsume      : 25715
% 100.73/81.66  #Demod        : 36405
% 100.73/81.66  #Tautology    : 11699
% 100.73/81.66  #SimpNegUnit  : 1980
% 100.73/81.66  #BackRed      : 1133
% 100.73/81.66  
% 100.73/81.66  #Partial instantiations: 0
% 100.73/81.66  #Strategies tried      : 1
% 100.73/81.66  
% 100.73/81.66  Timing (in seconds)
% 100.73/81.66  ----------------------
% 100.73/81.66  Preprocessing        : 0.72
% 100.73/81.66  Parsing              : 0.38
% 100.73/81.66  CNF conversion       : 0.05
% 100.73/81.66  Main loop            : 79.87
% 100.73/81.66  Inferencing          : 10.72
% 100.73/81.66  Reduction            : 36.66
% 100.73/81.66  Demodulation         : 26.36
% 100.73/81.66  BG Simplification    : 0.43
% 100.73/81.66  Subsumption          : 24.89
% 100.73/81.66  Abstraction          : 0.68
% 100.73/81.66  MUC search           : 0.00
% 100.73/81.66  Cooper               : 0.00
% 100.73/81.66  Total                : 80.64
% 100.73/81.66  Index Insertion      : 0.00
% 100.73/81.66  Index Deletion       : 0.00
% 100.73/81.66  Index Matching       : 0.00
% 100.73/81.66  BG Taut test         : 0.00
%------------------------------------------------------------------------------