TSTP Solution File: NUM155-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM155-1 : 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 : n004.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 10:26:42 EDT 2023

% Result   : Unsatisfiable 24.17s 24.25s
% Output   : CNFRefutation 24.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :  105
% Syntax   : Number of formulae    :  196 (  38 unt;  80 typ;   0 def)
%            Number of atoms       :  226 (  59 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  200 (  90   ~; 110   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    5 (   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    :   64 (  64 usr;  20 con; 0-3 aty)
%            Number of variables   :  180 (  21 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 ).

tff(decl_100,type,
    x: $i ).

tff(decl_101,type,
    y: $i ).

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

cnf(regularity1,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).

cnf(complement1,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).

cnf(class_elements_are_sets,axiom,
    subclass(X1,universal_class),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).

cnf(intersection1,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).

cnf(domain1,axiom,
    ( restrict(X1,singleton(X2),universal_class) != null_class
    | ~ member(X2,domain_of(X1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain1) ).

cnf(singleton_set,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).

cnf(restriction1,axiom,
    intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).

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

cnf(successor,axiom,
    union(X1,singleton(X1)) = successor(X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',successor) ).

cnf(intersection3,axiom,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).

cnf(regularity2,axiom,
    ( X1 = null_class
    | intersection(X1,regular(X1)) = null_class ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).

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(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(prove_no_ordinal_between_4,negated_conjecture,
    member(y,successor(x)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_no_ordinal_between_4) ).

cnf(union,axiom,
    complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).

cnf(prove_no_ordinal_between_2,negated_conjecture,
    member(y,ordinal_numbers),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_no_ordinal_between_2) ).

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

cnf(unordered_pair2,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).

cnf(complement2,axiom,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).

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

cnf(well_ordering3,axiom,
    ( member(least(X1,X3),X3)
    | ~ well_ordering(X1,X2)
    | ~ subclass(X3,X2)
    | ~ member(X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',well_ordering3) ).

cnf(ordinal_numbers1,axiom,
    ( well_ordering(element_relation,X1)
    | ~ member(X1,ordinal_numbers) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',ordinal_numbers1) ).

cnf(prove_no_ordinal_between_3,negated_conjecture,
    member(x,y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_no_ordinal_between_3) ).

cnf(unordered_pair3,axiom,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).

cnf(c_0_25,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    subclass_members ).

cnf(c_0_26,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    regularity1 ).

cnf(c_0_27,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    complement1 ).

cnf(c_0_28,plain,
    ( X1 = null_class
    | member(regular(X1),X2)
    | ~ subclass(X1,X2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_29,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_30,plain,
    ( complement(X1) = null_class
    | ~ member(regular(complement(X1)),X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_26]) ).

cnf(c_0_31,plain,
    ( X1 = null_class
    | member(regular(X1),universal_class) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_32,plain,
    complement(universal_class) = null_class,
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_33,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    intersection1 ).

cnf(c_0_34,axiom,
    ( restrict(X1,singleton(X2),universal_class) != null_class
    | ~ member(X2,domain_of(X1)) ),
    domain1 ).

cnf(c_0_35,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_36,axiom,
    intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
    restriction1 ).

cnf(c_0_37,plain,
    ( ~ member(X1,null_class)
    | ~ member(X1,universal_class) ),
    inference(spm,[status(thm)],[c_0_27,c_0_32]) ).

cnf(c_0_38,plain,
    ( intersection(X1,X2) = null_class
    | member(regular(intersection(X1,X2)),X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_26]) ).

cnf(c_0_39,plain,
    ( intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)) != null_class
    | ~ member(X2,domain_of(X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_40,plain,
    intersection(null_class,X1) = null_class,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31]) ).

cnf(c_0_41,plain,
    ~ member(X1,domain_of(null_class)),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_42,plain,
    domain_of(null_class) = null_class,
    inference(spm,[status(thm)],[c_0_41,c_0_26]) ).

cnf(c_0_43,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    unordered_pair_member ).

cnf(c_0_44,axiom,
    union(X1,singleton(X1)) = successor(X1),
    successor ).

cnf(c_0_45,axiom,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    intersection3 ).

cnf(c_0_46,axiom,
    ( X1 = null_class
    | intersection(X1,regular(X1)) = null_class ),
    regularity2 ).

cnf(c_0_47,plain,
    ~ member(X1,null_class),
    inference(rw,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_48,plain,
    ( regular(unordered_pair(X1,X2)) = X1
    | regular(unordered_pair(X1,X2)) = X2
    | unordered_pair(X1,X2) = null_class ),
    inference(spm,[status(thm)],[c_0_43,c_0_26]) ).

cnf(c_0_49,axiom,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    not_subclass_members2 ).

cnf(c_0_50,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    not_subclass_members1 ).

cnf(c_0_51,negated_conjecture,
    member(y,successor(x)),
    prove_no_ordinal_between_4 ).

cnf(c_0_52,plain,
    union(X1,unordered_pair(X1,X1)) = successor(X1),
    inference(rw,[status(thm)],[c_0_44,c_0_35]) ).

cnf(c_0_53,axiom,
    complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
    union ).

cnf(c_0_54,negated_conjecture,
    member(y,ordinal_numbers),
    prove_no_ordinal_between_2 ).

cnf(c_0_55,plain,
    ( X1 = null_class
    | ~ member(X2,regular(X1))
    | ~ member(X2,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).

cnf(c_0_56,plain,
    ( regular(unordered_pair(X1,X1)) = X1
    | unordered_pair(X1,X1) = null_class ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_48])]) ).

cnf(c_0_57,plain,
    ( subclass(X1,intersection(X2,X3))
    | ~ member(not_subclass_element(X1,intersection(X2,X3)),X3)
    | ~ member(not_subclass_element(X1,intersection(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_49,c_0_45]) ).

cnf(c_0_58,plain,
    ( member(not_subclass_element(X1,X2),X3)
    | subclass(X1,X2)
    | ~ subclass(X1,X3) ),
    inference(spm,[status(thm)],[c_0_25,c_0_50]) ).

cnf(c_0_59,axiom,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    intersection2 ).

cnf(c_0_60,negated_conjecture,
    member(y,complement(intersection(complement(x),complement(unordered_pair(x,x))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).

cnf(c_0_61,negated_conjecture,
    ( member(y,X1)
    | ~ subclass(ordinal_numbers,X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_54]) ).

cnf(c_0_62,plain,
    ( unordered_pair(X1,X1) = null_class
    | ~ member(X2,unordered_pair(X1,X1))
    | ~ member(X2,X1) ),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_63,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    unordered_pair2 ).

cnf(c_0_64,plain,
    ( subclass(X1,intersection(X2,X1))
    | ~ member(not_subclass_element(X1,intersection(X2,X1)),X2) ),
    inference(spm,[status(thm)],[c_0_57,c_0_50]) ).

cnf(c_0_65,plain,
    ( member(not_subclass_element(X1,X2),universal_class)
    | subclass(X1,X2) ),
    inference(spm,[status(thm)],[c_0_58,c_0_29]) ).

cnf(c_0_66,plain,
    ( member(not_subclass_element(intersection(X1,X2),X3),X2)
    | subclass(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_59,c_0_50]) ).

cnf(c_0_67,negated_conjecture,
    ~ member(y,intersection(complement(x),complement(unordered_pair(x,x)))),
    inference(spm,[status(thm)],[c_0_27,c_0_60]) ).

cnf(c_0_68,axiom,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    complement2 ).

cnf(c_0_69,negated_conjecture,
    member(y,universal_class),
    inference(spm,[status(thm)],[c_0_61,c_0_29]) ).

cnf(c_0_70,plain,
    ( unordered_pair(X1,X1) = null_class
    | ~ member(X1,universal_class)
    | ~ member(X1,X1) ),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_71,plain,
    ( unordered_pair(X1,X1) = null_class
    | member(X1,universal_class) ),
    inference(spm,[status(thm)],[c_0_31,c_0_56]) ).

cnf(c_0_72,axiom,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    subclass_implies_equal ).

cnf(c_0_73,plain,
    subclass(X1,intersection(universal_class,X1)),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_74,plain,
    subclass(intersection(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_49,c_0_66]) ).

cnf(c_0_75,negated_conjecture,
    ( ~ member(y,complement(unordered_pair(x,x)))
    | ~ member(y,complement(x)) ),
    inference(spm,[status(thm)],[c_0_67,c_0_45]) ).

cnf(c_0_76,negated_conjecture,
    ( member(y,complement(X1))
    | member(y,X1) ),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_77,plain,
    ( not_subclass_element(unordered_pair(X1,X2),X3) = X1
    | not_subclass_element(unordered_pair(X1,X2),X3) = X2
    | subclass(unordered_pair(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_43,c_0_50]) ).

cnf(c_0_78,plain,
    ( unordered_pair(X1,X1) = null_class
    | ~ member(X1,X1) ),
    inference(spm,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_79,plain,
    intersection(universal_class,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]) ).

cnf(c_0_80,plain,
    ( member(not_subclass_element(intersection(X1,X2),X3),X1)
    | subclass(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_33,c_0_50]) ).

cnf(c_0_81,axiom,
    ( member(least(X1,X3),X3)
    | ~ well_ordering(X1,X2)
    | ~ subclass(X3,X2)
    | ~ member(X4,X3) ),
    well_ordering3 ).

cnf(c_0_82,axiom,
    ( well_ordering(element_relation,X1)
    | ~ member(X1,ordinal_numbers) ),
    ordinal_numbers1 ).

cnf(c_0_83,negated_conjecture,
    ( member(y,unordered_pair(x,x))
    | ~ member(y,complement(x)) ),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_84,plain,
    ( not_subclass_element(unordered_pair(X1,X2),X3) = X1
    | subclass(unordered_pair(X1,X2),X3)
    | ~ member(X2,X3) ),
    inference(spm,[status(thm)],[c_0_49,c_0_77]) ).

cnf(c_0_85,negated_conjecture,
    member(x,y),
    prove_no_ordinal_between_3 ).

cnf(c_0_86,plain,
    ( unordered_pair(intersection(X1,X2),intersection(X1,X2)) = null_class
    | ~ member(intersection(X1,X2),X2)
    | ~ member(intersection(X1,X2),X1) ),
    inference(spm,[status(thm)],[c_0_78,c_0_45]) ).

cnf(c_0_87,plain,
    ( member(X1,universal_class)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_33,c_0_79]) ).

cnf(c_0_88,plain,
    subclass(X1,intersection(X1,X1)),
    inference(spm,[status(thm)],[c_0_64,c_0_50]) ).

cnf(c_0_89,plain,
    subclass(intersection(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_49,c_0_80]) ).

cnf(c_0_90,plain,
    ( member(least(element_relation,X1),X1)
    | ~ member(X2,ordinal_numbers)
    | ~ member(X3,X1)
    | ~ subclass(X1,X2) ),
    inference(spm,[status(thm)],[c_0_81,c_0_82]) ).

cnf(c_0_91,negated_conjecture,
    ( member(y,unordered_pair(x,x))
    | member(y,x) ),
    inference(spm,[status(thm)],[c_0_83,c_0_76]) ).

cnf(c_0_92,negated_conjecture,
    ( not_subclass_element(unordered_pair(X1,x),y) = X1
    | subclass(unordered_pair(X1,x),y) ),
    inference(spm,[status(thm)],[c_0_84,c_0_85]) ).

cnf(c_0_93,plain,
    ( ~ member(intersection(X1,X2),X2)
    | ~ member(intersection(X1,X2),X1) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_86]),c_0_47]),c_0_87]) ).

cnf(c_0_94,plain,
    intersection(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_88]),c_0_89])]) ).

cnf(c_0_95,negated_conjecture,
    ( member(least(element_relation,X1),X1)
    | ~ member(X2,X1)
    | ~ subclass(X1,y) ),
    inference(spm,[status(thm)],[c_0_90,c_0_54]) ).

cnf(c_0_96,plain,
    ( regular(unordered_pair(X1,X2)) = X2
    | unordered_pair(X1,X2) = null_class
    | ~ member(X3,unordered_pair(X1,X2))
    | ~ member(X3,X1) ),
    inference(spm,[status(thm)],[c_0_55,c_0_48]) ).

cnf(c_0_97,axiom,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    unordered_pair3 ).

cnf(c_0_98,negated_conjecture,
    ( member(y,x)
    | member(y,X1)
    | ~ subclass(unordered_pair(x,x),X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_91]) ).

cnf(c_0_99,negated_conjecture,
    ( subclass(unordered_pair(X1,x),y)
    | ~ member(X1,y) ),
    inference(spm,[status(thm)],[c_0_49,c_0_92]) ).

cnf(c_0_100,plain,
    ~ member(X1,X1),
    inference(spm,[status(thm)],[c_0_93,c_0_94]) ).

cnf(c_0_101,plain,
    ( subclass(intersection(X1,X2),intersection(X3,X1))
    | ~ member(not_subclass_element(intersection(X1,X2),intersection(X3,X1)),X3) ),
    inference(spm,[status(thm)],[c_0_57,c_0_80]) ).

cnf(c_0_102,negated_conjecture,
    ( member(least(element_relation,intersection(y,X1)),intersection(y,X1))
    | ~ member(X2,intersection(y,X1)) ),
    inference(spm,[status(thm)],[c_0_95,c_0_89]) ).

cnf(c_0_103,plain,
    ( regular(unordered_pair(X1,X2)) = X2
    | unordered_pair(X1,X2) = null_class
    | ~ member(X2,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_87]) ).

cnf(c_0_104,negated_conjecture,
    member(y,x),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_85])]),c_0_100]) ).

cnf(c_0_105,plain,
    subclass(intersection(X1,X2),intersection(X2,X1)),
    inference(spm,[status(thm)],[c_0_101,c_0_66]) ).

cnf(c_0_106,negated_conjecture,
    ( member(least(element_relation,intersection(y,X1)),intersection(y,X1))
    | ~ member(X2,y)
    | ~ member(X2,X1) ),
    inference(spm,[status(thm)],[c_0_102,c_0_45]) ).

cnf(c_0_107,negated_conjecture,
    ( regular(unordered_pair(x,y)) = y
    | unordered_pair(x,y) = null_class ),
    inference(spm,[status(thm)],[c_0_103,c_0_104]) ).

cnf(c_0_108,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_105]),c_0_105])]) ).

cnf(c_0_109,negated_conjecture,
    ( member(least(element_relation,intersection(y,X1)),intersection(y,X1))
    | ~ member(x,X1) ),
    inference(spm,[status(thm)],[c_0_106,c_0_85]) ).

cnf(c_0_110,negated_conjecture,
    ( intersection(y,unordered_pair(x,y)) = null_class
    | unordered_pair(x,y) = null_class ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_107]),c_0_108]) ).

cnf(c_0_111,negated_conjecture,
    ( member(x,X1)
    | ~ subclass(y,X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_85]) ).

cnf(c_0_112,negated_conjecture,
    ( unordered_pair(x,y) = null_class
    | ~ member(x,unordered_pair(x,y)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_47]) ).

cnf(c_0_113,negated_conjecture,
    member(x,universal_class),
    inference(spm,[status(thm)],[c_0_111,c_0_29]) ).

cnf(c_0_114,negated_conjecture,
    unordered_pair(x,y) = null_class,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_63]),c_0_113])]) ).

cnf(c_0_115,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_114]),c_0_113])]),c_0_47]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM155-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n004.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Aug 25 11:14:53 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.56  start to proof: theBenchmark
% 24.17/24.25  % Version  : CSE_E---1.5
% 24.17/24.25  % Problem  : theBenchmark.p
% 24.17/24.25  % Proof found
% 24.17/24.25  % SZS status Theorem for theBenchmark.p
% 24.17/24.25  % SZS output start Proof
% See solution above
% 24.22/24.25  % Total time : 23.679000 s
% 24.22/24.25  % SZS output end Proof
% 24.22/24.25  % Total time : 23.687000 s
%------------------------------------------------------------------------------