TSTP Solution File: NUM183-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM183-1 : 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 : n022.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 10:51:02 EDT 2023

% Result   : Unsatisfiable 83.12s 67.39s
% Output   : CNFRefutation 83.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   87
% Syntax   : Number of formulae    :  102 (  12 unt;  79 typ;   0 def)
%            Number of atoms       :   44 (   2 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   41 (  20   ~;  21   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 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   :   21 (;  21   !;   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_1116,axiom,
    ~ member(x,kind_1_ordinals),
    file(unknown,unknown) ).

tff(f_1118,axiom,
    ~ member(x,limit_ordinals),
    file(unknown,unknown) ).

tff(f_1114,axiom,
    member(x,ordinal_numbers),
    file(unknown,unknown) ).

tff(f_77,axiom,
    ! [X] : subclass(X,universal_class),
    file(unknown,unknown) ).

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

tff(f_220,axiom,
    ! [Z,X] :
      ( ~ member(Z,universal_class)
      | member(Z,complement(X))
      | member(Z,X) ),
    file(unknown,unknown) ).

tff(f_995,axiom,
    intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
    file(unknown,unknown) ).

tff(f_205,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,X)
      | ~ member(Z,Y)
      | member(Z,intersection(X,Y)) ),
    file(unknown,unknown) ).

tff(c_320,plain,
    ~ member(x,kind_1_ordinals),
    inference(cnfTransformation,[status(thm)],[f_1116]) ).

tff(c_322,plain,
    ~ member(x,limit_ordinals),
    inference(cnfTransformation,[status(thm)],[f_1118]) ).

tff(c_318,plain,
    member(x,ordinal_numbers),
    inference(cnfTransformation,[status(thm)],[f_1114]) ).

tff(c_8,plain,
    ! [X_8] : subclass(X_8,universal_class),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_9780,plain,
    ! [U_1177,Y_1178,X_1179] :
      ( member(U_1177,Y_1178)
      | ~ member(U_1177,X_1179)
      | ~ subclass(X_1179,Y_1178) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_9856,plain,
    ! [Y_1181] :
      ( member(x,Y_1181)
      | ~ subclass(ordinal_numbers,Y_1181) ),
    inference(resolution,[status(thm)],[c_318,c_9780]) ).

tff(c_9870,plain,
    member(x,universal_class),
    inference(resolution,[status(thm)],[c_8,c_9856]) ).

tff(c_50,plain,
    ! [Z_57,X_58] :
      ( member(Z_57,X_58)
      | member(Z_57,complement(X_58))
      | ~ member(Z_57,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_220]) ).

tff(c_278,plain,
    intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
    inference(cnfTransformation,[status(thm)],[f_995]) ).

tff(c_11145,plain,
    ! [Z_1301,X_1302,Y_1303] :
      ( member(Z_1301,intersection(X_1302,Y_1303))
      | ~ member(Z_1301,Y_1303)
      | ~ member(Z_1301,X_1302) ),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_19167,plain,
    ! [Z_1615] :
      ( member(Z_1615,limit_ordinals)
      | ~ member(Z_1615,ordinal_numbers)
      | ~ member(Z_1615,complement(kind_1_ordinals)) ),
    inference(superposition,[status(thm),theory(equality)],[c_278,c_11145]) ).

tff(c_223857,plain,
    ! [Z_4802] :
      ( member(Z_4802,limit_ordinals)
      | ~ member(Z_4802,ordinal_numbers)
      | member(Z_4802,kind_1_ordinals)
      | ~ member(Z_4802,universal_class) ),
    inference(resolution,[status(thm)],[c_50,c_19167]) ).

tff(c_224062,plain,
    ( member(x,limit_ordinals)
    | ~ member(x,ordinal_numbers)
    | member(x,kind_1_ordinals) ),
    inference(resolution,[status(thm)],[c_9870,c_223857]) ).

tff(c_224206,plain,
    ( member(x,limit_ordinals)
    | member(x,kind_1_ordinals) ),
    inference(demodulation,[status(thm),theory(equality)],[c_318,c_224062]) ).

tff(c_224208,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_320,c_322,c_224206]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM183-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % 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
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 14:25:03 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 83.12/67.39  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 83.12/67.39  
% 83.12/67.39  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 83.12/67.42  
% 83.12/67.42  Inference rules
% 83.12/67.42  ----------------------
% 83.12/67.42  #Ref     : 1
% 83.12/67.42  #Sup     : 58847
% 83.12/67.42  #Fact    : 24
% 83.12/67.42  #Define  : 0
% 83.12/67.42  #Split   : 364
% 83.12/67.42  #Chain   : 0
% 83.12/67.42  #Close   : 0
% 83.12/67.42  
% 83.12/67.42  Ordering : KBO
% 83.12/67.42  
% 83.12/67.42  Simplification rules
% 83.12/67.42  ----------------------
% 83.12/67.42  #Subsume      : 23289
% 83.12/67.43  #Demod        : 26179
% 83.12/67.43  #Tautology    : 10500
% 83.12/67.43  #SimpNegUnit  : 5604
% 83.12/67.43  #BackRed      : 1866
% 83.12/67.43  
% 83.12/67.43  #Partial instantiations: 0
% 83.12/67.43  #Strategies tried      : 1
% 83.12/67.43  
% 83.12/67.43  Timing (in seconds)
% 83.12/67.43  ----------------------
% 83.26/67.43  Preprocessing        : 0.81
% 83.26/67.43  Parsing              : 0.43
% 83.26/67.43  CNF conversion       : 0.06
% 83.26/67.43  Main loop            : 65.61
% 83.26/67.43  Inferencing          : 7.96
% 83.26/67.43  Reduction            : 29.95
% 83.26/67.43  Demodulation         : 21.43
% 83.26/67.43  BG Simplification    : 0.29
% 83.26/67.43  Subsumption          : 18.96
% 83.26/67.43  Abstraction          : 0.47
% 83.26/67.43  MUC search           : 0.00
% 83.26/67.43  Cooper               : 0.00
% 83.26/67.43  Total                : 66.48
% 83.26/67.43  Index Insertion      : 0.00
% 83.26/67.43  Index Deletion       : 0.00
% 83.26/67.43  Index Matching       : 0.00
% 83.26/67.43  BG Taut test         : 0.00
%------------------------------------------------------------------------------