TSTP Solution File: NUM042-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM042-1 : 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 : n027.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 10:50:53 EDT 2023

% Result   : Unsatisfiable 264.54s 238.05s
% Output   : CNFRefutation 264.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   87
% Syntax   : Number of formulae    :  102 (   8 unt;  79 typ;   0 def)
%            Number of atoms       :   41 (   2 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   34 (  16   ~;  18   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  103 (  60   >;  43   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-3 aty)
%            Number of functors    :   63 (  63 usr;  19 con; 0-3 aty)
%            Number of variables   :   47 (;  47   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ section > maps > homomorphism > compatible > well_ordering > transitive > subclass > member > irreflexive > connected > asymmetric > single_valued_class > operation > one_to_one > inductive > function > segment > restrict > recursion > range > not_homomorphism2 > not_homomorphism1 > domain > unordered_pair > union > symmetric_difference > ordinal_multiply > ordinal_add > ordered_pair > not_well_ordering > not_subclass_element > least > intersection > image > cross_product > compose > apply > #nlpp > symmetrization_of > sum_class > successor > singleton > single_valued3 > single_valued2 > single_valued1 > second > rotate > rest_of > regular > recursion_equation_functions > range_of > power_class > inverse > integer_of > flip > first > domain_of > diagonalise > compose_class > complement > cantor > x > universal_class > union_of_range_map > successor_relation > subset_relation > singleton_relation > rest_relation > ordinal_numbers > omega > null_class > limit_ordinals > kind_1_ordinals > identity_relation > element_relation > domain_relation > composition_function > choice > application_function > add_relation

%Foreground sorts:

%Background operators:

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

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

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

tff(kind_1_ordinals,type,
    kind_1_ordinals: $i ).

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

tff(rest_relation,type,
    rest_relation: $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_of_range_map,type,
    union_of_range_map: $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(transitive,type,
    transitive: ( $i * $i ) > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(integer_of,type,
    integer_of: $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(least,type,
    least: ( $i * $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(recursion_equation_functions,type,
    recursion_equation_functions: $i > $i ).

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

tff(add_relation,type,
    add_relation: $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(rest_of,type,
    rest_of: $i > $i ).

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

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

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

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

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

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

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

tff(f_1114,axiom,
    subclass(x,complement(identity_relation)),
    file(unknown,unknown) ).

tff(f_234,axiom,
    ! [Xr,X,Y] : ( intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ),
    file(unknown,unknown) ).

tff(f_67,axiom,
    ! [X,Y] :
      ( member(not_subclass_element(X,Y),X)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(f_191,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    file(unknown,unknown) ).

tff(f_63,axiom,
    ! [X,Y,U] :
      ( ~ subclass(X,Y)
      | ~ member(U,X)
      | member(U,Y) ),
    file(unknown,unknown) ).

tff(f_72,axiom,
    ! [X,Y] :
      ( ~ member(not_subclass_element(X,Y),Y)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(f_808,axiom,
    ! [X,Y] :
      ( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
      | irreflexive(X,Y) ),
    file(unknown,unknown) ).

tff(f_1116,axiom,
    ~ irreflexive(x,domain_of(symmetrization_of(x))),
    file(unknown,unknown) ).

tff(c_318,plain,
    subclass(x,complement(identity_relation)),
    inference(cnfTransformation,[status(thm)],[f_1114]) ).

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_234]) ).

tff(c_1357,plain,
    ! [X_439,Y_440] :
      ( subclass(X_439,Y_440)
      | member(not_subclass_element(X_439,Y_440),X_439) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_42,plain,
    ! [Z_46,X_47,Y_48] :
      ( member(Z_46,X_47)
      | ~ member(Z_46,intersection(X_47,Y_48)) ),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_453074,plain,
    ! [X_11258,Y_11259,Y_11260] :
      ( member(not_subclass_element(intersection(X_11258,Y_11259),Y_11260),X_11258)
      | subclass(intersection(X_11258,Y_11259),Y_11260) ),
    inference(resolution,[status(thm)],[c_1357,c_42]) ).

tff(c_2,plain,
    ! [U_3,Y_2,X_1] :
      ( member(U_3,Y_2)
      | ~ member(U_3,X_1)
      | ~ subclass(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_740643,plain,
    ! [X_15235,Y_15236,Y_15237,Y_15238] :
      ( member(not_subclass_element(intersection(X_15235,Y_15236),Y_15237),Y_15238)
      | ~ subclass(X_15235,Y_15238)
      | subclass(intersection(X_15235,Y_15236),Y_15237) ),
    inference(resolution,[status(thm)],[c_453074,c_2]) ).

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_72]) ).

tff(c_742198,plain,
    ! [X_15245,Y_15246,Y_15247] :
      ( ~ subclass(X_15245,Y_15246)
      | subclass(intersection(X_15245,Y_15247),Y_15246) ),
    inference(resolution,[status(thm)],[c_740643,c_6]) ).

tff(c_750656,plain,
    ! [Xr_15296,Y_15297,X_15298,Y_15299] :
      ( ~ subclass(Xr_15296,Y_15297)
      | subclass(restrict(Xr_15296,X_15298,Y_15299),Y_15297) ),
    inference(superposition,[status(thm),theory(equality)],[c_56,c_742198]) ).

tff(c_230,plain,
    ! [X_218,Y_219] :
      ( irreflexive(X_218,Y_219)
      | ~ subclass(restrict(X_218,Y_219,Y_219),complement(identity_relation)) ),
    inference(cnfTransformation,[status(thm)],[f_808]) ).

tff(c_750979,plain,
    ! [Xr_15300,Y_15301] :
      ( irreflexive(Xr_15300,Y_15301)
      | ~ subclass(Xr_15300,complement(identity_relation)) ),
    inference(resolution,[status(thm)],[c_750656,c_230]) ).

tff(c_751188,plain,
    ! [Y_15301] : irreflexive(x,Y_15301),
    inference(resolution,[status(thm)],[c_318,c_750979]) ).

tff(c_320,plain,
    ~ irreflexive(x,domain_of(symmetrization_of(x))),
    inference(cnfTransformation,[status(thm)],[f_1116]) ).

tff(c_751193,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_751188,c_320]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM042-1 : 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
% 0.14/0.35  % Computer : n027.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 15:13:24 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 264.54/238.05  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 264.54/238.06  
% 264.54/238.06  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 264.64/238.09  
% 264.64/238.09  Inference rules
% 264.64/238.09  ----------------------
% 264.64/238.09  #Ref     : 13
% 264.64/238.09  #Sup     : 204438
% 264.64/238.09  #Fact    : 10
% 264.64/238.09  #Define  : 0
% 264.64/238.09  #Split   : 1539
% 264.64/238.09  #Chain   : 0
% 264.64/238.09  #Close   : 0
% 264.64/238.09  
% 264.64/238.09  Ordering : KBO
% 264.64/238.09  
% 264.64/238.09  Simplification rules
% 264.64/238.09  ----------------------
% 264.64/238.09  #Subsume      : 74447
% 264.64/238.09  #Demod        : 52637
% 264.64/238.09  #Tautology    : 19733
% 264.64/238.09  #SimpNegUnit  : 3967
% 264.64/238.09  #BackRed      : 2941
% 264.64/238.09  
% 264.64/238.09  #Partial instantiations: 0
% 264.64/238.09  #Strategies tried      : 1
% 264.64/238.09  
% 264.64/238.09  Timing (in seconds)
% 264.64/238.09  ----------------------
% 264.64/238.09  Preprocessing        : 0.81
% 264.64/238.09  Parsing              : 0.44
% 264.64/238.09  CNF conversion       : 0.06
% 264.64/238.09  Main loop            : 236.19
% 264.64/238.09  Inferencing          : 28.08
% 264.64/238.09  Reduction            : 101.93
% 264.64/238.09  Demodulation         : 70.94
% 264.64/238.09  BG Simplification    : 0.86
% 264.64/238.09  Subsumption          : 78.73
% 264.64/238.09  Abstraction          : 1.47
% 264.64/238.09  MUC search           : 0.00
% 264.64/238.09  Cooper               : 0.00
% 264.64/238.09  Total                : 237.06
% 264.64/238.09  Index Insertion      : 0.00
% 264.64/238.09  Index Deletion       : 0.00
% 264.64/238.09  Index Matching       : 0.00
% 264.64/238.09  BG Taut test         : 0.00
%------------------------------------------------------------------------------