TSTP Solution File: NUM190-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM190-1 : 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 : n007.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 6.77s 2.51s
% Output   : CNFRefutation 6.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   85
% Syntax   : Number of formulae    :  103 (  10 unt;  78 typ;   0 def)
%            Number of atoms       :   41 (  10 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   33 (  17   ~;  16   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   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    :   62 (  62 usr;  18 con; 0-3 aty)
%            Number of variables   :   22 (;  22   !;   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 > 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(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,
    omega = null_class,
    file(unknown,unknown) ).

tff(f_374,axiom,
    inductive(omega),
    file(unknown,unknown) ).

tff(f_380,axiom,
    member(omega,universal_class),
    file(unknown,unknown) ).

tff(f_480,axiom,
    ! [X] :
      ( ( X = null_class )
      | ( intersection(X,regular(X)) = null_class ) ),
    file(unknown,unknown) ).

tff(f_355,axiom,
    ! [X] :
      ( ~ inductive(X)
      | member(null_class,X) ),
    file(unknown,unknown) ).

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

tff(f_213,axiom,
    ! [Z,X] :
      ( ~ member(Z,complement(X))
      | ~ member(Z,X) ),
    file(unknown,unknown) ).

tff(c_318,plain,
    omega = null_class,
    inference(cnfTransformation,[status(thm)],[f_1114]) ).

tff(c_100,plain,
    inductive(omega),
    inference(cnfTransformation,[status(thm)],[f_374]) ).

tff(c_323,plain,
    inductive(null_class),
    inference(demodulation,[status(thm),theory(equality)],[c_318,c_100]) ).

tff(c_104,plain,
    member(omega,universal_class),
    inference(cnfTransformation,[status(thm)],[f_380]) ).

tff(c_321,plain,
    member(null_class,universal_class),
    inference(demodulation,[status(thm),theory(equality)],[c_318,c_104]) ).

tff(c_134,plain,
    ! [X_132] :
      ( ( intersection(X_132,regular(X_132)) = null_class )
      | ( null_class = X_132 ) ),
    inference(cnfTransformation,[status(thm)],[f_480]) ).

tff(c_94,plain,
    ! [X_106] :
      ( member(null_class,X_106)
      | ~ inductive(X_106) ),
    inference(cnfTransformation,[status(thm)],[f_355]) ).

tff(c_700,plain,
    ! [Z_389,X_390,Y_391] :
      ( member(Z_389,X_390)
      | ~ member(Z_389,intersection(X_390,Y_391)) ),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_726,plain,
    ! [X_393,Y_394] :
      ( member(null_class,X_393)
      | ~ inductive(intersection(X_393,Y_394)) ),
    inference(resolution,[status(thm)],[c_94,c_700]) ).

tff(c_729,plain,
    ! [X_132] :
      ( member(null_class,X_132)
      | ~ inductive(null_class)
      | ( null_class = X_132 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_134,c_726]) ).

tff(c_738,plain,
    ! [X_395] :
      ( member(null_class,X_395)
      | ( null_class = X_395 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_323,c_729]) ).

tff(c_48,plain,
    ! [Z_55,X_56] :
      ( ~ member(Z_55,X_56)
      | ~ member(Z_55,complement(X_56)) ),
    inference(cnfTransformation,[status(thm)],[f_213]) ).

tff(c_890,plain,
    ! [X_409] :
      ( ~ member(null_class,X_409)
      | ( complement(X_409) = null_class ) ),
    inference(resolution,[status(thm)],[c_738,c_48]) ).

tff(c_941,plain,
    complement(universal_class) = null_class,
    inference(resolution,[status(thm)],[c_321,c_890]) ).

tff(c_460,plain,
    ! [Z_346,X_347] :
      ( ~ member(Z_346,X_347)
      | ~ member(Z_346,complement(X_347)) ),
    inference(cnfTransformation,[status(thm)],[f_213]) ).

tff(c_470,plain,
    ! [X_347] :
      ( ~ member(null_class,X_347)
      | ~ inductive(complement(X_347)) ),
    inference(resolution,[status(thm)],[c_94,c_460]) ).

tff(c_962,plain,
    ( ~ member(null_class,universal_class)
    | ~ inductive(null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_941,c_470]) ).

tff(c_970,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_323,c_321,c_962]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : NUM190-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15  % 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 : n007.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
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 300
% 0.14/0.37  % DateTime : Thu Aug  3 15:07:54 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 6.77/2.51  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.77/2.52  
% 6.77/2.52  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.77/2.55  
% 6.77/2.55  Inference rules
% 6.77/2.55  ----------------------
% 6.77/2.55  #Ref     : 0
% 6.77/2.55  #Sup     : 135
% 6.77/2.55  #Fact    : 2
% 6.77/2.55  #Define  : 0
% 6.77/2.55  #Split   : 8
% 6.77/2.55  #Chain   : 0
% 6.77/2.55  #Close   : 0
% 6.77/2.55  
% 6.77/2.55  Ordering : KBO
% 6.77/2.55  
% 6.77/2.55  Simplification rules
% 6.77/2.55  ----------------------
% 6.77/2.55  #Subsume      : 14
% 6.77/2.55  #Demod        : 32
% 6.77/2.55  #Tautology    : 54
% 6.87/2.55  #SimpNegUnit  : 2
% 6.87/2.55  #BackRed      : 7
% 6.87/2.55  
% 6.87/2.55  #Partial instantiations: 0
% 6.87/2.55  #Strategies tried      : 1
% 6.87/2.55  
% 6.87/2.55  Timing (in seconds)
% 6.87/2.55  ----------------------
% 6.87/2.55  Preprocessing        : 0.81
% 6.87/2.55  Parsing              : 0.43
% 6.87/2.55  CNF conversion       : 0.06
% 6.87/2.55  Main loop            : 0.60
% 6.87/2.55  Inferencing          : 0.18
% 6.87/2.55  Reduction            : 0.21
% 6.87/2.55  Demodulation         : 0.15
% 6.87/2.55  BG Simplification    : 0.05
% 6.87/2.55  Subsumption          : 0.13
% 6.87/2.55  Abstraction          : 0.02
% 6.87/2.55  MUC search           : 0.00
% 6.87/2.55  Cooper               : 0.00
% 6.87/2.55  Total                : 1.46
% 6.87/2.55  Index Insertion      : 0.00
% 6.87/2.55  Index Deletion       : 0.00
% 6.87/2.55  Index Matching       : 0.00
% 6.87/2.55  BG Taut test         : 0.00
%------------------------------------------------------------------------------