TSTP Solution File: SET152-6 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET152-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n013.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 14:33:21 EDT 2023

% Result   : Unsatisfiable 0.19s 0.63s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   61
% Syntax   : Number of formulae    :   70 (   5 unt;  56 typ;   0 def)
%            Number of atoms       :   26 (   7 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   24 (  12   ~;  12   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 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   :   18 (   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 ).

cnf(subclass_members,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).

cnf(regularity1,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).

cnf(complement1,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).

cnf(class_elements_are_sets,axiom,
    subclass(X1,universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).

cnf(prove_complement_of_universal_class_1,negated_conjecture,
    complement(universal_class) != null_class,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_complement_of_universal_class_1) ).

cnf(c_0_5,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    subclass_members ).

cnf(c_0_6,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    regularity1 ).

cnf(c_0_7,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    complement1 ).

cnf(c_0_8,plain,
    ( X1 = null_class
    | member(regular(X1),X2)
    | ~ subclass(X1,X2) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_10,plain,
    ( complement(X1) = null_class
    | ~ member(regular(complement(X1)),X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_6]) ).

cnf(c_0_11,plain,
    ( X1 = null_class
    | member(regular(X1),universal_class) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    complement(universal_class) != null_class,
    prove_complement_of_universal_class_1 ).

cnf(c_0_13,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET152-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n013.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Aug 26 15:36:17 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.59  start to proof: theBenchmark
% 0.19/0.63  % Version  : CSE_E---1.5
% 0.19/0.63  % Problem  : theBenchmark.p
% 0.19/0.63  % Proof found
% 0.19/0.63  % SZS status Theorem for theBenchmark.p
% 0.19/0.63  % SZS output start Proof
% See solution above
% 0.19/0.64  % Total time : 0.027000 s
% 0.19/0.64  % SZS output end Proof
% 0.19/0.64  % Total time : 0.030000 s
%------------------------------------------------------------------------------