%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET097-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n021.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 : Mon Jun 24 14:33:14 EDT 2024

% Result   : Unsatisfiable 209.98s 28.23s
% Output   : CNFRefutation 210.52s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
cnf(c_49,plain,
    ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
    | member(X0,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_unordered_pair) ).

cnf(c_50,plain,
    ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
    | member(X1,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_unordered_pair) ).

cnf(c_51,plain,
    ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
    | member(X0,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).

cnf(c_52,plain,
    ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
    | member(X1,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).

cnf(c_53,plain,
    subclass(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_is_reflexive) ).

cnf(c_54,plain,
    ( ~ subclass(X0,X1)
    | ~ subclass(X1,X2)
    | subclass(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subclass) ).

cnf(c_55,plain,
    ( X0 = X1
    | member(not_subclass_element(X0,X1),X0)
    | member(not_subclass_element(X1,X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality1) ).

cnf(c_57,plain,
    ( ~ member(not_subclass_element(X0,X1),X1)
    | X0 = X1
    | member(not_subclass_element(X1,X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality3) ).

cnf(c_58,plain,
    ( ~ member(not_subclass_element(X0,X1),X1)
    | ~ member(not_subclass_element(X1,X0),X0)
    | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality4) ).

cnf(c_59,plain,
    ~ member(X0,intersection(complement(X1),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',special_classes_lemma) ).

cnf(c_60,plain,
    ~ member(X0,null_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).

cnf(c_61,plain,
    subclass(null_class,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_subclass) ).

cnf(c_62,plain,
    ( ~ subclass(X0,null_class)
    | X0 = null_class ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).

cnf(c_63,plain,
    ( X0 = null_class
    | member(not_subclass_element(X0,null_class),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_unique) ).

cnf(c_64,plain,
    member(null_class,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).

cnf(c_65,plain,
    unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).

cnf(c_66,plain,
    subclass(singleton(X0),unordered_pair(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair1) ).

cnf(c_67,plain,
    subclass(singleton(X0),unordered_pair(X1,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).

cnf(c_68,plain,
    ( unordered_pair(X0,X1) = singleton(X0)
    | member(X1,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).

cnf(c_69,plain,
    ( unordered_pair(X0,X1) = singleton(X1)
    | member(X0,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).

cnf(c_70,plain,
    ( unordered_pair(X0,X1) = null_class
    | member(X0,universal_class)
    | member(X1,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_unordered_pair) ).

cnf(c_71,plain,
    ( unordered_pair(X0,X1) != unordered_pair(X0,X2)
    | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).

cnf(c_72,plain,
    ( unordered_pair(X0,X1) != unordered_pair(X2,X1)
    | ~ member(ordered_pair(X0,X2),cross_product(universal_class,universal_class))
    | X0 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation) ).

cnf(c_73,plain,
    ( unordered_pair(X0,X1) != null_class
    | ~ member(X0,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).

cnf(c_74,plain,
    ( unordered_pair(X0,X1) != null_class
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).

cnf(c_75,plain,
    ( unordered_pair(X0,X1) != null_class
    | ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom3) ).

cnf(c_76,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | subclass(unordered_pair(X0,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_is_subset) ).

cnf(c_77,plain,
    member(singleton(X0),universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletons_are_sets) ).

cnf(c_78,plain,
    member(singleton(X0),unordered_pair(X1,singleton(X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_singletons_are_sets) ).

cnf(c_79,plain,
    ( ~ member(X0,universal_class)
    | member(X0,singleton(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_in_its_singleton) ).

cnf(c_80,plain,
    ( singleton(X0) != null_class
    | ~ member(X0,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).

cnf(c_81,plain,
    member(null_class,singleton(null_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_in_its_singleton) ).

cnf(c_82,plain,
    ( ~ member(X0,singleton(X1))
    | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).

cnf(c_83,plain,
    ( singleton(X0) = null_class
    | member(X0,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).

cnf(c_84,plain,
    ( singleton(X0) != singleton(X1)
    | ~ member(X0,universal_class)
    | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_identified_by_element1) ).

cnf(c_85,plain,
    ( singleton(X0) != singleton(X1)
    | ~ member(X1,universal_class)
    | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_identified_by_element2) ).

cnf(c_86,plain,
    ( unordered_pair(X0,X1) != singleton(X2)
    | ~ member(X2,universal_class)
    | X0 = X2
    | X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair3) ).

cnf(c_87,plain,
    ( ~ member(X0,universal_class)
    | member(member_of(singleton(X0)),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_exists1) ).

cnf(c_88,plain,
    ( ~ member(X0,universal_class)
    | singleton(member_of(singleton(X0))) = singleton(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_exists2) ).

cnf(c_89,plain,
    ( member_of(X0) = X0
    | member(member_of(X0),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_exists3) ).

cnf(c_90,plain,
    ( singleton(member_of(X0)) = X0
    | member_of(X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_exists4) ).

cnf(c_91,plain,
    ( ~ member(X0,universal_class)
    | member_of(singleton(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_singleton_is_unique) ).

cnf(c_92,plain,
    ( member_of(X0) = X0
    | member(member_of1(X0),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_non_singleton_unique1) ).

cnf(c_93,plain,
    ( singleton(member_of1(X0)) = X0
    | member_of(X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_non_singleton_unique2) ).

cnf(c_94,plain,
    ( singleton(member_of(X0)) != X0
    | member(X0,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_singletons_are_sets) ).

cnf(c_95,plain,
    ( singleton(member_of(X0)) != X0
    | ~ member(X1,X0)
    | member_of(X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_singletons1) ).

cnf(c_96,plain,
    ( ~ member(X0,X1)
    | subclass(singleton(X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_singletons2) ).

cnf(c_97,plain,
    ( ~ subclass(X0,singleton(X1))
    | singleton(X1) = X0
    | X0 = null_class ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_subsets_of_singleton) ).

cnf(c_98,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_number_of_elements_in_class_1) ).

cnf(c_99,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_number_of_elements_in_class_2) ).

cnf(c_100,negated_conjecture,
    null_class != x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_number_of_elements_in_class_3) ).

cnf(c_101,plain,
    ( ~ member(X0,X1)
    | ~ subclass(X1,X2)
    | member(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).

cnf(c_102,plain,
    ( member(not_subclass_element(X0,X1),X0)
    | subclass(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).

cnf(c_103,plain,
    ( ~ member(not_subclass_element(X0,X1),X1)
    | subclass(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).

cnf(c_104,plain,
    subclass(X0,universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).

cnf(c_107,plain,
    ( ~ subclass(X0,X1)
    | ~ subclass(X1,X0)
    | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).

cnf(c_108,plain,
    ( ~ member(X0,unordered_pair(X1,X2))
    | X0 = X1
    | X0 = X2 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).

cnf(c_109,plain,
    ( ~ member(X0,universal_class)
    | member(X0,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).

cnf(c_110,plain,
    ( ~ member(X0,universal_class)
    | member(X0,unordered_pair(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).

cnf(c_111,plain,
    member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).

cnf(c_112,plain,
    unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).

cnf(c_113,plain,
    unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).

cnf(c_114,plain,
    ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
    | member(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).

cnf(c_115,plain,
    ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
    | member(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).

cnf(c_116,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X3)
    | member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).

cnf(c_117,plain,
    ( ~ member(X0,cross_product(X1,X2))
    | ordered_pair(first(X0),second(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).

cnf(c_118,plain,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',element_relation1) ).

cnf(c_119,plain,
    ( ~ member(ordered_pair(X0,X1),element_relation)
    | member(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',element_relation2) ).

cnf(c_120,plain,
    ( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
    | ~ member(X0,X1)
    | member(ordered_pair(X0,X1),element_relation) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',element_relation3) ).

cnf(c_121,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).

cnf(c_122,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).

cnf(c_123,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).

cnf(c_124,plain,
    ( ~ member(X0,complement(X1))
    | ~ member(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).

cnf(c_125,plain,
    ( ~ member(X0,universal_class)
    | member(X0,complement(X1))
    | member(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).

cnf(c_126,plain,
    complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).

cnf(c_127,plain,
    intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1)))) = symmetric_difference(X0,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',symmetric_difference) ).

cnf(c_128,plain,
    intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).

cnf(c_129,plain,
    intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).

cnf(c_130,plain,
    ( restrict(X0,singleton(X1),universal_class) != null_class
    | ~ member(X1,domain_of(X0)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain1) ).

cnf(c_131,plain,
    ( ~ member(X0,universal_class)
    | restrict(X1,singleton(X0),universal_class) = null_class
    | member(X0,domain_of(X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain2) ).

cnf(c_132,plain,
    subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',rotate1) ).

cnf(c_133,plain,
    ( ~ member(ordered_pair(ordered_pair(X0,X1),X2),rotate(X3))
    | member(ordered_pair(ordered_pair(X1,X2),X0),X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',rotate2) ).

cnf(c_134,plain,
    ( ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ member(ordered_pair(ordered_pair(X1,X2),X0),X3)
    | member(ordered_pair(ordered_pair(X0,X1),X2),rotate(X3)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',rotate3) ).

cnf(c_135,plain,
    subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',flip1) ).

cnf(c_136,plain,
    ( ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
    | member(ordered_pair(ordered_pair(X1,X0),X2),X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',flip2) ).

cnf(c_137,plain,
    ( ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
    | member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',flip3) ).

cnf(c_138,plain,
    domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).

cnf(c_139,plain,
    domain_of(inverse(X0)) = range_of(X0),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',range_of) ).

cnf(c_140,plain,
    first(not_subclass_element(restrict(X0,X1,singleton(X2)),null_class)) = domain(X0,X1,X2),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain) ).

cnf(c_141,plain,
    second(not_subclass_element(restrict(X0,singleton(X1),X2),null_class)) = range(X0,X1,X2),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',range) ).

cnf(c_142,plain,
    range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',image) ).

cnf(c_143,plain,
    union(X0,singleton(X0)) = successor(X0),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor) ).

cnf(c_144,plain,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor_relation1) ).

cnf(c_145,plain,
    ( ~ member(ordered_pair(X0,X1),successor_relation)
    | successor(X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor_relation2) ).

cnf(c_146,plain,
    ( successor(X0) != X1
    | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
    | member(ordered_pair(X0,X1),successor_relation) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor_relation3) ).

cnf(c_147,plain,
    ( ~ inductive(X0)
    | member(null_class,X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive1) ).

cnf(c_148,plain,
    ( ~ inductive(X0)
    | subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive2) ).

cnf(c_149,plain,
    ( ~ subclass(image(successor_relation,X0),X0)
    | ~ member(null_class,X0)
    | inductive(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive3) ).

cnf(c_150,plain,
    inductive(omega),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).

cnf(c_151,plain,
    ( ~ inductive(X0)
    | subclass(omega,X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive2) ).

cnf(c_152,plain,
    member(omega,universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_in_universal) ).

cnf(c_153,plain,
    domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',sum_class_definition) ).

cnf(c_154,plain,
    ( ~ member(X0,universal_class)
    | member(sum_class(X0),universal_class) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',sum_class2) ).

cnf(c_155,plain,
    complement(image(element_relation,complement(X0))) = power_class(X0),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',power_class_definition) ).

cnf(c_156,plain,
    ( ~ member(X0,universal_class)
    | member(power_class(X0),universal_class) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',power_class2) ).

cnf(c_157,plain,
    subclass(compose(X0,X1),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compose1) ).

cnf(c_158,plain,
    ( ~ member(ordered_pair(X0,X1),compose(X2,X3))
    | member(X1,image(X2,image(X3,singleton(X0)))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compose2) ).

cnf(c_159,plain,
    ( ~ member(X0,image(X1,image(X2,singleton(X3))))
    | ~ member(ordered_pair(X3,X0),cross_product(universal_class,universal_class))
    | member(ordered_pair(X3,X0),compose(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compose3) ).

cnf(c_162,plain,
    ( ~ function(X0)
    | subclass(X0,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',function1) ).

cnf(c_163,plain,
    ( ~ function(X0)
    | subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',function2) ).

cnf(c_164,plain,
    ( ~ subclass(compose(X0,inverse(X0)),identity_relation)
    | ~ subclass(X0,cross_product(universal_class,universal_class))
    | function(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',function3) ).

cnf(c_165,plain,
    ( ~ member(X0,universal_class)
    | ~ function(X1)
    | member(image(X1,X0),universal_class) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',replacement) ).

cnf(c_166,plain,
    ( X0 = null_class
    | member(regular(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).

cnf(c_167,plain,
    ( intersection(X0,regular(X0)) = null_class
    | X0 = null_class ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).

cnf(c_168,plain,
    sum_class(image(X0,singleton(X1))) = apply(X0,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',apply) ).

cnf(c_169,plain,
    function(choice),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',choice1) ).

cnf(c_170,plain,
    ( ~ member(X0,universal_class)
    | X0 = null_class
    | member(apply(choice,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',choice2) ).

cnf(c_174,plain,
    intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subset_relation) ).

cnf(c_175,plain,
    intersection(inverse(subset_relation),subset_relation) = identity_relation,
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',identity_relation) ).

cnf(c_176,plain,
    complement(domain_of(intersection(X0,identity_relation))) = diagonalise(X0),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',diagonalisation) ).

cnf(c_177,plain,
    intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cantor_class) ).

cnf(c_178,plain,
    ( ~ operation(X0)
    | function(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',operation1) ).

cnf(c_179,plain,
    ( ~ operation(X0)
    | cross_product(domain_of(domain_of(X0)),domain_of(domain_of(X0))) = domain_of(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',operation2) ).

cnf(c_180,plain,
    ( ~ operation(X0)
    | subclass(range_of(X0),domain_of(domain_of(X0))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',operation3) ).

cnf(c_181,plain,
    ( cross_product(domain_of(domain_of(X0)),domain_of(domain_of(X0))) != domain_of(X0)
    | ~ subclass(range_of(X0),domain_of(domain_of(X0)))
    | ~ function(X0)
    | operation(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',operation4) ).

cnf(c_182,plain,
    ( ~ compatible(X0,X1,X2)
    | function(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compatible1) ).

cnf(c_183,plain,
    ( ~ compatible(X0,X1,X2)
    | domain_of(domain_of(X1)) = domain_of(X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compatible2) ).

cnf(c_184,plain,
    ( ~ compatible(X0,X1,X2)
    | subclass(range_of(X0),domain_of(domain_of(X2))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compatible3) ).

cnf(c_185,plain,
    ( domain_of(domain_of(X0)) != domain_of(X1)
    | ~ subclass(range_of(X1),domain_of(domain_of(X2)))
    | ~ function(X1)
    | compatible(X1,X0,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compatible4) ).

cnf(c_186,plain,
    ( ~ homomorphism(X0,X1,X2)
    | operation(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism1) ).

cnf(c_187,plain,
    ( ~ homomorphism(X0,X1,X2)
    | operation(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism2) ).

cnf(c_188,plain,
    ( ~ homomorphism(X0,X1,X2)
    | compatible(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism3) ).

cnf(c_189,plain,
    ( ~ member(ordered_pair(X0,X1),domain_of(X2))
    | ~ homomorphism(X3,X2,X4)
    | apply(X4,ordered_pair(apply(X3,X0),apply(X3,X1))) = apply(X3,apply(X2,ordered_pair(X0,X1))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism4) ).

cnf(c_190,plain,
    ( ~ compatible(X0,X1,X2)
    | ~ operation(X1)
    | ~ operation(X2)
    | member(ordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)),domain_of(X1))
    | homomorphism(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism5) ).

cnf(c_191,plain,
    ( apply(X0,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X0)),apply(X1,not_homomorphism2(X1,X2,X0)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism2(X1,X2,X0))))
    | ~ compatible(X1,X2,X0)
    | ~ operation(X0)
    | ~ operation(X2)
    | homomorphism(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism6) ).

cnf(c_194,plain,
    ( ~ member(ordered_pair(X0,successor(X0)),cross_product(universal_class,universal_class))
    | member(ordered_pair(X0,successor(X0)),successor_relation) ),
    inference(unflattening,[status(thm)],[c_146]) ).

cnf(c_414,plain,
    ( ~ inductive(X0)
    | member(null_class,X0) ),
    inference(prop_impl_just,[status(thm)],[c_147]) ).

cnf(c_416,plain,
    ( ~ inductive(X0)
    | subclass(image(successor_relation,X0),X0) ),
    inference(prop_impl_just,[status(thm)],[c_148]) ).

cnf(c_418,plain,
    ( ~ inductive(X0)
    | subclass(omega,X0) ),
    inference(prop_impl_just,[status(thm)],[c_151]) ).

cnf(c_1297,plain,
    intersection(complement(intersection(X0,X1)),union(X0,X1)) = symmetric_difference(X0,X1),
    inference(light_normalisation,[status(thm)],[c_127,c_126]) ).

cnf(c_1298,plain,
    restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) = subset_relation,
    inference(demodulation,[status(thm)],[c_174,c_129]) ).

cnf(c_1360,plain,
    ( X0 != X1
    | ~ subclass(image(successor_relation,X0),X0)
    | ~ member(null_class,X0)
    | subclass(omega,X1) ),
    inference(resolution_lifted,[status(thm)],[c_149,c_418]) ).

cnf(c_1361,plain,
    ( ~ subclass(image(successor_relation,X0),X0)
    | ~ member(null_class,X0)
    | subclass(omega,X0) ),
    inference(unflattening,[status(thm)],[c_1360]) ).

cnf(c_1378,plain,
    ( X0 != omega
    | subclass(image(successor_relation,X0),X0) ),
    inference(resolution_lifted,[status(thm)],[c_416,c_150]) ).

cnf(c_1379,plain,
    subclass(image(successor_relation,omega),omega),
    inference(unflattening,[status(thm)],[c_1378]) ).

cnf(c_1383,plain,
    ( X0 != omega
    | member(null_class,X0) ),
    inference(resolution_lifted,[status(thm)],[c_414,c_150]) ).

cnf(c_1384,plain,
    member(null_class,omega),
    inference(unflattening,[status(thm)],[c_1383]) ).

cnf(c_3173,plain,
    not_subclass_element(x,null_class) = sP0_iProver_def,
    definition ).

cnf(c_3174,plain,
    singleton(sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_3175,plain,
    complement(sP1_iProver_def) = sP2_iProver_def,
    definition ).

cnf(c_3176,plain,
    intersection(sP2_iProver_def,x) = sP3_iProver_def,
    definition ).

cnf(c_3177,plain,
    not_subclass_element(sP3_iProver_def,null_class) = sP4_iProver_def,
    definition ).

cnf(c_3178,negated_conjecture,
    null_class != x,
    inference(demodulation,[status(thm)],[c_100]) ).

cnf(c_3179,negated_conjecture,
    sP1_iProver_def != x,
    inference(demodulation,[status(thm)],[c_99,c_3173,c_3174]) ).

cnf(c_3180,negated_conjecture,
    ~ member(sP4_iProver_def,sP3_iProver_def),
    inference(demodulation,[status(thm)],[c_98,c_3175,c_3176,c_3177]) ).

cnf(c_5585,plain,
    ( ~ member(sP0_iProver_def,universal_class)
    | member(sP0_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_3174,c_79]) ).

cnf(c_5587,plain,
    ( ~ member(sP0_iProver_def,X0)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_3174,c_96]) ).

cnf(c_5592,plain,
    ( member(sP0_iProver_def,x)
    | subclass(x,null_class) ),
    inference(superposition,[status(thm)],[c_3173,c_102]) ).

cnf(c_5593,plain,
    ( member(sP4_iProver_def,sP3_iProver_def)
    | subclass(sP3_iProver_def,null_class) ),
    inference(superposition,[status(thm)],[c_3177,c_102]) ).

cnf(c_5600,plain,
    ( null_class = x
    | member(sP0_iProver_def,x) ),
    inference(superposition,[status(thm)],[c_5592,c_62]) ).

cnf(c_5602,plain,
    subclass(sP3_iProver_def,null_class),
    inference(global_subsumption_just,[status(thm)],[c_5593,c_3180,c_5593]) ).

cnf(c_5604,plain,
    null_class = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_5602,c_62]) ).

cnf(c_5606,plain,
    ( member(sP0_iProver_def,x)
    | subclass(x,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_5604,c_5592]) ).

cnf(c_5612,plain,
    ~ member(X0,sP3_iProver_def),
    inference(superposition,[status(thm)],[c_5604,c_60]) ).

cnf(c_5643,plain,
    member(sP0_iProver_def,x),
    inference(global_subsumption_just,[status(thm)],[c_5606,c_100,c_5600]) ).

cnf(c_5645,plain,
    subclass(sP1_iProver_def,x),
    inference(superposition,[status(thm)],[c_5643,c_5587]) ).

cnf(c_5681,plain,
    ( ~ member(X0,sP1_iProver_def)
    | X0 = sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_3174,c_82]) ).

cnf(c_5694,plain,
    ( regular(sP1_iProver_def) = sP0_iProver_def
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_166,c_5681]) ).

cnf(c_5705,plain,
    ( ~ member(sP0_iProver_def,universal_class)
    | member(member_of(sP1_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_3174,c_87]) ).

cnf(c_5709,plain,
    ( ~ member(sP0_iProver_def,null_class)
    | subclass(x,null_class) ),
    inference(superposition,[status(thm)],[c_3173,c_103]) ).

cnf(c_5734,plain,
    ( ~ member(X0,identity_relation)
    | member(X0,inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_175,c_121]) ).

cnf(c_5746,plain,
    ( ~ member(not_subclass_element(X0,inverse(subset_relation)),identity_relation)
    | subclass(X0,inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_5734,c_103]) ).

cnf(c_5784,plain,
    ( ~ member(X0,sP1_iProver_def)
    | ~ member(X0,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_3175,c_124]) ).

cnf(c_5819,plain,
    ( ~ member(not_subclass_element(sP1_iProver_def,null_class),sP2_iProver_def)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_63,c_5784]) ).

cnf(c_5820,plain,
    ( ~ member(regular(sP1_iProver_def),sP2_iProver_def)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_166,c_5784]) ).

cnf(c_5935,plain,
    ( ~ member(singleton(X0),universal_class)
    | ~ subclass(universal_class,X1)
    | member(singleton(X0),X1) ),
    inference(instantiation,[status(thm)],[c_101]) ).

cnf(c_5940,plain,
    ( ~ subclass(omega,X0)
    | ~ member(null_class,omega)
    | member(null_class,X0) ),
    inference(instantiation,[status(thm)],[c_101]) ).

cnf(c_5941,plain,
    ( null_class != sP1_iProver_def
    | ~ member(sP0_iProver_def,universal_class) ),
    inference(superposition,[status(thm)],[c_3174,c_80]) ).

cnf(c_5971,plain,
    ( ~ subclass(null_class,x)
    | ~ subclass(x,null_class)
    | null_class = x ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_5972,plain,
    ( ~ subclass(x,sP1_iProver_def)
    | ~ subclass(sP1_iProver_def,x)
    | sP1_iProver_def = x ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_6081,plain,
    member(sP0_iProver_def,x),
    inference(global_subsumption_just,[status(thm)],[c_5606,c_100,c_5600]) ).

cnf(c_6090,plain,
    subclass(singleton(X0),singleton(X0)),
    inference(superposition,[status(thm)],[c_112,c_67]) ).

cnf(c_6144,plain,
    subclass(intersection(complement(X0),X0),X1),
    inference(superposition,[status(thm)],[c_102,c_59]) ).

cnf(c_6151,plain,
    intersection(complement(X0),X0) = null_class,
    inference(superposition,[status(thm)],[c_6144,c_62]) ).

cnf(c_6403,plain,
    ( ~ subclass(X0,sP1_iProver_def)
    | ~ subclass(x,X0)
    | subclass(x,sP1_iProver_def) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_6406,plain,
    ( ~ subclass(universal_class,sP1_iProver_def)
    | ~ subclass(x,universal_class)
    | subclass(x,sP1_iProver_def) ),
    inference(instantiation,[status(thm)],[c_6403]) ).

cnf(c_6489,plain,
    ( ~ subclass(X0,X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_61,c_54]) ).

cnf(c_6689,plain,
    ( ~ function(X0)
    | subclass(null_class,identity_relation) ),
    inference(superposition,[status(thm)],[c_163,c_6489]) ).

cnf(c_6695,plain,
    subclass(null_class,singleton(X0)),
    inference(superposition,[status(thm)],[c_6090,c_6489]) ).

cnf(c_6706,plain,
    subclass(null_class,x),
    inference(superposition,[status(thm)],[c_5645,c_6489]) ).

cnf(c_6805,plain,
    ( ~ member(X0,X1)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_104,c_101]) ).

cnf(c_6829,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,x) ),
    inference(superposition,[status(thm)],[c_5645,c_101]) ).

cnf(c_6983,plain,
    ( ~ subclass(singleton(X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_6695,c_54]) ).

cnf(c_6991,plain,
    member(sP1_iProver_def,universal_class),
    inference(superposition,[status(thm)],[c_3174,c_77]) ).

cnf(c_7009,plain,
    subclass(sP1_iProver_def,unordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_3174,c_66]) ).

cnf(c_7010,plain,
    subclass(sP1_iProver_def,unordered_pair(X0,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_3174,c_67]) ).

cnf(c_7011,plain,
    ~ member(X0,intersection(sP2_iProver_def,sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_3175,c_59]) ).

cnf(c_7046,plain,
    union(complement(X0),X0) = complement(null_class),
    inference(superposition,[status(thm)],[c_6151,c_126]) ).

cnf(c_7086,plain,
    member(sP1_iProver_def,unordered_pair(X0,sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_3174,c_78]) ).

cnf(c_7090,plain,
    subclass(singleton(X0),singleton(X0)),
    inference(superposition,[status(thm)],[c_112,c_67]) ).

cnf(c_7091,plain,
    member(singleton(X0),singleton(singleton(X0))),
    inference(superposition,[status(thm)],[c_112,c_78]) ).

cnf(c_7092,plain,
    subclass(sP1_iProver_def,singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_112,c_7009]) ).

cnf(c_7094,plain,
    member(sP1_iProver_def,singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_112,c_7086]) ).

cnf(c_7095,plain,
    subclass(sP1_iProver_def,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_3174,c_7092]) ).

cnf(c_7112,plain,
    member(singleton(X0),unordered_pair(singleton(X0),X1)),
    inference(superposition,[status(thm)],[c_65,c_78]) ).

cnf(c_7115,plain,
    member(sP1_iProver_def,unordered_pair(sP1_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_65,c_7086]) ).

cnf(c_7135,plain,
    ( ~ member(sP0_iProver_def,universal_class)
    | member(sP0_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_3174,c_79]) ).

cnf(c_7147,plain,
    ( singleton(sP0_iProver_def) = null_class
    | member(sP0_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_83,c_7135]) ).

cnf(c_7161,plain,
    ( ~ member(sP0_iProver_def,X0)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_3174,c_96]) ).

cnf(c_7163,plain,
    ( singleton(sP0_iProver_def) = null_class
    | subclass(sP1_iProver_def,universal_class) ),
    inference(superposition,[status(thm)],[c_83,c_7161]) ).

cnf(c_7165,plain,
    ( member(sP0_iProver_def,x)
    | subclass(x,null_class) ),
    inference(superposition,[status(thm)],[c_3173,c_102]) ).

cnf(c_7166,plain,
    ( member(sP4_iProver_def,sP3_iProver_def)
    | subclass(sP3_iProver_def,null_class) ),
    inference(superposition,[status(thm)],[c_3177,c_102]) ).

cnf(c_7167,plain,
    subclass(intersection(complement(X0),X0),X1),
    inference(superposition,[status(thm)],[c_102,c_59]) ).

cnf(c_7169,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),X0),
    inference(superposition,[status(thm)],[c_102,c_7011]) ).

cnf(c_7180,plain,
    subclass(identity_relation,inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_102,c_5746]) ).

cnf(c_7277,plain,
    intersection(sP2_iProver_def,sP1_iProver_def) = null_class,
    inference(superposition,[status(thm)],[c_7169,c_62]) ).

cnf(c_7296,plain,
    member(sP0_iProver_def,x),
    inference(global_subsumption_just,[status(thm)],[c_7165,c_100,c_5600]) ).

cnf(c_7298,plain,
    subclass(sP1_iProver_def,x),
    inference(superposition,[status(thm)],[c_7296,c_7161]) ).

cnf(c_7299,plain,
    union(sP0_iProver_def,sP1_iProver_def) = successor(sP0_iProver_def),
    inference(superposition,[status(thm)],[c_3174,c_143]) ).

cnf(c_7300,plain,
    subclass(sP3_iProver_def,null_class),
    inference(global_subsumption_just,[status(thm)],[c_7166,c_3180,c_5593]) ).

cnf(c_7302,plain,
    null_class = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_7300,c_62]) ).

cnf(c_7303,plain,
    subclass(sP3_iProver_def,sP3_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_7300]) ).

cnf(c_7304,plain,
    ( ~ subclass(X0,sP3_iProver_def)
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_7302,c_62]) ).

cnf(c_7305,plain,
    not_subclass_element(sP3_iProver_def,sP3_iProver_def) = sP4_iProver_def,
    inference(superposition,[status(thm)],[c_7302,c_3177]) ).

cnf(c_7306,plain,
    not_subclass_element(x,sP3_iProver_def) = sP0_iProver_def,
    inference(superposition,[status(thm)],[c_7302,c_3173]) ).

cnf(c_7307,plain,
    member(sP3_iProver_def,omega),
    inference(superposition,[status(thm)],[c_7302,c_1384]) ).

cnf(c_7308,plain,
    member(sP3_iProver_def,singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_81]) ).

cnf(c_7309,plain,
    ~ member(X0,sP3_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_60]) ).

cnf(c_7310,plain,
    member(sP3_iProver_def,universal_class),
    inference(superposition,[status(thm)],[c_7302,c_64]) ).

cnf(c_7311,plain,
    subclass(sP3_iProver_def,X0),
    inference(superposition,[status(thm)],[c_7302,c_61]) ).

cnf(c_7316,plain,
    subclass(null_class,inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_7180,c_6489]) ).

cnf(c_7611,plain,
    intersection(complement(X0),X0) = null_class,
    inference(superposition,[status(thm)],[c_7167,c_62]) ).

cnf(c_7628,plain,
    ( X0 = null_class
    | member(not_subclass_element(X0,sP3_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_7302,c_63]) ).

cnf(c_7669,plain,
    ( not_subclass_element(singleton(X0),X1) = X0
    | subclass(singleton(X0),X1) ),
    inference(superposition,[status(thm)],[c_102,c_82]) ).

cnf(c_7670,plain,
    ( not_subclass_element(singleton(X0),null_class) = X0
    | singleton(X0) = null_class ),
    inference(superposition,[status(thm)],[c_63,c_82]) ).

cnf(c_7673,plain,
    ( regular(singleton(X0)) = X0
    | singleton(X0) = null_class ),
    inference(superposition,[status(thm)],[c_166,c_82]) ).

cnf(c_7677,plain,
    ( ~ member(X0,sP1_iProver_def)
    | X0 = sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_3174,c_82]) ).

cnf(c_7758,plain,
    ( not_subclass_element(sP1_iProver_def,X0) = sP0_iProver_def
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_102,c_7677]) ).

cnf(c_7759,plain,
    ( not_subclass_element(sP1_iProver_def,null_class) = sP0_iProver_def
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_63,c_7677]) ).

cnf(c_7760,plain,
    ( regular(sP1_iProver_def) = sP0_iProver_def
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_166,c_7677]) ).

cnf(c_7762,plain,
    subclass(null_class,identity_relation),
    inference(superposition,[status(thm)],[c_169,c_6689]) ).

cnf(c_7866,plain,
    ( ~ member(sP0_iProver_def,universal_class)
    | member(member_of(sP1_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_3174,c_87]) ).

cnf(c_7978,plain,
    ( ~ member(sP0_iProver_def,null_class)
    | subclass(x,null_class) ),
    inference(superposition,[status(thm)],[c_3173,c_103]) ).

cnf(c_7981,plain,
    ( ~ member(sP0_iProver_def,sP3_iProver_def)
    | subclass(x,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_7306,c_103]) ).

cnf(c_7990,plain,
    ~ member(sP0_iProver_def,null_class),
    inference(global_subsumption_just,[status(thm)],[c_7978,c_100,c_5709,c_5971,c_6706]) ).

cnf(c_7992,plain,
    ~ member(sP0_iProver_def,sP3_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_7990]) ).

cnf(c_7993,plain,
    ( member(not_subclass_element(intersection(X0,X1),X2),X0)
    | subclass(intersection(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_102,c_121]) ).

cnf(c_7994,plain,
    ( intersection(X0,X1) = null_class
    | member(not_subclass_element(intersection(X0,X1),null_class),X0) ),
    inference(superposition,[status(thm)],[c_63,c_121]) ).

cnf(c_7995,plain,
    ( intersection(X0,X1) = null_class
    | member(regular(intersection(X0,X1)),X0) ),
    inference(superposition,[status(thm)],[c_166,c_121]) ).

cnf(c_7997,plain,
    ( ~ member(X0,identity_relation)
    | member(X0,inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_175,c_121]) ).

cnf(c_8014,plain,
    subclass(singleton(X0),singleton(X0)),
    inference(superposition,[status(thm)],[c_112,c_67]) ).

cnf(c_8116,plain,
    member(sP0_iProver_def,universal_class),
    inference(superposition,[status(thm)],[c_6081,c_6805]) ).

cnf(c_8198,plain,
    ( null_class = sP1_iProver_def
    | member(regular(sP1_iProver_def),x) ),
    inference(superposition,[status(thm)],[c_166,c_6829]) ).

cnf(c_8215,plain,
    subclass(null_class,singleton(X0)),
    inference(superposition,[status(thm)],[c_8014,c_6983]) ).

cnf(c_8227,plain,
    subclass(null_class,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_3174,c_8215]) ).

cnf(c_8262,plain,
    ( null_class = sP1_iProver_def
    | member(not_subclass_element(sP1_iProver_def,null_class),x) ),
    inference(superposition,[status(thm)],[c_63,c_6829]) ).

cnf(c_8324,plain,
    ( ~ member(not_subclass_element(X0,inverse(subset_relation)),identity_relation)
    | subclass(X0,inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_7997,c_103]) ).

cnf(c_8325,plain,
    ( ~ member(sP0_iProver_def,identity_relation)
    | subclass(sP1_iProver_def,inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_7997,c_7161]) ).

cnf(c_8372,plain,
    ( member(not_subclass_element(intersection(X0,X1),X2),X1)
    | subclass(intersection(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_102,c_122]) ).

cnf(c_8373,plain,
    ( intersection(X0,X1) = null_class
    | member(not_subclass_element(intersection(X0,X1),null_class),X1) ),
    inference(superposition,[status(thm)],[c_63,c_122]) ).

cnf(c_8374,plain,
    ( intersection(X0,X1) = null_class
    | member(regular(intersection(X0,X1)),X1) ),
    inference(superposition,[status(thm)],[c_166,c_122]) ).

cnf(c_8376,plain,
    ( ~ member(X0,identity_relation)
    | member(X0,subset_relation) ),
    inference(superposition,[status(thm)],[c_175,c_122]) ).

cnf(c_8437,plain,
    ( member(not_subclass_element(identity_relation,X0),subset_relation)
    | subclass(identity_relation,X0) ),
    inference(superposition,[status(thm)],[c_102,c_8376]) ).

cnf(c_8438,plain,
    ( null_class = identity_relation
    | member(not_subclass_element(identity_relation,null_class),subset_relation) ),
    inference(superposition,[status(thm)],[c_63,c_8376]) ).

cnf(c_8439,plain,
    ( null_class = identity_relation
    | member(regular(identity_relation),subset_relation) ),
    inference(superposition,[status(thm)],[c_166,c_8376]) ).

cnf(c_8440,plain,
    subclass(identity_relation,subset_relation),
    inference(superposition,[status(thm)],[c_8437,c_103]) ).

cnf(c_8503,plain,
    ( ~ member(not_subclass_element(complement(X0),X1),X0)
    | subclass(complement(X0),X1) ),
    inference(superposition,[status(thm)],[c_102,c_124]) ).

cnf(c_8504,plain,
    ( ~ member(not_subclass_element(complement(X0),null_class),X0)
    | complement(X0) = null_class ),
    inference(superposition,[status(thm)],[c_63,c_124]) ).

cnf(c_8505,plain,
    ( ~ member(regular(complement(X0)),X0)
    | complement(X0) = null_class ),
    inference(superposition,[status(thm)],[c_166,c_124]) ).

cnf(c_8506,plain,
    ( ~ member(X0,sP1_iProver_def)
    | ~ member(X0,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_3175,c_124]) ).

cnf(c_8578,plain,
    complement(image(element_relation,sP2_iProver_def)) = power_class(sP1_iProver_def),
    inference(superposition,[status(thm)],[c_3175,c_155]) ).

cnf(c_8579,plain,
    complement(image(element_relation,power_class(X0))) = power_class(image(element_relation,complement(X0))),
    inference(superposition,[status(thm)],[c_155,c_155]) ).

cnf(c_8580,plain,
    intersection(power_class(X0),image(element_relation,complement(X0))) = null_class,
    inference(superposition,[status(thm)],[c_155,c_7611]) ).

cnf(c_8581,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),X1),
    inference(superposition,[status(thm)],[c_155,c_7167]) ).

cnf(c_8582,plain,
    ( ~ member(X0,image(element_relation,complement(X1)))
    | ~ member(X0,power_class(X1)) ),
    inference(superposition,[status(thm)],[c_155,c_124]) ).

cnf(c_8583,plain,
    ~ member(X0,intersection(power_class(X1),image(element_relation,complement(X1)))),
    inference(superposition,[status(thm)],[c_155,c_59]) ).

cnf(c_8729,plain,
    ( ~ member(not_subclass_element(sP1_iProver_def,X0),sP2_iProver_def)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_102,c_8506]) ).

cnf(c_8730,plain,
    ( ~ member(not_subclass_element(sP1_iProver_def,null_class),sP2_iProver_def)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_63,c_8506]) ).

cnf(c_8731,plain,
    ( ~ member(regular(sP1_iProver_def),sP2_iProver_def)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_166,c_8506]) ).

cnf(c_8732,plain,
    ( ~ member(sP0_iProver_def,sP2_iProver_def)
    | singleton(sP0_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_7147,c_8506]) ).

cnf(c_8802,plain,
    complement(image(element_relation,power_class(sP1_iProver_def))) = power_class(image(element_relation,sP2_iProver_def)),
    inference(superposition,[status(thm)],[c_8578,c_155]) ).

cnf(c_8803,plain,
    intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)) = null_class,
    inference(superposition,[status(thm)],[c_8578,c_7611]) ).

cnf(c_8804,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),X0),
    inference(superposition,[status(thm)],[c_8578,c_7167]) ).

cnf(c_8805,plain,
    ( ~ member(X0,image(element_relation,sP2_iProver_def))
    | ~ member(X0,power_class(sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_8578,c_124]) ).

cnf(c_8806,plain,
    ~ member(X0,intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def))),
    inference(superposition,[status(thm)],[c_8578,c_59]) ).

cnf(c_8912,plain,
    complement(domain_of(null_class)) = diagonalise(complement(identity_relation)),
    inference(superposition,[status(thm)],[c_7611,c_176]) ).

cnf(c_8913,plain,
    complement(image(element_relation,diagonalise(X0))) = power_class(domain_of(intersection(X0,identity_relation))),
    inference(superposition,[status(thm)],[c_176,c_155]) ).

cnf(c_8914,plain,
    intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))) = null_class,
    inference(superposition,[status(thm)],[c_176,c_7611]) ).

cnf(c_8915,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),X1),
    inference(superposition,[status(thm)],[c_176,c_7167]) ).

cnf(c_8916,plain,
    ( ~ member(X0,domain_of(intersection(X1,identity_relation)))
    | ~ member(X0,diagonalise(X1)) ),
    inference(superposition,[status(thm)],[c_176,c_124]) ).

cnf(c_8917,plain,
    ~ member(X0,intersection(diagonalise(X1),domain_of(intersection(X1,identity_relation)))),
    inference(superposition,[status(thm)],[c_176,c_59]) ).

cnf(c_9184,plain,
    ( ~ operation(flip(cross_product(X0,universal_class)))
    | subclass(range_of(flip(cross_product(X0,universal_class))),domain_of(inverse(X0))) ),
    inference(superposition,[status(thm)],[c_138,c_180]) ).

cnf(c_9185,plain,
    ( ~ operation(inverse(X0))
    | subclass(range_of(inverse(X0)),domain_of(range_of(X0))) ),
    inference(superposition,[status(thm)],[c_139,c_180]) ).

cnf(c_9186,plain,
    ( ~ operation(restrict(element_relation,universal_class,X0))
    | subclass(range_of(restrict(element_relation,universal_class,X0)),domain_of(sum_class(X0))) ),
    inference(superposition,[status(thm)],[c_153,c_180]) ).

cnf(c_9231,plain,
    ( not_subclass_element(singleton(X0),sP3_iProver_def) = X0
    | singleton(X0) = null_class ),
    inference(superposition,[status(thm)],[c_7628,c_82]) ).

cnf(c_9232,plain,
    ( intersection(X0,X1) = null_class
    | member(not_subclass_element(intersection(X0,X1),sP3_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_7628,c_122]) ).

cnf(c_9233,plain,
    ( intersection(X0,X1) = null_class
    | member(not_subclass_element(intersection(X0,X1),sP3_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_7628,c_121]) ).

cnf(c_9234,plain,
    ( ~ member(not_subclass_element(complement(X0),sP3_iProver_def),X0)
    | complement(X0) = null_class ),
    inference(superposition,[status(thm)],[c_7628,c_124]) ).

cnf(c_9237,plain,
    ( ~ member(not_subclass_element(sP1_iProver_def,sP3_iProver_def),sP2_iProver_def)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_7628,c_8506]) ).

cnf(c_9238,plain,
    ( not_subclass_element(sP1_iProver_def,sP3_iProver_def) = sP0_iProver_def
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_7628,c_7677]) ).

cnf(c_9239,plain,
    ( null_class = identity_relation
    | member(not_subclass_element(identity_relation,sP3_iProver_def),subset_relation) ),
    inference(superposition,[status(thm)],[c_7628,c_8376]) ).

cnf(c_9397,plain,
    ~ member(null_class,null_class),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_9419,plain,
    regular(sP1_iProver_def) = sP0_iProver_def,
    inference(global_subsumption_just,[status(thm)],[c_7760,c_5694,c_5941,c_8116]) ).

cnf(c_9421,plain,
    ( null_class = sP1_iProver_def
    | member(sP0_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_9419,c_166]) ).

cnf(c_9422,plain,
    member(sP0_iProver_def,sP1_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_9421,c_5585,c_8116]) ).

cnf(c_9425,plain,
    ~ member(sP0_iProver_def,sP2_iProver_def),
    inference(superposition,[status(thm)],[c_9422,c_8506]) ).

cnf(c_9458,plain,
    ( unordered_pair(X0,not_subclass_element(X1,universal_class)) = singleton(X0)
    | subclass(X1,universal_class) ),
    inference(superposition,[status(thm)],[c_68,c_103]) ).

cnf(c_9460,plain,
    ( unordered_pair(X0,sP0_iProver_def) = singleton(X0)
    | subclass(sP1_iProver_def,universal_class) ),
    inference(superposition,[status(thm)],[c_68,c_7161]) ).

cnf(c_9481,plain,
    ( unordered_pair(sP0_iProver_def,X0) = singleton(X0)
    | subclass(sP1_iProver_def,universal_class) ),
    inference(superposition,[status(thm)],[c_69,c_7161]) ).

cnf(c_9482,plain,
    ( null_class != sP1_iProver_def
    | ~ member(sP0_iProver_def,universal_class) ),
    inference(superposition,[status(thm)],[c_3174,c_80]) ).

cnf(c_9483,plain,
    ( unordered_pair(X0,X1) = singleton(X1)
    | member_of(singleton(X0)) = X0 ),
    inference(superposition,[status(thm)],[c_69,c_91]) ).

cnf(c_9484,plain,
    ( member_of(singleton(X0)) = X0
    | singleton(X0) = null_class ),
    inference(superposition,[status(thm)],[c_83,c_91]) ).

cnf(c_9485,plain,
    ( unordered_pair(X0,X1) = singleton(X0)
    | member_of(singleton(X1)) = X1 ),
    inference(superposition,[status(thm)],[c_68,c_91]) ).

cnf(c_9486,plain,
    ( member_of(singleton(not_subclass_element(universal_class,X0))) = not_subclass_element(universal_class,X0)
    | subclass(universal_class,X0) ),
    inference(superposition,[status(thm)],[c_102,c_91]) ).

cnf(c_9487,plain,
    ( member_of(singleton(not_subclass_element(universal_class,null_class))) = not_subclass_element(universal_class,null_class)
    | universal_class = null_class ),
    inference(superposition,[status(thm)],[c_63,c_91]) ).

cnf(c_9488,plain,
    member_of(singleton(null_class)) = null_class,
    inference(superposition,[status(thm)],[c_64,c_91]) ).

cnf(c_9489,plain,
    member_of(singleton(singleton(X0))) = singleton(X0),
    inference(superposition,[status(thm)],[c_77,c_91]) ).

cnf(c_9490,plain,
    ( ~ member(X0,universal_class)
    | member_of(singleton(member_of(singleton(X0)))) = member_of(singleton(X0)) ),
    inference(superposition,[status(thm)],[c_87,c_91]) ).

cnf(c_9491,plain,
    ( member_of(singleton(member_of(X0))) = member_of(X0)
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_89,c_91]) ).

cnf(c_9492,plain,
    ( member_of(singleton(member_of1(X0))) = member_of1(X0)
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_92,c_91]) ).

cnf(c_9493,plain,
    member_of(singleton(unordered_pair(X0,X1))) = unordered_pair(X0,X1),
    inference(superposition,[status(thm)],[c_111,c_91]) ).

cnf(c_9494,plain,
    member_of(singleton(omega)) = omega,
    inference(superposition,[status(thm)],[c_152,c_91]) ).

cnf(c_9495,plain,
    ( ~ member(X0,universal_class)
    | member_of(singleton(sum_class(X0))) = sum_class(X0) ),
    inference(superposition,[status(thm)],[c_154,c_91]) ).

cnf(c_9496,plain,
    ( ~ member(X0,universal_class)
    | member_of(singleton(power_class(X0))) = power_class(X0) ),
    inference(superposition,[status(thm)],[c_156,c_91]) ).

cnf(c_9497,plain,
    ( member_of(singleton(regular(universal_class))) = regular(universal_class)
    | universal_class = null_class ),
    inference(superposition,[status(thm)],[c_166,c_91]) ).

cnf(c_9498,plain,
    member_of(singleton(sP1_iProver_def)) = sP1_iProver_def,
    inference(superposition,[status(thm)],[c_6991,c_91]) ).

cnf(c_9499,plain,
    member_of(singleton(sP3_iProver_def)) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_7310,c_91]) ).

cnf(c_9500,plain,
    ( member_of(singleton(not_subclass_element(universal_class,sP3_iProver_def))) = not_subclass_element(universal_class,sP3_iProver_def)
    | universal_class = null_class ),
    inference(superposition,[status(thm)],[c_7628,c_91]) ).

cnf(c_9501,plain,
    ( ~ member(sP0_iProver_def,universal_class)
    | member_of(singleton(member_of(sP1_iProver_def))) = member_of(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_7866,c_91]) ).

cnf(c_10152,plain,
    subclass(intersection(power_class(image(element_relation,complement(X0))),image(element_relation,power_class(X0))),X1),
    inference(superposition,[status(thm)],[c_155,c_8581]) ).

cnf(c_10153,plain,
    subclass(intersection(power_class(domain_of(intersection(X0,identity_relation))),image(element_relation,diagonalise(X0))),X1),
    inference(superposition,[status(thm)],[c_176,c_8581]) ).

cnf(c_10155,plain,
    subclass(intersection(power_class(image(element_relation,sP2_iProver_def)),image(element_relation,power_class(sP1_iProver_def))),X0),
    inference(superposition,[status(thm)],[c_8578,c_8581]) ).

cnf(c_10305,plain,
    ~ member(regular(sP1_iProver_def),sP2_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_8731,c_5820,c_5941,c_8116]) ).

cnf(c_10316,plain,
    member(singleton(null_class),universal_class),
    inference(superposition,[status(thm)],[c_9488,c_94]) ).

cnf(c_10317,plain,
    member(singleton(singleton(X0)),universal_class),
    inference(superposition,[status(thm)],[c_9489,c_94]) ).

cnf(c_10318,plain,
    member(singleton(omega),universal_class),
    inference(superposition,[status(thm)],[c_9494,c_94]) ).

cnf(c_10319,plain,
    member(singleton(sP1_iProver_def),universal_class),
    inference(superposition,[status(thm)],[c_9498,c_94]) ).

cnf(c_10320,plain,
    member(singleton(sP3_iProver_def),universal_class),
    inference(superposition,[status(thm)],[c_9499,c_94]) ).

cnf(c_10368,plain,
    ( ~ member(singleton(X0),universal_class)
    | ~ subclass(universal_class,null_class)
    | member(singleton(X0),null_class) ),
    inference(instantiation,[status(thm)],[c_5935]) ).

cnf(c_10369,plain,
    ~ member(singleton(X0),null_class),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_10480,plain,
    ( ~ operation(restrict(X0,X1,universal_class))
    | subclass(image(X0,X1),domain_of(domain_of(restrict(X0,X1,universal_class)))) ),
    inference(superposition,[status(thm)],[c_142,c_180]) ).

cnf(c_10565,plain,
    sum_class(image(X0,sP1_iProver_def)) = apply(X0,sP0_iProver_def),
    inference(superposition,[status(thm)],[c_3174,c_168]) ).

cnf(c_10566,plain,
    ( ~ member(image(X0,singleton(X1)),universal_class)
    | member(apply(X0,X1),universal_class) ),
    inference(superposition,[status(thm)],[c_168,c_154]) ).

cnf(c_10617,plain,
    ( ~ subclass(sP1_iProver_def,null_class)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_8227,c_107]) ).

cnf(c_10845,plain,
    member_of(singleton(singleton(null_class))) = singleton(null_class),
    inference(superposition,[status(thm)],[c_10316,c_91]) ).

cnf(c_10846,plain,
    member_of(singleton(singleton(omega))) = singleton(omega),
    inference(superposition,[status(thm)],[c_10318,c_91]) ).

cnf(c_10847,plain,
    member_of(singleton(singleton(sP1_iProver_def))) = singleton(sP1_iProver_def),
    inference(superposition,[status(thm)],[c_10319,c_91]) ).

cnf(c_10848,plain,
    member_of(singleton(singleton(sP3_iProver_def))) = singleton(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_10320,c_91]) ).

cnf(c_10850,plain,
    member_of(singleton(singleton(singleton(X0)))) = singleton(singleton(X0)),
    inference(superposition,[status(thm)],[c_10317,c_91]) ).

cnf(c_10858,plain,
    member(singleton(singleton(null_class)),universal_class),
    inference(superposition,[status(thm)],[c_10845,c_94]) ).

cnf(c_10865,plain,
    member(singleton(singleton(sP3_iProver_def)),universal_class),
    inference(superposition,[status(thm)],[c_7302,c_10858]) ).

cnf(c_10866,plain,
    member_of(singleton(singleton(singleton(null_class)))) = singleton(singleton(null_class)),
    inference(superposition,[status(thm)],[c_10858,c_91]) ).

cnf(c_10943,plain,
    member_of(singleton(singleton(singleton(sP3_iProver_def)))) = singleton(singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_10865,c_91]) ).

cnf(c_10945,plain,
    member(singleton(singleton(omega)),universal_class),
    inference(superposition,[status(thm)],[c_10846,c_94]) ).

cnf(c_10947,plain,
    member_of(singleton(singleton(singleton(omega)))) = singleton(singleton(omega)),
    inference(superposition,[status(thm)],[c_10945,c_91]) ).

cnf(c_10949,plain,
    member(singleton(singleton(sP1_iProver_def)),universal_class),
    inference(superposition,[status(thm)],[c_10847,c_94]) ).

cnf(c_10951,plain,
    member_of(singleton(singleton(singleton(sP1_iProver_def)))) = singleton(singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_10949,c_91]) ).

cnf(c_10981,plain,
    ( ~ subclass(X0,X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_61,c_54]) ).

cnf(c_10982,plain,
    ( ~ subclass(unordered_pair(X0,X1),X2)
    | subclass(singleton(X0),X2) ),
    inference(superposition,[status(thm)],[c_66,c_54]) ).

cnf(c_10983,plain,
    ( ~ subclass(unordered_pair(X0,X1),X2)
    | subclass(singleton(X1),X2) ),
    inference(superposition,[status(thm)],[c_67,c_54]) ).

cnf(c_10984,plain,
    ( ~ member(X0,X1)
    | ~ subclass(X1,X2)
    | subclass(singleton(X0),X2) ),
    inference(superposition,[status(thm)],[c_96,c_54]) ).

cnf(c_10985,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(X1,X0) ),
    inference(superposition,[status(thm)],[c_104,c_54]) ).

cnf(c_10986,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | subclass(element_relation,X0) ),
    inference(superposition,[status(thm)],[c_118,c_54]) ).

cnf(c_10987,plain,
    ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
    | subclass(rotate(X1),X0) ),
    inference(superposition,[status(thm)],[c_132,c_54]) ).

cnf(c_10988,plain,
    ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
    | subclass(flip(X1),X0) ),
    inference(superposition,[status(thm)],[c_135,c_54]) ).

cnf(c_10989,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | subclass(successor_relation,X0) ),
    inference(superposition,[status(thm)],[c_144,c_54]) ).

cnf(c_10990,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | subclass(compose(X1,X2),X0) ),
    inference(superposition,[status(thm)],[c_157,c_54]) ).

cnf(c_10991,plain,
    ( ~ subclass(identity_relation,X0)
    | ~ function(X1)
    | subclass(compose(X1,inverse(X1)),X0) ),
    inference(superposition,[status(thm)],[c_163,c_54]) ).

cnf(c_10992,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | ~ function(X1)
    | subclass(X1,X0) ),
    inference(superposition,[status(thm)],[c_162,c_54]) ).

cnf(c_10993,plain,
    ( ~ subclass(domain_of(domain_of(X0)),X1)
    | ~ operation(X0)
    | subclass(range_of(X0),X1) ),
    inference(superposition,[status(thm)],[c_180,c_54]) ).

cnf(c_10994,plain,
    ( ~ subclass(omega,X0)
    | subclass(image(successor_relation,omega),X0) ),
    inference(superposition,[status(thm)],[c_1379,c_54]) ).

cnf(c_10995,plain,
    ( ~ subclass(unordered_pair(sP0_iProver_def,X0),X1)
    | subclass(sP1_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_7009,c_54]) ).

cnf(c_10996,plain,
    ( ~ subclass(unordered_pair(X0,sP0_iProver_def),X1)
    | subclass(sP1_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_7010,c_54]) ).

cnf(c_10998,plain,
    ( ~ subclass(singleton(sP0_iProver_def),X0)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_7092,c_54]) ).

cnf(c_11000,plain,
    ( ~ subclass(X0,X1)
    | not_subclass_element(sP1_iProver_def,X0) = sP0_iProver_def
    | subclass(sP1_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_7758,c_54]) ).

cnf(c_11001,plain,
    ( ~ subclass(universal_class,X0)
    | singleton(sP0_iProver_def) = null_class
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_7163,c_54]) ).

cnf(c_11003,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(complement(X2),X2),X1) ),
    inference(superposition,[status(thm)],[c_7167,c_54]) ).

cnf(c_11004,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_7169,c_54]) ).

cnf(c_11006,plain,
    ( ~ subclass(X0,X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_7311,c_54]) ).

cnf(c_11007,plain,
    ( ~ subclass(x,X0)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_7298,c_54]) ).

cnf(c_11008,plain,
    ( ~ subclass(inverse(subset_relation),X0)
    | ~ member(sP0_iProver_def,identity_relation)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_8325,c_54]) ).

cnf(c_11009,plain,
    ( ~ subclass(subset_relation,X0)
    | subclass(identity_relation,X0) ),
    inference(superposition,[status(thm)],[c_8440,c_54]) ).

cnf(c_11010,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(power_class(X2),image(element_relation,complement(X2))),X1) ),
    inference(superposition,[status(thm)],[c_8581,c_54]) ).

cnf(c_11011,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_8804,c_54]) ).

cnf(c_11573,plain,
    subclass(null_class,unordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_66,c_10981]) ).

cnf(c_11575,plain,
    ( ~ member(X0,X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_96,c_10981]) ).

cnf(c_11576,plain,
    subclass(null_class,universal_class),
    inference(superposition,[status(thm)],[c_104,c_10981]) ).

cnf(c_11578,plain,
    subclass(null_class,cross_product(cross_product(universal_class,universal_class),universal_class)),
    inference(superposition,[status(thm)],[c_132,c_10981]) ).

cnf(c_11580,plain,
    subclass(null_class,cross_product(universal_class,universal_class)),
    inference(superposition,[status(thm)],[c_144,c_10981]) ).

cnf(c_11582,plain,
    ( ~ function(X0)
    | subclass(null_class,identity_relation) ),
    inference(superposition,[status(thm)],[c_163,c_10981]) ).

cnf(c_11584,plain,
    ( ~ operation(X0)
    | subclass(null_class,domain_of(domain_of(X0))) ),
    inference(superposition,[status(thm)],[c_180,c_10981]) ).

cnf(c_11585,plain,
    subclass(null_class,omega),
    inference(superposition,[status(thm)],[c_1379,c_10981]) ).

cnf(c_11586,plain,
    subclass(null_class,unordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_7009,c_10981]) ).

cnf(c_11587,plain,
    subclass(null_class,unordered_pair(X0,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_7010,c_10981]) ).

cnf(c_11588,plain,
    subclass(null_class,singleton(X0)),
    inference(superposition,[status(thm)],[c_7090,c_10981]) ).

cnf(c_11589,plain,
    subclass(null_class,singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_7092,c_10981]) ).

cnf(c_11590,plain,
    subclass(null_class,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_7095,c_10981]) ).

cnf(c_11593,plain,
    subclass(null_class,null_class),
    inference(superposition,[status(thm)],[c_7300,c_10981]) ).

cnf(c_11596,plain,
    subclass(null_class,sP3_iProver_def),
    inference(superposition,[status(thm)],[c_7303,c_10981]) ).

cnf(c_11598,plain,
    subclass(null_class,x),
    inference(superposition,[status(thm)],[c_7298,c_10981]) ).

cnf(c_11599,plain,
    ( ~ member(sP0_iProver_def,identity_relation)
    | subclass(null_class,inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_8325,c_10981]) ).

cnf(c_11600,plain,
    subclass(null_class,subset_relation),
    inference(superposition,[status(thm)],[c_8440,c_10981]) ).

cnf(c_11869,plain,
    subclass(sP3_iProver_def,universal_class),
    inference(superposition,[status(thm)],[c_7302,c_11576]) ).

cnf(c_11890,plain,
    subclass(sP3_iProver_def,omega),
    inference(superposition,[status(thm)],[c_7302,c_11585]) ).

cnf(c_11901,plain,
    subclass(sP3_iProver_def,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_11590]) ).

cnf(c_12006,plain,
    subclass(sP3_iProver_def,x),
    inference(superposition,[status(thm)],[c_7302,c_11598]) ).

cnf(c_12009,plain,
    subclass(sP3_iProver_def,subset_relation),
    inference(superposition,[status(thm)],[c_7302,c_11600]) ).

cnf(c_12023,plain,
    ( member_of(singleton(X0)) = X0
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_90,c_9489]) ).

cnf(c_12024,plain,
    ( X0 != null_class
    | ~ member(member_of(X0),universal_class)
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_90,c_80]) ).

cnf(c_12026,plain,
    ( union(member_of(X0),X0) = successor(member_of(X0))
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_90,c_143]) ).

cnf(c_12027,plain,
    ( ~ member(member_of(X0),X1)
    | member_of(X0) = X0
    | subclass(X0,X1) ),
    inference(superposition,[status(thm)],[c_90,c_96]) ).

cnf(c_12028,plain,
    ( ~ member(member_of(X0),universal_class)
    | member_of(X0) = X0
    | member(member_of(X0),X0) ),
    inference(superposition,[status(thm)],[c_90,c_79]) ).

cnf(c_12029,plain,
    ( member_of(X0) = X0
    | member(X0,unordered_pair(X0,X1)) ),
    inference(superposition,[status(thm)],[c_90,c_7112]) ).

cnf(c_12030,plain,
    ( member_of(X0) = X0
    | member(X0,singleton(X0)) ),
    inference(superposition,[status(thm)],[c_90,c_7091]) ).

cnf(c_12032,plain,
    ( member_of(X0) = X0
    | member(X0,unordered_pair(X1,X0)) ),
    inference(superposition,[status(thm)],[c_90,c_78]) ).

cnf(c_12033,plain,
    ( member_of(X0) = X0
    | subclass(X0,unordered_pair(X1,member_of(X0))) ),
    inference(superposition,[status(thm)],[c_90,c_67]) ).

cnf(c_12034,plain,
    ( member_of(X0) = X0
    | subclass(X0,unordered_pair(member_of(X0),X1)) ),
    inference(superposition,[status(thm)],[c_90,c_66]) ).

cnf(c_12036,plain,
    ( sum_class(image(X0,X1)) = apply(X0,member_of(X1))
    | member_of(X1) = X1 ),
    inference(superposition,[status(thm)],[c_90,c_168]) ).

cnf(c_12037,plain,
    ( ~ member(X0,X1)
    | member_of(X1) = X0
    | member_of(X1) = X1 ),
    inference(superposition,[status(thm)],[c_90,c_82]) ).

cnf(c_12038,plain,
    ( member_of(X0) = X0
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_90,c_94]) ).

cnf(c_12503,plain,
    ( X0 != null_class
    | ~ member(member_of1(X0),universal_class)
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_93,c_80]) ).

cnf(c_12505,plain,
    ( union(member_of1(X0),X0) = successor(member_of1(X0))
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_93,c_143]) ).

cnf(c_12506,plain,
    ( ~ member(member_of1(X0),X1)
    | member_of(X0) = X0
    | subclass(X0,X1) ),
    inference(superposition,[status(thm)],[c_93,c_96]) ).

cnf(c_12507,plain,
    ( ~ member(member_of1(X0),universal_class)
    | member_of(X0) = X0
    | member(member_of1(X0),X0) ),
    inference(superposition,[status(thm)],[c_93,c_79]) ).

cnf(c_12512,plain,
    ( member_of(X0) = X0
    | subclass(X0,unordered_pair(X1,member_of1(X0))) ),
    inference(superposition,[status(thm)],[c_93,c_67]) ).

cnf(c_12513,plain,
    ( member_of(X0) = X0
    | subclass(X0,unordered_pair(member_of1(X0),X1)) ),
    inference(superposition,[status(thm)],[c_93,c_66]) ).

cnf(c_12515,plain,
    ( sum_class(image(X0,X1)) = apply(X0,member_of1(X1))
    | member_of(X1) = X1 ),
    inference(superposition,[status(thm)],[c_93,c_168]) ).

cnf(c_12516,plain,
    ( ~ member(X0,X1)
    | member_of(X1) = X1
    | member_of1(X1) = X0 ),
    inference(superposition,[status(thm)],[c_93,c_82]) ).

cnf(c_12559,plain,
    ( ~ member(X0,singleton(X1))
    | member(X0,unordered_pair(X1,X2)) ),
    inference(superposition,[status(thm)],[c_66,c_101]) ).

cnf(c_12560,plain,
    ( ~ member(X0,singleton(X1))
    | member(X0,unordered_pair(X2,X1)) ),
    inference(superposition,[status(thm)],[c_67,c_101]) ).

cnf(c_12561,plain,
    ( ~ member(X0,singleton(X1))
    | ~ member(X1,X2)
    | member(X0,X2) ),
    inference(superposition,[status(thm)],[c_96,c_101]) ).

cnf(c_12562,plain,
    ( ~ member(X0,X1)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_104,c_101]) ).

cnf(c_12563,plain,
    ( ~ member(X0,element_relation)
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_118,c_101]) ).

cnf(c_12564,plain,
    ( ~ member(X0,rotate(X1))
    | member(X0,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(superposition,[status(thm)],[c_132,c_101]) ).

cnf(c_12565,plain,
    ( ~ member(X0,flip(X1))
    | member(X0,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(superposition,[status(thm)],[c_135,c_101]) ).

cnf(c_12566,plain,
    ( ~ member(X0,successor_relation)
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_144,c_101]) ).

cnf(c_12567,plain,
    ( ~ member(X0,compose(X1,X2))
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_157,c_101]) ).

cnf(c_12568,plain,
    ( ~ member(X0,compose(X1,inverse(X1)))
    | ~ function(X1)
    | member(X0,identity_relation) ),
    inference(superposition,[status(thm)],[c_163,c_101]) ).

cnf(c_12569,plain,
    ( ~ member(X0,X1)
    | ~ function(X1)
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_101]) ).

cnf(c_12570,plain,
    ( ~ member(X0,range_of(X1))
    | ~ operation(X1)
    | member(X0,domain_of(domain_of(X1))) ),
    inference(superposition,[status(thm)],[c_180,c_101]) ).

cnf(c_12572,plain,
    ( ~ member(X0,image(successor_relation,omega))
    | member(X0,omega) ),
    inference(superposition,[status(thm)],[c_1379,c_101]) ).

cnf(c_12573,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,unordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_7009,c_101]) ).

cnf(c_12574,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,unordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_7010,c_101]) ).

cnf(c_12576,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,singleton(sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_7092,c_101]) ).

cnf(c_12578,plain,
    ( ~ member(X0,sP1_iProver_def)
    | not_subclass_element(sP1_iProver_def,X1) = sP0_iProver_def
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_7758,c_101]) ).

cnf(c_12579,plain,
    ( ~ member(X0,sP1_iProver_def)
    | singleton(sP0_iProver_def) = null_class
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_7163,c_101]) ).

cnf(c_12586,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,x) ),
    inference(superposition,[status(thm)],[c_7298,c_101]) ).

cnf(c_12588,plain,
    ( ~ member(X0,sP1_iProver_def)
    | ~ member(sP0_iProver_def,identity_relation)
    | member(X0,inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_8325,c_101]) ).

cnf(c_13014,plain,
    ( ~ member(sP0_iProver_def,universal_class)
    | member(sP0_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_3174,c_79]) ).

cnf(c_13020,plain,
    member(sP0_iProver_def,sP1_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_13014,c_5585,c_8116]) ).

cnf(c_13382,plain,
    member(sP0_iProver_def,universal_class),
    inference(superposition,[status(thm)],[c_13020,c_6805]) ).

cnf(c_14319,plain,
    singleton(member_of(singleton(sP0_iProver_def))) = singleton(sP0_iProver_def),
    inference(superposition,[status(thm)],[c_13382,c_88]) ).

cnf(c_14523,plain,
    singleton(member_of(sP1_iProver_def)) = sP1_iProver_def,
    inference(superposition,[status(thm)],[c_3174,c_14319]) ).

cnf(c_15164,plain,
    ( ~ member(member_of(sP1_iProver_def),universal_class)
    | member(member_of(sP1_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_14523,c_79]) ).

cnf(c_15337,plain,
    subclass(sP3_iProver_def,singleton(X0)),
    inference(superposition,[status(thm)],[c_7302,c_11588]) ).

cnf(c_15342,plain,
    ( ~ subclass(singleton(X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_11588,c_54]) ).

cnf(c_15344,plain,
    subclass(sP3_iProver_def,singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_11589]) ).

cnf(c_15360,plain,
    ( ~ subclass(singleton(X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_15337,c_54]) ).

cnf(c_15372,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_7302,c_11573]) ).

cnf(c_15377,plain,
    ( ~ subclass(unordered_pair(X0,X1),X2)
    | subclass(null_class,X2) ),
    inference(superposition,[status(thm)],[c_11573,c_54]) ).

cnf(c_15447,plain,
    subclass(sP3_iProver_def,cross_product(universal_class,universal_class)),
    inference(superposition,[status(thm)],[c_7302,c_11580]) ).

cnf(c_15451,plain,
    subclass(sP3_iProver_def,unordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_7302,c_11586]) ).

cnf(c_15456,plain,
    ( ~ subclass(unordered_pair(sP0_iProver_def,X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_11586,c_54]) ).

cnf(c_15551,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_11587]) ).

cnf(c_15556,plain,
    ( ~ subclass(unordered_pair(X0,sP0_iProver_def),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_11587,c_54]) ).

cnf(c_15583,plain,
    ( ~ subclass(unordered_pair(X0,X1),X2)
    | subclass(sP3_iProver_def,X2) ),
    inference(superposition,[status(thm)],[c_15372,c_54]) ).

cnf(c_15629,plain,
    ( ~ subclass(unordered_pair(sP0_iProver_def,X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_15451,c_54]) ).

cnf(c_15648,plain,
    ( ~ member(X0,universal_class)
    | member(X0,image(element_relation,complement(X1)))
    | member(X0,power_class(X1)) ),
    inference(superposition,[status(thm)],[c_155,c_125]) ).

cnf(c_15649,plain,
    ( ~ member(X0,universal_class)
    | member(X0,domain_of(intersection(X1,identity_relation)))
    | member(X0,diagonalise(X1)) ),
    inference(superposition,[status(thm)],[c_176,c_125]) ).

cnf(c_15650,plain,
    ( ~ member(X0,universal_class)
    | member(X0,sP1_iProver_def)
    | member(X0,sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_3175,c_125]) ).

cnf(c_15651,plain,
    ( ~ member(X0,universal_class)
    | member(X0,image(element_relation,sP2_iProver_def))
    | member(X0,power_class(sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_8578,c_125]) ).

cnf(c_15652,plain,
    ( ~ member(not_subclass_element(X0,complement(X1)),universal_class)
    | member(not_subclass_element(X0,complement(X1)),X1)
    | subclass(X0,complement(X1)) ),
    inference(superposition,[status(thm)],[c_125,c_103]) ).

cnf(c_15654,plain,
    ( ~ member(sP0_iProver_def,universal_class)
    | subclass(sP1_iProver_def,complement(X0))
    | member(sP0_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_125,c_7161]) ).

cnf(c_15800,plain,
    union(complement(X0),X0) = complement(null_class),
    inference(superposition,[status(thm)],[c_7611,c_126]) ).

cnf(c_15802,plain,
    complement(intersection(power_class(X0),complement(X1))) = union(image(element_relation,complement(X0)),X1),
    inference(superposition,[status(thm)],[c_155,c_126]) ).

cnf(c_15803,plain,
    complement(intersection(diagonalise(X0),complement(X1))) = union(domain_of(intersection(X0,identity_relation)),X1),
    inference(superposition,[status(thm)],[c_176,c_126]) ).

cnf(c_15804,plain,
    complement(intersection(sP2_iProver_def,complement(X0))) = union(sP1_iProver_def,X0),
    inference(superposition,[status(thm)],[c_3175,c_126]) ).

cnf(c_15805,plain,
    complement(intersection(power_class(sP1_iProver_def),complement(X0))) = union(image(element_relation,sP2_iProver_def),X0),
    inference(superposition,[status(thm)],[c_8578,c_126]) ).

cnf(c_15807,plain,
    complement(intersection(complement(X0),power_class(X1))) = union(X0,image(element_relation,complement(X1))),
    inference(superposition,[status(thm)],[c_155,c_126]) ).

cnf(c_15808,plain,
    complement(intersection(complement(X0),diagonalise(X1))) = union(X0,domain_of(intersection(X1,identity_relation))),
    inference(superposition,[status(thm)],[c_176,c_126]) ).

cnf(c_15809,plain,
    complement(intersection(complement(X0),sP2_iProver_def)) = union(X0,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_3175,c_126]) ).

cnf(c_15810,plain,
    complement(intersection(complement(X0),power_class(sP1_iProver_def))) = union(X0,image(element_relation,sP2_iProver_def)),
    inference(superposition,[status(thm)],[c_8578,c_126]) ).

cnf(c_15811,plain,
    complement(intersection(union(X0,X1),complement(X2))) = union(intersection(complement(X0),complement(X1)),X2),
    inference(superposition,[status(thm)],[c_126,c_126]) ).

cnf(c_15812,plain,
    subclass(intersection(power_class(intersection(complement(X0),complement(X1))),image(element_relation,union(X0,X1))),X2),
    inference(superposition,[status(thm)],[c_126,c_8581]) ).

cnf(c_15813,plain,
    complement(image(element_relation,union(X0,X1))) = power_class(intersection(complement(X0),complement(X1))),
    inference(superposition,[status(thm)],[c_126,c_155]) ).

cnf(c_15814,plain,
    intersection(union(X0,X1),intersection(complement(X0),complement(X1))) = null_class,
    inference(superposition,[status(thm)],[c_126,c_7611]) ).

cnf(c_15815,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),X2),
    inference(superposition,[status(thm)],[c_126,c_7167]) ).

cnf(c_15816,plain,
    complement(intersection(complement(X0),union(X1,X2))) = union(X0,intersection(complement(X1),complement(X2))),
    inference(superposition,[status(thm)],[c_126,c_126]) ).

cnf(c_15817,plain,
    ( ~ member(X0,universal_class)
    | member(X0,intersection(complement(X1),complement(X2)))
    | member(X0,union(X1,X2)) ),
    inference(superposition,[status(thm)],[c_126,c_125]) ).

cnf(c_15818,plain,
    ( ~ member(X0,intersection(complement(X1),complement(X2)))
    | ~ member(X0,union(X1,X2)) ),
    inference(superposition,[status(thm)],[c_126,c_124]) ).

cnf(c_15819,plain,
    ~ member(X0,intersection(union(X1,X2),intersection(complement(X1),complement(X2)))),
    inference(superposition,[status(thm)],[c_126,c_59]) ).

cnf(c_16178,plain,
    restrict(complement(cross_product(X0,X1)),X0,X1) = null_class,
    inference(superposition,[status(thm)],[c_7611,c_128]) ).

cnf(c_16180,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),X2),
    inference(superposition,[status(thm)],[c_128,c_7167]) ).

cnf(c_16181,plain,
    ~ member(X0,restrict(complement(cross_product(X1,X2)),X1,X2)),
    inference(superposition,[status(thm)],[c_128,c_59]) ).

cnf(c_16182,plain,
    ( ~ member(X0,restrict(X1,X2,X3))
    | member(X0,cross_product(X2,X3)) ),
    inference(superposition,[status(thm)],[c_128,c_122]) ).

cnf(c_16183,plain,
    ( ~ member(X0,restrict(X1,X2,X3))
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_128,c_121]) ).

cnf(c_16220,plain,
    ( ~ subclass(unordered_pair(X0,sP0_iProver_def),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_15551,c_54]) ).

cnf(c_16329,plain,
    subclass(null_class,identity_relation),
    inference(global_subsumption_just,[status(thm)],[c_11582,c_7762]) ).

cnf(c_16331,plain,
    subclass(sP3_iProver_def,identity_relation),
    inference(superposition,[status(thm)],[c_7302,c_16329]) ).

cnf(c_16377,plain,
    ( ~ function(universal_class)
    | subclass(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_10985]) ).

cnf(c_16382,plain,
    ( ~ member(X0,X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_96,c_11006]) ).

cnf(c_16385,plain,
    subclass(sP3_iProver_def,cross_product(cross_product(universal_class,universal_class),universal_class)),
    inference(superposition,[status(thm)],[c_132,c_11006]) ).

cnf(c_16391,plain,
    ( ~ operation(X0)
    | subclass(sP3_iProver_def,domain_of(domain_of(X0))) ),
    inference(superposition,[status(thm)],[c_180,c_11006]) ).

cnf(c_16409,plain,
    ( ~ member(sP0_iProver_def,identity_relation)
    | subclass(sP3_iProver_def,inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_8325,c_11006]) ).

cnf(c_16501,plain,
    subclass(sP1_iProver_def,universal_class),
    inference(superposition,[status(thm)],[c_104,c_11007]) ).

cnf(c_16502,plain,
    ( ~ function(x)
    | subclass(sP1_iProver_def,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_11007]) ).

cnf(c_16548,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_16501,c_54]) ).

cnf(c_16549,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_16501,c_101]) ).

cnf(c_16563,plain,
    subclass(identity_relation,universal_class),
    inference(superposition,[status(thm)],[c_104,c_11009]) ).

cnf(c_16564,plain,
    ( ~ function(subset_relation)
    | subclass(identity_relation,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_11009]) ).

cnf(c_16701,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(identity_relation,X0) ),
    inference(superposition,[status(thm)],[c_16563,c_54]) ).

cnf(c_16702,plain,
    ( ~ member(X0,identity_relation)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_16563,c_101]) ).

cnf(c_16711,plain,
    subclass(null_class,unordered_pair(X0,singleton(X1))),
    inference(superposition,[status(thm)],[c_78,c_11575]) ).

cnf(c_16713,plain,
    subclass(null_class,singleton(null_class)),
    inference(superposition,[status(thm)],[c_81,c_11575]) ).

cnf(c_16717,plain,
    ( ~ member(X0,universal_class)
    | subclass(null_class,unordered_pair(X1,X0)) ),
    inference(superposition,[status(thm)],[c_110,c_11575]) ).

cnf(c_16719,plain,
    ( ~ member(X0,universal_class)
    | subclass(null_class,complement(X1))
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_125,c_11575]) ).

cnf(c_16726,plain,
    subclass(null_class,unordered_pair(X0,sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_7086,c_11575]) ).

cnf(c_16727,plain,
    subclass(null_class,singleton(singleton(X0))),
    inference(superposition,[status(thm)],[c_7091,c_11575]) ).

cnf(c_16728,plain,
    subclass(null_class,singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_7094,c_11575]) ).

cnf(c_16729,plain,
    subclass(null_class,unordered_pair(singleton(X0),X1)),
    inference(superposition,[status(thm)],[c_7112,c_11575]) ).

cnf(c_16730,plain,
    subclass(null_class,unordered_pair(sP1_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_7115,c_11575]) ).

cnf(c_16735,plain,
    subclass(null_class,singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_7308,c_11575]) ).

cnf(c_16739,plain,
    ( ~ member(X0,identity_relation)
    | subclass(null_class,inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_7997,c_11575]) ).

cnf(c_16958,plain,
    subclass(sP3_iProver_def,singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_16713]) ).

cnf(c_16960,plain,
    subclass(sP3_iProver_def,singleton(null_class)),
    inference(superposition,[status(thm)],[c_16713,c_11006]) ).

cnf(c_17004,plain,
    subclass(sP3_iProver_def,singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_16728]) ).

cnf(c_17091,plain,
    restrict(cross_product(X0,X1),X2,X3) = restrict(cross_product(X2,X3),X0,X1),
    inference(superposition,[status(thm)],[c_129,c_128]) ).

cnf(c_17092,plain,
    complement(domain_of(restrict(identity_relation,X0,X1))) = diagonalise(cross_product(X0,X1)),
    inference(superposition,[status(thm)],[c_129,c_176]) ).

cnf(c_17217,plain,
    ( intersection(sP1_iProver_def,sP0_iProver_def) = null_class
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_9419,c_167]) ).

cnf(c_17220,plain,
    ( restrict(regular(cross_product(X0,X1)),X0,X1) = null_class
    | cross_product(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_167,c_129]) ).

cnf(c_17243,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_16726,c_11006]) ).

cnf(c_17245,plain,
    ( ~ subclass(unordered_pair(X0,sP1_iProver_def),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_16726,c_54]) ).

cnf(c_17251,plain,
    subclass(sP3_iProver_def,singleton(singleton(X0))),
    inference(superposition,[status(thm)],[c_16727,c_11006]) ).

cnf(c_17253,plain,
    ( ~ subclass(singleton(singleton(X0)),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_16727,c_54]) ).

cnf(c_17286,plain,
    subclass(sP3_iProver_def,unordered_pair(sP1_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_16730,c_11006]) ).

cnf(c_17288,plain,
    ( ~ subclass(unordered_pair(sP1_iProver_def,X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_16730,c_54]) ).

cnf(c_17309,plain,
    ( ~ subclass(unordered_pair(X0,sP1_iProver_def),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_17243,c_54]) ).

cnf(c_17316,plain,
    ( ~ subclass(singleton(singleton(X0)),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_17251,c_54]) ).

cnf(c_17336,plain,
    ( ~ subclass(unordered_pair(sP1_iProver_def,X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_17286,c_54]) ).

cnf(c_17349,plain,
    ( member_of(X0) = X0
    | subclass(null_class,unordered_pair(X1,X0)) ),
    inference(superposition,[status(thm)],[c_90,c_16711]) ).

cnf(c_17352,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,singleton(X1))),
    inference(superposition,[status(thm)],[c_16711,c_11006]) ).

cnf(c_17354,plain,
    ( ~ subclass(unordered_pair(X0,singleton(X1)),X2)
    | subclass(null_class,X2) ),
    inference(superposition,[status(thm)],[c_16711,c_54]) ).

cnf(c_17421,plain,
    subclass(sP3_iProver_def,unordered_pair(singleton(X0),X1)),
    inference(superposition,[status(thm)],[c_16729,c_11006]) ).

cnf(c_17423,plain,
    ( ~ subclass(unordered_pair(singleton(X0),X1),X2)
    | subclass(null_class,X2) ),
    inference(superposition,[status(thm)],[c_16729,c_54]) ).

cnf(c_17541,plain,
    ( unordered_pair(X0,X1) = null_class
    | member_of(singleton(X1)) = X1
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_70,c_91]) ).

cnf(c_17542,plain,
    ( unordered_pair(X0,not_subclass_element(X1,universal_class)) = null_class
    | member(X0,universal_class)
    | subclass(X1,universal_class) ),
    inference(superposition,[status(thm)],[c_70,c_103]) ).

cnf(c_17546,plain,
    ( unordered_pair(X0,X1) = null_class
    | member_of(singleton(X0)) = X0
    | member(X1,universal_class) ),
    inference(superposition,[status(thm)],[c_70,c_91]) ).

cnf(c_17551,plain,
    ( unordered_pair(X0,X0) = null_class
    | member(X0,universal_class) ),
    inference(equality_factoring,[status(thm)],[c_70]) ).

cnf(c_17664,plain,
    ( singleton(member_of(singleton(X0))) = singleton(X0)
    | unordered_pair(X0,X1) = null_class
    | member(X1,universal_class) ),
    inference(superposition,[status(thm)],[c_70,c_88]) ).

cnf(c_17665,plain,
    ( singleton(member_of(singleton(X0))) = singleton(X0)
    | unordered_pair(X0,X1) = singleton(X1) ),
    inference(superposition,[status(thm)],[c_69,c_88]) ).

cnf(c_17666,plain,
    ( singleton(member_of(singleton(X0))) = singleton(X0)
    | singleton(X0) = null_class ),
    inference(superposition,[status(thm)],[c_83,c_88]) ).

cnf(c_17667,plain,
    ( singleton(member_of(singleton(X0))) = singleton(X0)
    | unordered_pair(X1,X0) = null_class
    | member(X1,universal_class) ),
    inference(superposition,[status(thm)],[c_70,c_88]) ).

cnf(c_17668,plain,
    ( singleton(member_of(singleton(X0))) = singleton(X0)
    | unordered_pair(X1,X0) = singleton(X1) ),
    inference(superposition,[status(thm)],[c_68,c_88]) ).

cnf(c_17669,plain,
    ( singleton(member_of(singleton(not_subclass_element(universal_class,X0)))) = singleton(not_subclass_element(universal_class,X0))
    | subclass(universal_class,X0) ),
    inference(superposition,[status(thm)],[c_102,c_88]) ).

cnf(c_17670,plain,
    ( singleton(member_of(singleton(not_subclass_element(universal_class,null_class)))) = singleton(not_subclass_element(universal_class,null_class))
    | universal_class = null_class ),
    inference(superposition,[status(thm)],[c_63,c_88]) ).

cnf(c_17671,plain,
    singleton(member_of(singleton(null_class))) = singleton(null_class),
    inference(superposition,[status(thm)],[c_64,c_88]) ).

cnf(c_17672,plain,
    singleton(member_of(singleton(singleton(X0)))) = singleton(singleton(X0)),
    inference(superposition,[status(thm)],[c_77,c_88]) ).

cnf(c_17673,plain,
    ( ~ member(X0,universal_class)
    | singleton(member_of(singleton(member_of(singleton(X0))))) = singleton(member_of(singleton(X0))) ),
    inference(superposition,[status(thm)],[c_87,c_88]) ).

cnf(c_17674,plain,
    ( singleton(member_of(singleton(member_of(X0)))) = singleton(member_of(X0))
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_89,c_88]) ).

cnf(c_17675,plain,
    ( singleton(member_of(singleton(member_of1(X0)))) = singleton(member_of1(X0))
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_92,c_88]) ).

cnf(c_17676,plain,
    singleton(member_of(singleton(unordered_pair(X0,X1)))) = singleton(unordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_111,c_88]) ).

cnf(c_17677,plain,
    singleton(member_of(singleton(omega))) = singleton(omega),
    inference(superposition,[status(thm)],[c_152,c_88]) ).

cnf(c_17678,plain,
    ( ~ member(X0,universal_class)
    | singleton(member_of(singleton(sum_class(X0)))) = singleton(sum_class(X0)) ),
    inference(superposition,[status(thm)],[c_154,c_88]) ).

cnf(c_17679,plain,
    ( ~ member(X0,universal_class)
    | singleton(member_of(singleton(power_class(X0)))) = singleton(power_class(X0)) ),
    inference(superposition,[status(thm)],[c_156,c_88]) ).

cnf(c_17680,plain,
    ( singleton(member_of(singleton(regular(universal_class)))) = singleton(regular(universal_class))
    | universal_class = null_class ),
    inference(superposition,[status(thm)],[c_166,c_88]) ).

cnf(c_17681,plain,
    singleton(member_of(singleton(sP1_iProver_def))) = singleton(sP1_iProver_def),
    inference(superposition,[status(thm)],[c_6991,c_88]) ).

cnf(c_17682,plain,
    singleton(member_of(singleton(sP3_iProver_def))) = singleton(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_7310,c_88]) ).

cnf(c_17683,plain,
    ( singleton(member_of(singleton(not_subclass_element(universal_class,sP3_iProver_def)))) = singleton(not_subclass_element(universal_class,sP3_iProver_def))
    | universal_class = null_class ),
    inference(superposition,[status(thm)],[c_7628,c_88]) ).

cnf(c_17684,plain,
    ( ~ member(sP0_iProver_def,universal_class)
    | singleton(member_of(singleton(member_of(sP1_iProver_def)))) = singleton(member_of(sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_7866,c_88]) ).

cnf(c_17685,plain,
    singleton(member_of(singleton(singleton(null_class)))) = singleton(singleton(null_class)),
    inference(superposition,[status(thm)],[c_10316,c_88]) ).

cnf(c_17686,plain,
    singleton(member_of(singleton(singleton(singleton(X0))))) = singleton(singleton(singleton(X0))),
    inference(superposition,[status(thm)],[c_10317,c_88]) ).

cnf(c_17687,plain,
    singleton(member_of(singleton(singleton(omega)))) = singleton(singleton(omega)),
    inference(superposition,[status(thm)],[c_10318,c_88]) ).

cnf(c_17688,plain,
    singleton(member_of(singleton(singleton(sP1_iProver_def)))) = singleton(singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_10319,c_88]) ).

cnf(c_17689,plain,
    singleton(member_of(singleton(singleton(sP3_iProver_def)))) = singleton(singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_10320,c_88]) ).

cnf(c_17690,plain,
    singleton(member_of(singleton(singleton(singleton(null_class))))) = singleton(singleton(singleton(null_class))),
    inference(superposition,[status(thm)],[c_10858,c_88]) ).

cnf(c_17691,plain,
    singleton(member_of(singleton(singleton(singleton(omega))))) = singleton(singleton(singleton(omega))),
    inference(superposition,[status(thm)],[c_10945,c_88]) ).

cnf(c_17692,plain,
    singleton(member_of(singleton(singleton(singleton(sP1_iProver_def))))) = singleton(singleton(singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_10949,c_88]) ).

cnf(c_17693,plain,
    singleton(member_of(singleton(singleton(singleton(sP3_iProver_def))))) = singleton(singleton(singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_10865,c_88]) ).

cnf(c_18270,plain,
    ( ~ subclass(unordered_pair(X0,X1),singleton(X0))
    | unordered_pair(X0,X1) = singleton(X0) ),
    inference(superposition,[status(thm)],[c_66,c_107]) ).

cnf(c_18271,plain,
    ( ~ subclass(unordered_pair(X0,X1),singleton(X1))
    | unordered_pair(X0,X1) = singleton(X1) ),
    inference(superposition,[status(thm)],[c_67,c_107]) ).

cnf(c_18272,plain,
    ( ~ subclass(X0,singleton(X1))
    | ~ member(X1,X0)
    | singleton(X1) = X0 ),
    inference(superposition,[status(thm)],[c_96,c_107]) ).

cnf(c_18273,plain,
    ( ~ subclass(universal_class,X0)
    | X0 = universal_class ),
    inference(superposition,[status(thm)],[c_104,c_107]) ).

cnf(c_18274,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | cross_product(universal_class,universal_class) = element_relation ),
    inference(superposition,[status(thm)],[c_118,c_107]) ).

cnf(c_18275,plain,
    ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
    | cross_product(cross_product(universal_class,universal_class),universal_class) = rotate(X0) ),
    inference(superposition,[status(thm)],[c_132,c_107]) ).

cnf(c_18276,plain,
    ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
    | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ),
    inference(superposition,[status(thm)],[c_135,c_107]) ).

cnf(c_18277,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | cross_product(universal_class,universal_class) = successor_relation ),
    inference(superposition,[status(thm)],[c_144,c_107]) ).

cnf(c_18278,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
    | compose(X0,X1) = cross_product(universal_class,universal_class) ),
    inference(superposition,[status(thm)],[c_157,c_107]) ).

cnf(c_18279,plain,
    ( ~ subclass(identity_relation,compose(X0,inverse(X0)))
    | ~ function(X0)
    | compose(X0,inverse(X0)) = identity_relation ),
    inference(superposition,[status(thm)],[c_163,c_107]) ).

cnf(c_18280,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | ~ function(X0)
    | cross_product(universal_class,universal_class) = X0 ),
    inference(superposition,[status(thm)],[c_162,c_107]) ).

cnf(c_18281,plain,
    ( ~ subclass(domain_of(domain_of(X0)),range_of(X0))
    | ~ operation(X0)
    | domain_of(domain_of(X0)) = range_of(X0) ),
    inference(superposition,[status(thm)],[c_180,c_107]) ).

cnf(c_18282,plain,
    ( ~ subclass(universal_class,null_class)
    | universal_class = null_class ),
    inference(superposition,[status(thm)],[c_11576,c_107]) ).

cnf(c_18283,plain,
    ( ~ subclass(omega,image(successor_relation,omega))
    | image(successor_relation,omega) = omega ),
    inference(superposition,[status(thm)],[c_1379,c_107]) ).

cnf(c_18284,plain,
    ( ~ subclass(unordered_pair(sP0_iProver_def,X0),sP1_iProver_def)
    | unordered_pair(sP0_iProver_def,X0) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_7009,c_107]) ).

cnf(c_18285,plain,
    ( ~ subclass(unordered_pair(X0,sP0_iProver_def),sP1_iProver_def)
    | unordered_pair(X0,sP0_iProver_def) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_7010,c_107]) ).

cnf(c_18289,plain,
    ( ~ subclass(X0,sP1_iProver_def)
    | not_subclass_element(sP1_iProver_def,X0) = sP0_iProver_def
    | X0 = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_7758,c_107]) ).

cnf(c_18290,plain,
    ( ~ subclass(universal_class,sP1_iProver_def)
    | universal_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_16501,c_107]) ).

cnf(c_18291,plain,
    ( ~ subclass(universal_class,sP1_iProver_def)
    | singleton(sP0_iProver_def) = null_class
    | universal_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_7163,c_107]) ).

cnf(c_18293,plain,
    ( ~ subclass(X0,intersection(complement(X1),X1))
    | intersection(complement(X1),X1) = X0 ),
    inference(superposition,[status(thm)],[c_7167,c_107]) ).

cnf(c_18294,plain,
    ( ~ subclass(X0,intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = X0 ),
    inference(superposition,[status(thm)],[c_7169,c_107]) ).

cnf(c_18296,plain,
    ( ~ subclass(X0,sP3_iProver_def)
    | X0 = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_7311,c_107]) ).

cnf(c_18297,plain,
    ( ~ subclass(universal_class,sP3_iProver_def)
    | universal_class = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_11869,c_107]) ).

cnf(c_18298,plain,
    ( ~ subclass(x,sP1_iProver_def)
    | x = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_7298,c_107]) ).

cnf(c_18300,plain,
    ( ~ subclass(inverse(subset_relation),sP1_iProver_def)
    | ~ member(sP0_iProver_def,identity_relation)
    | inverse(subset_relation) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_8325,c_107]) ).

cnf(c_18301,plain,
    ( ~ subclass(universal_class,identity_relation)
    | universal_class = identity_relation ),
    inference(superposition,[status(thm)],[c_16563,c_107]) ).

cnf(c_18302,plain,
    ( ~ subclass(subset_relation,identity_relation)
    | identity_relation = subset_relation ),
    inference(superposition,[status(thm)],[c_8440,c_107]) ).

cnf(c_18303,plain,
    ( ~ subclass(X0,intersection(power_class(X1),image(element_relation,complement(X1))))
    | intersection(power_class(X1),image(element_relation,complement(X1))) = X0 ),
    inference(superposition,[status(thm)],[c_8581,c_107]) ).

cnf(c_18304,plain,
    ( ~ subclass(X0,intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)))
    | intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_8804,c_107]) ).

cnf(c_18305,plain,
    ( ~ subclass(singleton(X0),null_class)
    | singleton(X0) = null_class ),
    inference(superposition,[status(thm)],[c_11588,c_107]) ).

cnf(c_18306,plain,
    ( ~ subclass(x,null_class)
    | null_class = x ),
    inference(superposition,[status(thm)],[c_11598,c_107]) ).

cnf(c_18307,plain,
    ( ~ subclass(singleton(null_class),null_class)
    | singleton(null_class) = null_class ),
    inference(superposition,[status(thm)],[c_16713,c_107]) ).

cnf(c_18308,plain,
    ( ~ subclass(unordered_pair(X0,X1),null_class)
    | unordered_pair(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_11573,c_107]) ).

cnf(c_18309,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),null_class)
    | cross_product(universal_class,universal_class) = null_class ),
    inference(superposition,[status(thm)],[c_11580,c_107]) ).

cnf(c_18310,plain,
    ( ~ subclass(identity_relation,null_class)
    | null_class = identity_relation ),
    inference(superposition,[status(thm)],[c_16329,c_107]) ).

cnf(c_18311,plain,
    ( ~ subclass(omega,null_class)
    | null_class = omega ),
    inference(superposition,[status(thm)],[c_11585,c_107]) ).

cnf(c_18312,plain,
    ( ~ subclass(unordered_pair(sP0_iProver_def,X0),null_class)
    | unordered_pair(sP0_iProver_def,X0) = null_class ),
    inference(superposition,[status(thm)],[c_11586,c_107]) ).

cnf(c_18313,plain,
    ( ~ subclass(unordered_pair(X0,sP0_iProver_def),null_class)
    | unordered_pair(X0,sP0_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_11587,c_107]) ).

cnf(c_18314,plain,
    ( ~ subclass(singleton(sP0_iProver_def),null_class)
    | singleton(sP0_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_11589,c_107]) ).

cnf(c_18315,plain,
    ( ~ subclass(sP1_iProver_def,null_class)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_11590,c_107]) ).

cnf(c_18317,plain,
    ( ~ subclass(subset_relation,null_class)
    | null_class = subset_relation ),
    inference(superposition,[status(thm)],[c_11600,c_107]) ).

cnf(c_18318,plain,
    ( ~ subclass(omega,sP3_iProver_def)
    | omega = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_11890,c_107]) ).

cnf(c_18319,plain,
    ( ~ subclass(sP1_iProver_def,sP3_iProver_def)
    | sP1_iProver_def = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_11901,c_107]) ).

cnf(c_18320,plain,
    ( ~ subclass(x,sP3_iProver_def)
    | x = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_12006,c_107]) ).

cnf(c_18321,plain,
    ( ~ subclass(subset_relation,sP3_iProver_def)
    | subset_relation = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_12009,c_107]) ).

cnf(c_18322,plain,
    ( ~ subclass(singleton(X0),sP3_iProver_def)
    | singleton(X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_15337,c_107]) ).

cnf(c_18323,plain,
    ( ~ subclass(singleton(sP0_iProver_def),sP3_iProver_def)
    | singleton(sP0_iProver_def) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_15344,c_107]) ).

cnf(c_18324,plain,
    ( ~ subclass(unordered_pair(X0,X1),sP3_iProver_def)
    | unordered_pair(X0,X1) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_15372,c_107]) ).

cnf(c_18325,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),sP3_iProver_def)
    | cross_product(universal_class,universal_class) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_15447,c_107]) ).

cnf(c_18326,plain,
    ( ~ subclass(unordered_pair(sP0_iProver_def,X0),sP3_iProver_def)
    | unordered_pair(sP0_iProver_def,X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_15451,c_107]) ).

cnf(c_18327,plain,
    ( ~ subclass(unordered_pair(X0,sP0_iProver_def),sP3_iProver_def)
    | unordered_pair(X0,sP0_iProver_def) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_15551,c_107]) ).

cnf(c_18328,plain,
    ( ~ subclass(identity_relation,sP3_iProver_def)
    | identity_relation = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_16331,c_107]) ).

cnf(c_18329,plain,
    ( ~ subclass(singleton(singleton(X0)),null_class)
    | singleton(singleton(X0)) = null_class ),
    inference(superposition,[status(thm)],[c_16727,c_107]) ).

cnf(c_18330,plain,
    ( ~ subclass(unordered_pair(X0,singleton(X1)),null_class)
    | unordered_pair(X0,singleton(X1)) = null_class ),
    inference(superposition,[status(thm)],[c_16711,c_107]) ).

cnf(c_18331,plain,
    ( ~ subclass(unordered_pair(X0,sP1_iProver_def),null_class)
    | unordered_pair(X0,sP1_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_16726,c_107]) ).

cnf(c_18332,plain,
    ( ~ subclass(singleton(sP1_iProver_def),null_class)
    | singleton(sP1_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_16728,c_107]) ).

cnf(c_18333,plain,
    ( ~ subclass(singleton(sP3_iProver_def),null_class)
    | singleton(sP3_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_16735,c_107]) ).

cnf(c_18334,plain,
    ( ~ subclass(singleton(sP3_iProver_def),sP3_iProver_def)
    | singleton(sP3_iProver_def) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_16958,c_107]) ).

cnf(c_18335,plain,
    ( ~ subclass(singleton(null_class),sP3_iProver_def)
    | singleton(null_class) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_16960,c_107]) ).

cnf(c_18336,plain,
    ( ~ subclass(singleton(sP1_iProver_def),sP3_iProver_def)
    | singleton(sP1_iProver_def) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_17004,c_107]) ).

cnf(c_18337,plain,
    ( ~ subclass(unordered_pair(sP1_iProver_def,X0),null_class)
    | unordered_pair(sP1_iProver_def,X0) = null_class ),
    inference(superposition,[status(thm)],[c_16730,c_107]) ).

cnf(c_18338,plain,
    ( ~ subclass(unordered_pair(X0,sP1_iProver_def),sP3_iProver_def)
    | unordered_pair(X0,sP1_iProver_def) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_17243,c_107]) ).

cnf(c_18339,plain,
    ( ~ subclass(unordered_pair(sP1_iProver_def,X0),sP3_iProver_def)
    | unordered_pair(sP1_iProver_def,X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_17286,c_107]) ).

cnf(c_18340,plain,
    ( ~ subclass(singleton(singleton(X0)),sP3_iProver_def)
    | singleton(singleton(X0)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_17251,c_107]) ).

cnf(c_18341,plain,
    ( ~ subclass(unordered_pair(singleton(X0),X1),null_class)
    | unordered_pair(singleton(X0),X1) = null_class ),
    inference(superposition,[status(thm)],[c_16729,c_107]) ).

cnf(c_18361,plain,
    subclass(x,universal_class),
    inference(instantiation,[status(thm)],[c_104]) ).

cnf(c_20039,plain,
    ( unordered_pair(X0,unordered_pair(member_of(X0),singleton(X1))) = ordered_pair(member_of(X0),X1)
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_90,c_113]) ).

cnf(c_20040,plain,
    ( unordered_pair(X0,unordered_pair(member_of1(X0),singleton(X1))) = ordered_pair(member_of1(X0),X1)
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_93,c_113]) ).

cnf(c_20041,plain,
    unordered_pair(sP1_iProver_def,unordered_pair(sP0_iProver_def,singleton(X0))) = ordered_pair(sP0_iProver_def,X0),
    inference(superposition,[status(thm)],[c_3174,c_113]) ).

cnf(c_20042,plain,
    unordered_pair(singleton(X0),unordered_pair(singleton(X1),X0)) = ordered_pair(X0,X1),
    inference(superposition,[status(thm)],[c_65,c_113]) ).

cnf(c_20044,plain,
    unordered_pair(singleton(singleton(X0)),singleton(singleton(X0))) = ordered_pair(singleton(X0),X0),
    inference(superposition,[status(thm)],[c_112,c_113]) ).

cnf(c_20045,plain,
    ( unordered_pair(singleton(X0),unordered_pair(X0,X1)) = ordered_pair(X0,member_of(X1))
    | member_of(X1) = X1 ),
    inference(superposition,[status(thm)],[c_90,c_113]) ).

cnf(c_20046,plain,
    ( unordered_pair(singleton(X0),unordered_pair(X0,X1)) = ordered_pair(X0,member_of1(X1))
    | member_of(X1) = X1 ),
    inference(superposition,[status(thm)],[c_93,c_113]) ).

cnf(c_20047,plain,
    unordered_pair(singleton(X0),unordered_pair(X0,sP1_iProver_def)) = ordered_pair(X0,sP0_iProver_def),
    inference(superposition,[status(thm)],[c_3174,c_113]) ).

cnf(c_20048,plain,
    subclass(sP3_iProver_def,ordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_113,c_15372]) ).

cnf(c_20050,plain,
    ( ordered_pair(X0,X1) != null_class
    | ~ member(unordered_pair(X0,singleton(X1)),universal_class) ),
    inference(superposition,[status(thm)],[c_113,c_74]) ).

cnf(c_20051,plain,
    ( ordered_pair(X0,X1) != null_class
    | ~ member(singleton(X0),universal_class) ),
    inference(superposition,[status(thm)],[c_113,c_73]) ).

cnf(c_20053,plain,
    subclass(singleton(singleton(X0)),ordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_113,c_66]) ).

cnf(c_20054,plain,
    member(ordered_pair(X0,X1),universal_class),
    inference(superposition,[status(thm)],[c_113,c_111]) ).

cnf(c_20055,plain,
    ( ~ member(unordered_pair(X0,singleton(X1)),universal_class)
    | member(unordered_pair(X0,singleton(X1)),ordered_pair(X0,X1)) ),
    inference(superposition,[status(thm)],[c_113,c_110]) ).

cnf(c_20056,plain,
    subclass(singleton(unordered_pair(X0,singleton(X1))),ordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_113,c_67]) ).

cnf(c_20057,plain,
    subclass(null_class,ordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_113,c_16729]) ).

cnf(c_20058,plain,
    member(singleton(X0),ordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_113,c_7112]) ).

cnf(c_20252,plain,
    ( ~ member(null_class,omega)
    | ~ subclass(omega,null_class)
    | member(null_class,null_class) ),
    inference(instantiation,[status(thm)],[c_5940]) ).

cnf(c_20487,plain,
    ( ~ subclass(ordered_pair(X0,X1),sP3_iProver_def)
    | ordered_pair(X0,X1) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_20048,c_107]) ).

cnf(c_20490,plain,
    ( ~ subclass(ordered_pair(X0,X1),X2)
    | subclass(sP3_iProver_def,X2) ),
    inference(superposition,[status(thm)],[c_20048,c_54]) ).

cnf(c_20837,plain,
    singleton(member_of(singleton(ordered_pair(X0,X1)))) = singleton(ordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_20054,c_88]) ).

cnf(c_20838,plain,
    member_of(singleton(ordered_pair(X0,X1))) = ordered_pair(X0,X1),
    inference(superposition,[status(thm)],[c_20054,c_91]) ).

cnf(c_21061,plain,
    ( ~ subclass(ordered_pair(X0,X1),null_class)
    | ordered_pair(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_20057,c_107]) ).

cnf(c_21064,plain,
    ( ~ subclass(ordered_pair(X0,X1),X2)
    | subclass(null_class,X2) ),
    inference(superposition,[status(thm)],[c_20057,c_54]) ).

cnf(c_21081,plain,
    ( member_of(X0) = X0
    | subclass(sP3_iProver_def,unordered_pair(X1,X0)) ),
    inference(superposition,[status(thm)],[c_90,c_17352]) ).

cnf(c_21084,plain,
    ( ~ subclass(unordered_pair(X0,singleton(X1)),sP3_iProver_def)
    | unordered_pair(X0,singleton(X1)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_17352,c_107]) ).

cnf(c_21087,plain,
    ( ~ subclass(unordered_pair(X0,singleton(X1)),X2)
    | subclass(sP3_iProver_def,X2) ),
    inference(superposition,[status(thm)],[c_17352,c_54]) ).

cnf(c_21118,plain,
    ( ~ subclass(unordered_pair(singleton(X0),X1),sP3_iProver_def)
    | unordered_pair(singleton(X0),X1) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_17421,c_107]) ).

cnf(c_21121,plain,
    ( ~ subclass(unordered_pair(singleton(X0),X1),X2)
    | subclass(sP3_iProver_def,X2) ),
    inference(superposition,[status(thm)],[c_17421,c_54]) ).

cnf(c_21141,plain,
    ( member_of(X0) = X0
    | member(X0,ordered_pair(member_of(X0),X1)) ),
    inference(superposition,[status(thm)],[c_90,c_20058]) ).

cnf(c_21142,plain,
    ( member_of(X0) = X0
    | member(X0,ordered_pair(member_of1(X0),X1)) ),
    inference(superposition,[status(thm)],[c_93,c_20058]) ).

cnf(c_21143,plain,
    member(sP1_iProver_def,ordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_3174,c_20058]) ).

cnf(c_21190,plain,
    subclass(null_class,ordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_21143,c_11575]) ).

cnf(c_21200,plain,
    ( ~ subclass(ordered_pair(sP0_iProver_def,X0),null_class)
    | ordered_pair(sP0_iProver_def,X0) = null_class ),
    inference(superposition,[status(thm)],[c_21190,c_107]) ).

cnf(c_21201,plain,
    subclass(sP3_iProver_def,ordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_21190,c_11006]) ).

cnf(c_21203,plain,
    ( ~ subclass(ordered_pair(sP0_iProver_def,X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_21190,c_54]) ).

cnf(c_21258,plain,
    ( ~ subclass(ordered_pair(sP0_iProver_def,X0),sP3_iProver_def)
    | ordered_pair(sP0_iProver_def,X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_21201,c_107]) ).

cnf(c_21261,plain,
    ( ~ subclass(ordered_pair(sP0_iProver_def,X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_21201,c_54]) ).

cnf(c_21283,plain,
    ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),null_class)
    | cross_product(cross_product(universal_class,universal_class),universal_class) = null_class ),
    inference(superposition,[status(thm)],[c_11578,c_107]) ).

cnf(c_21310,plain,
    ( member(not_subclass_element(X0,X1),universal_class)
    | subclass(X0,X1) ),
    inference(superposition,[status(thm)],[c_102,c_12562]) ).

cnf(c_21311,plain,
    ( X0 = null_class
    | member(not_subclass_element(X0,null_class),universal_class) ),
    inference(superposition,[status(thm)],[c_63,c_12562]) ).

cnf(c_21326,plain,
    ( X0 = null_class
    | member(regular(X0),universal_class) ),
    inference(superposition,[status(thm)],[c_166,c_12562]) ).

cnf(c_21336,plain,
    member(sP0_iProver_def,universal_class),
    inference(superposition,[status(thm)],[c_7296,c_12562]) ).

cnf(c_21340,plain,
    ( X0 = null_class
    | member(not_subclass_element(X0,sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_7628,c_12562]) ).

cnf(c_21343,plain,
    ( member(not_subclass_element(identity_relation,X0),universal_class)
    | subclass(identity_relation,X0) ),
    inference(superposition,[status(thm)],[c_8437,c_12562]) ).

cnf(c_21344,plain,
    ( null_class = identity_relation
    | member(not_subclass_element(identity_relation,null_class),universal_class) ),
    inference(superposition,[status(thm)],[c_8438,c_12562]) ).

cnf(c_21345,plain,
    ( null_class = identity_relation
    | member(regular(identity_relation),universal_class) ),
    inference(superposition,[status(thm)],[c_8439,c_12562]) ).

cnf(c_21807,plain,
    singleton(member_of(singleton(sP0_iProver_def))) = singleton(sP0_iProver_def),
    inference(superposition,[status(thm)],[c_21336,c_88]) ).

cnf(c_21808,plain,
    member_of(singleton(sP0_iProver_def)) = sP0_iProver_def,
    inference(superposition,[status(thm)],[c_21336,c_91]) ).

cnf(c_21825,plain,
    ( ~ member(X0,universal_class)
    | ~ function(X1)
    | singleton(member_of(singleton(image(X1,X0)))) = singleton(image(X1,X0)) ),
    inference(superposition,[status(thm)],[c_165,c_88]) ).

cnf(c_21826,plain,
    ( ~ member(X0,universal_class)
    | ~ function(X1)
    | member_of(singleton(image(X1,X0))) = image(X1,X0) ),
    inference(superposition,[status(thm)],[c_165,c_91]) ).

cnf(c_21851,plain,
    intersection(inverse(X0),diagonalise(compose(inverse(element_relation),flip(cross_product(X0,universal_class))))) = cantor(flip(cross_product(X0,universal_class))),
    inference(superposition,[status(thm)],[c_138,c_177]) ).

cnf(c_21852,plain,
    intersection(range_of(X0),diagonalise(compose(inverse(element_relation),inverse(X0)))) = cantor(inverse(X0)),
    inference(superposition,[status(thm)],[c_139,c_177]) ).

cnf(c_21853,plain,
    intersection(sum_class(X0),diagonalise(compose(inverse(element_relation),restrict(element_relation,universal_class,X0)))) = cantor(restrict(element_relation,universal_class,X0)),
    inference(superposition,[status(thm)],[c_153,c_177]) ).

cnf(c_21854,plain,
    ( ~ member(X0,cantor(X1))
    | member(X0,diagonalise(compose(inverse(element_relation),X1))) ),
    inference(superposition,[status(thm)],[c_177,c_122]) ).

cnf(c_21855,plain,
    ( ~ member(X0,cantor(X1))
    | member(X0,domain_of(X1)) ),
    inference(superposition,[status(thm)],[c_177,c_121]) ).

cnf(c_21960,plain,
    member_of(sP1_iProver_def) = sP0_iProver_def,
    inference(superposition,[status(thm)],[c_3174,c_21808]) ).

cnf(c_21962,plain,
    member(singleton(sP0_iProver_def),universal_class),
    inference(superposition,[status(thm)],[c_21808,c_94]) ).

cnf(c_21974,plain,
    singleton(member_of(singleton(singleton(sP0_iProver_def)))) = singleton(singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_21962,c_88]) ).

cnf(c_21975,plain,
    member_of(singleton(singleton(sP0_iProver_def))) = singleton(sP0_iProver_def),
    inference(superposition,[status(thm)],[c_21962,c_91]) ).

cnf(c_21994,plain,
    ( member(not_subclass_element(sP1_iProver_def,X0),x)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_102,c_12586]) ).

cnf(c_21995,plain,
    ( null_class = sP1_iProver_def
    | member(not_subclass_element(sP1_iProver_def,null_class),x) ),
    inference(superposition,[status(thm)],[c_63,c_12586]) ).

cnf(c_21996,plain,
    ( null_class = sP1_iProver_def
    | member(regular(sP1_iProver_def),x) ),
    inference(superposition,[status(thm)],[c_166,c_12586]) ).

cnf(c_21999,plain,
    ( null_class = sP1_iProver_def
    | member(not_subclass_element(sP1_iProver_def,sP3_iProver_def),x) ),
    inference(superposition,[status(thm)],[c_7628,c_12586]) ).

cnf(c_22148,plain,
    ( ~ member(X0,universal_class)
    | subclass(sP3_iProver_def,unordered_pair(X1,X0)) ),
    inference(superposition,[status(thm)],[c_110,c_16382]) ).

cnf(c_22150,plain,
    ( ~ member(X0,universal_class)
    | subclass(sP3_iProver_def,complement(X1))
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_125,c_16382]) ).

cnf(c_22172,plain,
    ( ~ member(X0,identity_relation)
    | subclass(sP3_iProver_def,inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_7997,c_16382]) ).

cnf(c_22203,plain,
    ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),sP3_iProver_def)
    | cross_product(cross_product(universal_class,universal_class),universal_class) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_16385,c_107]) ).

cnf(c_22219,plain,
    ( ~ function(universal_class)
    | subclass(sP1_iProver_def,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_16548]) ).

cnf(c_22236,plain,
    ( member(not_subclass_element(sP1_iProver_def,X0),universal_class)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_102,c_16549]) ).

cnf(c_22237,plain,
    ( null_class = sP1_iProver_def
    | member(not_subclass_element(sP1_iProver_def,null_class),universal_class) ),
    inference(superposition,[status(thm)],[c_63,c_16549]) ).

cnf(c_22238,plain,
    ( null_class = sP1_iProver_def
    | member(regular(sP1_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_166,c_16549]) ).

cnf(c_22241,plain,
    ( null_class = sP1_iProver_def
    | member(not_subclass_element(sP1_iProver_def,sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_7628,c_16549]) ).

cnf(c_22394,plain,
    ( ~ function(universal_class)
    | subclass(identity_relation,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_16701]) ).

cnf(c_22402,plain,
    ( null_class = identity_relation
    | member(not_subclass_element(identity_relation,sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_7628,c_16702]) ).

cnf(c_22414,plain,
    ( member_of(X0) = X0
    | subclass(singleton(X0),ordered_pair(member_of(X0),X1)) ),
    inference(superposition,[status(thm)],[c_90,c_20053]) ).

cnf(c_22415,plain,
    ( member_of(X0) = X0
    | subclass(singleton(X0),ordered_pair(member_of1(X0),X1)) ),
    inference(superposition,[status(thm)],[c_93,c_20053]) ).

cnf(c_22416,plain,
    subclass(singleton(sP1_iProver_def),ordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_3174,c_20053]) ).

cnf(c_22417,plain,
    ( ~ subclass(ordered_pair(X0,X1),singleton(singleton(X0)))
    | ordered_pair(X0,X1) = singleton(singleton(X0)) ),
    inference(superposition,[status(thm)],[c_20053,c_107]) ).

cnf(c_22420,plain,
    ( ~ subclass(ordered_pair(X0,X1),X2)
    | subclass(singleton(singleton(X0)),X2) ),
    inference(superposition,[status(thm)],[c_20053,c_54]) ).

cnf(c_22421,plain,
    ( ~ member(X0,singleton(singleton(X1)))
    | member(X0,ordered_pair(X1,X2)) ),
    inference(superposition,[status(thm)],[c_20053,c_101]) ).

cnf(c_22606,plain,
    ( ~ subclass(ordered_pair(sP0_iProver_def,X0),singleton(sP1_iProver_def))
    | ordered_pair(sP0_iProver_def,X0) = singleton(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_22416,c_107]) ).

cnf(c_22609,plain,
    ( ~ subclass(ordered_pair(sP0_iProver_def,X0),X1)
    | subclass(singleton(sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_22416,c_54]) ).

cnf(c_22610,plain,
    ( ~ member(X0,singleton(sP1_iProver_def))
    | member(X0,ordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_22416,c_101]) ).

cnf(c_22658,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | subclass(unordered_pair(X2,X0),X1) ),
    inference(superposition,[status(thm)],[c_65,c_76]) ).

cnf(c_22661,plain,
    ( ~ member(unordered_pair(X0,singleton(X1)),X2)
    | ~ member(singleton(X0),X2)
    | subclass(ordered_pair(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_113,c_76]) ).

cnf(c_22662,plain,
    ( ~ subclass(X0,unordered_pair(X1,X2))
    | ~ member(X1,X0)
    | ~ member(X2,X0)
    | unordered_pair(X1,X2) = X0 ),
    inference(superposition,[status(thm)],[c_76,c_107]) ).

cnf(c_22663,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_76,c_11006]) ).

cnf(c_22664,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_76,c_10981]) ).

cnf(c_22665,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | ~ subclass(X1,X3)
    | subclass(unordered_pair(X0,X2),X3) ),
    inference(superposition,[status(thm)],[c_76,c_54]) ).

cnf(c_22666,plain,
    ( ~ member(X0,unordered_pair(X1,X2))
    | ~ member(X1,X3)
    | ~ member(X2,X3)
    | member(X0,X3) ),
    inference(superposition,[status(thm)],[c_76,c_101]) ).

cnf(c_22895,plain,
    ( ~ member(X0,cross_product(X1,X2))
    | ~ member(X0,X3)
    | member(X0,restrict(X3,X1,X2)) ),
    inference(superposition,[status(thm)],[c_128,c_123]) ).

cnf(c_22897,plain,
    ( ~ member(X0,regular(X1))
    | ~ member(X0,X1)
    | X1 = null_class
    | member(X0,null_class) ),
    inference(superposition,[status(thm)],[c_167,c_123]) ).

cnf(c_22898,plain,
    ( ~ member(X0,inverse(subset_relation))
    | ~ member(X0,subset_relation)
    | member(X0,identity_relation) ),
    inference(superposition,[status(thm)],[c_175,c_123]) ).

cnf(c_22899,plain,
    ( ~ member(X0,diagonalise(compose(inverse(element_relation),X1)))
    | ~ member(X0,domain_of(X1))
    | member(X0,cantor(X1)) ),
    inference(superposition,[status(thm)],[c_177,c_123]) ).

cnf(c_22900,plain,
    ( ~ member(X0,x)
    | ~ member(X0,sP2_iProver_def)
    | member(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_3176,c_123]) ).

cnf(c_22903,plain,
    ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
    | ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
    | subclass(X0,intersection(X1,X2)) ),
    inference(superposition,[status(thm)],[c_123,c_103]) ).

cnf(c_22905,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | subclass(sP3_iProver_def,intersection(X1,X2)) ),
    inference(superposition,[status(thm)],[c_123,c_16382]) ).

cnf(c_22906,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_123,c_12562]) ).

cnf(c_22907,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | subclass(null_class,intersection(X1,X2)) ),
    inference(superposition,[status(thm)],[c_123,c_11575]) ).

cnf(c_22911,plain,
    ( ~ member(sP0_iProver_def,X0)
    | ~ member(sP0_iProver_def,X1)
    | subclass(sP1_iProver_def,intersection(X0,X1)) ),
    inference(superposition,[status(thm)],[c_123,c_7161]) ).

cnf(c_23215,plain,
    ( ~ member(universal_class,universal_class)
    | singleton(member_of(singleton(apply(choice,universal_class)))) = singleton(apply(choice,universal_class))
    | universal_class = null_class ),
    inference(superposition,[status(thm)],[c_170,c_88]) ).

cnf(c_23216,plain,
    ( ~ member(universal_class,universal_class)
    | member_of(singleton(apply(choice,universal_class))) = apply(choice,universal_class)
    | universal_class = null_class ),
    inference(superposition,[status(thm)],[c_170,c_91]) ).

cnf(c_23220,plain,
    ( ~ member(X0,universal_class)
    | X0 = null_class
    | member(apply(choice,X0),universal_class) ),
    inference(superposition,[status(thm)],[c_170,c_12562]) ).

cnf(c_23222,plain,
    ( ~ member(singleton(X0),universal_class)
    | apply(choice,singleton(X0)) = X0
    | singleton(X0) = null_class ),
    inference(superposition,[status(thm)],[c_170,c_82]) ).

cnf(c_23223,plain,
    ( ~ member(intersection(X0,X1),universal_class)
    | intersection(X0,X1) = null_class
    | member(apply(choice,intersection(X0,X1)),X1) ),
    inference(superposition,[status(thm)],[c_170,c_122]) ).

cnf(c_23224,plain,
    ( ~ member(intersection(X0,X1),universal_class)
    | intersection(X0,X1) = null_class
    | member(apply(choice,intersection(X0,X1)),X0) ),
    inference(superposition,[status(thm)],[c_170,c_121]) ).

cnf(c_23225,plain,
    ( ~ member(apply(choice,complement(X0)),X0)
    | ~ member(complement(X0),universal_class)
    | complement(X0) = null_class ),
    inference(superposition,[status(thm)],[c_170,c_124]) ).

cnf(c_23228,plain,
    ( ~ member(sP1_iProver_def,universal_class)
    | null_class = sP1_iProver_def
    | member(apply(choice,sP1_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_170,c_16549]) ).

cnf(c_23229,plain,
    ( ~ member(sP1_iProver_def,universal_class)
    | null_class = sP1_iProver_def
    | member(apply(choice,sP1_iProver_def),x) ),
    inference(superposition,[status(thm)],[c_170,c_12586]) ).

cnf(c_23230,plain,
    ( ~ member(apply(choice,sP1_iProver_def),sP2_iProver_def)
    | ~ member(sP1_iProver_def,universal_class)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_170,c_8506]) ).

cnf(c_23231,plain,
    ( ~ member(sP1_iProver_def,universal_class)
    | apply(choice,sP1_iProver_def) = sP0_iProver_def
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_170,c_7677]) ).

cnf(c_23232,plain,
    ( ~ member(identity_relation,universal_class)
    | null_class = identity_relation
    | member(apply(choice,identity_relation),universal_class) ),
    inference(superposition,[status(thm)],[c_170,c_16702]) ).

cnf(c_23233,plain,
    ( ~ member(identity_relation,universal_class)
    | null_class = identity_relation
    | member(apply(choice,identity_relation),subset_relation) ),
    inference(superposition,[status(thm)],[c_170,c_8376]) ).

cnf(c_23805,plain,
    ( ~ function(singleton(sP0_iProver_def))
    | subclass(sP1_iProver_def,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_10998]) ).

cnf(c_23809,plain,
    ( ~ operation(flip(cross_product(X0,universal_class)))
    | subclass(null_class,domain_of(inverse(X0))) ),
    inference(superposition,[status(thm)],[c_138,c_11584]) ).

cnf(c_23810,plain,
    ( ~ operation(inverse(X0))
    | subclass(null_class,domain_of(range_of(X0))) ),
    inference(superposition,[status(thm)],[c_139,c_11584]) ).

cnf(c_23811,plain,
    ( ~ operation(restrict(element_relation,universal_class,X0))
    | subclass(null_class,domain_of(sum_class(X0))) ),
    inference(superposition,[status(thm)],[c_153,c_11584]) ).

cnf(c_23812,plain,
    ( ~ subclass(domain_of(domain_of(X0)),null_class)
    | ~ operation(X0)
    | domain_of(domain_of(X0)) = null_class ),
    inference(superposition,[status(thm)],[c_11584,c_107]) ).

cnf(c_23815,plain,
    ( ~ subclass(domain_of(domain_of(X0)),X1)
    | ~ operation(X0)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_11584,c_54]) ).

cnf(c_23900,plain,
    subclass(null_class,inverse(subset_relation)),
    inference(global_subsumption_just,[status(thm)],[c_11599,c_7316]) ).

cnf(c_23903,plain,
    ( ~ subclass(inverse(subset_relation),null_class)
    | inverse(subset_relation) = null_class ),
    inference(superposition,[status(thm)],[c_23900,c_107]) ).

cnf(c_23904,plain,
    subclass(sP3_iProver_def,inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_23900,c_11006]) ).

cnf(c_23908,plain,
    ( ~ subclass(inverse(subset_relation),sP3_iProver_def)
    | inverse(subset_relation) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_23904,c_107]) ).

cnf(c_23913,plain,
    ( singleton(member_of(singleton(X0))) = singleton(X0)
    | member_of(X0) = X0 ),
    inference(superposition,[status(thm)],[c_12038,c_88]) ).

cnf(c_23944,plain,
    ( ~ member(not_subclass_element(X0,singleton(sP0_iProver_def)),sP1_iProver_def)
    | subclass(X0,singleton(sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_12576,c_103]) ).

cnf(c_23959,plain,
    ( ~ subclass(X0,X1)
    | member_of(X0) = X0
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_90,c_15342]) ).

cnf(c_23971,plain,
    ( ~ subclass(X0,X1)
    | member_of(X0) = X0
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_90,c_15360]) ).

cnf(c_23974,plain,
    union(union(X0,X1),intersection(complement(X0),complement(X1))) = complement(null_class),
    inference(superposition,[status(thm)],[c_126,c_15800]) ).

cnf(c_23975,plain,
    union(power_class(X0),image(element_relation,complement(X0))) = complement(null_class),
    inference(superposition,[status(thm)],[c_155,c_15800]) ).

cnf(c_23976,plain,
    union(diagonalise(X0),domain_of(intersection(X0,identity_relation))) = complement(null_class),
    inference(superposition,[status(thm)],[c_176,c_15800]) ).

cnf(c_23977,plain,
    union(sP2_iProver_def,sP1_iProver_def) = complement(null_class),
    inference(superposition,[status(thm)],[c_3175,c_15800]) ).

cnf(c_23978,plain,
    union(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)) = complement(null_class),
    inference(superposition,[status(thm)],[c_8578,c_15800]) ).

cnf(c_24022,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | ~ function(universal_class)
    | cross_product(universal_class,universal_class) = X0 ),
    inference(superposition,[status(thm)],[c_16377,c_107]) ).

cnf(c_24025,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | ~ function(universal_class)
    | subclass(X1,X0) ),
    inference(superposition,[status(thm)],[c_16377,c_54]) ).

cnf(c_24026,plain,
    ( ~ member(X0,X1)
    | ~ function(universal_class)
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_16377,c_101]) ).

cnf(c_24061,plain,
    intersection(union(X0,X1),union(complement(X0),complement(X1))) = symmetric_difference(complement(X0),complement(X1)),
    inference(superposition,[status(thm)],[c_126,c_1297]) ).

cnf(c_24062,plain,
    intersection(complement(null_class),union(complement(X0),X0)) = symmetric_difference(complement(X0),X0),
    inference(superposition,[status(thm)],[c_7611,c_1297]) ).

cnf(c_24063,plain,
    intersection(complement(restrict(X0,X1,X2)),union(X0,cross_product(X1,X2))) = symmetric_difference(X0,cross_product(X1,X2)),
    inference(superposition,[status(thm)],[c_128,c_1297]) ).

cnf(c_24064,plain,
    intersection(complement(restrict(X0,X1,X2)),union(cross_product(X1,X2),X0)) = symmetric_difference(cross_product(X1,X2),X0),
    inference(superposition,[status(thm)],[c_129,c_1297]) ).

cnf(c_24065,plain,
    ( intersection(complement(null_class),union(X0,regular(X0))) = symmetric_difference(X0,regular(X0))
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_167,c_1297]) ).

cnf(c_24066,plain,
    intersection(complement(identity_relation),union(inverse(subset_relation),subset_relation)) = symmetric_difference(inverse(subset_relation),subset_relation),
    inference(superposition,[status(thm)],[c_175,c_1297]) ).

cnf(c_24067,plain,
    intersection(complement(cantor(X0)),union(domain_of(X0),diagonalise(compose(inverse(element_relation),X0)))) = symmetric_difference(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))),
    inference(superposition,[status(thm)],[c_177,c_1297]) ).

cnf(c_24069,plain,
    intersection(complement(sP3_iProver_def),union(sP2_iProver_def,x)) = symmetric_difference(sP2_iProver_def,x),
    inference(superposition,[status(thm)],[c_3176,c_1297]) ).

cnf(c_24070,plain,
    intersection(complement(null_class),union(sP2_iProver_def,sP1_iProver_def)) = symmetric_difference(sP2_iProver_def,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_7277,c_1297]) ).

cnf(c_24071,plain,
    intersection(complement(null_class),union(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def))) = symmetric_difference(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),
    inference(superposition,[status(thm)],[c_8803,c_1297]) ).

cnf(c_24072,plain,
    intersection(complement(intersection(X0,singleton(X0))),successor(X0)) = symmetric_difference(X0,singleton(X0)),
    inference(superposition,[status(thm)],[c_143,c_1297]) ).

cnf(c_24073,plain,
    intersection(complement(intersection(sP0_iProver_def,sP1_iProver_def)),successor(sP0_iProver_def)) = symmetric_difference(sP0_iProver_def,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_7299,c_1297]) ).

cnf(c_24074,plain,
    intersection(complement(intersection(complement(X0),X0)),complement(null_class)) = symmetric_difference(complement(X0),X0),
    inference(superposition,[status(thm)],[c_15800,c_1297]) ).

cnf(c_24075,plain,
    intersection(complement(intersection(sP2_iProver_def,sP1_iProver_def)),complement(null_class)) = symmetric_difference(sP2_iProver_def,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_23977,c_1297]) ).

cnf(c_24076,plain,
    intersection(complement(symmetric_difference(X0,X1)),union(complement(intersection(X0,X1)),union(X0,X1))) = symmetric_difference(complement(intersection(X0,X1)),union(X0,X1)),
    inference(superposition,[status(thm)],[c_1297,c_1297]) ).

cnf(c_24077,plain,
    ( ~ member(X0,complement(intersection(X1,X2)))
    | ~ member(X0,union(X1,X2))
    | member(X0,symmetric_difference(X1,X2)) ),
    inference(superposition,[status(thm)],[c_1297,c_123]) ).

cnf(c_24078,plain,
    ( ~ member(X0,symmetric_difference(X1,X2))
    | member(X0,union(X1,X2)) ),
    inference(superposition,[status(thm)],[c_1297,c_122]) ).

cnf(c_24079,plain,
    ( ~ member(X0,symmetric_difference(X1,X2))
    | member(X0,complement(intersection(X1,X2))) ),
    inference(superposition,[status(thm)],[c_1297,c_121]) ).

cnf(c_24588,plain,
    ( X0 = X1
    | member(not_subclass_element(X0,X1),X0)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_55,c_16382]) ).

cnf(c_24589,plain,
    ( X0 = X1
    | member(not_subclass_element(X0,X1),X0)
    | member(not_subclass_element(X1,X0),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_12562]) ).

cnf(c_24590,plain,
    ( X0 = X1
    | member(not_subclass_element(X0,X1),X0)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_55,c_11575]) ).

cnf(c_24604,plain,
    ( singleton(member_of(singleton(not_subclass_element(universal_class,X0)))) = singleton(not_subclass_element(universal_class,X0))
    | X0 = universal_class
    | member(not_subclass_element(X0,universal_class),X0) ),
    inference(superposition,[status(thm)],[c_55,c_88]) ).

cnf(c_24605,plain,
    ( member_of(singleton(not_subclass_element(universal_class,X0))) = not_subclass_element(universal_class,X0)
    | X0 = universal_class
    | member(not_subclass_element(X0,universal_class),X0) ),
    inference(superposition,[status(thm)],[c_55,c_91]) ).

cnf(c_24607,plain,
    ( intersection(complement(X0),X0) = X1
    | member(not_subclass_element(X1,intersection(complement(X0),X0)),X1) ),
    inference(superposition,[status(thm)],[c_55,c_59]) ).

cnf(c_24610,plain,
    ( X0 = X1
    | member(not_subclass_element(X1,X0),X1)
    | member(not_subclass_element(X0,X1),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_12562]) ).

cnf(c_24612,plain,
    ( not_subclass_element(singleton(X0),X1) = X0
    | singleton(X0) = X1
    | member(not_subclass_element(X1,singleton(X0)),X1) ),
    inference(superposition,[status(thm)],[c_55,c_82]) ).

cnf(c_24613,plain,
    ( intersection(X0,X1) = X2
    | member(not_subclass_element(intersection(X0,X1),X2),X1)
    | member(not_subclass_element(X2,intersection(X0,X1)),X2) ),
    inference(superposition,[status(thm)],[c_55,c_122]) ).

cnf(c_24614,plain,
    ( intersection(X0,X1) = X2
    | member(not_subclass_element(intersection(X0,X1),X2),X0)
    | member(not_subclass_element(X2,intersection(X0,X1)),X2) ),
    inference(superposition,[status(thm)],[c_55,c_121]) ).

cnf(c_24615,plain,
    ( ~ member(not_subclass_element(complement(X0),X1),X0)
    | complement(X0) = X1
    | member(not_subclass_element(X1,complement(X0)),X1) ),
    inference(superposition,[status(thm)],[c_55,c_124]) ).

cnf(c_24616,plain,
    ( intersection(sP2_iProver_def,sP1_iProver_def) = X0
    | member(not_subclass_element(X0,intersection(sP2_iProver_def,sP1_iProver_def)),X0) ),
    inference(superposition,[status(thm)],[c_55,c_7011]) ).

cnf(c_24617,plain,
    ( X0 = sP3_iProver_def
    | member(not_subclass_element(X0,sP3_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_55,c_7309]) ).

cnf(c_24618,plain,
    ( X0 = sP1_iProver_def
    | member(not_subclass_element(X0,sP1_iProver_def),X0)
    | member(not_subclass_element(sP1_iProver_def,X0),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_16549]) ).

cnf(c_24619,plain,
    ( X0 = sP1_iProver_def
    | member(not_subclass_element(X0,sP1_iProver_def),X0)
    | member(not_subclass_element(sP1_iProver_def,X0),x) ),
    inference(superposition,[status(thm)],[c_55,c_12586]) ).

cnf(c_24620,plain,
    ( ~ member(not_subclass_element(sP1_iProver_def,X0),sP2_iProver_def)
    | X0 = sP1_iProver_def
    | member(not_subclass_element(X0,sP1_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_55,c_8506]) ).

cnf(c_24621,plain,
    ( not_subclass_element(sP1_iProver_def,X0) = sP0_iProver_def
    | X0 = sP1_iProver_def
    | member(not_subclass_element(X0,sP1_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_55,c_7677]) ).

cnf(c_24622,plain,
    ( X0 = identity_relation
    | member(not_subclass_element(X0,identity_relation),X0)
    | member(not_subclass_element(identity_relation,X0),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_16702]) ).

cnf(c_24623,plain,
    ( X0 = identity_relation
    | member(not_subclass_element(X0,identity_relation),X0)
    | member(not_subclass_element(identity_relation,X0),subset_relation) ),
    inference(superposition,[status(thm)],[c_55,c_8376]) ).

cnf(c_24624,plain,
    ( intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)) = X0
    | member(not_subclass_element(X0,intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def))),X0) ),
    inference(superposition,[status(thm)],[c_55,c_8806]) ).

cnf(c_26908,plain,
    ( X0 = sP3_iProver_def
    | member(not_subclass_element(X0,sP3_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_55,c_5612]) ).

cnf(c_27113,plain,
    intersection(complement(X0),X0) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_26908,c_59]) ).

cnf(c_27781,plain,
    ( ~ member(X0,singleton(X1))
    | ~ member(X2,singleton(X1))
    | unordered_pair(X0,X2) = singleton(X1)
    | unordered_pair(X0,X2) = null_class ),
    inference(superposition,[status(thm)],[c_76,c_97]) ).

cnf(c_27782,plain,
    ( ~ member(X0,singleton(X1))
    | singleton(X0) = singleton(X1)
    | singleton(X0) = null_class ),
    inference(superposition,[status(thm)],[c_96,c_97]) ).

cnf(c_27785,plain,
    ( not_subclass_element(sP1_iProver_def,singleton(X0)) = sP0_iProver_def
    | singleton(X0) = sP1_iProver_def
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_7758,c_97]) ).

cnf(c_27803,plain,
    ( ~ subclass(X0,X1)
    | singleton(member_of(X1)) = X0
    | member_of(X1) = X1
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_90,c_97]) ).

cnf(c_27804,plain,
    ( ~ subclass(X0,X1)
    | singleton(member_of1(X1)) = X0
    | member_of(X1) = X1
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_93,c_97]) ).

cnf(c_27805,plain,
    ( ~ subclass(X0,sP1_iProver_def)
    | singleton(sP0_iProver_def) = X0
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_3174,c_97]) ).

cnf(c_28106,plain,
    union(complement(X0),X0) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_27113,c_126]) ).

cnf(c_30494,plain,
    complement(null_class) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_28106,c_7046]) ).

cnf(c_30539,plain,
    complement(image(element_relation,complement(sP3_iProver_def))) = power_class(null_class),
    inference(superposition,[status(thm)],[c_30494,c_155]) ).

cnf(c_30709,plain,
    ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
    | not_subclass_element(unordered_pair(X0,X1),X2) = X1
    | subclass(unordered_pair(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_102,c_108]) ).

cnf(c_30710,plain,
    ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
    | not_subclass_element(unordered_pair(X0,X1),X2) = X1
    | unordered_pair(X0,X1) = X2
    | member(not_subclass_element(X2,unordered_pair(X0,X1)),X2) ),
    inference(superposition,[status(thm)],[c_55,c_108]) ).

cnf(c_30711,plain,
    ( not_subclass_element(unordered_pair(X0,X1),null_class) = X0
    | not_subclass_element(unordered_pair(X0,X1),null_class) = X1
    | unordered_pair(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_63,c_108]) ).

cnf(c_30714,plain,
    ( regular(unordered_pair(X0,X1)) = X0
    | regular(unordered_pair(X0,X1)) = X1
    | unordered_pair(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_166,c_108]) ).

cnf(c_30715,plain,
    ( ~ member(unordered_pair(X0,X1),universal_class)
    | apply(choice,unordered_pair(X0,X1)) = X0
    | apply(choice,unordered_pair(X0,X1)) = X1
    | unordered_pair(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_170,c_108]) ).

cnf(c_30719,plain,
    ( not_subclass_element(unordered_pair(X0,X1),sP3_iProver_def) = X0
    | not_subclass_element(unordered_pair(X0,X1),sP3_iProver_def) = X1
    | unordered_pair(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_7628,c_108]) ).

cnf(c_30723,plain,
    ( ~ member(X0,ordered_pair(X1,X2))
    | unordered_pair(X1,singleton(X2)) = X0
    | singleton(X1) = X0 ),
    inference(superposition,[status(thm)],[c_113,c_108]) ).

cnf(c_30783,plain,
    power_class(null_class) = power_class(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_30539,c_155]) ).

cnf(c_30790,plain,
    ( ~ operation(flip(cross_product(X0,universal_class)))
    | subclass(sP3_iProver_def,domain_of(inverse(X0))) ),
    inference(superposition,[status(thm)],[c_138,c_16391]) ).

cnf(c_30791,plain,
    ( ~ operation(inverse(X0))
    | subclass(sP3_iProver_def,domain_of(range_of(X0))) ),
    inference(superposition,[status(thm)],[c_139,c_16391]) ).

cnf(c_30792,plain,
    ( ~ operation(restrict(element_relation,universal_class,X0))
    | subclass(sP3_iProver_def,domain_of(sum_class(X0))) ),
    inference(superposition,[status(thm)],[c_153,c_16391]) ).

cnf(c_30793,plain,
    ( ~ subclass(domain_of(domain_of(X0)),sP3_iProver_def)
    | ~ operation(X0)
    | domain_of(domain_of(X0)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_16391,c_107]) ).

cnf(c_30796,plain,
    ( ~ subclass(domain_of(domain_of(X0)),X1)
    | ~ operation(X0)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_16391,c_54]) ).

cnf(c_30899,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),sP1_iProver_def)
    | ~ function(x)
    | cross_product(universal_class,universal_class) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_16502,c_107]) ).

cnf(c_30902,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | ~ function(x)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_16502,c_54]) ).

cnf(c_30903,plain,
    ( ~ member(X0,sP1_iProver_def)
    | ~ function(x)
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_16502,c_101]) ).

cnf(c_30918,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),identity_relation)
    | ~ function(subset_relation)
    | cross_product(universal_class,universal_class) = identity_relation ),
    inference(superposition,[status(thm)],[c_16564,c_107]) ).

cnf(c_30921,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | ~ function(subset_relation)
    | subclass(identity_relation,X0) ),
    inference(superposition,[status(thm)],[c_16564,c_54]) ).

cnf(c_30922,plain,
    ( ~ member(X0,identity_relation)
    | ~ function(subset_relation)
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_16564,c_101]) ).

cnf(c_30928,plain,
    subclass(singleton(singleton(null_class)),ordered_pair(member_of(singleton(null_class)),X0)),
    inference(superposition,[status(thm)],[c_17671,c_20053]) ).

cnf(c_30929,plain,
    member(singleton(null_class),ordered_pair(member_of(singleton(null_class)),X0)),
    inference(superposition,[status(thm)],[c_17671,c_20058]) ).

cnf(c_30930,plain,
    subclass(sP3_iProver_def,unordered_pair(singleton(null_class),X0)),
    inference(superposition,[status(thm)],[c_17671,c_17421]) ).

cnf(c_30931,plain,
    unordered_pair(singleton(null_class),unordered_pair(member_of(singleton(null_class)),singleton(X0))) = ordered_pair(member_of(singleton(null_class)),X0),
    inference(superposition,[status(thm)],[c_17671,c_113]) ).

cnf(c_30932,plain,
    subclass(null_class,unordered_pair(singleton(null_class),X0)),
    inference(superposition,[status(thm)],[c_17671,c_16729]) ).

cnf(c_30933,plain,
    subclass(sP3_iProver_def,singleton(singleton(null_class))),
    inference(superposition,[status(thm)],[c_17671,c_17251]) ).

cnf(c_30934,plain,
    subclass(null_class,singleton(singleton(null_class))),
    inference(superposition,[status(thm)],[c_17671,c_16727]) ).

cnf(c_30939,plain,
    ( singleton(null_class) != null_class
    | ~ member(member_of(singleton(null_class)),universal_class) ),
    inference(superposition,[status(thm)],[c_17671,c_80]) ).

cnf(c_30941,plain,
    union(member_of(singleton(null_class)),singleton(null_class)) = successor(member_of(singleton(null_class))),
    inference(superposition,[status(thm)],[c_17671,c_143]) ).

cnf(c_30942,plain,
    ( ~ member(member_of(singleton(null_class)),X0)
    | subclass(singleton(null_class),X0) ),
    inference(superposition,[status(thm)],[c_17671,c_96]) ).

cnf(c_30943,plain,
    ( ~ member(member_of(singleton(null_class)),universal_class)
    | member(member_of(singleton(null_class)),singleton(null_class)) ),
    inference(superposition,[status(thm)],[c_17671,c_79]) ).

cnf(c_30944,plain,
    member(singleton(null_class),unordered_pair(singleton(null_class),X0)),
    inference(superposition,[status(thm)],[c_17671,c_7112]) ).

cnf(c_30945,plain,
    member(singleton(null_class),singleton(singleton(null_class))),
    inference(superposition,[status(thm)],[c_17671,c_7091]) ).

cnf(c_30946,plain,
    subclass(singleton(null_class),singleton(null_class)),
    inference(superposition,[status(thm)],[c_17671,c_7090]) ).

cnf(c_30947,plain,
    member(singleton(null_class),unordered_pair(X0,singleton(null_class))),
    inference(superposition,[status(thm)],[c_17671,c_78]) ).

cnf(c_30948,plain,
    subclass(singleton(null_class),unordered_pair(X0,member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_17671,c_67]) ).

cnf(c_30949,plain,
    subclass(singleton(null_class),unordered_pair(member_of(singleton(null_class)),X0)),
    inference(superposition,[status(thm)],[c_17671,c_66]) ).

cnf(c_30951,plain,
    ( ~ subclass(X0,singleton(null_class))
    | singleton(member_of(singleton(null_class))) = X0
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_17671,c_97]) ).

cnf(c_30952,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,singleton(null_class))),
    inference(superposition,[status(thm)],[c_17671,c_17352]) ).

cnf(c_30953,plain,
    unordered_pair(singleton(X0),unordered_pair(X0,singleton(null_class))) = ordered_pair(X0,member_of(singleton(null_class))),
    inference(superposition,[status(thm)],[c_17671,c_113]) ).

cnf(c_30954,plain,
    subclass(null_class,unordered_pair(X0,singleton(null_class))),
    inference(superposition,[status(thm)],[c_17671,c_16711]) ).

cnf(c_30955,plain,
    sum_class(image(X0,singleton(null_class))) = apply(X0,member_of(singleton(null_class))),
    inference(superposition,[status(thm)],[c_17671,c_168]) ).

cnf(c_30956,plain,
    ( ~ member(X0,singleton(null_class))
    | member_of(singleton(null_class)) = X0 ),
    inference(superposition,[status(thm)],[c_17671,c_82]) ).

cnf(c_30967,plain,
    ( ~ member(null_class,universal_class)
    | member(power_class(sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_30783,c_156]) ).

cnf(c_31580,plain,
    subclass(sP3_iProver_def,singleton(singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_7302,c_30933]) ).

cnf(c_31581,plain,
    ( ~ subclass(singleton(singleton(null_class)),sP3_iProver_def)
    | singleton(singleton(null_class)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_30933,c_107]) ).

cnf(c_31599,plain,
    ( ~ subclass(singleton(singleton(null_class)),null_class)
    | singleton(singleton(null_class)) = null_class ),
    inference(superposition,[status(thm)],[c_30934,c_107]) ).

cnf(c_31605,plain,
    subclass(singleton(sP3_iProver_def),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_30946]) ).

cnf(c_31624,plain,
    ( ~ subclass(singleton(singleton(sP3_iProver_def)),sP3_iProver_def)
    | singleton(singleton(sP3_iProver_def)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_31580,c_107]) ).

cnf(c_31626,plain,
    subclass(null_class,singleton(singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_31580,c_10981]) ).

cnf(c_31683,plain,
    ( ~ subclass(singleton(singleton(sP3_iProver_def)),null_class)
    | singleton(singleton(sP3_iProver_def)) = null_class ),
    inference(superposition,[status(thm)],[c_31626,c_107]) ).

cnf(c_31698,plain,
    ( ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))) = not_subclass_element(cross_product(X0,X1),X2)
    | subclass(cross_product(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_102,c_117]) ).

cnf(c_31699,plain,
    ( ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))) = not_subclass_element(cross_product(X0,X1),X2)
    | cross_product(X0,X1) = X2
    | member(not_subclass_element(X2,cross_product(X0,X1)),X2) ),
    inference(superposition,[status(thm)],[c_55,c_117]) ).

cnf(c_31700,plain,
    ( ordered_pair(first(not_subclass_element(cross_product(X0,X1),null_class)),second(not_subclass_element(cross_product(X0,X1),null_class))) = not_subclass_element(cross_product(X0,X1),null_class)
    | cross_product(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_63,c_117]) ).

cnf(c_31701,plain,
    ( ordered_pair(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))) = regular(cross_product(X0,X1))
    | cross_product(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_166,c_117]) ).

cnf(c_31702,plain,
    ( ~ member(cross_product(X0,X1),universal_class)
    | ordered_pair(first(apply(choice,cross_product(X0,X1))),second(apply(choice,cross_product(X0,X1)))) = apply(choice,cross_product(X0,X1))
    | cross_product(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_170,c_117]) ).

cnf(c_31703,plain,
    ( ordered_pair(first(not_subclass_element(cross_product(X0,X1),sP3_iProver_def)),second(not_subclass_element(cross_product(X0,X1),sP3_iProver_def))) = not_subclass_element(cross_product(X0,X1),sP3_iProver_def)
    | cross_product(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_7628,c_117]) ).

cnf(c_31801,plain,
    ( restrict(X0,X1,universal_class) != null_class
    | ~ member(member_of(X1),domain_of(X0))
    | member_of(X1) = X1 ),
    inference(superposition,[status(thm)],[c_90,c_130]) ).

cnf(c_31802,plain,
    ( restrict(X0,X1,universal_class) != null_class
    | ~ member(member_of1(X1),domain_of(X0))
    | member_of(X1) = X1 ),
    inference(superposition,[status(thm)],[c_93,c_130]) ).

cnf(c_31803,plain,
    ( restrict(X0,sP1_iProver_def,universal_class) != null_class
    | ~ member(sP0_iProver_def,domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_3174,c_130]) ).

cnf(c_31804,plain,
    ( restrict(X0,singleton(null_class),universal_class) != null_class
    | ~ member(member_of(singleton(null_class)),domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_17671,c_130]) ).

cnf(c_31843,plain,
    ( first(not_subclass_element(restrict(X0,X1,X2),null_class)) = domain(X0,X1,member_of(X2))
    | member_of(X2) = X2 ),
    inference(superposition,[status(thm)],[c_90,c_140]) ).

cnf(c_31844,plain,
    ( first(not_subclass_element(restrict(X0,X1,X2),null_class)) = domain(X0,X1,member_of1(X2))
    | member_of(X2) = X2 ),
    inference(superposition,[status(thm)],[c_93,c_140]) ).

cnf(c_31845,plain,
    first(not_subclass_element(restrict(X0,X1,sP1_iProver_def),null_class)) = domain(X0,X1,sP0_iProver_def),
    inference(superposition,[status(thm)],[c_3174,c_140]) ).

cnf(c_31846,plain,
    first(not_subclass_element(restrict(X0,X1,singleton(null_class)),null_class)) = domain(X0,X1,member_of(singleton(null_class))),
    inference(superposition,[status(thm)],[c_17671,c_140]) ).

cnf(c_31847,plain,
    first(not_subclass_element(restrict(X0,X1,singleton(X2)),sP3_iProver_def)) = domain(X0,X1,X2),
    inference(superposition,[status(thm)],[c_7302,c_140]) ).

cnf(c_31984,plain,
    ( second(not_subclass_element(restrict(X0,X1,X2),null_class)) = range(X0,member_of(X1),X2)
    | member_of(X1) = X1 ),
    inference(superposition,[status(thm)],[c_90,c_141]) ).

cnf(c_31985,plain,
    ( second(not_subclass_element(restrict(X0,X1,X2),null_class)) = range(X0,member_of1(X1),X2)
    | member_of(X1) = X1 ),
    inference(superposition,[status(thm)],[c_93,c_141]) ).

cnf(c_31986,plain,
    second(not_subclass_element(restrict(X0,sP1_iProver_def,X1),null_class)) = range(X0,sP0_iProver_def,X1),
    inference(superposition,[status(thm)],[c_3174,c_141]) ).

cnf(c_31987,plain,
    second(not_subclass_element(restrict(X0,singleton(null_class),X1),null_class)) = range(X0,member_of(singleton(null_class)),X1),
    inference(superposition,[status(thm)],[c_17671,c_141]) ).

cnf(c_31988,plain,
    second(not_subclass_element(restrict(X0,singleton(X1),X2),sP3_iProver_def)) = range(X0,X1,X2),
    inference(superposition,[status(thm)],[c_7302,c_141]) ).

cnf(c_32032,plain,
    subclass(sP3_iProver_def,ordered_pair(null_class,X0)),
    inference(superposition,[status(thm)],[c_113,c_30930]) ).

cnf(c_32033,plain,
    subclass(sP3_iProver_def,unordered_pair(singleton(sP3_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_7302,c_30930]) ).

cnf(c_32034,plain,
    ( ~ subclass(unordered_pair(singleton(null_class),X0),sP3_iProver_def)
    | unordered_pair(singleton(null_class),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_30930,c_107]) ).

cnf(c_32037,plain,
    ( ~ subclass(unordered_pair(singleton(null_class),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_30930,c_54]) ).

cnf(c_32105,plain,
    subclass(sP3_iProver_def,ordered_pair(sP3_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_7302,c_32032]) ).

cnf(c_32106,plain,
    ( ~ subclass(ordered_pair(null_class,X0),sP3_iProver_def)
    | ordered_pair(null_class,X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_32032,c_107]) ).

cnf(c_32108,plain,
    subclass(null_class,ordered_pair(null_class,X0)),
    inference(superposition,[status(thm)],[c_32032,c_10981]) ).

cnf(c_32109,plain,
    ( ~ subclass(ordered_pair(null_class,X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_32032,c_54]) ).

cnf(c_32233,plain,
    ( ~ subclass(ordered_pair(sP3_iProver_def,X0),sP3_iProver_def)
    | ordered_pair(sP3_iProver_def,X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_32105,c_107]) ).

cnf(c_32235,plain,
    subclass(null_class,ordered_pair(sP3_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_32105,c_10981]) ).

cnf(c_32236,plain,
    ( ~ subclass(ordered_pair(sP3_iProver_def,X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_32105,c_54]) ).

cnf(c_32280,plain,
    ( ~ subclass(ordered_pair(null_class,X0),null_class)
    | ordered_pair(null_class,X0) = null_class ),
    inference(superposition,[status(thm)],[c_32108,c_107]) ).

cnf(c_32283,plain,
    ( ~ subclass(ordered_pair(null_class,X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_32108,c_54]) ).

cnf(c_32334,plain,
    ( ~ subclass(ordered_pair(sP3_iProver_def,X0),null_class)
    | ordered_pair(sP3_iProver_def,X0) = null_class ),
    inference(superposition,[status(thm)],[c_32235,c_107]) ).

cnf(c_32337,plain,
    ( ~ subclass(ordered_pair(sP3_iProver_def,X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_32235,c_54]) ).

cnf(c_32408,plain,
    ( ~ subclass(unordered_pair(singleton(null_class),X0),null_class)
    | unordered_pair(singleton(null_class),X0) = null_class ),
    inference(superposition,[status(thm)],[c_30932,c_107]) ).

cnf(c_32411,plain,
    ( ~ subclass(unordered_pair(singleton(null_class),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_30932,c_54]) ).

cnf(c_32413,plain,
    member(singleton(sP3_iProver_def),singleton(singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_7302,c_30945]) ).

cnf(c_32432,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_7302,c_30952]) ).

cnf(c_32433,plain,
    ( ~ subclass(unordered_pair(X0,singleton(null_class)),sP3_iProver_def)
    | unordered_pair(X0,singleton(null_class)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_30952,c_107]) ).

cnf(c_32436,plain,
    ( ~ subclass(unordered_pair(X0,singleton(null_class)),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_30952,c_54]) ).

cnf(c_32488,plain,
    ( ~ subclass(unordered_pair(X0,singleton(null_class)),null_class)
    | unordered_pair(X0,singleton(null_class)) = null_class ),
    inference(superposition,[status(thm)],[c_30954,c_107]) ).

cnf(c_32491,plain,
    ( ~ subclass(unordered_pair(X0,singleton(null_class)),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_30954,c_54]) ).

cnf(c_32524,plain,
    ( ~ subclass(unordered_pair(singleton(sP3_iProver_def),X0),sP3_iProver_def)
    | unordered_pair(singleton(sP3_iProver_def),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_32033,c_107]) ).

cnf(c_32526,plain,
    subclass(null_class,unordered_pair(singleton(sP3_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_32033,c_10981]) ).

cnf(c_32527,plain,
    ( ~ subclass(unordered_pair(singleton(sP3_iProver_def),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_32033,c_54]) ).

cnf(c_32605,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP3_iProver_def)),sP3_iProver_def)
    | unordered_pair(X0,singleton(sP3_iProver_def)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_32432,c_107]) ).

cnf(c_32607,plain,
    subclass(null_class,unordered_pair(X0,singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_32432,c_10981]) ).

cnf(c_32608,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP3_iProver_def)),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_32432,c_54]) ).

cnf(c_32704,plain,
    ( member_of(not_subclass_element(X0,universal_class)) = not_subclass_element(X0,universal_class)
    | X0 = universal_class
    | member(not_subclass_element(universal_class,X0),universal_class) ),
    inference(superposition,[status(thm)],[c_12038,c_57]) ).

cnf(c_32705,plain,
    ( unordered_pair(not_subclass_element(X0,universal_class),X1) = null_class
    | X0 = universal_class
    | member(not_subclass_element(universal_class,X0),universal_class)
    | member(X1,universal_class) ),
    inference(superposition,[status(thm)],[c_70,c_57]) ).

cnf(c_32706,plain,
    ( unordered_pair(not_subclass_element(X0,universal_class),X1) = singleton(X1)
    | X0 = universal_class
    | member(not_subclass_element(universal_class,X0),universal_class) ),
    inference(superposition,[status(thm)],[c_69,c_57]) ).

cnf(c_32707,plain,
    ( singleton(not_subclass_element(X0,universal_class)) = null_class
    | X0 = universal_class
    | member(not_subclass_element(universal_class,X0),universal_class) ),
    inference(superposition,[status(thm)],[c_83,c_57]) ).

cnf(c_32708,plain,
    ( unordered_pair(X0,not_subclass_element(X1,universal_class)) = null_class
    | X1 = universal_class
    | member(not_subclass_element(universal_class,X1),universal_class)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_70,c_57]) ).

cnf(c_32709,plain,
    ( unordered_pair(X0,not_subclass_element(X1,universal_class)) = singleton(X0)
    | X1 = universal_class
    | member(not_subclass_element(universal_class,X1),universal_class) ),
    inference(superposition,[status(thm)],[c_68,c_57]) ).

cnf(c_32714,plain,
    ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
    | ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
    | intersection(X1,X2) = X0
    | member(not_subclass_element(intersection(X1,X2),X0),intersection(X1,X2)) ),
    inference(superposition,[status(thm)],[c_123,c_57]) ).

cnf(c_32715,plain,
    ( ~ member(not_subclass_element(X0,complement(X1)),universal_class)
    | complement(X1) = X0
    | member(not_subclass_element(complement(X1),X0),complement(X1))
    | member(not_subclass_element(X0,complement(X1)),X1) ),
    inference(superposition,[status(thm)],[c_125,c_57]) ).

cnf(c_32717,plain,
    ( ~ member(not_subclass_element(X0,inverse(subset_relation)),identity_relation)
    | inverse(subset_relation) = X0
    | member(not_subclass_element(inverse(subset_relation),X0),inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_7997,c_57]) ).

cnf(c_32719,plain,
    ( ~ member(not_subclass_element(X0,singleton(sP0_iProver_def)),sP1_iProver_def)
    | singleton(sP0_iProver_def) = X0
    | member(not_subclass_element(singleton(sP0_iProver_def),X0),singleton(sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_12576,c_57]) ).

cnf(c_32767,plain,
    ( unordered_pair(X0,X1) != null_class
    | ~ member(ordered_pair(X1,X0),cross_product(X2,X3)) ),
    inference(superposition,[status(thm)],[c_65,c_75]) ).

cnf(c_32769,plain,
    ( singleton(X0) != null_class
    | ~ member(ordered_pair(X0,X0),cross_product(X1,X2)) ),
    inference(superposition,[status(thm)],[c_112,c_75]) ).

cnf(c_32770,plain,
    ( ordered_pair(X0,X1) != null_class
    | ~ member(ordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),cross_product(X2,X3)) ),
    inference(superposition,[status(thm)],[c_113,c_75]) ).

cnf(c_32829,plain,
    ( singleton(X0) != X1
    | ~ member(member_of(X1),universal_class)
    | member_of(X1) = X0
    | member_of(X1) = X1 ),
    inference(superposition,[status(thm)],[c_90,c_84]) ).

cnf(c_32830,plain,
    ( singleton(X0) != X1
    | ~ member(member_of1(X1),universal_class)
    | member_of(X1) = X1
    | member_of1(X1) = X0 ),
    inference(superposition,[status(thm)],[c_93,c_84]) ).

cnf(c_32831,plain,
    ( singleton(X0) != sP1_iProver_def
    | ~ member(sP0_iProver_def,universal_class)
    | X0 = sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_3174,c_84]) ).

cnf(c_32832,plain,
    ( singleton(X0) != singleton(null_class)
    | ~ member(member_of(singleton(null_class)),universal_class)
    | member_of(singleton(null_class)) = X0 ),
    inference(superposition,[status(thm)],[c_17671,c_84]) ).

cnf(c_32833,plain,
    ( singleton(X0) != X1
    | ~ member(X0,universal_class)
    | member_of(X1) = X0
    | member_of(X1) = X1 ),
    inference(superposition,[status(thm)],[c_90,c_84]) ).

cnf(c_32834,plain,
    ( singleton(X0) != X1
    | ~ member(X0,universal_class)
    | member_of(X1) = X1
    | member_of1(X1) = X0 ),
    inference(superposition,[status(thm)],[c_93,c_84]) ).

cnf(c_32835,plain,
    ( singleton(X0) != sP1_iProver_def
    | ~ member(X0,universal_class)
    | X0 = sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_3174,c_84]) ).

cnf(c_32836,plain,
    ( singleton(X0) != singleton(null_class)
    | ~ member(X0,universal_class)
    | member_of(singleton(null_class)) = X0 ),
    inference(superposition,[status(thm)],[c_17671,c_84]) ).

cnf(c_32983,plain,
    ( ~ subclass(unordered_pair(singleton(sP3_iProver_def),X0),null_class)
    | unordered_pair(singleton(sP3_iProver_def),X0) = null_class ),
    inference(superposition,[status(thm)],[c_32526,c_107]) ).

cnf(c_32986,plain,
    ( ~ subclass(unordered_pair(singleton(sP3_iProver_def),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_32526,c_54]) ).

cnf(c_33017,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP3_iProver_def)),null_class)
    | unordered_pair(X0,singleton(sP3_iProver_def)) = null_class ),
    inference(superposition,[status(thm)],[c_32607,c_107]) ).

cnf(c_33020,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP3_iProver_def)),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_32607,c_54]) ).

cnf(c_33047,plain,
    member(singleton(null_class),ordered_pair(null_class,X0)),
    inference(superposition,[status(thm)],[c_113,c_30944]) ).

cnf(c_33048,plain,
    member(singleton(sP3_iProver_def),unordered_pair(singleton(sP3_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_7302,c_30944]) ).

cnf(c_33198,plain,
    member(singleton(sP3_iProver_def),ordered_pair(sP3_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_7302,c_33047]) ).

cnf(c_33210,plain,
    member(singleton(sP3_iProver_def),unordered_pair(X0,singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_7302,c_30947]) ).

cnf(c_33239,plain,
    ( singleton(X0) != singleton(omega)
    | ~ member(member_of(singleton(omega)),universal_class)
    | member_of(singleton(omega)) = X0 ),
    inference(superposition,[status(thm)],[c_17677,c_84]) ).

cnf(c_33242,plain,
    subclass(singleton(singleton(omega)),ordered_pair(member_of(singleton(omega)),X0)),
    inference(superposition,[status(thm)],[c_17677,c_20053]) ).

cnf(c_33243,plain,
    member(singleton(omega),ordered_pair(member_of(singleton(omega)),X0)),
    inference(superposition,[status(thm)],[c_17677,c_20058]) ).

cnf(c_33244,plain,
    subclass(sP3_iProver_def,unordered_pair(singleton(omega),X0)),
    inference(superposition,[status(thm)],[c_17677,c_17421]) ).

cnf(c_33245,plain,
    unordered_pair(singleton(omega),unordered_pair(member_of(singleton(omega)),singleton(X0))) = ordered_pair(member_of(singleton(omega)),X0),
    inference(superposition,[status(thm)],[c_17677,c_113]) ).

cnf(c_33246,plain,
    subclass(null_class,unordered_pair(singleton(omega),X0)),
    inference(superposition,[status(thm)],[c_17677,c_16729]) ).

cnf(c_33247,plain,
    subclass(sP3_iProver_def,singleton(singleton(omega))),
    inference(superposition,[status(thm)],[c_17677,c_17251]) ).

cnf(c_33248,plain,
    subclass(null_class,singleton(singleton(omega))),
    inference(superposition,[status(thm)],[c_17677,c_16727]) ).

cnf(c_33249,plain,
    subclass(sP3_iProver_def,singleton(omega)),
    inference(superposition,[status(thm)],[c_17677,c_15337]) ).

cnf(c_33250,plain,
    subclass(null_class,singleton(omega)),
    inference(superposition,[status(thm)],[c_17677,c_11588]) ).

cnf(c_33253,plain,
    ( singleton(omega) != null_class
    | ~ member(member_of(singleton(omega)),universal_class) ),
    inference(superposition,[status(thm)],[c_17677,c_80]) ).

cnf(c_33255,plain,
    union(member_of(singleton(omega)),singleton(omega)) = successor(member_of(singleton(omega))),
    inference(superposition,[status(thm)],[c_17677,c_143]) ).

cnf(c_33256,plain,
    ( ~ member(member_of(singleton(omega)),X0)
    | subclass(singleton(omega),X0) ),
    inference(superposition,[status(thm)],[c_17677,c_96]) ).

cnf(c_33257,plain,
    ( ~ member(member_of(singleton(omega)),universal_class)
    | member(member_of(singleton(omega)),singleton(omega)) ),
    inference(superposition,[status(thm)],[c_17677,c_79]) ).

cnf(c_33258,plain,
    member(singleton(omega),unordered_pair(singleton(omega),X0)),
    inference(superposition,[status(thm)],[c_17677,c_7112]) ).

cnf(c_33259,plain,
    member(singleton(omega),singleton(singleton(omega))),
    inference(superposition,[status(thm)],[c_17677,c_7091]) ).

cnf(c_33260,plain,
    subclass(singleton(omega),singleton(omega)),
    inference(superposition,[status(thm)],[c_17677,c_7090]) ).

cnf(c_33261,plain,
    member(singleton(omega),unordered_pair(X0,singleton(omega))),
    inference(superposition,[status(thm)],[c_17677,c_78]) ).

cnf(c_33262,plain,
    subclass(singleton(omega),unordered_pair(X0,member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_17677,c_67]) ).

cnf(c_33263,plain,
    subclass(singleton(omega),unordered_pair(member_of(singleton(omega)),X0)),
    inference(superposition,[status(thm)],[c_17677,c_66]) ).

cnf(c_33265,plain,
    ( singleton(X0) != singleton(omega)
    | ~ member(X0,universal_class)
    | member_of(singleton(omega)) = X0 ),
    inference(superposition,[status(thm)],[c_17677,c_84]) ).

cnf(c_33266,plain,
    second(not_subclass_element(restrict(X0,singleton(omega),X1),null_class)) = range(X0,member_of(singleton(omega)),X1),
    inference(superposition,[status(thm)],[c_17677,c_141]) ).

cnf(c_33267,plain,
    ( restrict(X0,singleton(omega),universal_class) != null_class
    | ~ member(member_of(singleton(omega)),domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_17677,c_130]) ).

cnf(c_33268,plain,
    ( ~ subclass(X0,singleton(omega))
    | singleton(member_of(singleton(omega))) = X0
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_17677,c_97]) ).

cnf(c_33269,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,singleton(omega))),
    inference(superposition,[status(thm)],[c_17677,c_17352]) ).

cnf(c_33270,plain,
    unordered_pair(singleton(X0),unordered_pair(X0,singleton(omega))) = ordered_pair(X0,member_of(singleton(omega))),
    inference(superposition,[status(thm)],[c_17677,c_113]) ).

cnf(c_33271,plain,
    subclass(null_class,unordered_pair(X0,singleton(omega))),
    inference(superposition,[status(thm)],[c_17677,c_16711]) ).

cnf(c_33272,plain,
    sum_class(image(X0,singleton(omega))) = apply(X0,member_of(singleton(omega))),
    inference(superposition,[status(thm)],[c_17677,c_168]) ).

cnf(c_33273,plain,
    ( ~ member(X0,singleton(omega))
    | member_of(singleton(omega)) = X0 ),
    inference(superposition,[status(thm)],[c_17677,c_82]) ).

cnf(c_33274,plain,
    first(not_subclass_element(restrict(X0,X1,singleton(omega)),null_class)) = domain(X0,X1,member_of(singleton(omega))),
    inference(superposition,[status(thm)],[c_17677,c_140]) ).

cnf(c_34052,plain,
    ( ~ subclass(singleton(omega),sP3_iProver_def)
    | singleton(omega) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_33249,c_107]) ).

cnf(c_34073,plain,
    ( ~ subclass(singleton(omega),null_class)
    | singleton(omega) = null_class ),
    inference(superposition,[status(thm)],[c_33250,c_107]) ).

cnf(c_34079,plain,
    ( ~ subclass(singleton(singleton(omega)),sP3_iProver_def)
    | singleton(singleton(omega)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_33247,c_107]) ).

cnf(c_34096,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X3)
    | member(X2,unordered_pair(X0,X2)) ),
    inference(superposition,[status(thm)],[c_116,c_50]) ).

cnf(c_34097,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X3)
    | member(X0,unordered_pair(X0,X2)) ),
    inference(superposition,[status(thm)],[c_116,c_49]) ).

cnf(c_34100,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X3)
    | member(X2,universal_class) ),
    inference(superposition,[status(thm)],[c_116,c_52]) ).

cnf(c_34101,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X3)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_116,c_51]) ).

cnf(c_34102,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X3)
    | subclass(sP3_iProver_def,cross_product(X1,X3)) ),
    inference(superposition,[status(thm)],[c_116,c_16382]) ).

cnf(c_34103,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X3)
    | member(ordered_pair(X0,X2),universal_class) ),
    inference(superposition,[status(thm)],[c_116,c_12562]) ).

cnf(c_34104,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X3)
    | subclass(null_class,cross_product(X1,X3)) ),
    inference(superposition,[status(thm)],[c_116,c_11575]) ).

cnf(c_34105,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X3)
    | ordered_pair(first(ordered_pair(X0,X2)),second(ordered_pair(X0,X2))) = ordered_pair(X0,X2) ),
    inference(superposition,[status(thm)],[c_116,c_117]) ).

cnf(c_34208,plain,
    ( ~ member(successor(X0),universal_class)
    | ~ member(X0,universal_class)
    | member(ordered_pair(X0,successor(X0)),successor_relation) ),
    inference(superposition,[status(thm)],[c_116,c_194]) ).

cnf(c_34210,plain,
    ( ~ subclass(singleton(singleton(omega)),null_class)
    | singleton(singleton(omega)) = null_class ),
    inference(superposition,[status(thm)],[c_33248,c_107]) ).

cnf(c_34227,plain,
    subclass(sP3_iProver_def,ordered_pair(omega,X0)),
    inference(superposition,[status(thm)],[c_113,c_33244]) ).

cnf(c_34228,plain,
    ( ~ subclass(unordered_pair(singleton(omega),X0),sP3_iProver_def)
    | unordered_pair(singleton(omega),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_33244,c_107]) ).

cnf(c_34231,plain,
    ( ~ subclass(unordered_pair(singleton(omega),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_33244,c_54]) ).

cnf(c_34244,plain,
    ( ~ subclass(ordered_pair(omega,X0),sP3_iProver_def)
    | ordered_pair(omega,X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_34227,c_107]) ).

cnf(c_34246,plain,
    subclass(null_class,ordered_pair(omega,X0)),
    inference(superposition,[status(thm)],[c_34227,c_10981]) ).

cnf(c_34247,plain,
    ( ~ subclass(ordered_pair(omega,X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_34227,c_54]) ).

cnf(c_34274,plain,
    ( ~ subclass(ordered_pair(omega,X0),null_class)
    | ordered_pair(omega,X0) = null_class ),
    inference(superposition,[status(thm)],[c_34246,c_107]) ).

cnf(c_34277,plain,
    ( ~ subclass(ordered_pair(omega,X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_34246,c_54]) ).

cnf(c_34284,plain,
    ( ~ subclass(unordered_pair(singleton(omega),X0),null_class)
    | unordered_pair(singleton(omega),X0) = null_class ),
    inference(superposition,[status(thm)],[c_33246,c_107]) ).

cnf(c_34287,plain,
    ( ~ subclass(unordered_pair(singleton(omega),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_33246,c_54]) ).

cnf(c_34346,plain,
    ( ~ subclass(unordered_pair(X0,singleton(omega)),sP3_iProver_def)
    | unordered_pair(X0,singleton(omega)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_33269,c_107]) ).

cnf(c_34349,plain,
    ( ~ subclass(unordered_pair(X0,singleton(omega)),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_33269,c_54]) ).

cnf(c_34355,plain,
    ( ~ subclass(unordered_pair(X0,singleton(omega)),null_class)
    | unordered_pair(X0,singleton(omega)) = null_class ),
    inference(superposition,[status(thm)],[c_33271,c_107]) ).

cnf(c_34358,plain,
    ( ~ subclass(unordered_pair(X0,singleton(omega)),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_33271,c_54]) ).

cnf(c_34403,plain,
    member(singleton(omega),ordered_pair(omega,X0)),
    inference(superposition,[status(thm)],[c_113,c_33258]) ).

cnf(c_34993,plain,
    image(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class) = range_of(subset_relation),
    inference(superposition,[status(thm)],[c_1298,c_142]) ).

cnf(c_34994,plain,
    ( ~ member(not_subclass_element(universal_class,X0),X0)
    | member_of(not_subclass_element(X0,universal_class)) = not_subclass_element(X0,universal_class)
    | X0 = universal_class ),
    inference(superposition,[status(thm)],[c_12038,c_58]) ).

cnf(c_34995,plain,
    ( ~ member(not_subclass_element(universal_class,X0),X0)
    | unordered_pair(not_subclass_element(X0,universal_class),X1) = null_class
    | X0 = universal_class
    | member(X1,universal_class) ),
    inference(superposition,[status(thm)],[c_70,c_58]) ).

cnf(c_34996,plain,
    ( ~ member(not_subclass_element(universal_class,X0),X0)
    | unordered_pair(not_subclass_element(X0,universal_class),X1) = singleton(X1)
    | X0 = universal_class ),
    inference(superposition,[status(thm)],[c_69,c_58]) ).

cnf(c_34997,plain,
    ( ~ member(not_subclass_element(universal_class,X0),X0)
    | singleton(not_subclass_element(X0,universal_class)) = null_class
    | X0 = universal_class ),
    inference(superposition,[status(thm)],[c_83,c_58]) ).

cnf(c_34998,plain,
    ( ~ member(not_subclass_element(universal_class,X0),X0)
    | unordered_pair(X1,not_subclass_element(X0,universal_class)) = null_class
    | X0 = universal_class
    | member(X1,universal_class) ),
    inference(superposition,[status(thm)],[c_70,c_58]) ).

cnf(c_34999,plain,
    ( ~ member(not_subclass_element(universal_class,X0),X0)
    | unordered_pair(X1,not_subclass_element(X0,universal_class)) = singleton(X1)
    | X0 = universal_class ),
    inference(superposition,[status(thm)],[c_68,c_58]) ).

cnf(c_35004,plain,
    ( ~ member(not_subclass_element(intersection(X0,X1),X2),X2)
    | ~ member(not_subclass_element(X2,intersection(X0,X1)),X0)
    | ~ member(not_subclass_element(X2,intersection(X0,X1)),X1)
    | intersection(X0,X1) = X2 ),
    inference(superposition,[status(thm)],[c_123,c_58]) ).

cnf(c_35005,plain,
    ( ~ member(not_subclass_element(complement(X0),X1),X1)
    | ~ member(not_subclass_element(X1,complement(X0)),universal_class)
    | complement(X0) = X1
    | member(not_subclass_element(X1,complement(X0)),X0) ),
    inference(superposition,[status(thm)],[c_125,c_58]) ).

cnf(c_35007,plain,
    ( ~ member(not_subclass_element(inverse(subset_relation),X0),X0)
    | ~ member(not_subclass_element(X0,inverse(subset_relation)),identity_relation)
    | inverse(subset_relation) = X0 ),
    inference(superposition,[status(thm)],[c_7997,c_58]) ).

cnf(c_35009,plain,
    ( ~ member(not_subclass_element(singleton(sP0_iProver_def),X0),X0)
    | ~ member(not_subclass_element(X0,singleton(sP0_iProver_def)),sP1_iProver_def)
    | singleton(sP0_iProver_def) = X0 ),
    inference(superposition,[status(thm)],[c_12576,c_58]) ).

cnf(c_35088,plain,
    ( ~ member(X0,singleton(singleton(X1)))
    | member_of(singleton(singleton(X1))) = X0 ),
    inference(superposition,[status(thm)],[c_9489,c_95]) ).

cnf(c_35090,plain,
    ( singleton(sP0_iProver_def) != sP1_iProver_def
    | ~ member(X0,sP1_iProver_def)
    | member_of(sP1_iProver_def) = X0 ),
    inference(superposition,[status(thm)],[c_21960,c_95]) ).

cnf(c_35091,plain,
    ( ~ member(X0,singleton(sP1_iProver_def))
    | member_of(singleton(sP1_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_9498,c_95]) ).

cnf(c_35092,plain,
    ( ~ member(X0,singleton(sP3_iProver_def))
    | member_of(singleton(sP3_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_9499,c_95]) ).

cnf(c_35093,plain,
    ( ~ member(X0,singleton(singleton(null_class)))
    | member_of(singleton(singleton(null_class))) = X0 ),
    inference(superposition,[status(thm)],[c_10845,c_95]) ).

cnf(c_35094,plain,
    ( ~ member(X0,singleton(singleton(omega)))
    | member_of(singleton(singleton(omega))) = X0 ),
    inference(superposition,[status(thm)],[c_10846,c_95]) ).

cnf(c_35095,plain,
    ( ~ member(X0,singleton(singleton(sP1_iProver_def)))
    | member_of(singleton(singleton(sP1_iProver_def))) = X0 ),
    inference(superposition,[status(thm)],[c_10847,c_95]) ).

cnf(c_35096,plain,
    ( ~ member(X0,singleton(singleton(sP3_iProver_def)))
    | member_of(singleton(singleton(sP3_iProver_def))) = X0 ),
    inference(superposition,[status(thm)],[c_10848,c_95]) ).

cnf(c_35097,plain,
    ( ~ member(X0,singleton(sP0_iProver_def))
    | member_of(singleton(sP0_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_21808,c_95]) ).

cnf(c_35224,plain,
    ( ~ member(X0,universal_class)
    | restrict(flip(cross_product(X1,universal_class)),singleton(X0),universal_class) = null_class
    | member(X0,inverse(X1)) ),
    inference(superposition,[status(thm)],[c_138,c_131]) ).

cnf(c_35225,plain,
    ( ~ member(X0,universal_class)
    | restrict(inverse(X1),singleton(X0),universal_class) = null_class
    | member(X0,range_of(X1)) ),
    inference(superposition,[status(thm)],[c_139,c_131]) ).

cnf(c_35226,plain,
    ( ~ member(X0,universal_class)
    | restrict(restrict(element_relation,universal_class,X1),singleton(X0),universal_class) = null_class
    | member(X0,sum_class(X1)) ),
    inference(superposition,[status(thm)],[c_153,c_131]) ).

cnf(c_35227,plain,
    ( ~ member(not_subclass_element(domain_of(X0),X1),X1)
    | ~ member(not_subclass_element(X1,domain_of(X0)),universal_class)
    | restrict(X0,singleton(not_subclass_element(X1,domain_of(X0))),universal_class) = null_class
    | domain_of(X0) = X1 ),
    inference(superposition,[status(thm)],[c_131,c_58]) ).

cnf(c_35228,plain,
    ( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
    | restrict(X1,singleton(not_subclass_element(X0,domain_of(X1))),universal_class) = null_class
    | domain_of(X1) = X0
    | member(not_subclass_element(domain_of(X1),X0),domain_of(X1)) ),
    inference(superposition,[status(thm)],[c_131,c_57]) ).

cnf(c_35229,plain,
    ( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
    | restrict(X1,singleton(not_subclass_element(X0,domain_of(X1))),universal_class) = null_class
    | subclass(X0,domain_of(X1)) ),
    inference(superposition,[status(thm)],[c_131,c_103]) ).

cnf(c_35230,plain,
    ( ~ member(X0,universal_class)
    | restrict(X1,singleton(X0),universal_class) = null_class
    | subclass(sP3_iProver_def,domain_of(X1)) ),
    inference(superposition,[status(thm)],[c_131,c_16382]) ).

cnf(c_35232,plain,
    ( ~ member(X0,universal_class)
    | restrict(X1,singleton(X0),universal_class) = null_class
    | subclass(null_class,domain_of(X1)) ),
    inference(superposition,[status(thm)],[c_131,c_11575]) ).

cnf(c_35233,plain,
    ( ~ member(sP0_iProver_def,universal_class)
    | restrict(X0,singleton(sP0_iProver_def),universal_class) = null_class
    | subclass(sP1_iProver_def,domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_131,c_7161]) ).

cnf(c_35403,plain,
    subclass(singleton(singleton(sP1_iProver_def)),ordered_pair(member_of(singleton(sP1_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_17681,c_20053]) ).

cnf(c_35404,plain,
    member(singleton(sP1_iProver_def),ordered_pair(member_of(singleton(sP1_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_17681,c_20058]) ).

cnf(c_35405,plain,
    subclass(sP3_iProver_def,unordered_pair(singleton(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_17681,c_17421]) ).

cnf(c_35406,plain,
    unordered_pair(singleton(sP1_iProver_def),unordered_pair(member_of(singleton(sP1_iProver_def)),singleton(X0))) = ordered_pair(member_of(singleton(sP1_iProver_def)),X0),
    inference(superposition,[status(thm)],[c_17681,c_113]) ).

cnf(c_35407,plain,
    subclass(null_class,unordered_pair(singleton(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_17681,c_16729]) ).

cnf(c_35408,plain,
    subclass(sP3_iProver_def,singleton(singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_17681,c_17251]) ).

cnf(c_35409,plain,
    subclass(null_class,singleton(singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_17681,c_16727]) ).

cnf(c_35414,plain,
    ( singleton(sP1_iProver_def) != null_class
    | ~ member(member_of(singleton(sP1_iProver_def)),universal_class) ),
    inference(superposition,[status(thm)],[c_17681,c_80]) ).

cnf(c_35416,plain,
    union(member_of(singleton(sP1_iProver_def)),singleton(sP1_iProver_def)) = successor(member_of(singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_17681,c_143]) ).

cnf(c_35417,plain,
    ( ~ member(member_of(singleton(sP1_iProver_def)),X0)
    | subclass(singleton(sP1_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_17681,c_96]) ).

cnf(c_35418,plain,
    ( ~ member(member_of(singleton(sP1_iProver_def)),universal_class)
    | member(member_of(singleton(sP1_iProver_def)),singleton(sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_17681,c_79]) ).

cnf(c_35419,plain,
    member(singleton(sP1_iProver_def),unordered_pair(singleton(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_17681,c_7112]) ).

cnf(c_35420,plain,
    member(singleton(sP1_iProver_def),singleton(singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_17681,c_7091]) ).

cnf(c_35421,plain,
    subclass(singleton(sP1_iProver_def),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_17681,c_7090]) ).

cnf(c_35422,plain,
    member(singleton(sP1_iProver_def),unordered_pair(X0,singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_17681,c_78]) ).

cnf(c_35423,plain,
    subclass(singleton(sP1_iProver_def),unordered_pair(X0,member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_17681,c_67]) ).

cnf(c_35424,plain,
    subclass(singleton(sP1_iProver_def),unordered_pair(member_of(singleton(sP1_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_17681,c_66]) ).

cnf(c_35426,plain,
    ( singleton(X0) != singleton(sP1_iProver_def)
    | ~ member(member_of(singleton(sP1_iProver_def)),universal_class)
    | member_of(singleton(sP1_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_17681,c_85]) ).

cnf(c_35427,plain,
    ( singleton(X0) != singleton(sP1_iProver_def)
    | ~ member(X0,universal_class)
    | member_of(singleton(sP1_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_17681,c_84]) ).

cnf(c_35428,plain,
    second(not_subclass_element(restrict(X0,singleton(sP1_iProver_def),X1),null_class)) = range(X0,member_of(singleton(sP1_iProver_def)),X1),
    inference(superposition,[status(thm)],[c_17681,c_141]) ).

cnf(c_35429,plain,
    ( restrict(X0,singleton(sP1_iProver_def),universal_class) != null_class
    | ~ member(member_of(singleton(sP1_iProver_def)),domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_17681,c_130]) ).

cnf(c_35430,plain,
    ( ~ subclass(X0,singleton(sP1_iProver_def))
    | singleton(member_of(singleton(sP1_iProver_def))) = X0
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_17681,c_97]) ).

cnf(c_35431,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_17681,c_17352]) ).

cnf(c_35432,plain,
    unordered_pair(singleton(X0),unordered_pair(X0,singleton(sP1_iProver_def))) = ordered_pair(X0,member_of(singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_17681,c_113]) ).

cnf(c_35433,plain,
    subclass(null_class,unordered_pair(X0,singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_17681,c_16711]) ).

cnf(c_35434,plain,
    sum_class(image(X0,singleton(sP1_iProver_def))) = apply(X0,member_of(singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_17681,c_168]) ).

cnf(c_35436,plain,
    first(not_subclass_element(restrict(X0,X1,singleton(sP1_iProver_def)),null_class)) = domain(X0,X1,member_of(singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_17681,c_140]) ).

cnf(c_35840,plain,
    ( ~ subclass(singleton(singleton(sP1_iProver_def)),sP3_iProver_def)
    | singleton(singleton(sP1_iProver_def)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_35408,c_107]) ).

cnf(c_35861,plain,
    ( ~ subclass(singleton(singleton(sP1_iProver_def)),null_class)
    | singleton(singleton(sP1_iProver_def)) = null_class ),
    inference(superposition,[status(thm)],[c_35409,c_107]) ).

cnf(c_35902,plain,
    subclass(sP3_iProver_def,ordered_pair(sP1_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_113,c_35405]) ).

cnf(c_35903,plain,
    ( ~ subclass(unordered_pair(singleton(sP1_iProver_def),X0),sP3_iProver_def)
    | unordered_pair(singleton(sP1_iProver_def),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_35405,c_107]) ).

cnf(c_35906,plain,
    ( ~ subclass(unordered_pair(singleton(sP1_iProver_def),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_35405,c_54]) ).

cnf(c_35969,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,X0),sP3_iProver_def)
    | ordered_pair(sP1_iProver_def,X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_35902,c_107]) ).

cnf(c_35971,plain,
    subclass(null_class,ordered_pair(sP1_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_35902,c_10981]) ).

cnf(c_35972,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_35902,c_54]) ).

cnf(c_36308,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,X0),null_class)
    | ordered_pair(sP1_iProver_def,X0) = null_class ),
    inference(superposition,[status(thm)],[c_35971,c_107]) ).

cnf(c_36311,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_35971,c_54]) ).

cnf(c_36327,plain,
    ( ~ subclass(unordered_pair(singleton(sP1_iProver_def),X0),null_class)
    | unordered_pair(singleton(sP1_iProver_def),X0) = null_class ),
    inference(superposition,[status(thm)],[c_35407,c_107]) ).

cnf(c_36330,plain,
    ( ~ subclass(unordered_pair(singleton(sP1_iProver_def),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_35407,c_54]) ).

cnf(c_36362,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP1_iProver_def)),sP3_iProver_def)
    | unordered_pair(X0,singleton(sP1_iProver_def)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_35431,c_107]) ).

cnf(c_36365,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP1_iProver_def)),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_35431,c_54]) ).

cnf(c_36391,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP1_iProver_def)),null_class)
    | unordered_pair(X0,singleton(sP1_iProver_def)) = null_class ),
    inference(superposition,[status(thm)],[c_35433,c_107]) ).

cnf(c_36394,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP1_iProver_def)),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_35433,c_54]) ).

cnf(c_36409,plain,
    member(singleton(sP1_iProver_def),ordered_pair(sP1_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_113,c_35419]) ).

cnf(c_36474,plain,
    ( ~ member(ordered_pair(member_of(X0),X1),compose(X2,X3))
    | member_of(X0) = X0
    | member(X1,image(X2,image(X3,X0))) ),
    inference(superposition,[status(thm)],[c_90,c_158]) ).

cnf(c_36475,plain,
    ( ~ member(ordered_pair(member_of1(X0),X1),compose(X2,X3))
    | member_of(X0) = X0
    | member(X1,image(X2,image(X3,X0))) ),
    inference(superposition,[status(thm)],[c_93,c_158]) ).

cnf(c_36476,plain,
    ( ~ member(ordered_pair(sP0_iProver_def,X0),compose(X1,X2))
    | member(X0,image(X1,image(X2,sP1_iProver_def))) ),
    inference(superposition,[status(thm)],[c_3174,c_158]) ).

cnf(c_36477,plain,
    ( ~ member(ordered_pair(member_of(singleton(null_class)),X0),compose(X1,X2))
    | member(X0,image(X1,image(X2,singleton(null_class)))) ),
    inference(superposition,[status(thm)],[c_17671,c_158]) ).

cnf(c_36478,plain,
    ( ~ member(ordered_pair(member_of(singleton(omega)),X0),compose(X1,X2))
    | member(X0,image(X1,image(X2,singleton(omega)))) ),
    inference(superposition,[status(thm)],[c_17677,c_158]) ).

cnf(c_36479,plain,
    ( ~ member(ordered_pair(member_of(singleton(sP1_iProver_def)),X0),compose(X1,X2))
    | member(X0,image(X1,image(X2,singleton(sP1_iProver_def)))) ),
    inference(superposition,[status(thm)],[c_17681,c_158]) ).

cnf(c_36480,plain,
    ( ~ member(ordered_pair(X0,not_subclass_element(X1,image(X2,image(X3,singleton(X0))))),compose(X2,X3))
    | ~ member(not_subclass_element(image(X2,image(X3,singleton(X0))),X1),X1)
    | image(X2,image(X3,singleton(X0))) = X1 ),
    inference(superposition,[status(thm)],[c_158,c_58]) ).

cnf(c_36481,plain,
    ( ~ member(ordered_pair(X0,not_subclass_element(X1,image(X2,image(X3,singleton(X0))))),compose(X2,X3))
    | image(X2,image(X3,singleton(X0))) = X1
    | member(not_subclass_element(image(X2,image(X3,singleton(X0))),X1),image(X2,image(X3,singleton(X0)))) ),
    inference(superposition,[status(thm)],[c_158,c_57]) ).

cnf(c_36482,plain,
    ( ~ member(ordered_pair(X0,not_subclass_element(X1,image(X2,image(X3,singleton(X0))))),compose(X2,X3))
    | subclass(X1,image(X2,image(X3,singleton(X0)))) ),
    inference(superposition,[status(thm)],[c_158,c_103]) ).

cnf(c_36483,plain,
    ( ~ member(ordered_pair(X0,X1),compose(X2,X3))
    | subclass(sP3_iProver_def,image(X2,image(X3,singleton(X0)))) ),
    inference(superposition,[status(thm)],[c_158,c_16382]) ).

cnf(c_36484,plain,
    ( ~ member(ordered_pair(X0,X1),compose(X2,X3))
    | member(X1,universal_class) ),
    inference(superposition,[status(thm)],[c_158,c_12562]) ).

cnf(c_36485,plain,
    ( ~ member(ordered_pair(X0,X1),compose(X2,X3))
    | subclass(null_class,image(X2,image(X3,singleton(X0)))) ),
    inference(superposition,[status(thm)],[c_158,c_11575]) ).

cnf(c_36486,plain,
    ( ~ member(ordered_pair(X0,sP0_iProver_def),compose(X1,X2))
    | subclass(sP1_iProver_def,image(X1,image(X2,singleton(X0)))) ),
    inference(superposition,[status(thm)],[c_158,c_7161]) ).

cnf(c_36523,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,universal_class)
    | ~ member(X1,universal_class)
    | member(ordered_pair(X0,X1),element_relation) ),
    inference(superposition,[status(thm)],[c_116,c_120]) ).

cnf(c_36573,plain,
    ( ~ member(ordered_pair(member_of(singleton(sP3_iProver_def)),X0),compose(X1,X2))
    | member(X0,image(X1,image(X2,singleton(sP3_iProver_def)))) ),
    inference(superposition,[status(thm)],[c_17682,c_158]) ).

cnf(c_36578,plain,
    subclass(singleton(singleton(sP3_iProver_def)),ordered_pair(member_of(singleton(sP3_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_17682,c_20053]) ).

cnf(c_36579,plain,
    member(singleton(sP3_iProver_def),ordered_pair(member_of(singleton(sP3_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_17682,c_20058]) ).

cnf(c_36581,plain,
    unordered_pair(singleton(sP3_iProver_def),unordered_pair(member_of(singleton(sP3_iProver_def)),singleton(X0))) = ordered_pair(member_of(singleton(sP3_iProver_def)),X0),
    inference(superposition,[status(thm)],[c_17682,c_113]) ).

cnf(c_36589,plain,
    ( singleton(sP3_iProver_def) != null_class
    | ~ member(member_of(singleton(sP3_iProver_def)),universal_class) ),
    inference(superposition,[status(thm)],[c_17682,c_80]) ).

cnf(c_36591,plain,
    union(member_of(singleton(sP3_iProver_def)),singleton(sP3_iProver_def)) = successor(member_of(singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_17682,c_143]) ).

cnf(c_36592,plain,
    ( ~ member(member_of(singleton(sP3_iProver_def)),X0)
    | subclass(singleton(sP3_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_17682,c_96]) ).

cnf(c_36593,plain,
    ( ~ member(member_of(singleton(sP3_iProver_def)),universal_class)
    | member(member_of(singleton(sP3_iProver_def)),singleton(sP3_iProver_def)) ),
    inference(superposition,[status(thm)],[c_17682,c_79]) ).

cnf(c_36598,plain,
    subclass(singleton(sP3_iProver_def),unordered_pair(X0,member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_17682,c_67]) ).

cnf(c_36599,plain,
    subclass(singleton(sP3_iProver_def),unordered_pair(member_of(singleton(sP3_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_17682,c_66]) ).

cnf(c_36601,plain,
    ( singleton(X0) != singleton(sP3_iProver_def)
    | ~ member(member_of(singleton(sP3_iProver_def)),universal_class)
    | member_of(singleton(sP3_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_17682,c_85]) ).

cnf(c_36602,plain,
    ( singleton(X0) != singleton(sP3_iProver_def)
    | ~ member(X0,universal_class)
    | member_of(singleton(sP3_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_17682,c_84]) ).

cnf(c_36603,plain,
    second(not_subclass_element(restrict(X0,singleton(sP3_iProver_def),X1),null_class)) = range(X0,member_of(singleton(sP3_iProver_def)),X1),
    inference(superposition,[status(thm)],[c_17682,c_141]) ).

cnf(c_36604,plain,
    ( restrict(X0,singleton(sP3_iProver_def),universal_class) != null_class
    | ~ member(member_of(singleton(sP3_iProver_def)),domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_17682,c_130]) ).

cnf(c_36605,plain,
    ( ~ subclass(X0,singleton(sP3_iProver_def))
    | singleton(member_of(singleton(sP3_iProver_def))) = X0
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_17682,c_97]) ).

cnf(c_36607,plain,
    unordered_pair(singleton(X0),unordered_pair(X0,singleton(sP3_iProver_def))) = ordered_pair(X0,member_of(singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_17682,c_113]) ).

cnf(c_36609,plain,
    sum_class(image(X0,singleton(sP3_iProver_def))) = apply(X0,member_of(singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_17682,c_168]) ).

cnf(c_36611,plain,
    first(not_subclass_element(restrict(X0,X1,singleton(sP3_iProver_def)),null_class)) = domain(X0,X1,member_of(singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_17682,c_140]) ).

cnf(c_37075,plain,
    ( ~ function(universal_class)
    | cross_product(universal_class,universal_class) = universal_class ),
    inference(superposition,[status(thm)],[c_16377,c_18273]) ).

cnf(c_37088,plain,
    ~ subclass(universal_class,null_class),
    inference(global_subsumption_just,[status(thm)],[c_18282,c_77,c_10368,c_10369]) ).

cnf(c_37090,plain,
    ~ subclass(universal_class,sP3_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_37088]) ).

cnf(c_37104,plain,
    ~ subclass(universal_class,sP1_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_18290,c_3179,c_5645,c_5972,c_6406,c_18361]) ).

cnf(c_37110,plain,
    ( not_subclass_element(sP1_iProver_def,sP3_iProver_def) = sP0_iProver_def
    | sP1_iProver_def = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_7758,c_18296]) ).

cnf(c_37111,plain,
    intersection(complement(X0),X0) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_7167,c_18296]) ).

cnf(c_37112,plain,
    intersection(sP2_iProver_def,sP1_iProver_def) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_7169,c_18296]) ).

cnf(c_37115,plain,
    intersection(power_class(X0),image(element_relation,complement(X0))) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_8581,c_18296]) ).

cnf(c_37116,plain,
    intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_8804,c_18296]) ).

cnf(c_37147,plain,
    intersection(complement(sP3_iProver_def),union(sP2_iProver_def,sP1_iProver_def)) = symmetric_difference(sP2_iProver_def,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_37112,c_1297]) ).

cnf(c_37156,plain,
    intersection(union(X0,X1),intersection(complement(X0),complement(X1))) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_126,c_37111]) ).

cnf(c_37158,plain,
    intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_176,c_37111]) ).

cnf(c_37164,plain,
    intersection(complement(sP3_iProver_def),union(complement(X0),X0)) = symmetric_difference(complement(X0),X0),
    inference(superposition,[status(thm)],[c_37111,c_1297]) ).

cnf(c_37168,plain,
    union(complement(X0),X0) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_37111,c_126]) ).

cnf(c_37169,plain,
    restrict(complement(cross_product(X0,X1)),X0,X1) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_37111,c_128]) ).

cnf(c_37170,plain,
    complement(domain_of(sP3_iProver_def)) = diagonalise(complement(identity_relation)),
    inference(superposition,[status(thm)],[c_37111,c_176]) ).

cnf(c_37268,plain,
    ~ subclass(x,sP1_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_18298,c_3179,c_5645,c_5972]) ).

cnf(c_37294,plain,
    ( ordered_pair(X0,X1) != singleton(X2)
    | ~ member(X2,universal_class)
    | unordered_pair(X0,singleton(X1)) = X2
    | singleton(X0) = X2 ),
    inference(superposition,[status(thm)],[c_113,c_86]) ).

cnf(c_37295,plain,
    ( unordered_pair(X0,X1) != X2
    | ~ member(member_of(X2),universal_class)
    | member_of(X2) = X0
    | member_of(X2) = X1
    | member_of(X2) = X2 ),
    inference(superposition,[status(thm)],[c_90,c_86]) ).

cnf(c_37296,plain,
    ( unordered_pair(X0,X1) != X2
    | ~ member(member_of1(X2),universal_class)
    | member_of(X2) = X2
    | member_of1(X2) = X0
    | member_of1(X2) = X1 ),
    inference(superposition,[status(thm)],[c_93,c_86]) ).

cnf(c_37297,plain,
    ( unordered_pair(X0,X1) != singleton(null_class)
    | ~ member(member_of(singleton(null_class)),universal_class)
    | member_of(singleton(null_class)) = X0
    | member_of(singleton(null_class)) = X1 ),
    inference(superposition,[status(thm)],[c_17671,c_86]) ).

cnf(c_37298,plain,
    ( unordered_pair(X0,X1) != singleton(omega)
    | ~ member(member_of(singleton(omega)),universal_class)
    | member_of(singleton(omega)) = X0
    | member_of(singleton(omega)) = X1 ),
    inference(superposition,[status(thm)],[c_17677,c_86]) ).

cnf(c_37299,plain,
    ( unordered_pair(X0,X1) != singleton(sP1_iProver_def)
    | ~ member(member_of(singleton(sP1_iProver_def)),universal_class)
    | member_of(singleton(sP1_iProver_def)) = X0
    | member_of(singleton(sP1_iProver_def)) = X1 ),
    inference(superposition,[status(thm)],[c_17681,c_86]) ).

cnf(c_37300,plain,
    ( unordered_pair(X0,X1) != singleton(sP3_iProver_def)
    | ~ member(member_of(singleton(sP3_iProver_def)),universal_class)
    | member_of(singleton(sP3_iProver_def)) = X0
    | member_of(singleton(sP3_iProver_def)) = X1 ),
    inference(superposition,[status(thm)],[c_17682,c_86]) ).

cnf(c_37457,plain,
    ( unordered_pair(X0,X1) != unordered_pair(X1,X2)
    | ~ member(ordered_pair(X0,X2),cross_product(universal_class,universal_class))
    | X0 = X2 ),
    inference(superposition,[status(thm)],[c_65,c_71]) ).

cnf(c_37459,plain,
    ( unordered_pair(X0,X1) != singleton(X0)
    | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
    | X0 = X1 ),
    inference(superposition,[status(thm)],[c_112,c_71]) ).

cnf(c_37460,plain,
    ( unordered_pair(singleton(X0),X1) != ordered_pair(X0,X2)
    | ~ member(ordered_pair(unordered_pair(X0,singleton(X2)),X1),cross_product(universal_class,universal_class))
    | unordered_pair(X0,singleton(X2)) = X1 ),
    inference(superposition,[status(thm)],[c_113,c_71]) ).

cnf(c_37461,plain,
    ( unordered_pair(X0,X1) != unordered_pair(X1,X2)
    | ~ member(ordered_pair(X2,X0),cross_product(universal_class,universal_class))
    | X0 = X2 ),
    inference(superposition,[status(thm)],[c_65,c_71]) ).

cnf(c_37463,plain,
    ( unordered_pair(X0,X1) != singleton(X0)
    | ~ member(ordered_pair(X1,X0),cross_product(universal_class,universal_class))
    | X0 = X1 ),
    inference(superposition,[status(thm)],[c_112,c_71]) ).

cnf(c_37464,plain,
    ( unordered_pair(singleton(X0),X1) != ordered_pair(X0,X2)
    | ~ member(ordered_pair(X1,unordered_pair(X0,singleton(X2))),cross_product(universal_class,universal_class))
    | unordered_pair(X0,singleton(X2)) = X1 ),
    inference(superposition,[status(thm)],[c_113,c_71]) ).

cnf(c_37727,plain,
    ( unordered_pair(X0,X1) != singleton(X1)
    | ~ member(ordered_pair(X1,X0),cross_product(universal_class,universal_class))
    | X0 = X1 ),
    inference(superposition,[status(thm)],[c_112,c_72]) ).

cnf(c_37728,plain,
    ( unordered_pair(X0,unordered_pair(X1,singleton(X2))) != ordered_pair(X1,X2)
    | ~ member(ordered_pair(singleton(X1),X0),cross_product(universal_class,universal_class))
    | singleton(X1) = X0 ),
    inference(superposition,[status(thm)],[c_113,c_72]) ).

cnf(c_37731,plain,
    ( unordered_pair(X0,X1) != singleton(X1)
    | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
    | X0 = X1 ),
    inference(superposition,[status(thm)],[c_112,c_72]) ).

cnf(c_37732,plain,
    ( unordered_pair(X0,unordered_pair(X1,singleton(X2))) != ordered_pair(X1,X2)
    | ~ member(ordered_pair(X0,singleton(X1)),cross_product(universal_class,universal_class))
    | singleton(X1) = X0 ),
    inference(superposition,[status(thm)],[c_113,c_72]) ).

cnf(c_37780,plain,
    ( domain_of(inverse(X0)) != domain_of(X1)
    | ~ subclass(range_of(X1),domain_of(domain_of(X2)))
    | ~ function(X1)
    | compatible(X1,flip(cross_product(X0,universal_class)),X2) ),
    inference(superposition,[status(thm)],[c_138,c_185]) ).

cnf(c_37781,plain,
    ( domain_of(range_of(X0)) != domain_of(X1)
    | ~ subclass(range_of(X1),domain_of(domain_of(X2)))
    | ~ function(X1)
    | compatible(X1,inverse(X0),X2) ),
    inference(superposition,[status(thm)],[c_139,c_185]) ).

cnf(c_37782,plain,
    ( domain_of(sum_class(X0)) != domain_of(X1)
    | ~ subclass(range_of(X1),domain_of(domain_of(X2)))
    | ~ function(X1)
    | compatible(X1,restrict(element_relation,universal_class,X0),X2) ),
    inference(superposition,[status(thm)],[c_153,c_185]) ).

cnf(c_37783,plain,
    ( domain_of(domain_of(X0)) != inverse(X1)
    | ~ subclass(range_of(flip(cross_product(X1,universal_class))),domain_of(domain_of(X2)))
    | ~ function(flip(cross_product(X1,universal_class)))
    | compatible(flip(cross_product(X1,universal_class)),X0,X2) ),
    inference(superposition,[status(thm)],[c_138,c_185]) ).

cnf(c_37784,plain,
    ( domain_of(domain_of(X0)) != range_of(X1)
    | ~ subclass(range_of(inverse(X1)),domain_of(domain_of(X2)))
    | ~ function(inverse(X1))
    | compatible(inverse(X1),X0,X2) ),
    inference(superposition,[status(thm)],[c_139,c_185]) ).

cnf(c_37785,plain,
    ( domain_of(domain_of(X0)) != sum_class(X1)
    | ~ subclass(range_of(restrict(element_relation,universal_class,X1)),domain_of(domain_of(X2)))
    | ~ function(restrict(element_relation,universal_class,X1))
    | compatible(restrict(element_relation,universal_class,X1),X0,X2) ),
    inference(superposition,[status(thm)],[c_153,c_185]) ).

cnf(c_37786,plain,
    ( ~ subclass(range_of(domain_of(X0)),domain_of(domain_of(X1)))
    | ~ function(domain_of(X0))
    | compatible(domain_of(X0),X0,X1) ),
    inference(equality_resolution,[status(thm)],[c_185]) ).

cnf(c_38270,plain,
    ~ subclass(x,null_class),
    inference(global_subsumption_just,[status(thm)],[c_18306,c_100,c_5971,c_6706]) ).

cnf(c_38272,plain,
    ~ subclass(x,sP3_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_38270]) ).

cnf(c_38273,plain,
    ( ~ subclass(identity_relation,sP3_iProver_def)
    | null_class = identity_relation ),
    inference(superposition,[status(thm)],[c_7302,c_18310]) ).

cnf(c_38274,plain,
    ~ subclass(omega,null_class),
    inference(global_subsumption_just,[status(thm)],[c_18311,c_1384,c_9397,c_20252]) ).

cnf(c_38276,plain,
    ~ subclass(omega,sP3_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_38274]) ).

cnf(c_38277,plain,
    ~ subclass(sP1_iProver_def,null_class),
    inference(global_subsumption_just,[status(thm)],[c_18315,c_5941,c_8116,c_10617]) ).

cnf(c_38279,plain,
    not_subclass_element(sP1_iProver_def,null_class) = sP0_iProver_def,
    inference(superposition,[status(thm)],[c_7758,c_38277]) ).

cnf(c_38280,plain,
    ~ subclass(sP1_iProver_def,sP3_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_38277]) ).

cnf(c_38281,plain,
    not_subclass_element(sP1_iProver_def,sP3_iProver_def) = sP0_iProver_def,
    inference(superposition,[status(thm)],[c_7758,c_38280]) ).

cnf(c_38299,plain,
    ( ~ subclass(subset_relation,sP3_iProver_def)
    | null_class = subset_relation ),
    inference(superposition,[status(thm)],[c_7302,c_18317]) ).

cnf(c_38301,plain,
    ( ~ member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),X3)),cross_product(universal_class,universal_class))
    | member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),X3)),compose(X1,X2))
    | subclass(image(X1,image(X2,singleton(X0))),X3) ),
    inference(superposition,[status(thm)],[c_102,c_159]) ).

cnf(c_38302,plain,
    ( ~ member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),X3)),cross_product(universal_class,universal_class))
    | image(X1,image(X2,singleton(X0))) = X3
    | member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),X3)),compose(X1,X2))
    | member(not_subclass_element(X3,image(X1,image(X2,singleton(X0)))),X3) ),
    inference(superposition,[status(thm)],[c_55,c_159]) ).

cnf(c_38303,plain,
    ( ~ member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),null_class)),cross_product(universal_class,universal_class))
    | image(X1,image(X2,singleton(X0))) = null_class
    | member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),null_class)),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_63,c_159]) ).

cnf(c_38305,plain,
    ( ~ member(ordered_pair(X0,regular(image(X1,image(X2,singleton(X0))))),cross_product(universal_class,universal_class))
    | image(X1,image(X2,singleton(X0))) = null_class
    | member(ordered_pair(X0,regular(image(X1,image(X2,singleton(X0))))),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_166,c_159]) ).

cnf(c_38306,plain,
    ( ~ member(ordered_pair(X0,apply(choice,image(X1,image(X2,singleton(X0))))),cross_product(universal_class,universal_class))
    | ~ member(image(X1,image(X2,singleton(X0))),universal_class)
    | image(X1,image(X2,singleton(X0))) = null_class
    | member(ordered_pair(X0,apply(choice,image(X1,image(X2,singleton(X0))))),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_170,c_159]) ).

cnf(c_38307,plain,
    ( ~ member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),sP3_iProver_def)),cross_product(universal_class,universal_class))
    | image(X1,image(X2,singleton(X0))) = null_class
    | member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),sP3_iProver_def)),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_7628,c_159]) ).

cnf(c_38308,plain,
    ( ~ member(ordered_pair(member_of(X0),X1),cross_product(universal_class,universal_class))
    | ~ member(X1,image(X2,image(X3,X0)))
    | member_of(X0) = X0
    | member(ordered_pair(member_of(X0),X1),compose(X2,X3)) ),
    inference(superposition,[status(thm)],[c_90,c_159]) ).

cnf(c_38309,plain,
    ( ~ member(ordered_pair(member_of1(X0),X1),cross_product(universal_class,universal_class))
    | ~ member(X1,image(X2,image(X3,X0)))
    | member_of(X0) = X0
    | member(ordered_pair(member_of1(X0),X1),compose(X2,X3)) ),
    inference(superposition,[status(thm)],[c_93,c_159]) ).

cnf(c_38310,plain,
    ( ~ member(X0,image(X1,image(X2,sP1_iProver_def)))
    | ~ member(ordered_pair(sP0_iProver_def,X0),cross_product(universal_class,universal_class))
    | member(ordered_pair(sP0_iProver_def,X0),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_3174,c_159]) ).

cnf(c_38311,plain,
    ( ~ member(ordered_pair(member_of(singleton(null_class)),X0),cross_product(universal_class,universal_class))
    | ~ member(X0,image(X1,image(X2,singleton(null_class))))
    | member(ordered_pair(member_of(singleton(null_class)),X0),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_17671,c_159]) ).

cnf(c_38312,plain,
    ( ~ member(ordered_pair(member_of(singleton(omega)),X0),cross_product(universal_class,universal_class))
    | ~ member(X0,image(X1,image(X2,singleton(omega))))
    | member(ordered_pair(member_of(singleton(omega)),X0),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_17677,c_159]) ).

cnf(c_38313,plain,
    ( ~ member(ordered_pair(member_of(singleton(sP1_iProver_def)),X0),cross_product(universal_class,universal_class))
    | ~ member(X0,image(X1,image(X2,singleton(sP1_iProver_def))))
    | member(ordered_pair(member_of(singleton(sP1_iProver_def)),X0),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_17681,c_159]) ).

cnf(c_38314,plain,
    ( ~ member(ordered_pair(member_of(singleton(sP3_iProver_def)),X0),cross_product(universal_class,universal_class))
    | ~ member(X0,image(X1,image(X2,singleton(sP3_iProver_def))))
    | member(ordered_pair(member_of(singleton(sP3_iProver_def)),X0),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_17682,c_159]) ).

cnf(c_38341,plain,
    ( cross_product(domain_of(inverse(X0)),domain_of(inverse(X0))) != inverse(X0)
    | ~ subclass(range_of(flip(cross_product(X0,universal_class))),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
    | ~ function(flip(cross_product(X0,universal_class)))
    | operation(flip(cross_product(X0,universal_class))) ),
    inference(superposition,[status(thm)],[c_138,c_181]) ).

cnf(c_38342,plain,
    ( cross_product(domain_of(range_of(X0)),domain_of(range_of(X0))) != range_of(X0)
    | ~ subclass(range_of(inverse(X0)),domain_of(domain_of(inverse(X0))))
    | ~ function(inverse(X0))
    | operation(inverse(X0)) ),
    inference(superposition,[status(thm)],[c_139,c_181]) ).

cnf(c_38343,plain,
    ( cross_product(domain_of(sum_class(X0)),domain_of(sum_class(X0))) != sum_class(X0)
    | ~ subclass(range_of(restrict(element_relation,universal_class,X0)),domain_of(domain_of(restrict(element_relation,universal_class,X0))))
    | ~ function(restrict(element_relation,universal_class,X0))
    | operation(restrict(element_relation,universal_class,X0)) ),
    inference(superposition,[status(thm)],[c_153,c_181]) ).

cnf(c_38411,plain,
    ( ~ compatible(X0,flip(cross_product(X1,universal_class)),X2)
    | ~ operation(flip(cross_product(X1,universal_class)))
    | ~ operation(X2)
    | member(ordered_pair(not_homomorphism1(X0,flip(cross_product(X1,universal_class)),X2),not_homomorphism2(X0,flip(cross_product(X1,universal_class)),X2)),inverse(X1))
    | homomorphism(X0,flip(cross_product(X1,universal_class)),X2) ),
    inference(superposition,[status(thm)],[c_138,c_190]) ).

cnf(c_38412,plain,
    ( ~ compatible(X0,inverse(X1),X2)
    | ~ operation(inverse(X1))
    | ~ operation(X2)
    | member(ordered_pair(not_homomorphism1(X0,inverse(X1),X2),not_homomorphism2(X0,inverse(X1),X2)),range_of(X1))
    | homomorphism(X0,inverse(X1),X2) ),
    inference(superposition,[status(thm)],[c_139,c_190]) ).

cnf(c_38413,plain,
    ( ~ compatible(X0,restrict(element_relation,universal_class,X1),X2)
    | ~ operation(restrict(element_relation,universal_class,X1))
    | ~ operation(X2)
    | member(ordered_pair(not_homomorphism1(X0,restrict(element_relation,universal_class,X1),X2),not_homomorphism2(X0,restrict(element_relation,universal_class,X1),X2)),sum_class(X1))
    | homomorphism(X0,restrict(element_relation,universal_class,X1),X2) ),
    inference(superposition,[status(thm)],[c_153,c_190]) ).

cnf(c_38414,plain,
    ( ~ compatible(X0,X1,X2)
    | ~ operation(X1)
    | ~ operation(X2)
    | homomorphism(X0,X1,X2)
    | subclass(sP3_iProver_def,domain_of(X1)) ),
    inference(superposition,[status(thm)],[c_190,c_16382]) ).

cnf(c_38415,plain,
    ( ~ compatible(X0,X1,X2)
    | ~ operation(X1)
    | ~ operation(X2)
    | member(ordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class)
    | homomorphism(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_190,c_12562]) ).

cnf(c_38416,plain,
    ( ~ compatible(X0,X1,X2)
    | ~ operation(X1)
    | ~ operation(X2)
    | homomorphism(X0,X1,X2)
    | subclass(null_class,domain_of(X1)) ),
    inference(superposition,[status(thm)],[c_190,c_11575]) ).

cnf(c_38497,plain,
    ( ~ member(ordered_pair(ordered_pair(X0,X1),X2),X3)
    | ~ member(ordered_pair(X2,X0),cross_product(universal_class,universal_class))
    | ~ member(X1,universal_class)
    | member(ordered_pair(ordered_pair(X2,X0),X1),rotate(X3)) ),
    inference(superposition,[status(thm)],[c_116,c_134]) ).

cnf(c_38504,plain,
    ( singleton(member_of(singleton(not_subclass_element(X0,X1)))) = singleton(not_subclass_element(X0,X1))
    | subclass(X0,X1) ),
    inference(superposition,[status(thm)],[c_21310,c_88]) ).

cnf(c_38505,plain,
    ( member_of(singleton(not_subclass_element(X0,X1))) = not_subclass_element(X0,X1)
    | subclass(X0,X1) ),
    inference(superposition,[status(thm)],[c_21310,c_91]) ).

cnf(c_38513,plain,
    ( singleton(member_of(singleton(regular(X0)))) = singleton(regular(X0))
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_21326,c_88]) ).

cnf(c_38514,plain,
    ( member_of(singleton(regular(X0))) = regular(X0)
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_21326,c_91]) ).

cnf(c_38540,plain,
    ( singleton(member_of(singleton(not_subclass_element(identity_relation,X0)))) = singleton(not_subclass_element(identity_relation,X0))
    | subclass(identity_relation,X0) ),
    inference(superposition,[status(thm)],[c_21343,c_88]) ).

cnf(c_38541,plain,
    ( member_of(singleton(not_subclass_element(identity_relation,X0))) = not_subclass_element(identity_relation,X0)
    | subclass(identity_relation,X0) ),
    inference(superposition,[status(thm)],[c_21343,c_91]) ).

cnf(c_38573,plain,
    ( singleton(member_of(singleton(regular(identity_relation)))) = singleton(regular(identity_relation))
    | null_class = identity_relation ),
    inference(superposition,[status(thm)],[c_21345,c_88]) ).

cnf(c_38574,plain,
    ( member_of(singleton(regular(identity_relation))) = regular(identity_relation)
    | null_class = identity_relation ),
    inference(superposition,[status(thm)],[c_21345,c_91]) ).

cnf(c_38619,plain,
    singleton(member_of(sP1_iProver_def)) = sP1_iProver_def,
    inference(superposition,[status(thm)],[c_3174,c_21807]) ).

cnf(c_38620,plain,
    ( ~ member(ordered_pair(member_of(singleton(sP0_iProver_def)),X0),compose(X1,X2))
    | member(X0,image(X1,image(X2,singleton(sP0_iProver_def)))) ),
    inference(superposition,[status(thm)],[c_21807,c_158]) ).

cnf(c_38625,plain,
    subclass(singleton(singleton(sP0_iProver_def)),ordered_pair(member_of(singleton(sP0_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_21807,c_20053]) ).

cnf(c_38626,plain,
    member(singleton(sP0_iProver_def),ordered_pair(member_of(singleton(sP0_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_21807,c_20058]) ).

cnf(c_38627,plain,
    subclass(sP3_iProver_def,unordered_pair(singleton(sP0_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_21807,c_17421]) ).

cnf(c_38628,plain,
    unordered_pair(singleton(sP0_iProver_def),unordered_pair(member_of(singleton(sP0_iProver_def)),singleton(X0))) = ordered_pair(member_of(singleton(sP0_iProver_def)),X0),
    inference(superposition,[status(thm)],[c_21807,c_113]) ).

cnf(c_38629,plain,
    subclass(null_class,unordered_pair(singleton(sP0_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_21807,c_16729]) ).

cnf(c_38630,plain,
    subclass(sP3_iProver_def,singleton(singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_21807,c_17251]) ).

cnf(c_38631,plain,
    subclass(null_class,singleton(singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_21807,c_16727]) ).

cnf(c_38634,plain,
    member(singleton(singleton(sP0_iProver_def)),universal_class),
    inference(superposition,[status(thm)],[c_21807,c_10317]) ).

cnf(c_38636,plain,
    ( singleton(sP0_iProver_def) != null_class
    | ~ member(member_of(singleton(sP0_iProver_def)),universal_class) ),
    inference(superposition,[status(thm)],[c_21807,c_80]) ).

cnf(c_38638,plain,
    union(member_of(singleton(sP0_iProver_def)),singleton(sP0_iProver_def)) = successor(member_of(singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_21807,c_143]) ).

cnf(c_38639,plain,
    ( ~ member(member_of(singleton(sP0_iProver_def)),X0)
    | subclass(singleton(sP0_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_21807,c_96]) ).

cnf(c_38640,plain,
    ( ~ member(member_of(singleton(sP0_iProver_def)),universal_class)
    | member(member_of(singleton(sP0_iProver_def)),singleton(sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_21807,c_79]) ).

cnf(c_38641,plain,
    member(singleton(sP0_iProver_def),unordered_pair(singleton(sP0_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_21807,c_7112]) ).

cnf(c_38642,plain,
    member(singleton(sP0_iProver_def),singleton(singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_21807,c_7091]) ).

cnf(c_38643,plain,
    subclass(singleton(sP0_iProver_def),singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_21807,c_7090]) ).

cnf(c_38644,plain,
    member(singleton(sP0_iProver_def),unordered_pair(X0,singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_21807,c_78]) ).

cnf(c_38645,plain,
    subclass(singleton(sP0_iProver_def),unordered_pair(X0,member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_21807,c_67]) ).

cnf(c_38646,plain,
    subclass(singleton(sP0_iProver_def),unordered_pair(member_of(singleton(sP0_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_21807,c_66]) ).

cnf(c_38648,plain,
    ( singleton(X0) != singleton(sP0_iProver_def)
    | ~ member(member_of(singleton(sP0_iProver_def)),universal_class)
    | member_of(singleton(sP0_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_21807,c_85]) ).

cnf(c_38649,plain,
    ( singleton(X0) != singleton(sP0_iProver_def)
    | ~ member(X0,universal_class)
    | member_of(singleton(sP0_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_21807,c_84]) ).

cnf(c_38650,plain,
    second(not_subclass_element(restrict(X0,singleton(sP0_iProver_def),X1),null_class)) = range(X0,member_of(singleton(sP0_iProver_def)),X1),
    inference(superposition,[status(thm)],[c_21807,c_141]) ).

cnf(c_38651,plain,
    ( restrict(X0,singleton(sP0_iProver_def),universal_class) != null_class
    | ~ member(member_of(singleton(sP0_iProver_def)),domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_21807,c_130]) ).

cnf(c_38652,plain,
    ( ~ subclass(X0,singleton(sP0_iProver_def))
    | singleton(member_of(singleton(sP0_iProver_def))) = X0
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_21807,c_97]) ).

cnf(c_38653,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_21807,c_17352]) ).

cnf(c_38654,plain,
    unordered_pair(singleton(X0),unordered_pair(X0,singleton(sP0_iProver_def))) = ordered_pair(X0,member_of(singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_21807,c_113]) ).

cnf(c_38655,plain,
    subclass(null_class,unordered_pair(X0,singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_21807,c_16711]) ).

cnf(c_38656,plain,
    sum_class(image(X0,singleton(sP0_iProver_def))) = apply(X0,member_of(singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_21807,c_168]) ).

cnf(c_38658,plain,
    ( unordered_pair(X0,X1) != singleton(sP0_iProver_def)
    | ~ member(member_of(singleton(sP0_iProver_def)),universal_class)
    | member_of(singleton(sP0_iProver_def)) = X0
    | member_of(singleton(sP0_iProver_def)) = X1 ),
    inference(superposition,[status(thm)],[c_21807,c_86]) ).

cnf(c_38659,plain,
    first(not_subclass_element(restrict(X0,X1,singleton(sP0_iProver_def)),null_class)) = domain(X0,X1,member_of(singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_21807,c_140]) ).

cnf(c_38662,plain,
    ( ~ member(ordered_pair(member_of(singleton(sP0_iProver_def)),X0),cross_product(universal_class,universal_class))
    | ~ member(X0,image(X1,image(X2,singleton(sP0_iProver_def))))
    | member(ordered_pair(member_of(singleton(sP0_iProver_def)),X0),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_21807,c_159]) ).

cnf(c_39397,plain,
    ( ~ subclass(singleton(singleton(sP0_iProver_def)),sP3_iProver_def)
    | singleton(singleton(sP0_iProver_def)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_38630,c_107]) ).

cnf(c_39419,plain,
    ( ~ subclass(singleton(singleton(sP0_iProver_def)),null_class)
    | singleton(singleton(sP0_iProver_def)) = null_class ),
    inference(superposition,[status(thm)],[c_38631,c_107]) ).

cnf(c_39425,plain,
    ( ~ member(ordered_pair(ordered_pair(X0,X1),X2),X3)
    | ~ member(ordered_pair(X1,X0),cross_product(universal_class,universal_class))
    | ~ member(X2,universal_class)
    | member(ordered_pair(ordered_pair(X1,X0),X2),flip(X3)) ),
    inference(superposition,[status(thm)],[c_116,c_137]) ).

cnf(c_39433,plain,
    ( ~ member(ordered_pair(X0,X1),universal_class)
    | ~ homomorphism(X2,X3,X4)
    | apply(X4,ordered_pair(apply(X2,X0),apply(X2,X1))) = apply(X2,apply(X3,ordered_pair(X0,X1)))
    | restrict(X3,singleton(ordered_pair(X0,X1)),universal_class) = null_class ),
    inference(superposition,[status(thm)],[c_131,c_189]) ).

cnf(c_39434,plain,
    ( ~ compatible(X0,X1,X2)
    | ~ homomorphism(X3,X1,X4)
    | ~ operation(X1)
    | ~ operation(X2)
    | apply(X4,ordered_pair(apply(X3,not_homomorphism1(X0,X1,X2)),apply(X3,not_homomorphism2(X0,X1,X2)))) = apply(X3,apply(X1,ordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2))))
    | homomorphism(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_190,c_189]) ).

cnf(c_39435,plain,
    ( ~ homomorphism(X0,flip(cross_product(X1,universal_class)),X2)
    | ~ member(ordered_pair(X3,X4),inverse(X1))
    | apply(X0,apply(flip(cross_product(X1,universal_class)),ordered_pair(X3,X4))) = apply(X2,ordered_pair(apply(X0,X3),apply(X0,X4))) ),
    inference(superposition,[status(thm)],[c_138,c_189]) ).

cnf(c_39436,plain,
    ( ~ member(ordered_pair(X0,X1),range_of(X2))
    | ~ homomorphism(X3,inverse(X2),X4)
    | apply(X4,ordered_pair(apply(X3,X0),apply(X3,X1))) = apply(X3,apply(inverse(X2),ordered_pair(X0,X1))) ),
    inference(superposition,[status(thm)],[c_139,c_189]) ).

cnf(c_39437,plain,
    ( ~ homomorphism(X0,restrict(element_relation,universal_class,X1),X2)
    | ~ member(ordered_pair(X3,X4),sum_class(X1))
    | apply(X0,apply(restrict(element_relation,universal_class,X1),ordered_pair(X3,X4))) = apply(X2,ordered_pair(apply(X0,X3),apply(X0,X4))) ),
    inference(superposition,[status(thm)],[c_153,c_189]) ).

cnf(c_39609,plain,
    ( ~ member(ordered_pair(member_of(sP1_iProver_def),X0),compose(X1,X2))
    | member(X0,image(X1,image(X2,sP1_iProver_def))) ),
    inference(superposition,[status(thm)],[c_38619,c_158]) ).

cnf(c_39614,plain,
    subclass(singleton(sP1_iProver_def),ordered_pair(member_of(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_38619,c_20053]) ).

cnf(c_39615,plain,
    member(sP1_iProver_def,ordered_pair(member_of(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_38619,c_20058]) ).

cnf(c_39617,plain,
    unordered_pair(sP1_iProver_def,unordered_pair(member_of(sP1_iProver_def),singleton(X0))) = ordered_pair(member_of(sP1_iProver_def),X0),
    inference(superposition,[status(thm)],[c_38619,c_113]) ).

cnf(c_39625,plain,
    ( null_class != sP1_iProver_def
    | ~ member(member_of(sP1_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_38619,c_80]) ).

cnf(c_39627,plain,
    union(member_of(sP1_iProver_def),sP1_iProver_def) = successor(member_of(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_38619,c_143]) ).

cnf(c_39628,plain,
    ( ~ member(member_of(sP1_iProver_def),X0)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_38619,c_96]) ).

cnf(c_39629,plain,
    ( ~ member(member_of(sP1_iProver_def),universal_class)
    | member(member_of(sP1_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_38619,c_79]) ).

cnf(c_39634,plain,
    subclass(sP1_iProver_def,unordered_pair(X0,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_38619,c_67]) ).

cnf(c_39635,plain,
    subclass(sP1_iProver_def,unordered_pair(member_of(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_38619,c_66]) ).

cnf(c_39637,plain,
    ( singleton(X0) != sP1_iProver_def
    | ~ member(member_of(sP1_iProver_def),universal_class)
    | member_of(sP1_iProver_def) = X0 ),
    inference(superposition,[status(thm)],[c_38619,c_85]) ).

cnf(c_39638,plain,
    ( singleton(X0) != sP1_iProver_def
    | ~ member(X0,universal_class)
    | member_of(sP1_iProver_def) = X0 ),
    inference(superposition,[status(thm)],[c_38619,c_84]) ).

cnf(c_39639,plain,
    second(not_subclass_element(restrict(X0,sP1_iProver_def,X1),null_class)) = range(X0,member_of(sP1_iProver_def),X1),
    inference(superposition,[status(thm)],[c_38619,c_141]) ).

cnf(c_39640,plain,
    ( restrict(X0,sP1_iProver_def,universal_class) != null_class
    | ~ member(member_of(sP1_iProver_def),domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_38619,c_130]) ).

cnf(c_39641,plain,
    ( ~ subclass(X0,sP1_iProver_def)
    | singleton(member_of(sP1_iProver_def)) = X0
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_38619,c_97]) ).

cnf(c_39643,plain,
    unordered_pair(singleton(X0),unordered_pair(X0,sP1_iProver_def)) = ordered_pair(X0,member_of(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_38619,c_113]) ).

cnf(c_39645,plain,
    sum_class(image(X0,sP1_iProver_def)) = apply(X0,member_of(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_38619,c_168]) ).

cnf(c_39647,plain,
    first(not_subclass_element(restrict(X0,X1,sP1_iProver_def),null_class)) = domain(X0,X1,member_of(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_38619,c_140]) ).

cnf(c_39648,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member_of(sP1_iProver_def) = X0 ),
    inference(superposition,[status(thm)],[c_38619,c_95]) ).

cnf(c_39650,plain,
    ( ~ member(ordered_pair(member_of(sP1_iProver_def),X0),cross_product(universal_class,universal_class))
    | ~ member(X0,image(X1,image(X2,sP1_iProver_def)))
    | member(ordered_pair(member_of(sP1_iProver_def),X0),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_38619,c_159]) ).

cnf(c_40624,plain,
    singleton(member_of(singleton(singleton(singleton(sP0_iProver_def))))) = singleton(singleton(singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_38634,c_88]) ).

cnf(c_40625,plain,
    member_of(singleton(singleton(singleton(sP0_iProver_def)))) = singleton(singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_38634,c_91]) ).

cnf(c_40645,plain,
    ( ~ subclass(unordered_pair(singleton(sP0_iProver_def),X0),sP3_iProver_def)
    | unordered_pair(singleton(sP0_iProver_def),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_38627,c_107]) ).

cnf(c_40648,plain,
    ( ~ subclass(unordered_pair(singleton(sP0_iProver_def),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_38627,c_54]) ).

cnf(c_40656,plain,
    ( ~ subclass(unordered_pair(singleton(sP0_iProver_def),X0),null_class)
    | unordered_pair(singleton(sP0_iProver_def),X0) = null_class ),
    inference(superposition,[status(thm)],[c_38629,c_107]) ).

cnf(c_40659,plain,
    ( ~ subclass(unordered_pair(singleton(sP0_iProver_def),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_38629,c_54]) ).

cnf(c_40681,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP0_iProver_def)),sP3_iProver_def)
    | unordered_pair(X0,singleton(sP0_iProver_def)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_38653,c_107]) ).

cnf(c_40684,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP0_iProver_def)),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_38653,c_54]) ).

cnf(c_40755,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP0_iProver_def)),null_class)
    | unordered_pair(X0,singleton(sP0_iProver_def)) = null_class ),
    inference(superposition,[status(thm)],[c_38655,c_107]) ).

cnf(c_40758,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP0_iProver_def)),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_38655,c_54]) ).

cnf(c_40827,plain,
    subclass(sP3_iProver_def,ordered_pair(member_of(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_39615,c_16382]) ).

cnf(c_40829,plain,
    subclass(null_class,ordered_pair(member_of(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_39615,c_11575]) ).

cnf(c_40971,plain,
    subclass(sP1_iProver_def,singleton(member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_112,c_39634]) ).

cnf(c_40973,plain,
    ( ~ subclass(unordered_pair(X0,member_of(sP1_iProver_def)),sP1_iProver_def)
    | unordered_pair(X0,member_of(sP1_iProver_def)) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_39634,c_107]) ).

cnf(c_40974,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_39634,c_11006]) ).

cnf(c_40975,plain,
    subclass(null_class,unordered_pair(X0,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_39634,c_10981]) ).

cnf(c_40976,plain,
    ( ~ subclass(unordered_pair(X0,member_of(sP1_iProver_def)),X1)
    | subclass(sP1_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_39634,c_54]) ).

cnf(c_40977,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,unordered_pair(X1,member_of(sP1_iProver_def))) ),
    inference(superposition,[status(thm)],[c_39634,c_101]) ).

cnf(c_41352,plain,
    subclass(sP3_iProver_def,singleton(member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_40971,c_11006]) ).

cnf(c_41353,plain,
    subclass(null_class,singleton(member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_40971,c_10981]) ).

cnf(c_41354,plain,
    ( ~ subclass(singleton(member_of(sP1_iProver_def)),X0)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_40971,c_54]) ).

cnf(c_41355,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,singleton(member_of(sP1_iProver_def))) ),
    inference(superposition,[status(thm)],[c_40971,c_101]) ).

cnf(c_41681,plain,
    ( ~ subclass(singleton(member_of(sP1_iProver_def)),sP3_iProver_def)
    | singleton(member_of(sP1_iProver_def)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_41352,c_107]) ).

cnf(c_41691,plain,
    ( ~ subclass(singleton(member_of(sP1_iProver_def)),null_class)
    | singleton(member_of(sP1_iProver_def)) = null_class ),
    inference(superposition,[status(thm)],[c_41353,c_107]) ).

cnf(c_41701,plain,
    ( ~ subclass(unordered_pair(member_of(sP1_iProver_def),X0),sP1_iProver_def)
    | unordered_pair(member_of(sP1_iProver_def),X0) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_39635,c_107]) ).

cnf(c_41702,plain,
    subclass(sP3_iProver_def,unordered_pair(member_of(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_39635,c_11006]) ).

cnf(c_41703,plain,
    subclass(null_class,unordered_pair(member_of(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_39635,c_10981]) ).

cnf(c_41704,plain,
    ( ~ subclass(unordered_pair(member_of(sP1_iProver_def),X0),X1)
    | subclass(sP1_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_39635,c_54]) ).

cnf(c_41705,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,unordered_pair(member_of(sP1_iProver_def),X1)) ),
    inference(superposition,[status(thm)],[c_39635,c_101]) ).

cnf(c_41784,plain,
    ( ~ member(X0,singleton(singleton(sP0_iProver_def)))
    | member_of(singleton(singleton(sP0_iProver_def))) = X0 ),
    inference(superposition,[status(thm)],[c_21975,c_95]) ).

cnf(c_41811,plain,
    ( ~ subclass(ordered_pair(member_of(sP1_iProver_def),X0),sP3_iProver_def)
    | ordered_pair(member_of(sP1_iProver_def),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_40827,c_107]) ).

cnf(c_41814,plain,
    ( ~ subclass(ordered_pair(member_of(sP1_iProver_def),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_40827,c_54]) ).

cnf(c_41859,plain,
    ( ~ subclass(ordered_pair(member_of(sP1_iProver_def),X0),null_class)
    | ordered_pair(member_of(sP1_iProver_def),X0) = null_class ),
    inference(superposition,[status(thm)],[c_40829,c_107]) ).

cnf(c_41862,plain,
    ( ~ subclass(ordered_pair(member_of(sP1_iProver_def),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_40829,c_54]) ).

cnf(c_42204,plain,
    ( ~ subclass(unordered_pair(X0,member_of(sP1_iProver_def)),sP3_iProver_def)
    | unordered_pair(X0,member_of(sP1_iProver_def)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_40974,c_107]) ).

cnf(c_42207,plain,
    ( ~ subclass(unordered_pair(X0,member_of(sP1_iProver_def)),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_40974,c_54]) ).

cnf(c_42214,plain,
    ( ~ subclass(unordered_pair(X0,member_of(sP1_iProver_def)),null_class)
    | unordered_pair(X0,member_of(sP1_iProver_def)) = null_class ),
    inference(superposition,[status(thm)],[c_40975,c_107]) ).

cnf(c_42217,plain,
    ( ~ subclass(unordered_pair(X0,member_of(sP1_iProver_def)),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_40975,c_54]) ).

cnf(c_42223,plain,
    ( ~ subclass(unordered_pair(member_of(sP1_iProver_def),X0),sP3_iProver_def)
    | unordered_pair(member_of(sP1_iProver_def),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_41702,c_107]) ).

cnf(c_42226,plain,
    ( ~ subclass(unordered_pair(member_of(sP1_iProver_def),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_41702,c_54]) ).

cnf(c_42409,plain,
    ( ~ subclass(unordered_pair(member_of(sP1_iProver_def),X0),null_class)
    | unordered_pair(member_of(sP1_iProver_def),X0) = null_class ),
    inference(superposition,[status(thm)],[c_41703,c_107]) ).

cnf(c_42412,plain,
    ( ~ subclass(unordered_pair(member_of(sP1_iProver_def),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_41703,c_54]) ).

cnf(c_42418,plain,
    member(singleton(sP0_iProver_def),ordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_113,c_38641]) ).

cnf(c_42442,plain,
    ( ~ subclass(ordered_pair(member_of(sP1_iProver_def),X0),singleton(sP1_iProver_def))
    | ordered_pair(member_of(sP1_iProver_def),X0) = singleton(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_39614,c_107]) ).

cnf(c_42445,plain,
    ( ~ subclass(ordered_pair(member_of(sP1_iProver_def),X0),X1)
    | subclass(singleton(sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_39614,c_54]) ).

cnf(c_42446,plain,
    ( ~ member(X0,singleton(sP1_iProver_def))
    | member(X0,ordered_pair(member_of(sP1_iProver_def),X1)) ),
    inference(superposition,[status(thm)],[c_39614,c_101]) ).

cnf(c_42449,plain,
    member(regular(sP1_iProver_def),x),
    inference(global_subsumption_just,[status(thm)],[c_21996,c_5941,c_8116,c_8198]) ).

cnf(c_42453,plain,
    member(regular(sP1_iProver_def),universal_class),
    inference(superposition,[status(thm)],[c_42449,c_12562]) ).

cnf(c_42501,plain,
    singleton(member_of(singleton(regular(sP1_iProver_def)))) = singleton(regular(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_42453,c_88]) ).

cnf(c_42502,plain,
    member_of(singleton(regular(sP1_iProver_def))) = regular(sP1_iProver_def),
    inference(superposition,[status(thm)],[c_42453,c_91]) ).

cnf(c_42923,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),sP1_iProver_def)
    | ~ function(universal_class)
    | cross_product(universal_class,universal_class) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_22219,c_107]) ).

cnf(c_42926,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | ~ function(universal_class)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_22219,c_54]) ).

cnf(c_42927,plain,
    ( ~ member(X0,sP1_iProver_def)
    | ~ function(universal_class)
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_22219,c_101]) ).

cnf(c_42967,plain,
    ( singleton(member_of(singleton(not_subclass_element(sP1_iProver_def,X0)))) = singleton(not_subclass_element(sP1_iProver_def,X0))
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_22236,c_88]) ).

cnf(c_42968,plain,
    ( member_of(singleton(not_subclass_element(sP1_iProver_def,X0))) = not_subclass_element(sP1_iProver_def,X0)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_22236,c_91]) ).

cnf(c_42977,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),identity_relation)
    | ~ function(universal_class)
    | cross_product(universal_class,universal_class) = identity_relation ),
    inference(superposition,[status(thm)],[c_22394,c_107]) ).

cnf(c_42980,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | ~ function(universal_class)
    | subclass(identity_relation,X0) ),
    inference(superposition,[status(thm)],[c_22394,c_54]) ).

cnf(c_42981,plain,
    ( ~ member(X0,identity_relation)
    | ~ function(universal_class)
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_22394,c_101]) ).

cnf(c_42985,plain,
    subclass(sP3_iProver_def,ordered_pair(member_of(singleton(null_class)),X0)),
    inference(superposition,[status(thm)],[c_30929,c_16382]) ).

cnf(c_42987,plain,
    subclass(null_class,ordered_pair(member_of(singleton(null_class)),X0)),
    inference(superposition,[status(thm)],[c_30929,c_11575]) ).

cnf(c_42998,plain,
    subclass(sP3_iProver_def,ordered_pair(member_of(singleton(sP3_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_7302,c_42985]) ).

cnf(c_42999,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(null_class)),X0),sP3_iProver_def)
    | ordered_pair(member_of(singleton(null_class)),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_42985,c_107]) ).

cnf(c_43002,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(null_class)),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_42985,c_54]) ).

cnf(c_43430,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(null_class)),X0),null_class)
    | ordered_pair(member_of(singleton(null_class)),X0) = null_class ),
    inference(superposition,[status(thm)],[c_42987,c_107]) ).

cnf(c_43433,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(null_class)),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_42987,c_54]) ).

cnf(c_43436,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP3_iProver_def)),X0),sP3_iProver_def)
    | ordered_pair(member_of(singleton(sP3_iProver_def)),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_42998,c_107]) ).

cnf(c_43438,plain,
    subclass(null_class,ordered_pair(member_of(singleton(sP3_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_42998,c_10981]) ).

cnf(c_43439,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP3_iProver_def)),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_42998,c_54]) ).

cnf(c_43479,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP3_iProver_def)),X0),null_class)
    | ordered_pair(member_of(singleton(sP3_iProver_def)),X0) = null_class ),
    inference(superposition,[status(thm)],[c_43438,c_107]) ).

cnf(c_43482,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP3_iProver_def)),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_43438,c_54]) ).

cnf(c_43538,plain,
    subclass(singleton(null_class),singleton(member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_112,c_30948]) ).

cnf(c_43539,plain,
    subclass(singleton(null_class),unordered_pair(X0,null_class)),
    inference(superposition,[status(thm)],[c_9488,c_30948]) ).

cnf(c_43541,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(null_class))),singleton(null_class))
    | unordered_pair(X0,member_of(singleton(null_class))) = singleton(null_class) ),
    inference(superposition,[status(thm)],[c_30948,c_107]) ).

cnf(c_43544,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(null_class))),X1)
    | subclass(singleton(null_class),X1) ),
    inference(superposition,[status(thm)],[c_30948,c_54]) ).

cnf(c_43545,plain,
    ( ~ member(X0,singleton(null_class))
    | member(X0,unordered_pair(X1,member_of(singleton(null_class)))) ),
    inference(superposition,[status(thm)],[c_30948,c_101]) ).

cnf(c_43546,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_30948,c_15360]) ).

cnf(c_43547,plain,
    subclass(null_class,unordered_pair(X0,member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_30948,c_15342]) ).

cnf(c_43729,plain,
    subclass(singleton(null_class),unordered_pair(null_class,X0)),
    inference(superposition,[status(thm)],[c_65,c_43539]) ).

cnf(c_43732,plain,
    subclass(singleton(sP3_iProver_def),unordered_pair(X0,sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_43539]) ).

cnf(c_43733,plain,
    ( ~ subclass(unordered_pair(X0,null_class),singleton(null_class))
    | unordered_pair(X0,null_class) = singleton(null_class) ),
    inference(superposition,[status(thm)],[c_43539,c_107]) ).

cnf(c_43736,plain,
    ( ~ subclass(unordered_pair(X0,null_class),X1)
    | subclass(singleton(null_class),X1) ),
    inference(superposition,[status(thm)],[c_43539,c_54]) ).

cnf(c_43737,plain,
    ( ~ member(X0,singleton(null_class))
    | member(X0,unordered_pair(X1,null_class)) ),
    inference(superposition,[status(thm)],[c_43539,c_101]) ).

cnf(c_43738,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,null_class)),
    inference(superposition,[status(thm)],[c_43539,c_15360]) ).

cnf(c_43739,plain,
    subclass(null_class,unordered_pair(X0,null_class)),
    inference(superposition,[status(thm)],[c_43539,c_15342]) ).

cnf(c_43921,plain,
    subclass(sP3_iProver_def,unordered_pair(null_class,X0)),
    inference(superposition,[status(thm)],[c_65,c_43738]) ).

cnf(c_43924,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_43738]) ).

cnf(c_43925,plain,
    ( ~ subclass(unordered_pair(X0,null_class),sP3_iProver_def)
    | unordered_pair(X0,null_class) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_43738,c_107]) ).

cnf(c_43928,plain,
    ( ~ subclass(unordered_pair(X0,null_class),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_43738,c_54]) ).

cnf(c_43989,plain,
    subclass(null_class,unordered_pair(null_class,X0)),
    inference(superposition,[status(thm)],[c_65,c_43739]) ).

cnf(c_43993,plain,
    ( ~ subclass(unordered_pair(X0,null_class),null_class)
    | unordered_pair(X0,null_class) = null_class ),
    inference(superposition,[status(thm)],[c_43739,c_107]) ).

cnf(c_43996,plain,
    ( ~ subclass(unordered_pair(X0,null_class),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_43739,c_54]) ).

cnf(c_44445,plain,
    subclass(sP3_iProver_def,unordered_pair(sP3_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_7302,c_43921]) ).

cnf(c_44446,plain,
    ( ~ subclass(unordered_pair(null_class,X0),sP3_iProver_def)
    | unordered_pair(null_class,X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_43921,c_107]) ).

cnf(c_44449,plain,
    ( ~ subclass(unordered_pair(null_class,X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_43921,c_54]) ).

cnf(c_44454,plain,
    ( ~ subclass(unordered_pair(X0,sP3_iProver_def),sP3_iProver_def)
    | unordered_pair(X0,sP3_iProver_def) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_43924,c_107]) ).

cnf(c_44456,plain,
    subclass(null_class,unordered_pair(X0,sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_43924,c_10981]) ).

cnf(c_44457,plain,
    ( ~ subclass(unordered_pair(X0,sP3_iProver_def),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_43924,c_54]) ).

cnf(c_44464,plain,
    ( ~ subclass(unordered_pair(null_class,X0),null_class)
    | unordered_pair(null_class,X0) = null_class ),
    inference(superposition,[status(thm)],[c_43989,c_107]) ).

cnf(c_44467,plain,
    ( ~ subclass(unordered_pair(null_class,X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_43989,c_54]) ).

cnf(c_44473,plain,
    subclass(singleton(sP3_iProver_def),unordered_pair(sP3_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_7302,c_43729]) ).

cnf(c_44474,plain,
    ( ~ subclass(unordered_pair(null_class,X0),singleton(null_class))
    | unordered_pair(null_class,X0) = singleton(null_class) ),
    inference(superposition,[status(thm)],[c_43729,c_107]) ).

cnf(c_44477,plain,
    ( ~ subclass(unordered_pair(null_class,X0),X1)
    | subclass(singleton(null_class),X1) ),
    inference(superposition,[status(thm)],[c_43729,c_54]) ).

cnf(c_44478,plain,
    ( ~ member(X0,singleton(null_class))
    | member(X0,unordered_pair(null_class,X1)) ),
    inference(superposition,[status(thm)],[c_43729,c_101]) ).

cnf(c_44946,plain,
    subclass(singleton(sP3_iProver_def),singleton(member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_7302,c_43538]) ).

cnf(c_44950,plain,
    ( ~ subclass(singleton(member_of(singleton(null_class))),X0)
    | subclass(singleton(null_class),X0) ),
    inference(superposition,[status(thm)],[c_43538,c_54]) ).

cnf(c_44951,plain,
    ( ~ member(X0,singleton(null_class))
    | member(X0,singleton(member_of(singleton(null_class)))) ),
    inference(superposition,[status(thm)],[c_43538,c_101]) ).

cnf(c_44952,plain,
    subclass(sP3_iProver_def,singleton(member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_43538,c_15360]) ).

cnf(c_44953,plain,
    subclass(null_class,singleton(member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_43538,c_15342]) ).

cnf(c_44991,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(null_class)),X0),singleton(null_class))
    | unordered_pair(member_of(singleton(null_class)),X0) = singleton(null_class) ),
    inference(superposition,[status(thm)],[c_30949,c_107]) ).

cnf(c_44994,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(null_class)),X0),X1)
    | subclass(singleton(null_class),X1) ),
    inference(superposition,[status(thm)],[c_30949,c_54]) ).

cnf(c_44995,plain,
    ( ~ member(X0,singleton(null_class))
    | member(X0,unordered_pair(member_of(singleton(null_class)),X1)) ),
    inference(superposition,[status(thm)],[c_30949,c_101]) ).

cnf(c_44996,plain,
    subclass(sP3_iProver_def,unordered_pair(member_of(singleton(null_class)),X0)),
    inference(superposition,[status(thm)],[c_30949,c_15360]) ).

cnf(c_44997,plain,
    subclass(null_class,unordered_pair(member_of(singleton(null_class)),X0)),
    inference(superposition,[status(thm)],[c_30949,c_15342]) ).

cnf(c_45009,plain,
    subclass(singleton(omega),singleton(member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_112,c_33262]) ).

cnf(c_45010,plain,
    subclass(singleton(omega),unordered_pair(X0,omega)),
    inference(superposition,[status(thm)],[c_9494,c_33262]) ).

cnf(c_45011,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(omega))),singleton(omega))
    | unordered_pair(X0,member_of(singleton(omega))) = singleton(omega) ),
    inference(superposition,[status(thm)],[c_33262,c_107]) ).

cnf(c_45014,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(omega))),X1)
    | subclass(singleton(omega),X1) ),
    inference(superposition,[status(thm)],[c_33262,c_54]) ).

cnf(c_45015,plain,
    ( ~ member(X0,singleton(omega))
    | member(X0,unordered_pair(X1,member_of(singleton(omega)))) ),
    inference(superposition,[status(thm)],[c_33262,c_101]) ).

cnf(c_45016,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_33262,c_15360]) ).

cnf(c_45017,plain,
    subclass(null_class,unordered_pair(X0,member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_33262,c_15342]) ).

cnf(c_45300,plain,
    ( ~ subclass(unordered_pair(sP3_iProver_def,X0),sP3_iProver_def)
    | unordered_pair(sP3_iProver_def,X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_44445,c_107]) ).

cnf(c_45302,plain,
    subclass(null_class,unordered_pair(sP3_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_44445,c_10981]) ).

cnf(c_45303,plain,
    ( ~ subclass(unordered_pair(sP3_iProver_def,X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_44445,c_54]) ).

cnf(c_45380,plain,
    ( ~ subclass(unordered_pair(X0,sP3_iProver_def),null_class)
    | unordered_pair(X0,sP3_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_44456,c_107]) ).

cnf(c_45383,plain,
    ( ~ subclass(unordered_pair(X0,sP3_iProver_def),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_44456,c_54]) ).

cnf(c_45406,plain,
    ( ~ subclass(unordered_pair(sP3_iProver_def,X0),null_class)
    | unordered_pair(sP3_iProver_def,X0) = null_class ),
    inference(superposition,[status(thm)],[c_45302,c_107]) ).

cnf(c_45409,plain,
    ( ~ subclass(unordered_pair(sP3_iProver_def,X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_45302,c_54]) ).

cnf(c_45414,plain,
    ( ~ subclass(unordered_pair(X0,sP3_iProver_def),singleton(sP3_iProver_def))
    | unordered_pair(X0,sP3_iProver_def) = singleton(sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_43732,c_107]) ).

cnf(c_45417,plain,
    ( ~ subclass(unordered_pair(X0,sP3_iProver_def),X1)
    | subclass(singleton(sP3_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_43732,c_54]) ).

cnf(c_45418,plain,
    ( ~ member(X0,singleton(sP3_iProver_def))
    | member(X0,unordered_pair(X1,sP3_iProver_def)) ),
    inference(superposition,[status(thm)],[c_43732,c_101]) ).

cnf(c_45520,plain,
    ( ~ subclass(unordered_pair(sP3_iProver_def,X0),singleton(sP3_iProver_def))
    | unordered_pair(sP3_iProver_def,X0) = singleton(sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_44473,c_107]) ).

cnf(c_45523,plain,
    ( ~ subclass(unordered_pair(sP3_iProver_def,X0),X1)
    | subclass(singleton(sP3_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_44473,c_54]) ).

cnf(c_45524,plain,
    ( ~ member(X0,singleton(sP3_iProver_def))
    | member(X0,unordered_pair(sP3_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_44473,c_101]) ).

cnf(c_45899,plain,
    subclass(sP3_iProver_def,singleton(member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_7302,c_44952]) ).

cnf(c_45900,plain,
    ( ~ subclass(singleton(member_of(singleton(null_class))),sP3_iProver_def)
    | singleton(member_of(singleton(null_class))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_44952,c_107]) ).

cnf(c_45930,plain,
    ( ~ subclass(singleton(member_of(singleton(null_class))),null_class)
    | singleton(member_of(singleton(null_class))) = null_class ),
    inference(superposition,[status(thm)],[c_44953,c_107]) ).

cnf(c_45936,plain,
    subclass(singleton(omega),unordered_pair(omega,X0)),
    inference(superposition,[status(thm)],[c_65,c_45010]) ).

cnf(c_45939,plain,
    ( ~ subclass(unordered_pair(X0,omega),singleton(omega))
    | unordered_pair(X0,omega) = singleton(omega) ),
    inference(superposition,[status(thm)],[c_45010,c_107]) ).

cnf(c_45942,plain,
    ( ~ subclass(unordered_pair(X0,omega),X1)
    | subclass(singleton(omega),X1) ),
    inference(superposition,[status(thm)],[c_45010,c_54]) ).

cnf(c_45943,plain,
    ( ~ member(X0,singleton(omega))
    | member(X0,unordered_pair(X1,omega)) ),
    inference(superposition,[status(thm)],[c_45010,c_101]) ).

cnf(c_45944,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,omega)),
    inference(superposition,[status(thm)],[c_45010,c_15360]) ).

cnf(c_45945,plain,
    subclass(null_class,unordered_pair(X0,omega)),
    inference(superposition,[status(thm)],[c_45010,c_15342]) ).

cnf(c_45996,plain,
    subclass(sP3_iProver_def,unordered_pair(omega,X0)),
    inference(superposition,[status(thm)],[c_65,c_45944]) ).

cnf(c_45999,plain,
    ( ~ subclass(unordered_pair(X0,omega),sP3_iProver_def)
    | unordered_pair(X0,omega) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_45944,c_107]) ).

cnf(c_46002,plain,
    ( ~ subclass(unordered_pair(X0,omega),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_45944,c_54]) ).

cnf(c_46044,plain,
    subclass(null_class,unordered_pair(omega,X0)),
    inference(superposition,[status(thm)],[c_65,c_45945]) ).

cnf(c_46047,plain,
    ( ~ subclass(unordered_pair(X0,omega),null_class)
    | unordered_pair(X0,omega) = null_class ),
    inference(superposition,[status(thm)],[c_45945,c_107]) ).

cnf(c_46050,plain,
    ( ~ subclass(unordered_pair(X0,omega),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_45945,c_54]) ).

cnf(c_46094,plain,
    ( ~ subclass(unordered_pair(omega,X0),sP3_iProver_def)
    | unordered_pair(omega,X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_45996,c_107]) ).

cnf(c_46097,plain,
    ( ~ subclass(unordered_pair(omega,X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_45996,c_54]) ).

cnf(c_46126,plain,
    ( ~ subclass(unordered_pair(omega,X0),null_class)
    | unordered_pair(omega,X0) = null_class ),
    inference(superposition,[status(thm)],[c_46044,c_107]) ).

cnf(c_46129,plain,
    ( ~ subclass(unordered_pair(omega,X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_46044,c_54]) ).

cnf(c_46235,plain,
    ( ~ subclass(unordered_pair(omega,X0),singleton(omega))
    | unordered_pair(omega,X0) = singleton(omega) ),
    inference(superposition,[status(thm)],[c_45936,c_107]) ).

cnf(c_46238,plain,
    ( ~ subclass(unordered_pair(omega,X0),X1)
    | subclass(singleton(omega),X1) ),
    inference(superposition,[status(thm)],[c_45936,c_54]) ).

cnf(c_46239,plain,
    ( ~ member(X0,singleton(omega))
    | member(X0,unordered_pair(omega,X1)) ),
    inference(superposition,[status(thm)],[c_45936,c_101]) ).

cnf(c_46326,plain,
    ( ~ subclass(singleton(member_of(singleton(omega))),X0)
    | subclass(singleton(omega),X0) ),
    inference(superposition,[status(thm)],[c_45009,c_54]) ).

cnf(c_46327,plain,
    ( ~ member(X0,singleton(omega))
    | member(X0,singleton(member_of(singleton(omega)))) ),
    inference(superposition,[status(thm)],[c_45009,c_101]) ).

cnf(c_46328,plain,
    subclass(sP3_iProver_def,singleton(member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_45009,c_15360]) ).

cnf(c_46329,plain,
    subclass(null_class,singleton(member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_45009,c_15342]) ).

cnf(c_46516,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(omega)),X0),singleton(omega))
    | unordered_pair(member_of(singleton(omega)),X0) = singleton(omega) ),
    inference(superposition,[status(thm)],[c_33263,c_107]) ).

cnf(c_46519,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(omega)),X0),X1)
    | subclass(singleton(omega),X1) ),
    inference(superposition,[status(thm)],[c_33263,c_54]) ).

cnf(c_46520,plain,
    ( ~ member(X0,singleton(omega))
    | member(X0,unordered_pair(member_of(singleton(omega)),X1)) ),
    inference(superposition,[status(thm)],[c_33263,c_101]) ).

cnf(c_46521,plain,
    subclass(sP3_iProver_def,unordered_pair(member_of(singleton(omega)),X0)),
    inference(superposition,[status(thm)],[c_33263,c_15360]) ).

cnf(c_46522,plain,
    subclass(null_class,unordered_pair(member_of(singleton(omega)),X0)),
    inference(superposition,[status(thm)],[c_33263,c_15342]) ).

cnf(c_46618,plain,
    subclass(singleton(sP1_iProver_def),singleton(member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_112,c_35423]) ).

cnf(c_46619,plain,
    subclass(singleton(sP1_iProver_def),unordered_pair(X0,sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_9498,c_35423]) ).

cnf(c_46620,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP1_iProver_def))),singleton(sP1_iProver_def))
    | unordered_pair(X0,member_of(singleton(sP1_iProver_def))) = singleton(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_35423,c_107]) ).

cnf(c_46623,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP1_iProver_def))),X1)
    | subclass(singleton(sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_35423,c_54]) ).

cnf(c_46624,plain,
    ( ~ member(X0,singleton(sP1_iProver_def))
    | member(X0,unordered_pair(X1,member_of(singleton(sP1_iProver_def)))) ),
    inference(superposition,[status(thm)],[c_35423,c_101]) ).

cnf(c_46625,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_35423,c_15360]) ).

cnf(c_46626,plain,
    subclass(null_class,unordered_pair(X0,member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_35423,c_15342]) ).

cnf(c_46793,plain,
    ( ~ subclass(singleton(member_of(singleton(sP3_iProver_def))),sP3_iProver_def)
    | singleton(member_of(singleton(sP3_iProver_def))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_45899,c_107]) ).

cnf(c_46795,plain,
    subclass(null_class,singleton(member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_45899,c_10981]) ).

cnf(c_46977,plain,
    ( ~ subclass(singleton(member_of(singleton(omega))),sP3_iProver_def)
    | singleton(member_of(singleton(omega))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_46328,c_107]) ).

cnf(c_46987,plain,
    ( ~ subclass(singleton(member_of(singleton(omega))),null_class)
    | singleton(member_of(singleton(omega))) = null_class ),
    inference(superposition,[status(thm)],[c_46329,c_107]) ).

cnf(c_47192,plain,
    subclass(singleton(sP1_iProver_def),unordered_pair(sP1_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_65,c_46619]) ).

cnf(c_47195,plain,
    ( ~ subclass(unordered_pair(X0,sP1_iProver_def),singleton(sP1_iProver_def))
    | unordered_pair(X0,sP1_iProver_def) = singleton(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_46619,c_107]) ).

cnf(c_47198,plain,
    ( ~ subclass(unordered_pair(X0,sP1_iProver_def),X1)
    | subclass(singleton(sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_46619,c_54]) ).

cnf(c_47199,plain,
    ( ~ member(X0,singleton(sP1_iProver_def))
    | member(X0,unordered_pair(X1,sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_46619,c_101]) ).

cnf(c_47206,plain,
    ( ~ subclass(singleton(member_of(singleton(sP3_iProver_def))),null_class)
    | singleton(member_of(singleton(sP3_iProver_def))) = null_class ),
    inference(superposition,[status(thm)],[c_46795,c_107]) ).

cnf(c_47215,plain,
    ( ~ subclass(unordered_pair(sP1_iProver_def,X0),singleton(sP1_iProver_def))
    | unordered_pair(sP1_iProver_def,X0) = singleton(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_47192,c_107]) ).

cnf(c_47218,plain,
    ( ~ subclass(unordered_pair(sP1_iProver_def,X0),X1)
    | subclass(singleton(sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_47192,c_54]) ).

cnf(c_47219,plain,
    ( ~ member(X0,singleton(sP1_iProver_def))
    | member(X0,unordered_pair(sP1_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_47192,c_101]) ).

cnf(c_47283,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_7302,c_43546]) ).

cnf(c_47284,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(null_class))),sP3_iProver_def)
    | unordered_pair(X0,member_of(singleton(null_class))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_43546,c_107]) ).

cnf(c_47287,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(null_class))),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_43546,c_54]) ).

cnf(c_47752,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(null_class))),null_class)
    | unordered_pair(X0,member_of(singleton(null_class))) = null_class ),
    inference(superposition,[status(thm)],[c_43547,c_107]) ).

cnf(c_47755,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(null_class))),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_43547,c_54]) ).

cnf(c_47774,plain,
    ( ~ subclass(singleton(member_of(singleton(sP3_iProver_def))),X0)
    | subclass(singleton(sP3_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_44946,c_54]) ).

cnf(c_47775,plain,
    ( ~ member(X0,singleton(sP3_iProver_def))
    | member(X0,singleton(member_of(singleton(sP3_iProver_def)))) ),
    inference(superposition,[status(thm)],[c_44946,c_101]) ).

cnf(c_47783,plain,
    subclass(sP3_iProver_def,unordered_pair(member_of(singleton(sP3_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_7302,c_44996]) ).

cnf(c_47784,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(null_class)),X0),sP3_iProver_def)
    | unordered_pair(member_of(singleton(null_class)),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_44996,c_107]) ).

cnf(c_47787,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(null_class)),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_44996,c_54]) ).

cnf(c_47873,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(null_class)),X0),null_class)
    | unordered_pair(member_of(singleton(null_class)),X0) = null_class ),
    inference(superposition,[status(thm)],[c_44997,c_107]) ).

cnf(c_47876,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(null_class)),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_44997,c_54]) ).

cnf(c_48018,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(omega))),sP3_iProver_def)
    | unordered_pair(X0,member_of(singleton(omega))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_45016,c_107]) ).

cnf(c_48021,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(omega))),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_45016,c_54]) ).

cnf(c_48029,plain,
    ( ~ subclass(singleton(member_of(singleton(sP1_iProver_def))),X0)
    | subclass(singleton(sP1_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_46618,c_54]) ).

cnf(c_48030,plain,
    ( ~ member(X0,singleton(sP1_iProver_def))
    | member(X0,singleton(member_of(singleton(sP1_iProver_def)))) ),
    inference(superposition,[status(thm)],[c_46618,c_101]) ).

cnf(c_48031,plain,
    subclass(sP3_iProver_def,singleton(member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_46618,c_15360]) ).

cnf(c_48032,plain,
    subclass(null_class,singleton(member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_46618,c_15342]) ).

cnf(c_48038,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP1_iProver_def)),X0),singleton(sP1_iProver_def))
    | unordered_pair(member_of(singleton(sP1_iProver_def)),X0) = singleton(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_35424,c_107]) ).

cnf(c_48041,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP1_iProver_def)),X0),X1)
    | subclass(singleton(sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_35424,c_54]) ).

cnf(c_48042,plain,
    ( ~ member(X0,singleton(sP1_iProver_def))
    | member(X0,unordered_pair(member_of(singleton(sP1_iProver_def)),X1)) ),
    inference(superposition,[status(thm)],[c_35424,c_101]) ).

cnf(c_48043,plain,
    subclass(sP3_iProver_def,unordered_pair(member_of(singleton(sP1_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_35424,c_15360]) ).

cnf(c_48044,plain,
    subclass(null_class,unordered_pair(member_of(singleton(sP1_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_35424,c_15342]) ).

cnf(c_48097,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP3_iProver_def))),singleton(sP3_iProver_def))
    | unordered_pair(X0,member_of(singleton(sP3_iProver_def))) = singleton(sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_36598,c_107]) ).

cnf(c_48100,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP3_iProver_def))),X1)
    | subclass(singleton(sP3_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_36598,c_54]) ).

cnf(c_48101,plain,
    ( ~ member(X0,singleton(sP3_iProver_def))
    | member(X0,unordered_pair(X1,member_of(singleton(sP3_iProver_def)))) ),
    inference(superposition,[status(thm)],[c_36598,c_101]) ).

cnf(c_48103,plain,
    subclass(null_class,unordered_pair(X0,member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_36598,c_15342]) ).

cnf(c_48271,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP3_iProver_def)),X0),singleton(sP3_iProver_def))
    | unordered_pair(member_of(singleton(sP3_iProver_def)),X0) = singleton(sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_36599,c_107]) ).

cnf(c_48274,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP3_iProver_def)),X0),X1)
    | subclass(singleton(sP3_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_36599,c_54]) ).

cnf(c_48275,plain,
    ( ~ member(X0,singleton(sP3_iProver_def))
    | member(X0,unordered_pair(member_of(singleton(sP3_iProver_def)),X1)) ),
    inference(superposition,[status(thm)],[c_36599,c_101]) ).

cnf(c_48277,plain,
    subclass(null_class,unordered_pair(member_of(singleton(sP3_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_36599,c_15342]) ).

cnf(c_48332,plain,
    ( ~ subclass(singleton(member_of(singleton(sP1_iProver_def))),sP3_iProver_def)
    | singleton(member_of(singleton(sP1_iProver_def))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_48031,c_107]) ).

cnf(c_48393,plain,
    ( ~ subclass(singleton(member_of(singleton(sP1_iProver_def))),null_class)
    | singleton(member_of(singleton(sP1_iProver_def))) = null_class ),
    inference(superposition,[status(thm)],[c_48032,c_107]) ).

cnf(c_48460,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(omega))),null_class)
    | unordered_pair(X0,member_of(singleton(omega))) = null_class ),
    inference(superposition,[status(thm)],[c_45017,c_107]) ).

cnf(c_48463,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(omega))),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_45017,c_54]) ).

cnf(c_48513,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(omega)),X0),sP3_iProver_def)
    | unordered_pair(member_of(singleton(omega)),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_46521,c_107]) ).

cnf(c_48516,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(omega)),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_46521,c_54]) ).

cnf(c_48558,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(omega)),X0),null_class)
    | unordered_pair(member_of(singleton(omega)),X0) = null_class ),
    inference(superposition,[status(thm)],[c_46522,c_107]) ).

cnf(c_48561,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(omega)),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_46522,c_54]) ).

cnf(c_48655,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP1_iProver_def))),sP3_iProver_def)
    | unordered_pair(X0,member_of(singleton(sP1_iProver_def))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_46625,c_107]) ).

cnf(c_48658,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP1_iProver_def))),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_46625,c_54]) ).

cnf(c_48680,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP1_iProver_def))),null_class)
    | unordered_pair(X0,member_of(singleton(sP1_iProver_def))) = null_class ),
    inference(superposition,[status(thm)],[c_46626,c_107]) ).

cnf(c_48683,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP1_iProver_def))),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_46626,c_54]) ).

cnf(c_48689,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP3_iProver_def))),sP3_iProver_def)
    | unordered_pair(X0,member_of(singleton(sP3_iProver_def))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_47283,c_107]) ).

cnf(c_48692,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP3_iProver_def))),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_47283,c_54]) ).

cnf(c_48723,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP3_iProver_def)),X0),sP3_iProver_def)
    | unordered_pair(member_of(singleton(sP3_iProver_def)),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_47783,c_107]) ).

cnf(c_48726,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP3_iProver_def)),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_47783,c_54]) ).

cnf(c_48761,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP1_iProver_def)),X0),sP3_iProver_def)
    | unordered_pair(member_of(singleton(sP1_iProver_def)),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_48043,c_107]) ).

cnf(c_48764,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP1_iProver_def)),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_48043,c_54]) ).

cnf(c_48773,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP1_iProver_def)),X0),null_class)
    | unordered_pair(member_of(singleton(sP1_iProver_def)),X0) = null_class ),
    inference(superposition,[status(thm)],[c_48044,c_107]) ).

cnf(c_48776,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP1_iProver_def)),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_48044,c_54]) ).

cnf(c_48855,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP3_iProver_def))),null_class)
    | unordered_pair(X0,member_of(singleton(sP3_iProver_def))) = null_class ),
    inference(superposition,[status(thm)],[c_48103,c_107]) ).

cnf(c_48858,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP3_iProver_def))),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_48103,c_54]) ).

cnf(c_49118,plain,
    union(union(X0,X1),intersection(complement(X0),complement(X1))) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_126,c_37168]) ).

cnf(c_49119,plain,
    union(power_class(X0),image(element_relation,complement(X0))) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_155,c_37168]) ).

cnf(c_49120,plain,
    union(diagonalise(X0),domain_of(intersection(X0,identity_relation))) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_176,c_37168]) ).

cnf(c_49121,plain,
    union(sP2_iProver_def,sP1_iProver_def) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_3175,c_37168]) ).

cnf(c_49122,plain,
    union(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_8578,c_37168]) ).

cnf(c_49123,plain,
    intersection(complement(intersection(complement(X0),X0)),complement(sP3_iProver_def)) = symmetric_difference(complement(X0),X0),
    inference(superposition,[status(thm)],[c_37168,c_1297]) ).

cnf(c_49124,plain,
    complement(null_class) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_37168,c_15800]) ).

cnf(c_49160,plain,
    intersection(complement(intersection(sP2_iProver_def,sP1_iProver_def)),complement(sP3_iProver_def)) = symmetric_difference(sP2_iProver_def,sP1_iProver_def),
    inference(superposition,[status(thm)],[c_49121,c_1297]) ).

cnf(c_49184,plain,
    complement(domain_of(null_class)) = complement(domain_of(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_8912,c_37170]) ).

cnf(c_49189,plain,
    subclass(singleton(sP0_iProver_def),singleton(member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_112,c_38645]) ).

cnf(c_49190,plain,
    subclass(singleton(sP0_iProver_def),unordered_pair(X0,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_21808,c_38645]) ).

cnf(c_49192,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP0_iProver_def))),singleton(sP0_iProver_def))
    | unordered_pair(X0,member_of(singleton(sP0_iProver_def))) = singleton(sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_38645,c_107]) ).

cnf(c_49195,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP0_iProver_def))),X1)
    | subclass(singleton(sP0_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_38645,c_54]) ).

cnf(c_49196,plain,
    ( ~ member(X0,singleton(sP0_iProver_def))
    | member(X0,unordered_pair(X1,member_of(singleton(sP0_iProver_def)))) ),
    inference(superposition,[status(thm)],[c_38645,c_101]) ).

cnf(c_49197,plain,
    subclass(sP3_iProver_def,unordered_pair(X0,member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_38645,c_15360]) ).

cnf(c_49198,plain,
    subclass(null_class,unordered_pair(X0,member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_38645,c_15342]) ).

cnf(c_49199,plain,
    subclass(sP1_iProver_def,unordered_pair(X0,member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_38645,c_10998]) ).

cnf(c_49292,plain,
    intersection(complement(sP3_iProver_def),null_class) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_49124,c_37111]) ).

cnf(c_49293,plain,
    union(complement(sP3_iProver_def),null_class) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_49124,c_15800]) ).

cnf(c_49294,plain,
    complement(intersection(complement(sP3_iProver_def),complement(X0))) = union(null_class,X0),
    inference(superposition,[status(thm)],[c_49124,c_126]) ).

cnf(c_49295,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),X0),
    inference(superposition,[status(thm)],[c_49124,c_8581]) ).

cnf(c_49296,plain,
    complement(image(element_relation,complement(sP3_iProver_def))) = power_class(null_class),
    inference(superposition,[status(thm)],[c_49124,c_155]) ).

cnf(c_49297,plain,
    intersection(complement(sP3_iProver_def),null_class) = null_class,
    inference(superposition,[status(thm)],[c_49124,c_7611]) ).

cnf(c_49298,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),X0),
    inference(superposition,[status(thm)],[c_49124,c_7167]) ).

cnf(c_49299,plain,
    complement(intersection(complement(X0),complement(sP3_iProver_def))) = union(X0,null_class),
    inference(superposition,[status(thm)],[c_49124,c_126]) ).

cnf(c_49300,plain,
    ( ~ member(X0,universal_class)
    | member(X0,complement(sP3_iProver_def))
    | member(X0,null_class) ),
    inference(superposition,[status(thm)],[c_49124,c_125]) ).

cnf(c_49302,plain,
    ~ member(X0,intersection(complement(sP3_iProver_def),null_class)),
    inference(superposition,[status(thm)],[c_49124,c_59]) ).

cnf(c_49647,plain,
    subclass(singleton(sP0_iProver_def),unordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_65,c_49190]) ).

cnf(c_49650,plain,
    ( ~ subclass(unordered_pair(X0,sP0_iProver_def),singleton(sP0_iProver_def))
    | unordered_pair(X0,sP0_iProver_def) = singleton(sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_49190,c_107]) ).

cnf(c_49653,plain,
    ( ~ subclass(unordered_pair(X0,sP0_iProver_def),X1)
    | subclass(singleton(sP0_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_49190,c_54]) ).

cnf(c_49654,plain,
    ( ~ member(X0,singleton(sP0_iProver_def))
    | member(X0,unordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_49190,c_101]) ).

cnf(c_49695,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),X0),
    inference(superposition,[status(thm)],[c_7302,c_49298]) ).

cnf(c_49696,plain,
    ( ~ subclass(X0,intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = X0 ),
    inference(superposition,[status(thm)],[c_49298,c_107]) ).

cnf(c_49699,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(complement(sP3_iProver_def),null_class),X1) ),
    inference(superposition,[status(thm)],[c_49298,c_54]) ).

cnf(c_49709,plain,
    ( ~ subclass(unordered_pair(sP0_iProver_def,X0),singleton(sP0_iProver_def))
    | unordered_pair(sP0_iProver_def,X0) = singleton(sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_49647,c_107]) ).

cnf(c_49712,plain,
    ( ~ subclass(unordered_pair(sP0_iProver_def,X0),X1)
    | subclass(singleton(sP0_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_49647,c_54]) ).

cnf(c_49713,plain,
    ( ~ member(X0,singleton(sP0_iProver_def))
    | member(X0,unordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_49647,c_101]) ).

cnf(c_49808,plain,
    ( ~ subclass(X0,intersection(complement(sP3_iProver_def),sP3_iProver_def))
    | intersection(complement(sP3_iProver_def),sP3_iProver_def) = X0 ),
    inference(superposition,[status(thm)],[c_49695,c_107]) ).

cnf(c_49811,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_49695,c_54]) ).

cnf(c_49812,plain,
    ( ~ member(X0,intersection(complement(sP3_iProver_def),sP3_iProver_def))
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_49695,c_101]) ).

cnf(c_49815,plain,
    intersection(complement(sP3_iProver_def),sP3_iProver_def) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_49695,c_18296]) ).

cnf(c_49816,plain,
    intersection(complement(sP3_iProver_def),sP3_iProver_def) = null_class,
    inference(superposition,[status(thm)],[c_49695,c_7304]) ).

cnf(c_49850,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP3_iProver_def)),X0),null_class)
    | unordered_pair(member_of(singleton(sP3_iProver_def)),X0) = null_class ),
    inference(superposition,[status(thm)],[c_48277,c_107]) ).

cnf(c_49853,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP3_iProver_def)),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_48277,c_54]) ).

cnf(c_49931,plain,
    ( ~ subclass(singleton(member_of(singleton(sP0_iProver_def))),X0)
    | subclass(singleton(sP0_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_49189,c_54]) ).

cnf(c_49932,plain,
    ( ~ member(X0,singleton(sP0_iProver_def))
    | member(X0,singleton(member_of(singleton(sP0_iProver_def)))) ),
    inference(superposition,[status(thm)],[c_49189,c_101]) ).

cnf(c_49933,plain,
    subclass(sP3_iProver_def,singleton(member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_49189,c_15360]) ).

cnf(c_49934,plain,
    subclass(null_class,singleton(member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_49189,c_15342]) ).

cnf(c_49936,plain,
    subclass(sP1_iProver_def,singleton(member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_49189,c_10998]) ).

cnf(c_50051,plain,
    ( ~ subclass(singleton(member_of(singleton(sP0_iProver_def))),sP3_iProver_def)
    | singleton(member_of(singleton(sP0_iProver_def))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_49933,c_107]) ).

cnf(c_50089,plain,
    ( ~ subclass(singleton(member_of(singleton(sP0_iProver_def))),null_class)
    | singleton(member_of(singleton(sP0_iProver_def))) = null_class ),
    inference(superposition,[status(thm)],[c_49934,c_107]) ).

cnf(c_50099,plain,
    ( ~ subclass(singleton(member_of(singleton(sP0_iProver_def))),sP1_iProver_def)
    | singleton(member_of(singleton(sP0_iProver_def))) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_49936,c_107]) ).

cnf(c_50102,plain,
    ( ~ subclass(singleton(member_of(singleton(sP0_iProver_def))),X0)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_49936,c_54]) ).

cnf(c_50103,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,singleton(member_of(singleton(sP0_iProver_def)))) ),
    inference(superposition,[status(thm)],[c_49936,c_101]) ).

cnf(c_50104,plain,
    ( singleton(member_of(singleton(sP0_iProver_def))) = sP1_iProver_def
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_49936,c_97]) ).

cnf(c_50352,plain,
    subclass(sP3_iProver_def,unordered_pair(member_of(singleton(sP0_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_65,c_49197]) ).

cnf(c_50357,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP0_iProver_def))),sP3_iProver_def)
    | unordered_pair(X0,member_of(singleton(sP0_iProver_def))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_49197,c_107]) ).

cnf(c_50360,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP0_iProver_def))),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_49197,c_54]) ).

cnf(c_50489,plain,
    subclass(null_class,unordered_pair(member_of(singleton(sP0_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_65,c_49198]) ).

cnf(c_50494,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP0_iProver_def))),null_class)
    | unordered_pair(X0,member_of(singleton(sP0_iProver_def))) = null_class ),
    inference(superposition,[status(thm)],[c_49198,c_107]) ).

cnf(c_50497,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP0_iProver_def))),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_49198,c_54]) ).

cnf(c_50536,plain,
    ( intersection(complement(sP3_iProver_def),null_class) = X0
    | member(not_subclass_element(X0,intersection(complement(sP3_iProver_def),null_class)),X0) ),
    inference(superposition,[status(thm)],[c_55,c_49302]) ).

cnf(c_50542,plain,
    ~ member(X0,intersection(complement(sP3_iProver_def),sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_49302]) ).

cnf(c_50571,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP0_iProver_def)),X0),sP3_iProver_def)
    | unordered_pair(member_of(singleton(sP0_iProver_def)),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_50352,c_107]) ).

cnf(c_50574,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP0_iProver_def)),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_50352,c_54]) ).

cnf(c_50592,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP0_iProver_def)),X0),null_class)
    | unordered_pair(member_of(singleton(sP0_iProver_def)),X0) = null_class ),
    inference(superposition,[status(thm)],[c_50489,c_107]) ).

cnf(c_50595,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP0_iProver_def)),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_50489,c_54]) ).

cnf(c_50623,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP0_iProver_def)),X0),singleton(sP0_iProver_def))
    | unordered_pair(member_of(singleton(sP0_iProver_def)),X0) = singleton(sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_38646,c_107]) ).

cnf(c_50626,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP0_iProver_def)),X0),X1)
    | subclass(singleton(sP0_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_38646,c_54]) ).

cnf(c_50627,plain,
    ( ~ member(X0,singleton(sP0_iProver_def))
    | member(X0,unordered_pair(member_of(singleton(sP0_iProver_def)),X1)) ),
    inference(superposition,[status(thm)],[c_38646,c_101]) ).

cnf(c_50630,plain,
    subclass(sP1_iProver_def,unordered_pair(member_of(singleton(sP0_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_38646,c_10998]) ).

cnf(c_50674,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP0_iProver_def))),sP1_iProver_def)
    | unordered_pair(X0,member_of(singleton(sP0_iProver_def))) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_49199,c_107]) ).

cnf(c_50677,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP0_iProver_def))),X1)
    | subclass(sP1_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_49199,c_54]) ).

cnf(c_50678,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,unordered_pair(X1,member_of(singleton(sP0_iProver_def)))) ),
    inference(superposition,[status(thm)],[c_49199,c_101]) ).

cnf(c_50818,plain,
    intersection(complement(sP3_iProver_def),union(complement(sP3_iProver_def),null_class)) = symmetric_difference(complement(sP3_iProver_def),null_class),
    inference(superposition,[status(thm)],[c_49292,c_1297]) ).

cnf(c_50826,plain,
    intersection(complement(null_class),union(complement(sP3_iProver_def),null_class)) = symmetric_difference(complement(sP3_iProver_def),null_class),
    inference(superposition,[status(thm)],[c_49297,c_1297]) ).

cnf(c_50837,plain,
    intersection(complement(sP3_iProver_def),union(complement(sP3_iProver_def),sP3_iProver_def)) = symmetric_difference(complement(sP3_iProver_def),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_49815,c_1297]) ).

cnf(c_50847,plain,
    intersection(complement(null_class),union(complement(sP3_iProver_def),sP3_iProver_def)) = symmetric_difference(complement(sP3_iProver_def),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_49816,c_1297]) ).

cnf(c_65528,plain,
    ( intersection(complement(sP3_iProver_def),sP3_iProver_def) = X0
    | member(not_subclass_element(X0,intersection(complement(sP3_iProver_def),sP3_iProver_def)),X0) ),
    inference(superposition,[status(thm)],[c_55,c_50542]) ).

cnf(c_65604,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP0_iProver_def)),X0),sP1_iProver_def)
    | unordered_pair(member_of(singleton(sP0_iProver_def)),X0) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_50630,c_107]) ).

cnf(c_65607,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP0_iProver_def)),X0),X1)
    | subclass(sP1_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_50630,c_54]) ).

cnf(c_65608,plain,
    ( ~ member(X0,sP1_iProver_def)
    | member(X0,unordered_pair(member_of(singleton(sP0_iProver_def)),X1)) ),
    inference(superposition,[status(thm)],[c_50630,c_101]) ).

cnf(c_65610,plain,
    subclass(sP3_iProver_def,ordered_pair(member_of(singleton(omega)),X0)),
    inference(superposition,[status(thm)],[c_33243,c_16382]) ).

cnf(c_65612,plain,
    subclass(null_class,ordered_pair(member_of(singleton(omega)),X0)),
    inference(superposition,[status(thm)],[c_33243,c_11575]) ).

cnf(c_65653,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(omega)),X0),sP3_iProver_def)
    | ordered_pair(member_of(singleton(omega)),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_65610,c_107]) ).

cnf(c_65656,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(omega)),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_65610,c_54]) ).

cnf(c_65778,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(omega)),X0),null_class)
    | ordered_pair(member_of(singleton(omega)),X0) = null_class ),
    inference(superposition,[status(thm)],[c_65612,c_107]) ).

cnf(c_65781,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(omega)),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_65612,c_54]) ).

cnf(c_65801,plain,
    subclass(sP3_iProver_def,ordered_pair(member_of(singleton(sP1_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_35404,c_16382]) ).

cnf(c_65803,plain,
    subclass(null_class,ordered_pair(member_of(singleton(sP1_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_35404,c_11575]) ).

cnf(c_66167,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP1_iProver_def)),X0),sP3_iProver_def)
    | ordered_pair(member_of(singleton(sP1_iProver_def)),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_65801,c_107]) ).

cnf(c_66170,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP1_iProver_def)),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_65801,c_54]) ).

cnf(c_66195,plain,
    ( ~ member(member_of(sP1_iProver_def),X0)
    | ~ member(member_of(sP1_iProver_def),X1)
    | subclass(sP1_iProver_def,intersection(X0,X1)) ),
    inference(superposition,[status(thm)],[c_123,c_39628]) ).

cnf(c_66196,plain,
    ( ~ member(member_of(sP1_iProver_def),universal_class)
    | member(member_of(sP1_iProver_def),X0)
    | subclass(sP1_iProver_def,complement(X0)) ),
    inference(superposition,[status(thm)],[c_125,c_39628]) ).

cnf(c_66197,plain,
    ( ~ member(member_of(sP1_iProver_def),universal_class)
    | restrict(X0,singleton(member_of(sP1_iProver_def)),universal_class) = null_class
    | subclass(sP1_iProver_def,domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_131,c_39628]) ).

cnf(c_66198,plain,
    ( ~ member(ordered_pair(X0,member_of(sP1_iProver_def)),compose(X1,X2))
    | subclass(sP1_iProver_def,image(X1,image(X2,singleton(X0)))) ),
    inference(superposition,[status(thm)],[c_158,c_39628]) ).

cnf(c_66200,plain,
    ( ~ member(member_of(sP1_iProver_def),identity_relation)
    | subclass(sP1_iProver_def,inverse(subset_relation)) ),
    inference(superposition,[status(thm)],[c_7997,c_39628]) ).

cnf(c_66355,plain,
    ( ~ member(X0,singleton(regular(sP1_iProver_def)))
    | member_of(singleton(regular(sP1_iProver_def))) = X0 ),
    inference(superposition,[status(thm)],[c_42502,c_95]) ).

cnf(c_66356,plain,
    member(singleton(regular(sP1_iProver_def)),universal_class),
    inference(superposition,[status(thm)],[c_42502,c_94]) ).

cnf(c_66359,plain,
    singleton(member_of(singleton(singleton(regular(sP1_iProver_def))))) = singleton(singleton(regular(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_66356,c_88]) ).

cnf(c_66360,plain,
    member_of(singleton(singleton(regular(sP1_iProver_def)))) = singleton(regular(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_66356,c_91]) ).

cnf(c_66384,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(intersection(complement(identity_relation),identity_relation))),X0),
    inference(superposition,[status(thm)],[c_37170,c_8915]) ).

cnf(c_66385,plain,
    subclass(intersection(complement(domain_of(null_class)),domain_of(intersection(complement(identity_relation),identity_relation))),X0),
    inference(superposition,[status(thm)],[c_8912,c_8915]) ).

cnf(c_66386,plain,
    subclass(intersection(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)),X0),
    inference(superposition,[status(thm)],[c_37111,c_8915]) ).

cnf(c_66387,plain,
    subclass(intersection(diagonalise(complement(identity_relation)),domain_of(null_class)),X0),
    inference(superposition,[status(thm)],[c_7611,c_8915]) ).

cnf(c_66388,plain,
    subclass(intersection(diagonalise(cross_product(X0,X1)),domain_of(restrict(identity_relation,X0,X1))),X2),
    inference(superposition,[status(thm)],[c_129,c_8915]) ).

cnf(c_66389,plain,
    ( ~ subclass(X0,intersection(diagonalise(X1),domain_of(intersection(X1,identity_relation))))
    | intersection(diagonalise(X1),domain_of(intersection(X1,identity_relation))) = X0 ),
    inference(superposition,[status(thm)],[c_8915,c_107]) ).

cnf(c_66392,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(diagonalise(X2),domain_of(intersection(X2,identity_relation))),X1) ),
    inference(superposition,[status(thm)],[c_8915,c_54]) ).

cnf(c_66434,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP1_iProver_def)),X0),null_class)
    | ordered_pair(member_of(singleton(sP1_iProver_def)),X0) = null_class ),
    inference(superposition,[status(thm)],[c_65803,c_107]) ).

cnf(c_66437,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP1_iProver_def)),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_65803,c_54]) ).

cnf(c_66446,plain,
    subclass(sP3_iProver_def,ordered_pair(member_of(singleton(sP0_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_38626,c_16382]) ).

cnf(c_66448,plain,
    subclass(null_class,ordered_pair(member_of(singleton(sP0_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_38626,c_11575]) ).

cnf(c_66471,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP0_iProver_def)),X0),sP3_iProver_def)
    | ordered_pair(member_of(singleton(sP0_iProver_def)),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_66446,c_107]) ).

cnf(c_66474,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP0_iProver_def)),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_66446,c_54]) ).

cnf(c_66500,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP0_iProver_def)),X0),null_class)
    | ordered_pair(member_of(singleton(sP0_iProver_def)),X0) = null_class ),
    inference(superposition,[status(thm)],[c_66448,c_107]) ).

cnf(c_66503,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP0_iProver_def)),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_66448,c_54]) ).

cnf(c_66845,plain,
    union(complement(domain_of(sP3_iProver_def)),domain_of(null_class)) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_49184,c_37168]) ).

cnf(c_66846,plain,
    intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_49184,c_37111]) ).

cnf(c_66847,plain,
    union(complement(domain_of(sP3_iProver_def)),domain_of(null_class)) = complement(null_class),
    inference(superposition,[status(thm)],[c_49184,c_15800]) ).

cnf(c_66848,plain,
    complement(intersection(complement(domain_of(sP3_iProver_def)),complement(X0))) = union(domain_of(null_class),X0),
    inference(superposition,[status(thm)],[c_49184,c_126]) ).

cnf(c_66849,plain,
    subclass(intersection(power_class(domain_of(null_class)),image(element_relation,complement(domain_of(sP3_iProver_def)))),X0),
    inference(superposition,[status(thm)],[c_49184,c_8581]) ).

cnf(c_66850,plain,
    complement(image(element_relation,complement(domain_of(sP3_iProver_def)))) = power_class(domain_of(null_class)),
    inference(superposition,[status(thm)],[c_49184,c_155]) ).

cnf(c_66851,plain,
    intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)) = null_class,
    inference(superposition,[status(thm)],[c_49184,c_7611]) ).

cnf(c_66852,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),X0),
    inference(superposition,[status(thm)],[c_49184,c_7167]) ).

cnf(c_66853,plain,
    complement(intersection(complement(X0),complement(domain_of(sP3_iProver_def)))) = union(X0,domain_of(null_class)),
    inference(superposition,[status(thm)],[c_49184,c_126]) ).

cnf(c_66854,plain,
    ( ~ member(X0,universal_class)
    | member(X0,complement(domain_of(sP3_iProver_def)))
    | member(X0,domain_of(null_class)) ),
    inference(superposition,[status(thm)],[c_49184,c_125]) ).

cnf(c_66855,plain,
    ( ~ member(X0,complement(domain_of(sP3_iProver_def)))
    | ~ member(X0,domain_of(null_class)) ),
    inference(superposition,[status(thm)],[c_49184,c_124]) ).

cnf(c_66856,plain,
    ~ member(X0,intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class))),
    inference(superposition,[status(thm)],[c_49184,c_59]) ).

cnf(c_67422,plain,
    union(complement(sP3_iProver_def),sP3_iProver_def) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_49293]) ).

cnf(c_67423,plain,
    intersection(complement(intersection(complement(sP3_iProver_def),null_class)),complement(sP3_iProver_def)) = symmetric_difference(complement(sP3_iProver_def),null_class),
    inference(superposition,[status(thm)],[c_49293,c_1297]) ).

cnf(c_67444,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def)),X0),
    inference(superposition,[status(thm)],[c_37170,c_66386]) ).

cnf(c_67445,plain,
    subclass(intersection(complement(domain_of(null_class)),domain_of(sP3_iProver_def)),X0),
    inference(superposition,[status(thm)],[c_8912,c_66386]) ).

cnf(c_67446,plain,
    ( ~ subclass(X0,intersection(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)))
    | intersection(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_66386,c_107]) ).

cnf(c_67449,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_66386,c_54]) ).

cnf(c_67450,plain,
    ( ~ member(X0,intersection(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)))
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_66386,c_101]) ).

cnf(c_67453,plain,
    intersection(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_66386,c_18296]) ).

cnf(c_67454,plain,
    intersection(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)) = null_class,
    inference(superposition,[status(thm)],[c_66386,c_7304]) ).

cnf(c_67535,plain,
    subclass(intersection(complement(domain_of(null_class)),domain_of(null_class)),X0),
    inference(superposition,[status(thm)],[c_8912,c_66387]) ).

cnf(c_67537,plain,
    ( ~ subclass(X0,intersection(diagonalise(complement(identity_relation)),domain_of(null_class)))
    | intersection(diagonalise(complement(identity_relation)),domain_of(null_class)) = X0 ),
    inference(superposition,[status(thm)],[c_66387,c_107]) ).

cnf(c_67540,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(diagonalise(complement(identity_relation)),domain_of(null_class)),X1) ),
    inference(superposition,[status(thm)],[c_66387,c_54]) ).

cnf(c_67541,plain,
    ( ~ member(X0,intersection(diagonalise(complement(identity_relation)),domain_of(null_class)))
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_66387,c_101]) ).

cnf(c_67544,plain,
    intersection(diagonalise(complement(identity_relation)),domain_of(null_class)) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_66387,c_18296]) ).

cnf(c_67545,plain,
    intersection(diagonalise(complement(identity_relation)),domain_of(null_class)) = null_class,
    inference(superposition,[status(thm)],[c_66387,c_7304]) ).

cnf(c_67620,plain,
    ( ~ subclass(X0,intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)))
    | intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)) = X0 ),
    inference(superposition,[status(thm)],[c_66852,c_107]) ).

cnf(c_67623,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),X1) ),
    inference(superposition,[status(thm)],[c_66852,c_54]) ).

cnf(c_67669,plain,
    null_class != sP1_iProver_def,
    inference(global_subsumption_just,[status(thm)],[c_9482,c_5941,c_8116]) ).

cnf(c_67671,plain,
    sP1_iProver_def != sP3_iProver_def,
    inference(superposition,[status(thm)],[c_7302,c_67669]) ).

cnf(c_67672,plain,
    ( ~ member(image(X0,sP1_iProver_def),universal_class)
    | member(apply(X0,sP0_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_10565,c_154]) ).

cnf(c_67674,plain,
    subclass(element_relation,universal_class),
    inference(superposition,[status(thm)],[c_104,c_10986]) ).

cnf(c_67717,plain,
    ( ~ subclass(universal_class,element_relation)
    | universal_class = element_relation ),
    inference(superposition,[status(thm)],[c_67674,c_107]) ).

cnf(c_67720,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(element_relation,X0) ),
    inference(superposition,[status(thm)],[c_67674,c_54]) ).

cnf(c_67721,plain,
    ( ~ member(X0,element_relation)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_67674,c_101]) ).

cnf(c_67772,plain,
    ( member(not_subclass_element(element_relation,X0),universal_class)
    | subclass(element_relation,X0) ),
    inference(superposition,[status(thm)],[c_102,c_67721]) ).

cnf(c_67773,plain,
    ( X0 = element_relation
    | member(not_subclass_element(X0,element_relation),X0)
    | member(not_subclass_element(element_relation,X0),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_67721]) ).

cnf(c_67774,plain,
    ( null_class = element_relation
    | member(not_subclass_element(element_relation,null_class),universal_class) ),
    inference(superposition,[status(thm)],[c_63,c_67721]) ).

cnf(c_67775,plain,
    ( null_class = element_relation
    | member(regular(element_relation),universal_class) ),
    inference(superposition,[status(thm)],[c_166,c_67721]) ).

cnf(c_67776,plain,
    ( ~ member(element_relation,universal_class)
    | null_class = element_relation
    | member(apply(choice,element_relation),universal_class) ),
    inference(superposition,[status(thm)],[c_170,c_67721]) ).

cnf(c_67777,plain,
    ( null_class = element_relation
    | member(not_subclass_element(element_relation,sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_7628,c_67721]) ).

cnf(c_67870,plain,
    intersection(complement(intersection(complement(sP3_iProver_def),sP3_iProver_def)),complement(sP3_iProver_def)) = symmetric_difference(complement(sP3_iProver_def),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_67422,c_1297]) ).

cnf(c_67921,plain,
    ( ~ subclass(X0,intersection(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def)))
    | intersection(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_67444,c_107]) ).

cnf(c_67924,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_67444,c_54]) ).

cnf(c_67925,plain,
    ( ~ member(X0,intersection(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def)))
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_67444,c_101]) ).

cnf(c_67928,plain,
    intersection(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def)) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_67444,c_18296]) ).

cnf(c_67929,plain,
    intersection(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def)) = null_class,
    inference(superposition,[status(thm)],[c_67444,c_7304]) ).

cnf(c_68035,plain,
    ( ~ subclass(X0,intersection(complement(domain_of(null_class)),domain_of(sP3_iProver_def)))
    | intersection(complement(domain_of(null_class)),domain_of(sP3_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_67445,c_107]) ).

cnf(c_68038,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(complement(domain_of(null_class)),domain_of(sP3_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_67445,c_54]) ).

cnf(c_68039,plain,
    ( ~ member(X0,intersection(complement(domain_of(null_class)),domain_of(sP3_iProver_def)))
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_67445,c_101]) ).

cnf(c_68042,plain,
    intersection(complement(domain_of(null_class)),domain_of(sP3_iProver_def)) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_67445,c_18296]) ).

cnf(c_68043,plain,
    intersection(complement(domain_of(null_class)),domain_of(sP3_iProver_def)) = null_class,
    inference(superposition,[status(thm)],[c_67445,c_7304]) ).

cnf(c_68134,plain,
    ( ~ subclass(X0,intersection(complement(domain_of(null_class)),domain_of(null_class)))
    | intersection(complement(domain_of(null_class)),domain_of(null_class)) = X0 ),
    inference(superposition,[status(thm)],[c_67535,c_107]) ).

cnf(c_68137,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(complement(domain_of(null_class)),domain_of(null_class)),X1) ),
    inference(superposition,[status(thm)],[c_67535,c_54]) ).

cnf(c_68138,plain,
    ( ~ member(X0,intersection(complement(domain_of(null_class)),domain_of(null_class)))
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_67535,c_101]) ).

cnf(c_68141,plain,
    intersection(complement(domain_of(null_class)),domain_of(null_class)) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_67535,c_18296]) ).

cnf(c_68142,plain,
    intersection(complement(domain_of(null_class)),domain_of(null_class)) = null_class,
    inference(superposition,[status(thm)],[c_67535,c_7304]) ).

cnf(c_68298,plain,
    ( singleton(member_of(singleton(not_subclass_element(element_relation,X0)))) = singleton(not_subclass_element(element_relation,X0))
    | subclass(element_relation,X0) ),
    inference(superposition,[status(thm)],[c_67772,c_88]) ).

cnf(c_68299,plain,
    ( member_of(singleton(not_subclass_element(element_relation,X0))) = not_subclass_element(element_relation,X0)
    | subclass(element_relation,X0) ),
    inference(superposition,[status(thm)],[c_67772,c_91]) ).

cnf(c_68341,plain,
    ( singleton(member_of(singleton(regular(element_relation)))) = singleton(regular(element_relation))
    | null_class = element_relation ),
    inference(superposition,[status(thm)],[c_67775,c_88]) ).

cnf(c_68342,plain,
    ( member_of(singleton(regular(element_relation))) = regular(element_relation)
    | null_class = element_relation ),
    inference(superposition,[status(thm)],[c_67775,c_91]) ).

cnf(c_68426,plain,
    subclass(successor_relation,universal_class),
    inference(superposition,[status(thm)],[c_104,c_10989]) ).

cnf(c_68429,plain,
    ( ~ subclass(universal_class,successor_relation)
    | universal_class = successor_relation ),
    inference(superposition,[status(thm)],[c_68426,c_107]) ).

cnf(c_68432,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(successor_relation,X0) ),
    inference(superposition,[status(thm)],[c_68426,c_54]) ).

cnf(c_68433,plain,
    ( ~ member(X0,successor_relation)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_68426,c_101]) ).

cnf(c_68541,plain,
    ( member(not_subclass_element(successor_relation,X0),universal_class)
    | subclass(successor_relation,X0) ),
    inference(superposition,[status(thm)],[c_102,c_68433]) ).

cnf(c_68542,plain,
    ( X0 = successor_relation
    | member(not_subclass_element(X0,successor_relation),X0)
    | member(not_subclass_element(successor_relation,X0),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_68433]) ).

cnf(c_68543,plain,
    ( null_class = successor_relation
    | member(not_subclass_element(successor_relation,null_class),universal_class) ),
    inference(superposition,[status(thm)],[c_63,c_68433]) ).

cnf(c_68544,plain,
    ( null_class = successor_relation
    | member(regular(successor_relation),universal_class) ),
    inference(superposition,[status(thm)],[c_166,c_68433]) ).

cnf(c_68545,plain,
    ( ~ member(successor_relation,universal_class)
    | null_class = successor_relation
    | member(apply(choice,successor_relation),universal_class) ),
    inference(superposition,[status(thm)],[c_170,c_68433]) ).

cnf(c_68546,plain,
    ( null_class = successor_relation
    | member(not_subclass_element(successor_relation,sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_7628,c_68433]) ).

cnf(c_68870,plain,
    ( singleton(member_of(singleton(not_subclass_element(successor_relation,X0)))) = singleton(not_subclass_element(successor_relation,X0))
    | subclass(successor_relation,X0) ),
    inference(superposition,[status(thm)],[c_68541,c_88]) ).

cnf(c_68871,plain,
    ( member_of(singleton(not_subclass_element(successor_relation,X0))) = not_subclass_element(successor_relation,X0)
    | subclass(successor_relation,X0) ),
    inference(superposition,[status(thm)],[c_68541,c_91]) ).

cnf(c_68894,plain,
    ( singleton(member_of(singleton(regular(successor_relation)))) = singleton(regular(successor_relation))
    | null_class = successor_relation ),
    inference(superposition,[status(thm)],[c_68544,c_88]) ).

cnf(c_68895,plain,
    ( member_of(singleton(regular(successor_relation))) = regular(successor_relation)
    | null_class = successor_relation ),
    inference(superposition,[status(thm)],[c_68544,c_91]) ).

cnf(c_68951,plain,
    ( ~ subclass(X0,image(successor_relation,omega))
    | ~ subclass(omega,X0)
    | image(successor_relation,omega) = X0 ),
    inference(superposition,[status(thm)],[c_10994,c_107]) ).

cnf(c_68954,plain,
    ( ~ subclass(X0,X1)
    | ~ subclass(omega,X0)
    | subclass(image(successor_relation,omega),X1) ),
    inference(superposition,[status(thm)],[c_10994,c_54]) ).

cnf(c_68955,plain,
    ( ~ member(X0,image(successor_relation,omega))
    | ~ subclass(omega,X1)
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_10994,c_101]) ).

cnf(c_68957,plain,
    ( ~ subclass(omega,singleton(X0))
    | image(successor_relation,omega) = singleton(X0)
    | image(successor_relation,omega) = null_class ),
    inference(superposition,[status(thm)],[c_10994,c_97]) ).

cnf(c_69063,plain,
    ( ~ member(X0,X1)
    | ~ member(sP0_iProver_def,X1)
    | subclass(sP1_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_76,c_10995]) ).

cnf(c_69066,plain,
    ( ~ function(unordered_pair(sP0_iProver_def,X0))
    | subclass(sP1_iProver_def,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_10995]) ).

cnf(c_69121,plain,
    ( ~ function(unordered_pair(X0,sP0_iProver_def))
    | subclass(sP1_iProver_def,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_10996]) ).

cnf(c_69142,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_76,c_11004]) ).

cnf(c_69143,plain,
    ( ~ member(X0,X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_96,c_11004]) ).

cnf(c_69171,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),null_class),
    inference(superposition,[status(thm)],[c_11593,c_11004]) ).

cnf(c_69187,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),universal_class),
    inference(superposition,[status(thm)],[c_68426,c_11004]) ).

cnf(c_69201,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_11596,c_11004]) ).

cnf(c_69204,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),omega),
    inference(superposition,[status(thm)],[c_11890,c_11004]) ).

cnf(c_69205,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_11901,c_11004]) ).

cnf(c_69206,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),x),
    inference(superposition,[status(thm)],[c_12006,c_11004]) ).

cnf(c_69207,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),subset_relation),
    inference(superposition,[status(thm)],[c_12009,c_11004]) ).

cnf(c_69208,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(X0)),
    inference(superposition,[status(thm)],[c_15337,c_11004]) ).

cnf(c_69211,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_23904,c_11004]) ).

cnf(c_69212,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_15372,c_11004]) ).

cnf(c_69213,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),cross_product(universal_class,universal_class)),
    inference(superposition,[status(thm)],[c_15447,c_11004]) ).

cnf(c_69222,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),identity_relation),
    inference(superposition,[status(thm)],[c_16331,c_11004]) ).

cnf(c_69229,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),cross_product(cross_product(universal_class,universal_class),universal_class)),
    inference(superposition,[status(thm)],[c_16385,c_11004]) ).

cnf(c_69232,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(null_class)),
    inference(superposition,[status(thm)],[c_16960,c_11004]) ).

cnf(c_69234,plain,
    ( ~ operation(X0)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),domain_of(domain_of(X0))) ),
    inference(superposition,[status(thm)],[c_16391,c_11004]) ).

cnf(c_69243,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(omega)),
    inference(superposition,[status(thm)],[c_33249,c_11004]) ).

cnf(c_69247,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_35421,c_11004]) ).

cnf(c_69250,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_31605,c_11004]) ).

cnf(c_69253,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(singleton(X0))),
    inference(superposition,[status(thm)],[c_17251,c_11004]) ).

cnf(c_69257,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_31626,c_11004]) ).

cnf(c_69259,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(singleton(null_class))),
    inference(superposition,[status(thm)],[c_30933,c_11004]) ).

cnf(c_69260,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(singleton(omega))),
    inference(superposition,[status(thm)],[c_33247,c_11004]) ).

cnf(c_69261,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_35408,c_11004]) ).

cnf(c_69262,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,singleton(X1))),
    inference(superposition,[status(thm)],[c_17352,c_11004]) ).

cnf(c_69268,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(singleton(X0),X1)),
    inference(superposition,[status(thm)],[c_17421,c_11004]) ).

cnf(c_69273,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_32432,c_11004]) ).

cnf(c_69274,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,singleton(null_class))),
    inference(superposition,[status(thm)],[c_30952,c_11004]) ).

cnf(c_69275,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,singleton(omega))),
    inference(superposition,[status(thm)],[c_33269,c_11004]) ).

cnf(c_69276,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_35431,c_11004]) ).

cnf(c_69277,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(singleton(sP3_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_32033,c_11004]) ).

cnf(c_69278,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(singleton(null_class),X0)),
    inference(superposition,[status(thm)],[c_30930,c_11004]) ).

cnf(c_69279,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(singleton(omega),X0)),
    inference(superposition,[status(thm)],[c_33244,c_11004]) ).

cnf(c_69280,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(singleton(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_35405,c_11004]) ).

cnf(c_69281,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_20057,c_11004]) ).

cnf(c_69284,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(null_class,X0)),
    inference(superposition,[status(thm)],[c_32032,c_11004]) ).

cnf(c_69286,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(omega,X0)),
    inference(superposition,[status(thm)],[c_34227,c_11004]) ).

cnf(c_69289,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(sP3_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_32105,c_11004]) ).

cnf(c_69291,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(sP1_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_35902,c_11004]) ).

cnf(c_69293,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_43547,c_11004]) ).

cnf(c_69295,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(member_of(singleton(null_class)),X0)),
    inference(superposition,[status(thm)],[c_44997,c_11004]) ).

cnf(c_69300,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_48103,c_11004]) ).

cnf(c_69303,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(member_of(singleton(sP3_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_48277,c_11004]) ).

cnf(c_69307,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(singleton(sP0_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_38627,c_11004]) ).

cnf(c_69308,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_38630,c_11004]) ).

cnf(c_69309,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_38643,c_11004]) ).

cnf(c_69312,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_38655,c_11004]) ).

cnf(c_69314,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,null_class)),
    inference(superposition,[status(thm)],[c_43738,c_11004]) ).

cnf(c_69315,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(null_class,X0)),
    inference(superposition,[status(thm)],[c_43921,c_11004]) ).

cnf(c_69318,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_44456,c_11004]) ).

cnf(c_69319,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(sP3_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_45302,c_11004]) ).

cnf(c_69320,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_21190,c_11004]) ).

cnf(c_69325,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(member_of(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_40829,c_11004]) ).

cnf(c_69328,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_40975,c_11004]) ).

cnf(c_69330,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_41353,c_11004]) ).

cnf(c_69332,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(member_of(sP1_iProver_def),X0)),
    inference(superposition,[status(thm)],[c_41703,c_11004]) ).

cnf(c_69334,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_44953,c_11004]) ).

cnf(c_69336,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_45899,c_11004]) ).

cnf(c_69339,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_45017,c_11004]) ).

cnf(c_69341,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(member_of(singleton(omega)),X0)),
    inference(superposition,[status(thm)],[c_46522,c_11004]) ).

cnf(c_69343,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_46329,c_11004]) ).

cnf(c_69346,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_46619,c_11004]) ).

cnf(c_69347,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_46626,c_11004]) ).

cnf(c_69349,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(sP1_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_47192,c_11004]) ).

cnf(c_69350,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(member_of(singleton(sP1_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_48044,c_11004]) ).

cnf(c_69352,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,omega)),
    inference(superposition,[status(thm)],[c_45944,c_11004]) ).

cnf(c_69353,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(omega,X0)),
    inference(superposition,[status(thm)],[c_45996,c_11004]) ).

cnf(c_69354,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_48032,c_11004]) ).

cnf(c_69357,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_49190,c_11004]) ).

cnf(c_69358,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X0,member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_49198,c_11004]) ).

cnf(c_69361,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),singleton(member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_49934,c_11004]) ).

cnf(c_69364,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_49647,c_11004]) ).

cnf(c_69365,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(member_of(singleton(sP0_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_50489,c_11004]) ).

cnf(c_69371,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(member_of(singleton(null_class)),X0)),
    inference(superposition,[status(thm)],[c_42987,c_11004]) ).

cnf(c_69373,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(member_of(singleton(sP3_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_42998,c_11004]) ).

cnf(c_69375,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(member_of(singleton(sP0_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_66448,c_11004]) ).

cnf(c_69377,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(member_of(singleton(omega)),X0)),
    inference(superposition,[status(thm)],[c_65612,c_11004]) ).

cnf(c_69379,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(member_of(singleton(sP1_iProver_def)),X0)),
    inference(superposition,[status(thm)],[c_65803,c_11004]) ).

cnf(c_73003,plain,
    ( ~ subclass(universal_class,intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = universal_class ),
    inference(superposition,[status(thm)],[c_69187,c_107]) ).

cnf(c_73021,plain,
    ( ~ subclass(omega,intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = omega ),
    inference(superposition,[status(thm)],[c_69204,c_107]) ).

cnf(c_73029,plain,
    ( ~ subclass(sP1_iProver_def,intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_69205,c_107]) ).

cnf(c_73037,plain,
    ( ~ subclass(x,intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = x ),
    inference(superposition,[status(thm)],[c_69206,c_107]) ).

cnf(c_73042,plain,
    ( member_of(member_of(X0)) = member_of(X0)
    | member_of(X0) = X0
    | member(member_of(X0),X0) ),
    inference(superposition,[status(thm)],[c_90,c_12030]) ).

cnf(c_73043,plain,
    ( member_of(member_of1(X0)) = member_of1(X0)
    | member_of(X0) = X0
    | member(member_of1(X0),X0) ),
    inference(superposition,[status(thm)],[c_93,c_12030]) ).

cnf(c_73045,plain,
    ( member_of(member_of(singleton(null_class))) = member_of(singleton(null_class))
    | member(member_of(singleton(null_class)),singleton(null_class)) ),
    inference(superposition,[status(thm)],[c_17671,c_12030]) ).

cnf(c_73046,plain,
    ( member_of(member_of(singleton(omega))) = member_of(singleton(omega))
    | member(member_of(singleton(omega)),singleton(omega)) ),
    inference(superposition,[status(thm)],[c_17677,c_12030]) ).

cnf(c_73047,plain,
    ( member_of(member_of(sP1_iProver_def)) = member_of(sP1_iProver_def)
    | member(member_of(sP1_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_38619,c_12030]) ).

cnf(c_73048,plain,
    ( member_of(member_of(singleton(sP1_iProver_def))) = member_of(singleton(sP1_iProver_def))
    | member(member_of(singleton(sP1_iProver_def)),singleton(sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_17681,c_12030]) ).

cnf(c_73049,plain,
    ( member_of(member_of(singleton(sP3_iProver_def))) = member_of(singleton(sP3_iProver_def))
    | member(member_of(singleton(sP3_iProver_def)),singleton(sP3_iProver_def)) ),
    inference(superposition,[status(thm)],[c_17682,c_12030]) ).

cnf(c_73050,plain,
    ( member_of(member_of(singleton(sP0_iProver_def))) = member_of(singleton(sP0_iProver_def))
    | member(member_of(singleton(sP0_iProver_def)),singleton(sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_21807,c_12030]) ).

cnf(c_73219,plain,
    ( ~ member(ordered_pair(X0,X1),element_relation)
    | member(X1,unordered_pair(X0,X1)) ),
    inference(superposition,[status(thm)],[c_12563,c_50]) ).

cnf(c_73220,plain,
    ( ~ member(ordered_pair(X0,X1),element_relation)
    | member(X0,unordered_pair(X0,X1)) ),
    inference(superposition,[status(thm)],[c_12563,c_49]) ).

cnf(c_73223,plain,
    ( ~ member(ordered_pair(X0,X1),element_relation)
    | member(X1,universal_class) ),
    inference(superposition,[status(thm)],[c_12563,c_52]) ).

cnf(c_73224,plain,
    ( ~ member(ordered_pair(X0,X1),element_relation)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_12563,c_51]) ).

cnf(c_73225,plain,
    ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),X0),X0)
    | ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),element_relation)
    | cross_product(universal_class,universal_class) = X0 ),
    inference(superposition,[status(thm)],[c_12563,c_58]) ).

cnf(c_73226,plain,
    ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),element_relation)
    | cross_product(universal_class,universal_class) = X0
    | member(not_subclass_element(cross_product(universal_class,universal_class),X0),cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_12563,c_57]) ).

cnf(c_73227,plain,
    ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),element_relation)
    | subclass(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_12563,c_103]) ).

cnf(c_73232,plain,
    ( ~ member(X0,element_relation)
    | ordered_pair(first(X0),second(X0)) = X0 ),
    inference(superposition,[status(thm)],[c_12563,c_117]) ).

cnf(c_73233,plain,
    ( ~ member(ordered_pair(X0,successor(X0)),element_relation)
    | member(ordered_pair(X0,successor(X0)),successor_relation) ),
    inference(superposition,[status(thm)],[c_12563,c_194]) ).

cnf(c_73234,plain,
    ( ~ member(sP0_iProver_def,element_relation)
    | subclass(sP1_iProver_def,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_12563,c_7161]) ).

cnf(c_73235,plain,
    ( ~ member(member_of(sP1_iProver_def),element_relation)
    | subclass(sP1_iProver_def,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_12563,c_39628]) ).

cnf(c_73236,plain,
    ( ~ member(ordered_pair(X0,X1),successor_relation)
    | member(X1,unordered_pair(X0,X1)) ),
    inference(superposition,[status(thm)],[c_12566,c_50]) ).

cnf(c_73237,plain,
    ( ~ member(ordered_pair(X0,X1),successor_relation)
    | member(X0,unordered_pair(X0,X1)) ),
    inference(superposition,[status(thm)],[c_12566,c_49]) ).

cnf(c_73240,plain,
    ( ~ member(ordered_pair(X0,X1),successor_relation)
    | member(X1,universal_class) ),
    inference(superposition,[status(thm)],[c_12566,c_52]) ).

cnf(c_73241,plain,
    ( ~ member(ordered_pair(X0,X1),successor_relation)
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_12566,c_51]) ).

cnf(c_73242,plain,
    ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),X0),X0)
    | ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),successor_relation)
    | cross_product(universal_class,universal_class) = X0 ),
    inference(superposition,[status(thm)],[c_12566,c_58]) ).

cnf(c_73243,plain,
    ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),successor_relation)
    | cross_product(universal_class,universal_class) = X0
    | member(not_subclass_element(cross_product(universal_class,universal_class),X0),cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_12566,c_57]) ).

cnf(c_73244,plain,
    ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),successor_relation)
    | subclass(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_12566,c_103]) ).

cnf(c_73245,plain,
    ( ~ member(ordered_pair(X0,X1),successor_relation)
    | ~ member(X0,X1)
    | member(ordered_pair(X0,X1),element_relation) ),
    inference(superposition,[status(thm)],[c_12566,c_120]) ).

cnf(c_73249,plain,
    ( ~ member(X0,successor_relation)
    | ordered_pair(first(X0),second(X0)) = X0 ),
    inference(superposition,[status(thm)],[c_12566,c_117]) ).

cnf(c_73251,plain,
    ( ~ member(sP0_iProver_def,successor_relation)
    | subclass(sP1_iProver_def,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_12566,c_7161]) ).

cnf(c_73252,plain,
    ( ~ member(member_of(sP1_iProver_def),successor_relation)
    | subclass(sP1_iProver_def,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_12566,c_39628]) ).

cnf(c_73377,plain,
    ( member(not_subclass_element(image(successor_relation,omega),X0),omega)
    | subclass(image(successor_relation,omega),X0) ),
    inference(superposition,[status(thm)],[c_102,c_12572]) ).

cnf(c_73378,plain,
    ( image(successor_relation,omega) = X0
    | member(not_subclass_element(X0,image(successor_relation,omega)),X0)
    | member(not_subclass_element(image(successor_relation,omega),X0),omega) ),
    inference(superposition,[status(thm)],[c_55,c_12572]) ).

cnf(c_73379,plain,
    ( image(successor_relation,omega) = null_class
    | member(not_subclass_element(image(successor_relation,omega),null_class),omega) ),
    inference(superposition,[status(thm)],[c_63,c_12572]) ).

cnf(c_73380,plain,
    ( image(successor_relation,omega) = null_class
    | member(regular(image(successor_relation,omega)),omega) ),
    inference(superposition,[status(thm)],[c_166,c_12572]) ).

cnf(c_73381,plain,
    ( ~ member(image(successor_relation,omega),universal_class)
    | image(successor_relation,omega) = null_class
    | member(apply(choice,image(successor_relation,omega)),omega) ),
    inference(superposition,[status(thm)],[c_170,c_12572]) ).

cnf(c_73382,plain,
    ( image(successor_relation,omega) = null_class
    | member(not_subclass_element(image(successor_relation,omega),sP3_iProver_def),omega) ),
    inference(superposition,[status(thm)],[c_7628,c_12572]) ).

cnf(c_73386,plain,
    ( ~ subclass(subset_relation,intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = subset_relation ),
    inference(superposition,[status(thm)],[c_69207,c_107]) ).

cnf(c_73394,plain,
    ( ~ subclass(identity_relation,intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = identity_relation ),
    inference(superposition,[status(thm)],[c_69222,c_107]) ).

cnf(c_73411,plain,
    ( ~ subclass(singleton(X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(X0) ),
    inference(superposition,[status(thm)],[c_69208,c_107]) ).

cnf(c_73414,plain,
    ( ~ subclass(singleton(X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69208,c_54]) ).

cnf(c_73420,plain,
    ( ~ subclass(inverse(subset_relation),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = inverse(subset_relation) ),
    inference(superposition,[status(thm)],[c_69211,c_107]) ).

cnf(c_73429,plain,
    ( ~ subclass(singleton(null_class),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(null_class) ),
    inference(superposition,[status(thm)],[c_69232,c_107]) ).

cnf(c_73554,plain,
    ( ~ subclass(singleton(omega),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(omega) ),
    inference(superposition,[status(thm)],[c_69243,c_107]) ).

cnf(c_73563,plain,
    ( ~ subclass(singleton(sP1_iProver_def),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69247,c_107]) ).

cnf(c_73572,plain,
    ( ~ subclass(singleton(sP3_iProver_def),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_69250,c_107]) ).

cnf(c_73582,plain,
    ( ~ subclass(singleton(sP0_iProver_def),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_69309,c_107]) ).

cnf(c_73607,plain,
    ( ~ subclass(unordered_pair(X0,X1),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,X1) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69212,c_107]) ).

cnf(c_73610,plain,
    ( ~ subclass(unordered_pair(X0,X1),X2)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X2) ),
    inference(superposition,[status(thm)],[c_69212,c_54]) ).

cnf(c_73645,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),intersection(sP2_iProver_def,sP1_iProver_def))
    | cross_product(universal_class,universal_class) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69213,c_107]) ).

cnf(c_73662,plain,
    ( ~ subclass(singleton(singleton(X0)),intersection(sP2_iProver_def,sP1_iProver_def))
    | singleton(singleton(X0)) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69253,c_107]) ).

cnf(c_73665,plain,
    ( ~ subclass(singleton(singleton(X0)),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69253,c_54]) ).

cnf(c_73677,plain,
    ( ~ member(not_subclass_element(unordered_pair(sP0_iProver_def,X0),X1),X1)
    | ~ member(not_subclass_element(X1,unordered_pair(sP0_iProver_def,X0)),sP1_iProver_def)
    | unordered_pair(sP0_iProver_def,X0) = X1 ),
    inference(superposition,[status(thm)],[c_12573,c_58]) ).

cnf(c_73678,plain,
    ( ~ member(not_subclass_element(X0,unordered_pair(sP0_iProver_def,X1)),sP1_iProver_def)
    | unordered_pair(sP0_iProver_def,X1) = X0
    | member(not_subclass_element(unordered_pair(sP0_iProver_def,X1),X0),unordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_12573,c_57]) ).

cnf(c_73679,plain,
    ( ~ member(not_subclass_element(X0,unordered_pair(sP0_iProver_def,X1)),sP1_iProver_def)
    | subclass(X0,unordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_12573,c_103]) ).

cnf(c_73680,plain,
    ( ~ member(X0,sP1_iProver_def)
    | subclass(sP3_iProver_def,unordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_12573,c_16382]) ).

cnf(c_73682,plain,
    ( ~ member(X0,sP1_iProver_def)
    | subclass(null_class,unordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_12573,c_11575]) ).

cnf(c_73683,plain,
    ( ~ member(X0,sP1_iProver_def)
    | X0 = X1
    | X0 = sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_12573,c_108]) ).

cnf(c_73703,plain,
    ( ~ member(not_subclass_element(unordered_pair(X0,sP0_iProver_def),X1),X1)
    | ~ member(not_subclass_element(X1,unordered_pair(X0,sP0_iProver_def)),sP1_iProver_def)
    | unordered_pair(X0,sP0_iProver_def) = X1 ),
    inference(superposition,[status(thm)],[c_12574,c_58]) ).

cnf(c_73704,plain,
    ( ~ member(not_subclass_element(X0,unordered_pair(X1,sP0_iProver_def)),sP1_iProver_def)
    | unordered_pair(X1,sP0_iProver_def) = X0
    | member(not_subclass_element(unordered_pair(X1,sP0_iProver_def),X0),unordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_12574,c_57]) ).

cnf(c_73705,plain,
    ( ~ member(not_subclass_element(X0,unordered_pair(X1,sP0_iProver_def)),sP1_iProver_def)
    | subclass(X0,unordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_12574,c_103]) ).

cnf(c_73706,plain,
    ( ~ member(X0,sP1_iProver_def)
    | subclass(sP3_iProver_def,unordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_12574,c_16382]) ).

cnf(c_73708,plain,
    ( ~ member(X0,sP1_iProver_def)
    | subclass(null_class,unordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_12574,c_11575]) ).

cnf(c_73756,plain,
    ( ~ member(X0,X1)
    | ~ member(sP0_iProver_def,X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_76,c_15456]) ).

cnf(c_73766,plain,
    ( ~ subclass(singleton(singleton(sP3_iProver_def)),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(singleton(sP3_iProver_def)) ),
    inference(superposition,[status(thm)],[c_69257,c_107]) ).

cnf(c_73776,plain,
    ( ~ subclass(singleton(singleton(null_class)),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(singleton(null_class)) ),
    inference(superposition,[status(thm)],[c_69259,c_107]) ).

cnf(c_73934,plain,
    ( ~ subclass(singleton(singleton(omega)),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(singleton(omega)) ),
    inference(superposition,[status(thm)],[c_69260,c_107]) ).

cnf(c_73943,plain,
    ( ~ subclass(singleton(singleton(sP1_iProver_def)),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(singleton(sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_69261,c_107]) ).

cnf(c_73952,plain,
    ( ~ subclass(ordered_pair(X0,X1),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(X0,X1) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69281,c_107]) ).

cnf(c_73955,plain,
    ( ~ subclass(ordered_pair(X0,X1),X2)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X2) ),
    inference(superposition,[status(thm)],[c_69281,c_54]) ).

cnf(c_73961,plain,
    ( ~ subclass(ordered_pair(null_class,X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(null_class,X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69284,c_107]) ).

cnf(c_73964,plain,
    ( ~ subclass(ordered_pair(null_class,X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69284,c_54]) ).

cnf(c_73969,plain,
    ( ~ subclass(ordered_pair(omega,X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(omega,X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69286,c_107]) ).

cnf(c_73972,plain,
    ( ~ subclass(ordered_pair(omega,X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69286,c_54]) ).

cnf(c_73977,plain,
    ( ~ subclass(ordered_pair(sP3_iProver_def,X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(sP3_iProver_def,X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69289,c_107]) ).

cnf(c_73980,plain,
    ( ~ subclass(ordered_pair(sP3_iProver_def,X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69289,c_54]) ).

cnf(c_73985,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(sP1_iProver_def,X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69291,c_107]) ).

cnf(c_73988,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69291,c_54]) ).

cnf(c_73994,plain,
    ( ~ subclass(singleton(singleton(sP0_iProver_def)),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(singleton(sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_69308,c_107]) ).

cnf(c_74008,plain,
    ( ~ subclass(unordered_pair(X0,null_class),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,null_class) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69314,c_107]) ).

cnf(c_74011,plain,
    ( ~ subclass(unordered_pair(X0,null_class),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69314,c_54]) ).

cnf(c_74137,plain,
    ( ~ subclass(unordered_pair(null_class,X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(null_class,X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69315,c_107]) ).

cnf(c_74140,plain,
    ( ~ subclass(unordered_pair(null_class,X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69315,c_54]) ).

cnf(c_74160,plain,
    ( ~ member(X0,X1)
    | ~ member(sP0_iProver_def,X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_76,c_15629]) ).

cnf(c_74168,plain,
    ( ~ subclass(X0,restrict(complement(cross_product(X1,X2)),X1,X2))
    | restrict(complement(cross_product(X1,X2)),X1,X2) = X0 ),
    inference(superposition,[status(thm)],[c_16180,c_107]) ).

cnf(c_74171,plain,
    ( ~ subclass(X0,X1)
    | subclass(restrict(complement(cross_product(X2,X3)),X2,X3),X1) ),
    inference(superposition,[status(thm)],[c_16180,c_54]) ).

cnf(c_74281,plain,
    ( ~ subclass(unordered_pair(X0,sP3_iProver_def),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,sP3_iProver_def) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69318,c_107]) ).

cnf(c_74284,plain,
    ( ~ subclass(unordered_pair(X0,sP3_iProver_def),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69318,c_54]) ).

cnf(c_74292,plain,
    ( ~ subclass(unordered_pair(sP3_iProver_def,X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(sP3_iProver_def,X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69319,c_107]) ).

cnf(c_74295,plain,
    ( ~ subclass(unordered_pair(sP3_iProver_def,X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69319,c_54]) ).

cnf(c_74310,plain,
    ( ~ subclass(ordered_pair(sP0_iProver_def,X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(sP0_iProver_def,X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69320,c_107]) ).

cnf(c_74313,plain,
    ( ~ subclass(ordered_pair(sP0_iProver_def,X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69320,c_54]) ).

cnf(c_74326,plain,
    ( ~ subclass(singleton(member_of(sP1_iProver_def)),intersection(sP2_iProver_def,sP1_iProver_def))
    | intersection(sP2_iProver_def,sP1_iProver_def) = singleton(member_of(sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_69330,c_107]) ).

cnf(c_74416,plain,
    ( ~ subclass(unordered_pair(X0,sP1_iProver_def),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,sP1_iProver_def) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69346,c_107]) ).

cnf(c_74419,plain,
    ( ~ subclass(unordered_pair(X0,sP1_iProver_def),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69346,c_54]) ).

cnf(c_74427,plain,
    ( ~ subclass(unordered_pair(sP1_iProver_def,X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(sP1_iProver_def,X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69349,c_107]) ).

cnf(c_74430,plain,
    ( ~ subclass(unordered_pair(sP1_iProver_def,X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69349,c_54]) ).

cnf(c_74442,plain,
    ( ~ subclass(unordered_pair(X0,omega),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,omega) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69352,c_107]) ).

cnf(c_74445,plain,
    ( ~ subclass(unordered_pair(X0,omega),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69352,c_54]) ).

cnf(c_74677,plain,
    ( ~ subclass(unordered_pair(omega,X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(omega,X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69353,c_107]) ).

cnf(c_74680,plain,
    ( ~ subclass(unordered_pair(omega,X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69353,c_54]) ).

cnf(c_75239,plain,
    ( ~ subclass(unordered_pair(X0,sP0_iProver_def),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,sP0_iProver_def) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69357,c_107]) ).

cnf(c_75242,plain,
    ( ~ subclass(unordered_pair(X0,sP0_iProver_def),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69357,c_54]) ).

cnf(c_75282,plain,
    ( ~ subclass(unordered_pair(sP0_iProver_def,X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(sP0_iProver_def,X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69364,c_107]) ).

cnf(c_75285,plain,
    ( ~ subclass(unordered_pair(sP0_iProver_def,X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69364,c_54]) ).

cnf(c_75292,plain,
    ( member_of(X0) = X0
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X1,X0)) ),
    inference(superposition,[status(thm)],[c_90,c_69262]) ).

cnf(c_75302,plain,
    ( ~ subclass(unordered_pair(X0,singleton(X1)),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,singleton(X1)) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69262,c_107]) ).

cnf(c_75305,plain,
    ( ~ subclass(unordered_pair(X0,singleton(X1)),X2)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X2) ),
    inference(superposition,[status(thm)],[c_69262,c_54]) ).

cnf(c_75332,plain,
    ( ~ subclass(unordered_pair(singleton(X0),X1),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(singleton(X0),X1) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69268,c_107]) ).

cnf(c_75335,plain,
    ( ~ subclass(unordered_pair(singleton(X0),X1),X2)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X2) ),
    inference(superposition,[status(thm)],[c_69268,c_54]) ).

cnf(c_75375,plain,
    ( ~ member(X0,universal_class)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X1,X0)) ),
    inference(superposition,[status(thm)],[c_16717,c_11004]) ).

cnf(c_75376,plain,
    ( ~ subclass(unordered_pair(X0,X1),null_class)
    | ~ member(X1,universal_class)
    | unordered_pair(X0,X1) = null_class ),
    inference(superposition,[status(thm)],[c_16717,c_107]) ).

cnf(c_75379,plain,
    ( ~ subclass(unordered_pair(X0,X1),X2)
    | ~ member(X1,universal_class)
    | subclass(null_class,X2) ),
    inference(superposition,[status(thm)],[c_16717,c_54]) ).

cnf(c_75380,plain,
    ( ~ member(X0,universal_class)
    | ~ member(X1,null_class)
    | member(X1,unordered_pair(X2,X0)) ),
    inference(superposition,[status(thm)],[c_16717,c_101]) ).

cnf(c_75794,plain,
    ( ~ member(X0,X1)
    | ~ member(sP1_iProver_def,X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_76,c_17245]) ).

cnf(c_75804,plain,
    ( ~ member(singleton(X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_96,c_17253]) ).

cnf(c_75810,plain,
    ( ~ subclass(singleton(X0),X1)
    | member_of(X0) = X0
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_90,c_17253]) ).

cnf(c_75862,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP3_iProver_def)),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,singleton(sP3_iProver_def)) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69273,c_107]) ).

cnf(c_75865,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP3_iProver_def)),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69273,c_54]) ).

cnf(c_75874,plain,
    ( ~ subclass(unordered_pair(X0,singleton(null_class)),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,singleton(null_class)) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69274,c_107]) ).

cnf(c_75877,plain,
    ( ~ subclass(unordered_pair(X0,singleton(null_class)),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69274,c_54]) ).

cnf(c_75893,plain,
    ( ~ subclass(unordered_pair(X0,singleton(omega)),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,singleton(omega)) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69275,c_107]) ).

cnf(c_75896,plain,
    ( ~ subclass(unordered_pair(X0,singleton(omega)),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69275,c_54]) ).

cnf(c_75963,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP1_iProver_def)),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,singleton(sP1_iProver_def)) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69276,c_107]) ).

cnf(c_75966,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP1_iProver_def)),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69276,c_54]) ).

cnf(c_76026,plain,
    ( ~ subclass(unordered_pair(singleton(sP3_iProver_def),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(singleton(sP3_iProver_def),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69277,c_107]) ).

cnf(c_76029,plain,
    ( ~ subclass(unordered_pair(singleton(sP3_iProver_def),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69277,c_54]) ).

cnf(c_76039,plain,
    ( ~ subclass(unordered_pair(singleton(null_class),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(singleton(null_class),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69278,c_107]) ).

cnf(c_76042,plain,
    ( ~ subclass(unordered_pair(singleton(null_class),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69278,c_54]) ).

cnf(c_76105,plain,
    ( ~ subclass(unordered_pair(singleton(omega),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(singleton(omega),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69279,c_107]) ).

cnf(c_76108,plain,
    ( ~ subclass(unordered_pair(singleton(omega),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69279,c_54]) ).

cnf(c_76440,plain,
    ( ~ subclass(unordered_pair(singleton(sP1_iProver_def),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(singleton(sP1_iProver_def),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69280,c_107]) ).

cnf(c_76443,plain,
    ( ~ subclass(unordered_pair(singleton(sP1_iProver_def),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69280,c_54]) ).

cnf(c_76453,plain,
    ( ~ subclass(unordered_pair(singleton(sP0_iProver_def),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(singleton(sP0_iProver_def),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69307,c_107]) ).

cnf(c_76456,plain,
    ( ~ subclass(unordered_pair(singleton(sP0_iProver_def),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69307,c_54]) ).

cnf(c_76465,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP0_iProver_def)),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,singleton(sP0_iProver_def)) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69312,c_107]) ).

cnf(c_76468,plain,
    ( ~ subclass(unordered_pair(X0,singleton(sP0_iProver_def)),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69312,c_54]) ).

cnf(c_76474,plain,
    ( ~ subclass(ordered_pair(member_of(sP1_iProver_def),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(member_of(sP1_iProver_def),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69325,c_107]) ).

cnf(c_76477,plain,
    ( ~ subclass(ordered_pair(member_of(sP1_iProver_def),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69325,c_54]) ).

cnf(c_76486,plain,
    ( ~ subclass(unordered_pair(X0,member_of(sP1_iProver_def)),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,member_of(sP1_iProver_def)) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69328,c_107]) ).

cnf(c_76489,plain,
    ( ~ subclass(unordered_pair(X0,member_of(sP1_iProver_def)),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69328,c_54]) ).

cnf(c_76502,plain,
    ( ~ member(singleton(X0),universal_class)
    | subclass(null_class,unordered_pair(X1,singleton(X0))) ),
    inference(superposition,[status(thm)],[c_110,c_75804]) ).

cnf(c_76503,plain,
    ( ~ member(singleton(X0),X1)
    | ~ member(singleton(X0),X2)
    | subclass(null_class,intersection(X1,X2)) ),
    inference(superposition,[status(thm)],[c_123,c_75804]) ).

cnf(c_76504,plain,
    ( ~ member(singleton(X0),universal_class)
    | member(singleton(X0),X1)
    | subclass(null_class,complement(X1)) ),
    inference(superposition,[status(thm)],[c_125,c_75804]) ).

cnf(c_76505,plain,
    ( ~ member(singleton(X0),universal_class)
    | restrict(X1,singleton(singleton(X0)),universal_class) = null_class
    | subclass(null_class,domain_of(X1)) ),
    inference(superposition,[status(thm)],[c_131,c_75804]) ).

cnf(c_76506,plain,
    ( ~ member(ordered_pair(X0,singleton(X1)),compose(X2,X3))
    | subclass(null_class,image(X2,image(X3,singleton(X0)))) ),
    inference(superposition,[status(thm)],[c_158,c_75804]) ).

cnf(c_76521,plain,
    ( ~ member(singleton(X0),sP1_iProver_def)
    | subclass(null_class,unordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_12573,c_75804]) ).

cnf(c_76522,plain,
    ( ~ member(singleton(X0),sP1_iProver_def)
    | subclass(null_class,unordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_12574,c_75804]) ).

cnf(c_76553,plain,
    ( ~ member(X0,X1)
    | member_of(X0) = X0
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_90,c_75804]) ).

cnf(c_77073,plain,
    ( ~ member(X0,X1)
    | ~ member(sP1_iProver_def,X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_76,c_17309]) ).

cnf(c_77083,plain,
    ( ~ member(singleton(X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_96,c_17316]) ).

cnf(c_77089,plain,
    ( ~ subclass(singleton(X0),X1)
    | member_of(X0) = X0
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_90,c_17316]) ).

cnf(c_77105,plain,
    ( ~ subclass(unordered_pair(member_of(sP1_iProver_def),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(member_of(sP1_iProver_def),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69332,c_107]) ).

cnf(c_77108,plain,
    ( ~ subclass(unordered_pair(member_of(sP1_iProver_def),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69332,c_54]) ).

cnf(c_77117,plain,
    ( ~ subclass(singleton(member_of(singleton(null_class))),intersection(sP2_iProver_def,sP1_iProver_def))
    | singleton(member_of(singleton(null_class))) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69334,c_107]) ).

cnf(c_77129,plain,
    ( ~ subclass(singleton(member_of(singleton(sP3_iProver_def))),intersection(sP2_iProver_def,sP1_iProver_def))
    | singleton(member_of(singleton(sP3_iProver_def))) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69336,c_107]) ).

cnf(c_77156,plain,
    ( ~ subclass(singleton(member_of(singleton(omega))),intersection(sP2_iProver_def,sP1_iProver_def))
    | singleton(member_of(singleton(omega))) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69343,c_107]) ).

cnf(c_77168,plain,
    ( ~ subclass(singleton(member_of(singleton(sP1_iProver_def))),intersection(sP2_iProver_def,sP1_iProver_def))
    | singleton(member_of(singleton(sP1_iProver_def))) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69354,c_107]) ).

cnf(c_77181,plain,
    ( ~ subclass(singleton(member_of(singleton(sP0_iProver_def))),intersection(sP2_iProver_def,sP1_iProver_def))
    | singleton(member_of(singleton(sP0_iProver_def))) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69361,c_107]) ).

cnf(c_77198,plain,
    ( ~ member(singleton(X0),universal_class)
    | subclass(sP3_iProver_def,unordered_pair(X1,singleton(X0))) ),
    inference(superposition,[status(thm)],[c_110,c_77083]) ).

cnf(c_77199,plain,
    ( ~ member(singleton(X0),X1)
    | ~ member(singleton(X0),X2)
    | subclass(sP3_iProver_def,intersection(X1,X2)) ),
    inference(superposition,[status(thm)],[c_123,c_77083]) ).

cnf(c_77200,plain,
    ( ~ member(singleton(X0),universal_class)
    | member(singleton(X0),X1)
    | subclass(sP3_iProver_def,complement(X1)) ),
    inference(superposition,[status(thm)],[c_125,c_77083]) ).

cnf(c_77201,plain,
    ( ~ member(singleton(X0),universal_class)
    | restrict(X1,singleton(singleton(X0)),universal_class) = null_class
    | subclass(sP3_iProver_def,domain_of(X1)) ),
    inference(superposition,[status(thm)],[c_131,c_77083]) ).

cnf(c_77202,plain,
    ( ~ member(ordered_pair(X0,singleton(X1)),compose(X2,X3))
    | subclass(sP3_iProver_def,image(X2,image(X3,singleton(X0)))) ),
    inference(superposition,[status(thm)],[c_158,c_77083]) ).

cnf(c_77217,plain,
    ( ~ member(singleton(X0),sP1_iProver_def)
    | subclass(sP3_iProver_def,unordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_12573,c_77083]) ).

cnf(c_77218,plain,
    ( ~ member(singleton(X0),sP1_iProver_def)
    | subclass(sP3_iProver_def,unordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_12574,c_77083]) ).

cnf(c_77249,plain,
    ( ~ member(X0,X1)
    | member_of(X0) = X0
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_90,c_77083]) ).

cnf(c_77454,plain,
    ( singleton(member_of(singleton(X0))) = singleton(X0)
    | unordered_pair(X0,X0) = null_class ),
    inference(superposition,[status(thm)],[c_17551,c_88]) ).

cnf(c_77455,plain,
    ( unordered_pair(X0,X0) = null_class
    | member_of(singleton(X0)) = X0 ),
    inference(superposition,[status(thm)],[c_17551,c_91]) ).

cnf(c_77456,plain,
    ( ~ member(not_subclass_element(universal_class,X0),X0)
    | unordered_pair(not_subclass_element(X0,universal_class),not_subclass_element(X0,universal_class)) = null_class
    | X0 = universal_class ),
    inference(superposition,[status(thm)],[c_17551,c_58]) ).

cnf(c_77457,plain,
    ( unordered_pair(not_subclass_element(X0,universal_class),not_subclass_element(X0,universal_class)) = null_class
    | X0 = universal_class
    | member(not_subclass_element(universal_class,X0),universal_class) ),
    inference(superposition,[status(thm)],[c_17551,c_57]) ).

cnf(c_77467,plain,
    subclass(singleton(unordered_pair(singleton(X0),X1)),ordered_pair(X1,X0)),
    inference(superposition,[status(thm)],[c_65,c_20056]) ).

cnf(c_77469,plain,
    subclass(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),X0)),
    inference(superposition,[status(thm)],[c_112,c_20056]) ).

cnf(c_77470,plain,
    ( member_of(X0) = X0
    | subclass(singleton(unordered_pair(X1,X0)),ordered_pair(X1,member_of(X0))) ),
    inference(superposition,[status(thm)],[c_90,c_20056]) ).

cnf(c_77471,plain,
    ( member_of(X0) = X0
    | subclass(singleton(unordered_pair(X1,X0)),ordered_pair(X1,member_of1(X0))) ),
    inference(superposition,[status(thm)],[c_93,c_20056]) ).

cnf(c_77472,plain,
    subclass(singleton(unordered_pair(X0,sP1_iProver_def)),ordered_pair(X0,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_3174,c_20056]) ).

cnf(c_77473,plain,
    subclass(singleton(unordered_pair(X0,singleton(null_class))),ordered_pair(X0,member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_17671,c_20056]) ).

cnf(c_77474,plain,
    subclass(singleton(unordered_pair(X0,singleton(omega))),ordered_pair(X0,member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_17677,c_20056]) ).

cnf(c_77475,plain,
    subclass(singleton(unordered_pair(X0,sP1_iProver_def)),ordered_pair(X0,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_38619,c_20056]) ).

cnf(c_77476,plain,
    subclass(singleton(unordered_pair(X0,singleton(sP1_iProver_def))),ordered_pair(X0,member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_17681,c_20056]) ).

cnf(c_77477,plain,
    subclass(singleton(unordered_pair(X0,singleton(sP3_iProver_def))),ordered_pair(X0,member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_17682,c_20056]) ).

cnf(c_77478,plain,
    subclass(singleton(unordered_pair(X0,singleton(sP0_iProver_def))),ordered_pair(X0,member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_21807,c_20056]) ).

cnf(c_77480,plain,
    ( ~ subclass(ordered_pair(X0,X1),singleton(unordered_pair(X0,singleton(X1))))
    | singleton(unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1) ),
    inference(superposition,[status(thm)],[c_20056,c_107]) ).

cnf(c_77483,plain,
    ( ~ subclass(ordered_pair(X0,X1),X2)
    | subclass(singleton(unordered_pair(X0,singleton(X1))),X2) ),
    inference(superposition,[status(thm)],[c_20056,c_54]) ).

cnf(c_77484,plain,
    ( ~ member(X0,singleton(unordered_pair(X1,singleton(X2))))
    | member(X0,ordered_pair(X1,X2)) ),
    inference(superposition,[status(thm)],[c_20056,c_101]) ).

cnf(c_77487,plain,
    subclass(singleton(unordered_pair(sP1_iProver_def,X0)),ordered_pair(X0,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_65,c_77472]) ).

cnf(c_77489,plain,
    subclass(singleton(singleton(sP1_iProver_def)),ordered_pair(sP1_iProver_def,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_112,c_77472]) ).

cnf(c_77490,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(X0,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_77472,c_11004]) ).

cnf(c_77491,plain,
    ( ~ subclass(ordered_pair(X0,sP0_iProver_def),singleton(unordered_pair(X0,sP1_iProver_def)))
    | singleton(unordered_pair(X0,sP1_iProver_def)) = ordered_pair(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_77472,c_107]) ).

cnf(c_77494,plain,
    ( ~ subclass(ordered_pair(X0,sP0_iProver_def),X1)
    | subclass(singleton(unordered_pair(X0,sP1_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_77472,c_54]) ).

cnf(c_77495,plain,
    ( ~ member(X0,singleton(unordered_pair(X1,sP1_iProver_def)))
    | member(X0,ordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_77472,c_101]) ).

cnf(c_77496,plain,
    subclass(sP3_iProver_def,ordered_pair(X0,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_77472,c_15360]) ).

cnf(c_77497,plain,
    subclass(null_class,ordered_pair(X0,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_77472,c_15342]) ).

cnf(c_77579,plain,
    ( ~ subclass(ordered_pair(X0,sP0_iProver_def),sP3_iProver_def)
    | ordered_pair(X0,sP0_iProver_def) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_77496,c_107]) ).

cnf(c_77582,plain,
    ( ~ subclass(ordered_pair(X0,sP0_iProver_def),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_77496,c_54]) ).

cnf(c_77614,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(sP1_iProver_def,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_77489,c_11004]) ).

cnf(c_77615,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,sP0_iProver_def),singleton(singleton(sP1_iProver_def)))
    | ordered_pair(sP1_iProver_def,sP0_iProver_def) = singleton(singleton(sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_77489,c_107]) ).

cnf(c_77618,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,sP0_iProver_def),X0)
    | subclass(singleton(singleton(sP1_iProver_def)),X0) ),
    inference(superposition,[status(thm)],[c_77489,c_54]) ).

cnf(c_77619,plain,
    ( ~ member(X0,singleton(singleton(sP1_iProver_def)))
    | member(X0,ordered_pair(sP1_iProver_def,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_77489,c_101]) ).

cnf(c_77622,plain,
    subclass(sP3_iProver_def,ordered_pair(sP1_iProver_def,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_77489,c_17316]) ).

cnf(c_77623,plain,
    subclass(null_class,ordered_pair(sP1_iProver_def,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_77489,c_17253]) ).

cnf(c_77658,plain,
    ( ~ subclass(ordered_pair(X0,sP0_iProver_def),singleton(unordered_pair(sP1_iProver_def,X0)))
    | singleton(unordered_pair(sP1_iProver_def,X0)) = ordered_pair(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_77487,c_107]) ).

cnf(c_77661,plain,
    ( ~ subclass(ordered_pair(X0,sP0_iProver_def),X1)
    | subclass(singleton(unordered_pair(sP1_iProver_def,X0)),X1) ),
    inference(superposition,[status(thm)],[c_77487,c_54]) ).

cnf(c_77662,plain,
    ( ~ member(X0,singleton(unordered_pair(sP1_iProver_def,X1)))
    | member(X0,ordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_77487,c_101]) ).

cnf(c_77700,plain,
    ( ~ subclass(ordered_pair(X0,sP0_iProver_def),null_class)
    | ordered_pair(X0,sP0_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_77497,c_107]) ).

cnf(c_77703,plain,
    ( ~ subclass(ordered_pair(X0,sP0_iProver_def),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_77497,c_54]) ).

cnf(c_77706,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,sP0_iProver_def),sP3_iProver_def)
    | ordered_pair(sP1_iProver_def,sP0_iProver_def) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_77622,c_107]) ).

cnf(c_77713,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,sP0_iProver_def),null_class)
    | ordered_pair(sP1_iProver_def,sP0_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_77623,c_107]) ).

cnf(c_77927,plain,
    ( ~ subclass(ordered_pair(X0,sP0_iProver_def),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(X0,sP0_iProver_def) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_77490,c_107]) ).

cnf(c_77930,plain,
    ( ~ subclass(ordered_pair(X0,sP0_iProver_def),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_77490,c_54]) ).

cnf(c_77935,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,sP0_iProver_def),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(sP1_iProver_def,sP0_iProver_def) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_77614,c_107]) ).

cnf(c_77952,plain,
    ( singleton(member_of(singleton(not_subclass_element(X0,null_class)))) = singleton(not_subclass_element(X0,null_class))
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_21311,c_88]) ).

cnf(c_77953,plain,
    ( member_of(singleton(not_subclass_element(X0,null_class))) = not_subclass_element(X0,null_class)
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_21311,c_91]) ).

cnf(c_77960,plain,
    ( singleton(member_of(singleton(not_subclass_element(X0,sP3_iProver_def)))) = singleton(not_subclass_element(X0,sP3_iProver_def))
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_21340,c_88]) ).

cnf(c_77961,plain,
    ( member_of(singleton(not_subclass_element(X0,sP3_iProver_def))) = not_subclass_element(X0,sP3_iProver_def)
    | X0 = null_class ),
    inference(superposition,[status(thm)],[c_21340,c_91]) ).

cnf(c_78064,plain,
    ( singleton(member_of(singleton(not_subclass_element(identity_relation,null_class)))) = singleton(not_subclass_element(identity_relation,null_class))
    | null_class = identity_relation ),
    inference(superposition,[status(thm)],[c_21344,c_88]) ).

cnf(c_78065,plain,
    ( member_of(singleton(not_subclass_element(identity_relation,null_class))) = not_subclass_element(identity_relation,null_class)
    | null_class = identity_relation ),
    inference(superposition,[status(thm)],[c_21344,c_91]) ).

cnf(c_78259,plain,
    ( member(not_subclass_element(cantor(X0),X1),domain_of(X0))
    | subclass(cantor(X0),X1) ),
    inference(superposition,[status(thm)],[c_102,c_21855]) ).

cnf(c_78260,plain,
    ( cantor(X0) = X1
    | member(not_subclass_element(cantor(X0),X1),domain_of(X0))
    | member(not_subclass_element(X1,cantor(X0)),X1) ),
    inference(superposition,[status(thm)],[c_55,c_21855]) ).

cnf(c_78261,plain,
    ( cantor(X0) = null_class
    | member(not_subclass_element(cantor(X0),null_class),domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_63,c_21855]) ).

cnf(c_78262,plain,
    ( cantor(X0) = null_class
    | member(regular(cantor(X0)),domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_166,c_21855]) ).

cnf(c_78263,plain,
    ( ~ member(cantor(X0),universal_class)
    | cantor(X0) = null_class
    | member(apply(choice,cantor(X0)),domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_170,c_21855]) ).

cnf(c_78264,plain,
    ( cantor(X0) = null_class
    | member(not_subclass_element(cantor(X0),sP3_iProver_def),domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_7628,c_21855]) ).

cnf(c_78302,plain,
    member(not_subclass_element(sP1_iProver_def,null_class),x),
    inference(global_subsumption_just,[status(thm)],[c_21995,c_5941,c_8116,c_8262]) ).

cnf(c_78305,plain,
    member(not_subclass_element(sP1_iProver_def,sP3_iProver_def),x),
    inference(superposition,[status(thm)],[c_7302,c_78302]) ).

cnf(c_78307,plain,
    member(not_subclass_element(sP1_iProver_def,null_class),universal_class),
    inference(superposition,[status(thm)],[c_78302,c_12562]) ).

cnf(c_78559,plain,
    ( ~ subclass(unordered_pair(X0,X1),sP3_iProver_def)
    | ~ member(X1,universal_class)
    | unordered_pair(X0,X1) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_22148,c_107]) ).

cnf(c_78562,plain,
    ( ~ subclass(unordered_pair(X0,X1),X2)
    | ~ member(X1,universal_class)
    | subclass(sP3_iProver_def,X2) ),
    inference(superposition,[status(thm)],[c_22148,c_54]) ).

cnf(c_78563,plain,
    ( ~ member(X0,universal_class)
    | ~ member(X1,sP3_iProver_def)
    | member(X1,unordered_pair(X2,X0)) ),
    inference(superposition,[status(thm)],[c_22148,c_101]) ).

cnf(c_78576,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),sP1_iProver_def)
    | ~ function(singleton(sP0_iProver_def))
    | cross_product(universal_class,universal_class) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_23805,c_107]) ).

cnf(c_78579,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | ~ function(singleton(sP0_iProver_def))
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_23805,c_54]) ).

cnf(c_78580,plain,
    ( ~ member(X0,sP1_iProver_def)
    | ~ function(singleton(sP0_iProver_def))
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_23805,c_101]) ).

cnf(c_78604,plain,
    ( ~ operation(inverse(restrict(X0,X1,universal_class)))
    | subclass(null_class,domain_of(image(X0,X1))) ),
    inference(superposition,[status(thm)],[c_142,c_23810]) ).

cnf(c_78605,plain,
    ( ~ operation(inverse(X0))
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),domain_of(range_of(X0))) ),
    inference(superposition,[status(thm)],[c_23810,c_11004]) ).

cnf(c_78606,plain,
    ( ~ subclass(domain_of(range_of(X0)),null_class)
    | ~ operation(inverse(X0))
    | domain_of(range_of(X0)) = null_class ),
    inference(superposition,[status(thm)],[c_23810,c_107]) ).

cnf(c_78609,plain,
    ( ~ subclass(domain_of(range_of(X0)),X1)
    | ~ operation(inverse(X0))
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_23810,c_54]) ).

cnf(c_78753,plain,
    member(not_subclass_element(sP1_iProver_def,sP3_iProver_def),universal_class),
    inference(superposition,[status(thm)],[c_78305,c_12562]) ).

cnf(c_78781,plain,
    singleton(member_of(singleton(not_subclass_element(sP1_iProver_def,null_class)))) = singleton(not_subclass_element(sP1_iProver_def,null_class)),
    inference(superposition,[status(thm)],[c_78307,c_88]) ).

cnf(c_78782,plain,
    member_of(singleton(not_subclass_element(sP1_iProver_def,null_class))) = not_subclass_element(sP1_iProver_def,null_class),
    inference(superposition,[status(thm)],[c_78307,c_91]) ).

cnf(c_78787,plain,
    singleton(member_of(singleton(not_subclass_element(sP1_iProver_def,sP3_iProver_def)))) = singleton(not_subclass_element(sP1_iProver_def,sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_78753,c_88]) ).

cnf(c_78788,plain,
    member_of(singleton(not_subclass_element(sP1_iProver_def,sP3_iProver_def))) = not_subclass_element(sP1_iProver_def,sP3_iProver_def),
    inference(superposition,[status(thm)],[c_78753,c_91]) ).

cnf(c_78796,plain,
    ( singleton(member_of(singleton(not_subclass_element(identity_relation,sP3_iProver_def)))) = singleton(not_subclass_element(identity_relation,sP3_iProver_def))
    | null_class = identity_relation ),
    inference(superposition,[status(thm)],[c_22402,c_88]) ).

cnf(c_78797,plain,
    ( member_of(singleton(not_subclass_element(identity_relation,sP3_iProver_def))) = not_subclass_element(identity_relation,sP3_iProver_def)
    | null_class = identity_relation ),
    inference(superposition,[status(thm)],[c_22402,c_91]) ).

cnf(c_78838,plain,
    ( singleton(member_of(singleton(not_subclass_element(universal_class,sP3_iProver_def)))) = singleton(not_subclass_element(universal_class,sP3_iProver_def))
    | universal_class = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_24617,c_88]) ).

cnf(c_78839,plain,
    ( member_of(singleton(not_subclass_element(universal_class,sP3_iProver_def))) = not_subclass_element(universal_class,sP3_iProver_def)
    | universal_class = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_24617,c_91]) ).

cnf(c_78846,plain,
    ( X0 = sP3_iProver_def
    | member(not_subclass_element(X0,sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_24617,c_12562]) ).

cnf(c_78848,plain,
    ( not_subclass_element(singleton(X0),sP3_iProver_def) = X0
    | singleton(X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_24617,c_82]) ).

cnf(c_78849,plain,
    ( not_subclass_element(unordered_pair(X0,X1),sP3_iProver_def) = X0
    | not_subclass_element(unordered_pair(X0,X1),sP3_iProver_def) = X1
    | unordered_pair(X0,X1) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_24617,c_108]) ).

cnf(c_78850,plain,
    ( ordered_pair(first(not_subclass_element(cross_product(X0,X1),sP3_iProver_def)),second(not_subclass_element(cross_product(X0,X1),sP3_iProver_def))) = not_subclass_element(cross_product(X0,X1),sP3_iProver_def)
    | cross_product(X0,X1) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_24617,c_117]) ).

cnf(c_78851,plain,
    ( intersection(X0,X1) = sP3_iProver_def
    | member(not_subclass_element(intersection(X0,X1),sP3_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_24617,c_122]) ).

cnf(c_78852,plain,
    ( intersection(X0,X1) = sP3_iProver_def
    | member(not_subclass_element(intersection(X0,X1),sP3_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_24617,c_121]) ).

cnf(c_78853,plain,
    ( ~ member(not_subclass_element(complement(X0),sP3_iProver_def),X0)
    | complement(X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_24617,c_124]) ).

cnf(c_78854,plain,
    ( ~ member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),sP3_iProver_def)),cross_product(universal_class,universal_class))
    | image(X1,image(X2,singleton(X0))) = sP3_iProver_def
    | member(ordered_pair(X0,not_subclass_element(image(X1,image(X2,singleton(X0))),sP3_iProver_def)),compose(X1,X2)) ),
    inference(superposition,[status(thm)],[c_24617,c_159]) ).

cnf(c_78859,plain,
    ( ~ member(not_subclass_element(sP1_iProver_def,sP3_iProver_def),sP2_iProver_def)
    | sP1_iProver_def = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_24617,c_8506]) ).

cnf(c_78861,plain,
    ( identity_relation = sP3_iProver_def
    | member(not_subclass_element(identity_relation,sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_24617,c_16702]) ).

cnf(c_78862,plain,
    ( identity_relation = sP3_iProver_def
    | member(not_subclass_element(identity_relation,sP3_iProver_def),subset_relation) ),
    inference(superposition,[status(thm)],[c_24617,c_8376]) ).

cnf(c_78864,plain,
    ( element_relation = sP3_iProver_def
    | member(not_subclass_element(element_relation,sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_24617,c_67721]) ).

cnf(c_78865,plain,
    ( successor_relation = sP3_iProver_def
    | member(not_subclass_element(successor_relation,sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_24617,c_68433]) ).

cnf(c_78866,plain,
    ( image(successor_relation,omega) = sP3_iProver_def
    | member(not_subclass_element(image(successor_relation,omega),sP3_iProver_def),omega) ),
    inference(superposition,[status(thm)],[c_24617,c_12572]) ).

cnf(c_78867,plain,
    ( cantor(X0) = sP3_iProver_def
    | member(not_subclass_element(cantor(X0),sP3_iProver_def),domain_of(X0)) ),
    inference(superposition,[status(thm)],[c_24617,c_21855]) ).

cnf(c_79804,plain,
    ( ~ operation(inverse(restrict(X0,X1,universal_class)))
    | subclass(sP3_iProver_def,domain_of(image(X0,X1))) ),
    inference(superposition,[status(thm)],[c_142,c_30791]) ).

cnf(c_79806,plain,
    ( ~ subclass(domain_of(range_of(X0)),sP3_iProver_def)
    | ~ operation(inverse(X0))
    | domain_of(range_of(X0)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_30791,c_107]) ).

cnf(c_79809,plain,
    ( ~ subclass(domain_of(range_of(X0)),X1)
    | ~ operation(inverse(X0))
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_30791,c_54]) ).

cnf(c_79812,plain,
    subclass(singleton(singleton(null_class)),ordered_pair(null_class,X0)),
    inference(superposition,[status(thm)],[c_9488,c_30928]) ).

cnf(c_79815,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(null_class)),X0),singleton(singleton(null_class)))
    | ordered_pair(member_of(singleton(null_class)),X0) = singleton(singleton(null_class)) ),
    inference(superposition,[status(thm)],[c_30928,c_107]) ).

cnf(c_79818,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(null_class)),X0),X1)
    | subclass(singleton(singleton(null_class)),X1) ),
    inference(superposition,[status(thm)],[c_30928,c_54]) ).

cnf(c_79819,plain,
    ( ~ member(X0,singleton(singleton(null_class)))
    | member(X0,ordered_pair(member_of(singleton(null_class)),X1)) ),
    inference(superposition,[status(thm)],[c_30928,c_101]) ).

cnf(c_80017,plain,
    subclass(singleton(singleton(sP3_iProver_def)),ordered_pair(sP3_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_7302,c_79812]) ).

cnf(c_80020,plain,
    ( ~ subclass(ordered_pair(null_class,X0),singleton(singleton(null_class)))
    | ordered_pair(null_class,X0) = singleton(singleton(null_class)) ),
    inference(superposition,[status(thm)],[c_79812,c_107]) ).

cnf(c_80023,plain,
    ( ~ subclass(ordered_pair(null_class,X0),X1)
    | subclass(singleton(singleton(null_class)),X1) ),
    inference(superposition,[status(thm)],[c_79812,c_54]) ).

cnf(c_80024,plain,
    ( ~ member(X0,singleton(singleton(null_class)))
    | member(X0,ordered_pair(null_class,X1)) ),
    inference(superposition,[status(thm)],[c_79812,c_101]) ).

cnf(c_80199,plain,
    ( ~ subclass(ordered_pair(sP3_iProver_def,X0),singleton(singleton(sP3_iProver_def)))
    | ordered_pair(sP3_iProver_def,X0) = singleton(singleton(sP3_iProver_def)) ),
    inference(superposition,[status(thm)],[c_80017,c_107]) ).

cnf(c_80202,plain,
    ( ~ subclass(ordered_pair(sP3_iProver_def,X0),X1)
    | subclass(singleton(singleton(sP3_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_80017,c_54]) ).

cnf(c_80203,plain,
    ( ~ member(X0,singleton(singleton(sP3_iProver_def)))
    | member(X0,ordered_pair(sP3_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_80017,c_101]) ).

cnf(c_80267,plain,
    subclass(singleton(singleton(omega)),ordered_pair(omega,X0)),
    inference(superposition,[status(thm)],[c_9494,c_33242]) ).

cnf(c_80269,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(omega)),X0),singleton(singleton(omega)))
    | ordered_pair(member_of(singleton(omega)),X0) = singleton(singleton(omega)) ),
    inference(superposition,[status(thm)],[c_33242,c_107]) ).

cnf(c_80272,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(omega)),X0),X1)
    | subclass(singleton(singleton(omega)),X1) ),
    inference(superposition,[status(thm)],[c_33242,c_54]) ).

cnf(c_80273,plain,
    ( ~ member(X0,singleton(singleton(omega)))
    | member(X0,ordered_pair(member_of(singleton(omega)),X1)) ),
    inference(superposition,[status(thm)],[c_33242,c_101]) ).

cnf(c_80490,plain,
    ( ~ subclass(ordered_pair(omega,X0),singleton(singleton(omega)))
    | ordered_pair(omega,X0) = singleton(singleton(omega)) ),
    inference(superposition,[status(thm)],[c_80267,c_107]) ).

cnf(c_80493,plain,
    ( ~ subclass(ordered_pair(omega,X0),X1)
    | subclass(singleton(singleton(omega)),X1) ),
    inference(superposition,[status(thm)],[c_80267,c_54]) ).

cnf(c_80494,plain,
    ( ~ member(X0,singleton(singleton(omega)))
    | member(X0,ordered_pair(omega,X1)) ),
    inference(superposition,[status(thm)],[c_80267,c_101]) ).

cnf(c_80574,plain,
    subclass(singleton(singleton(sP1_iProver_def)),ordered_pair(sP1_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_9498,c_35403]) ).

cnf(c_80576,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP1_iProver_def)),X0),singleton(singleton(sP1_iProver_def)))
    | ordered_pair(member_of(singleton(sP1_iProver_def)),X0) = singleton(singleton(sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_35403,c_107]) ).

cnf(c_80579,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP1_iProver_def)),X0),X1)
    | subclass(singleton(singleton(sP1_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_35403,c_54]) ).

cnf(c_80580,plain,
    ( ~ member(X0,singleton(singleton(sP1_iProver_def)))
    | member(X0,ordered_pair(member_of(singleton(sP1_iProver_def)),X1)) ),
    inference(superposition,[status(thm)],[c_35403,c_101]) ).

cnf(c_80728,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,X0),singleton(singleton(sP1_iProver_def)))
    | ordered_pair(sP1_iProver_def,X0) = singleton(singleton(sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_80574,c_107]) ).

cnf(c_80731,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,X0),X1)
    | subclass(singleton(singleton(sP1_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_80574,c_54]) ).

cnf(c_80732,plain,
    ( ~ member(X0,singleton(singleton(sP1_iProver_def)))
    | member(X0,ordered_pair(sP1_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_80574,c_101]) ).

cnf(c_80821,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP3_iProver_def)),X0),singleton(singleton(sP3_iProver_def)))
    | ordered_pair(member_of(singleton(sP3_iProver_def)),X0) = singleton(singleton(sP3_iProver_def)) ),
    inference(superposition,[status(thm)],[c_36578,c_107]) ).

cnf(c_80824,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP3_iProver_def)),X0),X1)
    | subclass(singleton(singleton(sP3_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_36578,c_54]) ).

cnf(c_80825,plain,
    ( ~ member(X0,singleton(singleton(sP3_iProver_def)))
    | member(X0,ordered_pair(member_of(singleton(sP3_iProver_def)),X1)) ),
    inference(superposition,[status(thm)],[c_36578,c_101]) ).

cnf(c_81044,plain,
    intersection(complement(sP3_iProver_def),union(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def))) = symmetric_difference(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),
    inference(superposition,[status(thm)],[c_37116,c_1297]) ).

cnf(c_81052,plain,
    subclass(singleton(singleton(sP0_iProver_def)),ordered_pair(sP0_iProver_def,X0)),
    inference(superposition,[status(thm)],[c_21808,c_38625]) ).

cnf(c_81055,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP0_iProver_def)),X0),singleton(singleton(sP0_iProver_def)))
    | ordered_pair(member_of(singleton(sP0_iProver_def)),X0) = singleton(singleton(sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_38625,c_107]) ).

cnf(c_81058,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP0_iProver_def)),X0),X1)
    | subclass(singleton(singleton(sP0_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_38625,c_54]) ).

cnf(c_81059,plain,
    ( ~ member(X0,singleton(singleton(sP0_iProver_def)))
    | member(X0,ordered_pair(member_of(singleton(sP0_iProver_def)),X1)) ),
    inference(superposition,[status(thm)],[c_38625,c_101]) ).

cnf(c_81127,plain,
    ( ~ subclass(ordered_pair(sP0_iProver_def,X0),singleton(singleton(sP0_iProver_def)))
    | ordered_pair(sP0_iProver_def,X0) = singleton(singleton(sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_81052,c_107]) ).

cnf(c_81130,plain,
    ( ~ subclass(ordered_pair(sP0_iProver_def,X0),X1)
    | subclass(singleton(singleton(sP0_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_81052,c_54]) ).

cnf(c_81131,plain,
    ( ~ member(X0,singleton(singleton(sP0_iProver_def)))
    | member(X0,ordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_81052,c_101]) ).

cnf(c_81632,plain,
    intersection(complement(intersection(member_of(sP1_iProver_def),sP1_iProver_def)),successor(member_of(sP1_iProver_def))) = symmetric_difference(member_of(sP1_iProver_def),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_39627,c_1297]) ).

cnf(c_81633,plain,
    member(member_of(sP1_iProver_def),sP1_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_39629,c_5705,c_8116,c_15164]) ).

cnf(c_81639,plain,
    member(member_of(sP1_iProver_def),universal_class),
    inference(superposition,[status(thm)],[c_81633,c_16549]) ).

cnf(c_81640,plain,
    member(member_of(sP1_iProver_def),x),
    inference(superposition,[status(thm)],[c_81633,c_12586]) ).

cnf(c_81641,plain,
    ~ member(member_of(sP1_iProver_def),sP2_iProver_def),
    inference(superposition,[status(thm)],[c_81633,c_8506]) ).

cnf(c_81904,plain,
    ( not_subclass_element(sP1_iProver_def,X0) = member_of(sP1_iProver_def)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_102,c_39648]) ).

cnf(c_81905,plain,
    ( not_subclass_element(sP1_iProver_def,X0) = member_of(sP1_iProver_def)
    | X0 = sP1_iProver_def
    | member(not_subclass_element(X0,sP1_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_55,c_39648]) ).

cnf(c_81906,plain,
    ( not_subclass_element(sP1_iProver_def,null_class) = member_of(sP1_iProver_def)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_63,c_39648]) ).

cnf(c_81907,plain,
    ( member_of(sP1_iProver_def) = regular(sP1_iProver_def)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_166,c_39648]) ).

cnf(c_81908,plain,
    ( ~ member(sP1_iProver_def,universal_class)
    | apply(choice,sP1_iProver_def) = member_of(sP1_iProver_def)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_170,c_39648]) ).

cnf(c_81911,plain,
    ( not_subclass_element(sP1_iProver_def,sP3_iProver_def) = member_of(sP1_iProver_def)
    | sP1_iProver_def = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_24617,c_39648]) ).

cnf(c_81912,plain,
    ( not_subclass_element(sP1_iProver_def,sP3_iProver_def) = member_of(sP1_iProver_def)
    | null_class = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_7628,c_39648]) ).

cnf(c_82632,plain,
    ( ~ function(singleton(member_of(sP1_iProver_def)))
    | subclass(sP1_iProver_def,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_41354]) ).

cnf(c_82638,plain,
    singleton(member_of(singleton(member_of(sP1_iProver_def)))) = singleton(member_of(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_81639,c_88]) ).

cnf(c_82639,plain,
    member_of(singleton(member_of(sP1_iProver_def))) = member_of(sP1_iProver_def),
    inference(superposition,[status(thm)],[c_81639,c_91]) ).

cnf(c_82652,plain,
    ( ~ member(X0,singleton(member_of(sP1_iProver_def)))
    | member_of(singleton(member_of(sP1_iProver_def))) = X0 ),
    inference(superposition,[status(thm)],[c_82639,c_95]) ).

cnf(c_82653,plain,
    member(singleton(member_of(sP1_iProver_def)),universal_class),
    inference(superposition,[status(thm)],[c_82639,c_94]) ).

cnf(c_82931,plain,
    singleton(member_of(singleton(singleton(member_of(sP1_iProver_def))))) = singleton(singleton(member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_82653,c_88]) ).

cnf(c_82932,plain,
    member_of(singleton(singleton(member_of(sP1_iProver_def)))) = singleton(member_of(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_82653,c_91]) ).

cnf(c_82941,plain,
    ( ~ member(not_subclass_element(singleton(member_of(sP1_iProver_def)),X0),X0)
    | ~ member(not_subclass_element(X0,singleton(member_of(sP1_iProver_def))),sP1_iProver_def)
    | singleton(member_of(sP1_iProver_def)) = X0 ),
    inference(superposition,[status(thm)],[c_41355,c_58]) ).

cnf(c_82942,plain,
    ( ~ member(not_subclass_element(X0,singleton(member_of(sP1_iProver_def))),sP1_iProver_def)
    | singleton(member_of(sP1_iProver_def)) = X0
    | member(not_subclass_element(singleton(member_of(sP1_iProver_def)),X0),singleton(member_of(sP1_iProver_def))) ),
    inference(superposition,[status(thm)],[c_41355,c_57]) ).

cnf(c_82943,plain,
    ( ~ member(not_subclass_element(X0,singleton(member_of(sP1_iProver_def))),sP1_iProver_def)
    | subclass(X0,singleton(member_of(sP1_iProver_def))) ),
    inference(superposition,[status(thm)],[c_41355,c_103]) ).

cnf(c_83254,plain,
    ( ~ member(X0,X1)
    | ~ member(null_class,X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_76,c_43928]) ).

cnf(c_83571,plain,
    ( ~ member(X0,X1)
    | ~ member(null_class,X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_76,c_43996]) ).

cnf(c_83826,plain,
    ( ~ member(X0,X1)
    | ~ member(sP3_iProver_def,X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_76,c_44457]) ).

cnf(c_83898,plain,
    ( ~ member(X0,X1)
    | ~ member(sP3_iProver_def,X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_76,c_45383]) ).

cnf(c_84210,plain,
    ( ~ member(X0,X1)
    | ~ member(omega,X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_76,c_46002]) ).

cnf(c_84479,plain,
    ( ~ member(X0,X1)
    | ~ member(omega,X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_76,c_46050]) ).

cnf(c_84954,plain,
    subclass(intersection(power_class(sP3_iProver_def),image(element_relation,complement(sP3_iProver_def))),X0),
    inference(superposition,[status(thm)],[c_7302,c_49295]) ).

cnf(c_84956,plain,
    ( ~ subclass(X0,intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))))
    | intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))) = X0 ),
    inference(superposition,[status(thm)],[c_49295,c_107]) ).

cnf(c_84959,plain,
    ( ~ subclass(X0,X1)
    | subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),X1) ),
    inference(superposition,[status(thm)],[c_49295,c_54]) ).

cnf(c_84960,plain,
    ( ~ member(X0,intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))))
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_49295,c_101]) ).

cnf(c_84963,plain,
    intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_49295,c_18296]) ).

cnf(c_84964,plain,
    intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))) = null_class,
    inference(superposition,[status(thm)],[c_49295,c_7304]) ).

cnf(c_85560,plain,
    union(power_class(null_class),image(element_relation,complement(sP3_iProver_def))) = complement(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_49296,c_37168]) ).

cnf(c_85562,plain,
    union(power_class(null_class),image(element_relation,complement(sP3_iProver_def))) = complement(null_class),
    inference(superposition,[status(thm)],[c_49296,c_15800]) ).

cnf(c_85563,plain,
    complement(intersection(power_class(null_class),complement(X0))) = union(image(element_relation,complement(sP3_iProver_def)),X0),
    inference(superposition,[status(thm)],[c_49296,c_126]) ).

cnf(c_85564,plain,
    subclass(intersection(power_class(image(element_relation,complement(sP3_iProver_def))),image(element_relation,power_class(null_class))),X0),
    inference(superposition,[status(thm)],[c_49296,c_8581]) ).

cnf(c_85565,plain,
    complement(image(element_relation,power_class(null_class))) = power_class(image(element_relation,complement(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_49296,c_155]) ).

cnf(c_85568,plain,
    complement(intersection(complement(X0),power_class(null_class))) = union(X0,image(element_relation,complement(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_49296,c_126]) ).

cnf(c_85569,plain,
    ( ~ member(X0,universal_class)
    | member(X0,image(element_relation,complement(sP3_iProver_def)))
    | member(X0,power_class(null_class)) ),
    inference(superposition,[status(thm)],[c_49296,c_125]) ).

cnf(c_85570,plain,
    ( ~ member(X0,image(element_relation,complement(sP3_iProver_def)))
    | ~ member(X0,power_class(null_class)) ),
    inference(superposition,[status(thm)],[c_49296,c_124]) ).

cnf(c_85571,plain,
    ~ member(X0,intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_49296,c_59]) ).

cnf(c_85572,plain,
    power_class(null_class) = power_class(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_49296,c_155]) ).

cnf(c_85760,plain,
    subclass(intersection(power_class(sP3_iProver_def),image(element_relation,complement(null_class))),X0),
    inference(superposition,[status(thm)],[c_85572,c_8581]) ).

cnf(c_85761,plain,
    ( ~ member(null_class,universal_class)
    | member(power_class(sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_85572,c_156]) ).

cnf(c_85781,plain,
    member(power_class(sP3_iProver_def),universal_class),
    inference(global_subsumption_just,[status(thm)],[c_85761,c_64,c_30967]) ).

cnf(c_85783,plain,
    singleton(member_of(singleton(power_class(sP3_iProver_def)))) = singleton(power_class(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_85781,c_88]) ).

cnf(c_85784,plain,
    member_of(singleton(power_class(sP3_iProver_def))) = power_class(sP3_iProver_def),
    inference(superposition,[status(thm)],[c_85781,c_91]) ).

cnf(c_85812,plain,
    ( ~ member(X0,singleton(power_class(sP3_iProver_def)))
    | member_of(singleton(power_class(sP3_iProver_def))) = X0 ),
    inference(superposition,[status(thm)],[c_85784,c_95]) ).

cnf(c_85813,plain,
    member(singleton(power_class(sP3_iProver_def)),universal_class),
    inference(superposition,[status(thm)],[c_85784,c_94]) ).

cnf(c_86297,plain,
    singleton(member_of(singleton(singleton(power_class(sP3_iProver_def))))) = singleton(singleton(power_class(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_85813,c_88]) ).

cnf(c_86298,plain,
    member_of(singleton(singleton(power_class(sP3_iProver_def)))) = singleton(power_class(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_85813,c_91]) ).

cnf(c_86306,plain,
    intersection(complement(sP3_iProver_def),union(complement(domain_of(sP3_iProver_def)),domain_of(null_class))) = symmetric_difference(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),
    inference(superposition,[status(thm)],[c_66846,c_1297]) ).

cnf(c_86313,plain,
    intersection(complement(null_class),union(complement(domain_of(sP3_iProver_def)),domain_of(null_class))) = symmetric_difference(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),
    inference(superposition,[status(thm)],[c_66851,c_1297]) ).

cnf(c_86414,plain,
    ( intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)) = X0
    | member(not_subclass_element(X0,intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class))),X0) ),
    inference(superposition,[status(thm)],[c_55,c_66856]) ).

cnf(c_86423,plain,
    ~ member(X0,intersection(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_7302,c_66856]) ).

cnf(c_86425,plain,
    ( singleton(member_of(singleton(not_subclass_element(element_relation,null_class)))) = singleton(not_subclass_element(element_relation,null_class))
    | null_class = element_relation ),
    inference(superposition,[status(thm)],[c_67774,c_88]) ).

cnf(c_86426,plain,
    ( member_of(singleton(not_subclass_element(element_relation,null_class))) = not_subclass_element(element_relation,null_class)
    | null_class = element_relation ),
    inference(superposition,[status(thm)],[c_67774,c_91]) ).

cnf(c_86431,plain,
    ( singleton(member_of(singleton(not_subclass_element(successor_relation,null_class)))) = singleton(not_subclass_element(successor_relation,null_class))
    | null_class = successor_relation ),
    inference(superposition,[status(thm)],[c_68543,c_88]) ).

cnf(c_86432,plain,
    ( member_of(singleton(not_subclass_element(successor_relation,null_class))) = not_subclass_element(successor_relation,null_class)
    | null_class = successor_relation ),
    inference(superposition,[status(thm)],[c_68543,c_91]) ).

cnf(c_86446,plain,
    ( X0 = X1
    | member(not_subclass_element(X0,X1),X0)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_55,c_69143]) ).

cnf(c_86459,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X3)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),cross_product(X1,X3)) ),
    inference(superposition,[status(thm)],[c_116,c_69143]) ).

cnf(c_86460,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),intersection(X1,X2)) ),
    inference(superposition,[status(thm)],[c_123,c_69143]) ).

cnf(c_86461,plain,
    ( ~ member(X0,universal_class)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),complement(X1))
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_125,c_69143]) ).

cnf(c_86462,plain,
    ( ~ member(X0,universal_class)
    | restrict(X1,singleton(X0),universal_class) = null_class
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),domain_of(X1)) ),
    inference(superposition,[status(thm)],[c_131,c_69143]) ).

cnf(c_86466,plain,
    ( ~ member(ordered_pair(X0,X1),compose(X2,X3))
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),image(X2,image(X3,singleton(X0)))) ),
    inference(superposition,[status(thm)],[c_158,c_69143]) ).

cnf(c_86470,plain,
    ( ~ compatible(X0,X1,X2)
    | ~ operation(X1)
    | ~ operation(X2)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),domain_of(X1))
    | homomorphism(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_190,c_69143]) ).

cnf(c_86505,plain,
    ( ~ member(X0,sP1_iProver_def)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_12573,c_69143]) ).

cnf(c_86506,plain,
    ( ~ member(X0,sP1_iProver_def)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),unordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_12574,c_69143]) ).

cnf(c_86678,plain,
    intersection(complement(sP3_iProver_def),union(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def))) = symmetric_difference(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_67453,c_1297]) ).

cnf(c_86679,plain,
    ( ~ member(X0,diagonalise(complement(identity_relation)))
    | ~ member(X0,domain_of(sP3_iProver_def))
    | member(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_67453,c_123]) ).

cnf(c_86686,plain,
    intersection(complement(null_class),union(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def))) = symmetric_difference(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_67454,c_1297]) ).

cnf(c_86687,plain,
    ( ~ member(X0,diagonalise(complement(identity_relation)))
    | ~ member(X0,domain_of(sP3_iProver_def))
    | member(X0,null_class) ),
    inference(superposition,[status(thm)],[c_67454,c_123]) ).

cnf(c_86740,plain,
    intersection(complement(sP3_iProver_def),union(diagonalise(complement(identity_relation)),domain_of(null_class))) = symmetric_difference(diagonalise(complement(identity_relation)),domain_of(null_class)),
    inference(superposition,[status(thm)],[c_67544,c_1297]) ).

cnf(c_86741,plain,
    ( ~ member(X0,diagonalise(complement(identity_relation)))
    | ~ member(X0,domain_of(null_class))
    | member(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_67544,c_123]) ).

cnf(c_86758,plain,
    intersection(complement(null_class),union(diagonalise(complement(identity_relation)),domain_of(null_class))) = symmetric_difference(diagonalise(complement(identity_relation)),domain_of(null_class)),
    inference(superposition,[status(thm)],[c_67545,c_1297]) ).

cnf(c_86759,plain,
    ( ~ member(X0,diagonalise(complement(identity_relation)))
    | ~ member(X0,domain_of(null_class))
    | member(X0,null_class) ),
    inference(superposition,[status(thm)],[c_67545,c_123]) ).

cnf(c_86826,plain,
    ( singleton(member_of(singleton(not_subclass_element(element_relation,sP3_iProver_def)))) = singleton(not_subclass_element(element_relation,sP3_iProver_def))
    | null_class = element_relation ),
    inference(superposition,[status(thm)],[c_67777,c_88]) ).

cnf(c_86827,plain,
    ( member_of(singleton(not_subclass_element(element_relation,sP3_iProver_def))) = not_subclass_element(element_relation,sP3_iProver_def)
    | null_class = element_relation ),
    inference(superposition,[status(thm)],[c_67777,c_91]) ).

cnf(c_86879,plain,
    intersection(complement(sP3_iProver_def),union(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def))) = symmetric_difference(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_67928,c_1297]) ).

cnf(c_86880,plain,
    ( ~ member(X0,complement(domain_of(sP3_iProver_def)))
    | ~ member(X0,domain_of(sP3_iProver_def))
    | member(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_67928,c_123]) ).

cnf(c_86889,plain,
    intersection(complement(null_class),union(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def))) = symmetric_difference(complement(domain_of(sP3_iProver_def)),domain_of(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_67929,c_1297]) ).

cnf(c_86890,plain,
    ( ~ member(X0,complement(domain_of(sP3_iProver_def)))
    | ~ member(X0,domain_of(sP3_iProver_def))
    | member(X0,null_class) ),
    inference(superposition,[status(thm)],[c_67929,c_123]) ).

cnf(c_87814,plain,
    intersection(complement(sP3_iProver_def),union(complement(domain_of(null_class)),domain_of(sP3_iProver_def))) = symmetric_difference(complement(domain_of(null_class)),domain_of(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_68042,c_1297]) ).

cnf(c_87815,plain,
    ( ~ member(X0,complement(domain_of(null_class)))
    | ~ member(X0,domain_of(sP3_iProver_def))
    | member(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_68042,c_123]) ).

cnf(c_87833,plain,
    intersection(complement(null_class),union(complement(domain_of(null_class)),domain_of(sP3_iProver_def))) = symmetric_difference(complement(domain_of(null_class)),domain_of(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_68043,c_1297]) ).

cnf(c_87834,plain,
    ( ~ member(X0,complement(domain_of(null_class)))
    | ~ member(X0,domain_of(sP3_iProver_def))
    | member(X0,null_class) ),
    inference(superposition,[status(thm)],[c_68043,c_123]) ).

cnf(c_87872,plain,
    intersection(complement(sP3_iProver_def),union(complement(domain_of(null_class)),domain_of(null_class))) = symmetric_difference(complement(domain_of(null_class)),domain_of(null_class)),
    inference(superposition,[status(thm)],[c_68141,c_1297]) ).

cnf(c_87873,plain,
    ( ~ member(X0,complement(domain_of(null_class)))
    | ~ member(X0,domain_of(null_class))
    | member(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_68141,c_123]) ).

cnf(c_87885,plain,
    intersection(complement(null_class),union(complement(domain_of(null_class)),domain_of(null_class))) = symmetric_difference(complement(domain_of(null_class)),domain_of(null_class)),
    inference(superposition,[status(thm)],[c_68142,c_1297]) ).

cnf(c_87886,plain,
    ( ~ member(X0,complement(domain_of(null_class)))
    | ~ member(X0,domain_of(null_class))
    | member(X0,null_class) ),
    inference(superposition,[status(thm)],[c_68142,c_123]) ).

cnf(c_87966,plain,
    ( singleton(member_of(singleton(not_subclass_element(successor_relation,sP3_iProver_def)))) = singleton(not_subclass_element(successor_relation,sP3_iProver_def))
    | null_class = successor_relation ),
    inference(superposition,[status(thm)],[c_68546,c_88]) ).

cnf(c_87967,plain,
    ( member_of(singleton(not_subclass_element(successor_relation,sP3_iProver_def))) = not_subclass_element(successor_relation,sP3_iProver_def)
    | null_class = successor_relation ),
    inference(superposition,[status(thm)],[c_68546,c_91]) ).

cnf(c_88002,plain,
    subclass(singleton(ordered_pair(X0,X1)),ordered_pair(unordered_pair(X0,singleton(X1)),X0)),
    inference(superposition,[status(thm)],[c_113,c_77467]) ).

cnf(c_88003,plain,
    ( member_of(X0) = X0
    | subclass(singleton(unordered_pair(X0,X1)),ordered_pair(X1,member_of(X0))) ),
    inference(superposition,[status(thm)],[c_90,c_77467]) ).

cnf(c_88004,plain,
    ( member_of(X0) = X0
    | subclass(singleton(unordered_pair(X0,X1)),ordered_pair(X1,member_of1(X0))) ),
    inference(superposition,[status(thm)],[c_93,c_77467]) ).

cnf(c_88006,plain,
    subclass(singleton(unordered_pair(singleton(null_class),X0)),ordered_pair(X0,member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_17671,c_77467]) ).

cnf(c_88007,plain,
    subclass(singleton(unordered_pair(singleton(omega),X0)),ordered_pair(X0,member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_17677,c_77467]) ).

cnf(c_88008,plain,
    subclass(singleton(unordered_pair(sP1_iProver_def,X0)),ordered_pair(X0,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_38619,c_77467]) ).

cnf(c_88009,plain,
    subclass(singleton(unordered_pair(singleton(sP1_iProver_def),X0)),ordered_pair(X0,member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_17681,c_77467]) ).

cnf(c_88010,plain,
    subclass(singleton(unordered_pair(singleton(sP3_iProver_def),X0)),ordered_pair(X0,member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_17682,c_77467]) ).

cnf(c_88011,plain,
    subclass(singleton(unordered_pair(singleton(sP0_iProver_def),X0)),ordered_pair(X0,member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_21807,c_77467]) ).

cnf(c_88013,plain,
    ( ~ subclass(ordered_pair(X0,X1),singleton(unordered_pair(singleton(X1),X0)))
    | singleton(unordered_pair(singleton(X1),X0)) = ordered_pair(X0,X1) ),
    inference(superposition,[status(thm)],[c_77467,c_107]) ).

cnf(c_88016,plain,
    ( ~ subclass(ordered_pair(X0,X1),X2)
    | subclass(singleton(unordered_pair(singleton(X1),X0)),X2) ),
    inference(superposition,[status(thm)],[c_77467,c_54]) ).

cnf(c_88017,plain,
    ( ~ member(X0,singleton(unordered_pair(singleton(X1),X2)))
    | member(X0,ordered_pair(X2,X1)) ),
    inference(superposition,[status(thm)],[c_77467,c_101]) ).

cnf(c_88484,plain,
    ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),intersection(sP2_iProver_def,sP1_iProver_def))
    | cross_product(cross_product(universal_class,universal_class),universal_class) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69229,c_107]) ).

cnf(c_88497,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(null_class))),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,member_of(singleton(null_class))) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69293,c_107]) ).

cnf(c_88500,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(null_class))),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69293,c_54]) ).

cnf(c_88510,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(null_class)),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(member_of(singleton(null_class)),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69295,c_107]) ).

cnf(c_88513,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(null_class)),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69295,c_54]) ).

cnf(c_88522,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP3_iProver_def))),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,member_of(singleton(sP3_iProver_def))) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69300,c_107]) ).

cnf(c_88525,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP3_iProver_def))),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69300,c_54]) ).

cnf(c_88534,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP3_iProver_def)),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(member_of(singleton(sP3_iProver_def)),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69303,c_107]) ).

cnf(c_88537,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP3_iProver_def)),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69303,c_54]) ).

cnf(c_88546,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(omega))),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,member_of(singleton(omega))) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69339,c_107]) ).

cnf(c_88549,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(omega))),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69339,c_54]) ).

cnf(c_88569,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(omega)),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(member_of(singleton(omega)),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69341,c_107]) ).

cnf(c_88572,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(omega)),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69341,c_54]) ).

cnf(c_88581,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP1_iProver_def))),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,member_of(singleton(sP1_iProver_def))) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69347,c_107]) ).

cnf(c_88584,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP1_iProver_def))),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69347,c_54]) ).

cnf(c_88657,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP1_iProver_def)),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(member_of(singleton(sP1_iProver_def)),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69350,c_107]) ).

cnf(c_88660,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP1_iProver_def)),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69350,c_54]) ).

cnf(c_88782,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP0_iProver_def))),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(X0,member_of(singleton(sP0_iProver_def))) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69358,c_107]) ).

cnf(c_88785,plain,
    ( ~ subclass(unordered_pair(X0,member_of(singleton(sP0_iProver_def))),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69358,c_54]) ).

cnf(c_88795,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP0_iProver_def)),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | unordered_pair(member_of(singleton(sP0_iProver_def)),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69365,c_107]) ).

cnf(c_88798,plain,
    ( ~ subclass(unordered_pair(member_of(singleton(sP0_iProver_def)),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69365,c_54]) ).

cnf(c_88805,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(null_class)),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(member_of(singleton(null_class)),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69371,c_107]) ).

cnf(c_88808,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(null_class)),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69371,c_54]) ).

cnf(c_88819,plain,
    ( member_of(X0) = X0
    | subclass(singleton(singleton(X0)),ordered_pair(X0,member_of(X0))) ),
    inference(superposition,[status(thm)],[c_90,c_77469]) ).

cnf(c_88820,plain,
    ( member_of(X0) = X0
    | subclass(singleton(singleton(X0)),ordered_pair(X0,member_of1(X0))) ),
    inference(superposition,[status(thm)],[c_93,c_77469]) ).

cnf(c_88822,plain,
    subclass(singleton(singleton(singleton(null_class))),ordered_pair(singleton(null_class),member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_17671,c_77469]) ).

cnf(c_88823,plain,
    subclass(singleton(singleton(singleton(omega))),ordered_pair(singleton(omega),member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_17677,c_77469]) ).

cnf(c_88824,plain,
    subclass(singleton(singleton(sP1_iProver_def)),ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_38619,c_77469]) ).

cnf(c_88825,plain,
    subclass(singleton(singleton(singleton(sP1_iProver_def))),ordered_pair(singleton(sP1_iProver_def),member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_17681,c_77469]) ).

cnf(c_88826,plain,
    subclass(singleton(singleton(singleton(sP3_iProver_def))),ordered_pair(singleton(sP3_iProver_def),member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_17682,c_77469]) ).

cnf(c_88827,plain,
    subclass(singleton(singleton(singleton(sP0_iProver_def))),ordered_pair(singleton(sP0_iProver_def),member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_21807,c_77469]) ).

cnf(c_88828,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(singleton(X0),X0)),
    inference(superposition,[status(thm)],[c_77469,c_11004]) ).

cnf(c_88829,plain,
    ( ~ subclass(ordered_pair(singleton(X0),X0),singleton(singleton(singleton(X0))))
    | ordered_pair(singleton(X0),X0) = singleton(singleton(singleton(X0))) ),
    inference(superposition,[status(thm)],[c_77469,c_107]) ).

cnf(c_88832,plain,
    ( ~ subclass(ordered_pair(singleton(X0),X0),X1)
    | subclass(singleton(singleton(singleton(X0))),X1) ),
    inference(superposition,[status(thm)],[c_77469,c_54]) ).

cnf(c_88833,plain,
    ( ~ member(X0,singleton(singleton(singleton(X1))))
    | member(X0,ordered_pair(singleton(X1),X1)) ),
    inference(superposition,[status(thm)],[c_77469,c_101]) ).

cnf(c_88836,plain,
    subclass(sP3_iProver_def,ordered_pair(singleton(X0),X0)),
    inference(superposition,[status(thm)],[c_77469,c_17316]) ).

cnf(c_88837,plain,
    subclass(null_class,ordered_pair(singleton(X0),X0)),
    inference(superposition,[status(thm)],[c_77469,c_17253]) ).

cnf(c_88863,plain,
    ( member_of(X0) = X0
    | subclass(sP3_iProver_def,ordered_pair(X0,member_of(X0))) ),
    inference(superposition,[status(thm)],[c_90,c_88836]) ).

cnf(c_88864,plain,
    ( member_of(X0) = X0
    | subclass(sP3_iProver_def,ordered_pair(X0,member_of1(X0))) ),
    inference(superposition,[status(thm)],[c_93,c_88836]) ).

cnf(c_88866,plain,
    subclass(sP3_iProver_def,ordered_pair(singleton(null_class),member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_17671,c_88836]) ).

cnf(c_88867,plain,
    subclass(sP3_iProver_def,ordered_pair(singleton(omega),member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_17677,c_88836]) ).

cnf(c_88868,plain,
    subclass(sP3_iProver_def,ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_38619,c_88836]) ).

cnf(c_88869,plain,
    subclass(sP3_iProver_def,ordered_pair(singleton(sP1_iProver_def),member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_17681,c_88836]) ).

cnf(c_88870,plain,
    subclass(sP3_iProver_def,ordered_pair(singleton(sP3_iProver_def),member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_17682,c_88836]) ).

cnf(c_88871,plain,
    subclass(sP3_iProver_def,ordered_pair(singleton(sP0_iProver_def),member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_21807,c_88836]) ).

cnf(c_88873,plain,
    ( ~ subclass(ordered_pair(singleton(X0),X0),sP3_iProver_def)
    | ordered_pair(singleton(X0),X0) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_88836,c_107]) ).

cnf(c_88876,plain,
    ( ~ subclass(ordered_pair(singleton(X0),X0),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_88836,c_54]) ).

cnf(c_88902,plain,
    ( member_of(X0) = X0
    | subclass(null_class,ordered_pair(X0,member_of(X0))) ),
    inference(superposition,[status(thm)],[c_90,c_88837]) ).

cnf(c_88903,plain,
    ( member_of(X0) = X0
    | subclass(null_class,ordered_pair(X0,member_of1(X0))) ),
    inference(superposition,[status(thm)],[c_93,c_88837]) ).

cnf(c_88905,plain,
    subclass(null_class,ordered_pair(singleton(null_class),member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_17671,c_88837]) ).

cnf(c_88906,plain,
    subclass(null_class,ordered_pair(singleton(omega),member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_17677,c_88837]) ).

cnf(c_88907,plain,
    subclass(null_class,ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_38619,c_88837]) ).

cnf(c_88908,plain,
    subclass(null_class,ordered_pair(singleton(sP1_iProver_def),member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_17681,c_88837]) ).

cnf(c_88909,plain,
    subclass(null_class,ordered_pair(singleton(sP3_iProver_def),member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_17682,c_88837]) ).

cnf(c_88910,plain,
    subclass(null_class,ordered_pair(singleton(sP0_iProver_def),member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_21807,c_88837]) ).

cnf(c_88912,plain,
    ( ~ subclass(ordered_pair(singleton(X0),X0),null_class)
    | ordered_pair(singleton(X0),X0) = null_class ),
    inference(superposition,[status(thm)],[c_88837,c_107]) ).

cnf(c_88915,plain,
    ( ~ subclass(ordered_pair(singleton(X0),X0),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_88837,c_54]) ).

cnf(c_89221,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_88868,c_11004]) ).

cnf(c_89222,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def)),sP3_iProver_def)
    | ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_88868,c_107]) ).

cnf(c_89230,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def)),null_class)
    | ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def)) = null_class ),
    inference(superposition,[status(thm)],[c_88907,c_107]) ).

cnf(c_89237,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def)),singleton(singleton(sP1_iProver_def)))
    | ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def)) = singleton(singleton(sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_88824,c_107]) ).

cnf(c_89240,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def)),X0)
    | subclass(singleton(singleton(sP1_iProver_def)),X0) ),
    inference(superposition,[status(thm)],[c_88824,c_54]) ).

cnf(c_89241,plain,
    ( ~ member(X0,singleton(singleton(sP1_iProver_def)))
    | member(X0,ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def))) ),
    inference(superposition,[status(thm)],[c_88824,c_101]) ).

cnf(c_89248,plain,
    ( member_of(X0) = X0
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(X0,member_of(X0))) ),
    inference(superposition,[status(thm)],[c_90,c_88828]) ).

cnf(c_89249,plain,
    ( member_of(X0) = X0
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(X0,member_of1(X0))) ),
    inference(superposition,[status(thm)],[c_93,c_88828]) ).

cnf(c_89251,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(singleton(null_class),member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_17671,c_88828]) ).

cnf(c_89252,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(singleton(omega),member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_17677,c_88828]) ).

cnf(c_89254,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(singleton(sP1_iProver_def),member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_17681,c_88828]) ).

cnf(c_89255,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(singleton(sP3_iProver_def),member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_17682,c_88828]) ).

cnf(c_89256,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(singleton(sP0_iProver_def),member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_21807,c_88828]) ).

cnf(c_89258,plain,
    ( ~ subclass(ordered_pair(singleton(X0),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(singleton(X0),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_88828,c_107]) ).

cnf(c_89261,plain,
    ( ~ subclass(ordered_pair(singleton(X0),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_88828,c_54]) ).

cnf(c_89414,plain,
    subclass(sP3_iProver_def,ordered_pair(singleton(null_class),null_class)),
    inference(superposition,[status(thm)],[c_9488,c_88866]) ).

cnf(c_89417,plain,
    ( ~ subclass(ordered_pair(singleton(null_class),member_of(singleton(null_class))),sP3_iProver_def)
    | ordered_pair(singleton(null_class),member_of(singleton(null_class))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_88866,c_107]) ).

cnf(c_90121,plain,
    subclass(sP3_iProver_def,ordered_pair(singleton(sP3_iProver_def),sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_89414]) ).

cnf(c_90123,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(singleton(null_class),null_class)),
    inference(superposition,[status(thm)],[c_89414,c_11004]) ).

cnf(c_90124,plain,
    ( ~ subclass(ordered_pair(singleton(null_class),null_class),sP3_iProver_def)
    | ordered_pair(singleton(null_class),null_class) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_89414,c_107]) ).

cnf(c_90126,plain,
    subclass(null_class,ordered_pair(singleton(null_class),null_class)),
    inference(superposition,[status(thm)],[c_89414,c_10981]) ).

cnf(c_90129,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(singleton(sP3_iProver_def),sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_90121,c_11004]) ).

cnf(c_90130,plain,
    ( ~ subclass(ordered_pair(singleton(sP3_iProver_def),sP3_iProver_def),sP3_iProver_def)
    | ordered_pair(singleton(sP3_iProver_def),sP3_iProver_def) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_90121,c_107]) ).

cnf(c_90132,plain,
    subclass(null_class,ordered_pair(singleton(sP3_iProver_def),sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_90121,c_10981]) ).

cnf(c_90139,plain,
    ( ~ subclass(ordered_pair(singleton(null_class),null_class),null_class)
    | ordered_pair(singleton(null_class),null_class) = null_class ),
    inference(superposition,[status(thm)],[c_90126,c_107]) ).

cnf(c_90146,plain,
    ( ~ subclass(ordered_pair(singleton(sP3_iProver_def),sP3_iProver_def),null_class)
    | ordered_pair(singleton(sP3_iProver_def),sP3_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_90132,c_107]) ).

cnf(c_90153,plain,
    subclass(sP3_iProver_def,ordered_pair(singleton(omega),omega)),
    inference(superposition,[status(thm)],[c_9494,c_88867]) ).

cnf(c_90155,plain,
    ( ~ subclass(ordered_pair(singleton(omega),member_of(singleton(omega))),sP3_iProver_def)
    | ordered_pair(singleton(omega),member_of(singleton(omega))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_88867,c_107]) ).

cnf(c_90300,plain,
    intersection(power_class(sP3_iProver_def),image(element_relation,complement(null_class))) = null_class,
    inference(superposition,[status(thm)],[c_85572,c_8580]) ).

cnf(c_90301,plain,
    intersection(power_class(intersection(complement(X0),complement(X1))),image(element_relation,union(X0,X1))) = null_class,
    inference(superposition,[status(thm)],[c_126,c_8580]) ).

cnf(c_90302,plain,
    intersection(power_class(image(element_relation,complement(X0))),image(element_relation,power_class(X0))) = null_class,
    inference(superposition,[status(thm)],[c_155,c_8580]) ).

cnf(c_90303,plain,
    intersection(power_class(domain_of(intersection(X0,identity_relation))),image(element_relation,diagonalise(X0))) = null_class,
    inference(superposition,[status(thm)],[c_176,c_8580]) ).

cnf(c_90305,plain,
    intersection(power_class(image(element_relation,sP2_iProver_def)),image(element_relation,power_class(sP1_iProver_def))) = null_class,
    inference(superposition,[status(thm)],[c_8578,c_8580]) ).

cnf(c_90306,plain,
    intersection(power_class(domain_of(null_class)),image(element_relation,complement(domain_of(sP3_iProver_def)))) = null_class,
    inference(superposition,[status(thm)],[c_49184,c_8580]) ).

cnf(c_90308,plain,
    intersection(power_class(image(element_relation,complement(sP3_iProver_def))),image(element_relation,power_class(null_class))) = null_class,
    inference(superposition,[status(thm)],[c_49296,c_8580]) ).

cnf(c_90309,plain,
    intersection(complement(null_class),union(power_class(X0),image(element_relation,complement(X0)))) = symmetric_difference(power_class(X0),image(element_relation,complement(X0))),
    inference(superposition,[status(thm)],[c_8580,c_1297]) ).

cnf(c_90452,plain,
    ( intersection(power_class(X0),image(element_relation,complement(X0))) = X1
    | member(not_subclass_element(X1,intersection(power_class(X0),image(element_relation,complement(X0)))),X1) ),
    inference(superposition,[status(thm)],[c_55,c_8583]) ).

cnf(c_90460,plain,
    ~ member(X0,intersection(power_class(sP3_iProver_def),image(element_relation,complement(null_class)))),
    inference(superposition,[status(thm)],[c_85572,c_8583]) ).

cnf(c_90461,plain,
    ~ member(X0,intersection(power_class(intersection(complement(X1),complement(X2))),image(element_relation,union(X1,X2)))),
    inference(superposition,[status(thm)],[c_126,c_8583]) ).

cnf(c_90462,plain,
    ~ member(X0,intersection(power_class(image(element_relation,complement(X1))),image(element_relation,power_class(X1)))),
    inference(superposition,[status(thm)],[c_155,c_8583]) ).

cnf(c_90463,plain,
    ~ member(X0,intersection(power_class(domain_of(intersection(X1,identity_relation))),image(element_relation,diagonalise(X1)))),
    inference(superposition,[status(thm)],[c_176,c_8583]) ).

cnf(c_90465,plain,
    ~ member(X0,intersection(power_class(image(element_relation,sP2_iProver_def)),image(element_relation,power_class(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_8578,c_8583]) ).

cnf(c_90466,plain,
    ~ member(X0,intersection(power_class(domain_of(null_class)),image(element_relation,complement(domain_of(sP3_iProver_def))))),
    inference(superposition,[status(thm)],[c_49184,c_8583]) ).

cnf(c_90468,plain,
    ~ member(X0,intersection(power_class(image(element_relation,complement(sP3_iProver_def))),image(element_relation,power_class(null_class)))),
    inference(superposition,[status(thm)],[c_49296,c_8583]) ).

cnf(c_90702,plain,
    ~ member(not_subclass_element(sP1_iProver_def,null_class),sP2_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_8730,c_5819,c_5941,c_8116]) ).

cnf(c_90705,plain,
    ~ member(not_subclass_element(sP1_iProver_def,sP3_iProver_def),sP2_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_90702]) ).

cnf(c_90706,plain,
    intersection(complement(domain_of(sP3_iProver_def)),domain_of(intersection(complement(identity_relation),identity_relation))) = null_class,
    inference(superposition,[status(thm)],[c_37170,c_8914]) ).

cnf(c_90707,plain,
    intersection(complement(domain_of(null_class)),domain_of(intersection(complement(identity_relation),identity_relation))) = null_class,
    inference(superposition,[status(thm)],[c_8912,c_8914]) ).

cnf(c_90710,plain,
    intersection(diagonalise(cross_product(X0,X1)),domain_of(restrict(identity_relation,X0,X1))) = null_class,
    inference(superposition,[status(thm)],[c_129,c_8914]) ).

cnf(c_90711,plain,
    intersection(complement(null_class),union(diagonalise(X0),domain_of(intersection(X0,identity_relation)))) = symmetric_difference(diagonalise(X0),domain_of(intersection(X0,identity_relation))),
    inference(superposition,[status(thm)],[c_8914,c_1297]) ).

cnf(c_90716,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(singleton(omega),omega)),
    inference(superposition,[status(thm)],[c_90153,c_11004]) ).

cnf(c_90717,plain,
    ( ~ subclass(ordered_pair(singleton(omega),omega),sP3_iProver_def)
    | ordered_pair(singleton(omega),omega) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_90153,c_107]) ).

cnf(c_90719,plain,
    subclass(null_class,ordered_pair(singleton(omega),omega)),
    inference(superposition,[status(thm)],[c_90153,c_10981]) ).

cnf(c_91079,plain,
    ( ~ subclass(ordered_pair(singleton(omega),omega),null_class)
    | ordered_pair(singleton(omega),omega) = null_class ),
    inference(superposition,[status(thm)],[c_90719,c_107]) ).

cnf(c_91223,plain,
    subclass(sP3_iProver_def,ordered_pair(singleton(sP1_iProver_def),sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_9498,c_88869]) ).

cnf(c_91225,plain,
    ( ~ subclass(ordered_pair(singleton(sP1_iProver_def),member_of(singleton(sP1_iProver_def))),sP3_iProver_def)
    | ordered_pair(singleton(sP1_iProver_def),member_of(singleton(sP1_iProver_def))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_88869,c_107]) ).

cnf(c_91230,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(singleton(sP1_iProver_def),sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_91223,c_11004]) ).

cnf(c_91231,plain,
    ( ~ subclass(ordered_pair(singleton(sP1_iProver_def),sP1_iProver_def),sP3_iProver_def)
    | ordered_pair(singleton(sP1_iProver_def),sP1_iProver_def) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_91223,c_107]) ).

cnf(c_91233,plain,
    subclass(null_class,ordered_pair(singleton(sP1_iProver_def),sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_91223,c_10981]) ).

cnf(c_91308,plain,
    ( ~ subclass(ordered_pair(singleton(sP1_iProver_def),sP1_iProver_def),null_class)
    | ordered_pair(singleton(sP1_iProver_def),sP1_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_91233,c_107]) ).

cnf(c_91315,plain,
    ( ~ subclass(ordered_pair(singleton(sP3_iProver_def),member_of(singleton(sP3_iProver_def))),sP3_iProver_def)
    | ordered_pair(singleton(sP3_iProver_def),member_of(singleton(sP3_iProver_def))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_88870,c_107]) ).

cnf(c_91321,plain,
    subclass(sP3_iProver_def,ordered_pair(singleton(sP0_iProver_def),sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_21808,c_88871]) ).

cnf(c_91324,plain,
    ( ~ subclass(ordered_pair(singleton(sP0_iProver_def),member_of(singleton(sP0_iProver_def))),sP3_iProver_def)
    | ordered_pair(singleton(sP0_iProver_def),member_of(singleton(sP0_iProver_def))) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_88871,c_107]) ).

cnf(c_91330,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(singleton(sP0_iProver_def),sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_91321,c_11004]) ).

cnf(c_91331,plain,
    ( ~ subclass(ordered_pair(singleton(sP0_iProver_def),sP0_iProver_def),sP3_iProver_def)
    | ordered_pair(singleton(sP0_iProver_def),sP0_iProver_def) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_91321,c_107]) ).

cnf(c_91333,plain,
    subclass(null_class,ordered_pair(singleton(sP0_iProver_def),sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_91321,c_10981]) ).

cnf(c_91339,plain,
    ( ~ subclass(ordered_pair(singleton(sP0_iProver_def),sP0_iProver_def),null_class)
    | ordered_pair(singleton(sP0_iProver_def),sP0_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_91333,c_107]) ).

cnf(c_91349,plain,
    ( ~ subclass(ordered_pair(singleton(null_class),member_of(singleton(null_class))),null_class)
    | ordered_pair(singleton(null_class),member_of(singleton(null_class))) = null_class ),
    inference(superposition,[status(thm)],[c_88905,c_107]) ).

cnf(c_91357,plain,
    ( ~ subclass(ordered_pair(singleton(omega),member_of(singleton(omega))),null_class)
    | ordered_pair(singleton(omega),member_of(singleton(omega))) = null_class ),
    inference(superposition,[status(thm)],[c_88906,c_107]) ).

cnf(c_91364,plain,
    ( intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))) = X1
    | member(not_subclass_element(X1,intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation)))),X1) ),
    inference(superposition,[status(thm)],[c_55,c_8917]) ).

cnf(c_91372,plain,
    ~ member(X0,intersection(complement(domain_of(sP3_iProver_def)),domain_of(intersection(complement(identity_relation),identity_relation)))),
    inference(superposition,[status(thm)],[c_37170,c_8917]) ).

cnf(c_91373,plain,
    ~ member(X0,intersection(complement(domain_of(null_class)),domain_of(intersection(complement(identity_relation),identity_relation)))),
    inference(superposition,[status(thm)],[c_8912,c_8917]) ).

cnf(c_91374,plain,
    ~ member(X0,intersection(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_37111,c_8917]) ).

cnf(c_91375,plain,
    ~ member(X0,intersection(diagonalise(complement(identity_relation)),domain_of(null_class))),
    inference(superposition,[status(thm)],[c_7611,c_8917]) ).

cnf(c_91376,plain,
    ~ member(X0,intersection(diagonalise(cross_product(X1,X2)),domain_of(restrict(identity_relation,X1,X2)))),
    inference(superposition,[status(thm)],[c_129,c_8917]) ).

cnf(c_91615,plain,
    ( ~ member(X0,singleton(unordered_pair(X1,X2)))
    | member_of(singleton(unordered_pair(X1,X2))) = X0 ),
    inference(superposition,[status(thm)],[c_9493,c_95]) ).

cnf(c_91616,plain,
    member(singleton(unordered_pair(X0,X1)),universal_class),
    inference(superposition,[status(thm)],[c_9493,c_94]) ).

cnf(c_91748,plain,
    member(singleton(ordered_pair(X0,X1)),universal_class),
    inference(superposition,[status(thm)],[c_113,c_91616]) ).

cnf(c_91749,plain,
    singleton(member_of(singleton(singleton(unordered_pair(X0,X1))))) = singleton(singleton(unordered_pair(X0,X1))),
    inference(superposition,[status(thm)],[c_91616,c_88]) ).

cnf(c_91750,plain,
    member_of(singleton(singleton(unordered_pair(X0,X1)))) = singleton(unordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_91616,c_91]) ).

cnf(c_92028,plain,
    singleton(member_of(singleton(singleton(ordered_pair(X0,X1))))) = singleton(singleton(ordered_pair(X0,X1))),
    inference(superposition,[status(thm)],[c_91748,c_88]) ).

cnf(c_92029,plain,
    member_of(singleton(singleton(ordered_pair(X0,X1)))) = singleton(ordered_pair(X0,X1)),
    inference(superposition,[status(thm)],[c_91748,c_91]) ).

cnf(c_92039,plain,
    ( ~ subclass(ordered_pair(singleton(sP1_iProver_def),member_of(singleton(sP1_iProver_def))),null_class)
    | ordered_pair(singleton(sP1_iProver_def),member_of(singleton(sP1_iProver_def))) = null_class ),
    inference(superposition,[status(thm)],[c_88908,c_107]) ).

cnf(c_92047,plain,
    ( ~ subclass(ordered_pair(singleton(sP3_iProver_def),member_of(singleton(sP3_iProver_def))),null_class)
    | ordered_pair(singleton(sP3_iProver_def),member_of(singleton(sP3_iProver_def))) = null_class ),
    inference(superposition,[status(thm)],[c_88909,c_107]) ).

cnf(c_92057,plain,
    ( ~ subclass(ordered_pair(singleton(sP0_iProver_def),member_of(singleton(sP0_iProver_def))),null_class)
    | ordered_pair(singleton(sP0_iProver_def),member_of(singleton(sP0_iProver_def))) = null_class ),
    inference(superposition,[status(thm)],[c_88910,c_107]) ).

cnf(c_92066,plain,
    ( ~ subclass(ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def)),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def)) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_89221,c_107]) ).

cnf(c_92076,plain,
    ( ~ subclass(ordered_pair(singleton(null_class),null_class),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(singleton(null_class),null_class) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_90123,c_107]) ).

cnf(c_92084,plain,
    ( ~ subclass(ordered_pair(singleton(sP3_iProver_def),sP3_iProver_def),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(singleton(sP3_iProver_def),sP3_iProver_def) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_90129,c_107]) ).

cnf(c_92097,plain,
    ( ~ subclass(ordered_pair(singleton(omega),omega),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(singleton(omega),omega) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_90716,c_107]) ).

cnf(c_92105,plain,
    ( ~ subclass(ordered_pair(singleton(sP1_iProver_def),sP1_iProver_def),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(singleton(sP1_iProver_def),sP1_iProver_def) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_91230,c_107]) ).

cnf(c_92146,plain,
    ( ~ subclass(ordered_pair(singleton(sP0_iProver_def),sP0_iProver_def),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(singleton(sP0_iProver_def),sP0_iProver_def) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_91330,c_107]) ).

cnf(c_92182,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP3_iProver_def)),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(member_of(singleton(sP3_iProver_def)),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69373,c_107]) ).

cnf(c_92185,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP3_iProver_def)),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69373,c_54]) ).

cnf(c_92197,plain,
    ( ~ member(X0,singleton(singleton(singleton(X1))))
    | member_of(singleton(singleton(singleton(X1)))) = X0 ),
    inference(superposition,[status(thm)],[c_10850,c_95]) ).

cnf(c_92198,plain,
    member(singleton(singleton(singleton(X0))),universal_class),
    inference(superposition,[status(thm)],[c_10850,c_94]) ).

cnf(c_92203,plain,
    member(singleton(singleton(singleton(null_class))),universal_class),
    inference(superposition,[status(thm)],[c_17671,c_92198]) ).

cnf(c_92204,plain,
    member(singleton(singleton(singleton(omega))),universal_class),
    inference(superposition,[status(thm)],[c_17677,c_92198]) ).

cnf(c_92206,plain,
    member(singleton(singleton(singleton(sP1_iProver_def))),universal_class),
    inference(superposition,[status(thm)],[c_17681,c_92198]) ).

cnf(c_92207,plain,
    member(singleton(singleton(singleton(sP3_iProver_def))),universal_class),
    inference(superposition,[status(thm)],[c_17682,c_92198]) ).

cnf(c_92208,plain,
    member(singleton(singleton(singleton(sP0_iProver_def))),universal_class),
    inference(superposition,[status(thm)],[c_21807,c_92198]) ).

cnf(c_92209,plain,
    singleton(member_of(singleton(singleton(singleton(singleton(X0)))))) = singleton(singleton(singleton(singleton(X0)))),
    inference(superposition,[status(thm)],[c_92198,c_88]) ).

cnf(c_92210,plain,
    member_of(singleton(singleton(singleton(singleton(X0))))) = singleton(singleton(singleton(X0))),
    inference(superposition,[status(thm)],[c_92198,c_91]) ).

cnf(c_92331,plain,
    ( ~ member(X0,singleton(singleton(singleton(null_class))))
    | member_of(singleton(singleton(singleton(null_class)))) = X0 ),
    inference(superposition,[status(thm)],[c_10866,c_95]) ).

cnf(c_92335,plain,
    ( ~ member(X0,singleton(singleton(singleton(sP3_iProver_def))))
    | member_of(singleton(singleton(singleton(sP3_iProver_def)))) = X0 ),
    inference(superposition,[status(thm)],[c_10943,c_95]) ).

cnf(c_92339,plain,
    singleton(member_of(singleton(singleton(singleton(singleton(null_class)))))) = singleton(singleton(singleton(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_92203,c_88]) ).

cnf(c_92340,plain,
    member_of(singleton(singleton(singleton(singleton(null_class))))) = singleton(singleton(singleton(null_class))),
    inference(superposition,[status(thm)],[c_92203,c_91]) ).

cnf(c_92377,plain,
    singleton(member_of(singleton(singleton(singleton(singleton(omega)))))) = singleton(singleton(singleton(singleton(omega)))),
    inference(superposition,[status(thm)],[c_92204,c_88]) ).

cnf(c_92378,plain,
    member_of(singleton(singleton(singleton(singleton(omega))))) = singleton(singleton(singleton(omega))),
    inference(superposition,[status(thm)],[c_92204,c_91]) ).

cnf(c_92409,plain,
    singleton(member_of(singleton(singleton(singleton(singleton(sP1_iProver_def)))))) = singleton(singleton(singleton(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_92206,c_88]) ).

cnf(c_92410,plain,
    member_of(singleton(singleton(singleton(singleton(sP1_iProver_def))))) = singleton(singleton(singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_92206,c_91]) ).

cnf(c_92417,plain,
    singleton(member_of(singleton(singleton(singleton(singleton(sP3_iProver_def)))))) = singleton(singleton(singleton(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_92207,c_88]) ).

cnf(c_92418,plain,
    member_of(singleton(singleton(singleton(singleton(sP3_iProver_def))))) = singleton(singleton(singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_92207,c_91]) ).

cnf(c_92588,plain,
    singleton(member_of(singleton(singleton(singleton(singleton(sP0_iProver_def)))))) = singleton(singleton(singleton(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_92208,c_88]) ).

cnf(c_92589,plain,
    member_of(singleton(singleton(singleton(singleton(sP0_iProver_def))))) = singleton(singleton(singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_92208,c_91]) ).

cnf(c_92748,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP0_iProver_def)),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(member_of(singleton(sP0_iProver_def)),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69375,c_107]) ).

cnf(c_92751,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP0_iProver_def)),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69375,c_54]) ).

cnf(c_93003,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(omega)),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(member_of(singleton(omega)),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69377,c_107]) ).

cnf(c_93006,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(omega)),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69377,c_54]) ).

cnf(c_93027,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP1_iProver_def)),X0),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(member_of(singleton(sP1_iProver_def)),X0) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_69379,c_107]) ).

cnf(c_93030,plain,
    ( ~ subclass(ordered_pair(member_of(singleton(sP1_iProver_def)),X0),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_69379,c_54]) ).

cnf(c_93033,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),sP1_iProver_def)
    | ~ member(sP0_iProver_def,element_relation)
    | cross_product(universal_class,universal_class) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_73234,c_107]) ).

cnf(c_93036,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | ~ member(sP0_iProver_def,element_relation)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_73234,c_54]) ).

cnf(c_93037,plain,
    ( ~ member(X0,sP1_iProver_def)
    | ~ member(sP0_iProver_def,element_relation)
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_73234,c_101]) ).

cnf(c_93147,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),sP1_iProver_def)
    | ~ member(sP0_iProver_def,successor_relation)
    | cross_product(universal_class,universal_class) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_73251,c_107]) ).

cnf(c_93150,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),X0)
    | ~ member(sP0_iProver_def,successor_relation)
    | subclass(sP1_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_73251,c_54]) ).

cnf(c_93151,plain,
    ( ~ member(X0,sP1_iProver_def)
    | ~ member(sP0_iProver_def,successor_relation)
    | member(X0,cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_73251,c_101]) ).

cnf(c_93154,plain,
    ( X0 = sP1_iProver_def
    | member(not_subclass_element(X0,sP1_iProver_def),X0)
    | subclass(sP3_iProver_def,unordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_55,c_73680]) ).

cnf(c_93165,plain,
    ( X0 = sP1_iProver_def
    | member(not_subclass_element(X0,sP1_iProver_def),X0)
    | subclass(null_class,unordered_pair(sP0_iProver_def,X1)) ),
    inference(superposition,[status(thm)],[c_55,c_73682]) ).

cnf(c_93175,plain,
    ( ~ member(X0,singleton(singleton(singleton(omega))))
    | member_of(singleton(singleton(singleton(omega)))) = X0 ),
    inference(superposition,[status(thm)],[c_10947,c_95]) ).

cnf(c_93179,plain,
    ( ~ member(X0,singleton(singleton(singleton(sP1_iProver_def))))
    | member_of(singleton(singleton(singleton(sP1_iProver_def)))) = X0 ),
    inference(superposition,[status(thm)],[c_10951,c_95]) ).

cnf(c_93183,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | subclass(singleton(X0),X1) ),
    inference(superposition,[status(thm)],[c_76,c_10982]) ).

cnf(c_93184,plain,
    subclass(singleton(X0),universal_class),
    inference(superposition,[status(thm)],[c_104,c_10982]) ).

cnf(c_93185,plain,
    ( ~ function(universal_class)
    | subclass(singleton(X0),cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_16377,c_10982]) ).

cnf(c_93186,plain,
    ( ~ function(unordered_pair(X0,X1))
    | subclass(singleton(X0),cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_10982]) ).

cnf(c_93361,plain,
    subclass(singleton(null_class),universal_class),
    inference(superposition,[status(thm)],[c_17671,c_93184]) ).

cnf(c_93362,plain,
    subclass(singleton(omega),universal_class),
    inference(superposition,[status(thm)],[c_17677,c_93184]) ).

cnf(c_93364,plain,
    subclass(singleton(sP1_iProver_def),universal_class),
    inference(superposition,[status(thm)],[c_17681,c_93184]) ).

cnf(c_93365,plain,
    subclass(singleton(sP3_iProver_def),universal_class),
    inference(superposition,[status(thm)],[c_17682,c_93184]) ).

cnf(c_93366,plain,
    subclass(singleton(sP0_iProver_def),universal_class),
    inference(superposition,[status(thm)],[c_21807,c_93184]) ).

cnf(c_93368,plain,
    ( ~ subclass(universal_class,singleton(X0))
    | singleton(X0) = universal_class ),
    inference(superposition,[status(thm)],[c_93184,c_107]) ).

cnf(c_93371,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(singleton(X1),X0) ),
    inference(superposition,[status(thm)],[c_93184,c_54]) ).

cnf(c_93372,plain,
    ( ~ member(X0,singleton(X1))
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_93184,c_101]) ).

cnf(c_94392,plain,
    ( ~ subclass(universal_class,singleton(null_class))
    | singleton(null_class) = universal_class ),
    inference(superposition,[status(thm)],[c_93361,c_107]) ).

cnf(c_94395,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(singleton(null_class),X0) ),
    inference(superposition,[status(thm)],[c_93361,c_54]) ).

cnf(c_94396,plain,
    ( ~ member(X0,singleton(null_class))
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_93361,c_101]) ).

cnf(c_94753,plain,
    ( ~ subclass(universal_class,singleton(omega))
    | singleton(omega) = universal_class ),
    inference(superposition,[status(thm)],[c_93362,c_107]) ).

cnf(c_94756,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(singleton(omega),X0) ),
    inference(superposition,[status(thm)],[c_93362,c_54]) ).

cnf(c_94757,plain,
    ( ~ member(X0,singleton(omega))
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_93362,c_101]) ).

cnf(c_94761,plain,
    ( ~ subclass(universal_class,singleton(sP1_iProver_def))
    | singleton(sP1_iProver_def) = universal_class ),
    inference(superposition,[status(thm)],[c_93364,c_107]) ).

cnf(c_94764,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(singleton(sP1_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_93364,c_54]) ).

cnf(c_94765,plain,
    ( ~ member(X0,singleton(sP1_iProver_def))
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_93364,c_101]) ).

cnf(c_94936,plain,
    ( ~ subclass(universal_class,singleton(sP3_iProver_def))
    | singleton(sP3_iProver_def) = universal_class ),
    inference(superposition,[status(thm)],[c_93365,c_107]) ).

cnf(c_94939,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(singleton(sP3_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_93365,c_54]) ).

cnf(c_94940,plain,
    ( ~ member(X0,singleton(sP3_iProver_def))
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_93365,c_101]) ).

cnf(c_94945,plain,
    ( ~ subclass(universal_class,singleton(sP0_iProver_def))
    | singleton(sP0_iProver_def) = universal_class ),
    inference(superposition,[status(thm)],[c_93366,c_107]) ).

cnf(c_94948,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(singleton(sP0_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_93366,c_54]) ).

cnf(c_94949,plain,
    ( ~ member(X0,singleton(sP0_iProver_def))
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_93366,c_101]) ).

cnf(c_94953,plain,
    ( ~ subclass(universal_class,X0)
    | member_of(X1) = X1
    | subclass(X1,X0) ),
    inference(superposition,[status(thm)],[c_90,c_93371]) ).

cnf(c_94963,plain,
    ( ~ subclass(X0,singleton(X1))
    | ~ subclass(universal_class,X0)
    | singleton(X1) = X0 ),
    inference(superposition,[status(thm)],[c_93371,c_107]) ).

cnf(c_94966,plain,
    ( ~ subclass(X0,X1)
    | ~ subclass(universal_class,X0)
    | subclass(singleton(X2),X1) ),
    inference(superposition,[status(thm)],[c_93371,c_54]) ).

cnf(c_94967,plain,
    ( ~ member(X0,singleton(X1))
    | ~ subclass(universal_class,X2)
    | member(X0,X2) ),
    inference(superposition,[status(thm)],[c_93371,c_101]) ).

cnf(c_94971,plain,
    ( ~ subclass(universal_class,singleton(X0))
    | singleton(X0) = singleton(X1)
    | singleton(X1) = null_class ),
    inference(superposition,[status(thm)],[c_93371,c_97]) ).

cnf(c_95053,plain,
    ( member(not_subclass_element(singleton(X0),X1),universal_class)
    | subclass(singleton(X0),X1) ),
    inference(superposition,[status(thm)],[c_102,c_93372]) ).

cnf(c_95054,plain,
    ( singleton(X0) = X1
    | member(not_subclass_element(X1,singleton(X0)),X1)
    | member(not_subclass_element(singleton(X0),X1),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_93372]) ).

cnf(c_95055,plain,
    ( singleton(X0) = null_class
    | member(not_subclass_element(singleton(X0),null_class),universal_class) ),
    inference(superposition,[status(thm)],[c_63,c_93372]) ).

cnf(c_95059,plain,
    ( singleton(X0) = null_class
    | member(regular(singleton(X0)),universal_class) ),
    inference(superposition,[status(thm)],[c_166,c_93372]) ).

cnf(c_95060,plain,
    ( ~ member(singleton(X0),universal_class)
    | singleton(X0) = null_class
    | member(apply(choice,singleton(X0)),universal_class) ),
    inference(superposition,[status(thm)],[c_170,c_93372]) ).

cnf(c_95064,plain,
    ( singleton(X0) = sP3_iProver_def
    | member(not_subclass_element(singleton(X0),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_24617,c_93372]) ).

cnf(c_95065,plain,
    ( singleton(X0) = null_class
    | member(not_subclass_element(singleton(X0),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_7628,c_93372]) ).

cnf(c_95073,plain,
    ( ~ member(X0,X1)
    | member_of(X1) = X1
    | member(X0,universal_class) ),
    inference(superposition,[status(thm)],[c_90,c_93372]) ).

cnf(c_95098,plain,
    ( ~ subclass(X0,singleton(null_class))
    | ~ subclass(universal_class,X0)
    | singleton(null_class) = X0 ),
    inference(superposition,[status(thm)],[c_94395,c_107]) ).

cnf(c_95101,plain,
    ( ~ subclass(X0,X1)
    | ~ subclass(universal_class,X0)
    | subclass(singleton(null_class),X1) ),
    inference(superposition,[status(thm)],[c_94395,c_54]) ).

cnf(c_95102,plain,
    ( ~ member(X0,singleton(null_class))
    | ~ subclass(universal_class,X1)
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_94395,c_101]) ).

cnf(c_95106,plain,
    ( ~ subclass(universal_class,singleton(X0))
    | singleton(X0) = singleton(null_class)
    | singleton(null_class) = null_class ),
    inference(superposition,[status(thm)],[c_94395,c_97]) ).

cnf(c_95118,plain,
    ( member(not_subclass_element(singleton(null_class),X0),universal_class)
    | subclass(singleton(null_class),X0) ),
    inference(superposition,[status(thm)],[c_102,c_94396]) ).

cnf(c_95119,plain,
    ( singleton(null_class) = X0
    | member(not_subclass_element(X0,singleton(null_class)),X0)
    | member(not_subclass_element(singleton(null_class),X0),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_94396]) ).

cnf(c_95120,plain,
    ( singleton(null_class) = null_class
    | member(not_subclass_element(singleton(null_class),null_class),universal_class) ),
    inference(superposition,[status(thm)],[c_63,c_94396]) ).

cnf(c_95124,plain,
    ( singleton(null_class) = null_class
    | member(regular(singleton(null_class)),universal_class) ),
    inference(superposition,[status(thm)],[c_166,c_94396]) ).

cnf(c_95125,plain,
    ( ~ member(singleton(null_class),universal_class)
    | singleton(null_class) = null_class
    | member(apply(choice,singleton(null_class)),universal_class) ),
    inference(superposition,[status(thm)],[c_170,c_94396]) ).

cnf(c_95126,plain,
    ( singleton(null_class) = sP3_iProver_def
    | member(not_subclass_element(singleton(null_class),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_24617,c_94396]) ).

cnf(c_95127,plain,
    ( singleton(null_class) = null_class
    | member(not_subclass_element(singleton(null_class),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_7628,c_94396]) ).

cnf(c_95168,plain,
    ( ~ subclass(X0,singleton(omega))
    | ~ subclass(universal_class,X0)
    | singleton(omega) = X0 ),
    inference(superposition,[status(thm)],[c_94756,c_107]) ).

cnf(c_95171,plain,
    ( ~ subclass(X0,X1)
    | ~ subclass(universal_class,X0)
    | subclass(singleton(omega),X1) ),
    inference(superposition,[status(thm)],[c_94756,c_54]) ).

cnf(c_95172,plain,
    ( ~ member(X0,singleton(omega))
    | ~ subclass(universal_class,X1)
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_94756,c_101]) ).

cnf(c_95176,plain,
    ( ~ subclass(universal_class,singleton(X0))
    | singleton(X0) = singleton(omega)
    | singleton(omega) = null_class ),
    inference(superposition,[status(thm)],[c_94756,c_97]) ).

cnf(c_95251,plain,
    ( member(not_subclass_element(singleton(omega),X0),universal_class)
    | subclass(singleton(omega),X0) ),
    inference(superposition,[status(thm)],[c_102,c_94757]) ).

cnf(c_95252,plain,
    ( singleton(omega) = X0
    | member(not_subclass_element(X0,singleton(omega)),X0)
    | member(not_subclass_element(singleton(omega),X0),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_94757]) ).

cnf(c_95253,plain,
    ( singleton(omega) = null_class
    | member(not_subclass_element(singleton(omega),null_class),universal_class) ),
    inference(superposition,[status(thm)],[c_63,c_94757]) ).

cnf(c_95256,plain,
    ( singleton(omega) = null_class
    | member(regular(singleton(omega)),universal_class) ),
    inference(superposition,[status(thm)],[c_166,c_94757]) ).

cnf(c_95257,plain,
    ( ~ member(singleton(omega),universal_class)
    | singleton(omega) = null_class
    | member(apply(choice,singleton(omega)),universal_class) ),
    inference(superposition,[status(thm)],[c_170,c_94757]) ).

cnf(c_95258,plain,
    ( singleton(omega) = sP3_iProver_def
    | member(not_subclass_element(singleton(omega),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_24617,c_94757]) ).

cnf(c_95259,plain,
    ( singleton(omega) = null_class
    | member(not_subclass_element(singleton(omega),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_7628,c_94757]) ).

cnf(c_95630,plain,
    ( ~ subclass(X0,singleton(sP1_iProver_def))
    | ~ subclass(universal_class,X0)
    | singleton(sP1_iProver_def) = X0 ),
    inference(superposition,[status(thm)],[c_94764,c_107]) ).

cnf(c_95633,plain,
    ( ~ subclass(X0,X1)
    | ~ subclass(universal_class,X0)
    | subclass(singleton(sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_94764,c_54]) ).

cnf(c_95634,plain,
    ( ~ member(X0,singleton(sP1_iProver_def))
    | ~ subclass(universal_class,X1)
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_94764,c_101]) ).

cnf(c_95638,plain,
    ( ~ subclass(universal_class,singleton(X0))
    | singleton(X0) = singleton(sP1_iProver_def)
    | singleton(sP1_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_94764,c_97]) ).

cnf(c_95642,plain,
    ( member(not_subclass_element(singleton(sP1_iProver_def),X0),universal_class)
    | subclass(singleton(sP1_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_102,c_94765]) ).

cnf(c_95643,plain,
    ( singleton(sP1_iProver_def) = X0
    | member(not_subclass_element(X0,singleton(sP1_iProver_def)),X0)
    | member(not_subclass_element(singleton(sP1_iProver_def),X0),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_94765]) ).

cnf(c_95644,plain,
    ( singleton(sP1_iProver_def) = null_class
    | member(not_subclass_element(singleton(sP1_iProver_def),null_class),universal_class) ),
    inference(superposition,[status(thm)],[c_63,c_94765]) ).

cnf(c_95647,plain,
    ( singleton(sP1_iProver_def) = null_class
    | member(regular(singleton(sP1_iProver_def)),universal_class) ),
    inference(superposition,[status(thm)],[c_166,c_94765]) ).

cnf(c_95648,plain,
    ( ~ member(singleton(sP1_iProver_def),universal_class)
    | singleton(sP1_iProver_def) = null_class
    | member(apply(choice,singleton(sP1_iProver_def)),universal_class) ),
    inference(superposition,[status(thm)],[c_170,c_94765]) ).

cnf(c_95650,plain,
    ( singleton(sP1_iProver_def) = sP3_iProver_def
    | member(not_subclass_element(singleton(sP1_iProver_def),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_24617,c_94765]) ).

cnf(c_95651,plain,
    ( singleton(sP1_iProver_def) = null_class
    | member(not_subclass_element(singleton(sP1_iProver_def),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_7628,c_94765]) ).

cnf(c_96034,plain,
    ( ~ subclass(X0,singleton(sP3_iProver_def))
    | ~ subclass(universal_class,X0)
    | singleton(sP3_iProver_def) = X0 ),
    inference(superposition,[status(thm)],[c_94939,c_107]) ).

cnf(c_96037,plain,
    ( ~ subclass(X0,X1)
    | ~ subclass(universal_class,X0)
    | subclass(singleton(sP3_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_94939,c_54]) ).

cnf(c_96038,plain,
    ( ~ member(X0,singleton(sP3_iProver_def))
    | ~ subclass(universal_class,X1)
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_94939,c_101]) ).

cnf(c_96042,plain,
    ( ~ subclass(universal_class,singleton(X0))
    | singleton(X0) = singleton(sP3_iProver_def)
    | singleton(sP3_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_94939,c_97]) ).

cnf(c_96046,plain,
    ( member(not_subclass_element(singleton(sP3_iProver_def),X0),universal_class)
    | subclass(singleton(sP3_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_102,c_94940]) ).

cnf(c_96047,plain,
    ( singleton(sP3_iProver_def) = X0
    | member(not_subclass_element(X0,singleton(sP3_iProver_def)),X0)
    | member(not_subclass_element(singleton(sP3_iProver_def),X0),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_94940]) ).

cnf(c_96048,plain,
    ( singleton(sP3_iProver_def) = null_class
    | member(not_subclass_element(singleton(sP3_iProver_def),null_class),universal_class) ),
    inference(superposition,[status(thm)],[c_63,c_94940]) ).

cnf(c_96051,plain,
    ( singleton(sP3_iProver_def) = null_class
    | member(regular(singleton(sP3_iProver_def)),universal_class) ),
    inference(superposition,[status(thm)],[c_166,c_94940]) ).

cnf(c_96052,plain,
    ( ~ member(singleton(sP3_iProver_def),universal_class)
    | singleton(sP3_iProver_def) = null_class
    | member(apply(choice,singleton(sP3_iProver_def)),universal_class) ),
    inference(superposition,[status(thm)],[c_170,c_94940]) ).

cnf(c_96054,plain,
    ( singleton(sP3_iProver_def) = sP3_iProver_def
    | member(not_subclass_element(singleton(sP3_iProver_def),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_24617,c_94940]) ).

cnf(c_96055,plain,
    ( singleton(sP3_iProver_def) = null_class
    | member(not_subclass_element(singleton(sP3_iProver_def),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_7628,c_94940]) ).

cnf(c_96207,plain,
    ( ~ subclass(X0,singleton(sP0_iProver_def))
    | ~ subclass(universal_class,X0)
    | singleton(sP0_iProver_def) = X0 ),
    inference(superposition,[status(thm)],[c_94948,c_107]) ).

cnf(c_96210,plain,
    ( ~ subclass(X0,X1)
    | ~ subclass(universal_class,X0)
    | subclass(singleton(sP0_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_94948,c_54]) ).

cnf(c_96211,plain,
    ( ~ member(X0,singleton(sP0_iProver_def))
    | ~ subclass(universal_class,X1)
    | member(X0,X1) ),
    inference(superposition,[status(thm)],[c_94948,c_101]) ).

cnf(c_96215,plain,
    ( ~ subclass(universal_class,singleton(X0))
    | singleton(X0) = singleton(sP0_iProver_def)
    | singleton(sP0_iProver_def) = null_class ),
    inference(superposition,[status(thm)],[c_94948,c_97]) ).

cnf(c_96236,plain,
    ( member(not_subclass_element(singleton(sP0_iProver_def),X0),universal_class)
    | subclass(singleton(sP0_iProver_def),X0) ),
    inference(superposition,[status(thm)],[c_102,c_94949]) ).

cnf(c_96237,plain,
    ( singleton(sP0_iProver_def) = X0
    | member(not_subclass_element(X0,singleton(sP0_iProver_def)),X0)
    | member(not_subclass_element(singleton(sP0_iProver_def),X0),universal_class) ),
    inference(superposition,[status(thm)],[c_55,c_94949]) ).

cnf(c_96238,plain,
    ( singleton(sP0_iProver_def) = null_class
    | member(not_subclass_element(singleton(sP0_iProver_def),null_class),universal_class) ),
    inference(superposition,[status(thm)],[c_63,c_94949]) ).

cnf(c_96241,plain,
    ( singleton(sP0_iProver_def) = null_class
    | member(regular(singleton(sP0_iProver_def)),universal_class) ),
    inference(superposition,[status(thm)],[c_166,c_94949]) ).

cnf(c_96242,plain,
    ( ~ member(singleton(sP0_iProver_def),universal_class)
    | singleton(sP0_iProver_def) = null_class
    | member(apply(choice,singleton(sP0_iProver_def)),universal_class) ),
    inference(superposition,[status(thm)],[c_170,c_94949]) ).

cnf(c_96243,plain,
    ( singleton(sP0_iProver_def) = sP3_iProver_def
    | member(not_subclass_element(singleton(sP0_iProver_def),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_24617,c_94949]) ).

cnf(c_96244,plain,
    ( singleton(sP0_iProver_def) = null_class
    | member(not_subclass_element(singleton(sP0_iProver_def),sP3_iProver_def),universal_class) ),
    inference(superposition,[status(thm)],[c_7628,c_94949]) ).

cnf(c_97317,plain,
    ( X0 = sP1_iProver_def
    | member(not_subclass_element(X0,sP1_iProver_def),X0)
    | subclass(sP3_iProver_def,unordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_55,c_73706]) ).

cnf(c_97431,plain,
    ( X0 = sP1_iProver_def
    | member(not_subclass_element(X0,sP1_iProver_def),X0)
    | subclass(null_class,unordered_pair(X1,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_55,c_73708]) ).

cnf(c_97448,plain,
    subclass(intersection(sP2_iProver_def,sP1_iProver_def),ordered_pair(X0,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_77475,c_11004]) ).

cnf(c_97449,plain,
    ( ~ subclass(ordered_pair(X0,member_of(sP1_iProver_def)),singleton(unordered_pair(X0,sP1_iProver_def)))
    | ordered_pair(X0,member_of(sP1_iProver_def)) = singleton(unordered_pair(X0,sP1_iProver_def)) ),
    inference(superposition,[status(thm)],[c_77475,c_107]) ).

cnf(c_97452,plain,
    ( ~ subclass(ordered_pair(X0,member_of(sP1_iProver_def)),X1)
    | subclass(singleton(unordered_pair(X0,sP1_iProver_def)),X1) ),
    inference(superposition,[status(thm)],[c_77475,c_54]) ).

cnf(c_97453,plain,
    ( ~ member(X0,singleton(unordered_pair(X1,sP1_iProver_def)))
    | member(X0,ordered_pair(X1,member_of(sP1_iProver_def))) ),
    inference(superposition,[status(thm)],[c_77475,c_101]) ).

cnf(c_97454,plain,
    subclass(sP3_iProver_def,ordered_pair(X0,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_77475,c_15360]) ).

cnf(c_97455,plain,
    subclass(null_class,ordered_pair(X0,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_77475,c_15342]) ).

cnf(c_97711,plain,
    ( ~ subclass(ordered_pair(X0,member_of(sP1_iProver_def)),sP3_iProver_def)
    | ordered_pair(X0,member_of(sP1_iProver_def)) = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_97454,c_107]) ).

cnf(c_97714,plain,
    ( ~ subclass(ordered_pair(X0,member_of(sP1_iProver_def)),X1)
    | subclass(sP3_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_97454,c_54]) ).

cnf(c_97719,plain,
    ( ~ subclass(ordered_pair(X0,member_of(sP1_iProver_def)),null_class)
    | ordered_pair(X0,member_of(sP1_iProver_def)) = null_class ),
    inference(superposition,[status(thm)],[c_97455,c_107]) ).

cnf(c_97722,plain,
    ( ~ subclass(ordered_pair(X0,member_of(sP1_iProver_def)),X1)
    | subclass(null_class,X1) ),
    inference(superposition,[status(thm)],[c_97455,c_54]) ).

cnf(c_97728,plain,
    ( ~ subclass(ordered_pair(X0,member_of(sP1_iProver_def)),intersection(sP2_iProver_def,sP1_iProver_def))
    | ordered_pair(X0,member_of(sP1_iProver_def)) = intersection(sP2_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_97448,c_107]) ).

cnf(c_97731,plain,
    ( ~ subclass(ordered_pair(X0,member_of(sP1_iProver_def)),X1)
    | subclass(intersection(sP2_iProver_def,sP1_iProver_def),X1) ),
    inference(superposition,[status(thm)],[c_97448,c_54]) ).

cnf(c_98027,plain,
    ( singleton(member_of(singleton(not_subclass_element(X0,sP3_iProver_def)))) = singleton(not_subclass_element(X0,sP3_iProver_def))
    | X0 = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_78846,c_88]) ).

cnf(c_98028,plain,
    ( member_of(singleton(not_subclass_element(X0,sP3_iProver_def))) = not_subclass_element(X0,sP3_iProver_def)
    | X0 = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_78846,c_91]) ).

cnf(c_98052,plain,
    ( singleton(member_of(singleton(not_subclass_element(identity_relation,sP3_iProver_def)))) = singleton(not_subclass_element(identity_relation,sP3_iProver_def))
    | identity_relation = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_78861,c_88]) ).

cnf(c_98053,plain,
    ( member_of(singleton(not_subclass_element(identity_relation,sP3_iProver_def))) = not_subclass_element(identity_relation,sP3_iProver_def)
    | identity_relation = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_78861,c_91]) ).

cnf(c_98185,plain,
    ( singleton(member_of(singleton(not_subclass_element(element_relation,sP3_iProver_def)))) = singleton(not_subclass_element(element_relation,sP3_iProver_def))
    | element_relation = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_78864,c_88]) ).

cnf(c_98186,plain,
    ( member_of(singleton(not_subclass_element(element_relation,sP3_iProver_def))) = not_subclass_element(element_relation,sP3_iProver_def)
    | element_relation = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_78864,c_91]) ).

cnf(c_98246,plain,
    ( singleton(member_of(singleton(not_subclass_element(successor_relation,sP3_iProver_def)))) = singleton(not_subclass_element(successor_relation,sP3_iProver_def))
    | successor_relation = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_78865,c_88]) ).

cnf(c_98247,plain,
    ( member_of(singleton(not_subclass_element(successor_relation,sP3_iProver_def))) = not_subclass_element(successor_relation,sP3_iProver_def)
    | successor_relation = sP3_iProver_def ),
    inference(superposition,[status(thm)],[c_78865,c_91]) ).

cnf(c_98346,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | subclass(singleton(X2),X1) ),
    inference(superposition,[status(thm)],[c_76,c_10983]) ).

cnf(c_98349,plain,
    ( ~ function(unordered_pair(X0,X1))
    | subclass(singleton(X1),cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_10983]) ).

cnf(c_98379,plain,
    ( ~ member(X0,X1)
    | ~ member(X2,X1)
    | subclass(intersection(complement(X3),X3),X1) ),
    inference(superposition,[status(thm)],[c_76,c_11003]) ).

cnf(c_98380,plain,
    ( ~ member(X0,X1)
    | subclass(intersection(complement(X2),X2),X1) ),
    inference(superposition,[status(thm)],[c_96,c_11003]) ).

cnf(c_98387,plain,
    ( ~ function(X0)
    | subclass(intersection(complement(X1),X1),identity_relation) ),
    inference(superposition,[status(thm)],[c_163,c_11003]) ).

cnf(c_98389,plain,
    ( ~ function(X0)
    | subclass(intersection(complement(X1),X1),cross_product(universal_class,universal_class)) ),
    inference(superposition,[status(thm)],[c_162,c_11003]) ).

cnf(c_98398,plain,
    ( not_subclass_element(sP1_iProver_def,X0) = sP0_iProver_def
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_7758,c_11003]) ).

cnf(c_98427,plain,
    ( ~ subclass(omega,X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_10994,c_11003]) ).

cnf(c_98469,plain,
    ( ~ member(X0,universal_class)
    | subclass(intersection(complement(X1),X1),unordered_pair(X2,X0)) ),
    inference(superposition,[status(thm)],[c_22148,c_11003]) ).

cnf(c_98482,plain,
    ( ~ operation(X0)
    | subclass(intersection(complement(X1),X1),domain_of(domain_of(X0))) ),
    inference(superposition,[status(thm)],[c_16391,c_11003]) ).

cnf(c_98532,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,X2)),
    inference(superposition,[status(thm)],[c_69212,c_11003]) ).

cnf(c_98533,plain,
    subclass(intersection(complement(X0),X0),cross_product(universal_class,universal_class)),
    inference(superposition,[status(thm)],[c_69213,c_11003]) ).

cnf(c_98534,plain,
    subclass(intersection(complement(X0),X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    inference(superposition,[status(thm)],[c_69229,c_11003]) ).

cnf(c_98535,plain,
    subclass(intersection(complement(X0),X0),identity_relation),
    inference(superposition,[status(thm)],[c_69222,c_11003]) ).

cnf(c_98536,plain,
    subclass(intersection(complement(X0),X0),omega),
    inference(superposition,[status(thm)],[c_69204,c_11003]) ).

cnf(c_98539,plain,
    subclass(intersection(complement(X0),X0),singleton(X1)),
    inference(superposition,[status(thm)],[c_69208,c_11003]) ).

cnf(c_98541,plain,
    subclass(intersection(complement(X0),X0),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_69205,c_11003]) ).

cnf(c_98542,plain,
    subclass(intersection(complement(X0),X0),null_class),
    inference(superposition,[status(thm)],[c_69171,c_11003]) ).

cnf(c_98543,plain,
    subclass(intersection(complement(X0),X0),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_69201,c_11003]) ).

cnf(c_98544,plain,
    subclass(intersection(complement(X0),X0),x),
    inference(superposition,[status(thm)],[c_69206,c_11003]) ).

cnf(c_98545,plain,
    subclass(intersection(complement(X0),X0),subset_relation),
    inference(superposition,[status(thm)],[c_69207,c_11003]) ).

cnf(c_98546,plain,
    subclass(intersection(complement(X0),X0),singleton(null_class)),
    inference(superposition,[status(thm)],[c_69232,c_11003]) ).

cnf(c_98547,plain,
    subclass(intersection(complement(X0),X0),singleton(omega)),
    inference(superposition,[status(thm)],[c_69243,c_11003]) ).

cnf(c_98548,plain,
    subclass(intersection(complement(X0),X0),inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_69211,c_11003]) ).

cnf(c_98549,plain,
    subclass(intersection(complement(X0),X0),singleton(singleton(X1))),
    inference(superposition,[status(thm)],[c_69253,c_11003]) ).

cnf(c_98550,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,singleton(X2))),
    inference(superposition,[status(thm)],[c_69262,c_11003]) ).

cnf(c_98552,plain,
    subclass(intersection(complement(X0),X0),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_69247,c_11003]) ).

cnf(c_98553,plain,
    subclass(intersection(complement(X0),X0),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_69250,c_11003]) ).

cnf(c_98555,plain,
    subclass(intersection(complement(X0),X0),singleton(singleton(null_class))),
    inference(superposition,[status(thm)],[c_69259,c_11003]) ).

cnf(c_98556,plain,
    subclass(intersection(complement(X0),X0),singleton(singleton(omega))),
    inference(superposition,[status(thm)],[c_69260,c_11003]) ).

cnf(c_98557,plain,
    subclass(intersection(complement(X0),X0),singleton(singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_69261,c_11003]) ).

cnf(c_98558,plain,
    subclass(intersection(complement(X0),X0),singleton(singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_69257,c_11003]) ).

cnf(c_98559,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(singleton(X1),X2)),
    inference(superposition,[status(thm)],[c_69268,c_11003]) ).

cnf(c_98560,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,singleton(null_class))),
    inference(superposition,[status(thm)],[c_69274,c_11003]) ).

cnf(c_98561,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,singleton(omega))),
    inference(superposition,[status(thm)],[c_69275,c_11003]) ).

cnf(c_98562,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,singleton(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_69276,c_11003]) ).

cnf(c_98563,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,singleton(sP3_iProver_def))),
    inference(superposition,[status(thm)],[c_69273,c_11003]) ).

cnf(c_98565,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(singleton(null_class),X1)),
    inference(superposition,[status(thm)],[c_69278,c_11003]) ).

cnf(c_98567,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(singleton(omega),X1)),
    inference(superposition,[status(thm)],[c_33244,c_11003]) ).

cnf(c_98569,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(singleton(sP1_iProver_def),X1)),
    inference(superposition,[status(thm)],[c_35405,c_11003]) ).

cnf(c_98571,plain,
    ( ~ operation(inverse(X0))
    | subclass(intersection(complement(X1),X1),domain_of(range_of(X0))) ),
    inference(superposition,[status(thm)],[c_30791,c_11003]) ).

cnf(c_98572,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(singleton(sP3_iProver_def),X1)),
    inference(superposition,[status(thm)],[c_69277,c_11003]) ).

cnf(c_98584,plain,
    subclass(intersection(complement(X0),X0),universal_class),
    inference(superposition,[status(thm)],[c_93184,c_11003]) ).

cnf(c_98585,plain,
    ( ~ subclass(universal_class,X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_93371,c_11003]) ).

cnf(c_98611,plain,
    subclass(intersection(complement(X0),X0),singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_38643,c_11003]) ).

cnf(c_98636,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(X1,X2)),
    inference(superposition,[status(thm)],[c_77467,c_11003]) ).

cnf(c_98654,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_46619,c_11003]) ).

cnf(c_98657,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(sP1_iProver_def,X1)),
    inference(superposition,[status(thm)],[c_47192,c_11003]) ).

cnf(c_98666,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_49190,c_11003]) ).

cnf(c_98673,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(sP0_iProver_def,X1)),
    inference(superposition,[status(thm)],[c_49647,c_11003]) ).

cnf(c_98697,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(null_class,X1)),
    inference(superposition,[status(thm)],[c_69315,c_11003]) ).

cnf(c_98698,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(omega,X1)),
    inference(superposition,[status(thm)],[c_69353,c_11003]) ).

cnf(c_98699,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,null_class)),
    inference(superposition,[status(thm)],[c_69314,c_11003]) ).

cnf(c_98700,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,omega)),
    inference(superposition,[status(thm)],[c_69352,c_11003]) ).

cnf(c_98701,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_69293,c_11003]) ).

cnf(c_98702,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(member_of(singleton(null_class)),X1)),
    inference(superposition,[status(thm)],[c_69295,c_11003]) ).

cnf(c_98703,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_69339,c_11003]) ).

cnf(c_98704,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(member_of(singleton(omega)),X1)),
    inference(superposition,[status(thm)],[c_69341,c_11003]) ).

cnf(c_98705,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_69347,c_11003]) ).

cnf(c_98706,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(member_of(singleton(sP1_iProver_def)),X1)),
    inference(superposition,[status(thm)],[c_69350,c_11003]) ).

cnf(c_98707,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_69300,c_11003]) ).

cnf(c_98708,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(member_of(singleton(sP3_iProver_def)),X1)),
    inference(superposition,[status(thm)],[c_69303,c_11003]) ).

cnf(c_98709,plain,
    subclass(intersection(complement(X0),X0),singleton(member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_69334,c_11003]) ).

cnf(c_98711,plain,
    subclass(intersection(complement(X0),X0),singleton(member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_69336,c_11003]) ).

cnf(c_98712,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_69318,c_11003]) ).

cnf(c_98713,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(sP3_iProver_def,X1)),
    inference(superposition,[status(thm)],[c_69319,c_11003]) ).

cnf(c_98714,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(singleton(sP0_iProver_def),X1)),
    inference(superposition,[status(thm)],[c_69307,c_11003]) ).

cnf(c_98715,plain,
    subclass(intersection(complement(X0),X0),singleton(singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_69308,c_11003]) ).

cnf(c_98716,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_69358,c_11003]) ).

cnf(c_98717,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(member_of(singleton(sP0_iProver_def)),X1)),
    inference(superposition,[status(thm)],[c_69365,c_11003]) ).

cnf(c_98718,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,singleton(sP0_iProver_def))),
    inference(superposition,[status(thm)],[c_69312,c_11003]) ).

cnf(c_98719,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(member_of(sP1_iProver_def),X1)),
    inference(superposition,[status(thm)],[c_69325,c_11003]) ).

cnf(c_98720,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(X1,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_69328,c_11003]) ).

cnf(c_98721,plain,
    subclass(intersection(complement(X0),X0),unordered_pair(member_of(sP1_iProver_def),X1)),
    inference(superposition,[status(thm)],[c_69332,c_11003]) ).

cnf(c_98722,plain,
    subclass(intersection(complement(X0),X0),singleton(member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_69330,c_11003]) ).

cnf(c_98723,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(X1,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_77490,c_11003]) ).

cnf(c_98724,plain,
    subclass(intersection(complement(X0),X0),singleton(member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_69343,c_11003]) ).

cnf(c_98725,plain,
    subclass(intersection(complement(X0),X0),singleton(member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_69354,c_11003]) ).

cnf(c_98726,plain,
    subclass(intersection(complement(X0),X0),singleton(member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_69361,c_11003]) ).

cnf(c_98727,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(sP1_iProver_def,sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_77614,c_11003]) ).

cnf(c_98728,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(member_of(singleton(null_class)),X1)),
    inference(superposition,[status(thm)],[c_69371,c_11003]) ).

cnf(c_98729,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(member_of(singleton(sP3_iProver_def)),X1)),
    inference(superposition,[status(thm)],[c_69373,c_11003]) ).

cnf(c_98730,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(member_of(singleton(sP0_iProver_def)),X1)),
    inference(superposition,[status(thm)],[c_69375,c_11003]) ).

cnf(c_98731,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(member_of(singleton(omega)),X1)),
    inference(superposition,[status(thm)],[c_69377,c_11003]) ).

cnf(c_98732,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(member_of(singleton(sP1_iProver_def)),X1)),
    inference(superposition,[status(thm)],[c_69379,c_11003]) ).

cnf(c_98733,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(null_class,X1)),
    inference(superposition,[status(thm)],[c_79812,c_11003]) ).

cnf(c_98734,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(omega,X1)),
    inference(superposition,[status(thm)],[c_80267,c_11003]) ).

cnf(c_98735,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(sP3_iProver_def,X1)),
    inference(superposition,[status(thm)],[c_80017,c_11003]) ).

cnf(c_98736,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(sP1_iProver_def,X1)),
    inference(superposition,[status(thm)],[c_80574,c_11003]) ).

cnf(c_98737,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(sP0_iProver_def,X1)),
    inference(superposition,[status(thm)],[c_81052,c_11003]) ).

cnf(c_98739,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(singleton(X1),X1)),
    inference(superposition,[status(thm)],[c_88828,c_11003]) ).

cnf(c_98742,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(X1,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_97448,c_11003]) ).

cnf(c_98751,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(singleton(null_class),member_of(singleton(null_class)))),
    inference(superposition,[status(thm)],[c_88905,c_11003]) ).

cnf(c_98752,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(singleton(omega),member_of(singleton(omega)))),
    inference(superposition,[status(thm)],[c_88906,c_11003]) ).

cnf(c_98754,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(singleton(sP1_iProver_def),member_of(singleton(sP1_iProver_def)))),
    inference(superposition,[status(thm)],[c_88908,c_11003]) ).

cnf(c_98755,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(singleton(sP3_iProver_def),member_of(singleton(sP3_iProver_def)))),
    inference(superposition,[status(thm)],[c_88909,c_11003]) ).

cnf(c_98756,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(singleton(sP0_iProver_def),member_of(singleton(sP0_iProver_def)))),
    inference(superposition,[status(thm)],[c_88910,c_11003]) ).

cnf(c_98757,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(sP1_iProver_def,member_of(sP1_iProver_def))),
    inference(superposition,[status(thm)],[c_89221,c_11003]) ).

cnf(c_98758,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(singleton(sP0_iProver_def),sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_91321,c_11003]) ).

cnf(c_98765,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(singleton(null_class),null_class)),
    inference(superposition,[status(thm)],[c_90123,c_11003]) ).

cnf(c_98767,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(singleton(omega),omega)),
    inference(superposition,[status(thm)],[c_90716,c_11003]) ).

cnf(c_98769,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(singleton(sP1_iProver_def),sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_91230,c_11003]) ).

cnf(c_98771,plain,
    subclass(intersection(complement(X0),X0),ordered_pair(singleton(sP3_iProver_def),sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_90129,c_11003]) ).

cnf(c_101882,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),identity_relation),
    inference(superposition,[status(thm)],[c_128,c_98535]) ).

cnf(c_101889,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),identity_relation),
    inference(superposition,[status(thm)],[c_126,c_98535]) ).

cnf(c_101890,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),identity_relation),
    inference(superposition,[status(thm)],[c_155,c_98535]) ).

cnf(c_101891,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),identity_relation),
    inference(superposition,[status(thm)],[c_176,c_98535]) ).

cnf(c_101893,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),identity_relation),
    inference(superposition,[status(thm)],[c_8578,c_98535]) ).

cnf(c_101894,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),identity_relation),
    inference(superposition,[status(thm)],[c_49184,c_98535]) ).

cnf(c_101895,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),identity_relation),
    inference(superposition,[status(thm)],[c_49124,c_98535]) ).

cnf(c_101896,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),identity_relation),
    inference(superposition,[status(thm)],[c_49296,c_98535]) ).

cnf(c_101899,plain,
    ( ~ subclass(identity_relation,intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = identity_relation ),
    inference(superposition,[status(thm)],[c_98535,c_107]) ).

cnf(c_101902,plain,
    ( ~ subclass(identity_relation,X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98535,c_54]) ).

cnf(c_102089,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),omega),
    inference(superposition,[status(thm)],[c_128,c_98536]) ).

cnf(c_102096,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),omega),
    inference(superposition,[status(thm)],[c_126,c_98536]) ).

cnf(c_102097,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),omega),
    inference(superposition,[status(thm)],[c_155,c_98536]) ).

cnf(c_102098,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),omega),
    inference(superposition,[status(thm)],[c_176,c_98536]) ).

cnf(c_102100,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),omega),
    inference(superposition,[status(thm)],[c_8578,c_98536]) ).

cnf(c_102101,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),omega),
    inference(superposition,[status(thm)],[c_49184,c_98536]) ).

cnf(c_102102,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),omega),
    inference(superposition,[status(thm)],[c_49124,c_98536]) ).

cnf(c_102103,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),omega),
    inference(superposition,[status(thm)],[c_49296,c_98536]) ).

cnf(c_102106,plain,
    ( ~ subclass(omega,intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = omega ),
    inference(superposition,[status(thm)],[c_98536,c_107]) ).

cnf(c_102917,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_128,c_98541]) ).

cnf(c_102924,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_126,c_98541]) ).

cnf(c_102925,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_155,c_98541]) ).

cnf(c_102926,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_176,c_98541]) ).

cnf(c_102928,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_8578,c_98541]) ).

cnf(c_102929,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_49184,c_98541]) ).

cnf(c_102930,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_49124,c_98541]) ).

cnf(c_102931,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_49296,c_98541]) ).

cnf(c_102934,plain,
    ( ~ subclass(sP1_iProver_def,intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_98541,c_107]) ).

cnf(c_102937,plain,
    ( ~ subclass(sP1_iProver_def,X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98541,c_54]) ).

cnf(c_103850,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),null_class),
    inference(superposition,[status(thm)],[c_128,c_98542]) ).

cnf(c_103857,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),null_class),
    inference(superposition,[status(thm)],[c_126,c_98542]) ).

cnf(c_103858,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),null_class),
    inference(superposition,[status(thm)],[c_155,c_98542]) ).

cnf(c_103859,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),null_class),
    inference(superposition,[status(thm)],[c_176,c_98542]) ).

cnf(c_103861,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),null_class),
    inference(superposition,[status(thm)],[c_8578,c_98542]) ).

cnf(c_103862,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),null_class),
    inference(superposition,[status(thm)],[c_49184,c_98542]) ).

cnf(c_103863,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),null_class),
    inference(superposition,[status(thm)],[c_49124,c_98542]) ).

cnf(c_103864,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),null_class),
    inference(superposition,[status(thm)],[c_49296,c_98542]) ).

cnf(c_103871,plain,
    ( ~ subclass(null_class,X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98542,c_54]) ).

cnf(c_103926,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_128,c_98543]) ).

cnf(c_103933,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_126,c_98543]) ).

cnf(c_103934,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_155,c_98543]) ).

cnf(c_103935,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_176,c_98543]) ).

cnf(c_103937,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_8578,c_98543]) ).

cnf(c_103938,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_49184,c_98543]) ).

cnf(c_103939,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_49124,c_98543]) ).

cnf(c_103940,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_49296,c_98543]) ).

cnf(c_103946,plain,
    ( ~ subclass(sP3_iProver_def,X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98543,c_54]) ).

cnf(c_104010,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),x),
    inference(superposition,[status(thm)],[c_128,c_98544]) ).

cnf(c_104017,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),x),
    inference(superposition,[status(thm)],[c_126,c_98544]) ).

cnf(c_104018,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),x),
    inference(superposition,[status(thm)],[c_155,c_98544]) ).

cnf(c_104019,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),x),
    inference(superposition,[status(thm)],[c_176,c_98544]) ).

cnf(c_104021,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),x),
    inference(superposition,[status(thm)],[c_8578,c_98544]) ).

cnf(c_104022,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),x),
    inference(superposition,[status(thm)],[c_49184,c_98544]) ).

cnf(c_104023,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),x),
    inference(superposition,[status(thm)],[c_49124,c_98544]) ).

cnf(c_104024,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),x),
    inference(superposition,[status(thm)],[c_49296,c_98544]) ).

cnf(c_104027,plain,
    ( ~ subclass(x,intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = x ),
    inference(superposition,[status(thm)],[c_98544,c_107]) ).

cnf(c_104030,plain,
    ( ~ subclass(x,X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98544,c_54]) ).

cnf(c_104182,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),subset_relation),
    inference(superposition,[status(thm)],[c_128,c_98545]) ).

cnf(c_104189,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),subset_relation),
    inference(superposition,[status(thm)],[c_126,c_98545]) ).

cnf(c_104190,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),subset_relation),
    inference(superposition,[status(thm)],[c_155,c_98545]) ).

cnf(c_104191,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),subset_relation),
    inference(superposition,[status(thm)],[c_176,c_98545]) ).

cnf(c_104193,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),subset_relation),
    inference(superposition,[status(thm)],[c_8578,c_98545]) ).

cnf(c_104194,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),subset_relation),
    inference(superposition,[status(thm)],[c_49184,c_98545]) ).

cnf(c_104195,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),subset_relation),
    inference(superposition,[status(thm)],[c_49124,c_98545]) ).

cnf(c_104196,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),subset_relation),
    inference(superposition,[status(thm)],[c_49296,c_98545]) ).

cnf(c_104199,plain,
    ( ~ subclass(subset_relation,intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = subset_relation ),
    inference(superposition,[status(thm)],[c_98545,c_107]) ).

cnf(c_104202,plain,
    ( ~ subclass(subset_relation,X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98545,c_54]) ).

cnf(c_104517,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),universal_class),
    inference(superposition,[status(thm)],[c_128,c_98584]) ).

cnf(c_104524,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),universal_class),
    inference(superposition,[status(thm)],[c_126,c_98584]) ).

cnf(c_104525,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),universal_class),
    inference(superposition,[status(thm)],[c_155,c_98584]) ).

cnf(c_104526,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),universal_class),
    inference(superposition,[status(thm)],[c_176,c_98584]) ).

cnf(c_104528,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),universal_class),
    inference(superposition,[status(thm)],[c_8578,c_98584]) ).

cnf(c_104529,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),universal_class),
    inference(superposition,[status(thm)],[c_49184,c_98584]) ).

cnf(c_104530,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),universal_class),
    inference(superposition,[status(thm)],[c_49124,c_98584]) ).

cnf(c_104531,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),universal_class),
    inference(superposition,[status(thm)],[c_49296,c_98584]) ).

cnf(c_104534,plain,
    ( ~ subclass(universal_class,intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = universal_class ),
    inference(superposition,[status(thm)],[c_98584,c_107]) ).

cnf(c_104597,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),identity_relation),
    inference(superposition,[status(thm)],[c_7302,c_101895]) ).

cnf(c_104600,plain,
    ( ~ subclass(identity_relation,intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = identity_relation ),
    inference(superposition,[status(thm)],[c_101895,c_107]) ).

cnf(c_104623,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),omega),
    inference(superposition,[status(thm)],[c_7302,c_102102]) ).

cnf(c_104626,plain,
    ( ~ subclass(omega,intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = omega ),
    inference(superposition,[status(thm)],[c_102102,c_107]) ).

cnf(c_104633,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_102930]) ).

cnf(c_104636,plain,
    ( ~ subclass(sP1_iProver_def,intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_102930,c_107]) ).

cnf(c_104643,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),sP3_iProver_def),
    inference(superposition,[status(thm)],[c_7302,c_103863]) ).

cnf(c_104720,plain,
    ( ~ subclass(identity_relation,restrict(complement(cross_product(X0,X1)),X0,X1))
    | restrict(complement(cross_product(X0,X1)),X0,X1) = identity_relation ),
    inference(superposition,[status(thm)],[c_101882,c_107]) ).

cnf(c_104723,plain,
    ( ~ subclass(identity_relation,X0)
    | subclass(restrict(complement(cross_product(X1,X2)),X1,X2),X0) ),
    inference(superposition,[status(thm)],[c_101882,c_54]) ).

cnf(c_104726,plain,
    subclass(intersection(power_class(sP3_iProver_def),image(element_relation,complement(null_class))),identity_relation),
    inference(superposition,[status(thm)],[c_85572,c_101890]) ).

cnf(c_104727,plain,
    subclass(intersection(power_class(intersection(complement(X0),complement(X1))),image(element_relation,union(X0,X1))),identity_relation),
    inference(superposition,[status(thm)],[c_126,c_101890]) ).

cnf(c_104728,plain,
    subclass(intersection(power_class(image(element_relation,complement(X0))),image(element_relation,power_class(X0))),identity_relation),
    inference(superposition,[status(thm)],[c_155,c_101890]) ).

cnf(c_104729,plain,
    subclass(intersection(power_class(domain_of(intersection(X0,identity_relation))),image(element_relation,diagonalise(X0))),identity_relation),
    inference(superposition,[status(thm)],[c_176,c_101890]) ).

cnf(c_104731,plain,
    subclass(intersection(power_class(image(element_relation,sP2_iProver_def)),image(element_relation,power_class(sP1_iProver_def))),identity_relation),
    inference(superposition,[status(thm)],[c_8578,c_101890]) ).

cnf(c_104732,plain,
    subclass(intersection(power_class(domain_of(null_class)),image(element_relation,complement(domain_of(sP3_iProver_def)))),identity_relation),
    inference(superposition,[status(thm)],[c_49184,c_101890]) ).

cnf(c_104734,plain,
    subclass(intersection(power_class(image(element_relation,complement(sP3_iProver_def))),image(element_relation,power_class(null_class))),identity_relation),
    inference(superposition,[status(thm)],[c_49296,c_101890]) ).

cnf(c_104737,plain,
    ( ~ subclass(identity_relation,intersection(power_class(X0),image(element_relation,complement(X0))))
    | intersection(power_class(X0),image(element_relation,complement(X0))) = identity_relation ),
    inference(superposition,[status(thm)],[c_101890,c_107]) ).

cnf(c_104740,plain,
    ( ~ subclass(identity_relation,X0)
    | subclass(intersection(power_class(X1),image(element_relation,complement(X1))),X0) ),
    inference(superposition,[status(thm)],[c_101890,c_54]) ).

cnf(c_104777,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(intersection(complement(identity_relation),identity_relation))),identity_relation),
    inference(superposition,[status(thm)],[c_37170,c_101891]) ).

cnf(c_104778,plain,
    subclass(intersection(complement(domain_of(null_class)),domain_of(intersection(complement(identity_relation),identity_relation))),identity_relation),
    inference(superposition,[status(thm)],[c_8912,c_101891]) ).

cnf(c_104779,plain,
    subclass(intersection(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)),identity_relation),
    inference(superposition,[status(thm)],[c_37111,c_101891]) ).

cnf(c_104780,plain,
    subclass(intersection(diagonalise(complement(identity_relation)),domain_of(null_class)),identity_relation),
    inference(superposition,[status(thm)],[c_7611,c_101891]) ).

cnf(c_104781,plain,
    subclass(intersection(diagonalise(cross_product(X0,X1)),domain_of(restrict(identity_relation,X0,X1))),identity_relation),
    inference(superposition,[status(thm)],[c_129,c_101891]) ).

cnf(c_104784,plain,
    ( ~ subclass(identity_relation,intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))))
    | intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))) = identity_relation ),
    inference(superposition,[status(thm)],[c_101891,c_107]) ).

cnf(c_104787,plain,
    ( ~ subclass(identity_relation,X0)
    | subclass(intersection(diagonalise(X1),domain_of(intersection(X1,identity_relation))),X0) ),
    inference(superposition,[status(thm)],[c_101891,c_54]) ).

cnf(c_104808,plain,
    ( ~ subclass(omega,restrict(complement(cross_product(X0,X1)),X0,X1))
    | restrict(complement(cross_product(X0,X1)),X0,X1) = omega ),
    inference(superposition,[status(thm)],[c_102089,c_107]) ).

cnf(c_104811,plain,
    ( ~ subclass(omega,X0)
    | subclass(restrict(complement(cross_product(X1,X2)),X1,X2),X0) ),
    inference(superposition,[status(thm)],[c_102089,c_54]) ).

cnf(c_105254,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),x),
    inference(superposition,[status(thm)],[c_7302,c_104023]) ).

cnf(c_105257,plain,
    ( ~ subclass(x,intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = x ),
    inference(superposition,[status(thm)],[c_104023,c_107]) ).

cnf(c_105281,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),subset_relation),
    inference(superposition,[status(thm)],[c_7302,c_104195]) ).

cnf(c_105284,plain,
    ( ~ subclass(subset_relation,intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = subset_relation ),
    inference(superposition,[status(thm)],[c_104195,c_107]) ).

cnf(c_105326,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),universal_class),
    inference(superposition,[status(thm)],[c_7302,c_104530]) ).

cnf(c_105329,plain,
    ( ~ subclass(universal_class,intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = universal_class ),
    inference(superposition,[status(thm)],[c_104530,c_107]) ).

cnf(c_105340,plain,
    ( ~ subclass(identity_relation,intersection(complement(sP3_iProver_def),sP3_iProver_def))
    | intersection(complement(sP3_iProver_def),sP3_iProver_def) = identity_relation ),
    inference(superposition,[status(thm)],[c_104597,c_107]) ).

cnf(c_105374,plain,
    ( ~ subclass(omega,intersection(complement(sP3_iProver_def),sP3_iProver_def))
    | intersection(complement(sP3_iProver_def),sP3_iProver_def) = omega ),
    inference(superposition,[status(thm)],[c_104623,c_107]) ).

cnf(c_105420,plain,
    ( ~ subclass(sP1_iProver_def,intersection(complement(sP3_iProver_def),sP3_iProver_def))
    | intersection(complement(sP3_iProver_def),sP3_iProver_def) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_104633,c_107]) ).

cnf(c_105444,plain,
    ( ~ subclass(x,intersection(complement(sP3_iProver_def),sP3_iProver_def))
    | intersection(complement(sP3_iProver_def),sP3_iProver_def) = x ),
    inference(superposition,[status(thm)],[c_105254,c_107]) ).

cnf(c_105476,plain,
    ( ~ subclass(subset_relation,intersection(complement(sP3_iProver_def),sP3_iProver_def))
    | intersection(complement(sP3_iProver_def),sP3_iProver_def) = subset_relation ),
    inference(superposition,[status(thm)],[c_105281,c_107]) ).

cnf(c_105487,plain,
    ( ~ subclass(universal_class,intersection(complement(sP3_iProver_def),sP3_iProver_def))
    | intersection(complement(sP3_iProver_def),sP3_iProver_def) = universal_class ),
    inference(superposition,[status(thm)],[c_105326,c_107]) ).

cnf(c_105498,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),singleton(X2)),
    inference(superposition,[status(thm)],[c_128,c_98539]) ).

cnf(c_105505,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),singleton(X2)),
    inference(superposition,[status(thm)],[c_126,c_98539]) ).

cnf(c_105506,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),singleton(X1)),
    inference(superposition,[status(thm)],[c_155,c_98539]) ).

cnf(c_105507,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),singleton(X1)),
    inference(superposition,[status(thm)],[c_176,c_98539]) ).

cnf(c_105509,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),singleton(X0)),
    inference(superposition,[status(thm)],[c_8578,c_98539]) ).

cnf(c_105510,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),singleton(X0)),
    inference(superposition,[status(thm)],[c_49184,c_98539]) ).

cnf(c_105511,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),singleton(X0)),
    inference(superposition,[status(thm)],[c_49124,c_98539]) ).

cnf(c_105512,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),singleton(X0)),
    inference(superposition,[status(thm)],[c_49296,c_98539]) ).

cnf(c_105513,plain,
    ( member_of(X0) = X0
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_90,c_98539]) ).

cnf(c_105524,plain,
    ( ~ subclass(singleton(X0),intersection(complement(X1),X1))
    | intersection(complement(X1),X1) = singleton(X0) ),
    inference(superposition,[status(thm)],[c_98539,c_107]) ).

cnf(c_105527,plain,
    ( ~ subclass(singleton(X0),X1)
    | subclass(intersection(complement(X2),X2),X1) ),
    inference(superposition,[status(thm)],[c_98539,c_54]) ).

cnf(c_106182,plain,
    subclass(intersection(power_class(sP3_iProver_def),image(element_relation,complement(null_class))),omega),
    inference(superposition,[status(thm)],[c_85572,c_102097]) ).

cnf(c_106183,plain,
    subclass(intersection(power_class(intersection(complement(X0),complement(X1))),image(element_relation,union(X0,X1))),omega),
    inference(superposition,[status(thm)],[c_126,c_102097]) ).

cnf(c_106184,plain,
    subclass(intersection(power_class(image(element_relation,complement(X0))),image(element_relation,power_class(X0))),omega),
    inference(superposition,[status(thm)],[c_155,c_102097]) ).

cnf(c_106185,plain,
    subclass(intersection(power_class(domain_of(intersection(X0,identity_relation))),image(element_relation,diagonalise(X0))),omega),
    inference(superposition,[status(thm)],[c_176,c_102097]) ).

cnf(c_106187,plain,
    subclass(intersection(power_class(image(element_relation,sP2_iProver_def)),image(element_relation,power_class(sP1_iProver_def))),omega),
    inference(superposition,[status(thm)],[c_8578,c_102097]) ).

cnf(c_106188,plain,
    subclass(intersection(power_class(domain_of(null_class)),image(element_relation,complement(domain_of(sP3_iProver_def)))),omega),
    inference(superposition,[status(thm)],[c_49184,c_102097]) ).

cnf(c_106190,plain,
    subclass(intersection(power_class(image(element_relation,complement(sP3_iProver_def))),image(element_relation,power_class(null_class))),omega),
    inference(superposition,[status(thm)],[c_49296,c_102097]) ).

cnf(c_106193,plain,
    ( ~ subclass(omega,intersection(power_class(X0),image(element_relation,complement(X0))))
    | intersection(power_class(X0),image(element_relation,complement(X0))) = omega ),
    inference(superposition,[status(thm)],[c_102097,c_107]) ).

cnf(c_106196,plain,
    ( ~ subclass(omega,X0)
    | subclass(intersection(power_class(X1),image(element_relation,complement(X1))),X0) ),
    inference(superposition,[status(thm)],[c_102097,c_54]) ).

cnf(c_106333,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(intersection(complement(identity_relation),identity_relation))),omega),
    inference(superposition,[status(thm)],[c_37170,c_102098]) ).

cnf(c_106334,plain,
    subclass(intersection(complement(domain_of(null_class)),domain_of(intersection(complement(identity_relation),identity_relation))),omega),
    inference(superposition,[status(thm)],[c_8912,c_102098]) ).

cnf(c_106335,plain,
    subclass(intersection(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)),omega),
    inference(superposition,[status(thm)],[c_37111,c_102098]) ).

cnf(c_106336,plain,
    subclass(intersection(diagonalise(complement(identity_relation)),domain_of(null_class)),omega),
    inference(superposition,[status(thm)],[c_7611,c_102098]) ).

cnf(c_106337,plain,
    subclass(intersection(diagonalise(cross_product(X0,X1)),domain_of(restrict(identity_relation,X0,X1))),omega),
    inference(superposition,[status(thm)],[c_129,c_102098]) ).

cnf(c_106340,plain,
    ( ~ subclass(omega,intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))))
    | intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))) = omega ),
    inference(superposition,[status(thm)],[c_102098,c_107]) ).

cnf(c_106343,plain,
    ( ~ subclass(omega,X0)
    | subclass(intersection(diagonalise(X1),domain_of(intersection(X1,identity_relation))),X0) ),
    inference(superposition,[status(thm)],[c_102098,c_54]) ).

cnf(c_106404,plain,
    ( ~ subclass(sP1_iProver_def,restrict(complement(cross_product(X0,X1)),X0,X1))
    | restrict(complement(cross_product(X0,X1)),X0,X1) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_102917,c_107]) ).

cnf(c_106407,plain,
    ( ~ subclass(sP1_iProver_def,X0)
    | subclass(restrict(complement(cross_product(X1,X2)),X1,X2),X0) ),
    inference(superposition,[status(thm)],[c_102917,c_54]) ).

cnf(c_106475,plain,
    subclass(intersection(power_class(sP3_iProver_def),image(element_relation,complement(null_class))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_85572,c_102925]) ).

cnf(c_106476,plain,
    subclass(intersection(power_class(intersection(complement(X0),complement(X1))),image(element_relation,union(X0,X1))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_126,c_102925]) ).

cnf(c_106477,plain,
    subclass(intersection(power_class(image(element_relation,complement(X0))),image(element_relation,power_class(X0))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_155,c_102925]) ).

cnf(c_106478,plain,
    subclass(intersection(power_class(domain_of(intersection(X0,identity_relation))),image(element_relation,diagonalise(X0))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_176,c_102925]) ).

cnf(c_106480,plain,
    subclass(intersection(power_class(image(element_relation,sP2_iProver_def)),image(element_relation,power_class(sP1_iProver_def))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_8578,c_102925]) ).

cnf(c_106481,plain,
    subclass(intersection(power_class(domain_of(null_class)),image(element_relation,complement(domain_of(sP3_iProver_def)))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_49184,c_102925]) ).

cnf(c_106483,plain,
    subclass(intersection(power_class(image(element_relation,complement(sP3_iProver_def))),image(element_relation,power_class(null_class))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_49296,c_102925]) ).

cnf(c_106486,plain,
    ( ~ subclass(sP1_iProver_def,intersection(power_class(X0),image(element_relation,complement(X0))))
    | intersection(power_class(X0),image(element_relation,complement(X0))) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_102925,c_107]) ).

cnf(c_106489,plain,
    ( ~ subclass(sP1_iProver_def,X0)
    | subclass(intersection(power_class(X1),image(element_relation,complement(X1))),X0) ),
    inference(superposition,[status(thm)],[c_102925,c_54]) ).

cnf(c_106561,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),singleton(null_class)),
    inference(superposition,[status(thm)],[c_128,c_98546]) ).

cnf(c_106568,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),singleton(null_class)),
    inference(superposition,[status(thm)],[c_126,c_98546]) ).

cnf(c_106569,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),singleton(null_class)),
    inference(superposition,[status(thm)],[c_155,c_98546]) ).

cnf(c_106570,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),singleton(null_class)),
    inference(superposition,[status(thm)],[c_176,c_98546]) ).

cnf(c_106572,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),singleton(null_class)),
    inference(superposition,[status(thm)],[c_8578,c_98546]) ).

cnf(c_106573,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),singleton(null_class)),
    inference(superposition,[status(thm)],[c_49184,c_98546]) ).

cnf(c_106574,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),singleton(null_class)),
    inference(superposition,[status(thm)],[c_49124,c_98546]) ).

cnf(c_106575,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),singleton(null_class)),
    inference(superposition,[status(thm)],[c_49296,c_98546]) ).

cnf(c_106579,plain,
    ( ~ subclass(singleton(null_class),intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = singleton(null_class) ),
    inference(superposition,[status(thm)],[c_98546,c_107]) ).

cnf(c_106582,plain,
    ( ~ subclass(singleton(null_class),X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98546,c_54]) ).

cnf(c_106780,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),singleton(omega)),
    inference(superposition,[status(thm)],[c_128,c_98547]) ).

cnf(c_106787,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),singleton(omega)),
    inference(superposition,[status(thm)],[c_126,c_98547]) ).

cnf(c_106788,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),singleton(omega)),
    inference(superposition,[status(thm)],[c_155,c_98547]) ).

cnf(c_106789,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),singleton(omega)),
    inference(superposition,[status(thm)],[c_176,c_98547]) ).

cnf(c_106791,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),singleton(omega)),
    inference(superposition,[status(thm)],[c_8578,c_98547]) ).

cnf(c_106792,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),singleton(omega)),
    inference(superposition,[status(thm)],[c_49184,c_98547]) ).

cnf(c_106793,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),singleton(omega)),
    inference(superposition,[status(thm)],[c_49124,c_98547]) ).

cnf(c_106794,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),singleton(omega)),
    inference(superposition,[status(thm)],[c_49296,c_98547]) ).

cnf(c_106797,plain,
    ( ~ subclass(singleton(omega),intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = singleton(omega) ),
    inference(superposition,[status(thm)],[c_98547,c_107]) ).

cnf(c_106800,plain,
    ( ~ subclass(singleton(omega),X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98547,c_54]) ).

cnf(c_107047,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_128,c_98548]) ).

cnf(c_107054,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_126,c_98548]) ).

cnf(c_107055,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_155,c_98548]) ).

cnf(c_107056,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_176,c_98548]) ).

cnf(c_107058,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_8578,c_98548]) ).

cnf(c_107059,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_49184,c_98548]) ).

cnf(c_107060,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_49124,c_98548]) ).

cnf(c_107061,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_49296,c_98548]) ).

cnf(c_107064,plain,
    ( ~ subclass(inverse(subset_relation),intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = inverse(subset_relation) ),
    inference(superposition,[status(thm)],[c_98548,c_107]) ).

cnf(c_107067,plain,
    ( ~ subclass(inverse(subset_relation),X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98548,c_54]) ).

cnf(c_107301,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_128,c_98552]) ).

cnf(c_107308,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_126,c_98552]) ).

cnf(c_107309,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_155,c_98552]) ).

cnf(c_107310,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_176,c_98552]) ).

cnf(c_107312,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_8578,c_98552]) ).

cnf(c_107313,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_49184,c_98552]) ).

cnf(c_107314,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_49124,c_98552]) ).

cnf(c_107315,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_49296,c_98552]) ).

cnf(c_107318,plain,
    ( ~ subclass(singleton(sP1_iProver_def),intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = singleton(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_98552,c_107]) ).

cnf(c_107321,plain,
    ( ~ subclass(singleton(sP1_iProver_def),X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98552,c_54]) ).

cnf(c_107551,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_128,c_98553]) ).

cnf(c_107558,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_126,c_98553]) ).

cnf(c_107559,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_155,c_98553]) ).

cnf(c_107560,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_176,c_98553]) ).

cnf(c_107562,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_8578,c_98553]) ).

cnf(c_107563,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_49184,c_98553]) ).

cnf(c_107564,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_49124,c_98553]) ).

cnf(c_107565,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_49296,c_98553]) ).

cnf(c_107568,plain,
    ( ~ subclass(singleton(sP3_iProver_def),intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = singleton(sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_98553,c_107]) ).

cnf(c_107571,plain,
    ( ~ subclass(singleton(sP3_iProver_def),X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98553,c_54]) ).

cnf(c_107792,plain,
    subclass(restrict(complement(cross_product(X0,X1)),X0,X1),singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_128,c_98611]) ).

cnf(c_107799,plain,
    subclass(intersection(union(X0,X1),intersection(complement(X0),complement(X1))),singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_126,c_98611]) ).

cnf(c_107800,plain,
    subclass(intersection(power_class(X0),image(element_relation,complement(X0))),singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_155,c_98611]) ).

cnf(c_107801,plain,
    subclass(intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))),singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_176,c_98611]) ).

cnf(c_107803,plain,
    subclass(intersection(power_class(sP1_iProver_def),image(element_relation,sP2_iProver_def)),singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_8578,c_98611]) ).

cnf(c_107804,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(null_class)),singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_49184,c_98611]) ).

cnf(c_107805,plain,
    subclass(intersection(complement(sP3_iProver_def),null_class),singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_49124,c_98611]) ).

cnf(c_107806,plain,
    subclass(intersection(power_class(null_class),image(element_relation,complement(sP3_iProver_def))),singleton(sP0_iProver_def)),
    inference(superposition,[status(thm)],[c_49296,c_98611]) ).

cnf(c_107810,plain,
    ( ~ subclass(singleton(sP0_iProver_def),intersection(complement(X0),X0))
    | intersection(complement(X0),X0) = singleton(sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_98611,c_107]) ).

cnf(c_107813,plain,
    ( ~ subclass(singleton(sP0_iProver_def),X0)
    | subclass(intersection(complement(X1),X1),X0) ),
    inference(superposition,[status(thm)],[c_98611,c_54]) ).

cnf(c_108227,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),singleton(X0)),
    inference(superposition,[status(thm)],[c_7302,c_105511]) ).

cnf(c_108239,plain,
    ( ~ subclass(singleton(X0),intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = singleton(X0) ),
    inference(superposition,[status(thm)],[c_105511,c_107]) ).

cnf(c_108242,plain,
    ( ~ subclass(singleton(X0),X1)
    | subclass(intersection(complement(sP3_iProver_def),null_class),X1) ),
    inference(superposition,[status(thm)],[c_105511,c_54]) ).

cnf(c_108252,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),singleton(sP3_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_106574]) ).

cnf(c_108256,plain,
    ( ~ subclass(singleton(null_class),intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = singleton(null_class) ),
    inference(superposition,[status(thm)],[c_106574,c_107]) ).

cnf(c_108342,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),singleton(omega)),
    inference(superposition,[status(thm)],[c_7302,c_106793]) ).

cnf(c_108345,plain,
    ( ~ subclass(singleton(omega),intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = singleton(omega) ),
    inference(superposition,[status(thm)],[c_106793,c_107]) ).

cnf(c_108434,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),inverse(subset_relation)),
    inference(superposition,[status(thm)],[c_7302,c_107060]) ).

cnf(c_108437,plain,
    ( ~ subclass(inverse(subset_relation),intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = inverse(subset_relation) ),
    inference(superposition,[status(thm)],[c_107060,c_107]) ).

cnf(c_108538,plain,
    subclass(intersection(complement(sP3_iProver_def),sP3_iProver_def),singleton(sP1_iProver_def)),
    inference(superposition,[status(thm)],[c_7302,c_107314]) ).

cnf(c_108541,plain,
    ( ~ subclass(singleton(sP1_iProver_def),intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = singleton(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_107314,c_107]) ).

cnf(c_108597,plain,
    ( ~ subclass(singleton(sP3_iProver_def),intersection(complement(sP3_iProver_def),null_class))
    | intersection(complement(sP3_iProver_def),null_class) = singleton(sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_107564,c_107]) ).

cnf(c_116950,plain,
    subclass(intersection(complement(domain_of(sP3_iProver_def)),domain_of(intersection(complement(identity_relation),identity_relation))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_37170,c_102926]) ).

cnf(c_116951,plain,
    subclass(intersection(complement(domain_of(null_class)),domain_of(intersection(complement(identity_relation),identity_relation))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_8912,c_102926]) ).

cnf(c_116952,plain,
    subclass(intersection(diagonalise(complement(identity_relation)),domain_of(sP3_iProver_def)),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_37111,c_102926]) ).

cnf(c_116953,plain,
    subclass(intersection(diagonalise(complement(identity_relation)),domain_of(null_class)),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_7611,c_102926]) ).

cnf(c_116954,plain,
    subclass(intersection(diagonalise(cross_product(X0,X1)),domain_of(restrict(identity_relation,X0,X1))),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_129,c_102926]) ).

cnf(c_116957,plain,
    ( ~ subclass(sP1_iProver_def,intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))))
    | intersection(diagonalise(X0),domain_of(intersection(X0,identity_relation))) = sP1_iProver_def ),
    inference(superposition,[status(thm)],[c_102926,c_107]) ).

cnf(c_116960,plain,
    ( ~ subclass(sP1_iProver_def,X0)
    | subclass(intersection(diagonalise(X1),domain_of(intersection(X1,identity_relation))),X0) ),
    inference(superposition,[status(thm)],[c_102926,c_54]) ).

cnf(c_133163,plain,
    ( ~ subclass(null_class,X0)
    | subclass(restrict(complement(cross_product(X1,X2)),X1,X2),X0) ),
    inference(superposition,[status(thm)],[c_103850,c_54]) ).

cnf(c_133167,plain,
    subclass(intersection(power_class(sP3_iProver_def),image(element_relation,complement(null_class))),null_class),
    inference(superposition,[status(thm)],[c_85572,c_103858]) ).

cnf(c_133168,plain,
    subclass(intersection(power_class(intersection(complement(X0),complement(X1))),image(element_relation,union(X0,X1))),null_class),
    inference(superposition,[status(thm)],[c_126,c_103858]) ).

cnf(c_133169,plain,
    subclass(intersection(power_class(image(element_relation,complement(X0))),image(element_relation,power_class(X0))),null_class),
    inference(superposition,[status(thm)],[c_155,c_103858]) ).

cnf(c_133170,plain,
    subclass(intersection(power_class(domain_of(intersection(X0,identity_relation))),image(element_relation,diagonalise(X0))),null_class),
    inference(superposition,[status(thm)],[c_176,c_103858]) ).

cnf(c_133172,plain,
    subclass(intersection(power_class(image(element_relation,sP2_iProver_def)),image(element_relation,power_class(sP1_iProver_def))),null_class),
    inference(superposition,[status(thm)],[c_8578,c_103858]) ).

cnf(c_133173,plain,
    subclass(intersection(power_class(domain_of(null_class)),image(element_relation,complement(domain_of(sP3_iProver_def)))),null_class),
    inference(superposition,[status(thm)],[c_49184,c_103858]) ).

cnf(c_133175,plain,
    subclass(intersection(power_class(image(element_relation,complement(sP3_iProver_def))),image(element_relation,power_class(null_class))),null_class),
    inference(superposition,[status(thm)],[c_49296,c_103858]) ).

cnf(c_133182,plain,
    ( ~ subclass(null_class,X0)
    | subclass(intersection(power_class(X1),image(element_relation,complement(X1))),X0) ),
    inference(superposition,[status(thm)],[c_103858,c_54]) ).

cnf(c_133466,plain,
    $false,
    inference(smt_impl_just,[status(thm)],[c_107813,c_107810,c_107806,c_107804,c_107803,c_107801,c_107800,c_107799,c_107792,c_107571,c_107568,c_107565,c_107563,c_107562,c_107560,c_107559,c_107558,c_107551,c_107321,c_107318,c_107315,c_107313,c_107312,c_107310,c_107309,c_107308,c_107301,c_107067,c_107064,c_107061,c_107059,c_107058,c_107056,c_107055,c_107054,c_107047,c_106800,c_106797,c_106794,c_106792,c_106791,c_106789,c_106788,c_106787,c_106780,c_106582,c_106579,c_106575,c_106573,c_106572,c_106570,c_106569,c_106568,c_106561,c_105527,c_105524,c_105513,c_105512,c_105510,c_105509,c_105507,c_105506,c_105505,c_105498,c_87815,c_87814,c_86759,c_86741,c_84960,c_116960,c_116957,c_116954,c_116953,c_116952,c_116951,c_116950,c_106489,c_106486,c_106483,c_106481,c_106480,c_106478,c_106477,c_106476,c_106475,c_106407,c_106404,c_133182,c_133175,c_133173,c_133172,c_133170,c_133169,c_133168,c_133167,c_104534,c_104526,c_104525,c_104524,c_104517,c_133163,c_106343,c_106340,c_106337,c_106336,c_106335,c_106334,c_106333,c_106196,c_106193,c_106190,c_106188,c_106187,c_106185,c_106184,c_106183,c_106182,c_104811,c_104808,c_104787,c_104784,c_104781,c_104780,c_104779,c_104778,c_104777,c_104740,c_104737,c_104734,c_104732,c_104731,c_104729,c_104728,c_104727,c_104726,c_104723,c_104720,c_104027,c_104024,c_104022,c_104021,c_104019,c_104018,c_104017,c_104010,c_102934,c_102931,c_102929,c_102928,c_102926,c_102925,c_102924,c_102917,c_104202,c_104199,c_104196,c_104194,c_104193,c_104191,c_104190,c_104189,c_104182,c_103946,c_103940,c_103938,c_103937,c_103935,c_103934,c_103933,c_103926,c_103871,c_103864,c_103862,c_103861,c_103859,c_103858,c_103857,c_103850,c_102106,c_102103,c_102101,c_102100,c_102098,c_102097,c_102096,c_102089,c_101902,c_101899,c_101896,c_101894,c_101893,c_101891,c_101890,c_101889,c_101882,c_98771,c_98769,c_98767,c_98765,c_98758,c_98756,c_98755,c_98754,c_98757,c_98752,c_98751,c_98742,c_98732,c_98731,c_98730,c_98729,c_98728,c_98727,c_98726,c_98725,c_98724,c_98723,c_98739,c_98722,c_98721,c_98720,c_98719,c_98718,c_98717,c_98716,c_98715,c_98714,c_98713,c_98712,c_98711,c_98737,c_98709,c_98708,c_98707,c_98706,c_98705,c_98704,c_98703,c_98702,c_98701,c_98700,c_98699,c_98698,c_98697,c_98469,c_102937,c_104030,c_98585,c_98398,c_92084,c_92105,c_92097,c_92076,c_92146,c_67541,c_93185,c_92335,c_93179,c_93175,c_92331,c_92197,c_92057,c_92047,c_90702,c_90306,c_92039,c_91357,c_91349,c_91324,c_90146,c_91308,c_91079,c_90139,c_90132,c_90130,c_90129,c_91233,c_91231,c_91230,c_90719,c_90717,c_90716,c_90126,c_90124,c_90123,c_91315,c_90121,c_91225,c_91223,c_90155,c_90153,c_89417,c_89414,c_91339,c_91333,c_91331,c_91330,c_91321,c_89261,c_89258,c_89256,c_89255,c_89254,c_89252,c_89251,c_89249,c_89248,c_92066,c_97731,c_97728,c_89241,c_89240,c_89237,c_90460,c_90468,c_90705,c_98247,c_98246,c_98186,c_98185,c_98053,c_98052,c_98028,c_98027,c_95258,c_95126,c_92418,c_92417,c_92378,c_92377,c_92340,c_92339,c_92409,c_92209,c_92410,c_92210,c_91615,c_89230,c_89222,c_89221,c_97722,c_97719,c_97714,c_97711,c_88915,c_88912,c_88910,c_88909,c_88908,c_88907,c_88906,c_88905,c_88903,c_88902,c_88876,c_88873,c_88871,c_88870,c_88869,c_88868,c_88867,c_88866,c_88864,c_88863,c_97453,c_97454,c_97452,c_97455,c_97449,c_97448,c_88833,c_88836,c_88832,c_88837,c_88829,c_88828,c_88827,c_88826,c_88825,c_88824,c_88823,c_88822,c_88820,c_88819,c_88017,c_88016,c_88013,c_88011,c_88010,c_88009,c_88008,c_88007,c_88006,c_88004,c_88003,c_88002,c_77961,c_77960,c_95073,c_95064,c_95065,c_95060,c_95059,c_95055,c_95053,c_95054,c_94971,c_94967,c_94966,c_94963,c_94953,c_97431,c_97317,c_93165,c_93154,c_93151,c_93150,c_93147,c_93037,c_93036,c_93033,c_93030,c_93027,c_93006,c_93003,c_92751,c_92748,c_92185,c_92182,c_88808,c_88805,c_88584,c_88581,c_88572,c_88569,c_88549,c_88546,c_88798,c_88795,c_88785,c_88782,c_88513,c_88510,c_88500,c_88497,c_88537,c_88534,c_88525,c_88522,c_78867,c_88660,c_88657,c_88484,c_86506,c_86505,c_86470,c_86466,c_86462,c_86461,c_86460,c_86459,c_86446,c_77181,c_77168,c_77156,c_77129,c_77117,c_77108,c_77105,c_76489,c_76486,c_76477,c_76474,c_76468,c_76465,c_76456,c_76453,c_76443,c_76440,c_76108,c_76105,c_76042,c_76039,c_108597,c_108541,c_108345,c_108256,c_108437,c_108242,c_108239,c_76029,c_76026,c_75966,c_75963,c_75896,c_75893,c_75877,c_75874,c_96244,c_81912,c_74160,c_75865,c_75862,c_75335,c_75332,c_75305,c_75302,c_74313,c_74310,c_77457,c_77456,c_73756,c_77930,c_77927,c_74326,c_77935,c_75285,c_75282,c_75242,c_75239,c_74680,c_74677,c_74445,c_74442,c_74295,c_74292,c_78866,c_74284,c_74281,c_74140,c_74137,c_74011,c_74008,c_73994,c_87967,c_87966,c_86432,c_86431,c_78865,c_81131,c_81130,c_81127,c_86827,c_86826,c_86426,c_86425,c_78864,c_105340,c_105476,c_96054,c_105444,c_105420,c_105374,c_85564,c_85760,c_104600,c_105284,c_105257,c_104636,c_104626,c_108252,c_108538,c_108434,c_104597,c_108342,c_105281,c_105254,c_104643,c_104633,c_108227,c_104623,c_107564,c_107314,c_107060,c_101895,c_106793,c_106574,c_104195,c_104023,c_103939,c_103863,c_102930,c_107805,c_105511,c_102102,c_86298,c_86297,c_85813,c_85812,c_96243,c_96242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).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET097-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.00/0.10  % Command  : run_iprover %s %d THM
% 0.09/0.30  % Computer : n021.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Sun Jun 23 15:59:54 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.16/0.41  Running first-order theorem proving
% 0.16/0.41  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 209.98/28.23  % SZS status Started for theBenchmark.p
% 209.98/28.23  % SZS status Unsatisfiable for theBenchmark.p
% 209.98/28.23  
% 209.98/28.23  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 209.98/28.23  
% 209.98/28.23  ------  iProver source info
% 209.98/28.23  
% 209.98/28.23  git: date: 2024-06-12 09:56:46 +0000
% 209.98/28.23  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 209.98/28.23  git: non_committed_changes: false
% 209.98/28.23  
% 209.98/28.23  ------ Parsing...successful
% 209.98/28.23  
% 209.98/28.23  
% 209.98/28.23  
% 209.98/28.23  ------ Preprocessing... sup_sim: 2  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 209.98/28.23  
% 209.98/28.23  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 209.98/28.23  
% 209.98/28.23  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 209.98/28.23  ------ Proving...
% 209.98/28.23  ------ Problem Properties 
% 209.98/28.23  
% 209.98/28.23  
% 209.98/28.23  clauses                                 138
% 209.98/28.23  conjectures                             3
% 209.98/28.23  EPR                                     20
% 209.98/28.23  Horn                                    117
% 209.98/28.23  unary                                   49
% 209.98/28.23  binary                                  56
% 209.98/28.23  lits                                    267
% 209.98/28.23  lits eq                                 82
% 209.98/28.23  fd_pure                                 0
% 209.98/28.23  fd_pseudo                               0
% 209.98/28.23  fd_cond                                 5
% 209.98/28.23  fd_pseudo_cond                          14
% 209.98/28.23  AC symbols                              0
% 209.98/28.23  
% 209.98/28.23  ------ Input Options Time Limit: Unbounded
% 209.98/28.23  
% 209.98/28.23  
% 209.98/28.23  ------ 
% 209.98/28.23  Current options:
% 209.98/28.23  ------ 
% 209.98/28.23  
% 209.98/28.23  
% 209.98/28.23  
% 209.98/28.23  
% 209.98/28.23  ------ Proving...
% 209.98/28.23  
% 209.98/28.23  
% 209.98/28.23  % SZS status Unsatisfiable for theBenchmark.p
% 209.98/28.23  
% 209.98/28.23  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 210.52/28.25  
% 210.52/28.25  
%------------------------------------------------------------------------------