TSTP Solution File: NUM180-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM180-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n032.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 : Thu Aug 31 10:26:47 EDT 2023

% Result   : Unsatisfiable 0.15s 0.56s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   83
% Syntax   : Number of formulae    :   91 (   5 unt;  78 typ;   0 def)
%            Number of atoms       :   21 (   2 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   15 (   7   ~;   8   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 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   :   16 (   2 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    subclass: ( $i * $i ) > $o ).

tff(decl_23,type,
    member: ( $i * $i ) > $o ).

tff(decl_24,type,
    not_subclass_element: ( $i * $i ) > $i ).

tff(decl_25,type,
    universal_class: $i ).

tff(decl_26,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_27,type,
    singleton: $i > $i ).

tff(decl_28,type,
    ordered_pair: ( $i * $i ) > $i ).

tff(decl_29,type,
    cross_product: ( $i * $i ) > $i ).

tff(decl_30,type,
    first: $i > $i ).

tff(decl_31,type,
    second: $i > $i ).

tff(decl_32,type,
    element_relation: $i ).

tff(decl_33,type,
    intersection: ( $i * $i ) > $i ).

tff(decl_34,type,
    complement: $i > $i ).

tff(decl_35,type,
    union: ( $i * $i ) > $i ).

tff(decl_36,type,
    symmetric_difference: ( $i * $i ) > $i ).

tff(decl_37,type,
    restrict: ( $i * $i * $i ) > $i ).

tff(decl_38,type,
    null_class: $i ).

tff(decl_39,type,
    domain_of: $i > $i ).

tff(decl_40,type,
    rotate: $i > $i ).

tff(decl_41,type,
    flip: $i > $i ).

tff(decl_42,type,
    inverse: $i > $i ).

tff(decl_43,type,
    range_of: $i > $i ).

tff(decl_44,type,
    domain: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    range: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    image: ( $i * $i ) > $i ).

tff(decl_47,type,
    successor: $i > $i ).

tff(decl_48,type,
    successor_relation: $i ).

tff(decl_49,type,
    inductive: $i > $o ).

tff(decl_50,type,
    omega: $i ).

tff(decl_51,type,
    sum_class: $i > $i ).

tff(decl_52,type,
    power_class: $i > $i ).

tff(decl_53,type,
    compose: ( $i * $i ) > $i ).

tff(decl_54,type,
    single_valued_class: $i > $o ).

tff(decl_55,type,
    identity_relation: $i ).

tff(decl_56,type,
    function: $i > $o ).

tff(decl_57,type,
    regular: $i > $i ).

tff(decl_58,type,
    apply: ( $i * $i ) > $i ).

tff(decl_59,type,
    choice: $i ).

tff(decl_60,type,
    one_to_one: $i > $o ).

tff(decl_61,type,
    subset_relation: $i ).

tff(decl_62,type,
    diagonalise: $i > $i ).

tff(decl_63,type,
    cantor: $i > $i ).

tff(decl_64,type,
    operation: $i > $o ).

tff(decl_65,type,
    compatible: ( $i * $i * $i ) > $o ).

tff(decl_66,type,
    homomorphism: ( $i * $i * $i ) > $o ).

tff(decl_67,type,
    not_homomorphism1: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    not_homomorphism2: ( $i * $i * $i ) > $i ).

tff(decl_69,type,
    compose_class: $i > $i ).

tff(decl_70,type,
    composition_function: $i ).

tff(decl_71,type,
    domain_relation: $i ).

tff(decl_72,type,
    single_valued1: $i > $i ).

tff(decl_73,type,
    single_valued2: $i > $i ).

tff(decl_74,type,
    single_valued3: $i > $i ).

tff(decl_75,type,
    singleton_relation: $i ).

tff(decl_76,type,
    application_function: $i ).

tff(decl_77,type,
    maps: ( $i * $i * $i ) > $o ).

tff(decl_78,type,
    symmetrization_of: $i > $i ).

tff(decl_79,type,
    irreflexive: ( $i * $i ) > $o ).

tff(decl_80,type,
    connected: ( $i * $i ) > $o ).

tff(decl_81,type,
    transitive: ( $i * $i ) > $o ).

tff(decl_82,type,
    asymmetric: ( $i * $i ) > $o ).

tff(decl_83,type,
    segment: ( $i * $i * $i ) > $i ).

tff(decl_84,type,
    well_ordering: ( $i * $i ) > $o ).

tff(decl_85,type,
    least: ( $i * $i ) > $i ).

tff(decl_86,type,
    not_well_ordering: ( $i * $i ) > $i ).

tff(decl_87,type,
    section: ( $i * $i * $i ) > $o ).

tff(decl_88,type,
    ordinal_numbers: $i ).

tff(decl_89,type,
    kind_1_ordinals: $i ).

tff(decl_90,type,
    limit_ordinals: $i ).

tff(decl_91,type,
    rest_of: $i > $i ).

tff(decl_92,type,
    rest_relation: $i ).

tff(decl_93,type,
    recursion_equation_functions: $i > $i ).

tff(decl_94,type,
    union_of_range_map: $i ).

tff(decl_95,type,
    recursion: ( $i * $i * $i ) > $i ).

tff(decl_96,type,
    ordinal_add: ( $i * $i ) > $i ).

tff(decl_97,type,
    add_relation: $i ).

tff(decl_98,type,
    ordinal_multiply: ( $i * $i ) > $i ).

tff(decl_99,type,
    integer_of: $i > $i ).

cnf(intersection2,axiom,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).

cnf(limit_ordinals,axiom,
    intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',limit_ordinals) ).

cnf(not_subclass_members1,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).

cnf(not_subclass_members2,axiom,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).

cnf(prove_limit_ordinals_are_ordinals_1,negated_conjecture,
    ~ subclass(limit_ordinals,ordinal_numbers),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_limit_ordinals_are_ordinals_1) ).

cnf(c_0_5,axiom,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    intersection2 ).

cnf(c_0_6,axiom,
    intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
    limit_ordinals ).

cnf(c_0_7,plain,
    ( member(X1,ordinal_numbers)
    | ~ member(X1,limit_ordinals) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_8,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    not_subclass_members1 ).

cnf(c_0_9,axiom,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    not_subclass_members2 ).

cnf(c_0_10,plain,
    ( member(not_subclass_element(limit_ordinals,X1),ordinal_numbers)
    | subclass(limit_ordinals,X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    ~ subclass(limit_ordinals,ordinal_numbers),
    prove_limit_ordinals_are_ordinals_1 ).

cnf(c_0_12,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : NUM180-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.10  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit   : 300
% 0.10/0.29  % WCLimit    : 300
% 0.10/0.29  % DateTime   : Fri Aug 25 11:39:58 EDT 2023
% 0.10/0.29  % CPUTime  : 
% 0.15/0.53  start to proof: theBenchmark
% 0.15/0.56  % Version  : CSE_E---1.5
% 0.15/0.56  % Problem  : theBenchmark.p
% 0.15/0.56  % Proof found
% 0.15/0.56  % SZS status Theorem for theBenchmark.p
% 0.15/0.56  % SZS output start Proof
% See solution above
% 0.15/0.56  % Total time : 0.017000 s
% 0.15/0.56  % SZS output end Proof
% 0.15/0.56  % Total time : 0.023000 s
%------------------------------------------------------------------------------