TSTP Solution File: SET451-6 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET451-6 : 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/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 : n002.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 10:56:28 EDT 2023

% Result   : Unsatisfiable 14.57s 4.85s
% Output   : CNFRefutation 14.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   63
% Syntax   : Number of formulae    :   76 (  13 unt;  56 typ;   0 def)
%            Number of atoms       :   27 (   7 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   13 (   6   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    6 (   2 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    :   46 (  46 usr;  12 con; 0-3 aty)
%            Number of variables   :   34 (;  34   !;   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 > 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(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(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(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_779,axiom,
    ~ subclass(subset_relation,cross_product(universal_class,universal_class)),
    file(unknown,unknown) ).

tff(f_239,axiom,
    ! [X,Y,Xr] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
    file(unknown,unknown) ).

tff(f_521,axiom,
    intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
    file(unknown,unknown) ).

tff(f_237,axiom,
    ! [Xr,X,Y] : ( intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ),
    file(unknown,unknown) ).

tff(f_70,axiom,
    ! [X,Y] :
      ( member(not_subclass_element(X,Y),X)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

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

tff(f_75,axiom,
    ! [X,Y] :
      ( ~ member(not_subclass_element(X,Y),Y)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(c_226,plain,
    ~ subclass(subset_relation,cross_product(universal_class,universal_class)),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_58,plain,
    ! [X_66,Y_67,Xr_68] : ( intersection(cross_product(X_66,Y_67),Xr_68) = restrict(Xr_68,X_66,Y_67) ),
    inference(cnfTransformation,[status(thm)],[f_239]) ).

tff(c_148,plain,
    intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
    inference(cnfTransformation,[status(thm)],[f_521]) ).

tff(c_227,plain,
    restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) = subset_relation,
    inference(demodulation,[status(thm),theory(equality)],[c_58,c_58,c_148]) ).

tff(c_56,plain,
    ! [Xr_63,X_64,Y_65] : ( intersection(Xr_63,cross_product(X_64,Y_65)) = restrict(Xr_63,X_64,Y_65) ),
    inference(cnfTransformation,[status(thm)],[f_237]) ).

tff(c_641,plain,
    ! [X_308,Y_309] :
      ( subclass(X_308,Y_309)
      | member(not_subclass_element(X_308,Y_309),X_308) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

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_11600,plain,
    ! [X_892,Y_893,Y_894] :
      ( member(not_subclass_element(intersection(X_892,Y_893),Y_894),Y_893)
      | subclass(intersection(X_892,Y_893),Y_894) ),
    inference(resolution,[status(thm)],[c_641,c_44]) ).

tff(c_6,plain,
    ! [X_6,Y_7] :
      ( subclass(X_6,Y_7)
      | ~ member(not_subclass_element(X_6,Y_7),Y_7) ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_11796,plain,
    ! [X_895,Y_896] : subclass(intersection(X_895,Y_896),Y_896),
    inference(resolution,[status(thm)],[c_11600,c_6]) ).

tff(c_12183,plain,
    ! [Xr_908,X_909,Y_910] : subclass(restrict(Xr_908,X_909,Y_910),cross_product(X_909,Y_910)),
    inference(superposition,[status(thm),theory(equality)],[c_56,c_11796]) ).

tff(c_12210,plain,
    subclass(subset_relation,cross_product(universal_class,universal_class)),
    inference(superposition,[status(thm),theory(equality)],[c_227,c_12183]) ).

tff(c_12222,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_226,c_12210]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : SET451-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.15  % 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 : n002.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
% 0.20/0.36  % CPULimit : 300
% 0.20/0.36  % WCLimit  : 300
% 0.20/0.36  % DateTime : Thu Aug  3 16:36:46 EDT 2023
% 0.20/0.36  % CPUTime  : 
% 14.57/4.85  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.57/4.85  
% 14.57/4.85  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.57/4.88  
% 14.57/4.88  Inference rules
% 14.57/4.88  ----------------------
% 14.57/4.88  #Ref     : 0
% 14.57/4.88  #Sup     : 3004
% 14.57/4.88  #Fact    : 0
% 14.57/4.88  #Define  : 0
% 14.57/4.88  #Split   : 82
% 14.57/4.88  #Chain   : 0
% 14.57/4.88  #Close   : 0
% 14.57/4.88  
% 14.57/4.88  Ordering : KBO
% 14.57/4.88  
% 14.57/4.88  Simplification rules
% 14.57/4.88  ----------------------
% 14.57/4.88  #Subsume      : 735
% 14.57/4.88  #Demod        : 918
% 14.57/4.88  #Tautology    : 491
% 14.57/4.88  #SimpNegUnit  : 50
% 14.57/4.88  #BackRed      : 121
% 14.57/4.88  
% 14.57/4.88  #Partial instantiations: 0
% 14.57/4.88  #Strategies tried      : 1
% 14.57/4.88  
% 14.57/4.88  Timing (in seconds)
% 14.57/4.88  ----------------------
% 14.67/4.89  Preprocessing        : 0.78
% 14.67/4.89  Parsing              : 0.41
% 14.67/4.89  CNF conversion       : 0.05
% 14.67/4.89  Main loop            : 2.93
% 14.67/4.89  Inferencing          : 0.87
% 14.67/4.89  Reduction            : 1.05
% 14.67/4.89  Demodulation         : 0.72
% 14.67/4.89  BG Simplification    : 0.08
% 14.67/4.89  Subsumption          : 0.64
% 14.67/4.89  Abstraction          : 0.08
% 14.67/4.89  MUC search           : 0.00
% 14.67/4.89  Cooper               : 0.00
% 14.67/4.89  Total                : 3.75
% 14.67/4.89  Index Insertion      : 0.00
% 14.67/4.89  Index Deletion       : 0.00
% 14.67/4.89  Index Matching       : 0.00
% 14.67/4.89  BG Taut test         : 0.00
%------------------------------------------------------------------------------