%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET076-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:46:25 PM UTC 2026
% Result : Unsatisfiable 36.33s 5.92s
% Output : CNFRefutation 36.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 109
% Syntax : Number of formulae : 5286 ( 481 unt; 1 def)
% Number of atoms : 21083 (4108 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 12162 (3742 ~;8420 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 27 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 36 ( 36 usr; 11 con; 0-3 aty)
% Number of variables : 10940 ( 0 sgn10940 !; 0 ?;10581 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',element_relation1) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',element_relation2) ).
fof(f20,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',element_relation3) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).
fof(f30,axiom,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain1) ).
fof(f31,axiom,
! [X0,X1] :
( member(X0,domain_of(X1))
| restrict(X1,singleton(X0),universal_class) = null_class
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain2) ).
fof(f32,plain,
! [X0,X1] :
( member(X0,domain_of(X1))
| null_class = restrict(X1,singleton(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',rotate1) ).
fof(f34,axiom,
! [X2,X3,X0,X1] :
( 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',rotate2) ).
fof(f35,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X2,X0),X1),rotate(X3))
| ~ member(ordered_pair(ordered_pair(X2,X0),X1),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',rotate3) ).
fof(f36,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',flip1) ).
fof(f37,axiom,
! [X2,X3,X0,X1] :
( 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',flip2) ).
fof(f38,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X0),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',flip3) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',range_of) ).
fof(f43,axiom,
! [X0,X1] : range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',image) ).
fof(f44,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor) ).
fof(f45,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor_relation1) ).
fof(f46,axiom,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor_relation2) ).
fof(f47,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| successor(X0) != X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor_relation3) ).
fof(f48,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive1) ).
fof(f49,axiom,
! [X0] :
( subclass(image(successor_relation,X0),X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive2) ).
fof(f50,axiom,
! [X0] :
( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive3) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
fof(f52,axiom,
! [X0] :
( subclass(omega,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive2) ).
fof(f53,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_in_universal) ).
fof(f54,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',sum_class_definition) ).
fof(f55,axiom,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',sum_class2) ).
fof(f56,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',power_class_definition) ).
fof(f57,axiom,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',power_class2) ).
fof(f58,axiom,
! [X0,X1] : subclass(compose(X0,X1),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compose1) ).
fof(f59,axiom,
! [X2,X3,X0,X1] :
( member(X1,image(X2,image(X3,singleton(X0))))
| ~ member(ordered_pair(X0,X1),compose(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compose2) ).
fof(f60,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X3,X0),compose(X1,X2))
| ~ member(ordered_pair(X3,X0),cross_product(universal_class,universal_class))
| ~ member(X0,image(X1,image(X2,singleton(X3)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compose3) ).
fof(f63,axiom,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',function1) ).
fof(f64,axiom,
! [X0] :
( subclass(compose(X0,inverse(X0)),identity_relation)
| ~ function(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',function2) ).
fof(f65,axiom,
! [X0] :
( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',function3) ).
fof(f66,axiom,
! [X0,X1] :
( member(image(X0,X1),universal_class)
| ~ member(X1,universal_class)
| ~ function(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',replacement) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,axiom,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f71,axiom,
! [X0,X1] : sum_class(image(X0,singleton(X1))) = apply(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',apply) ).
fof(f72,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',choice1) ).
fof(f73,axiom,
! [X0] :
( member(apply(choice,X0),X0)
| X0 = null_class
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',choice2) ).
fof(f74,plain,
! [X0] :
( member(apply(choice,X0),X0)
| null_class = X0
| ~ member(X0,universal_class) ),
inference(reorient_equations,[],[f73]) ).
fof(f78,axiom,
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) ).
fof(f79,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',identity_relation) ).
fof(f80,plain,
identity_relation = intersection(inverse(subset_relation),subset_relation),
inference(reorient_equations,[],[f79]) ).
fof(f83,axiom,
! [X0] :
( function(X0)
| ~ operation(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',operation1) ).
fof(f84,axiom,
! [X0] :
( cross_product(domain_of(domain_of(X0)),domain_of(domain_of(X0))) = domain_of(X0)
| ~ operation(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',operation2) ).
fof(f85,plain,
! [X0] :
( domain_of(X0) = cross_product(domain_of(domain_of(X0)),domain_of(domain_of(X0)))
| ~ operation(X0) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,axiom,
! [X0] :
( subclass(range_of(X0),domain_of(domain_of(X0)))
| ~ operation(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',operation3) ).
fof(f87,axiom,
! [X0] :
( operation(X0)
| ~ subclass(range_of(X0),domain_of(domain_of(X0)))
| cross_product(domain_of(domain_of(X0)),domain_of(domain_of(X0))) != domain_of(X0)
| ~ function(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',operation4) ).
fof(f88,plain,
! [X0] :
( operation(X0)
| ~ subclass(range_of(X0),domain_of(domain_of(X0)))
| domain_of(X0) != cross_product(domain_of(domain_of(X0)),domain_of(domain_of(X0)))
| ~ function(X0) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,axiom,
! [X2,X0,X1] :
( function(X0)
| ~ compatible(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compatible1) ).
fof(f90,axiom,
! [X2,X0,X1] :
( domain_of(domain_of(X1)) = domain_of(X0)
| ~ compatible(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compatible2) ).
fof(f91,plain,
! [X2,X0,X1] :
( domain_of(X0) = domain_of(domain_of(X1))
| ~ compatible(X0,X1,X2) ),
inference(reorient_equations,[],[f90]) ).
fof(f92,axiom,
! [X2,X0,X1] :
( subclass(range_of(X0),domain_of(domain_of(X2)))
| ~ compatible(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compatible3) ).
fof(f93,axiom,
! [X2,X0,X1] :
( compatible(X0,X1,X2)
| ~ subclass(range_of(X0),domain_of(domain_of(X2)))
| domain_of(domain_of(X1)) != domain_of(X0)
| ~ function(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compatible4) ).
fof(f94,plain,
! [X2,X0,X1] :
( compatible(X0,X1,X2)
| ~ subclass(range_of(X0),domain_of(domain_of(X2)))
| domain_of(X0) != domain_of(domain_of(X1))
| ~ function(X0) ),
inference(reorient_equations,[],[f93]) ).
fof(f95,axiom,
! [X2,X0,X1] :
( operation(X1)
| ~ homomorphism(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism1) ).
fof(f96,axiom,
! [X2,X0,X1] :
( operation(X2)
| ~ homomorphism(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism2) ).
fof(f97,axiom,
! [X2,X0,X1] :
( compatible(X0,X1,X2)
| ~ homomorphism(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism3) ).
fof(f98,axiom,
! [X2,X3,X0,X1,X4] :
( apply(X2,ordered_pair(apply(X0,X3),apply(X0,X4))) = apply(X0,apply(X1,ordered_pair(X3,X4)))
| ~ member(ordered_pair(X3,X4),domain_of(X1))
| ~ homomorphism(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism4) ).
fof(f99,axiom,
! [X2,X0,X1] :
( homomorphism(X2,X0,X1)
| member(ordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism2(X2,X0,X1)),domain_of(X0))
| ~ compatible(X2,X0,X1)
| ~ operation(X1)
| ~ operation(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism5) ).
fof(f100,axiom,
! [X2,X0,X1] :
( homomorphism(X2,X0,X1)
| apply(X1,ordered_pair(apply(X2,not_homomorphism1(X2,X0,X1)),apply(X2,not_homomorphism2(X2,X0,X1)))) != apply(X2,apply(X0,ordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism2(X2,X0,X1))))
| ~ compatible(X2,X0,X1)
| ~ operation(X1)
| ~ operation(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',homomorphism6) ).
fof(f101,axiom,
! [X2,X3,X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_unordered_pair) ).
fof(f102,axiom,
! [X2,X3,X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_unordered_pair) ).
fof(f103,axiom,
! [X2,X3,X0,X1] :
( member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
fof(f104,axiom,
! [X2,X3,X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
fof(f105,axiom,
! [X0] : subclass(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_is_reflexive) ).
fof(f106,axiom,
! [X2,X0,X1] :
( subclass(X0,X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subclass) ).
fof(f107,axiom,
! [X0,X1] :
( member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality1) ).
fof(f109,axiom,
! [X0,X1] :
( member(not_subclass_element(X1,X0),X1)
| X1 = X0
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality3) ).
fof(f110,plain,
! [X0,X1] :
( member(not_subclass_element(X1,X0),X1)
| X0 = X1
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(reorient_equations,[],[f109]) ).
fof(f111,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality4) ).
fof(f112,axiom,
! [X0,X1] : ~ member(X0,intersection(complement(X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f114,axiom,
! [X0] : subclass(null_class,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_subclass) ).
fof(f115,axiom,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).
fof(f116,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class) ),
inference(reorient_equations,[],[f115]) ).
fof(f117,axiom,
! [X0] :
( member(not_subclass_element(X0,null_class),X0)
| X0 = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_unique) ).
fof(f118,plain,
! [X0] :
( member(not_subclass_element(X0,null_class),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f117]) ).
fof(f119,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f121,axiom,
! [X0,X1] : subclass(singleton(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair1) ).
fof(f122,axiom,
! [X0,X1] : subclass(singleton(X0),unordered_pair(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).
fof(f123,axiom,
! [X0,X1] :
( unordered_pair(X1,X0) = singleton(X1)
| member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
fof(f124,axiom,
! [X0,X1] :
( unordered_pair(X0,X1) = singleton(X1)
| member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
fof(f125,axiom,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(X0,X1) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_unordered_pair) ).
fof(f126,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| unordered_pair(X0,X1) != unordered_pair(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
fof(f127,axiom,
! [X2,X0,X1] :
( X0 = X2
| ~ member(ordered_pair(X0,X2),cross_product(universal_class,universal_class))
| unordered_pair(X0,X1) != unordered_pair(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation) ).
fof(f128,axiom,
! [X0,X1] :
( unordered_pair(X0,X1) != null_class
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
fof(f129,axiom,
! [X0,X1] :
( unordered_pair(X1,X0) != null_class
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
fof(f130,axiom,
! [X2,X3,X0,X1] :
( 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) ).
fof(f131,negated_conjecture,
member(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unordered_pair_is_subset_1) ).
fof(f132,negated_conjecture,
member(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unordered_pair_is_subset_2) ).
fof(f133,negated_conjecture,
~ subclass(unordered_pair(x,y),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unordered_pair_is_subset_3) ).
fof(f134,plain,
! [X0] : sum_class(X0) = domain_of(intersection(element_relation,cross_product(universal_class,X0))),
inference(definition_unfolding,[],[f54,f28]) ).
fof(f135,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f40,f39]) ).
fof(f136,plain,
! [X0,X1] : image(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f43,f135,f28]) ).
fof(f137,plain,
! [X0,X1] : apply(X0,X1) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),
inference(definition_unfolding,[],[f71,f134,f136,f12]) ).
fof(f138,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f141,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f44,f26,f12]) ).
fof(f142,plain,
! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),
inference(definition_unfolding,[],[f56,f136]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f14,f138]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f15,f138]) ).
fof(f146,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(definition_unfolding,[],[f16,f138]) ).
fof(f147,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(definition_unfolding,[],[f17,f138]) ).
fof(f148,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f19,f138]) ).
fof(f149,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f20,f138,f138]) ).
fof(f150,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f151,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) ),
inference(definition_unfolding,[],[f30,f28,f12]) ).
fof(f152,plain,
! [X0,X1] :
( member(X0,domain_of(X1))
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f32,f28,f12]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3)) ),
inference(definition_unfolding,[],[f34,f138,f138,f138,f138]) ).
fof(f154,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),X3) ),
inference(definition_unfolding,[],[f35,f138,f138,f138,f138,f138,f138]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ),
inference(definition_unfolding,[],[f37,f138,f138,f138,f138]) ).
fof(f156,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),X3) ),
inference(definition_unfolding,[],[f38,f138,f138,f138,f138,f138,f138]) ).
fof(f157,plain,
! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f46,f138,f141]) ).
fof(f158,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) != X1 ),
inference(definition_unfolding,[],[f47,f141,f138,f138]) ).
fof(f159,plain,
! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(definition_unfolding,[],[f49,f136]) ).
fof(f160,plain,
! [X0] :
( inductive(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ member(null_class,X0) ),
inference(definition_unfolding,[],[f50,f136]) ).
fof(f161,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f55,f134]) ).
fof(f162,plain,
! [X0] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f57,f142]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3)) ),
inference(definition_unfolding,[],[f59,f138,f136,f136,f12]) ).
fof(f164,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X0,X0))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X3,X3),universal_class)),universal_class)))),universal_class)),universal_class))))) ),
inference(definition_unfolding,[],[f60,f136,f136,f12,f138,f138]) ).
fof(f167,plain,
! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ),
inference(definition_unfolding,[],[f64,f39]) ).
fof(f168,plain,
! [X0] :
( function(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f65,f39]) ).
fof(f169,plain,
! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),universal_class)
| ~ member(X1,universal_class)
| ~ function(X0) ),
inference(definition_unfolding,[],[f66,f136]) ).
fof(f170,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X0)
| null_class = X0
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f74,f137]) ).
fof(f173,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(definition_unfolding,[],[f78,f39]) ).
fof(f174,plain,
identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
inference(definition_unfolding,[],[f80,f39]) ).
fof(f175,plain,
! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),domain_of(domain_of(X0)))
| ~ operation(X0) ),
inference(definition_unfolding,[],[f86,f135]) ).
fof(f176,plain,
! [X0] :
( operation(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),domain_of(domain_of(X0)))
| domain_of(X0) != cross_product(domain_of(domain_of(X0)),domain_of(domain_of(X0)))
| ~ function(X0) ),
inference(definition_unfolding,[],[f88,f135]) ).
fof(f177,plain,
! [X2,X0,X1] :
( subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),domain_of(domain_of(X2)))
| ~ compatible(X0,X1,X2) ),
inference(definition_unfolding,[],[f92,f135]) ).
fof(f178,plain,
! [X2,X0,X1] :
( compatible(X0,X1,X2)
| ~ subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),domain_of(domain_of(X2)))
| domain_of(X0) != domain_of(domain_of(X1))
| ~ function(X0) ),
inference(definition_unfolding,[],[f94,f135]) ).
fof(f179,plain,
! [X2,X3,X0,X1,X4] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X4,X4),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X4,X4),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X4,X4),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X4,X4),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),domain_of(X1))
| ~ homomorphism(X0,X1,X2) ),
inference(definition_unfolding,[],[f98,f138,f137,f138,f137,f137,f137,f137,f138]) ).
fof(f180,plain,
! [X2,X0,X1] :
( homomorphism(X2,X0,X1)
| member(unordered_pair(unordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism1(X2,X0,X1)),unordered_pair(not_homomorphism1(X2,X0,X1),unordered_pair(not_homomorphism2(X2,X0,X1),not_homomorphism2(X2,X0,X1)))),domain_of(X0))
| ~ compatible(X2,X0,X1)
| ~ operation(X1)
| ~ operation(X0) ),
inference(definition_unfolding,[],[f99,f138]) ).
fof(f181,plain,
! [X2,X0,X1] :
( homomorphism(X2,X0,X1)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism1(X2,X0,X1)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism1(X2,X0,X1)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism1(X2,X0,X1)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(not_homomorphism2(X2,X0,X1),not_homomorphism2(X2,X0,X1)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(not_homomorphism2(X2,X0,X1),not_homomorphism2(X2,X0,X1)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism1(X2,X0,X1)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism1(X2,X0,X1)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism1(X2,X0,X1)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(not_homomorphism2(X2,X0,X1),not_homomorphism2(X2,X0,X1)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(not_homomorphism2(X2,X0,X1),not_homomorphism2(X2,X0,X1)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism1(X2,X0,X1)),unordered_pair(not_homomorphism1(X2,X0,X1),unordered_pair(not_homomorphism2(X2,X0,X1),not_homomorphism2(X2,X0,X1)))),unordered_pair(unordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism1(X2,X0,X1)),unordered_pair(not_homomorphism1(X2,X0,X1),unordered_pair(not_homomorphism2(X2,X0,X1),not_homomorphism2(X2,X0,X1))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism1(X2,X0,X1)),unordered_pair(not_homomorphism1(X2,X0,X1),unordered_pair(not_homomorphism2(X2,X0,X1),not_homomorphism2(X2,X0,X1)))),unordered_pair(unordered_pair(not_homomorphism1(X2,X0,X1),not_homomorphism1(X2,X0,X1)),unordered_pair(not_homomorphism1(X2,X0,X1),unordered_pair(not_homomorphism2(X2,X0,X1),not_homomorphism2(X2,X0,X1))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
| ~ compatible(X2,X0,X1)
| ~ operation(X1)
| ~ operation(X0) ),
inference(definition_unfolding,[],[f100,f137,f138,f137,f137,f137,f137,f138]) ).
fof(f182,plain,
! [X2,X3,X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f101,f138]) ).
fof(f183,plain,
! [X2,X3,X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f102,f138]) ).
fof(f184,plain,
! [X2,X3,X0,X1] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f103,f138]) ).
fof(f185,plain,
! [X2,X3,X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f104,f138]) ).
fof(f186,plain,
! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)),
inference(definition_unfolding,[],[f121,f12]) ).
fof(f187,plain,
! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X1,X0)),
inference(definition_unfolding,[],[f122,f12]) ).
fof(f188,plain,
! [X0,X1] :
( unordered_pair(X1,X0) = unordered_pair(X1,X1)
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f123,f12]) ).
fof(f189,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = unordered_pair(X1,X1)
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f124,f12]) ).
fof(f190,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| unordered_pair(X0,X1) != unordered_pair(X0,X2) ),
inference(definition_unfolding,[],[f126,f138]) ).
fof(f191,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| unordered_pair(X0,X1) != unordered_pair(X2,X1) ),
inference(definition_unfolding,[],[f127,f138]) ).
fof(f192,plain,
! [X2,X3,X0,X1] :
( unordered_pair(X0,X1) != null_class
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f130,f138]) ).
fof(f195,plain,
! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ),
inference(equality_resolution,[],[f158]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_173,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f11]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_185,plain,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f150]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i] :
( ~ member(X1,domain_of(X0))
| ( intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) != null_class ) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i] :
( member(X0,domain_of(X1))
| ( intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)) = null_class )
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_196,plain,
! [X0: $i] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_199,plain,
! [X0: $i] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_202,plain,
subclass(successor_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f45]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i] :
( ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_204,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_205,plain,
! [X0: $i] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_206,plain,
! [X0: $i] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_207,plain,
! [X0: $i] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_208,plain,
inductive(omega),
inference(cnf_transformation,[],[f51]) ).
tcf(c_209,plain,
! [X0: $i] :
( subclass(omega,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_210,plain,
member(omega,universal_class),
inference(cnf_transformation,[],[f53]) ).
tcf(c_211,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_212,plain,
! [X0: $i] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i] : subclass(compose(X0,X1),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f58]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X0,X0))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X3,X3),universal_class)),universal_class)))),universal_class)),universal_class))))) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_218,plain,
! [X0: $i] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_219,plain,
! [X0: $i] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_220,plain,
! [X0: $i] :
( function(X0)
| ~ subclass(X0,cross_product(universal_class,universal_class))
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_222,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_223,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(X0,regular(X0)) = null_class ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_224,plain,
function(choice),
inference(cnf_transformation,[],[f72]) ).
tcf(c_225,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X0)
| ( X0 = null_class )
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_229,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = subset_relation,
inference(cnf_transformation,[],[f173]) ).
tcf(c_230,plain,
intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) = identity_relation,
inference(cnf_transformation,[],[f174]) ).
tcf(c_231,plain,
! [X0: $i] :
( function(X0)
| ~ operation(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( cross_product(domain_of(domain_of(X0)),domain_of(domain_of(X0))) = domain_of(X0) )
| ~ operation(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_233,plain,
! [X0: $i] :
( subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),domain_of(domain_of(X0)))
| ~ operation(X0) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_234,plain,
! [X0: $i] :
( operation(X0)
| ~ function(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),domain_of(domain_of(X0)))
| ( cross_product(domain_of(domain_of(X0)),domain_of(domain_of(X0))) != domain_of(X0) ) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i,X2: $i] :
( function(X0)
| ~ compatible(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain_of(domain_of(X1)) = domain_of(X0) )
| ~ compatible(X0,X1,X2) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),domain_of(domain_of(X2)))
| ~ compatible(X0,X1,X2) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] :
( compatible(X1,X0,X2)
| ~ function(X1)
| ~ subclass(domain_of(domain_of(flip(cross_product(X1,universal_class)))),domain_of(domain_of(X2)))
| ( domain_of(domain_of(X0)) != domain_of(X1) ) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i,X2: $i] :
( operation(X1)
| ~ homomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i,X2: $i] :
( operation(X2)
| ~ homomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i,X2: $i] :
( compatible(X0,X1,X2)
| ~ homomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) )
| ~ homomorphism(X3,X2,X4)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X2)) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(X0,X1,X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),domain_of(X1))
| ~ operation(X2)
| ~ operation(X1)
| ~ compatible(X0,X1,X2) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(X1,X2,X0)
| ~ operation(X2)
| ~ operation(X0)
| ~ compatible(X1,X2,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) ) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_249,plain,
! [X0: $i] : subclass(X0,X0),
inference(cnf_transformation,[],[f105]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,X0),X1)
| ( X0 = X1 )
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(not_subclass_element(X1,X0),X0)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i] : ~ member(X0,intersection(complement(X1),X1)),
inference(cnf_transformation,[],[f112]) ).
tcf(c_256,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f113]) ).
tcf(c_257,plain,
! [X0: $i] : subclass(null_class,X0),
inference(cnf_transformation,[],[f114]) ).
tcf(c_258,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ subclass(X0,null_class) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_259,plain,
! [X0: $i] :
( member(not_subclass_element(X0,null_class),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_260,plain,
member(null_class,universal_class),
inference(cnf_transformation,[],[f119]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f120]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f186]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] : subclass(unordered_pair(X0,X0),unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f187]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ( unordered_pair(X0,X0) = unordered_pair(X0,X1) ) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ( unordered_pair(X0,X0) = unordered_pair(X1,X0) ) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| member(X0,universal_class)
| ( unordered_pair(X0,X1) = null_class ) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ( unordered_pair(X0,X1) != unordered_pair(X0,X2) ) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ( unordered_pair(X0,X1) != unordered_pair(X2,X1) ) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,universal_class)
| ( unordered_pair(X0,X1) != null_class ) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i] :
( ~ member(X1,universal_class)
| ( unordered_pair(X0,X1) != null_class ) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| ( unordered_pair(X0,X1) != null_class ) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_272,negated_conjecture,
member(x,z),
inference(cnf_transformation,[],[f131]) ).
tcf(c_273,negated_conjecture,
member(y,z),
inference(cnf_transformation,[],[f132]) ).
tcf(c_274,negated_conjecture,
~ subclass(unordered_pair(x,y),z),
inference(cnf_transformation,[],[f133]) ).
tcf(c_404,plain,
! [X0: $i] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(prop_impl_just,[status(thm)],[c_205]) ).
tcf(c_406,plain,
! [X0: $i] :
( subclass(omega,X0)
| ~ inductive(X0) ),
inference(prop_impl_just,[status(thm)],[c_209]) ).
tcf(c_408,plain,
! [X0: $i] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(prop_impl_just,[status(thm)],[c_206]) ).
tcf(c_1546,plain,
! [X0: $i,X1: $i] :
( subclass(omega,X1)
| ~ member(null_class,X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_207,c_406]) ).
tcf(c_1547,plain,
! [X0: $i] :
( subclass(omega,X0)
| ~ member(null_class,X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0) ),
inference(unflattening,[status(thm)],[c_1546]) ).
tcf(c_1564,plain,
! [X0: $i] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ( X0 != omega ) ),
inference(resolution_lifted,[status(thm)],[c_408,c_208]) ).
tcf(c_1565,plain,
subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))),omega),
inference(unflattening,[status(thm)],[c_1564]) ).
tcf(c_1569,plain,
! [X0: $i] :
( member(null_class,X0)
| ( X0 != omega ) ),
inference(resolution_lifted,[status(thm)],[c_404,c_208]) ).
tcf(c_1570,plain,
member(null_class,omega),
inference(unflattening,[status(thm)],[c_1569]) ).
tcf(c_3161,definition,
iPr_def_10 = unordered_pair(x,y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3162,negated_conjecture,
~ subclass(iPr_def_10,z),
inference(demodulation,[status(thm)],[c_274,c_3161]) ).
tcf(c_3163,negated_conjecture,
member(y,z),
inference(demodulation,[status(thm)],[c_273]) ).
tcf(c_3164,negated_conjecture,
member(x,z),
inference(demodulation,[status(thm)],[c_272]) ).
tcf(c_4129,plain,
( subclass(omega,universal_class)
| ~ member(null_class,universal_class) ),
inference(superposition,[status(thm)],[c_173,c_1547]) ).
tcf(c_4134,plain,
member(iPr_def_10,universal_class),
inference(superposition,[status(thm)],[c_3161,c_180]) ).
tcf(c_4147,plain,
subclass(unordered_pair(x,x),iPr_def_10),
inference(superposition,[status(thm)],[c_3161,c_262]) ).
tcf(c_4148,plain,
( subclass(omega,omega)
| ~ member(null_class,omega) ),
inference(superposition,[status(thm)],[c_1565,c_1547]) ).
tcf(c_4149,plain,
subclass(unordered_pair(y,y),iPr_def_10),
inference(superposition,[status(thm)],[c_3161,c_263]) ).
tcf(c_4154,plain,
! [X0: $i,X1: $i] : subclass(intersection(complement(X0),X0),X1),
inference(superposition,[status(thm)],[c_171,c_255]) ).
tcf(c_4161,plain,
( subclass(omega,cross_product(universal_class,universal_class))
| ~ member(null_class,cross_product(universal_class,universal_class))
| ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_218,c_1547]) ).
tcf(c_4169,plain,
! [X0: $i] : intersection(complement(X0),X0) = null_class,
inference(superposition,[status(thm)],[c_222,c_255]) ).
tcf(c_4197,plain,
( member(x,iPr_def_10)
| ~ member(x,universal_class) ),
inference(superposition,[status(thm)],[c_3161,c_178]) ).
tcf(c_4210,plain,
( member(y,iPr_def_10)
| ~ member(y,universal_class) ),
inference(superposition,[status(thm)],[c_3161,c_179]) ).
tcf(c_4217,plain,
! [X0: $i,X1: $i] : intersection(cross_product(X0,X1),complement(cross_product(X0,X1))) = null_class,
inference(superposition,[status(thm)],[c_4169,c_193]) ).
tcf(c_4224,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_171,c_188]) ).
tcf(c_4225,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X0)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_188]) ).
tcf(c_4227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,cross_product(X2,X3))
| ~ member(X0,intersection(X1,cross_product(X2,X3))) ),
inference(superposition,[status(thm)],[c_193,c_188]) ).
tcf(c_4228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| ~ member(X0,intersection(cross_product(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_193,c_188]) ).
tcf(c_4245,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_171,c_189]) ).
tcf(c_4246,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X1)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_189]) ).
tcf(c_4248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,cross_product(X2,X3))) ),
inference(superposition,[status(thm)],[c_193,c_189]) ).
tcf(c_4249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,cross_product(X1,X2))
| ~ member(X0,intersection(cross_product(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_193,c_189]) ).
tcf(c_4264,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_171,c_191]) ).
tcf(c_4265,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_222,c_191]) ).
tcf(c_4282,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,X1),null_class),X1)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_189]) ).
tcf(c_4283,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,X1),null_class),X0)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_188]) ).
tcf(c_4284,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(not_subclass_element(complement(X0),null_class),X0) ),
inference(superposition,[status(thm)],[c_259,c_191]) ).
tcf(c_4293,plain,
! [X0: $i] :
( member(X0,subset_relation)
| ~ member(X0,identity_relation) ),
inference(superposition,[status(thm)],[c_230,c_189]) ).
tcf(c_4294,plain,
! [X0: $i] :
( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,identity_relation) ),
inference(superposition,[status(thm)],[c_230,c_188]) ).
tcf(c_4305,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),subset_relation) ),
inference(superposition,[status(thm)],[c_171,c_4293]) ).
tcf(c_4306,plain,
( member(not_subclass_element(identity_relation,null_class),subset_relation)
| ( null_class = identity_relation ) ),
inference(superposition,[status(thm)],[c_259,c_4293]) ).
tcf(c_4307,plain,
( member(regular(identity_relation),subset_relation)
| ( null_class = identity_relation ) ),
inference(superposition,[status(thm)],[c_222,c_4293]) ).
tcf(c_4319,plain,
subclass(identity_relation,subset_relation),
inference(superposition,[status(thm)],[c_4305,c_172]) ).
tcf(c_4336,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_173,c_170]) ).
tcf(c_4337,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,element_relation) ),
inference(superposition,[status(thm)],[c_185,c_170]) ).
tcf(c_4338,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(X0,rotate(X1)) ),
inference(superposition,[status(thm)],[c_196,c_170]) ).
tcf(c_4339,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(X0,flip(X1)) ),
inference(superposition,[status(thm)],[c_199,c_170]) ).
tcf(c_4340,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,successor_relation) ),
inference(superposition,[status(thm)],[c_202,c_170]) ).
tcf(c_4341,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,compose(X1,X2)) ),
inference(superposition,[status(thm)],[c_213,c_170]) ).
tcf(c_4342,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ function(X1)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_218,c_170]) ).
tcf(c_4343,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_262,c_170]) ).
tcf(c_4344,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,unordered_pair(X2,X1))
| ~ member(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_263,c_170]) ).
tcf(c_4345,plain,
! [X0: $i] :
( member(X0,omega)
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_1565,c_170]) ).
tcf(c_4346,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_4147,c_170]) ).
tcf(c_4347,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_4149,c_170]) ).
tcf(c_4388,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_171,c_4336]) ).
tcf(c_4389,plain,
! [X0: $i] :
( member(not_subclass_element(X0,null_class),universal_class)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_4336]) ).
tcf(c_4391,plain,
member(x,universal_class),
inference(superposition,[status(thm)],[c_3164,c_4336]) ).
tcf(c_4392,plain,
member(y,universal_class),
inference(superposition,[status(thm)],[c_3163,c_4336]) ).
tcf(c_4396,plain,
! [X0: $i] :
( member(regular(X0),universal_class)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_4336]) ).
tcf(c_4400,plain,
( member(not_subclass_element(identity_relation,null_class),universal_class)
| ( null_class = identity_relation ) ),
inference(superposition,[status(thm)],[c_4306,c_4336]) ).
tcf(c_4401,plain,
( member(regular(identity_relation),universal_class)
| ( null_class = identity_relation ) ),
inference(superposition,[status(thm)],[c_4307,c_4336]) ).
tcf(c_4414,plain,
member(x,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_4197,c_4391]) ).
tcf(c_4415,plain,
member(y,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_4210,c_4392]) ).
tcf(c_4423,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),complement(X0))
| subclass(intersection(complement(X0),X0),X1) ),
inference(superposition,[status(thm)],[c_4169,c_4224]) ).
tcf(c_4424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),X0),X3)
| member(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_193,c_4224]) ).
tcf(c_4425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),X2),X3),X2) ),
inference(superposition,[status(thm)],[c_193,c_4224]) ).
tcf(c_4426,plain,
! [X0: $i] :
( subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),X0)
| member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(superposition,[status(thm)],[c_230,c_4224]) ).
tcf(c_4427,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_4224,c_172]) ).
tcf(c_4428,plain,
! [X0: $i,X1: $i] : subclass(intersection(null_class,X0),X1),
inference(superposition,[status(thm)],[c_4224,c_256]) ).
tcf(c_4429,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),universal_class) ),
inference(superposition,[status(thm)],[c_4224,c_4336]) ).
tcf(c_4430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) ),
inference(superposition,[status(thm)],[c_4224,c_189]) ).
tcf(c_4431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_4224,c_188]) ).
tcf(c_4432,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) ),
inference(superposition,[status(thm)],[c_4224,c_191]) ).
tcf(c_4433,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) ),
inference(superposition,[status(thm)],[c_4224,c_4293]) ).
tcf(c_4438,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),complement(X1)) ),
inference(light_normalisation,[status(thm)],[c_4423,c_4169]) ).
tcf(c_4447,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(light_normalisation,[status(thm)],[c_4426,c_230]) ).
tcf(c_4465,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(X1))
| member(not_subclass_element(X0,complement(X1)),X1)
| ~ member(not_subclass_element(X0,complement(X1)),universal_class) ),
inference(superposition,[status(thm)],[c_192,c_172]) ).
tcf(c_4475,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),X0)
| subclass(intersection(X0,regular(X0)),X1)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4224]) ).
tcf(c_4489,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_257,c_250]) ).
tcf(c_4490,plain,
! [X0: $i,X1: $i] :
( subclass(X1,X0)
| ~ subclass(universal_class,X0) ),
inference(superposition,[status(thm)],[c_173,c_250]) ).
tcf(c_4491,plain,
! [X0: $i] :
( subclass(element_relation,X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_185,c_250]) ).
tcf(c_4492,plain,
! [X0: $i,X1: $i] :
( subclass(rotate(X1),X0)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0) ),
inference(superposition,[status(thm)],[c_196,c_250]) ).
tcf(c_4493,plain,
! [X0: $i,X1: $i] :
( subclass(flip(X1),X0)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0) ),
inference(superposition,[status(thm)],[c_199,c_250]) ).
tcf(c_4494,plain,
! [X0: $i] :
( subclass(successor_relation,X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_202,c_250]) ).
tcf(c_4495,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(compose(X1,X2),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_213,c_250]) ).
tcf(c_4496,plain,
! [X0: $i,X1: $i] :
( subclass(X1,X0)
| ~ function(X1)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_218,c_250]) ).
tcf(c_4497,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(X0,X0),X2)
| ~ subclass(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_262,c_250]) ).
tcf(c_4498,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(X1,X1),X2)
| ~ subclass(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_263,c_250]) ).
tcf(c_4499,plain,
! [X0: $i] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))),X0)
| ~ subclass(omega,X0) ),
inference(superposition,[status(thm)],[c_1565,c_250]) ).
tcf(c_4500,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4147,c_250]) ).
tcf(c_4501,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4149,c_250]) ).
tcf(c_4502,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4319,c_250]) ).
tcf(c_4543,plain,
! [X0: $i,X1: $i] :
( subclass(X1,universal_class)
| ( unordered_pair(X0,not_subclass_element(X1,universal_class)) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_264,c_172]) ).
tcf(c_4546,plain,
! [X0: $i] : subclass(null_class,complement(X0)),
inference(superposition,[status(thm)],[c_4169,c_4427]) ).
tcf(c_4547,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(X0,cross_product(X1,X2)),cross_product(X1,X2)),
inference(superposition,[status(thm)],[c_193,c_4427]) ).
tcf(c_4549,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(cross_product(X0,X1),X2),X2),
inference(superposition,[status(thm)],[c_193,c_4427]) ).
tcf(c_4550,plain,
subclass(identity_relation,domain_of(flip(cross_product(subset_relation,universal_class)))),
inference(superposition,[status(thm)],[c_230,c_4427]) ).
tcf(c_4551,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X2),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4427,c_250]) ).
tcf(c_4553,plain,
! [X0: $i] : intersection(null_class,X0) = null_class,
inference(superposition,[status(thm)],[c_4427,c_258]) ).
tcf(c_4560,plain,
subclass(null_class,null_class),
inference(superposition,[status(thm)],[c_4553,c_4427]) ).
tcf(c_4561,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),null_class)
| subclass(intersection(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_4553,c_4224]) ).
tcf(c_4564,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),null_class) ),
inference(light_normalisation,[status(thm)],[c_4561,c_4553]) ).
tcf(c_4571,plain,
! [X0: $i] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_218,c_4490]) ).
tcf(c_4579,plain,
subclass(identity_relation,universal_class),
inference(superposition,[status(thm)],[c_173,c_4502]) ).
tcf(c_4580,plain,
( subclass(identity_relation,cross_product(universal_class,universal_class))
| ~ function(subset_relation) ),
inference(superposition,[status(thm)],[c_218,c_4502]) ).
tcf(c_4583,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(X0,cross_product(X1,X2)),X0),
inference(superposition,[status(thm)],[c_193,c_4549]) ).
tcf(c_4584,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,regular(cross_product(X0,X1)))
| ( cross_product(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4549]) ).
tcf(c_4585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(cross_product(X0,X1),cross_product(X2,X3)),cross_product(X0,X1)),
inference(superposition,[status(thm)],[c_193,c_4549]) ).
tcf(c_4586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X2,X3),X0),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4549,c_250]) ).
tcf(c_4588,plain,
! [X0: $i,X1: $i] : intersection(cross_product(X0,X1),null_class) = null_class,
inference(superposition,[status(thm)],[c_4549,c_258]) ).
tcf(c_4592,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ),
inference(superposition,[status(thm)],[c_4550,c_250]) ).
tcf(c_4617,plain,
! [X0: $i,X1: $i] :
( subclass(X1,X0)
| ~ function(universal_class)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_4571,c_250]) ).
tcf(c_4618,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_4571,c_170]) ).
tcf(c_4619,plain,
( subclass(omega,cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ member(null_class,cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4571,c_1547]) ).
tcf(c_4621,plain,
( subclass(identity_relation,cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4571,c_4502]) ).
tcf(c_4637,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),X0)
| subclass(intersection(complement(X0),X0),X1) ),
inference(superposition,[status(thm)],[c_4169,c_4245]) ).
tcf(c_4638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),X0),X3)
| member(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3),X0) ),
inference(superposition,[status(thm)],[c_193,c_4245]) ).
tcf(c_4639,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),regular(X0))
| subclass(intersection(X0,regular(X0)),X1)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4245]) ).
tcf(c_4640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),X2),X3),cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_193,c_4245]) ).
tcf(c_4641,plain,
! [X0: $i] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),X0) ),
inference(superposition,[status(thm)],[c_230,c_4245]) ).
tcf(c_4642,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_4553,c_4245]) ).
tcf(c_4643,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X1),
inference(superposition,[status(thm)],[c_4245,c_172]) ).
tcf(c_4644,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,null_class),X1),
inference(superposition,[status(thm)],[c_4245,c_256]) ).
tcf(c_4646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) ),
inference(superposition,[status(thm)],[c_4245,c_189]) ).
tcf(c_4647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) ),
inference(superposition,[status(thm)],[c_4245,c_188]) ).
tcf(c_4648,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_4245,c_191]) ).
tcf(c_4649,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) ),
inference(superposition,[status(thm)],[c_4245,c_4293]) ).
tcf(c_4652,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_4637,c_4169]) ).
tcf(c_4691,plain,
( ~ member(x,universal_class)
| ( null_class != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3161,c_269]) ).
tcf(c_4692,plain,
null_class != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_4691,c_4391]) ).
tcf(c_4708,plain,
! [X0: $i] :
( ( X0 = universal_class )
| ~ subclass(universal_class,X0) ),
inference(superposition,[status(thm)],[c_173,c_176]) ).
tcf(c_4709,plain,
( ( cross_product(universal_class,universal_class) = element_relation )
| ~ subclass(cross_product(universal_class,universal_class),element_relation) ),
inference(superposition,[status(thm)],[c_185,c_176]) ).
tcf(c_4710,plain,
! [X0: $i] :
( ( cross_product(cross_product(universal_class,universal_class),universal_class) = rotate(X0) )
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) ),
inference(superposition,[status(thm)],[c_196,c_176]) ).
tcf(c_4711,plain,
! [X0: $i] :
( ( cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) ),
inference(superposition,[status(thm)],[c_199,c_176]) ).
tcf(c_4712,plain,
( ( cross_product(universal_class,universal_class) = successor_relation )
| ~ subclass(cross_product(universal_class,universal_class),successor_relation) ),
inference(superposition,[status(thm)],[c_202,c_176]) ).
tcf(c_4713,plain,
! [X0: $i,X1: $i] :
( ( compose(X0,X1) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1)) ),
inference(superposition,[status(thm)],[c_213,c_176]) ).
tcf(c_4714,plain,
! [X0: $i] :
( ( cross_product(universal_class,universal_class) = X0 )
| ~ function(universal_class)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_4571,c_176]) ).
tcf(c_4715,plain,
! [X0: $i] :
( ( cross_product(universal_class,universal_class) = X0 )
| ~ function(X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_218,c_176]) ).
tcf(c_4716,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = unordered_pair(X0,X1) )
| ~ subclass(unordered_pair(X0,X1),unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_262,c_176]) ).
tcf(c_4717,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = unordered_pair(X1,X1) )
| ~ subclass(unordered_pair(X0,X1),unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_263,c_176]) ).
tcf(c_4718,plain,
( ( domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))) = omega )
| ~ subclass(omega,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_1565,c_176]) ).
tcf(c_4719,plain,
( ( unordered_pair(x,x) = iPr_def_10 )
| ~ subclass(iPr_def_10,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_4147,c_176]) ).
tcf(c_4720,plain,
( ( unordered_pair(y,y) = iPr_def_10 )
| ~ subclass(iPr_def_10,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_4149,c_176]) ).
tcf(c_4721,plain,
( ( identity_relation = subset_relation )
| ~ subclass(subset_relation,identity_relation) ),
inference(superposition,[status(thm)],[c_4319,c_176]) ).
tcf(c_4722,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = X0 )
| ~ subclass(X0,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_4427,c_176]) ).
tcf(c_4723,plain,
( ( domain_of(flip(cross_product(subset_relation,universal_class))) = identity_relation )
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),identity_relation) ),
inference(superposition,[status(thm)],[c_4550,c_176]) ).
tcf(c_4783,plain,
! [X0: $i] :
( subclass(null_class,regular(X0))
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4643]) ).
tcf(c_4784,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(cross_product(X0,X1),X2),cross_product(X0,X1)),
inference(superposition,[status(thm)],[c_193,c_4643]) ).
tcf(c_4787,plain,
! [X0: $i,X1: $i] :
( ( intersection(X1,X0) = X0 )
| ~ subclass(X0,intersection(X1,X0)) ),
inference(superposition,[status(thm)],[c_4643,c_176]) ).
tcf(c_4788,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,X0),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4643,c_250]) ).
tcf(c_4790,plain,
! [X0: $i] : intersection(X0,null_class) = null_class,
inference(superposition,[status(thm)],[c_4643,c_258]) ).
tcf(c_4805,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),null_class)
| subclass(intersection(X0,null_class),X1) ),
inference(superposition,[status(thm)],[c_4790,c_4245]) ).
tcf(c_4807,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_4790,c_4224]) ).
tcf(c_4810,plain,
! [X0: $i,X1: $i] : intersection(null_class,cross_product(X0,X1)) = null_class,
inference(superposition,[status(thm)],[c_4790,c_193]) ).
tcf(c_4818,plain,
( ( cross_product(universal_class,universal_class) = identity_relation )
| ~ function(subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),identity_relation) ),
inference(superposition,[status(thm)],[c_4580,c_176]) ).
tcf(c_4819,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ~ function(subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_4580,c_250]) ).
tcf(c_4820,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ function(subset_relation)
| ~ member(X0,identity_relation) ),
inference(superposition,[status(thm)],[c_4580,c_170]) ).
tcf(c_4838,plain,
( ( cross_product(universal_class,universal_class) = universal_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4571,c_4708]) ).
tcf(c_4850,plain,
! [X0: $i] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_172]) ).
tcf(c_4851,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_4336]) ).
tcf(c_4862,plain,
! [X0: $i] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_172]) ).
tcf(c_4863,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_4336]) ).
tcf(c_4876,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0)
| ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) ),
inference(superposition,[status(thm)],[c_192,c_4264]) ).
tcf(c_4877,plain,
! [X0: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_4264]) ).
tcf(c_4878,plain,
! [X0: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_4264]) ).
tcf(c_4879,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(superposition,[status(thm)],[c_4388,c_4264]) ).
tcf(c_4912,plain,
! [X0: $i] :
( ( compose(X0,domain_of(flip(cross_product(X0,universal_class)))) = identity_relation )
| ~ function(X0)
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class))))) ),
inference(superposition,[status(thm)],[c_219,c_176]) ).
tcf(c_4913,plain,
! [X0: $i,X1: $i] :
( subclass(compose(X1,domain_of(flip(cross_product(X1,universal_class)))),X0)
| ~ function(X1)
| ~ subclass(identity_relation,X0) ),
inference(superposition,[status(thm)],[c_219,c_250]) ).
tcf(c_4914,plain,
! [X0: $i,X1: $i] :
( member(X0,identity_relation)
| ~ function(X1)
| ~ member(X0,compose(X1,domain_of(flip(cross_product(X1,universal_class))))) ),
inference(superposition,[status(thm)],[c_219,c_170]) ).
tcf(c_4937,plain,
! [X0: $i,X1: $i] :
( subclass(X1,universal_class)
| member(X0,universal_class)
| ( unordered_pair(X0,not_subclass_element(X1,universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_172]) ).
tcf(c_4939,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| subclass(complement(universal_class),X1)
| ( unordered_pair(X0,not_subclass_element(complement(universal_class),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_4264]) ).
tcf(c_4943,plain,
! [X0: $i] :
( member(X0,universal_class)
| ( unordered_pair(X0,X0) = null_class ) ),
inference(equality_factoring,[status(thm)],[c_266]) ).
tcf(c_4950,plain,
! [X0: $i] :
( ( complement(universal_class) = X0 )
| ~ subclass(X0,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_4879,c_176]) ).
tcf(c_4952,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_4879,c_170]) ).
tcf(c_4953,plain,
complement(universal_class) = null_class,
inference(superposition,[status(thm)],[c_4879,c_258]) ).
tcf(c_4961,plain,
! [X0: $i] :
( subclass(complement(universal_class),X0)
| ~ member(not_subclass_element(null_class,X0),universal_class) ),
inference(superposition,[status(thm)],[c_4953,c_4264]) ).
tcf(c_4962,plain,
intersection(null_class,universal_class) = null_class,
inference(superposition,[status(thm)],[c_4953,c_4169]) ).
tcf(c_4965,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ member(not_subclass_element(null_class,X0),universal_class) ),
inference(light_normalisation,[status(thm)],[c_4961,c_4953]) ).
tcf(c_4966,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(light_normalisation,[status(thm)],[c_4952,c_4953]) ).
tcf(c_4972,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(unordered_pair(x,x),X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_171,c_4346]) ).
tcf(c_4973,plain,
( member(not_subclass_element(unordered_pair(x,x),null_class),iPr_def_10)
| ( unordered_pair(x,x) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_4346]) ).
tcf(c_4975,plain,
( member(regular(unordered_pair(x,x)),iPr_def_10)
| ( unordered_pair(x,x) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_4346]) ).
tcf(c_4976,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X0),X1)
| member(not_subclass_element(intersection(unordered_pair(x,x),X0),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4224,c_4346]) ).
tcf(c_4977,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(x,x)),X1)
| member(not_subclass_element(intersection(X0,unordered_pair(x,x)),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4245,c_4346]) ).
tcf(c_4996,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(unordered_pair(y,y),X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_171,c_4347]) ).
tcf(c_4997,plain,
( member(not_subclass_element(unordered_pair(y,y),null_class),iPr_def_10)
| ( unordered_pair(y,y) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_4347]) ).
tcf(c_4999,plain,
( member(regular(unordered_pair(y,y)),iPr_def_10)
| ( unordered_pair(y,y) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_4347]) ).
tcf(c_5000,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(y,y),X0),X1)
| member(not_subclass_element(intersection(unordered_pair(y,y),X0),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4224,c_4347]) ).
tcf(c_5001,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(y,y)),X1)
| member(not_subclass_element(intersection(X0,unordered_pair(y,y)),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4245,c_4347]) ).
tcf(c_5039,plain,
subclass(element_relation,universal_class),
inference(superposition,[status(thm)],[c_173,c_4491]) ).
tcf(c_5047,plain,
subclass(successor_relation,universal_class),
inference(superposition,[status(thm)],[c_173,c_4494]) ).
tcf(c_5054,plain,
! [X0: $i] :
( ( unordered_pair(x,x) = X0 )
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_4500,c_176]) ).
tcf(c_5055,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4500,c_250]) ).
tcf(c_5056,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ subclass(iPr_def_10,X1)
| ~ member(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_4500,c_170]) ).
tcf(c_5057,plain,
( ( unordered_pair(x,x) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_4500,c_258]) ).
tcf(c_5075,plain,
! [X0: $i] :
( ( unordered_pair(y,y) = X0 )
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_4501,c_176]) ).
tcf(c_5076,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4501,c_250]) ).
tcf(c_5077,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ subclass(iPr_def_10,X1)
| ~ member(X0,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_4501,c_170]) ).
tcf(c_5078,plain,
( ( unordered_pair(y,y) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_4501,c_258]) ).
tcf(c_5100,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),cross_product(X0,X1))
| subclass(intersection(cross_product(X0,X1),complement(cross_product(X0,X1))),X2) ),
inference(superposition,[status(thm)],[c_4169,c_4424]) ).
tcf(c_5101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4),cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_193,c_4424]) ).
tcf(c_5102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),X2),X3),cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_193,c_4424]) ).
tcf(c_5103,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X1,X2),null_class),X0)
| member(not_subclass_element(null_class,X0),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_4553,c_4424]) ).
tcf(c_5104,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),cross_product(X0,X1))
| subclass(intersection(cross_product(X0,X1),X2),cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_4424,c_172]) ).
tcf(c_5105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),X0),X3)
| member(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3),universal_class) ),
inference(superposition,[status(thm)],[c_4424,c_4336]) ).
tcf(c_5110,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),cross_product(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_5100,c_4217]) ).
tcf(c_5128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,intersection(X3,cross_product(X1,X2)))
| ~ member(X0,X3)
| ~ member(X0,cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_193,c_190]) ).
tcf(c_5129,plain,
! [X0: $i,X1: $i] :
( member(X0,null_class)
| ( X1 = null_class )
| ~ member(X0,X1)
| ~ member(X0,regular(X1)) ),
inference(superposition,[status(thm)],[c_223,c_190]) ).
tcf(c_5130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,intersection(cross_product(X1,X2),X3))
| ~ member(X0,X3)
| ~ member(X0,cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_193,c_190]) ).
tcf(c_5131,plain,
! [X0: $i] :
( member(X0,identity_relation)
| ~ member(X0,subset_relation)
| ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(superposition,[status(thm)],[c_230,c_190]) ).
tcf(c_5134,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,intersection(X1,X2))
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_190,c_172]) ).
tcf(c_5135,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,universal_class)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_190,c_4336]) ).
tcf(c_5138,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(X0,X1)),X2)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X1)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X0) ),
inference(superposition,[status(thm)],[c_190,c_4264]) ).
tcf(c_5145,plain,
! [X0: $i,X1: $i] :
( ( X1 = null_class )
| ~ member(X0,X1)
| ~ member(X0,regular(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5129,c_256]) ).
tcf(c_5175,plain,
! [X0: $i] :
( ( domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) )
| ~ operation(X0)
| ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class))))) ),
inference(superposition,[status(thm)],[c_233,c_176]) ).
tcf(c_5176,plain,
! [X0: $i,X1: $i] :
( subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),X1)
| ~ operation(X0)
| ~ subclass(domain_of(domain_of(X0)),X1) ),
inference(superposition,[status(thm)],[c_233,c_250]) ).
tcf(c_5177,plain,
! [X0: $i,X1: $i] :
( member(X0,domain_of(domain_of(X1)))
| ~ operation(X1)
| ~ member(X0,domain_of(domain_of(flip(cross_product(X1,universal_class))))) ),
inference(superposition,[status(thm)],[c_233,c_170]) ).
tcf(c_5200,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(X0,X1),X2)
| ( not_subclass_element(unordered_pair(X0,X1),X2) = X1 )
| ( not_subclass_element(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_171,c_177]) ).
tcf(c_5201,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = null_class )
| ( not_subclass_element(unordered_pair(X0,X1),null_class) = X1 )
| ( not_subclass_element(unordered_pair(X0,X1),null_class) = X0 ) ),
inference(superposition,[status(thm)],[c_259,c_177]) ).
tcf(c_5203,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = null_class )
| ( regular(unordered_pair(X0,X1)) = X1 )
| ( regular(unordered_pair(X0,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_222,c_177]) ).
tcf(c_5204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(unordered_pair(X0,X1),X2),X3)
| ( not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X1 )
| ( not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X0 ) ),
inference(superposition,[status(thm)],[c_4224,c_177]) ).
tcf(c_5205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,unordered_pair(X1,X2)),X3)
| ( not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X2 )
| ( not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X1 ) ),
inference(superposition,[status(thm)],[c_4245,c_177]) ).
tcf(c_5208,plain,
! [X0: $i] :
( ( X0 = y )
| ( X0 = x )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3161,c_177]) ).
tcf(c_5247,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X1)
| ~ subclass(complement(X0),X1) ),
inference(superposition,[status(thm)],[c_4169,c_4551]) ).
tcf(c_5248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X3,cross_product(X0,X1)),X2)
| ~ subclass(cross_product(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_193,c_4551]) ).
tcf(c_5249,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X1)
| ( X0 = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_223,c_4551]) ).
tcf(c_5254,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X1,X2) = X0 )
| ~ subclass(X1,X0)
| ~ subclass(X0,intersection(X1,X2)) ),
inference(superposition,[status(thm)],[c_4551,c_176]) ).
tcf(c_5255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,X3),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4551,c_250]) ).
tcf(c_5256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| ~ subclass(X1,X3)
| ~ member(X0,intersection(X1,X2)) ),
inference(superposition,[status(thm)],[c_4551,c_170]) ).
tcf(c_5257,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4551,c_258]) ).
tcf(c_5278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,cross_product(X2,X3)),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_193,c_4788]) ).
tcf(c_5279,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X1)
| ( X0 = null_class )
| ~ subclass(regular(X0),X1) ),
inference(superposition,[status(thm)],[c_223,c_4788]) ).
tcf(c_5280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X0,X1),X3),X2)
| ~ subclass(cross_product(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_193,c_4788]) ).
tcf(c_5284,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X1,X2) = X0 )
| ~ subclass(X2,X0)
| ~ subclass(X0,intersection(X1,X2)) ),
inference(superposition,[status(thm)],[c_4788,c_176]) ).
tcf(c_5285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X3,X0),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4788,c_250]) ).
tcf(c_5286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| ~ subclass(X2,X3)
| ~ member(X0,intersection(X1,X2)) ),
inference(superposition,[status(thm)],[c_4788,c_170]) ).
tcf(c_5287,plain,
! [X0: $i,X1: $i] :
( ( intersection(X1,X0) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4788,c_258]) ).
tcf(c_5316,plain,
! [X0: $i] :
( subclass(iPr_def_10,z)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,z) ),
inference(instantiation,[status(thm)],[c_250]) ).
tcf(c_5324,plain,
! [X0: $i] :
( subclass(complement(universal_class),X0)
| ( unordered_pair(not_subclass_element(complement(universal_class),X0),not_subclass_element(complement(universal_class),X0)) = null_class ) ),
inference(superposition,[status(thm)],[c_4943,c_4264]) ).
tcf(c_5325,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ( unordered_pair(not_subclass_element(null_class,X0),not_subclass_element(null_class,X0)) = null_class ) ),
inference(light_normalisation,[status(thm)],[c_5324,c_4953]) ).
tcf(c_5343,plain,
! [X0: $i,X1: $i] : intersection(intersection(null_class,X0),X1) = null_class,
inference(superposition,[status(thm)],[c_4427,c_5257]) ).
tcf(c_5344,plain,
! [X0: $i] :
( ( intersection(unordered_pair(x,x),X0) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_4500,c_5257]) ).
tcf(c_5345,plain,
! [X0: $i] :
( ( intersection(unordered_pair(y,y),X0) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_4501,c_5257]) ).
tcf(c_5346,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,X1),X2) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4551,c_5257]) ).
tcf(c_5347,plain,
! [X0: $i,X1: $i] : intersection(intersection(X0,null_class),X1) = null_class,
inference(superposition,[status(thm)],[c_4643,c_5257]) ).
tcf(c_5348,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X1,X0),X2) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4788,c_5257]) ).
tcf(c_5368,plain,
! [X0: $i,X1: $i] : intersection(X0,intersection(null_class,X1)) = null_class,
inference(superposition,[status(thm)],[c_4427,c_5287]) ).
tcf(c_5369,plain,
! [X0: $i] :
( ( intersection(X0,unordered_pair(x,x)) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_4500,c_5287]) ).
tcf(c_5370,plain,
! [X0: $i] :
( ( intersection(X0,unordered_pair(y,y)) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_4501,c_5287]) ).
tcf(c_5371,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X1,intersection(X0,X2)) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4551,c_5287]) ).
tcf(c_5372,plain,
! [X0: $i,X1: $i] : intersection(X0,intersection(X1,null_class)) = null_class,
inference(superposition,[status(thm)],[c_4643,c_5287]) ).
tcf(c_5373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X1,intersection(X2,X0)) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4788,c_5287]) ).
tcf(c_5403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,cross_product(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3),X0) ),
inference(superposition,[status(thm)],[c_193,c_4425]) ).
tcf(c_5404,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),regular(cross_product(X0,X1)))
| subclass(intersection(regular(cross_product(X0,X1)),cross_product(X0,X1)),X2)
| ( cross_product(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4425]) ).
tcf(c_5407,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),X2)
| subclass(intersection(cross_product(X0,X1),X2),X2) ),
inference(superposition,[status(thm)],[c_4425,c_172]) ).
tcf(c_5408,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(null_class,cross_product(X0,X1)),X2),
inference(superposition,[status(thm)],[c_4425,c_256]) ).
tcf(c_5409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),X2),X3),universal_class) ),
inference(superposition,[status(thm)],[c_4425,c_4336]) ).
tcf(c_5410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(unordered_pair(X2,X3),cross_product(X0,X1)),X4)
| ( not_subclass_element(intersection(cross_product(X0,X1),unordered_pair(X2,X3)),X4) = X3 )
| ( not_subclass_element(intersection(cross_product(X0,X1),unordered_pair(X2,X3)),X4) = X2 ) ),
inference(superposition,[status(thm)],[c_4425,c_177]) ).
tcf(c_5411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,X3)),X4),X3) ),
inference(superposition,[status(thm)],[c_4425,c_189]) ).
tcf(c_5412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,X3)),X4),X2) ),
inference(superposition,[status(thm)],[c_4425,c_188]) ).
tcf(c_5413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(complement(X2),cross_product(X0,X1)),X3)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),complement(X2)),X3),X2) ),
inference(superposition,[status(thm)],[c_4425,c_191]) ).
tcf(c_5414,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(identity_relation,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),identity_relation),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4425,c_4293]) ).
tcf(c_5415,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(unordered_pair(x,x),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),unordered_pair(x,x)),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4425,c_4346]) ).
tcf(c_5416,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(unordered_pair(y,y),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),unordered_pair(y,y)),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4425,c_4347]) ).
tcf(c_5470,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,X0),universal_class)
| member(not_subclass_element(X0,X1),X0)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_4336]) ).
tcf(c_5480,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X0,X1),universal_class)
| member(not_subclass_element(X1,X0),X1)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_4336]) ).
tcf(c_5481,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(X2,unordered_pair(X0,X1)),X2)
| ( unordered_pair(X0,X1) = X2 )
| ( not_subclass_element(unordered_pair(X0,X1),X2) = X1 )
| ( not_subclass_element(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_177]) ).
tcf(c_5482,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(X2,intersection(X0,X1)),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1)
| ( intersection(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_251,c_189]) ).
tcf(c_5483,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(X2,intersection(X0,X1)),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0)
| ( intersection(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_251,c_188]) ).
tcf(c_5484,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,complement(X0)),X1)
| ( complement(X0) = X1 )
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_251,c_191]) ).
tcf(c_5485,plain,
! [X0: $i] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| member(not_subclass_element(X0,identity_relation),X0)
| ( X0 = identity_relation ) ),
inference(superposition,[status(thm)],[c_251,c_4293]) ).
tcf(c_5486,plain,
! [X0: $i] :
( member(not_subclass_element(unordered_pair(x,x),X0),iPr_def_10)
| member(not_subclass_element(X0,unordered_pair(x,x)),X0)
| ( unordered_pair(x,x) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_4346]) ).
tcf(c_5487,plain,
! [X0: $i] :
( member(not_subclass_element(unordered_pair(y,y),X0),iPr_def_10)
| member(not_subclass_element(X0,unordered_pair(y,y)),X0)
| ( unordered_pair(y,y) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_4347]) ).
tcf(c_5533,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),element_relation) ),
inference(superposition,[status(thm)],[c_261,c_186]) ).
tcf(c_5535,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),element_relation) ),
inference(superposition,[status(thm)],[c_261,c_186]) ).
tcf(c_5553,plain,
! [X0: $i] :
( member(not_subclass_element(universal_class,X0),universal_class)
| ( X0 = universal_class )
| ( unordered_pair(not_subclass_element(X0,universal_class),not_subclass_element(X0,universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4943,c_253]) ).
tcf(c_5554,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| member(not_subclass_element(universal_class,X0),universal_class)
| ( X0 = universal_class )
| ( unordered_pair(not_subclass_element(X0,universal_class),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_253]) ).
tcf(c_5555,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| member(not_subclass_element(universal_class,X1),universal_class)
| ( X1 = universal_class )
| ( unordered_pair(X0,not_subclass_element(X1,universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_253]) ).
tcf(c_5556,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(universal_class,X0),universal_class)
| ( X0 = universal_class )
| ( unordered_pair(not_subclass_element(X0,universal_class),X1) = unordered_pair(X1,X1) ) ),
inference(superposition,[status(thm)],[c_265,c_253]) ).
tcf(c_5557,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(universal_class,X1),universal_class)
| ( X1 = universal_class )
| ( unordered_pair(X0,not_subclass_element(X1,universal_class)) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_264,c_253]) ).
tcf(c_5562,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X1,X2),X0),intersection(X1,X2))
| ( intersection(X1,X2) = X0 )
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_190,c_253]) ).
tcf(c_5563,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X0,complement(X1)),X1)
| member(not_subclass_element(complement(X1),X0),complement(X1))
| ( complement(X1) = X0 )
| ~ member(not_subclass_element(X0,complement(X1)),universal_class) ),
inference(superposition,[status(thm)],[c_192,c_253]) ).
tcf(c_5567,plain,
! [X0: $i] :
( member(not_subclass_element(cross_product(universal_class,universal_class),X0),cross_product(universal_class,universal_class))
| ( cross_product(universal_class,universal_class) = X0 )
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_253]) ).
tcf(c_5568,plain,
! [X0: $i] :
( member(not_subclass_element(cross_product(universal_class,universal_class),X0),cross_product(universal_class,universal_class))
| ( cross_product(universal_class,universal_class) = X0 )
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_253]) ).
tcf(c_5570,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X1,X2),X0),cross_product(X1,X2))
| member(not_subclass_element(cross_product(X1,X2),intersection(X0,cross_product(X1,X2))),cross_product(X1,X2))
| ( intersection(X0,cross_product(X1,X2)) = cross_product(X1,X2) ) ),
inference(superposition,[status(thm)],[c_4424,c_253]) ).
tcf(c_5571,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),X2)
| member(not_subclass_element(X2,intersection(cross_product(X0,X1),X2)),X2)
| ( intersection(cross_product(X0,X1),X2) = X2 ) ),
inference(superposition,[status(thm)],[c_4425,c_253]) ).
tcf(c_5608,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(X0,X0))),cross_product(z,X1))
| ~ member(x,z)
| ~ member(X0,X1) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_5610,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(X0,X0))),cross_product(z,X1))
| ~ member(y,z)
| ~ member(X0,X1) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_5619,plain,
! [X0: $i,X1: $i] : subclass(null_class,complement(cross_product(X0,X1))),
inference(superposition,[status(thm)],[c_4217,c_4643]) ).
tcf(c_5620,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),complement(cross_product(X0,X1)))
| subclass(intersection(cross_product(X0,X1),complement(cross_product(X0,X1))),X2) ),
inference(superposition,[status(thm)],[c_4217,c_4245]) ).
tcf(c_5621,plain,
! [X0: $i,X1: $i] : subclass(null_class,cross_product(X0,X1)),
inference(superposition,[status(thm)],[c_4217,c_4427]) ).
tcf(c_5623,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,null_class)
| ~ member(X0,cross_product(X1,X2))
| ~ member(X0,complement(cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_4217,c_190]) ).
tcf(c_5626,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),complement(cross_product(X0,X1)))
| subclass(intersection(complement(cross_product(X0,X1)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_4217,c_4425]) ).
tcf(c_5627,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(null_class,X2)
| ~ subclass(cross_product(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_4217,c_4551]) ).
tcf(c_5628,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(null_class,X2)
| ~ subclass(complement(cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_4217,c_4788]) ).
tcf(c_5629,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,cross_product(X1,X2))
| ~ member(X0,complement(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5623,c_256]) ).
tcf(c_5634,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),complement(cross_product(X1,X2))) ),
inference(light_normalisation,[status(thm)],[c_5620,c_4217]) ).
tcf(c_5646,plain,
! [X0: $i,X1: $i] :
( ( complement(intersection(X0,X1)) = null_class )
| ~ member(regular(complement(intersection(X0,X1))),X1)
| ~ member(regular(complement(intersection(X0,X1))),X0) ),
inference(superposition,[status(thm)],[c_190,c_4265]) ).
tcf(c_5647,plain,
! [X0: $i] :
( member(regular(complement(complement(X0))),X0)
| ( complement(complement(X0)) = null_class )
| ~ member(regular(complement(complement(X0))),universal_class) ),
inference(superposition,[status(thm)],[c_192,c_4265]) ).
tcf(c_5648,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ member(regular(complement(cross_product(universal_class,universal_class))),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_4265]) ).
tcf(c_5649,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ member(regular(complement(cross_product(universal_class,universal_class))),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_4265]) ).
tcf(c_5667,plain,
! [X0: $i] :
( member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| ( domain_of(flip(cross_product(subset_relation,universal_class))) = X0 )
| ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
inference(superposition,[status(thm)],[c_4294,c_253]) ).
tcf(c_5668,plain,
! [X0: $i] :
( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
inference(superposition,[status(thm)],[c_4294,c_172]) ).
tcf(c_5669,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,identity_relation) ),
inference(superposition,[status(thm)],[c_4294,c_4336]) ).
tcf(c_5670,plain,
! [X0: $i] :
( subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0)
| ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation) ),
inference(superposition,[status(thm)],[c_4294,c_4264]) ).
tcf(c_5671,plain,
( ( complement(domain_of(flip(cross_product(subset_relation,universal_class)))) = null_class )
| ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ),
inference(superposition,[status(thm)],[c_4294,c_4265]) ).
tcf(c_5699,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(compose(X0,X1),X2)
| member(not_subclass_element(compose(X0,X1),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_4341]) ).
tcf(c_5700,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(X2,compose(X0,X1)),X2)
| member(not_subclass_element(compose(X0,X1),X2),cross_product(universal_class,universal_class))
| ( compose(X0,X1) = X2 ) ),
inference(superposition,[status(thm)],[c_251,c_4341]) ).
tcf(c_5701,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(compose(X0,X1),null_class),cross_product(universal_class,universal_class))
| ( compose(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_4341]) ).
tcf(c_5702,plain,
! [X0: $i,X1: $i] :
( member(regular(compose(X0,X1)),cross_product(universal_class,universal_class))
| ( compose(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_4341]) ).
tcf(c_5703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(compose(X0,X1),X2),X3)
| member(not_subclass_element(intersection(compose(X0,X1),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_4341]) ).
tcf(c_5704,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,compose(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,compose(X1,X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_4341]) ).
tcf(c_5705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(compose(X2,X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),compose(X2,X3)),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_4341]) ).
tcf(c_5746,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(X0,X0),X1)
| member(not_subclass_element(unordered_pair(X0,X0),X1),unordered_pair(X0,X2)) ),
inference(superposition,[status(thm)],[c_171,c_4343]) ).
tcf(c_5747,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(X1,unordered_pair(X0,X0)),X1)
| member(not_subclass_element(unordered_pair(X0,X0),X1),unordered_pair(X0,X2))
| ( unordered_pair(X0,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_4343]) ).
tcf(c_5748,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(unordered_pair(X0,X0),null_class),unordered_pair(X0,X1))
| ( unordered_pair(X0,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_4343]) ).
tcf(c_5750,plain,
! [X0: $i,X1: $i] :
( member(regular(unordered_pair(X0,X0)),unordered_pair(X0,X1))
| ( unordered_pair(X0,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_4343]) ).
tcf(c_5751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(unordered_pair(X0,X0),X1),X2)
| member(not_subclass_element(intersection(unordered_pair(X0,X0),X1),X2),unordered_pair(X0,X3)) ),
inference(superposition,[status(thm)],[c_4224,c_4343]) ).
tcf(c_5752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,unordered_pair(X1,X1)),X2)
| member(not_subclass_element(intersection(X0,unordered_pair(X1,X1)),X2),unordered_pair(X1,X3)) ),
inference(superposition,[status(thm)],[c_4245,c_4343]) ).
tcf(c_5753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(unordered_pair(X2,X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),unordered_pair(X2,X2)),X3),unordered_pair(X2,X4)) ),
inference(superposition,[status(thm)],[c_4425,c_4343]) ).
tcf(c_5782,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(X0,X0),X1)
| member(not_subclass_element(unordered_pair(X0,X0),X1),unordered_pair(X2,X0)) ),
inference(superposition,[status(thm)],[c_171,c_4344]) ).
tcf(c_5783,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(X1,unordered_pair(X0,X0)),X1)
| member(not_subclass_element(unordered_pair(X0,X0),X1),unordered_pair(X2,X0))
| ( unordered_pair(X0,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_4344]) ).
tcf(c_5784,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(unordered_pair(X0,X0),null_class),unordered_pair(X1,X0))
| ( unordered_pair(X0,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_4344]) ).
tcf(c_5786,plain,
! [X0: $i,X1: $i] :
( member(regular(unordered_pair(X0,X0)),unordered_pair(X1,X0))
| ( unordered_pair(X0,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_4344]) ).
tcf(c_5787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(unordered_pair(X0,X0),X1),X2)
| member(not_subclass_element(intersection(unordered_pair(X0,X0),X1),X2),unordered_pair(X3,X0)) ),
inference(superposition,[status(thm)],[c_4224,c_4344]) ).
tcf(c_5788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,unordered_pair(X1,X1)),X2)
| member(not_subclass_element(intersection(X0,unordered_pair(X1,X1)),X2),unordered_pair(X3,X1)) ),
inference(superposition,[status(thm)],[c_4245,c_4344]) ).
tcf(c_5789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(unordered_pair(X2,X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),unordered_pair(X2,X2)),X3),unordered_pair(X4,X2)) ),
inference(superposition,[status(thm)],[c_4425,c_4344]) ).
tcf(c_5852,plain,
! [X0: $i] : ~ member(X0,domain_of(complement(cross_product(unordered_pair(X0,X0),universal_class)))),
inference(superposition,[status(thm)],[c_4169,c_194]) ).
tcf(c_5853,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,domain_of(cross_product(X1,X2)))
| ( intersection(cross_product(unordered_pair(X0,X0),universal_class),cross_product(X1,X2)) != null_class ) ),
inference(superposition,[status(thm)],[c_193,c_194]) ).
tcf(c_5854,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,domain_of(X1))
| ( intersection(cross_product(unordered_pair(X0,X0),universal_class),X1) != null_class ) ),
inference(superposition,[status(thm)],[c_193,c_194]) ).
tcf(c_5855,plain,
! [X0: $i] : ~ member(X0,domain_of(null_class)),
inference(superposition,[status(thm)],[c_4553,c_194]) ).
tcf(c_5870,plain,
! [X0: $i] :
( ( X0 = universal_class )
| ( unordered_pair(not_subclass_element(X0,universal_class),not_subclass_element(X0,universal_class)) = null_class )
| ~ member(not_subclass_element(universal_class,X0),X0) ),
inference(superposition,[status(thm)],[c_4943,c_254]) ).
tcf(c_5871,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ( X0 = universal_class )
| ( unordered_pair(not_subclass_element(X0,universal_class),X1) = null_class )
| ~ member(not_subclass_element(universal_class,X0),X0) ),
inference(superposition,[status(thm)],[c_266,c_254]) ).
tcf(c_5872,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ( X0 = universal_class )
| ( unordered_pair(X1,not_subclass_element(X0,universal_class)) = null_class )
| ~ member(not_subclass_element(universal_class,X0),X0) ),
inference(superposition,[status(thm)],[c_266,c_254]) ).
tcf(c_5873,plain,
! [X0: $i,X1: $i] :
( ( X0 = universal_class )
| ( unordered_pair(not_subclass_element(X0,universal_class),X1) = unordered_pair(X1,X1) )
| ~ member(not_subclass_element(universal_class,X0),X0) ),
inference(superposition,[status(thm)],[c_265,c_254]) ).
tcf(c_5874,plain,
! [X0: $i,X1: $i] :
( ( X0 = universal_class )
| ( unordered_pair(X1,not_subclass_element(X0,universal_class)) = unordered_pair(X1,X1) )
| ~ member(not_subclass_element(universal_class,X0),X0) ),
inference(superposition,[status(thm)],[c_264,c_254]) ).
tcf(c_5879,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,X1) = X2 )
| ~ member(not_subclass_element(X2,intersection(X0,X1)),X1)
| ~ member(not_subclass_element(X2,intersection(X0,X1)),X0)
| ~ member(not_subclass_element(intersection(X0,X1),X2),X2) ),
inference(superposition,[status(thm)],[c_190,c_254]) ).
tcf(c_5880,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,complement(X0)),X0)
| ( complement(X0) = X1 )
| ~ member(not_subclass_element(X1,complement(X0)),universal_class)
| ~ member(not_subclass_element(complement(X0),X1),X1) ),
inference(superposition,[status(thm)],[c_192,c_254]) ).
tcf(c_5882,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,X0),X0)
| ( intersection(X1,X0) = X0 )
| ~ member(not_subclass_element(X0,intersection(X1,X0)),intersection(X1,X0)) ),
inference(superposition,[status(thm)],[c_4245,c_254]) ).
tcf(c_5883,plain,
! [X0: $i] :
( ( domain_of(flip(cross_product(subset_relation,universal_class))) = X0 )
| ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X0) ),
inference(superposition,[status(thm)],[c_4294,c_254]) ).
tcf(c_5885,plain,
! [X0: $i] :
( ( cross_product(universal_class,universal_class) = X0 )
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),successor_relation)
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),X0),X0) ),
inference(superposition,[status(thm)],[c_4340,c_254]) ).
tcf(c_5886,plain,
! [X0: $i] :
( ( cross_product(universal_class,universal_class) = X0 )
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),element_relation)
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),X0),X0) ),
inference(superposition,[status(thm)],[c_4337,c_254]) ).
tcf(c_5888,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),X2),cross_product(X0,X1))
| ( intersection(X2,cross_product(X0,X1)) = cross_product(X0,X1) )
| ~ member(not_subclass_element(cross_product(X0,X1),intersection(X2,cross_product(X0,X1))),intersection(X2,cross_product(X0,X1))) ),
inference(superposition,[status(thm)],[c_4424,c_254]) ).
tcf(c_5889,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,cross_product(X1,X2)),X0)
| ( intersection(cross_product(X1,X2),X0) = X0 )
| ~ member(not_subclass_element(X0,intersection(cross_product(X1,X2),X0)),intersection(cross_product(X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_4425,c_254]) ).
tcf(c_5932,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_181]) ).
tcf(c_5933,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_181]) ).
tcf(c_5934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_181]) ).
tcf(c_5936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_181]) ).
tcf(c_5953,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_182]) ).
tcf(c_5954,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_182]) ).
tcf(c_5955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_182]) ).
tcf(c_5957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_182]) ).
tcf(c_5968,plain,
! [X0: $i] : subclass(domain_of(null_class),X0),
inference(superposition,[status(thm)],[c_171,c_5855]) ).
tcf(c_5969,plain,
! [X0: $i] :
( member(not_subclass_element(X0,domain_of(null_class)),X0)
| ( domain_of(null_class) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_5855]) ).
tcf(c_5970,plain,
domain_of(null_class) = null_class,
inference(superposition,[status(thm)],[c_259,c_5855]) ).
tcf(c_5972,plain,
! [X0: $i,X1: $i] : subclass(intersection(domain_of(null_class),X0),X1),
inference(superposition,[status(thm)],[c_4224,c_5855]) ).
tcf(c_5973,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,domain_of(null_class)),X1),
inference(superposition,[status(thm)],[c_4245,c_5855]) ).
tcf(c_5983,plain,
( subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),null_class)
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_5970,c_233]) ).
tcf(c_5993,plain,
! [X0: $i,X1: $i] : subclass(compose(X0,X1),universal_class),
inference(superposition,[status(thm)],[c_173,c_4495]) ).
tcf(c_6001,plain,
! [X0: $i] : subclass(unordered_pair(X0,X0),universal_class),
inference(superposition,[status(thm)],[c_173,c_4497]) ).
tcf(c_6002,plain,
! [X0: $i] :
( subclass(unordered_pair(X0,X0),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4571,c_4497]) ).
tcf(c_6003,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(X0,X0),cross_product(universal_class,universal_class))
| ~ function(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_218,c_4497]) ).
tcf(c_6026,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(X1,X1),cross_product(universal_class,universal_class))
| ~ function(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_218,c_4498]) ).
tcf(c_6045,plain,
( subclass(identity_relation,cross_product(universal_class,universal_class))
| ~ function(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(superposition,[status(thm)],[c_218,c_4592]) ).
tcf(c_6052,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(intersection(X0,X1),regular(intersection(X0,X1))),X2)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4430]) ).
tcf(c_6054,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(intersection(X0,X1),null_class),X2) ),
inference(superposition,[status(thm)],[c_4790,c_4430]) ).
tcf(c_6055,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),X0)
| subclass(intersection(intersection(complement(X0),X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4169,c_4430]) ).
tcf(c_6056,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(cross_product(X1,X2),X0),X3),X4)
| member(not_subclass_element(intersection(intersection(X0,cross_product(X1,X2)),X3),X4),X0) ),
inference(superposition,[status(thm)],[c_193,c_4430]) ).
tcf(c_6057,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),regular(X0))
| subclass(intersection(intersection(X0,regular(X0)),X1),X2)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4430]) ).
tcf(c_6058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,cross_product(X0,X1)),X3),X4)
| member(not_subclass_element(intersection(intersection(cross_product(X0,X1),X2),X3),X4),cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_193,c_4430]) ).
tcf(c_6059,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation)
| subclass(intersection(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),X0),X1) ),
inference(superposition,[status(thm)],[c_230,c_4430]) ).
tcf(c_6060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),complement(cross_product(X0,X1)))
| subclass(intersection(intersection(cross_product(X0,X1),complement(cross_product(X0,X1))),X2),X3) ),
inference(superposition,[status(thm)],[c_4217,c_4430]) ).
tcf(c_6061,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(null_class,X2),X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4553,c_4430]) ).
tcf(c_6062,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),null_class)
| subclass(intersection(intersection(X0,null_class),X1),X2) ),
inference(superposition,[status(thm)],[c_4790,c_4430]) ).
tcf(c_6065,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(X0,X1),X2),X1),
inference(superposition,[status(thm)],[c_4430,c_172]) ).
tcf(c_6066,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(X0,null_class),X1),X2),
inference(superposition,[status(thm)],[c_4430,c_256]) ).
tcf(c_6067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),universal_class) ),
inference(superposition,[status(thm)],[c_4430,c_4336]) ).
tcf(c_6068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,unordered_pair(X1,X2)),X3),X4)
| ( not_subclass_element(intersection(intersection(X0,unordered_pair(X1,X2)),X3),X4) = X2 )
| ( not_subclass_element(intersection(intersection(X0,unordered_pair(X1,X2)),X3),X4) = X1 ) ),
inference(superposition,[status(thm)],[c_4430,c_177]) ).
tcf(c_6069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,intersection(X1,X2)),X3),X4)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,X2)),X3),X4),X2) ),
inference(superposition,[status(thm)],[c_4430,c_189]) ).
tcf(c_6070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,intersection(X1,X2)),X3),X4)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,X2)),X3),X4),X1) ),
inference(superposition,[status(thm)],[c_4430,c_188]) ).
tcf(c_6071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,complement(X1)),X2),X3)
| ~ member(not_subclass_element(intersection(intersection(X0,complement(X1)),X2),X3),X1) ),
inference(superposition,[status(thm)],[c_4430,c_191]) ).
tcf(c_6072,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,identity_relation),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,identity_relation),X1),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4430,c_4293]) ).
tcf(c_6073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,compose(X1,X2)),X3),X4)
| member(not_subclass_element(intersection(intersection(X0,compose(X1,X2)),X3),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_4341]) ).
tcf(c_6074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,unordered_pair(X1,X1)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,unordered_pair(X1,X1)),X2),X3),unordered_pair(X4,X1)) ),
inference(superposition,[status(thm)],[c_4430,c_4344]) ).
tcf(c_6075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,unordered_pair(X1,X1)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,unordered_pair(X1,X1)),X2),X3),unordered_pair(X1,X4)) ),
inference(superposition,[status(thm)],[c_4430,c_4343]) ).
tcf(c_6076,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,unordered_pair(x,x)),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,unordered_pair(x,x)),X1),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4430,c_4346]) ).
tcf(c_6077,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,unordered_pair(y,y)),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,unordered_pair(y,y)),X1),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4430,c_4347]) ).
tcf(c_6084,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(intersection(null_class,X0),X1),X2) ),
inference(light_normalisation,[status(thm)],[c_6061,c_4553]) ).
tcf(c_6085,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,X2),X0)
| member(not_subclass_element(null_class,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_6084,c_4553]) ).
tcf(c_6161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_247]) ).
tcf(c_6163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_247]) ).
tcf(c_6175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_248]) ).
tcf(c_6177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_248]) ).
tcf(c_6189,plain,
! [X0: $i] :
( member(X0,null_class)
| ( intersection(null_class,cross_product(unordered_pair(X0,X0),universal_class)) = null_class )
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_5970,c_195]) ).
tcf(c_6190,plain,
! [X0: $i,X1: $i] :
( ( domain_of(X0) = X1 )
| ( intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class)) = null_class )
| ~ member(not_subclass_element(X1,domain_of(X0)),universal_class)
| ~ member(not_subclass_element(domain_of(X0),X1),X1) ),
inference(superposition,[status(thm)],[c_195,c_254]) ).
tcf(c_6191,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(domain_of(X1),X0),domain_of(X1))
| ( domain_of(X1) = X0 )
| ( intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) = null_class )
| ~ member(not_subclass_element(X0,domain_of(X1)),universal_class) ),
inference(superposition,[status(thm)],[c_195,c_253]) ).
tcf(c_6192,plain,
! [X0: $i,X1: $i] :
( subclass(X0,domain_of(X1))
| ( intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) = null_class )
| ~ member(not_subclass_element(X0,domain_of(X1)),universal_class) ),
inference(superposition,[status(thm)],[c_195,c_172]) ).
tcf(c_6194,plain,
! [X0: $i,X1: $i] :
( subclass(complement(domain_of(X0)),X1)
| ( intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class)) = null_class )
| ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class) ),
inference(superposition,[status(thm)],[c_195,c_4264]) ).
tcf(c_6195,plain,
! [X0: $i] :
( ( complement(domain_of(X0)) = null_class )
| ( intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class)) = null_class )
| ~ member(regular(complement(domain_of(X0))),universal_class) ),
inference(superposition,[status(thm)],[c_195,c_4265]) ).
tcf(c_6196,plain,
! [X0: $i] :
( ( intersection(complement(cross_product(unordered_pair(X0,X0),universal_class)),cross_product(unordered_pair(X0,X0),universal_class)) = null_class )
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_195,c_5852]) ).
tcf(c_6227,plain,
( subclass(iPr_def_10,z)
| ~ subclass(iPr_def_10,null_class)
| ~ subclass(null_class,z) ),
inference(instantiation,[status(thm)],[c_5316]) ).
tcf(c_6228,plain,
subclass(null_class,z),
inference(instantiation,[status(thm)],[c_257]) ).
tcf(c_6233,plain,
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(null_class,universal_class)),universal_class))))),universal_class)
| ~ member(universal_class,universal_class) ),
inference(superposition,[status(thm)],[c_4953,c_212]) ).
tcf(c_6237,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X1)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_6065]) ).
tcf(c_6238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(cross_product(X0,X1),intersection(X2,X3)),X3),
inference(superposition,[status(thm)],[c_193,c_6065]) ).
tcf(c_6241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(X0,cross_product(X1,X2)),X3),X0),
inference(superposition,[status(thm)],[c_193,c_6065]) ).
tcf(c_6242,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),regular(X0))
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_6065]) ).
tcf(c_6243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(cross_product(X0,X1),X2),X3),cross_product(X0,X1)),
inference(superposition,[status(thm)],[c_193,c_6065]) ).
tcf(c_6244,plain,
! [X0: $i] : subclass(intersection(identity_relation,X0),subset_relation),
inference(superposition,[status(thm)],[c_230,c_6065]) ).
tcf(c_6245,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(null_class,X0),complement(cross_product(X1,X2))),
inference(superposition,[status(thm)],[c_4217,c_6065]) ).
tcf(c_6247,plain,
! [X0: $i] : subclass(intersection(null_class,X0),null_class),
inference(superposition,[status(thm)],[c_4790,c_6065]) ).
tcf(c_6248,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X1,X0),X2) = X0 )
| ~ subclass(X0,intersection(intersection(X1,X0),X2)) ),
inference(superposition,[status(thm)],[c_6065,c_176]) ).
tcf(c_6249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,X0),X3),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6065,c_250]) ).
tcf(c_6250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(X0,intersection(intersection(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_6065,c_170]) ).
tcf(c_6251,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(X0,intersection(intersection(X1,null_class),X2)) = null_class,
inference(superposition,[status(thm)],[c_6065,c_5287]) ).
tcf(c_6252,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(intersection(X0,null_class),X1),X2) = null_class,
inference(superposition,[status(thm)],[c_6065,c_5257]) ).
tcf(c_6314,plain,
( subclass(null_class,subset_relation)
| ( null_class = identity_relation ) ),
inference(superposition,[status(thm)],[c_223,c_6244]) ).
tcf(c_6315,plain,
subclass(null_class,subset_relation),
inference(superposition,[status(thm)],[c_4790,c_6244]) ).
tcf(c_6316,plain,
! [X0: $i] :
( ( intersection(identity_relation,X0) = subset_relation )
| ~ subclass(subset_relation,intersection(identity_relation,X0)) ),
inference(superposition,[status(thm)],[c_6244,c_176]) ).
tcf(c_6317,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(identity_relation,X1),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_6244,c_250]) ).
tcf(c_6318,plain,
! [X0: $i,X1: $i] :
( member(X0,subset_relation)
| ~ member(X0,intersection(identity_relation,X1)) ),
inference(superposition,[status(thm)],[c_6244,c_170]) ).
tcf(c_6333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(X0,X1),cross_product(X2,X3)),X1),
inference(superposition,[status(thm)],[c_193,c_6238]) ).
tcf(c_6335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : subclass(intersection(cross_product(X0,X1),intersection(X2,cross_product(X3,X4))),X2),
inference(superposition,[status(thm)],[c_193,c_6238]) ).
tcf(c_6337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : subclass(intersection(cross_product(X0,X1),intersection(cross_product(X2,X3),X4)),cross_product(X2,X3)),
inference(superposition,[status(thm)],[c_193,c_6238]) ).
tcf(c_6338,plain,
! [X0: $i,X1: $i] : subclass(intersection(cross_product(X0,X1),identity_relation),subset_relation),
inference(superposition,[status(thm)],[c_230,c_6238]) ).
tcf(c_6340,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(cross_product(X0,X1),null_class),X2),
inference(superposition,[status(thm)],[c_4553,c_6238]) ).
tcf(c_6341,plain,
! [X0: $i,X1: $i] : subclass(intersection(cross_product(X0,X1),null_class),null_class),
inference(superposition,[status(thm)],[c_4790,c_6238]) ).
tcf(c_6342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(cross_product(X1,X2),intersection(X3,X0)) = X0 )
| ~ subclass(X0,intersection(cross_product(X1,X2),intersection(X3,X0))) ),
inference(superposition,[status(thm)],[c_6238,c_176]) ).
tcf(c_6343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X2,X3),intersection(X4,X0)),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6238,c_250]) ).
tcf(c_6344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X4)
| ~ member(X0,intersection(cross_product(X1,X2),intersection(X3,X4))) ),
inference(superposition,[status(thm)],[c_6238,c_170]) ).
tcf(c_6345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(X0,intersection(cross_product(X1,X2),intersection(X3,null_class))) = null_class,
inference(superposition,[status(thm)],[c_6238,c_5287]) ).
tcf(c_6346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(intersection(cross_product(X0,X1),intersection(X2,null_class)),X3) = null_class,
inference(superposition,[status(thm)],[c_6238,c_5257]) ).
tcf(c_6347,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),intersection(X2,null_class)) = null_class,
inference(superposition,[status(thm)],[c_6238,c_258]) ).
tcf(c_6447,plain,
! [X0: $i,X1: $i] : subclass(intersection(identity_relation,cross_product(X0,X1)),subset_relation),
inference(demodulation,[status(thm)],[c_6338,c_193]) ).
tcf(c_6453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : subclass(intersection(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4),cross_product(X2,X3)),
inference(superposition,[status(thm)],[c_193,c_6241]) ).
tcf(c_6454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(cross_product(X0,X1),X2),X3),X2),
inference(superposition,[status(thm)],[c_193,c_6241]) ).
tcf(c_6456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(intersection(X0,cross_product(X1,X2)),X3) = X0 )
| ~ subclass(X0,intersection(intersection(X0,cross_product(X1,X2)),X3)) ),
inference(superposition,[status(thm)],[c_6241,c_176]) ).
tcf(c_6457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,cross_product(X2,X3)),X4),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6241,c_250]) ).
tcf(c_6458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X1)
| ~ member(X0,intersection(intersection(X1,cross_product(X2,X3)),X4)) ),
inference(superposition,[status(thm)],[c_6241,c_170]) ).
tcf(c_6459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(X0,intersection(intersection(null_class,cross_product(X1,X2)),X3)) = null_class,
inference(superposition,[status(thm)],[c_6241,c_5287]) ).
tcf(c_6460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(intersection(intersection(null_class,cross_product(X0,X1)),X2),X3) = null_class,
inference(superposition,[status(thm)],[c_6241,c_5257]) ).
tcf(c_6461,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(null_class,cross_product(X0,X1)),X2) = null_class,
inference(superposition,[status(thm)],[c_6241,c_258]) ).
tcf(c_6479,plain,
! [X0: $i,X1: $i] :
( ( intersection(identity_relation,X1) = X0 )
| ~ subclass(subset_relation,X0)
| ~ subclass(X0,intersection(identity_relation,X1)) ),
inference(superposition,[status(thm)],[c_6317,c_176]) ).
tcf(c_6480,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(identity_relation,X2),X1)
| ~ subclass(subset_relation,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6317,c_250]) ).
tcf(c_6481,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(subset_relation,X2)
| ~ member(X0,intersection(identity_relation,X1)) ),
inference(superposition,[status(thm)],[c_6317,c_170]) ).
tcf(c_6482,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(identity_relation,X1)) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_6317,c_5287]) ).
tcf(c_6483,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(identity_relation,X0),X1) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_6317,c_5257]) ).
tcf(c_6484,plain,
! [X0: $i] :
( ( intersection(identity_relation,X0) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_6317,c_258]) ).
tcf(c_6515,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation)
| member(not_subclass_element(X1,intersection(identity_relation,X0)),X1)
| ( intersection(identity_relation,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_6318]) ).
tcf(c_6516,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(identity_relation,X0),null_class),subset_relation)
| ( intersection(identity_relation,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_6318]) ).
tcf(c_6518,plain,
! [X0: $i] :
( member(regular(intersection(identity_relation,X0)),subset_relation)
| ( intersection(identity_relation,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_6318]) ).
tcf(c_6519,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(identity_relation,X0),X1),X2)
| member(not_subclass_element(intersection(intersection(identity_relation,X0),X1),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4224,c_6318]) ).
tcf(c_6520,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(identity_relation,X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(identity_relation,X1)),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4245,c_6318]) ).
tcf(c_6521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(identity_relation,X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(identity_relation,X2)),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4425,c_6318]) ).
tcf(c_6522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(identity_relation,X1)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(identity_relation,X1)),X2),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4430,c_6318]) ).
tcf(c_6570,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(intersection(X0,X1),regular(intersection(X0,X1))),X2)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4431]) ).
tcf(c_6572,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(intersection(X0,X1),null_class),X2) ),
inference(superposition,[status(thm)],[c_4790,c_4431]) ).
tcf(c_6573,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),complement(X0))
| subclass(intersection(intersection(complement(X0),X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4169,c_4431]) ).
tcf(c_6574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(cross_product(X1,X2),X0),X3),X4)
| member(not_subclass_element(intersection(intersection(X0,cross_product(X1,X2)),X3),X4),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_193,c_4431]) ).
tcf(c_6575,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),X0)
| subclass(intersection(intersection(X0,regular(X0)),X1),X2)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4431]) ).
tcf(c_6576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,cross_product(X0,X1)),X3),X4)
| member(not_subclass_element(intersection(intersection(cross_product(X0,X1),X2),X3),X4),X2) ),
inference(superposition,[status(thm)],[c_193,c_4431]) ).
tcf(c_6577,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(superposition,[status(thm)],[c_230,c_4431]) ).
tcf(c_6578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),cross_product(X0,X1))
| subclass(intersection(intersection(cross_product(X0,X1),complement(cross_product(X0,X1))),X2),X3) ),
inference(superposition,[status(thm)],[c_4217,c_4431]) ).
tcf(c_6579,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),null_class)
| subclass(intersection(intersection(null_class,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4553,c_4431]) ).
tcf(c_6580,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X2,null_class),X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),X2) ),
inference(superposition,[status(thm)],[c_4790,c_4431]) ).
tcf(c_6583,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(X0,X1),X2),X0),
inference(superposition,[status(thm)],[c_4431,c_172]) ).
tcf(c_6584,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(null_class,X0),X1),X2),
inference(superposition,[status(thm)],[c_4431,c_256]) ).
tcf(c_6586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(unordered_pair(X0,X1),X2),X3),X4)
| ( not_subclass_element(intersection(intersection(unordered_pair(X0,X1),X2),X3),X4) = X1 )
| ( not_subclass_element(intersection(intersection(unordered_pair(X0,X1),X2),X3),X4) = X0 ) ),
inference(superposition,[status(thm)],[c_4431,c_177]) ).
tcf(c_6587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X0,X1),X2),X3),X4)
| member(not_subclass_element(intersection(intersection(intersection(X0,X1),X2),X3),X4),X1) ),
inference(superposition,[status(thm)],[c_4431,c_189]) ).
tcf(c_6588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X0,X1),X2),X3),X4)
| member(not_subclass_element(intersection(intersection(intersection(X0,X1),X2),X3),X4),X0) ),
inference(superposition,[status(thm)],[c_4431,c_188]) ).
tcf(c_6589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(complement(X0),X1),X2),X3)
| ~ member(not_subclass_element(intersection(intersection(complement(X0),X1),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_4431,c_191]) ).
tcf(c_6591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(compose(X0,X1),X2),X3),X4)
| member(not_subclass_element(intersection(intersection(compose(X0,X1),X2),X3),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_4341]) ).
tcf(c_6592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(unordered_pair(X0,X0),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(unordered_pair(X0,X0),X1),X2),X3),unordered_pair(X4,X0)) ),
inference(superposition,[status(thm)],[c_4431,c_4344]) ).
tcf(c_6593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(unordered_pair(X0,X0),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(unordered_pair(X0,X0),X1),X2),X3),unordered_pair(X0,X4)) ),
inference(superposition,[status(thm)],[c_4431,c_4343]) ).
tcf(c_6594,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(unordered_pair(x,x),X0),X1),X2)
| member(not_subclass_element(intersection(intersection(unordered_pair(x,x),X0),X1),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4431,c_4346]) ).
tcf(c_6595,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(unordered_pair(y,y),X0),X1),X2)
| member(not_subclass_element(intersection(intersection(unordered_pair(y,y),X0),X1),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4431,c_4347]) ).
tcf(c_6596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(identity_relation,X0),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(identity_relation,X0),X1),X2),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4431,c_6318]) ).
tcf(c_6635,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(light_normalisation,[status(thm)],[c_6577,c_230]) ).
tcf(c_6692,plain,
! [X0: $i] :
( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(complement(cross_product(X0,universal_class))) ),
inference(superposition,[status(thm)],[c_4169,c_221]) ).
tcf(c_6693,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),cross_product(X0,X1)),universal_class)))),universal_class)
| ~ member(X2,universal_class)
| ~ function(cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_193,c_221]) ).
tcf(c_6694,plain,
! [X0: $i,X1: $i] :
( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_193,c_221]) ).
tcf(c_6695,plain,
! [X0: $i] :
( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
| ~ function(null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_4553,c_221]) ).
tcf(c_6734,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_245]) ).
tcf(c_6735,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_245]) ).
tcf(c_6736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_245]) ).
tcf(c_6738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_245]) ).
tcf(c_6756,plain,
! [X0: $i,X1: $i] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_246]) ).
tcf(c_6757,plain,
! [X0: $i,X1: $i] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_246]) ).
tcf(c_6758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_246]) ).
tcf(c_6760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_246]) ).
tcf(c_6771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(cross_product(X0,X1),intersection(X2,X3)),X2),
inference(superposition,[status(thm)],[c_193,c_6583]) ).
tcf(c_6773,plain,
! [X0: $i,X1: $i] : subclass(intersection(null_class,X0),complement(X1)),
inference(superposition,[status(thm)],[c_4169,c_6583]) ).
tcf(c_6774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(X0,cross_product(X1,X2)),X3),cross_product(X1,X2)),
inference(superposition,[status(thm)],[c_193,c_6583]) ).
tcf(c_6775,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_6583]) ).
tcf(c_6777,plain,
! [X0: $i] : subclass(intersection(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))),
inference(superposition,[status(thm)],[c_230,c_6583]) ).
tcf(c_6778,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(null_class,X0),cross_product(X1,X2)),
inference(superposition,[status(thm)],[c_4217,c_6583]) ).
tcf(c_6781,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,X1),X2) = X0 )
| ~ subclass(X0,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_6583,c_176]) ).
tcf(c_6782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,X2),X3),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6583,c_250]) ).
tcf(c_6783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X1)
| ~ member(X0,intersection(intersection(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_6583,c_170]) ).
tcf(c_6784,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(X0,intersection(intersection(null_class,X1),X2)) = null_class,
inference(superposition,[status(thm)],[c_6583,c_5287]) ).
tcf(c_6785,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(intersection(null_class,X0),X1),X2) = null_class,
inference(superposition,[status(thm)],[c_6583,c_5257]) ).
tcf(c_6817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(X0,X1),cross_product(X2,X3)),X0),
inference(superposition,[status(thm)],[c_193,c_6771]) ).
tcf(c_6818,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(cross_product(X0,X1),null_class),complement(X2)),
inference(superposition,[status(thm)],[c_4169,c_6771]) ).
tcf(c_6819,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : subclass(intersection(cross_product(X0,X1),intersection(X2,cross_product(X3,X4))),cross_product(X3,X4)),
inference(superposition,[status(thm)],[c_193,c_6771]) ).
tcf(c_6820,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X1,X2),null_class),X0)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_6771]) ).
tcf(c_6821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : subclass(intersection(cross_product(X0,X1),intersection(cross_product(X2,X3),X4)),X4),
inference(superposition,[status(thm)],[c_193,c_6771]) ).
tcf(c_6822,plain,
! [X0: $i,X1: $i] : subclass(intersection(cross_product(X0,X1),identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))),
inference(superposition,[status(thm)],[c_230,c_6771]) ).
tcf(c_6823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(cross_product(X0,X1),null_class),cross_product(X2,X3)),
inference(superposition,[status(thm)],[c_4217,c_6771]) ).
tcf(c_6826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(cross_product(X1,X2),intersection(X0,X3)) = X0 )
| ~ subclass(X0,intersection(cross_product(X1,X2),intersection(X0,X3))) ),
inference(superposition,[status(thm)],[c_6771,c_176]) ).
tcf(c_6827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X2,X3),intersection(X0,X4)),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6771,c_250]) ).
tcf(c_6828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X3)
| ~ member(X0,intersection(cross_product(X1,X2),intersection(X3,X4))) ),
inference(superposition,[status(thm)],[c_6771,c_170]) ).
tcf(c_6829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(X0,intersection(cross_product(X1,X2),intersection(null_class,X3))) = null_class,
inference(superposition,[status(thm)],[c_6771,c_5287]) ).
tcf(c_6830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(intersection(cross_product(X0,X1),intersection(null_class,X2)),X3) = null_class,
inference(superposition,[status(thm)],[c_6771,c_5257]) ).
tcf(c_6831,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),intersection(null_class,X2)) = null_class,
inference(superposition,[status(thm)],[c_6771,c_258]) ).
tcf(c_6876,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ( X0 = null_class ) ),
inference(demodulation,[status(thm)],[c_6775,c_4553]) ).
tcf(c_6877,plain,
( subclass(null_class,domain_of(flip(cross_product(subset_relation,universal_class))))
| ( null_class = identity_relation ) ),
inference(superposition,[status(thm)],[c_223,c_6777]) ).
tcf(c_6878,plain,
subclass(null_class,domain_of(flip(cross_product(subset_relation,universal_class)))),
inference(superposition,[status(thm)],[c_4790,c_6777]) ).
tcf(c_6879,plain,
! [X0: $i] :
( ( domain_of(flip(cross_product(subset_relation,universal_class))) = intersection(identity_relation,X0) )
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),intersection(identity_relation,X0)) ),
inference(superposition,[status(thm)],[c_6777,c_176]) ).
tcf(c_6880,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(identity_relation,X1),X0)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ),
inference(superposition,[status(thm)],[c_6777,c_250]) ).
tcf(c_6881,plain,
! [X0: $i,X1: $i] :
( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,intersection(identity_relation,X1)) ),
inference(superposition,[status(thm)],[c_6777,c_170]) ).
tcf(c_6902,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(universal_class),X0),X1)
| ( unordered_pair(not_subclass_element(intersection(complement(universal_class),X0),X1),not_subclass_element(intersection(complement(universal_class),X0),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4943,c_4432]) ).
tcf(c_6903,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,universal_class)
| subclass(intersection(complement(universal_class),X0),X1)
| ( unordered_pair(not_subclass_element(intersection(complement(universal_class),X0),X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_4432]) ).
tcf(c_6904,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,universal_class)
| subclass(intersection(complement(universal_class),X1),X2)
| ( unordered_pair(X0,not_subclass_element(intersection(complement(universal_class),X1),X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_4432]) ).
tcf(c_6905,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(universal_class),X0),X1)
| ( unordered_pair(not_subclass_element(intersection(complement(universal_class),X0),X1),X2) = unordered_pair(X2,X2) ) ),
inference(superposition,[status(thm)],[c_265,c_4432]) ).
tcf(c_6906,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(universal_class),X1),X2)
| ( unordered_pair(X0,not_subclass_element(intersection(complement(universal_class),X1),X2)) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_264,c_4432]) ).
tcf(c_6907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(complement(intersection(X0,X1)),X2),X3)
| ~ member(not_subclass_element(intersection(complement(intersection(X0,X1)),X2),X3),X1)
| ~ member(not_subclass_element(intersection(complement(intersection(X0,X1)),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_190,c_4432]) ).
tcf(c_6908,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(complement(X0)),X1),X2)
| member(not_subclass_element(intersection(complement(complement(X0)),X1),X2),X0)
| ~ member(not_subclass_element(intersection(complement(complement(X0)),X1),X2),universal_class) ),
inference(superposition,[status(thm)],[c_192,c_4432]) ).
tcf(c_6909,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(domain_of(X0)),X1),X2)
| ( intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(complement(domain_of(X0)),X1),X2),not_subclass_element(intersection(complement(domain_of(X0)),X1),X2)),universal_class)) = null_class )
| ~ member(not_subclass_element(intersection(complement(domain_of(X0)),X1),X2),universal_class) ),
inference(superposition,[status(thm)],[c_195,c_4432]) ).
tcf(c_6911,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),X1)
| ~ member(not_subclass_element(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),X1),identity_relation) ),
inference(superposition,[status(thm)],[c_4294,c_4432]) ).
tcf(c_6912,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X0),X1)
| ~ member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_4432]) ).
tcf(c_6913,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X0),X1)
| ~ member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_4432]) ).
tcf(c_6914,plain,
! [X0: $i,X1: $i] : subclass(intersection(complement(universal_class),X0),X1),
inference(superposition,[status(thm)],[c_4388,c_4432]) ).
tcf(c_6915,plain,
! [X0: $i] :
( subclass(intersection(complement(universal_class),X0),null_class)
| ( intersection(complement(universal_class),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4389,c_4432]) ).
tcf(c_6916,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),complement(cross_product(X0,X1))),X2)
| subclass(intersection(complement(cross_product(X0,X1)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_4424,c_4432]) ).
tcf(c_6917,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(X1),X1),X0)
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_4169,c_4432]) ).
tcf(c_6918,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(X1),regular(complement(X1))),X0)
| ( complement(X1) = null_class )
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_223,c_4432]) ).
tcf(c_6920,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(X1),null_class),X0)
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_4790,c_4432]) ).
tcf(c_6921,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(universal_class),X0),X1)
| ~ member(not_subclass_element(intersection(null_class,X0),X1),universal_class) ),
inference(superposition,[status(thm)],[c_4953,c_4432]) ).
tcf(c_6936,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,X1),X2)
| ( unordered_pair(X0,not_subclass_element(intersection(null_class,X1),X2)) = unordered_pair(X0,X0) ) ),
inference(light_normalisation,[status(thm)],[c_6906,c_4953]) ).
tcf(c_6939,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X0)
| ( unordered_pair(not_subclass_element(null_class,X0),X1) = unordered_pair(X1,X1) ) ),
inference(light_normalisation,[status(thm)],[c_6905,c_4553,c_4953]) ).
tcf(c_6940,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(null_class,X2)
| subclass(intersection(complement(cross_product(X0,X1)),cross_product(X0,X1)),X2) ),
inference(light_normalisation,[status(thm)],[c_6916,c_4217]) ).
tcf(c_6941,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,universal_class)
| subclass(intersection(null_class,X1),X2)
| ( unordered_pair(X0,not_subclass_element(intersection(null_class,X1),X2)) = null_class ) ),
inference(light_normalisation,[status(thm)],[c_6904,c_4953]) ).
tcf(c_6945,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X0)
| member(X1,universal_class)
| ( unordered_pair(not_subclass_element(null_class,X0),X1) = null_class ) ),
inference(light_normalisation,[status(thm)],[c_6903,c_4553,c_4953]) ).
tcf(c_6976,plain,
! [X0: $i] : subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_229,c_6583]) ).
tcf(c_6977,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class))
| subclass(intersection(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),X1) ),
inference(superposition,[status(thm)],[c_229,c_4431]) ).
tcf(c_6978,plain,
! [X0: $i] : subclass(intersection(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(superposition,[status(thm)],[c_229,c_6065]) ).
tcf(c_6979,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(subset_relation,X0),X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(intersection(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),X1) ),
inference(superposition,[status(thm)],[c_229,c_4430]) ).
tcf(c_6980,plain,
subclass(subset_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(superposition,[status(thm)],[c_229,c_4643]) ).
tcf(c_6981,plain,
! [X0: $i] :
( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) ),
inference(superposition,[status(thm)],[c_229,c_4245]) ).
tcf(c_6983,plain,
! [X0: $i] :
( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
| subclass(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) ),
inference(superposition,[status(thm)],[c_229,c_4224]) ).
tcf(c_6984,plain,
! [X0: $i] :
( member(X0,subset_relation)
| ~ member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
inference(superposition,[status(thm)],[c_229,c_190]) ).
tcf(c_6985,plain,
! [X0: $i] :
( member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,subset_relation) ),
inference(superposition,[status(thm)],[c_229,c_189]) ).
tcf(c_6986,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,subset_relation) ),
inference(superposition,[status(thm)],[c_229,c_188]) ).
tcf(c_6987,plain,
! [X0: $i] :
( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),cross_product(universal_class,universal_class)),X0) ),
inference(superposition,[status(thm)],[c_229,c_4425]) ).
tcf(c_6988,plain,
! [X0: $i] :
( subclass(subset_relation,X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_229,c_4551]) ).
tcf(c_6989,plain,
! [X0: $i] :
( subclass(subset_relation,X0)
| ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) ),
inference(superposition,[status(thm)],[c_229,c_4788]) ).
tcf(c_6990,plain,
! [X0: $i,X1: $i] : subclass(intersection(cross_product(X0,X1),subset_relation),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_229,c_6771]) ).
tcf(c_6991,plain,
! [X0: $i,X1: $i] : subclass(intersection(cross_product(X0,X1),subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(superposition,[status(thm)],[c_229,c_6238]) ).
tcf(c_6992,plain,
subclass(subset_relation,cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_229,c_6771]) ).
tcf(c_6993,plain,
subclass(subset_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),
inference(superposition,[status(thm)],[c_229,c_6238]) ).
tcf(c_7005,plain,
! [X0: $i] :
( subclass(subset_relation,X0)
| member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class)) ),
inference(light_normalisation,[status(thm)],[c_6983,c_229]) ).
tcf(c_7008,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(subset_relation,X0),X1)
| member(not_subclass_element(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class)) ),
inference(light_normalisation,[status(thm)],[c_6977,c_229]) ).
tcf(c_7013,plain,
! [X0: $i] :
( subclass(subset_relation,X0)
| member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
inference(light_normalisation,[status(thm)],[c_6981,c_229]) ).
tcf(c_7016,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(subset_relation,X0),X1)
| member(not_subclass_element(intersection(subset_relation,X0),X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
inference(light_normalisation,[status(thm)],[c_6979,c_229]) ).
tcf(c_7070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,unordered_pair(X2,X2)),unordered_pair(X0,X0)),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_261,c_183]) ).
tcf(c_7072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X2,X2),X0)),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_261,c_183]) ).
tcf(c_7074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),universal_class)
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_183,c_4336]) ).
tcf(c_7075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X2,unordered_pair(X0,X2))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_183,c_246]) ).
tcf(c_7076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,unordered_pair(X0,X2))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_183,c_245]) ).
tcf(c_7077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X2,universal_class)
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_183,c_248]) ).
tcf(c_7078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,universal_class)
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_183,c_247]) ).
tcf(c_7192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(X2,X3))
| ( unordered_pair(X0,X1) != null_class ) ),
inference(superposition,[status(thm)],[c_261,c_271]) ).
tcf(c_7202,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(cross_product(X0,X1),X2)
| ( unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(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) ) ),
inference(superposition,[status(thm)],[c_171,c_184]) ).
tcf(c_7203,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(X2,cross_product(X0,X1)),X2)
| ( cross_product(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(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) ) ),
inference(superposition,[status(thm)],[c_251,c_184]) ).
tcf(c_7204,plain,
! [X0: $i,X1: $i] :
( ( cross_product(X0,X1) = null_class )
| ( unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),null_class)),first(not_subclass_element(cross_product(X0,X1),null_class))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),null_class)),unordered_pair(second(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) ) ),
inference(superposition,[status(thm)],[c_259,c_184]) ).
tcf(c_7205,plain,
! [X0: $i,X1: $i] :
( ( cross_product(X0,X1) = null_class )
| ( unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))) = regular(cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_222,c_184]) ).
tcf(c_7206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))))))) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))) )
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_183,c_184]) ).
tcf(c_7207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) = not_subclass_element(intersection(cross_product(X0,X1),X2),X3) ) ),
inference(superposition,[status(thm)],[c_4224,c_184]) ).
tcf(c_7208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,cross_product(X1,X2)),X3)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))))) = not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) ) ),
inference(superposition,[status(thm)],[c_4245,c_184]) ).
tcf(c_7209,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_184]) ).
tcf(c_7210,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_184]) ).
tcf(c_7211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),X0),X3)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))))) = not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) ) ),
inference(superposition,[status(thm)],[c_4424,c_184]) ).
tcf(c_7212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X2,X3),cross_product(X0,X1)),X4)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4)),first(not_subclass_element(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4)),second(not_subclass_element(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4))))) = not_subclass_element(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4) ) ),
inference(superposition,[status(thm)],[c_4425,c_184]) ).
tcf(c_7213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,cross_product(X1,X2)),X3),X4)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(intersection(X0,cross_product(X1,X2)),X3),X4)),first(not_subclass_element(intersection(intersection(X0,cross_product(X1,X2)),X3),X4))),unordered_pair(first(not_subclass_element(intersection(intersection(X0,cross_product(X1,X2)),X3),X4)),unordered_pair(second(not_subclass_element(intersection(intersection(X0,cross_product(X1,X2)),X3),X4)),second(not_subclass_element(intersection(intersection(X0,cross_product(X1,X2)),X3),X4))))) = not_subclass_element(intersection(intersection(X0,cross_product(X1,X2)),X3),X4) ) ),
inference(superposition,[status(thm)],[c_4430,c_184]) ).
tcf(c_7214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(cross_product(X0,X1),X2),X3),X4)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(intersection(cross_product(X0,X1),X2),X3),X4)),first(not_subclass_element(intersection(intersection(cross_product(X0,X1),X2),X3),X4))),unordered_pair(first(not_subclass_element(intersection(intersection(cross_product(X0,X1),X2),X3),X4)),unordered_pair(second(not_subclass_element(intersection(intersection(cross_product(X0,X1),X2),X3),X4)),second(not_subclass_element(intersection(intersection(cross_product(X0,X1),X2),X3),X4))))) = not_subclass_element(intersection(intersection(cross_product(X0,X1),X2),X3),X4) ) ),
inference(superposition,[status(thm)],[c_4431,c_184]) ).
tcf(c_7253,plain,
( ( cross_product(universal_class,universal_class) = subset_relation )
| ~ subclass(cross_product(universal_class,universal_class),subset_relation) ),
inference(superposition,[status(thm)],[c_6992,c_176]) ).
tcf(c_7256,plain,
subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_6992,c_4502]) ).
tcf(c_7259,plain,
( ( cross_product(universal_class,universal_class) = identity_relation )
| ~ subclass(cross_product(universal_class,universal_class),identity_relation) ),
inference(superposition,[status(thm)],[c_7256,c_176]) ).
tcf(c_7260,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_7256,c_250]) ).
tcf(c_7261,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,identity_relation) ),
inference(superposition,[status(thm)],[c_7256,c_170]) ).
tcf(c_7270,plain,
( subclass(null_class,cross_product(universal_class,universal_class))
| ( null_class = subset_relation ) ),
inference(superposition,[status(thm)],[c_223,c_6976]) ).
tcf(c_7271,plain,
subclass(null_class,cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4790,c_6976]) ).
tcf(c_7272,plain,
! [X0: $i] :
( ( intersection(subset_relation,X0) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(subset_relation,X0)) ),
inference(superposition,[status(thm)],[c_6976,c_176]) ).
tcf(c_7273,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(subset_relation,X1),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_6976,c_250]) ).
tcf(c_7274,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(subset_relation,X1)) ),
inference(superposition,[status(thm)],[c_6976,c_170]) ).
tcf(c_7314,plain,
! [X0: $i] :
( ( cross_product(universal_class,universal_class) = X0 )
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),X0),X0) ),
inference(superposition,[status(thm)],[c_6986,c_254]) ).
tcf(c_7315,plain,
! [X0: $i] :
( member(not_subclass_element(cross_product(universal_class,universal_class),X0),cross_product(universal_class,universal_class))
| ( cross_product(universal_class,universal_class) = X0 )
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_253]) ).
tcf(c_7316,plain,
! [X0: $i] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_172]) ).
tcf(c_7317,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_4336]) ).
tcf(c_7318,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_184]) ).
tcf(c_7319,plain,
! [X0: $i,X1: $i] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_246]) ).
tcf(c_7320,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_245]) ).
tcf(c_7323,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_182]) ).
tcf(c_7324,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_181]) ).
tcf(c_7325,plain,
! [X0: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_4264]) ).
tcf(c_7326,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_4265]) ).
tcf(c_7327,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X0),X1)
| ~ member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_4432]) ).
tcf(c_7368,plain,
subclass(subset_relation,universal_class),
inference(superposition,[status(thm)],[c_173,c_6988]) ).
tcf(c_7371,plain,
! [X0: $i,X1: $i] : subclass(intersection(subset_relation,cross_product(X0,X1)),cross_product(universal_class,universal_class)),
inference(demodulation,[status(thm)],[c_6990,c_193]) ).
tcf(c_7384,plain,
! [X0: $i] :
( ( cross_product(universal_class,universal_class) = X0 )
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),identity_relation)
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),X0),X0) ),
inference(superposition,[status(thm)],[c_7261,c_254]) ).
tcf(c_7385,plain,
! [X0: $i] :
( member(not_subclass_element(cross_product(universal_class,universal_class),X0),cross_product(universal_class,universal_class))
| ( cross_product(universal_class,universal_class) = X0 )
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_253]) ).
tcf(c_7386,plain,
! [X0: $i] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_172]) ).
tcf(c_7388,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_184]) ).
tcf(c_7389,plain,
! [X0: $i,X1: $i] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_246]) ).
tcf(c_7390,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_245]) ).
tcf(c_7393,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_182]) ).
tcf(c_7394,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_181]) ).
tcf(c_7395,plain,
! [X0: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_4264]) ).
tcf(c_7396,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ member(regular(complement(cross_product(universal_class,universal_class))),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_4265]) ).
tcf(c_7397,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X0),X1)
| ~ member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_4432]) ).
tcf(c_7463,plain,
! [X0: $i] :
( subclass(subset_relation,X0)
| member(not_subclass_element(subset_relation,X0),universal_class) ),
inference(superposition,[status(thm)],[c_7005,c_4336]) ).
tcf(c_7464,plain,
! [X0: $i] :
( subclass(subset_relation,X0)
| ( unordered_pair(unordered_pair(first(not_subclass_element(subset_relation,X0)),first(not_subclass_element(subset_relation,X0))),unordered_pair(first(not_subclass_element(subset_relation,X0)),unordered_pair(second(not_subclass_element(subset_relation,X0)),second(not_subclass_element(subset_relation,X0))))) = not_subclass_element(subset_relation,X0) ) ),
inference(superposition,[status(thm)],[c_7005,c_184]) ).
tcf(c_7476,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),subset_relation)
| subclass(intersection(identity_relation,regular(identity_relation)),X0)
| ( null_class = identity_relation ) ),
inference(superposition,[status(thm)],[c_223,c_4433]) ).
tcf(c_7477,plain,
! [X0: $i] :
( subclass(intersection(identity_relation,null_class),X0)
| member(not_subclass_element(null_class,X0),subset_relation) ),
inference(superposition,[status(thm)],[c_4790,c_4433]) ).
tcf(c_7481,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),universal_class) ),
inference(superposition,[status(thm)],[c_4433,c_4336]) ).
tcf(c_7496,plain,
! [X0: $i,X1: $i] :
( ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
| ~ member(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),successor_relation) ),
inference(superposition,[status(thm)],[c_261,c_203]) ).
tcf(c_7498,plain,
! [X0: $i,X1: $i] :
( ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),successor_relation) ),
inference(superposition,[status(thm)],[c_261,c_203]) ).
tcf(c_7514,plain,
! [X0: $i,X1: $i] :
( compatible(X0,null_class,X1)
| ~ function(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),domain_of(domain_of(X1)))
| ( domain_of(X0) != null_class ) ),
inference(superposition,[status(thm)],[c_5970,c_238]) ).
tcf(c_7515,plain,
! [X0: $i,X1: $i] :
( compatible(domain_of(X0),X0,X1)
| ~ function(domain_of(X0))
| ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) ),
inference(equality_resolution,[status(thm)],[c_238]) ).
tcf(c_7532,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),universal_class)
| ( X0 = null_class )
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_225,c_4336]) ).
tcf(c_7533,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0 )
| ~ member(unordered_pair(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_177]) ).
tcf(c_7534,plain,
! [X0: $i,X1: $i] :
( ( cross_product(X0,X1) = null_class )
| ( unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) )
| ~ member(cross_product(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_184]) ).
tcf(c_7535,plain,
! [X0: $i,X1: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1)
| ( intersection(X0,X1) = null_class )
| ~ member(intersection(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_189]) ).
tcf(c_7536,plain,
! [X0: $i,X1: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0)
| ( intersection(X0,X1) = null_class )
| ~ member(intersection(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_188]) ).
tcf(c_7537,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(complement(X0),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) ),
inference(superposition,[status(thm)],[c_225,c_191]) ).
tcf(c_7538,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
| ( null_class = identity_relation )
| ~ member(identity_relation,universal_class) ),
inference(superposition,[status(thm)],[c_225,c_4293]) ).
tcf(c_7539,plain,
! [X0: $i,X1: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(compose(X0,X1),compose(X0,X1)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ( compose(X0,X1) = null_class )
| ~ member(compose(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_4341]) ).
tcf(c_7540,plain,
! [X0: $i,X1: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),universal_class)),universal_class))))))),unordered_pair(X1,X0))
| ( unordered_pair(X0,X0) = null_class )
| ~ member(unordered_pair(X0,X0),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_4344]) ).
tcf(c_7541,plain,
! [X0: $i,X1: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),universal_class)),universal_class))))))),unordered_pair(X0,X1))
| ( unordered_pair(X0,X0) = null_class )
| ~ member(unordered_pair(X0,X0),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_4343]) ).
tcf(c_7542,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(x,x),unordered_pair(x,x)),universal_class)),universal_class))))))),iPr_def_10)
| ( unordered_pair(x,x) = null_class )
| ~ member(unordered_pair(x,x),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_4346]) ).
tcf(c_7543,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(y,y),unordered_pair(y,y)),universal_class)),universal_class))))))),iPr_def_10)
| ( unordered_pair(y,y) = null_class )
| ~ member(unordered_pair(y,y),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_4347]) ).
tcf(c_7544,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation)
| ( intersection(identity_relation,X0) = null_class )
| ~ member(intersection(identity_relation,X0),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_6318]) ).
tcf(c_7557,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(y,y),unordered_pair(y,y)),universal_class)),universal_class))))))),iPr_def_10)
| ( unordered_pair(y,y) = null_class ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7543,c_180]) ).
tcf(c_7560,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(x,x),unordered_pair(x,x)),universal_class)),universal_class))))))),iPr_def_10)
| ( unordered_pair(x,x) = null_class ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7542,c_180]) ).
tcf(c_7569,plain,
! [X0: $i,X1: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),universal_class)),universal_class))))))),unordered_pair(X0,X1))
| ( unordered_pair(X0,X0) = null_class ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7541,c_180]) ).
tcf(c_7572,plain,
! [X0: $i,X1: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),universal_class)),universal_class))))))),unordered_pair(X1,X0))
| ( unordered_pair(X0,X0) = null_class ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7540,c_180]) ).
tcf(c_7578,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7533,c_180]) ).
tcf(c_7656,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ( unordered_pair(X0,X1) != unordered_pair(X1,X2) ) ),
inference(superposition,[status(thm)],[c_261,c_267]) ).
tcf(c_7658,plain,
! [X0: $i] :
( ( X0 = y )
| ~ member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ( unordered_pair(x,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3161,c_267]) ).
tcf(c_7659,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ( unordered_pair(X0,X1) != unordered_pair(X1,X2) ) ),
inference(superposition,[status(thm)],[c_261,c_267]) ).
tcf(c_7661,plain,
! [X0: $i] :
( ( X0 = y )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| ( unordered_pair(x,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3161,c_267]) ).
tcf(c_7677,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),subset_relation) ),
inference(demodulation,[status(thm)],[c_7477,c_4790]) ).
tcf(c_7683,plain,
! [X0: $i] :
( subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X0)
| ~ operation(null_class)
| ~ subclass(null_class,X0) ),
inference(superposition,[status(thm)],[c_5983,c_250]) ).
tcf(c_7684,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ operation(null_class)
| ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
inference(superposition,[status(thm)],[c_5983,c_170]) ).
tcf(c_7697,plain,
! [X0: $i] :
( subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X0)
| ~ operation(null_class) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7683,c_257]) ).
tcf(c_7707,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(null_class,X1)
| ( intersection(X2,X0) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_223,c_6249]) ).
tcf(c_7712,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,X2),X1)
| ( X0 = null_class )
| ~ subclass(regular(X0),X1) ),
inference(superposition,[status(thm)],[c_223,c_6249]) ).
tcf(c_7713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(cross_product(X0,X1),X3),X4),X2)
| ~ subclass(cross_product(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_193,c_6249]) ).
tcf(c_7714,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(subset_relation,X1),X0)
| ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) ),
inference(superposition,[status(thm)],[c_229,c_6249]) ).
tcf(c_7716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(null_class,X3),X2)
| ~ subclass(complement(cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_4217,c_6249]) ).
tcf(c_7717,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,X2),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4553,c_6249]) ).
tcf(c_7718,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ~ subclass(null_class,X0) ),
inference(superposition,[status(thm)],[c_4790,c_6249]) ).
tcf(c_7719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(intersection(X1,X2),X3) = X0 )
| ~ subclass(X2,X0)
| ~ subclass(X0,intersection(intersection(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_6249,c_176]) ).
tcf(c_7720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X3,X0),X4),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6249,c_250]) ).
tcf(c_7721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X4)
| ~ subclass(X2,X4)
| ~ member(X0,intersection(intersection(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_6249,c_170]) ).
tcf(c_7722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(X1,intersection(intersection(X2,X0),X3)) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6249,c_5287]) ).
tcf(c_7723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(intersection(intersection(X1,X0),X2),X3) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6249,c_5257]) ).
tcf(c_7762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(X3,intersection(intersection(X0,X1),X2)),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1)
| ( intersection(intersection(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_251,c_6250]) ).
tcf(c_7763,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(intersection(X0,X1),X2),null_class),X1)
| ( intersection(intersection(X0,X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_6250]) ).
tcf(c_7764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(X0,X3)
| ~ member(X0,intersection(X1,X2)) ),
inference(superposition,[status(thm)],[c_190,c_6250]) ).
tcf(c_7765,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(intersection(X0,X1),X2)),X1)
| ( intersection(intersection(X0,X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_6250]) ).
tcf(c_7766,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1)
| ( intersection(intersection(X0,X1),X2) = null_class )
| ~ member(intersection(intersection(X0,X1),X2),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_6250]) ).
tcf(c_7768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(intersection(X1,X2),X3)),X4)
| member(not_subclass_element(intersection(X0,intersection(intersection(X1,X2),X3)),X4),X2) ),
inference(superposition,[status(thm)],[c_4245,c_6250]) ).
tcf(c_7769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(X2,X3),X4),cross_product(X0,X1)),X5)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,X3),X4)),X5),X3) ),
inference(superposition,[status(thm)],[c_4425,c_6250]) ).
tcf(c_7770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X0,intersection(intersection(X1,X2),X3)),X4),X5)
| member(not_subclass_element(intersection(intersection(X0,intersection(intersection(X1,X2),X3)),X4),X5),X2) ),
inference(superposition,[status(thm)],[c_4430,c_6250]) ).
tcf(c_7771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(intersection(X0,X1),X2),X3),X4),X5)
| member(not_subclass_element(intersection(intersection(intersection(intersection(X0,X1),X2),X3),X4),X5),X1) ),
inference(superposition,[status(thm)],[c_4431,c_6250]) ).
tcf(c_7778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,cross_product(X1,X2))
| ~ member(X0,intersection(intersection(cross_product(X1,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_193,c_6250]) ).
tcf(c_7779,plain,
! [X0: $i,X1: $i] :
( member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,intersection(subset_relation,X1)) ),
inference(superposition,[status(thm)],[c_229,c_6250]) ).
tcf(c_7783,plain,
! [X0: $i,X1: $i] :
( member(X0,null_class)
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_4790,c_6250]) ).
tcf(c_7784,plain,
! [X0: $i,X1: $i] : ~ member(X0,intersection(null_class,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_7783,c_256]) ).
tcf(c_7897,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(null_class,X1)
| ( intersection(X0,X2) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_223,c_6782]) ).
tcf(c_7900,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,X2),X1)
| ~ subclass(complement(X0),X1) ),
inference(superposition,[status(thm)],[c_4169,c_6782]) ).
tcf(c_7901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X3,cross_product(X0,X1)),X4),X2)
| ~ subclass(cross_product(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_193,c_6782]) ).
tcf(c_7902,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,X2),X1)
| ( X0 = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_223,c_6782]) ).
tcf(c_7903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(cross_product(X2,X3),X0),X4),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_193,c_6782]) ).
tcf(c_7906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(null_class,X3),X2)
| ~ subclass(cross_product(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_4217,c_6782]) ).
tcf(c_7909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(intersection(X1,X2),X3) = X0 )
| ~ subclass(X1,X0)
| ~ subclass(X0,intersection(intersection(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_6782,c_176]) ).
tcf(c_7910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,X3),X4),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6782,c_250]) ).
tcf(c_7911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X4)
| ~ subclass(X1,X4)
| ~ member(X0,intersection(intersection(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_6782,c_170]) ).
tcf(c_7912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(X1,intersection(intersection(X0,X2),X3)) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6782,c_5287]) ).
tcf(c_7913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(intersection(intersection(X0,X1),X2),X3) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6782,c_5257]) ).
tcf(c_7947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(X3,intersection(intersection(X0,X1),X2)),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0)
| ( intersection(intersection(X0,X1),X2) = X3 ) ),
inference(superposition,[status(thm)],[c_251,c_6783]) ).
tcf(c_7948,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(intersection(X0,X1),X2),null_class),X0)
| ( intersection(intersection(X0,X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_6783]) ).
tcf(c_7949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X1)
| ~ member(X0,X3)
| ~ member(X0,intersection(X1,X2)) ),
inference(superposition,[status(thm)],[c_190,c_6783]) ).
tcf(c_7950,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(intersection(X0,X1),X2)),X0)
| ( intersection(intersection(X0,X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_6783]) ).
tcf(c_7951,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0)
| ( intersection(intersection(X0,X1),X2) = null_class )
| ~ member(intersection(intersection(X0,X1),X2),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_6783]) ).
tcf(c_7953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(intersection(X1,X2),X3)),X4)
| member(not_subclass_element(intersection(X0,intersection(intersection(X1,X2),X3)),X4),X1) ),
inference(superposition,[status(thm)],[c_4245,c_6783]) ).
tcf(c_7954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(X2,X3),X4),cross_product(X0,X1)),X5)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,X3),X4)),X5),X2) ),
inference(superposition,[status(thm)],[c_4425,c_6783]) ).
tcf(c_7955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X0,intersection(intersection(X1,X2),X3)),X4),X5)
| member(not_subclass_element(intersection(intersection(X0,intersection(intersection(X1,X2),X3)),X4),X5),X1) ),
inference(superposition,[status(thm)],[c_4430,c_6783]) ).
tcf(c_7956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(intersection(X0,X1),X2),X3),X4),X5)
| member(not_subclass_element(intersection(intersection(intersection(intersection(X0,X1),X2),X3),X4),X5),X0) ),
inference(superposition,[status(thm)],[c_4431,c_6783]) ).
tcf(c_7960,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,complement(X2))
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_4169,c_6783]) ).
tcf(c_7961,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,cross_product(X2,X3))
| ~ member(X0,intersection(intersection(X1,cross_product(X2,X3)),X4)) ),
inference(superposition,[status(thm)],[c_193,c_6783]) ).
tcf(c_7962,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ( X2 = null_class )
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_223,c_6783]) ).
tcf(c_7963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X3)
| ~ member(X0,intersection(intersection(cross_product(X1,X2),X3),X4)) ),
inference(superposition,[status(thm)],[c_193,c_6783]) ).
tcf(c_7966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,cross_product(X2,X3))
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_4217,c_6783]) ).
tcf(c_7968,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_4790,c_6783]) ).
tcf(c_8045,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),universal_class) ),
inference(superposition,[status(thm)],[c_4447,c_4336]) ).
tcf(c_8057,plain,
! [X0: $i] :
( ( X0 = x )
| ~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ( unordered_pair(X0,y) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3161,c_268]) ).
tcf(c_8060,plain,
! [X0: $i] :
( ( X0 = x )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),cross_product(universal_class,universal_class))
| ( unordered_pair(X0,y) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3161,c_268]) ).
tcf(c_8078,plain,
( operation(null_class)
| ~ function(null_class)
| ~ subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),domain_of(domain_of(null_class)))
| ( cross_product(null_class,null_class) != null_class ) ),
inference(superposition,[status(thm)],[c_5970,c_234]) ).
tcf(c_8080,plain,
( operation(null_class)
| ~ function(null_class)
| ~ subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),null_class)
| ( cross_product(null_class,null_class) != null_class ) ),
inference(light_normalisation,[status(thm)],[c_8078,c_5970]) ).
tcf(c_8091,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_183,c_187]) ).
tcf(c_8092,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_187]) ).
tcf(c_8093,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_187]) ).
tcf(c_8094,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_187]) ).
tcf(c_8096,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_261,c_187]) ).
tcf(c_8098,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_261,c_187]) ).
tcf(c_8136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),compose(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_214]) ).
tcf(c_8138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),compose(X2,X3)) ),
inference(superposition,[status(thm)],[c_261,c_214]) ).
tcf(c_8165,plain,
! [X0: $i,X1: $i] : subclass(intersection(identity_relation,cross_product(X0,X1)),domain_of(flip(cross_product(subset_relation,universal_class)))),
inference(demodulation,[status(thm)],[c_6822,c_193]) ).
tcf(c_8166,plain,
( ( complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))) = subset_relation )
| ~ subclass(complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))),subset_relation) ),
inference(superposition,[status(thm)],[c_6993,c_176]) ).
tcf(c_8167,plain,
! [X0: $i] :
( subclass(subset_relation,X0)
| ~ subclass(complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))),X0) ),
inference(superposition,[status(thm)],[c_6993,c_250]) ).
tcf(c_8168,plain,
! [X0: $i] :
( member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ member(X0,subset_relation) ),
inference(superposition,[status(thm)],[c_6993,c_170]) ).
tcf(c_8169,plain,
subclass(identity_relation,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),
inference(superposition,[status(thm)],[c_6993,c_4502]) ).
tcf(c_8185,plain,
! [X0: $i] : subclass(intersection(subset_relation,X0),universal_class),
inference(superposition,[status(thm)],[c_173,c_7273]) ).
tcf(c_8194,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,intersection(subset_relation,X0)),X1)
| member(not_subclass_element(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class))
| ( intersection(subset_relation,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_7274]) ).
tcf(c_8195,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(subset_relation,X0),null_class),cross_product(universal_class,universal_class))
| ( intersection(subset_relation,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_7274]) ).
tcf(c_8197,plain,
! [X0: $i] :
( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
| ( intersection(subset_relation,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_7274]) ).
tcf(c_8198,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(subset_relation,X0),intersection(subset_relation,X0)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ( intersection(subset_relation,X0) = null_class )
| ~ member(intersection(subset_relation,X0),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_7274]) ).
tcf(c_8199,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(subset_relation,X0),X1),X2)
| member(not_subclass_element(intersection(intersection(subset_relation,X0),X1),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_7274]) ).
tcf(c_8200,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(subset_relation,X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(subset_relation,X1)),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_7274]) ).
tcf(c_8201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(subset_relation,X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(subset_relation,X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_7274]) ).
tcf(c_8202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(subset_relation,X1)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(subset_relation,X1)),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_7274]) ).
tcf(c_8203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(subset_relation,X0),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(subset_relation,X0),X1),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_7274]) ).
tcf(c_8297,plain,
! [X0: $i] :
( ( domain_of(domain_of(flip(cross_product(null_class,universal_class)))) = X0 )
| ~ operation(null_class)
| ~ subclass(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
inference(superposition,[status(thm)],[c_7697,c_176]) ).
tcf(c_8298,plain,
! [X0: $i,X1: $i] :
( subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X1)
| ~ operation(null_class)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_7697,c_250]) ).
tcf(c_8299,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ operation(null_class)
| ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
inference(superposition,[status(thm)],[c_7697,c_170]) ).
tcf(c_8300,plain,
! [X0: $i] :
( ( intersection(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) = null_class )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_5287]) ).
tcf(c_8301,plain,
! [X0: $i] :
( ( intersection(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X0) = null_class )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_5257]) ).
tcf(c_8302,plain,
( ( domain_of(domain_of(flip(cross_product(null_class,universal_class)))) = null_class )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_258]) ).
tcf(c_8328,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(X1))
| member(not_subclass_element(X0,complement(X1)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4465,c_4388]) ).
tcf(c_8335,plain,
! [X0: $i] :
( subclass(X0,complement(universal_class))
| member(not_subclass_element(X0,null_class),universal_class) ),
inference(superposition,[status(thm)],[c_4953,c_8328]) ).
tcf(c_8336,plain,
! [X0: $i] : subclass(X0,complement(null_class)),
inference(superposition,[status(thm)],[c_8328,c_256]) ).
tcf(c_8337,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(X1))
| member(not_subclass_element(X0,complement(X1)),universal_class) ),
inference(superposition,[status(thm)],[c_8328,c_4336]) ).
tcf(c_8338,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,complement(unordered_pair(X1,X2)))
| ( not_subclass_element(X0,complement(unordered_pair(X1,X2))) = X2 )
| ( not_subclass_element(X0,complement(unordered_pair(X1,X2))) = X1 ) ),
inference(superposition,[status(thm)],[c_8328,c_177]) ).
tcf(c_8339,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,complement(cross_product(X1,X2)))
| ( unordered_pair(unordered_pair(first(not_subclass_element(X0,complement(cross_product(X1,X2)))),first(not_subclass_element(X0,complement(cross_product(X1,X2))))),unordered_pair(first(not_subclass_element(X0,complement(cross_product(X1,X2)))),unordered_pair(second(not_subclass_element(X0,complement(cross_product(X1,X2)))),second(not_subclass_element(X0,complement(cross_product(X1,X2))))))) = not_subclass_element(X0,complement(cross_product(X1,X2))) ) ),
inference(superposition,[status(thm)],[c_8328,c_184]) ).
tcf(c_8340,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,complement(intersection(X1,X2)))
| member(not_subclass_element(X0,complement(intersection(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_8328,c_189]) ).
tcf(c_8341,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,complement(intersection(X1,X2)))
| member(not_subclass_element(X0,complement(intersection(X1,X2))),X1) ),
inference(superposition,[status(thm)],[c_8328,c_188]) ).
tcf(c_8342,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(complement(X1)))
| ~ member(not_subclass_element(X0,complement(complement(X1))),X1) ),
inference(superposition,[status(thm)],[c_8328,c_191]) ).
tcf(c_8343,plain,
! [X0: $i] : subclass(complement(X0),complement(X0)),
inference(superposition,[status(thm)],[c_8328,c_4264]) ).
tcf(c_8344,plain,
! [X0: $i] :
( subclass(X0,complement(identity_relation))
| member(not_subclass_element(X0,complement(identity_relation)),subset_relation) ),
inference(superposition,[status(thm)],[c_8328,c_4293]) ).
tcf(c_8345,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,complement(compose(X1,X2)))
| member(not_subclass_element(X0,complement(compose(X1,X2))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_4341]) ).
tcf(c_8346,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,complement(unordered_pair(X1,X1)))
| member(not_subclass_element(X0,complement(unordered_pair(X1,X1))),unordered_pair(X2,X1)) ),
inference(superposition,[status(thm)],[c_8328,c_4344]) ).
tcf(c_8347,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,complement(unordered_pair(X1,X1)))
| member(not_subclass_element(X0,complement(unordered_pair(X1,X1))),unordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c_8328,c_4343]) ).
tcf(c_8348,plain,
! [X0: $i] :
( subclass(X0,complement(unordered_pair(x,x)))
| member(not_subclass_element(X0,complement(unordered_pair(x,x))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8328,c_4346]) ).
tcf(c_8349,plain,
! [X0: $i] :
( subclass(X0,complement(unordered_pair(y,y)))
| member(not_subclass_element(X0,complement(unordered_pair(y,y))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8328,c_4347]) ).
tcf(c_8350,plain,
! [X0: $i,X1: $i] : subclass(intersection(complement(X0),X1),complement(X0)),
inference(superposition,[status(thm)],[c_8328,c_4432]) ).
tcf(c_8351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X0,complement(intersection(intersection(X1,X2),X3)))
| member(not_subclass_element(X0,complement(intersection(intersection(X1,X2),X3))),X1) ),
inference(superposition,[status(thm)],[c_8328,c_6783]) ).
tcf(c_8352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X0,complement(intersection(intersection(X1,X2),X3)))
| member(not_subclass_element(X0,complement(intersection(intersection(X1,X2),X3))),X2) ),
inference(superposition,[status(thm)],[c_8328,c_6250]) ).
tcf(c_8353,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(identity_relation,X1)))
| member(not_subclass_element(X0,complement(intersection(identity_relation,X1))),subset_relation) ),
inference(superposition,[status(thm)],[c_8328,c_6318]) ).
tcf(c_8354,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(subset_relation,X1)))
| member(not_subclass_element(X0,complement(intersection(subset_relation,X1))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_7274]) ).
tcf(c_8355,plain,
! [X0: $i] :
( subclass(X0,null_class)
| member(not_subclass_element(X0,null_class),universal_class) ),
inference(light_normalisation,[status(thm)],[c_8335,c_4953]) ).
tcf(c_8441,plain,
! [X0: $i,X1: $i] :
( homomorphism(X0,null_class,X1)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,null_class,X1),not_homomorphism1(X0,null_class,X1)),unordered_pair(not_homomorphism1(X0,null_class,X1),unordered_pair(not_homomorphism2(X0,null_class,X1),not_homomorphism2(X0,null_class,X1)))),null_class)
| ~ operation(null_class)
| ~ operation(X1)
| ~ compatible(X0,null_class,X1) ),
inference(superposition,[status(thm)],[c_5970,c_243]) ).
tcf(c_8442,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(X0,X1,X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),universal_class)
| ~ operation(X2)
| ~ operation(X1)
| ~ compatible(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_243,c_4336]) ).
tcf(c_8443,plain,
! [X0: $i,X1: $i] :
( homomorphism(X0,null_class,X1)
| ~ operation(null_class)
| ~ operation(X1)
| ~ compatible(X0,null_class,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8441,c_256]) ).
tcf(c_8456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_215]) ).
tcf(c_8457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
| ( domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))) = X3 )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_251,c_215]) ).
tcf(c_8458,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),null_class),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),null_class)))),compose(X1,X2))
| ( domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))) = null_class )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),null_class),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),null_class)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_259,c_215]) ).
tcf(c_8459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ( intersection(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),cross_product(unordered_pair(X1,X1),universal_class)) = null_class )
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_195,c_215]) ).
tcf(c_8460,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
| ( domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))) = null_class )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_222,c_215]) ).
tcf(c_8461,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,X2))
| ( domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))) = null_class )
| ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_225,c_215]) ).
tcf(c_8462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( homomorphism(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4))))))),compose(X2,X3))
| ~ operation(X4)
| ~ operation(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))
| ~ compatible(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),X4))))))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_243,c_215]) ).
tcf(c_8463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),X4)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_215]) ).
tcf(c_8464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X4)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X4)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_215]) ).
tcf(c_8465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),cross_product(X1,X2)),X5)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(cross_product(X1,X2),domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X5),not_subclass_element(intersection(cross_product(X1,X2),domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X5)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(cross_product(X1,X2),domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X5),not_subclass_element(intersection(cross_product(X1,X2),domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X5)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_215]) ).
tcf(c_8466,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X4),X5)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X4),X5),not_subclass_element(intersection(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X4),X5)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X4),X5),not_subclass_element(intersection(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X4),X5)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_215]) ).
tcf(c_8467,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),X4),X5)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),X4),X5),not_subclass_element(intersection(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),X4),X5)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),X4),X5),not_subclass_element(intersection(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),X4),X5)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_215]) ).
tcf(c_8468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X1,complement(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,complement(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),not_subclass_element(X1,complement(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,complement(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),not_subclass_element(X1,complement(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_215]) ).
tcf(c_8469,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(complement(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),X2))
| ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4169,c_215]) ).
tcf(c_8470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),compose(cross_product(X3,X4),X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class),cross_product(X3,X4)),universal_class))))) ),
inference(superposition,[status(thm)],[c_193,c_215]) ).
tcf(c_8471,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),compose(X3,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class),X3),universal_class))))) ),
inference(superposition,[status(thm)],[c_193,c_215]) ).
tcf(c_8472,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(null_class,X2))
| ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4553,c_215]) ).
tcf(c_8473,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),compose(X1,complement(cross_product(unordered_pair(X2,X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_4169,c_215]) ).
tcf(c_8474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),compose(X1,cross_product(X3,X4)))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),cross_product(X3,X4)),universal_class)))),universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_193,c_215]) ).
tcf(c_8475,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),compose(X1,X3))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X3),universal_class)))),universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_193,c_215]) ).
tcf(c_8476,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),compose(X1,null_class))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_4553,c_215]) ).
tcf(c_8612,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(X0,universal_class)
| ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class) ),
inference(superposition,[status(thm)],[c_183,c_204]) ).
tcf(c_8613,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_204]) ).
tcf(c_8614,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_204]) ).
tcf(c_8616,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_204]) ).
tcf(c_8617,plain,
( member(unordered_pair(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,unordered_pair(complement(intersection(complement(universal_class),complement(unordered_pair(universal_class,universal_class)))),complement(intersection(complement(universal_class),complement(unordered_pair(universal_class,universal_class))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,unordered_pair(complement(intersection(null_class,complement(unordered_pair(universal_class,universal_class)))),complement(intersection(null_class,complement(unordered_pair(universal_class,universal_class))))))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4953,c_204]) ).
tcf(c_8622,plain,
( member(unordered_pair(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,unordered_pair(complement(intersection(null_class,complement(unordered_pair(universal_class,universal_class)))),complement(intersection(null_class,complement(unordered_pair(universal_class,universal_class))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,unordered_pair(complement(intersection(null_class,complement(unordered_pair(universal_class,universal_class)))),complement(intersection(null_class,complement(unordered_pair(universal_class,universal_class))))))),cross_product(universal_class,universal_class)) ),
inference(light_normalisation,[status(thm)],[c_8617,c_4953]) ).
tcf(c_8671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2)),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),rotate(X3)) ),
inference(superposition,[status(thm)],[c_261,c_197]) ).
tcf(c_8681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),rotate(X3)) ),
inference(superposition,[status(thm)],[c_261,c_197]) ).
tcf(c_8683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),unordered_pair(X2,X2))),rotate(X3)) ),
inference(superposition,[status(thm)],[c_261,c_197]) ).
tcf(c_8685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),unordered_pair(X2,X2))),rotate(X3)) ),
inference(superposition,[status(thm)],[c_261,c_197]) ).
tcf(c_8699,plain,
! [X0: $i] :
( ( complement(null_class) = X0 )
| ~ subclass(complement(null_class),X0) ),
inference(superposition,[status(thm)],[c_8336,c_176]) ).
tcf(c_8700,plain,
! [X0: $i,X1: $i] :
( subclass(X1,X0)
| ~ subclass(complement(null_class),X0) ),
inference(superposition,[status(thm)],[c_8336,c_250]) ).
tcf(c_8701,plain,
! [X0: $i,X1: $i] :
( member(X0,complement(null_class))
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_8336,c_170]) ).
tcf(c_8703,plain,
complement(null_class) = universal_class,
inference(superposition,[status(thm)],[c_8336,c_4708]) ).
tcf(c_8739,plain,
( member(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(complement(intersection(complement(null_class),complement(unordered_pair(null_class,null_class)))),complement(intersection(complement(null_class),complement(unordered_pair(null_class,null_class))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(complement(intersection(universal_class,complement(unordered_pair(null_class,null_class)))),complement(intersection(universal_class,complement(unordered_pair(null_class,null_class))))))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_8703,c_204]) ).
tcf(c_8740,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(null_class),X0),X1)
| ~ member(not_subclass_element(intersection(universal_class,X0),X1),null_class) ),
inference(superposition,[status(thm)],[c_8703,c_4432]) ).
tcf(c_8741,plain,
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,universal_class)),universal_class))))),universal_class)
| ~ member(null_class,universal_class) ),
inference(superposition,[status(thm)],[c_8703,c_212]) ).
tcf(c_8742,plain,
( ( complement(null_class) = null_class )
| ~ member(regular(universal_class),null_class) ),
inference(superposition,[status(thm)],[c_8703,c_4265]) ).
tcf(c_8743,plain,
! [X0: $i] :
( subclass(complement(null_class),X0)
| ~ member(not_subclass_element(universal_class,X0),null_class) ),
inference(superposition,[status(thm)],[c_8703,c_4264]) ).
tcf(c_8744,plain,
intersection(universal_class,null_class) = null_class,
inference(superposition,[status(thm)],[c_8703,c_4169]) ).
tcf(c_8745,plain,
! [X0: $i] :
( subclass(X0,complement(null_class))
| member(not_subclass_element(X0,universal_class),null_class) ),
inference(superposition,[status(thm)],[c_8703,c_8328]) ).
tcf(c_8748,plain,
! [X0: $i] :
( subclass(X0,universal_class)
| member(not_subclass_element(X0,universal_class),null_class) ),
inference(light_normalisation,[status(thm)],[c_8745,c_8703]) ).
tcf(c_8749,plain,
! [X0: $i] :
( subclass(universal_class,X0)
| ~ member(not_subclass_element(universal_class,X0),null_class) ),
inference(light_normalisation,[status(thm)],[c_8743,c_8703]) ).
tcf(c_8750,plain,
( ( universal_class = null_class )
| ~ member(regular(universal_class),null_class) ),
inference(light_normalisation,[status(thm)],[c_8742,c_8703]) ).
tcf(c_8751,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(universal_class,X0),X1)
| ~ member(not_subclass_element(intersection(universal_class,X0),X1),null_class) ),
inference(light_normalisation,[status(thm)],[c_8740,c_8703]) ).
tcf(c_8752,plain,
member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,universal_class)),universal_class))))),universal_class),
inference(forward_subsumption_resolution,[status(thm)],[c_8741,c_260]) ).
tcf(c_8753,plain,
( member(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(complement(intersection(universal_class,complement(unordered_pair(null_class,null_class)))),complement(intersection(universal_class,complement(unordered_pair(null_class,null_class))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(complement(intersection(universal_class,complement(unordered_pair(null_class,null_class)))),complement(intersection(universal_class,complement(unordered_pair(null_class,null_class))))))),cross_product(universal_class,universal_class)) ),
inference(light_normalisation,[status(thm)],[c_8739,c_8703]) ).
tcf(c_8762,plain,
! [X0: $i] :
( subclass(X0,complement(identity_relation))
| member(not_subclass_element(X0,complement(identity_relation)),universal_class) ),
inference(superposition,[status(thm)],[c_8344,c_4336]) ).
tcf(c_8763,plain,
subclass(complement(subset_relation),complement(identity_relation)),
inference(superposition,[status(thm)],[c_8344,c_4264]) ).
tcf(c_8764,plain,
! [X0: $i] : subclass(intersection(complement(subset_relation),X0),complement(identity_relation)),
inference(superposition,[status(thm)],[c_8344,c_4432]) ).
tcf(c_8769,plain,
( ( complement(identity_relation) = complement(subset_relation) )
| ~ subclass(complement(identity_relation),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_8763,c_176]) ).
tcf(c_8770,plain,
! [X0: $i] :
( subclass(complement(subset_relation),X0)
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_8763,c_250]) ).
tcf(c_8771,plain,
! [X0: $i] :
( member(X0,complement(identity_relation))
| ~ member(X0,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_8763,c_170]) ).
tcf(c_8781,plain,
( subclass(null_class,complement(identity_relation))
| ( complement(subset_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_8764]) ).
tcf(c_8782,plain,
subclass(null_class,complement(identity_relation)),
inference(superposition,[status(thm)],[c_4790,c_8764]) ).
tcf(c_8783,plain,
! [X0: $i] :
( ( intersection(complement(subset_relation),X0) = complement(identity_relation) )
| ~ subclass(complement(identity_relation),intersection(complement(subset_relation),X0)) ),
inference(superposition,[status(thm)],[c_8764,c_176]) ).
tcf(c_8784,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(subset_relation),X1),X0)
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_8764,c_250]) ).
tcf(c_8785,plain,
! [X0: $i,X1: $i] :
( member(X0,complement(identity_relation))
| ~ member(X0,intersection(complement(subset_relation),X1)) ),
inference(superposition,[status(thm)],[c_8764,c_170]) ).
tcf(c_8800,plain,
subclass(complement(subset_relation),universal_class),
inference(superposition,[status(thm)],[c_173,c_8770]) ).
tcf(c_8801,plain,
( subclass(complement(subset_relation),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4571,c_8770]) ).
tcf(c_8802,plain,
( subclass(complement(subset_relation),cross_product(universal_class,universal_class))
| ~ function(complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_218,c_8770]) ).
tcf(c_8812,plain,
! [X0: $i] :
( subclass(complement(subset_relation),X0)
| member(not_subclass_element(complement(subset_relation),X0),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_171,c_8771]) ).
tcf(c_8813,plain,
! [X0: $i] :
( member(not_subclass_element(X0,complement(subset_relation)),X0)
| member(not_subclass_element(complement(subset_relation),X0),complement(identity_relation))
| ( complement(subset_relation) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_8771]) ).
tcf(c_8814,plain,
( member(not_subclass_element(complement(subset_relation),null_class),complement(identity_relation))
| ( complement(subset_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_8771]) ).
tcf(c_8815,plain,
! [X0: $i] :
( member(X0,subset_relation)
| member(X0,complement(identity_relation))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_192,c_8771]) ).
tcf(c_8816,plain,
( member(regular(complement(subset_relation)),complement(identity_relation))
| ( complement(subset_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_8771]) ).
tcf(c_8817,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(subset_relation),complement(subset_relation)),universal_class)),universal_class))))))),complement(identity_relation))
| ( complement(subset_relation) = null_class )
| ~ member(complement(subset_relation),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_8771]) ).
tcf(c_8818,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(subset_relation),X0),X1)
| member(not_subclass_element(intersection(complement(subset_relation),X0),X1),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4224,c_8771]) ).
tcf(c_8819,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(subset_relation)),X1)
| member(not_subclass_element(intersection(X0,complement(subset_relation)),X1),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4245,c_8771]) ).
tcf(c_8820,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(subset_relation),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),complement(subset_relation)),X2),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4425,c_8771]) ).
tcf(c_8821,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,complement(subset_relation)),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,complement(subset_relation)),X1),X2),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4430,c_8771]) ).
tcf(c_8822,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(complement(subset_relation),X0),X1),X2)
| member(not_subclass_element(intersection(intersection(complement(subset_relation),X0),X1),X2),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4431,c_8771]) ).
tcf(c_8823,plain,
! [X0: $i] :
( subclass(X0,complement(complement(subset_relation)))
| member(not_subclass_element(X0,complement(complement(subset_relation))),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_8328,c_8771]) ).
tcf(c_8930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_193,c_4638]) ).
tcf(c_8931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),X2),X3),X2) ),
inference(superposition,[status(thm)],[c_193,c_4638]) ).
tcf(c_8932,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),null_class)
| subclass(intersection(cross_product(X0,X1),null_class),X2) ),
inference(superposition,[status(thm)],[c_4553,c_4638]) ).
tcf(c_8933,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X1,X2),X0),X0)
| ( intersection(X0,cross_product(X1,X2)) = X0 )
| ~ member(not_subclass_element(X0,intersection(X0,cross_product(X1,X2))),intersection(X0,cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_4638,c_254]) ).
tcf(c_8934,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X1,X2),X0),X0)
| member(not_subclass_element(X0,intersection(X0,cross_product(X1,X2))),X0)
| ( intersection(X0,cross_product(X1,X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_4638,c_253]) ).
tcf(c_8938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X2,X3),unordered_pair(X0,X1)),X4)
| ( not_subclass_element(intersection(unordered_pair(X0,X1),cross_product(X2,X3)),X4) = X1 )
| ( not_subclass_element(intersection(unordered_pair(X0,X1),cross_product(X2,X3)),X4) = X0 ) ),
inference(superposition,[status(thm)],[c_4638,c_177]) ).
tcf(c_8940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X2,X3),intersection(X0,X1)),X4)
| member(not_subclass_element(intersection(intersection(X0,X1),cross_product(X2,X3)),X4),X1) ),
inference(superposition,[status(thm)],[c_4638,c_189]) ).
tcf(c_8941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X2,X3),intersection(X0,X1)),X4)
| member(not_subclass_element(intersection(intersection(X0,X1),cross_product(X2,X3)),X4),X0) ),
inference(superposition,[status(thm)],[c_4638,c_188]) ).
tcf(c_8942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),complement(X0)),X3)
| ~ member(not_subclass_element(intersection(complement(X0),cross_product(X1,X2)),X3),X0) ),
inference(superposition,[status(thm)],[c_4638,c_191]) ).
tcf(c_8943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(cross_product(X3,X4),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),X5)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),cross_product(X3,X4)),X5),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),cross_product(X3,X4)),X5)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),cross_product(X3,X4)),X5),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),cross_product(X3,X4)),X5)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_215]) ).
tcf(c_8944,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),identity_relation),X2)
| member(not_subclass_element(intersection(identity_relation,cross_product(X0,X1)),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4638,c_4293]) ).
tcf(c_8945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X2,X3),compose(X0,X1)),X4)
| member(not_subclass_element(intersection(compose(X0,X1),cross_product(X2,X3)),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_4341]) ).
tcf(c_8946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X1,X2),unordered_pair(X0,X0)),X3)
| member(not_subclass_element(intersection(unordered_pair(X0,X0),cross_product(X1,X2)),X3),unordered_pair(X4,X0)) ),
inference(superposition,[status(thm)],[c_4638,c_4344]) ).
tcf(c_8947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X1,X2),unordered_pair(X0,X0)),X3)
| member(not_subclass_element(intersection(unordered_pair(X0,X0),cross_product(X1,X2)),X3),unordered_pair(X0,X4)) ),
inference(superposition,[status(thm)],[c_4638,c_4343]) ).
tcf(c_8948,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),unordered_pair(x,x)),X2)
| member(not_subclass_element(intersection(unordered_pair(x,x),cross_product(X0,X1)),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4638,c_4346]) ).
tcf(c_8949,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),unordered_pair(y,y)),X2)
| member(not_subclass_element(intersection(unordered_pair(y,y),cross_product(X0,X1)),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4638,c_4347]) ).
tcf(c_8950,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(cross_product(X3,X4),intersection(intersection(X0,X1),X2)),X5)
| member(not_subclass_element(intersection(intersection(intersection(X0,X1),X2),cross_product(X3,X4)),X5),X0) ),
inference(superposition,[status(thm)],[c_4638,c_6783]) ).
tcf(c_8951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(cross_product(X3,X4),intersection(intersection(X0,X1),X2)),X5)
| member(not_subclass_element(intersection(intersection(intersection(X0,X1),X2),cross_product(X3,X4)),X5),X1) ),
inference(superposition,[status(thm)],[c_4638,c_6250]) ).
tcf(c_8952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(identity_relation,X0)),X3)
| member(not_subclass_element(intersection(intersection(identity_relation,X0),cross_product(X1,X2)),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4638,c_6318]) ).
tcf(c_8953,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(subset_relation,X0)),X3)
| member(not_subclass_element(intersection(intersection(subset_relation,X0),cross_product(X1,X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_7274]) ).
tcf(c_8954,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),complement(subset_relation)),X2)
| member(not_subclass_element(intersection(complement(subset_relation),cross_product(X0,X1)),X2),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4638,c_8771]) ).
tcf(c_9074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2)),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),flip(X3)) ),
inference(superposition,[status(thm)],[c_261,c_200]) ).
tcf(c_9084,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),flip(X3)) ),
inference(superposition,[status(thm)],[c_261,c_200]) ).
tcf(c_9086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),unordered_pair(X2,X2))),flip(X3)) ),
inference(superposition,[status(thm)],[c_261,c_200]) ).
tcf(c_9088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),unordered_pair(X2,X2))),flip(X3)) ),
inference(superposition,[status(thm)],[c_261,c_200]) ).
tcf(c_9108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X3))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),X3) ),
inference(superposition,[status(thm)],[c_183,c_198]) ).
tcf(c_9109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2)),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_261,c_198]) ).
tcf(c_9119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_261,c_198]) ).
tcf(c_9121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_261,c_198]) ).
tcf(c_9123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_261,c_198]) ).
tcf(c_9160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),X3) ),
inference(superposition,[status(thm)],[c_183,c_201]) ).
tcf(c_9161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2)),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_261,c_201]) ).
tcf(c_9171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_261,c_201]) ).
tcf(c_9173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_261,c_201]) ).
tcf(c_9175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_261,c_201]) ).
tcf(c_9221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(X3,cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) )
| ~ homomorphism(X2,X3,X4)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ),
inference(superposition,[status(thm)],[c_195,c_242]) ).
tcf(c_9222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( homomorphism(X0,X1,X2)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) )
| ~ operation(X2)
| ~ operation(X1)
| ~ homomorphism(X3,X1,X4)
| ~ compatible(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_243,c_242]) ).
tcf(c_9223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) )
| ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation) ),
inference(superposition,[status(thm)],[c_4294,c_242]) ).
tcf(c_9224,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) )
| ~ homomorphism(X3,X2,X4)
| ~ member(unordered_pair(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(X0,X0)),domain_of(X2)) ),
inference(superposition,[status(thm)],[c_261,c_242]) ).
tcf(c_9226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) )
| ~ homomorphism(X3,X2,X4)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(unordered_pair(X1,X1),X0)),domain_of(X2)) ),
inference(superposition,[status(thm)],[c_261,c_242]) ).
tcf(c_9228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) )
| ~ homomorphism(X2,null_class,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),null_class) ),
inference(superposition,[status(thm)],[c_5970,c_242]) ).
tcf(c_9238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class)) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X4,X4),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X4,X4),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X4,X4),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X4,X4),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) )
| ~ homomorphism(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9221,c_180]) ).
tcf(c_9257,plain,
( ( cross_product(universal_class,universal_class) = complement(subset_relation) )
| ~ function(complement(identity_relation))
| ~ subclass(cross_product(universal_class,universal_class),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_8802,c_176]) ).
tcf(c_9258,plain,
! [X0: $i] :
( subclass(complement(subset_relation),X0)
| ~ function(complement(identity_relation))
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_8802,c_250]) ).
tcf(c_9259,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ function(complement(identity_relation))
| ~ member(X0,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_8802,c_170]) ).
tcf(c_9271,plain,
( ( complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))) = identity_relation )
| ~ subclass(complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))),identity_relation) ),
inference(superposition,[status(thm)],[c_8169,c_176]) ).
tcf(c_9272,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ~ subclass(complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))),X0) ),
inference(superposition,[status(thm)],[c_8169,c_250]) ).
tcf(c_9273,plain,
! [X0: $i] :
( member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ member(X0,identity_relation) ),
inference(superposition,[status(thm)],[c_8169,c_170]) ).
tcf(c_9325,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(subset_relation),X1) = X0 )
| ~ subclass(complement(identity_relation),X0)
| ~ subclass(X0,intersection(complement(subset_relation),X1)) ),
inference(superposition,[status(thm)],[c_8784,c_176]) ).
tcf(c_9326,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(subset_relation),X2),X1)
| ~ subclass(X0,X1)
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_8784,c_250]) ).
tcf(c_9327,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(complement(identity_relation),X2)
| ~ member(X0,intersection(complement(subset_relation),X1)) ),
inference(superposition,[status(thm)],[c_8784,c_170]) ).
tcf(c_9328,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(complement(subset_relation),X1)) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_8784,c_5287]) ).
tcf(c_9329,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(complement(subset_relation),X0),X1) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_8784,c_5257]) ).
tcf(c_9330,plain,
! [X0: $i] :
( ( intersection(complement(subset_relation),X0) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_8784,c_258]) ).
tcf(c_9357,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,intersection(complement(subset_relation),X0)),X1)
| member(not_subclass_element(intersection(complement(subset_relation),X0),X1),complement(identity_relation))
| ( intersection(complement(subset_relation),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_8785]) ).
tcf(c_9358,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(complement(subset_relation),X0),null_class),complement(identity_relation))
| ( intersection(complement(subset_relation),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_8785]) ).
tcf(c_9359,plain,
! [X0: $i,X1: $i] :
( member(X0,complement(identity_relation))
| ~ member(X0,X1)
| ~ member(X0,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_190,c_8785]) ).
tcf(c_9360,plain,
! [X0: $i] :
( member(regular(intersection(complement(subset_relation),X0)),complement(identity_relation))
| ( intersection(complement(subset_relation),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_8785]) ).
tcf(c_9361,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(subset_relation),X0),intersection(complement(subset_relation),X0)),universal_class)),universal_class))))))),complement(identity_relation))
| ( intersection(complement(subset_relation),X0) = null_class )
| ~ member(intersection(complement(subset_relation),X0),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_8785]) ).
tcf(c_9363,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(complement(subset_relation),X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(complement(subset_relation),X1)),X2),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4245,c_8785]) ).
tcf(c_9364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(complement(subset_relation),X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(complement(subset_relation),X2)),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4425,c_8785]) ).
tcf(c_9365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(complement(subset_relation),X1)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(complement(subset_relation),X1)),X2),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4430,c_8785]) ).
tcf(c_9366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(complement(subset_relation),X0),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(complement(subset_relation),X0),X1),X2),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4431,c_8785]) ).
tcf(c_9367,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(complement(subset_relation),X1)))
| member(not_subclass_element(X0,complement(intersection(complement(subset_relation),X1))),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_8328,c_8785]) ).
tcf(c_9368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(complement(subset_relation),X0)),X3)
| member(not_subclass_element(intersection(intersection(complement(subset_relation),X0),cross_product(X1,X2)),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4638,c_8785]) ).
tcf(c_9450,plain,
! [X0: $i] :
( subclass(complement(subset_relation),X0)
| member(not_subclass_element(complement(subset_relation),X0),universal_class) ),
inference(superposition,[status(thm)],[c_8812,c_4336]) ).
tcf(c_9451,plain,
! [X0: $i] :
( subclass(complement(subset_relation),X0)
| ~ member(not_subclass_element(complement(subset_relation),X0),identity_relation) ),
inference(superposition,[status(thm)],[c_8812,c_191]) ).
tcf(c_9464,plain,
! [X0: $i] :
( member(not_subclass_element(X0,complement(identity_relation)),subset_relation)
| ( complement(identity_relation) = X0 )
| ~ member(not_subclass_element(X0,complement(identity_relation)),universal_class)
| ~ member(not_subclass_element(complement(identity_relation),X0),X0) ),
inference(superposition,[status(thm)],[c_8815,c_254]) ).
tcf(c_9465,plain,
! [X0: $i] :
( member(not_subclass_element(X0,complement(identity_relation)),subset_relation)
| member(not_subclass_element(complement(identity_relation),X0),complement(identity_relation))
| ( complement(identity_relation) = X0 )
| ~ member(not_subclass_element(X0,complement(identity_relation)),universal_class) ),
inference(superposition,[status(thm)],[c_8815,c_253]) ).
tcf(c_9469,plain,
! [X0: $i] :
( subclass(complement(complement(identity_relation)),X0)
| member(not_subclass_element(complement(complement(identity_relation)),X0),subset_relation)
| ~ member(not_subclass_element(complement(complement(identity_relation)),X0),universal_class) ),
inference(superposition,[status(thm)],[c_8815,c_4264]) ).
tcf(c_9470,plain,
( member(regular(complement(complement(identity_relation))),subset_relation)
| ( complement(complement(identity_relation)) = null_class )
| ~ member(regular(complement(complement(identity_relation))),universal_class) ),
inference(superposition,[status(thm)],[c_8815,c_4265]) ).
tcf(c_9471,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(complement(identity_relation)),X0),X1)
| member(not_subclass_element(intersection(complement(complement(identity_relation)),X0),X1),subset_relation)
| ~ member(not_subclass_element(intersection(complement(complement(identity_relation)),X0),X1),universal_class) ),
inference(superposition,[status(thm)],[c_8815,c_4432]) ).
tcf(c_9516,plain,
( member(regular(complement(subset_relation)),universal_class)
| ( complement(subset_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_8816,c_4336]) ).
tcf(c_9517,plain,
( ( complement(subset_relation) = null_class )
| ~ member(regular(complement(subset_relation)),identity_relation) ),
inference(superposition,[status(thm)],[c_8816,c_191]) ).
tcf(c_9531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,cross_product(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_193,c_4640]) ).
tcf(c_9532,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),cross_product(X0,X1))
| subclass(intersection(regular(cross_product(X0,X1)),cross_product(X0,X1)),X2)
| ( cross_product(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4640]) ).
tcf(c_9534,plain,
! [X0: $i] :
( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
| subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),cross_product(universal_class,universal_class)),X0) ),
inference(superposition,[status(thm)],[c_229,c_4640]) ).
tcf(c_9535,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),cross_product(X0,X1))
| subclass(intersection(complement(cross_product(X0,X1)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_4217,c_4640]) ).
tcf(c_9536,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X1,X2)),X0)
| member(not_subclass_element(null_class,X0),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_4790,c_4640]) ).
tcf(c_9537,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),cross_product(X0,X1))
| ( intersection(cross_product(X0,X1),X2) = cross_product(X0,X1) )
| ~ member(not_subclass_element(cross_product(X0,X1),intersection(cross_product(X0,X1),X2)),intersection(cross_product(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_4640,c_254]) ).
tcf(c_9538,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),cross_product(X0,X1))
| member(not_subclass_element(cross_product(X0,X1),intersection(cross_product(X0,X1),X2)),cross_product(X0,X1))
| ( intersection(cross_product(X0,X1),X2) = cross_product(X0,X1) ) ),
inference(superposition,[status(thm)],[c_4640,c_253]) ).
tcf(c_9541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),X3)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) = not_subclass_element(intersection(cross_product(X0,X1),X2),X3) ) ),
inference(superposition,[status(thm)],[c_4640,c_184]) ).
tcf(c_9576,plain,
! [X0: $i,X1: $i] :
( homomorphism(X0,X1,null_class)
| ~ operation(null_class)
| ~ operation(X1)
| ~ compatible(X0,X1,null_class)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,null_class),not_homomorphism1(X0,X1,null_class)),unordered_pair(not_homomorphism1(X0,X1,null_class),unordered_pair(not_homomorphism2(X0,X1,null_class),not_homomorphism2(X0,X1,null_class)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,null_class),not_homomorphism1(X0,X1,null_class)),unordered_pair(not_homomorphism1(X0,X1,null_class),unordered_pair(not_homomorphism2(X0,X1,null_class),not_homomorphism2(X0,X1,null_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,null_class),not_homomorphism1(X0,X1,null_class)),unordered_pair(not_homomorphism1(X0,X1,null_class),unordered_pair(not_homomorphism2(X0,X1,null_class),not_homomorphism2(X0,X1,null_class)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,null_class),not_homomorphism1(X0,X1,null_class)),unordered_pair(not_homomorphism1(X0,X1,null_class),unordered_pair(not_homomorphism2(X0,X1,null_class),not_homomorphism2(X0,X1,null_class))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_4553,c_244]) ).
tcf(c_9582,plain,
! [X0: $i,X1: $i] :
( homomorphism(null_class,X1,X0)
| ~ operation(X1)
| ~ operation(X0)
| ~ compatible(null_class,X1,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),unordered_pair(not_homomorphism1(null_class,X1,X0),unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)))),unordered_pair(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),unordered_pair(not_homomorphism1(null_class,X1,X0),unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),unordered_pair(not_homomorphism1(null_class,X1,X0),unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)))),unordered_pair(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),unordered_pair(not_homomorphism1(null_class,X1,X0),unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_4553,c_244]) ).
tcf(c_9585,plain,
! [X0: $i,X1: $i] :
( homomorphism(null_class,X1,X0)
| ~ operation(X1)
| ~ operation(X0)
| ~ compatible(null_class,X1,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),unordered_pair(not_homomorphism1(null_class,X1,X0),unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)))),unordered_pair(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),unordered_pair(not_homomorphism1(null_class,X1,X0),unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),unordered_pair(not_homomorphism1(null_class,X1,X0),unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)))),unordered_pair(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),unordered_pair(not_homomorphism1(null_class,X1,X0),unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_4553,c_244]) ).
tcf(c_9587,plain,
! [X0: $i,X1: $i] :
( homomorphism(null_class,X1,X0)
| ~ operation(X1)
| ~ operation(X0)
| ~ compatible(null_class,X1,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism1(null_class,X1,X0),not_homomorphism1(null_class,X1,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(null_class,cross_product(unordered_pair(not_homomorphism2(null_class,X1,X0),not_homomorphism2(null_class,X1,X0)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_4553,c_244]) ).
tcf(c_9697,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(X2,cross_product(X0,X1))),cross_product(X0,X1))
| ( intersection(cross_product(X0,X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_193,c_4225]) ).
tcf(c_9699,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(cross_product(X1,X2),X0)),X0)
| ( intersection(X0,cross_product(X1,X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_193,c_4225]) ).
tcf(c_9700,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| ( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_229,c_4225]) ).
tcf(c_9701,plain,
( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ( intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_230,c_4225]) ).
tcf(c_9706,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),universal_class)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_4336]) ).
tcf(c_9707,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(unordered_pair(X0,X1),X2) = null_class )
| ( regular(intersection(unordered_pair(X0,X1),X2)) = X1 )
| ( regular(intersection(unordered_pair(X0,X1),X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_4225,c_177]) ).
tcf(c_9708,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(cross_product(X0,X1),X2) = null_class )
| ( unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) = regular(intersection(cross_product(X0,X1),X2)) ) ),
inference(superposition,[status(thm)],[c_4225,c_184]) ).
tcf(c_9711,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(X0),X1) = null_class )
| ~ member(regular(intersection(complement(X0),X1)),X0) ),
inference(superposition,[status(thm)],[c_4225,c_191]) ).
tcf(c_9712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
| ( intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3) = null_class )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4225,c_215]) ).
tcf(c_9714,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(compose(X0,X1),X2)),cross_product(universal_class,universal_class))
| ( intersection(compose(X0,X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_4341]) ).
tcf(c_9715,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(unordered_pair(X0,X0),X1)),unordered_pair(X2,X0))
| ( intersection(unordered_pair(X0,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_4344]) ).
tcf(c_9716,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(unordered_pair(X0,X0),X1)),unordered_pair(X0,X2))
| ( intersection(unordered_pair(X0,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_4343]) ).
tcf(c_9717,plain,
! [X0: $i] :
( member(regular(intersection(unordered_pair(x,x),X0)),iPr_def_10)
| ( intersection(unordered_pair(x,x),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_4346]) ).
tcf(c_9718,plain,
! [X0: $i] :
( member(regular(intersection(unordered_pair(y,y),X0)),iPr_def_10)
| ( intersection(unordered_pair(y,y),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_4347]) ).
tcf(c_9719,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(intersection(intersection(X0,X1),X2),X3)),X0)
| ( intersection(intersection(intersection(X0,X1),X2),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_6783]) ).
tcf(c_9720,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(intersection(intersection(X0,X1),X2),X3)),X1)
| ( intersection(intersection(intersection(X0,X1),X2),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_6250]) ).
tcf(c_9721,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation)
| ( intersection(intersection(identity_relation,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_6318]) ).
tcf(c_9722,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(subset_relation,X0),X1)),cross_product(universal_class,universal_class))
| ( intersection(intersection(subset_relation,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_7274]) ).
tcf(c_9724,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(complement(subset_relation),X0),X1)),complement(identity_relation))
| ( intersection(intersection(complement(subset_relation),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_8785]) ).
tcf(c_9745,plain,
( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ( null_class = identity_relation ) ),
inference(light_normalisation,[status(thm)],[c_9701,c_230]) ).
tcf(c_9759,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| ( null_class = subset_relation ) ),
inference(light_normalisation,[status(thm)],[c_9700,c_229]) ).
tcf(c_9801,plain,
( member(regular(subset_relation),universal_class)
| ( null_class = subset_relation ) ),
inference(superposition,[status(thm)],[c_9759,c_4336]) ).
tcf(c_9802,plain,
( ( null_class = subset_relation )
| ( unordered_pair(unordered_pair(first(regular(subset_relation)),first(regular(subset_relation))),unordered_pair(first(regular(subset_relation)),unordered_pair(second(regular(subset_relation)),second(regular(subset_relation))))) = regular(subset_relation) ) ),
inference(superposition,[status(thm)],[c_9759,c_184]) ).
tcf(c_9834,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(X2,cross_product(X0,X1))),X2)
| ( intersection(cross_product(X0,X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_193,c_4246]) ).
tcf(c_9836,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(cross_product(X1,X2),X0)),cross_product(X1,X2))
| ( intersection(X0,cross_product(X1,X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_193,c_4246]) ).
tcf(c_9837,plain,
( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_229,c_4246]) ).
tcf(c_9838,plain,
( member(regular(identity_relation),subset_relation)
| ( intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_230,c_4246]) ).
tcf(c_9844,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,unordered_pair(X1,X2)) = null_class )
| ( regular(intersection(X0,unordered_pair(X1,X2))) = X2 )
| ( regular(intersection(X0,unordered_pair(X1,X2))) = X1 ) ),
inference(superposition,[status(thm)],[c_4246,c_177]) ).
tcf(c_9845,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,cross_product(X1,X2)) = null_class )
| ( unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) = regular(intersection(X0,cross_product(X1,X2))) ) ),
inference(superposition,[status(thm)],[c_4246,c_184]) ).
tcf(c_9846,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(X0,intersection(X1,X2))),X2)
| ( intersection(X0,intersection(X1,X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_189]) ).
tcf(c_9847,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(X0,intersection(X1,X2))),X1)
| ( intersection(X0,intersection(X1,X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_188]) ).
tcf(c_9848,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,complement(X1)) = null_class )
| ~ member(regular(intersection(X0,complement(X1))),X1) ),
inference(superposition,[status(thm)],[c_4246,c_191]) ).
tcf(c_9849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
| ( intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))) = null_class )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4246,c_215]) ).
tcf(c_9850,plain,
! [X0: $i] :
( member(regular(intersection(X0,identity_relation)),subset_relation)
| ( intersection(X0,identity_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_4293]) ).
tcf(c_9851,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(X0,compose(X1,X2))),cross_product(universal_class,universal_class))
| ( intersection(X0,compose(X1,X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_4341]) ).
tcf(c_9852,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(X0,unordered_pair(X1,X1))),unordered_pair(X2,X1))
| ( intersection(X0,unordered_pair(X1,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_4344]) ).
tcf(c_9853,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(X0,unordered_pair(X1,X1))),unordered_pair(X1,X2))
| ( intersection(X0,unordered_pair(X1,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_4343]) ).
tcf(c_9854,plain,
! [X0: $i] :
( member(regular(intersection(X0,unordered_pair(x,x))),iPr_def_10)
| ( intersection(X0,unordered_pair(x,x)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_4346]) ).
tcf(c_9855,plain,
! [X0: $i] :
( member(regular(intersection(X0,unordered_pair(y,y))),iPr_def_10)
| ( intersection(X0,unordered_pair(y,y)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_4347]) ).
tcf(c_9856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(X0,intersection(intersection(X1,X2),X3))),X1)
| ( intersection(X0,intersection(intersection(X1,X2),X3)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_6783]) ).
tcf(c_9857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(X0,intersection(intersection(X1,X2),X3))),X2)
| ( intersection(X0,intersection(intersection(X1,X2),X3)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_6250]) ).
tcf(c_9858,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation)
| ( intersection(X0,intersection(identity_relation,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_6318]) ).
tcf(c_9859,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(subset_relation,X1))),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(subset_relation,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_7274]) ).
tcf(c_9860,plain,
! [X0: $i] :
( member(regular(intersection(X0,complement(subset_relation))),complement(identity_relation))
| ( intersection(X0,complement(subset_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_8771]) ).
tcf(c_9861,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(complement(subset_relation),X1))),complement(identity_relation))
| ( intersection(X0,intersection(complement(subset_relation),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_8785]) ).
tcf(c_9900,plain,
( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ( null_class = subset_relation ) ),
inference(light_normalisation,[status(thm)],[c_9837,c_229]) ).
tcf(c_9928,plain,
( member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(x,x))),cross_product(z,z))
| ~ member(x,z) ),
inference(instantiation,[status(thm)],[c_5608]) ).
tcf(c_9974,plain,
! [X0: $i,X1: $i] :
( ( complement(intersection(X0,X1)) = null_class )
| ~ member(not_subclass_element(complement(intersection(X0,X1)),null_class),X1)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),null_class),X0) ),
inference(superposition,[status(thm)],[c_190,c_4284]) ).
tcf(c_9975,plain,
! [X0: $i] :
( member(not_subclass_element(complement(complement(X0)),null_class),X0)
| ( complement(complement(X0)) = null_class )
| ~ member(not_subclass_element(complement(complement(X0)),null_class),universal_class) ),
inference(superposition,[status(thm)],[c_192,c_4284]) ).
tcf(c_9976,plain,
! [X0: $i] :
( ( complement(domain_of(X0)) = null_class )
| ( intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),null_class),not_subclass_element(complement(domain_of(X0)),null_class)),universal_class)) = null_class )
| ~ member(not_subclass_element(complement(domain_of(X0)),null_class),universal_class) ),
inference(superposition,[status(thm)],[c_195,c_4284]) ).
tcf(c_9977,plain,
( ( complement(domain_of(flip(cross_product(subset_relation,universal_class)))) = null_class )
| ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),null_class),identity_relation) ),
inference(superposition,[status(thm)],[c_4294,c_4284]) ).
tcf(c_9978,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),null_class),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_4284]) ).
tcf(c_9979,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),null_class),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_4284]) ).
tcf(c_9980,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),null_class),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_4284]) ).
tcf(c_9981,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),null_class),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_4284]) ).
tcf(c_9984,plain,
( member(not_subclass_element(complement(complement(identity_relation)),null_class),subset_relation)
| ( complement(complement(identity_relation)) = null_class )
| ~ member(not_subclass_element(complement(complement(identity_relation)),null_class),universal_class) ),
inference(superposition,[status(thm)],[c_8815,c_4284]) ).
tcf(c_9986,plain,
( ( complement(null_class) = null_class )
| ~ member(not_subclass_element(universal_class,null_class),null_class) ),
inference(superposition,[status(thm)],[c_8703,c_4284]) ).
tcf(c_9987,plain,
( ( universal_class = null_class )
| ~ member(not_subclass_element(universal_class,null_class),null_class) ),
inference(light_normalisation,[status(thm)],[c_9986,c_8703]) ).
tcf(c_10017,plain,
! [X0: $i,X1: $i] :
( subclass(rotate(X0),X1)
| member(not_subclass_element(rotate(X0),X1),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_4338]) ).
tcf(c_10018,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,rotate(X0)),X1)
| member(not_subclass_element(rotate(X0),X1),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( rotate(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_4338]) ).
tcf(c_10019,plain,
! [X0: $i] :
( member(not_subclass_element(rotate(X0),null_class),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( rotate(X0) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_4338]) ).
tcf(c_10020,plain,
! [X0: $i] :
( member(regular(rotate(X0)),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( rotate(X0) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_4338]) ).
tcf(c_10021,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(rotate(X0),rotate(X0)),universal_class)),universal_class))))))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( rotate(X0) = null_class )
| ~ member(rotate(X0),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_4338]) ).
tcf(c_10022,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(rotate(X0),X1),X2)
| member(not_subclass_element(intersection(rotate(X0),X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_4338]) ).
tcf(c_10023,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(rotate(X0),X1)),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( intersection(rotate(X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_4338]) ).
tcf(c_10024,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,rotate(X1)),X2)
| member(not_subclass_element(intersection(X0,rotate(X1)),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_4338]) ).
tcf(c_10025,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,rotate(X1))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( intersection(X0,rotate(X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_4338]) ).
tcf(c_10026,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(rotate(X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),rotate(X2)),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_4338]) ).
tcf(c_10027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,rotate(X1)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,rotate(X1)),X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_4338]) ).
tcf(c_10028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(rotate(X0),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(rotate(X0),X1),X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_4338]) ).
tcf(c_10029,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(rotate(X1)))
| member(not_subclass_element(X0,complement(rotate(X1))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_4338]) ).
tcf(c_10030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),rotate(X0)),X3)
| member(not_subclass_element(intersection(rotate(X0),cross_product(X1,X2)),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_4338]) ).
tcf(c_10079,plain,
( member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(y,y))),cross_product(z,z))
| ~ member(y,z) ),
inference(instantiation,[status(thm)],[c_5610]) ).
tcf(c_10120,plain,
! [X0: $i,X1: $i] :
( subclass(flip(X0),X1)
| member(not_subclass_element(flip(X0),X1),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_4339]) ).
tcf(c_10121,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,flip(X0)),X1)
| member(not_subclass_element(flip(X0),X1),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( flip(X0) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_4339]) ).
tcf(c_10122,plain,
! [X0: $i] :
( member(not_subclass_element(flip(X0),null_class),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( flip(X0) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_4339]) ).
tcf(c_10123,plain,
! [X0: $i] :
( member(regular(flip(X0)),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( flip(X0) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_4339]) ).
tcf(c_10124,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(flip(X0),flip(X0)),universal_class)),universal_class))))))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( flip(X0) = null_class )
| ~ member(flip(X0),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_4339]) ).
tcf(c_10125,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(flip(X0),X1),X2)
| member(not_subclass_element(intersection(flip(X0),X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_4339]) ).
tcf(c_10126,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(flip(X0),X1)),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( intersection(flip(X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_4339]) ).
tcf(c_10127,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,flip(X1)),X2)
| member(not_subclass_element(intersection(X0,flip(X1)),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_4339]) ).
tcf(c_10128,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,flip(X1))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( intersection(X0,flip(X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_4339]) ).
tcf(c_10129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(flip(X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),flip(X2)),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_4339]) ).
tcf(c_10130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,flip(X1)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,flip(X1)),X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_4339]) ).
tcf(c_10131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(flip(X0),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(flip(X0),X1),X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_4339]) ).
tcf(c_10132,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(flip(X1)))
| member(not_subclass_element(X0,complement(flip(X1))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_4339]) ).
tcf(c_10133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),flip(X0)),X3)
| member(not_subclass_element(intersection(flip(X0),cross_product(X1,X2)),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_4339]) ).
tcf(c_10198,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_178,c_4342]) ).
tcf(c_10199,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ( unordered_pair(X0,X0) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4943,c_4342]) ).
tcf(c_10200,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| member(X0,cross_product(universal_class,universal_class))
| ( unordered_pair(X0,X1) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_266,c_4342]) ).
tcf(c_10201,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| member(X1,cross_product(universal_class,universal_class))
| ( unordered_pair(X0,X1) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_266,c_4342]) ).
tcf(c_10202,plain,
! [X0: $i,X1: $i] :
( member(X1,cross_product(universal_class,universal_class))
| ( unordered_pair(X0,X0) = unordered_pair(X1,X0) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_265,c_4342]) ).
tcf(c_10203,plain,
! [X0: $i,X1: $i] :
( member(X1,cross_product(universal_class,universal_class))
| ( unordered_pair(X0,X0) = unordered_pair(X0,X1) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_264,c_4342]) ).
tcf(c_10205,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_171,c_4342]) ).
tcf(c_10206,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
| ( X0 = X1 )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_251,c_4342]) ).
tcf(c_10207,plain,
! [X0: $i] :
( member(not_subclass_element(X0,null_class),cross_product(universal_class,universal_class))
| ( X0 = null_class )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_259,c_4342]) ).
tcf(c_10208,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_260,c_4342]) ).
tcf(c_10209,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ function(z) ),
inference(superposition,[status(thm)],[c_3164,c_4342]) ).
tcf(c_10210,plain,
( member(y,cross_product(universal_class,universal_class))
| ~ function(z) ),
inference(superposition,[status(thm)],[c_3163,c_4342]) ).
tcf(c_10211,plain,
! [X0: $i,X1: $i] :
( member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| ~ function(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_179,c_4342]) ).
tcf(c_10212,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(X0,X1),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_180,c_4342]) ).
tcf(c_10213,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,cross_product(universal_class,universal_class))
| ~ member(X2,X1)
| ~ member(X2,X0)
| ~ function(intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_190,c_4342]) ).
tcf(c_10214,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(complement(X1))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_192,c_4342]) ).
tcf(c_10215,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ( intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)) = null_class )
| ~ function(domain_of(X1))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_195,c_4342]) ).
tcf(c_10216,plain,
( member(omega,cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_210,c_4342]) ).
tcf(c_10217,plain,
! [X0: $i] :
( member(regular(X0),cross_product(universal_class,universal_class))
| ( X0 = null_class )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_222,c_4342]) ).
tcf(c_10218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| ~ member(X3,X1)
| ~ member(X2,X0)
| ~ function(cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_183,c_4342]) ).
tcf(c_10219,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_211,c_4342]) ).
tcf(c_10220,plain,
! [X0: $i] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_212,c_4342]) ).
tcf(c_10221,plain,
! [X0: $i,X1: $i] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_221,c_4342]) ).
tcf(c_10222,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ( X0 = null_class )
| ~ function(X0)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_225,c_4342]) ).
tcf(c_10223,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(X0,X1,X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),cross_product(universal_class,universal_class))
| ~ operation(X2)
| ~ operation(X1)
| ~ function(domain_of(X1))
| ~ compatible(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_243,c_4342]) ).
tcf(c_10224,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ function(omega) ),
inference(superposition,[status(thm)],[c_1570,c_4342]) ).
tcf(c_10225,plain,
( member(iPr_def_10,cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4134,c_4342]) ).
tcf(c_10226,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4414,c_4342]) ).
tcf(c_10227,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4391,c_4342]) ).
tcf(c_10228,plain,
( member(y,cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4415,c_4342]) ).
tcf(c_10229,plain,
( member(y,cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4392,c_4342]) ).
tcf(c_10230,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4224,c_4342]) ).
tcf(c_10231,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),cross_product(universal_class,universal_class))
| ( intersection(X0,X1) = null_class )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4225,c_4342]) ).
tcf(c_10232,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,X0),X2)
| member(not_subclass_element(intersection(X1,X0),X2),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4245,c_4342]) ).
tcf(c_10233,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X1,X0)),cross_product(universal_class,universal_class))
| ( intersection(X1,X0) = null_class )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4246,c_4342]) ).
tcf(c_10235,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),cross_product(universal_class,universal_class))
| ~ function(subset_relation) ),
inference(superposition,[status(thm)],[c_4305,c_4342]) ).
tcf(c_10236,plain,
( member(not_subclass_element(identity_relation,null_class),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ function(subset_relation) ),
inference(superposition,[status(thm)],[c_4306,c_4342]) ).
tcf(c_10237,plain,
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ function(subset_relation) ),
inference(superposition,[status(thm)],[c_4307,c_4342]) ).
tcf(c_10242,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4388,c_4342]) ).
tcf(c_10243,plain,
! [X0: $i] :
( member(not_subclass_element(X0,null_class),cross_product(universal_class,universal_class))
| ( X0 = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4389,c_4342]) ).
tcf(c_10244,plain,
! [X0: $i] :
( member(regular(X0),cross_product(universal_class,universal_class))
| ( X0 = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4396,c_4342]) ).
tcf(c_10245,plain,
( member(not_subclass_element(identity_relation,null_class),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4400,c_4342]) ).
tcf(c_10246,plain,
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4401,c_4342]) ).
tcf(c_10247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| member(not_subclass_element(intersection(X2,cross_product(X0,X1)),X3),cross_product(universal_class,universal_class))
| ~ function(cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_4424,c_4342]) ).
tcf(c_10248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,cross_product(X1,X2)),X3)
| member(not_subclass_element(intersection(cross_product(X1,X2),X0),X3),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4425,c_4342]) ).
tcf(c_10249,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),cross_product(universal_class,universal_class))
| ~ function(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(superposition,[status(thm)],[c_4447,c_4342]) ).
tcf(c_10250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X1,X0),X2),X3)
| member(not_subclass_element(intersection(intersection(X1,X0),X2),X3),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4430,c_4342]) ).
tcf(c_10251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4431,c_4342]) ).
tcf(c_10252,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),cross_product(universal_class,universal_class))
| ~ function(subset_relation) ),
inference(superposition,[status(thm)],[c_4433,c_4342]) ).
tcf(c_10253,plain,
! [X0: $i,X1: $i] :
( subclass(X1,complement(X0))
| member(not_subclass_element(X1,complement(X0)),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_8328,c_4342]) ).
tcf(c_10254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),X0),X3)
| member(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4638,c_4342]) ).
tcf(c_10255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),X2),X3),cross_product(universal_class,universal_class))
| ~ function(cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_4640,c_4342]) ).
tcf(c_10257,plain,
! [X0: $i] :
( subclass(X0,complement(identity_relation))
| member(not_subclass_element(X0,complement(identity_relation)),cross_product(universal_class,universal_class))
| ~ function(subset_relation) ),
inference(superposition,[status(thm)],[c_8344,c_4342]) ).
tcf(c_10258,plain,
! [X0: $i] :
( member(X0,subset_relation)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(complement(identity_relation))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_8815,c_4342]) ).
tcf(c_10259,plain,
! [X0: $i] :
( subclass(complement(subset_relation),X0)
| member(not_subclass_element(complement(subset_relation),X0),cross_product(universal_class,universal_class))
| ~ function(complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_8812,c_4342]) ).
tcf(c_10260,plain,
( member(regular(complement(subset_relation)),cross_product(universal_class,universal_class))
| ( complement(subset_relation) = null_class )
| ~ function(complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_8816,c_4342]) ).
tcf(c_10674,plain,
( ( unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))) = x )
| ~ function(z) ),
inference(superposition,[status(thm)],[c_10209,c_184]) ).
tcf(c_10683,plain,
( ( unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y)))) = y )
| ~ function(z) ),
inference(superposition,[status(thm)],[c_10210,c_184]) ).
tcf(c_10692,plain,
( ( unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))) = x )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_10227,c_184]) ).
tcf(c_10701,plain,
( ( unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y)))) = y )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_10229,c_184]) ).
tcf(c_10716,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(complement(intersection(X0,X1)),intersection(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_4169,c_4646]) ).
tcf(c_10718,plain,
! [X0: $i] :
( member(not_subclass_element(subset_relation,X0),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| subclass(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) ),
inference(superposition,[status(thm)],[c_229,c_4646]) ).
tcf(c_10719,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(null_class,intersection(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_4553,c_4646]) ).
tcf(c_10720,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,null_class),X2),X1)
| subclass(intersection(X0,intersection(complement(X1),X1)),X2) ),
inference(superposition,[status(thm)],[c_4169,c_4646]) ).
tcf(c_10721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(cross_product(X2,X3),X1)),X4)
| member(not_subclass_element(intersection(X0,intersection(X1,cross_product(X2,X3))),X4),X1) ),
inference(superposition,[status(thm)],[c_193,c_4646]) ).
tcf(c_10722,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X1,null_class),X2),regular(X0))
| subclass(intersection(X1,intersection(X0,regular(X0))),X2)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4646]) ).
tcf(c_10723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(X3,cross_product(X1,X2))),X4)
| member(not_subclass_element(intersection(X0,intersection(cross_product(X1,X2),X3)),X4),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_193,c_4646]) ).
tcf(c_10724,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,subset_relation),X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1) ),
inference(superposition,[status(thm)],[c_229,c_4646]) ).
tcf(c_10725,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation)
| subclass(intersection(X0,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)),X1) ),
inference(superposition,[status(thm)],[c_230,c_4646]) ).
tcf(c_10726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),complement(cross_product(X1,X2)))
| subclass(intersection(X0,intersection(cross_product(X1,X2),complement(cross_product(X1,X2)))),X3) ),
inference(superposition,[status(thm)],[c_4217,c_4646]) ).
tcf(c_10727,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(null_class,X2)),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),X2) ),
inference(superposition,[status(thm)],[c_4553,c_4646]) ).
tcf(c_10731,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(X0,intersection(X1,X2)),X2),
inference(superposition,[status(thm)],[c_4646,c_172]) ).
tcf(c_10732,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(X0,intersection(X1,null_class)),X2),
inference(superposition,[status(thm)],[c_4646,c_256]) ).
tcf(c_10733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X1,intersection(X2,X0)),X3)
| member(not_subclass_element(intersection(X1,intersection(X2,X0)),X3),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4646,c_4342]) ).
tcf(c_10734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),universal_class) ),
inference(superposition,[status(thm)],[c_4646,c_4336]) ).
tcf(c_10735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(X1,unordered_pair(X2,X3))),X4)
| ( not_subclass_element(intersection(X0,intersection(X1,unordered_pair(X2,X3))),X4) = X3 )
| ( not_subclass_element(intersection(X0,intersection(X1,unordered_pair(X2,X3))),X4) = X2 ) ),
inference(superposition,[status(thm)],[c_4646,c_177]) ).
tcf(c_10736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(X1,cross_product(X2,X3))),X4)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,intersection(X1,cross_product(X2,X3))),X4)),first(not_subclass_element(intersection(X0,intersection(X1,cross_product(X2,X3))),X4))),unordered_pair(first(not_subclass_element(intersection(X0,intersection(X1,cross_product(X2,X3))),X4)),unordered_pair(second(not_subclass_element(intersection(X0,intersection(X1,cross_product(X2,X3))),X4)),second(not_subclass_element(intersection(X0,intersection(X1,cross_product(X2,X3))),X4))))) = not_subclass_element(intersection(X0,intersection(X1,cross_product(X2,X3))),X4) ) ),
inference(superposition,[status(thm)],[c_4646,c_184]) ).
tcf(c_10737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,X3))),X4)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,X3))),X4),X3) ),
inference(superposition,[status(thm)],[c_4646,c_189]) ).
tcf(c_10738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,X3))),X4)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,X3))),X4),X2) ),
inference(superposition,[status(thm)],[c_4646,c_188]) ).
tcf(c_10739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,complement(X2))),X3)
| ~ member(not_subclass_element(intersection(X0,intersection(X1,complement(X2))),X3),X2) ),
inference(superposition,[status(thm)],[c_4646,c_191]) ).
tcf(c_10740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X1,intersection(X2,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X5)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,intersection(X2,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X5),not_subclass_element(intersection(X1,intersection(X2,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X5)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,intersection(X2,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X5),not_subclass_element(intersection(X1,intersection(X2,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X5)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_215]) ).
tcf(c_10741,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,identity_relation)),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,identity_relation)),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4646,c_4293]) ).
tcf(c_10742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,rotate(X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,rotate(X2))),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_4338]) ).
tcf(c_10743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,flip(X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,flip(X2))),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_4339]) ).
tcf(c_10744,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(X1,compose(X2,X3))),X4)
| member(not_subclass_element(intersection(X0,intersection(X1,compose(X2,X3))),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_4341]) ).
tcf(c_10745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(X1,unordered_pair(X2,X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,unordered_pair(X2,X2))),X3),unordered_pair(X4,X2)) ),
inference(superposition,[status(thm)],[c_4646,c_4344]) ).
tcf(c_10746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(X1,unordered_pair(X2,X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,unordered_pair(X2,X2))),X3),unordered_pair(X2,X4)) ),
inference(superposition,[status(thm)],[c_4646,c_4343]) ).
tcf(c_10747,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,unordered_pair(x,x))),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,unordered_pair(x,x))),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4646,c_4346]) ).
tcf(c_10748,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,unordered_pair(y,y))),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,unordered_pair(y,y))),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4646,c_4347]) ).
tcf(c_10749,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(complement(X0),intersection(X1,X0)),X2),
inference(superposition,[status(thm)],[c_4646,c_4432]) ).
tcf(c_10750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X0,intersection(X1,intersection(intersection(X2,X3),X4))),X5)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(intersection(X2,X3),X4))),X5),X2) ),
inference(superposition,[status(thm)],[c_4646,c_6783]) ).
tcf(c_10751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X0,intersection(X1,intersection(intersection(X2,X3),X4))),X5)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(intersection(X2,X3),X4))),X5),X3) ),
inference(superposition,[status(thm)],[c_4646,c_6250]) ).
tcf(c_10752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(identity_relation,X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(identity_relation,X2))),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4646,c_6318]) ).
tcf(c_10753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(subset_relation,X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(subset_relation,X2))),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_7274]) ).
tcf(c_10754,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,complement(subset_relation))),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,complement(subset_relation))),X2),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4646,c_8771]) ).
tcf(c_10755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(complement(subset_relation),X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(complement(subset_relation),X2))),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4646,c_8785]) ).
tcf(c_10758,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(X0,intersection(null_class,X1)),X2) ),
inference(light_normalisation,[status(thm)],[c_10727,c_4790]) ).
tcf(c_10761,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(X0,intersection(complement(X1),X1)),X2) ),
inference(light_normalisation,[status(thm)],[c_10720,c_4790]) ).
tcf(c_10805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),complement(cross_product(X1,X2)))
| subclass(intersection(X0,intersection(cross_product(X1,X2),complement(cross_product(X1,X2)))),X3) ),
inference(light_normalisation,[status(thm)],[c_10726,c_4790]) ).
tcf(c_10816,plain,
! [X0: $i] :
( subclass(subset_relation,X0)
| member(not_subclass_element(subset_relation,X0),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ),
inference(light_normalisation,[status(thm)],[c_10718,c_229]) ).
tcf(c_10822,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,subset_relation),X1)
| member(not_subclass_element(intersection(X0,subset_relation),X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
inference(light_normalisation,[status(thm)],[c_10724,c_229]) ).
tcf(c_11009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(X0,intersection(X1,cross_product(X2,X3))),X1),
inference(superposition,[status(thm)],[c_193,c_10731]) ).
tcf(c_11010,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),regular(X0))
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_10731]) ).
tcf(c_11011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(X0,intersection(cross_product(X1,X2),X3)),cross_product(X1,X2)),
inference(superposition,[status(thm)],[c_193,c_10731]) ).
tcf(c_11012,plain,
! [X0: $i] : subclass(intersection(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(superposition,[status(thm)],[c_229,c_10731]) ).
tcf(c_11013,plain,
! [X0: $i] : subclass(intersection(X0,identity_relation),subset_relation),
inference(superposition,[status(thm)],[c_230,c_10731]) ).
tcf(c_11014,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(X0,null_class),complement(cross_product(X1,X2))),
inference(superposition,[status(thm)],[c_4217,c_10731]) ).
tcf(c_11016,plain,
! [X0: $i] : subclass(intersection(X0,null_class),null_class),
inference(superposition,[status(thm)],[c_4790,c_10731]) ).
tcf(c_11017,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X1,intersection(X2,X0)) = X0 )
| ~ subclass(X0,intersection(X1,intersection(X2,X0))) ),
inference(superposition,[status(thm)],[c_10731,c_176]) ).
tcf(c_11018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,intersection(X3,X0)),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_10731,c_250]) ).
tcf(c_11019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| ~ member(X0,intersection(X1,intersection(X2,X3))) ),
inference(superposition,[status(thm)],[c_10731,c_170]) ).
tcf(c_11020,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(X0,intersection(X1,intersection(X2,null_class))) = null_class,
inference(superposition,[status(thm)],[c_10731,c_5287]) ).
tcf(c_11021,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(X0,intersection(X1,null_class)),X2) = null_class,
inference(superposition,[status(thm)],[c_10731,c_5257]) ).
tcf(c_11104,plain,
! [X0: $i] :
( ( intersection(X0,identity_relation) = subset_relation )
| ~ subclass(subset_relation,intersection(X0,identity_relation)) ),
inference(superposition,[status(thm)],[c_11013,c_176]) ).
tcf(c_11105,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,identity_relation),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_11013,c_250]) ).
tcf(c_11106,plain,
! [X0: $i,X1: $i] :
( member(X0,subset_relation)
| ~ member(X0,intersection(X1,identity_relation)) ),
inference(superposition,[status(thm)],[c_11013,c_170]) ).
tcf(c_11123,plain,
( ( unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_10208,c_184]) ).
tcf(c_11157,plain,
( ( unordered_pair(unordered_pair(first(omega),first(omega)),unordered_pair(first(omega),unordered_pair(second(omega),second(omega)))) = omega )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_10216,c_184]) ).
tcf(c_11166,plain,
( ( unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))) = null_class )
| ~ function(omega) ),
inference(superposition,[status(thm)],[c_10224,c_184]) ).
tcf(c_11175,plain,
( ( unordered_pair(unordered_pair(first(iPr_def_10),first(iPr_def_10)),unordered_pair(first(iPr_def_10),unordered_pair(second(iPr_def_10),second(iPr_def_10)))) = iPr_def_10 )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_10225,c_184]) ).
tcf(c_11184,plain,
( ( unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))) = x )
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_10226,c_184]) ).
tcf(c_11193,plain,
( ( unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y)))) = y )
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_10228,c_184]) ).
tcf(c_11212,plain,
! [X0: $i,X1: $i] : subclass(intersection(null_class,intersection(X0,universal_class)),X1),
inference(superposition,[status(thm)],[c_4953,c_10749]) ).
tcf(c_11213,plain,
! [X0: $i,X1: $i] : subclass(intersection(universal_class,intersection(X0,null_class)),X1),
inference(superposition,[status(thm)],[c_8703,c_10749]) ).
tcf(c_11215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(complement(X0),intersection(X0,cross_product(X1,X2))),X3),
inference(superposition,[status(thm)],[c_193,c_10749]) ).
tcf(c_11217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(complement(cross_product(X0,X1)),intersection(cross_product(X0,X1),X2)),X3),
inference(superposition,[status(thm)],[c_193,c_10749]) ).
tcf(c_11218,plain,
! [X0: $i] : subclass(intersection(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation),X0),
inference(superposition,[status(thm)],[c_229,c_10749]) ).
tcf(c_11219,plain,
! [X0: $i] : subclass(intersection(complement(subset_relation),identity_relation),X0),
inference(superposition,[status(thm)],[c_230,c_10749]) ).
tcf(c_11221,plain,
! [X0: $i,X1: $i] : subclass(intersection(complement(X0),null_class),X1),
inference(superposition,[status(thm)],[c_4553,c_10749]) ).
tcf(c_11222,plain,
! [X0: $i] : subclass(intersection(complement(null_class),null_class),X0),
inference(superposition,[status(thm)],[c_4790,c_10749]) ).
tcf(c_11223,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(complement(X1),intersection(X2,X1)) = X0 )
| ~ subclass(X0,intersection(complement(X1),intersection(X2,X1))) ),
inference(superposition,[status(thm)],[c_10749,c_176]) ).
tcf(c_11225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| ~ member(X0,intersection(complement(X1),intersection(X2,X1))) ),
inference(superposition,[status(thm)],[c_10749,c_170]) ).
tcf(c_11226,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(X0,intersection(complement(X1),intersection(X2,X1))) = null_class,
inference(superposition,[status(thm)],[c_10749,c_5287]) ).
tcf(c_11227,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(complement(X0),intersection(X1,X0)),X2) = null_class,
inference(superposition,[status(thm)],[c_10749,c_5257]) ).
tcf(c_11228,plain,
! [X0: $i,X1: $i] : intersection(complement(X0),intersection(X1,X0)) = null_class,
inference(superposition,[status(thm)],[c_10749,c_258]) ).
tcf(c_11229,plain,
! [X0: $i] : subclass(intersection(universal_class,null_class),X0),
inference(light_normalisation,[status(thm)],[c_11222,c_8703]) ).
tcf(c_11306,plain,
! [X0: $i] :
( ( intersection(complement(subset_relation),identity_relation) = X0 )
| ~ subclass(X0,intersection(complement(subset_relation),identity_relation)) ),
inference(superposition,[status(thm)],[c_11219,c_176]) ).
tcf(c_11308,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,intersection(complement(subset_relation),identity_relation)) ),
inference(superposition,[status(thm)],[c_11219,c_170]) ).
tcf(c_11309,plain,
! [X0: $i] : intersection(X0,intersection(complement(subset_relation),identity_relation)) = null_class,
inference(superposition,[status(thm)],[c_11219,c_5287]) ).
tcf(c_11310,plain,
! [X0: $i] : intersection(intersection(complement(subset_relation),identity_relation),X0) = null_class,
inference(superposition,[status(thm)],[c_11219,c_5257]) ).
tcf(c_11311,plain,
intersection(complement(subset_relation),identity_relation) = null_class,
inference(superposition,[status(thm)],[c_11219,c_258]) ).
tcf(c_11325,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(complement(intersection(X0,X1)),intersection(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_4169,c_4647]) ).
tcf(c_11328,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(null_class,intersection(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_4553,c_4647]) ).
tcf(c_11329,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,null_class),X2),complement(X1))
| subclass(intersection(X0,intersection(complement(X1),X1)),X2) ),
inference(superposition,[status(thm)],[c_4169,c_4647]) ).
tcf(c_11330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(cross_product(X2,X3),X1)),X4)
| member(not_subclass_element(intersection(X0,intersection(X1,cross_product(X2,X3))),X4),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_193,c_4647]) ).
tcf(c_11331,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X1,null_class),X2),X0)
| subclass(intersection(X1,intersection(X0,regular(X0))),X2)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4647]) ).
tcf(c_11332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(X3,cross_product(X1,X2))),X4)
| member(not_subclass_element(intersection(X0,intersection(cross_product(X1,X2),X3)),X4),X3) ),
inference(superposition,[status(thm)],[c_193,c_4647]) ).
tcf(c_11333,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class))
| subclass(intersection(X0,intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1) ),
inference(superposition,[status(thm)],[c_229,c_4647]) ).
tcf(c_11334,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(superposition,[status(thm)],[c_230,c_4647]) ).
tcf(c_11335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),cross_product(X1,X2))
| subclass(intersection(X0,intersection(cross_product(X1,X2),complement(cross_product(X1,X2)))),X3) ),
inference(superposition,[status(thm)],[c_4217,c_4647]) ).
tcf(c_11337,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X2,null_class)),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),X2) ),
inference(superposition,[status(thm)],[c_4790,c_4647]) ).
tcf(c_11340,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(X0,intersection(X1,X2)),X1),
inference(superposition,[status(thm)],[c_4647,c_172]) ).
tcf(c_11341,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(X0,intersection(null_class,X1)),X2),
inference(superposition,[status(thm)],[c_4647,c_256]) ).
tcf(c_11342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X1,intersection(X0,X2)),X3)
| member(not_subclass_element(intersection(X1,intersection(X0,X2)),X3),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4647,c_4342]) ).
tcf(c_11344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(unordered_pair(X1,X2),X3)),X4)
| ( not_subclass_element(intersection(X0,intersection(unordered_pair(X1,X2),X3)),X4) = X2 )
| ( not_subclass_element(intersection(X0,intersection(unordered_pair(X1,X2),X3)),X4) = X1 ) ),
inference(superposition,[status(thm)],[c_4647,c_177]) ).
tcf(c_11345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(cross_product(X1,X2),X3)),X4)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,intersection(cross_product(X1,X2),X3)),X4)),first(not_subclass_element(intersection(X0,intersection(cross_product(X1,X2),X3)),X4))),unordered_pair(first(not_subclass_element(intersection(X0,intersection(cross_product(X1,X2),X3)),X4)),unordered_pair(second(not_subclass_element(intersection(X0,intersection(cross_product(X1,X2),X3)),X4)),second(not_subclass_element(intersection(X0,intersection(cross_product(X1,X2),X3)),X4))))) = not_subclass_element(intersection(X0,intersection(cross_product(X1,X2),X3)),X4) ) ),
inference(superposition,[status(thm)],[c_4647,c_184]) ).
tcf(c_11348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(complement(X1),X2)),X3)
| ~ member(not_subclass_element(intersection(X0,intersection(complement(X1),X2)),X3),X1) ),
inference(superposition,[status(thm)],[c_4647,c_191]) ).
tcf(c_11349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X1,intersection(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X4)),X5)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,intersection(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X4)),X5),not_subclass_element(intersection(X1,intersection(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X4)),X5)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,intersection(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X4)),X5),not_subclass_element(intersection(X1,intersection(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X4)),X5)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_215]) ).
tcf(c_11351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(rotate(X1),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(rotate(X1),X2)),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_4338]) ).
tcf(c_11352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(flip(X1),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(flip(X1),X2)),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_4339]) ).
tcf(c_11353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(compose(X1,X2),X3)),X4)
| member(not_subclass_element(intersection(X0,intersection(compose(X1,X2),X3)),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_4341]) ).
tcf(c_11354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(unordered_pair(X1,X1),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(unordered_pair(X1,X1),X2)),X3),unordered_pair(X4,X1)) ),
inference(superposition,[status(thm)],[c_4647,c_4344]) ).
tcf(c_11355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(unordered_pair(X1,X1),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(unordered_pair(X1,X1),X2)),X3),unordered_pair(X1,X4)) ),
inference(superposition,[status(thm)],[c_4647,c_4343]) ).
tcf(c_11356,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(unordered_pair(x,x),X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(unordered_pair(x,x),X1)),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4647,c_4346]) ).
tcf(c_11357,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(unordered_pair(y,y),X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(unordered_pair(y,y),X1)),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4647,c_4347]) ).
tcf(c_11358,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(complement(X0),intersection(X0,X1)),X2),
inference(superposition,[status(thm)],[c_4647,c_4432]) ).
tcf(c_11359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X0,intersection(intersection(intersection(X1,X2),X3),X4)),X5)
| member(not_subclass_element(intersection(X0,intersection(intersection(intersection(X1,X2),X3),X4)),X5),X1) ),
inference(superposition,[status(thm)],[c_4647,c_6783]) ).
tcf(c_11360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X0,intersection(intersection(intersection(X1,X2),X3),X4)),X5)
| member(not_subclass_element(intersection(X0,intersection(intersection(intersection(X1,X2),X3),X4)),X5),X2) ),
inference(superposition,[status(thm)],[c_4647,c_6250]) ).
tcf(c_11361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(identity_relation,X1),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(identity_relation,X1),X2)),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4647,c_6318]) ).
tcf(c_11362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(subset_relation,X1),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(subset_relation,X1),X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_7274]) ).
tcf(c_11364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(complement(subset_relation),X1),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(complement(subset_relation),X1),X2)),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4647,c_8785]) ).
tcf(c_11367,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(X0,intersection(X1,null_class)),X2) ),
inference(light_normalisation,[status(thm)],[c_11337,c_4790]) ).
tcf(c_11372,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),complement(X1))
| subclass(intersection(X0,intersection(complement(X1),X1)),X2) ),
inference(light_normalisation,[status(thm)],[c_11329,c_4790]) ).
tcf(c_11391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),cross_product(X1,X2))
| subclass(intersection(X0,intersection(cross_product(X1,X2),complement(cross_product(X1,X2)))),X3) ),
inference(light_normalisation,[status(thm)],[c_11335,c_4790]) ).
tcf(c_11406,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(light_normalisation,[status(thm)],[c_11334,c_230]) ).
tcf(c_11417,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,subset_relation),X1)
| member(not_subclass_element(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class)) ),
inference(light_normalisation,[status(thm)],[c_11333,c_229]) ).
tcf(c_11543,plain,
! [X0: $i] : subclass(intersection(null_class,X0),complement(subset_relation)),
inference(superposition,[status(thm)],[c_11311,c_6583]) ).
tcf(c_11544,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(complement(subset_relation),identity_relation),X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_11311,c_4431]) ).
tcf(c_11545,plain,
! [X0: $i] : subclass(intersection(null_class,X0),identity_relation),
inference(superposition,[status(thm)],[c_11311,c_6065]) ).
tcf(c_11546,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),identity_relation)
| subclass(intersection(intersection(complement(subset_relation),identity_relation),X0),X1) ),
inference(superposition,[status(thm)],[c_11311,c_4430]) ).
tcf(c_11547,plain,
subclass(null_class,identity_relation),
inference(superposition,[status(thm)],[c_11311,c_4643]) ).
tcf(c_11548,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),identity_relation)
| subclass(intersection(complement(subset_relation),identity_relation),X0) ),
inference(superposition,[status(thm)],[c_11311,c_4245]) ).
tcf(c_11549,plain,
subclass(null_class,complement(subset_relation)),
inference(superposition,[status(thm)],[c_11311,c_4427]) ).
tcf(c_11550,plain,
! [X0: $i] :
( subclass(intersection(complement(subset_relation),identity_relation),X0)
| member(not_subclass_element(null_class,X0),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_11311,c_4224]) ).
tcf(c_11551,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(complement(subset_relation),identity_relation)),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_11311,c_4647]) ).
tcf(c_11552,plain,
! [X0: $i] : subclass(intersection(X0,null_class),identity_relation),
inference(superposition,[status(thm)],[c_11311,c_10731]) ).
tcf(c_11553,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),identity_relation)
| subclass(intersection(X0,intersection(complement(subset_relation),identity_relation)),X1) ),
inference(superposition,[status(thm)],[c_11311,c_4646]) ).
tcf(c_11554,plain,
! [X0: $i,X1: $i] :
( member(X0,complement(subset_relation))
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_11311,c_6783]) ).
tcf(c_11555,plain,
! [X0: $i,X1: $i] :
( member(X0,identity_relation)
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_11311,c_6250]) ).
tcf(c_11556,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,identity_relation)
| ~ member(X0,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_11311,c_190]) ).
tcf(c_11560,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ~ subclass(complement(subset_relation),X0) ),
inference(superposition,[status(thm)],[c_11311,c_6782]) ).
tcf(c_11562,plain,
! [X0: $i] :
( subclass(intersection(complement(subset_relation),identity_relation),X0)
| ~ member(not_subclass_element(null_class,X0),subset_relation) ),
inference(superposition,[status(thm)],[c_11311,c_4432]) ).
tcf(c_11563,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ~ subclass(identity_relation,X0) ),
inference(superposition,[status(thm)],[c_11311,c_6249]) ).
tcf(c_11579,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),identity_relation) ),
inference(light_normalisation,[status(thm)],[c_11548,c_11311]) ).
tcf(c_11580,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ member(not_subclass_element(null_class,X0),subset_relation) ),
inference(light_normalisation,[status(thm)],[c_11562,c_11311]) ).
tcf(c_11581,plain,
! [X0: $i] :
( ~ member(X0,identity_relation)
| ~ member(X0,complement(subset_relation)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11556,c_256]) ).
tcf(c_11584,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),complement(subset_relation)) ),
inference(light_normalisation,[status(thm)],[c_11550,c_11311]) ).
tcf(c_11618,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,null_class),complement(X1)),
inference(superposition,[status(thm)],[c_4169,c_11340]) ).
tcf(c_11619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(X0,intersection(X1,cross_product(X2,X3))),cross_product(X2,X3)),
inference(superposition,[status(thm)],[c_193,c_11340]) ).
tcf(c_11620,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_11340]) ).
tcf(c_11621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(X0,intersection(cross_product(X1,X2),X3)),X3),
inference(superposition,[status(thm)],[c_193,c_11340]) ).
tcf(c_11622,plain,
! [X0: $i] : subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_229,c_11340]) ).
tcf(c_11623,plain,
! [X0: $i] : subclass(intersection(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))),
inference(superposition,[status(thm)],[c_230,c_11340]) ).
tcf(c_11624,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(X0,null_class),cross_product(X1,X2)),
inference(superposition,[status(thm)],[c_4217,c_11340]) ).
tcf(c_11627,plain,
! [X0: $i] : subclass(intersection(X0,null_class),complement(subset_relation)),
inference(superposition,[status(thm)],[c_11311,c_11340]) ).
tcf(c_11628,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X1,intersection(X0,X2)) = X0 )
| ~ subclass(X0,intersection(X1,intersection(X0,X2))) ),
inference(superposition,[status(thm)],[c_11340,c_176]) ).
tcf(c_11629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,intersection(X0,X3)),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11340,c_250]) ).
tcf(c_11630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,intersection(X2,X3))) ),
inference(superposition,[status(thm)],[c_11340,c_170]) ).
tcf(c_11631,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(X0,intersection(X1,intersection(null_class,X2))) = null_class,
inference(superposition,[status(thm)],[c_11340,c_5287]) ).
tcf(c_11632,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(X0,intersection(null_class,X1)),X2) = null_class,
inference(superposition,[status(thm)],[c_11340,c_5257]) ).
tcf(c_11654,plain,
! [X0: $i] :
( ( intersection(X0,subset_relation) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(X0,subset_relation)) ),
inference(superposition,[status(thm)],[c_11622,c_176]) ).
tcf(c_11655,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,subset_relation),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_11622,c_250]) ).
tcf(c_11656,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(X1,subset_relation)) ),
inference(superposition,[status(thm)],[c_11622,c_170]) ).
tcf(c_11668,plain,
! [X0: $i,X1: $i] : subclass(intersection(null_class,intersection(universal_class,X0)),X1),
inference(superposition,[status(thm)],[c_4953,c_11358]) ).
tcf(c_11669,plain,
! [X0: $i,X1: $i] : subclass(intersection(universal_class,intersection(null_class,X0)),X1),
inference(superposition,[status(thm)],[c_8703,c_11358]) ).
tcf(c_11670,plain,
! [X0: $i,X1: $i] : subclass(intersection(complement(complement(X0)),null_class),X1),
inference(superposition,[status(thm)],[c_4169,c_11358]) ).
tcf(c_11671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(complement(cross_product(X0,X1)),intersection(X2,cross_product(X0,X1))),X3),
inference(superposition,[status(thm)],[c_193,c_11358]) ).
tcf(c_11672,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(X0),null_class),X1)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_11358]) ).
tcf(c_11673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(complement(X0),intersection(cross_product(X1,X2),X0)),X3),
inference(superposition,[status(thm)],[c_193,c_11358]) ).
tcf(c_11674,plain,
! [X0: $i] : subclass(intersection(complement(cross_product(universal_class,universal_class)),subset_relation),X0),
inference(superposition,[status(thm)],[c_229,c_11358]) ).
tcf(c_11675,plain,
! [X0: $i] : subclass(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation),X0),
inference(superposition,[status(thm)],[c_230,c_11358]) ).
tcf(c_11676,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(complement(cross_product(X0,X1)),null_class),X2),
inference(superposition,[status(thm)],[c_4217,c_11358]) ).
tcf(c_11680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(complement(X1),intersection(X1,X2)) = X0 )
| ~ subclass(X0,intersection(complement(X1),intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_11358,c_176]) ).
tcf(c_11682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| ~ member(X0,intersection(complement(X1),intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_11358,c_170]) ).
tcf(c_11683,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(X0,intersection(complement(X1),intersection(X1,X2))) = null_class,
inference(superposition,[status(thm)],[c_11358,c_5287]) ).
tcf(c_11684,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(complement(X0),intersection(X0,X1)),X2) = null_class,
inference(superposition,[status(thm)],[c_11358,c_5257]) ).
tcf(c_11685,plain,
! [X0: $i,X1: $i] : intersection(complement(X0),intersection(X0,X1)) = null_class,
inference(superposition,[status(thm)],[c_11358,c_258]) ).
tcf(c_11758,plain,
! [X0: $i] :
( ( intersection(complement(cross_product(universal_class,universal_class)),subset_relation) = X0 )
| ~ subclass(X0,intersection(complement(cross_product(universal_class,universal_class)),subset_relation)) ),
inference(superposition,[status(thm)],[c_11674,c_176]) ).
tcf(c_11760,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,intersection(complement(cross_product(universal_class,universal_class)),subset_relation)) ),
inference(superposition,[status(thm)],[c_11674,c_170]) ).
tcf(c_11761,plain,
! [X0: $i] : intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),subset_relation)) = null_class,
inference(superposition,[status(thm)],[c_11674,c_5287]) ).
tcf(c_11762,plain,
! [X0: $i] : intersection(intersection(complement(cross_product(universal_class,universal_class)),subset_relation),X0) = null_class,
inference(superposition,[status(thm)],[c_11674,c_5257]) ).
tcf(c_11763,plain,
intersection(complement(cross_product(universal_class,universal_class)),subset_relation) = null_class,
inference(superposition,[status(thm)],[c_11674,c_258]) ).
tcf(c_11779,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(identity_relation,cross_product(X1,X2)),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_193,c_11105]) ).
tcf(c_11782,plain,
! [X0: $i,X1: $i] :
( ( intersection(X1,identity_relation) = X0 )
| ~ subclass(subset_relation,X0)
| ~ subclass(X0,intersection(X1,identity_relation)) ),
inference(superposition,[status(thm)],[c_11105,c_176]) ).
tcf(c_11783,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,identity_relation),X1)
| ~ subclass(subset_relation,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11105,c_250]) ).
tcf(c_11784,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(subset_relation,X2)
| ~ member(X0,intersection(X1,identity_relation)) ),
inference(superposition,[status(thm)],[c_11105,c_170]) ).
tcf(c_11785,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,identity_relation)) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_11105,c_5287]) ).
tcf(c_11786,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,identity_relation),X1) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_11105,c_5257]) ).
tcf(c_11787,plain,
! [X0: $i] :
( ( intersection(X0,identity_relation) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_11105,c_258]) ).
tcf(c_11833,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation)
| member(not_subclass_element(X1,intersection(X0,identity_relation)),X1)
| ( intersection(X0,identity_relation) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_11106]) ).
tcf(c_11834,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,identity_relation),null_class),subset_relation)
| ( intersection(X0,identity_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_11106]) ).
tcf(c_11837,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation)
| ( intersection(X0,identity_relation) = null_class )
| ~ member(intersection(X0,identity_relation),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_11106]) ).
tcf(c_11839,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation)
| ( intersection(intersection(X0,identity_relation),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_11106]) ).
tcf(c_11841,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation)
| ( intersection(X0,intersection(X1,identity_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_11106]) ).
tcf(c_11842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,identity_relation),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,identity_relation)),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4425,c_11106]) ).
tcf(c_11843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(X1,identity_relation)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,identity_relation)),X2),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4430,c_11106]) ).
tcf(c_11844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(X0,identity_relation),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(X0,identity_relation),X1),X2),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4431,c_11106]) ).
tcf(c_11845,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(X1,identity_relation)))
| member(not_subclass_element(X0,complement(intersection(X1,identity_relation))),subset_relation) ),
inference(superposition,[status(thm)],[c_8328,c_11106]) ).
tcf(c_11846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(X0,identity_relation)),X3)
| member(not_subclass_element(intersection(intersection(X0,identity_relation),cross_product(X1,X2)),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4638,c_11106]) ).
tcf(c_11847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,identity_relation))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,identity_relation))),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4646,c_11106]) ).
tcf(c_11848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(X1,identity_relation),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(X1,identity_relation),X2)),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_4647,c_11106]) ).
tcf(c_11850,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,subset_relation)
| ~ member(X0,intersection(identity_relation,cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_193,c_11106]) ).
tcf(c_11941,plain,
! [X0: $i] : intersection(null_class,intersection(X0,universal_class)) = null_class,
inference(superposition,[status(thm)],[c_4953,c_11228]) ).
tcf(c_11942,plain,
! [X0: $i] : intersection(universal_class,intersection(X0,null_class)) = null_class,
inference(superposition,[status(thm)],[c_8703,c_11228]) ).
tcf(c_11944,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(complement(X0),intersection(X0,cross_product(X1,X2))) = null_class,
inference(superposition,[status(thm)],[c_193,c_11228]) ).
tcf(c_11945,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(complement(regular(X0)),null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_11228]) ).
tcf(c_11946,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(complement(cross_product(X0,X1)),intersection(cross_product(X0,X1),X2)) = null_class,
inference(superposition,[status(thm)],[c_193,c_11228]) ).
tcf(c_11947,plain,
intersection(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) = null_class,
inference(superposition,[status(thm)],[c_229,c_11228]) ).
tcf(c_11949,plain,
! [X0: $i,X1: $i] : intersection(complement(complement(cross_product(X0,X1))),null_class) = null_class,
inference(superposition,[status(thm)],[c_4217,c_11228]) ).
tcf(c_11950,plain,
! [X0: $i] : intersection(complement(X0),null_class) = null_class,
inference(superposition,[status(thm)],[c_4553,c_11228]) ).
tcf(c_11951,plain,
intersection(complement(null_class),null_class) = null_class,
inference(superposition,[status(thm)],[c_4790,c_11228]) ).
tcf(c_11953,plain,
intersection(complement(identity_relation),null_class) = null_class,
inference(superposition,[status(thm)],[c_11311,c_11228]) ).
tcf(c_11957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),complement(X0))
| subclass(intersection(intersection(complement(X0),intersection(X1,X0)),X2),X3) ),
inference(superposition,[status(thm)],[c_11228,c_4431]) ).
tcf(c_11958,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(null_class,X0),intersection(X1,X2)),
inference(superposition,[status(thm)],[c_11228,c_6065]) ).
tcf(c_11959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),intersection(X1,X0))
| subclass(intersection(intersection(complement(X0),intersection(X1,X0)),X2),X3) ),
inference(superposition,[status(thm)],[c_11228,c_4430]) ).
tcf(c_11960,plain,
! [X0: $i,X1: $i] : subclass(null_class,intersection(X0,X1)),
inference(superposition,[status(thm)],[c_11228,c_4643]) ).
tcf(c_11961,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(X1,X0))
| subclass(intersection(complement(X0),intersection(X1,X0)),X2) ),
inference(superposition,[status(thm)],[c_11228,c_4245]) ).
tcf(c_11963,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),complement(X0))
| subclass(intersection(complement(X0),intersection(X1,X0)),X2) ),
inference(superposition,[status(thm)],[c_11228,c_4224]) ).
tcf(c_11965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),complement(X1))
| subclass(intersection(X0,intersection(complement(X1),intersection(X2,X1))),X3) ),
inference(superposition,[status(thm)],[c_11228,c_4647]) ).
tcf(c_11966,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(X0,null_class),intersection(X1,X2)),
inference(superposition,[status(thm)],[c_11228,c_10731]) ).
tcf(c_11967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),intersection(X2,X1))
| subclass(intersection(X0,intersection(complement(X1),intersection(X2,X1))),X3) ),
inference(superposition,[status(thm)],[c_11228,c_4646]) ).
tcf(c_11969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,intersection(X2,X3))
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_11228,c_6250]) ).
tcf(c_11970,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,null_class)
| ~ member(X0,complement(X2))
| ~ member(X0,intersection(X1,X2)) ),
inference(superposition,[status(thm)],[c_11228,c_190]) ).
tcf(c_11975,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(X1),intersection(X2,X1)),X0)
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_11228,c_4432]) ).
tcf(c_11977,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(complement(X0),intersection(X1,X0)),X2) ),
inference(superposition,[status(thm)],[c_11228,c_4647]) ).
tcf(c_11979,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(complement(X0),intersection(X1,X0)),X2) ),
inference(superposition,[status(thm)],[c_11228,c_4646]) ).
tcf(c_11980,plain,
! [X0: $i,X1: $i] : intersection(complement(intersection(X0,X1)),null_class) = null_class,
inference(superposition,[status(thm)],[c_11228,c_11228]) ).
tcf(c_11981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(null_class,X3),X2)
| ~ subclass(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_11228,c_6249]) ).
tcf(c_11982,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(null_class,X2)
| ~ subclass(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_11228,c_4788]) ).
tcf(c_11998,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,complement(X2))
| ~ member(X0,intersection(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11970,c_256]) ).
tcf(c_12002,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),intersection(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_11961,c_11228]) ).
tcf(c_12017,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(universal_class)),X1)
| ( unordered_pair(not_subclass_element(intersection(X0,complement(universal_class)),X1),not_subclass_element(intersection(X0,complement(universal_class)),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4943,c_4648]) ).
tcf(c_12018,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,universal_class)
| subclass(intersection(X0,complement(universal_class)),X1)
| ( unordered_pair(not_subclass_element(intersection(X0,complement(universal_class)),X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_4648]) ).
tcf(c_12019,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,universal_class)
| subclass(intersection(X1,complement(universal_class)),X2)
| ( unordered_pair(X0,not_subclass_element(intersection(X1,complement(universal_class)),X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_4648]) ).
tcf(c_12020,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,complement(universal_class)),X1)
| ( unordered_pair(not_subclass_element(intersection(X0,complement(universal_class)),X1),X2) = unordered_pair(X2,X2) ) ),
inference(superposition,[status(thm)],[c_265,c_4648]) ).
tcf(c_12021,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,complement(universal_class)),X2)
| ( unordered_pair(X0,not_subclass_element(intersection(X1,complement(universal_class)),X2)) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_264,c_4648]) ).
tcf(c_12022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,complement(intersection(X1,X2))),X3)
| ~ member(not_subclass_element(intersection(X0,complement(intersection(X1,X2))),X3),X2)
| ~ member(not_subclass_element(intersection(X0,complement(intersection(X1,X2))),X3),X1) ),
inference(superposition,[status(thm)],[c_190,c_4648]) ).
tcf(c_12023,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,complement(complement(X1))),X2)
| member(not_subclass_element(intersection(X0,complement(complement(X1))),X2),X1)
| ~ member(not_subclass_element(intersection(X0,complement(complement(X1))),X2),universal_class) ),
inference(superposition,[status(thm)],[c_192,c_4648]) ).
tcf(c_12024,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,complement(domain_of(X1))),X2)
| ( intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,complement(domain_of(X1))),X2),not_subclass_element(intersection(X0,complement(domain_of(X1))),X2)),universal_class)) = null_class )
| ~ member(not_subclass_element(intersection(X0,complement(domain_of(X1))),X2),universal_class) ),
inference(superposition,[status(thm)],[c_195,c_4648]) ).
tcf(c_12025,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,complement(X0)),X1),
inference(superposition,[status(thm)],[c_4224,c_4648]) ).
tcf(c_12026,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
| ~ member(not_subclass_element(intersection(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),X1),identity_relation) ),
inference(superposition,[status(thm)],[c_4294,c_4648]) ).
tcf(c_12027,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(cross_product(universal_class,universal_class))),X1)
| ~ member(not_subclass_element(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_4648]) ).
tcf(c_12028,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(cross_product(universal_class,universal_class))),X1)
| ~ member(not_subclass_element(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),subset_relation) ),
inference(superposition,[status(thm)],[c_6986,c_4648]) ).
tcf(c_12029,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(cross_product(universal_class,universal_class))),X1)
| ~ member(not_subclass_element(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_4648]) ).
tcf(c_12030,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(cross_product(universal_class,universal_class))),X1)
| ~ member(not_subclass_element(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_4648]) ).
tcf(c_12031,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,complement(universal_class)),X1),
inference(superposition,[status(thm)],[c_4388,c_4648]) ).
tcf(c_12032,plain,
! [X0: $i] :
( subclass(intersection(X0,complement(universal_class)),null_class)
| ( intersection(X0,complement(universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4389,c_4648]) ).
tcf(c_12033,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(X0,X1),complement(X1)),X2),
inference(superposition,[status(thm)],[c_4430,c_4648]) ).
tcf(c_12034,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(X0,X1),complement(X0)),X2),
inference(superposition,[status(thm)],[c_4431,c_4648]) ).
tcf(c_12035,plain,
! [X0: $i] : subclass(intersection(identity_relation,complement(subset_relation)),X0),
inference(superposition,[status(thm)],[c_4433,c_4648]) ).
tcf(c_12036,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,complement(X1)),complement(X1)),
inference(superposition,[status(thm)],[c_8328,c_4648]) ).
tcf(c_12038,plain,
! [X0: $i] : subclass(intersection(X0,complement(subset_relation)),complement(identity_relation)),
inference(superposition,[status(thm)],[c_8344,c_4648]) ).
tcf(c_12039,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(complement(identity_relation))),X1)
| member(not_subclass_element(intersection(X0,complement(complement(identity_relation))),X1),subset_relation)
| ~ member(not_subclass_element(intersection(X0,complement(complement(identity_relation))),X1),universal_class) ),
inference(superposition,[status(thm)],[c_8815,c_4648]) ).
tcf(c_12040,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(complement(X1)),complement(X1)),X0)
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_4169,c_4648]) ).
tcf(c_12043,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,complement(X1)),X0)
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_4553,c_4648]) ).
tcf(c_12044,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(universal_class)),X1)
| ~ member(not_subclass_element(intersection(X0,null_class),X1),universal_class) ),
inference(superposition,[status(thm)],[c_4953,c_4648]) ).
tcf(c_12045,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(null_class)),X1)
| ~ member(not_subclass_element(intersection(X0,universal_class),X1),null_class) ),
inference(superposition,[status(thm)],[c_8703,c_4648]) ).
tcf(c_12050,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,universal_class),X1)
| ~ member(not_subclass_element(intersection(X0,universal_class),X1),null_class) ),
inference(light_normalisation,[status(thm)],[c_12045,c_8703]) ).
tcf(c_12062,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,null_class),X2)
| ( unordered_pair(X0,not_subclass_element(intersection(X1,null_class),X2)) = unordered_pair(X0,X0) ) ),
inference(light_normalisation,[status(thm)],[c_12021,c_4953]) ).
tcf(c_12066,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,universal_class)
| subclass(intersection(X1,null_class),X2)
| ( unordered_pair(X0,not_subclass_element(intersection(X1,null_class),X2)) = null_class ) ),
inference(light_normalisation,[status(thm)],[c_12019,c_4953]) ).
tcf(c_12153,plain,
! [X0: $i] :
( member(not_subclass_element(X0,complement(subset_relation)),X0)
| ( complement(subset_relation) = X0 )
| ~ member(not_subclass_element(complement(subset_relation),X0),identity_relation) ),
inference(superposition,[status(thm)],[c_251,c_11581]) ).
tcf(c_12154,plain,
( ( complement(subset_relation) = null_class )
| ~ member(not_subclass_element(complement(subset_relation),null_class),identity_relation) ),
inference(superposition,[status(thm)],[c_259,c_11581]) ).
tcf(c_12157,plain,
( ( complement(subset_relation) = null_class )
| ~ member(complement(subset_relation),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(subset_relation),complement(subset_relation)),universal_class)),universal_class))))))),identity_relation) ),
inference(superposition,[status(thm)],[c_225,c_11581]) ).
tcf(c_12158,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(subset_relation),X0),X1)
| ~ member(not_subclass_element(intersection(complement(subset_relation),X0),X1),identity_relation) ),
inference(superposition,[status(thm)],[c_4224,c_11581]) ).
tcf(c_12159,plain,
! [X0: $i] :
( ( intersection(complement(subset_relation),X0) = null_class )
| ~ member(regular(intersection(complement(subset_relation),X0)),identity_relation) ),
inference(superposition,[status(thm)],[c_4225,c_11581]) ).
tcf(c_12160,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(subset_relation)),X1)
| ~ member(not_subclass_element(intersection(X0,complement(subset_relation)),X1),identity_relation) ),
inference(superposition,[status(thm)],[c_4245,c_11581]) ).
tcf(c_12161,plain,
! [X0: $i] :
( ( intersection(X0,complement(subset_relation)) = null_class )
| ~ member(regular(intersection(X0,complement(subset_relation))),identity_relation) ),
inference(superposition,[status(thm)],[c_4246,c_11581]) ).
tcf(c_12162,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(subset_relation),cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),complement(subset_relation)),X2),identity_relation) ),
inference(superposition,[status(thm)],[c_4425,c_11581]) ).
tcf(c_12163,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,complement(subset_relation)),X1),X2)
| ~ member(not_subclass_element(intersection(intersection(X0,complement(subset_relation)),X1),X2),identity_relation) ),
inference(superposition,[status(thm)],[c_4430,c_11581]) ).
tcf(c_12164,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(complement(subset_relation),X0),X1),X2)
| ~ member(not_subclass_element(intersection(intersection(complement(subset_relation),X0),X1),X2),identity_relation) ),
inference(superposition,[status(thm)],[c_4431,c_11581]) ).
tcf(c_12165,plain,
! [X0: $i] :
( subclass(X0,complement(complement(subset_relation)))
| ~ member(not_subclass_element(X0,complement(complement(subset_relation))),identity_relation) ),
inference(superposition,[status(thm)],[c_8328,c_11581]) ).
tcf(c_12166,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),complement(subset_relation)),X2)
| ~ member(not_subclass_element(intersection(complement(subset_relation),cross_product(X0,X1)),X2),identity_relation) ),
inference(superposition,[status(thm)],[c_4638,c_11581]) ).
tcf(c_12167,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,complement(subset_relation))),X2)
| ~ member(not_subclass_element(intersection(X0,intersection(X1,complement(subset_relation))),X2),identity_relation) ),
inference(superposition,[status(thm)],[c_4646,c_11581]) ).
tcf(c_12168,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(complement(subset_relation),X1)),X2)
| ~ member(not_subclass_element(intersection(X0,intersection(complement(subset_relation),X1)),X2),identity_relation) ),
inference(superposition,[status(thm)],[c_4647,c_11581]) ).
tcf(c_12263,plain,
! [X0: $i] :
( ( domain_of(flip(cross_product(subset_relation,universal_class))) = intersection(X0,identity_relation) )
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),intersection(X0,identity_relation)) ),
inference(superposition,[status(thm)],[c_11623,c_176]) ).
tcf(c_12264,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,identity_relation),X0)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ),
inference(superposition,[status(thm)],[c_11623,c_250]) ).
tcf(c_12265,plain,
! [X0: $i,X1: $i] :
( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,intersection(X1,identity_relation)) ),
inference(superposition,[status(thm)],[c_11623,c_170]) ).
tcf(c_12275,plain,
! [X0: $i] : intersection(null_class,intersection(universal_class,X0)) = null_class,
inference(superposition,[status(thm)],[c_4953,c_11685]) ).
tcf(c_12276,plain,
! [X0: $i] : intersection(universal_class,intersection(null_class,X0)) = null_class,
inference(superposition,[status(thm)],[c_8703,c_11685]) ).
tcf(c_12278,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(complement(cross_product(X0,X1)),intersection(X2,cross_product(X0,X1))) = null_class,
inference(superposition,[status(thm)],[c_193,c_11685]) ).
tcf(c_12279,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(complement(X0),null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_11685]) ).
tcf(c_12280,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(complement(X0),intersection(cross_product(X1,X2),X0)) = null_class,
inference(superposition,[status(thm)],[c_193,c_11685]) ).
tcf(c_12282,plain,
intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) = null_class,
inference(superposition,[status(thm)],[c_230,c_11685]) ).
tcf(c_12283,plain,
! [X0: $i,X1: $i] : intersection(complement(cross_product(X0,X1)),null_class) = null_class,
inference(superposition,[status(thm)],[c_4217,c_11685]) ).
tcf(c_12287,plain,
intersection(complement(complement(subset_relation)),null_class) = null_class,
inference(superposition,[status(thm)],[c_11311,c_11685]) ).
tcf(c_12288,plain,
! [X0: $i] : intersection(complement(complement(X0)),null_class) = null_class,
inference(superposition,[status(thm)],[c_11685,c_11685]) ).
tcf(c_12293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),complement(X0))
| subclass(intersection(intersection(complement(X0),intersection(X0,X1)),X2),X3) ),
inference(superposition,[status(thm)],[c_11685,c_4431]) ).
tcf(c_12295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),intersection(X0,X1))
| subclass(intersection(intersection(complement(X0),intersection(X0,X1)),X2),X3) ),
inference(superposition,[status(thm)],[c_11685,c_4430]) ).
tcf(c_12297,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(X0,X1))
| subclass(intersection(complement(X0),intersection(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_11685,c_4245]) ).
tcf(c_12299,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),complement(X0))
| subclass(intersection(complement(X0),intersection(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_11685,c_4224]) ).
tcf(c_12301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),complement(X1))
| subclass(intersection(X0,intersection(complement(X1),intersection(X1,X2))),X3) ),
inference(superposition,[status(thm)],[c_11685,c_4647]) ).
tcf(c_12303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),intersection(X1,X2))
| subclass(intersection(X0,intersection(complement(X1),intersection(X1,X2))),X3) ),
inference(superposition,[status(thm)],[c_11685,c_4646]) ).
tcf(c_12306,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,null_class)
| ~ member(X0,complement(X1))
| ~ member(X0,intersection(X1,X2)) ),
inference(superposition,[status(thm)],[c_11685,c_190]) ).
tcf(c_12311,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(X1),intersection(X1,X2)),X0)
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_11685,c_4432]) ).
tcf(c_12313,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(complement(X0),intersection(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_11685,c_4647]) ).
tcf(c_12315,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(complement(X0),intersection(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_11685,c_4646]) ).
tcf(c_12327,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,complement(X1))
| ~ member(X0,intersection(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12306,c_256]) ).
tcf(c_12371,plain,
! [X0: $i] : subclass(intersection(null_class,universal_class),X0),
inference(superposition,[status(thm)],[c_8703,c_12025]) ).
tcf(c_12372,plain,
! [X0: $i,X1: $i] :
( ( intersection(X1,complement(X1)) = X0 )
| ~ subclass(X0,intersection(X1,complement(X1))) ),
inference(superposition,[status(thm)],[c_12025,c_176]) ).
tcf(c_12374,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,complement(X1))) ),
inference(superposition,[status(thm)],[c_12025,c_170]) ).
tcf(c_12375,plain,
! [X0: $i,X1: $i] : intersection(X0,intersection(X1,complement(X1))) = null_class,
inference(superposition,[status(thm)],[c_12025,c_5287]) ).
tcf(c_12376,plain,
! [X0: $i,X1: $i] : intersection(intersection(X0,complement(X0)),X1) = null_class,
inference(superposition,[status(thm)],[c_12025,c_5257]) ).
tcf(c_12377,plain,
! [X0: $i] : intersection(X0,complement(X0)) = null_class,
inference(superposition,[status(thm)],[c_12025,c_258]) ).
tcf(c_12389,plain,
! [X0: $i] :
( ( intersection(identity_relation,complement(subset_relation)) = X0 )
| ~ subclass(X0,intersection(identity_relation,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_12035,c_176]) ).
tcf(c_12391,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,intersection(identity_relation,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_12035,c_170]) ).
tcf(c_12392,plain,
! [X0: $i] : intersection(X0,intersection(identity_relation,complement(subset_relation))) = null_class,
inference(superposition,[status(thm)],[c_12035,c_5287]) ).
tcf(c_12393,plain,
! [X0: $i] : intersection(intersection(identity_relation,complement(subset_relation)),X0) = null_class,
inference(superposition,[status(thm)],[c_12035,c_5257]) ).
tcf(c_12394,plain,
intersection(identity_relation,complement(subset_relation)) = null_class,
inference(superposition,[status(thm)],[c_12035,c_258]) ).
tcf(c_12405,plain,
! [X0: $i,X1: $i] : subclass(intersection(complement(subset_relation),cross_product(X0,X1)),complement(identity_relation)),
inference(superposition,[status(thm)],[c_193,c_12038]) ).
tcf(c_12407,plain,
! [X0: $i] :
( ( intersection(X0,complement(subset_relation)) = complement(identity_relation) )
| ~ subclass(complement(identity_relation),intersection(X0,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_12038,c_176]) ).
tcf(c_12408,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,complement(subset_relation)),X0)
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_12038,c_250]) ).
tcf(c_12409,plain,
! [X0: $i,X1: $i] :
( member(X0,complement(identity_relation))
| ~ member(X0,intersection(X1,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_12038,c_170]) ).
tcf(c_12425,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),X0)
| subclass(intersection(intersection(X0,complement(X0)),X1),X2) ),
inference(superposition,[status(thm)],[c_12377,c_4431]) ).
tcf(c_12427,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),complement(X0))
| subclass(intersection(intersection(X0,complement(X0)),X1),X2) ),
inference(superposition,[status(thm)],[c_12377,c_4430]) ).
tcf(c_12429,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),complement(X0))
| subclass(intersection(X0,complement(X0)),X1) ),
inference(superposition,[status(thm)],[c_12377,c_4245]) ).
tcf(c_12431,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),X0)
| subclass(intersection(X0,complement(X0)),X1) ),
inference(superposition,[status(thm)],[c_12377,c_4224]) ).
tcf(c_12433,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,null_class),X2),X1)
| subclass(intersection(X0,intersection(X1,complement(X1))),X2) ),
inference(superposition,[status(thm)],[c_12377,c_4647]) ).
tcf(c_12435,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,null_class),X2),complement(X1))
| subclass(intersection(X0,intersection(X1,complement(X1))),X2) ),
inference(superposition,[status(thm)],[c_12377,c_4646]) ).
tcf(c_12446,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(intersection(X0,X1),complement(intersection(X0,X1))),X2) ),
inference(superposition,[status(thm)],[c_12377,c_4431]) ).
tcf(c_12448,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(intersection(X0,X1),complement(intersection(X0,X1))),X2) ),
inference(superposition,[status(thm)],[c_12377,c_4430]) ).
tcf(c_12449,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(X1),complement(complement(X1))),X0)
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_12377,c_4432]) ).
tcf(c_12450,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),subset_relation)
| subclass(intersection(identity_relation,complement(identity_relation)),X0) ),
inference(superposition,[status(thm)],[c_12377,c_4433]) ).
tcf(c_12453,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,complement(X1)),X0)
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_12377,c_4648]) ).
tcf(c_12569,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),identity_relation)
| subclass(intersection(intersection(identity_relation,complement(subset_relation)),X0),X1) ),
inference(superposition,[status(thm)],[c_12394,c_4431]) ).
tcf(c_12571,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(identity_relation,complement(subset_relation)),X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_12394,c_4430]) ).
tcf(c_12573,plain,
! [X0: $i] :
( subclass(intersection(identity_relation,complement(subset_relation)),X0)
| member(not_subclass_element(null_class,X0),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_12394,c_4245]) ).
tcf(c_12575,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),identity_relation)
| subclass(intersection(identity_relation,complement(subset_relation)),X0) ),
inference(superposition,[status(thm)],[c_12394,c_4224]) ).
tcf(c_12577,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),identity_relation)
| subclass(intersection(X0,intersection(identity_relation,complement(subset_relation))),X1) ),
inference(superposition,[status(thm)],[c_12394,c_4647]) ).
tcf(c_12579,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(identity_relation,complement(subset_relation))),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_12394,c_4646]) ).
tcf(c_12587,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),subset_relation)
| subclass(intersection(identity_relation,complement(subset_relation)),X0) ),
inference(superposition,[status(thm)],[c_12394,c_4433]) ).
tcf(c_12590,plain,
! [X0: $i] :
( subclass(intersection(identity_relation,complement(subset_relation)),X0)
| ~ member(not_subclass_element(null_class,X0),subset_relation) ),
inference(superposition,[status(thm)],[c_12394,c_4648]) ).
tcf(c_12606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(X0,cross_product(X1,X2)),complement(X0)),X3),
inference(superposition,[status(thm)],[c_193,c_12033]) ).
tcf(c_12608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(cross_product(X0,X1),X2),complement(cross_product(X0,X1))),X3),
inference(superposition,[status(thm)],[c_193,c_12033]) ).
tcf(c_12609,plain,
! [X0: $i] : subclass(intersection(subset_relation,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X0),
inference(superposition,[status(thm)],[c_229,c_12033]) ).
tcf(c_12611,plain,
! [X0: $i,X1: $i] : subclass(intersection(null_class,complement(X0)),X1),
inference(superposition,[status(thm)],[c_4553,c_12033]) ).
tcf(c_12612,plain,
! [X0: $i] : subclass(intersection(null_class,complement(null_class)),X0),
inference(superposition,[status(thm)],[c_4790,c_12033]) ).
tcf(c_12618,plain,
! [X0: $i,X1: $i] : subclass(intersection(intersection(X0,universal_class),null_class),X1),
inference(superposition,[status(thm)],[c_4953,c_12033]) ).
tcf(c_12619,plain,
! [X0: $i,X1: $i] : subclass(intersection(intersection(X0,null_class),universal_class),X1),
inference(superposition,[status(thm)],[c_8703,c_12033]) ).
tcf(c_12620,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X1,X2),complement(X2)) = X0 )
| ~ subclass(X0,intersection(intersection(X1,X2),complement(X2))) ),
inference(superposition,[status(thm)],[c_12033,c_176]) ).
tcf(c_12622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| ~ member(X0,intersection(intersection(X1,X2),complement(X2))) ),
inference(superposition,[status(thm)],[c_12033,c_170]) ).
tcf(c_12623,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(X0,intersection(intersection(X1,X2),complement(X2))) = null_class,
inference(superposition,[status(thm)],[c_12033,c_5287]) ).
tcf(c_12624,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(intersection(X0,X1),complement(X1)),X2) = null_class,
inference(superposition,[status(thm)],[c_12033,c_5257]) ).
tcf(c_12625,plain,
! [X0: $i,X1: $i] : intersection(intersection(X0,X1),complement(X1)) = null_class,
inference(superposition,[status(thm)],[c_12033,c_258]) ).
tcf(c_12669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(X0,cross_product(X1,X2)),complement(cross_product(X1,X2))),X3),
inference(superposition,[status(thm)],[c_193,c_12034]) ).
tcf(c_12670,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,complement(X0)),X1)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_12034]) ).
tcf(c_12671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(cross_product(X0,X1),X2),complement(X2)),X3),
inference(superposition,[status(thm)],[c_193,c_12034]) ).
tcf(c_12672,plain,
! [X0: $i] : subclass(intersection(subset_relation,complement(cross_product(universal_class,universal_class))),X0),
inference(superposition,[status(thm)],[c_229,c_12034]) ).
tcf(c_12673,plain,
! [X0: $i] : subclass(intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),X0),
inference(superposition,[status(thm)],[c_230,c_12034]) ).
tcf(c_12678,plain,
! [X0: $i,X1: $i] : subclass(intersection(null_class,complement(complement(X0))),X1),
inference(superposition,[status(thm)],[c_11685,c_12034]) ).
tcf(c_12680,plain,
! [X0: $i] : subclass(intersection(null_class,complement(identity_relation)),X0),
inference(superposition,[status(thm)],[c_12394,c_12034]) ).
tcf(c_12681,plain,
! [X0: $i,X1: $i] : subclass(intersection(intersection(universal_class,X0),null_class),X1),
inference(superposition,[status(thm)],[c_4953,c_12034]) ).
tcf(c_12682,plain,
! [X0: $i,X1: $i] : subclass(intersection(intersection(null_class,X0),universal_class),X1),
inference(superposition,[status(thm)],[c_8703,c_12034]) ).
tcf(c_12683,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X1,X2),complement(X1)) = X0 )
| ~ subclass(X0,intersection(intersection(X1,X2),complement(X1))) ),
inference(superposition,[status(thm)],[c_12034,c_176]) ).
tcf(c_12685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| ~ member(X0,intersection(intersection(X1,X2),complement(X1))) ),
inference(superposition,[status(thm)],[c_12034,c_170]) ).
tcf(c_12686,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(X0,intersection(intersection(X1,X2),complement(X1))) = null_class,
inference(superposition,[status(thm)],[c_12034,c_5287]) ).
tcf(c_12687,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(intersection(X0,X1),complement(X0)),X2) = null_class,
inference(superposition,[status(thm)],[c_12034,c_5257]) ).
tcf(c_12688,plain,
! [X0: $i,X1: $i] : intersection(intersection(X0,X1),complement(X0)) = null_class,
inference(superposition,[status(thm)],[c_12034,c_258]) ).
tcf(c_12709,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),subset_relation)
| subclass(intersection(complement(identity_relation),identity_relation),X0) ),
inference(superposition,[status(thm)],[c_4169,c_4649]) ).
tcf(c_12711,plain,
! [X0: $i] :
( subclass(intersection(null_class,identity_relation),X0)
| member(not_subclass_element(null_class,X0),subset_relation) ),
inference(superposition,[status(thm)],[c_4553,c_4649]) ).
tcf(c_12712,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),subset_relation)
| subclass(intersection(complement(subset_relation),identity_relation),X0) ),
inference(superposition,[status(thm)],[c_11311,c_4649]) ).
tcf(c_12716,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),cross_product(universal_class,universal_class))
| ~ function(subset_relation) ),
inference(superposition,[status(thm)],[c_4649,c_4342]) ).
tcf(c_12717,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),universal_class) ),
inference(superposition,[status(thm)],[c_4649,c_4336]) ).
tcf(c_12733,plain,
! [X0: $i] :
( ( intersection(subset_relation,complement(cross_product(universal_class,universal_class))) = X0 )
| ~ subclass(X0,intersection(subset_relation,complement(cross_product(universal_class,universal_class)))) ),
inference(superposition,[status(thm)],[c_12672,c_176]) ).
tcf(c_12735,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,intersection(subset_relation,complement(cross_product(universal_class,universal_class)))) ),
inference(superposition,[status(thm)],[c_12672,c_170]) ).
tcf(c_12736,plain,
! [X0: $i] : intersection(X0,intersection(subset_relation,complement(cross_product(universal_class,universal_class)))) = null_class,
inference(superposition,[status(thm)],[c_12672,c_5287]) ).
tcf(c_12737,plain,
! [X0: $i] : intersection(intersection(subset_relation,complement(cross_product(universal_class,universal_class))),X0) = null_class,
inference(superposition,[status(thm)],[c_12672,c_5257]) ).
tcf(c_12738,plain,
intersection(subset_relation,complement(cross_product(universal_class,universal_class))) = null_class,
inference(superposition,[status(thm)],[c_12672,c_258]) ).
tcf(c_12748,plain,
intersection(complement(complement(cross_product(universal_class,universal_class))),null_class) = null_class,
inference(superposition,[status(thm)],[c_11763,c_11685]) ).
tcf(c_12751,plain,
! [X0: $i] : subclass(intersection(null_class,X0),complement(cross_product(universal_class,universal_class))),
inference(superposition,[status(thm)],[c_11763,c_6583]) ).
tcf(c_12752,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(complement(cross_product(universal_class,universal_class)),subset_relation),X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_11763,c_4431]) ).
tcf(c_12753,plain,
! [X0: $i] : subclass(intersection(null_class,X0),subset_relation),
inference(superposition,[status(thm)],[c_11763,c_6065]) ).
tcf(c_12754,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),subset_relation)
| subclass(intersection(intersection(complement(cross_product(universal_class,universal_class)),subset_relation),X0),X1) ),
inference(superposition,[status(thm)],[c_11763,c_4430]) ).
tcf(c_12756,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),subset_relation)
| subclass(intersection(complement(cross_product(universal_class,universal_class)),subset_relation),X0) ),
inference(superposition,[status(thm)],[c_11763,c_4245]) ).
tcf(c_12757,plain,
subclass(null_class,complement(cross_product(universal_class,universal_class))),
inference(superposition,[status(thm)],[c_11763,c_4427]) ).
tcf(c_12758,plain,
! [X0: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),subset_relation),X0)
| member(not_subclass_element(null_class,X0),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_11763,c_4224]) ).
tcf(c_12759,plain,
! [X0: $i] : subclass(intersection(X0,null_class),complement(cross_product(universal_class,universal_class))),
inference(superposition,[status(thm)],[c_11763,c_11340]) ).
tcf(c_12760,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),subset_relation)),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_11763,c_4647]) ).
tcf(c_12761,plain,
! [X0: $i] : subclass(intersection(X0,null_class),subset_relation),
inference(superposition,[status(thm)],[c_11763,c_10731]) ).
tcf(c_12762,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),subset_relation)
| subclass(intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),subset_relation)),X1) ),
inference(superposition,[status(thm)],[c_11763,c_4646]) ).
tcf(c_12763,plain,
! [X0: $i,X1: $i] :
( member(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_11763,c_6783]) ).
tcf(c_12764,plain,
! [X0: $i,X1: $i] :
( member(X0,subset_relation)
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_11763,c_6250]) ).
tcf(c_12765,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,subset_relation)
| ~ member(X0,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_11763,c_190]) ).
tcf(c_12768,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ~ subclass(complement(cross_product(universal_class,universal_class)),X0) ),
inference(superposition,[status(thm)],[c_11763,c_6782]) ).
tcf(c_12770,plain,
! [X0: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),subset_relation),X0)
| ~ member(not_subclass_element(null_class,X0),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_11763,c_4432]) ).
tcf(c_12771,plain,
intersection(complement(subset_relation),null_class) = null_class,
inference(superposition,[status(thm)],[c_11763,c_11228]) ).
tcf(c_12772,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_11763,c_6249]) ).
tcf(c_12788,plain,
! [X0: $i] :
( ~ member(X0,subset_relation)
| ~ member(X0,complement(cross_product(universal_class,universal_class))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12765,c_256]) ).
tcf(c_12791,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ member(not_subclass_element(null_class,X0),cross_product(universal_class,universal_class)) ),
inference(light_normalisation,[status(thm)],[c_12770,c_11763]) ).
tcf(c_12792,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),complement(cross_product(universal_class,universal_class))) ),
inference(light_normalisation,[status(thm)],[c_12758,c_11763]) ).
tcf(c_12878,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(X0,cross_product(X1,X2)),complement(X0)) = null_class,
inference(superposition,[status(thm)],[c_193,c_12625]) ).
tcf(c_12879,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(null_class,complement(regular(X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_12625]) ).
tcf(c_12880,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(cross_product(X0,X1),X2),complement(cross_product(X0,X1))) = null_class,
inference(superposition,[status(thm)],[c_193,c_12625]) ).
tcf(c_12881,plain,
intersection(subset_relation,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))) = null_class,
inference(superposition,[status(thm)],[c_229,c_12625]) ).
tcf(c_12883,plain,
! [X0: $i] : intersection(null_class,complement(X0)) = null_class,
inference(superposition,[status(thm)],[c_4553,c_12625]) ).
tcf(c_12884,plain,
intersection(null_class,complement(null_class)) = null_class,
inference(superposition,[status(thm)],[c_4790,c_12625]) ).
tcf(c_12886,plain,
intersection(null_class,complement(identity_relation)) = null_class,
inference(superposition,[status(thm)],[c_11311,c_12625]) ).
tcf(c_12887,plain,
! [X0: $i,X1: $i] : intersection(null_class,complement(intersection(X0,X1))) = null_class,
inference(superposition,[status(thm)],[c_11685,c_12625]) ).
tcf(c_12888,plain,
intersection(null_class,complement(subset_relation)) = null_class,
inference(superposition,[status(thm)],[c_11763,c_12625]) ).
tcf(c_12891,plain,
intersection(null_class,complement(complement(subset_relation))) = null_class,
inference(superposition,[status(thm)],[c_12394,c_12625]) ).
tcf(c_12892,plain,
! [X0: $i] : intersection(intersection(X0,universal_class),null_class) = null_class,
inference(superposition,[status(thm)],[c_4953,c_12625]) ).
tcf(c_12893,plain,
! [X0: $i] : intersection(intersection(X0,null_class),universal_class) = null_class,
inference(superposition,[status(thm)],[c_8703,c_12625]) ).
tcf(c_12894,plain,
! [X0: $i] : intersection(null_class,complement(complement(X0))) = null_class,
inference(superposition,[status(thm)],[c_12625,c_12625]) ).
tcf(c_12899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),intersection(X0,X1))
| subclass(intersection(intersection(intersection(X0,X1),complement(X1)),X2),X3) ),
inference(superposition,[status(thm)],[c_12625,c_4431]) ).
tcf(c_12901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),complement(X1))
| subclass(intersection(intersection(intersection(X0,X1),complement(X1)),X2),X3) ),
inference(superposition,[status(thm)],[c_12625,c_4430]) ).
tcf(c_12903,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),complement(X1))
| subclass(intersection(intersection(X0,X1),complement(X1)),X2) ),
inference(superposition,[status(thm)],[c_12625,c_4245]) ).
tcf(c_12905,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(X0,X1))
| subclass(intersection(intersection(X0,X1),complement(X1)),X2) ),
inference(superposition,[status(thm)],[c_12625,c_4224]) ).
tcf(c_12907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),intersection(X1,X2))
| subclass(intersection(X0,intersection(intersection(X1,X2),complement(X2))),X3) ),
inference(superposition,[status(thm)],[c_12625,c_4647]) ).
tcf(c_12909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),complement(X2))
| subclass(intersection(X0,intersection(intersection(X1,X2),complement(X2))),X3) ),
inference(superposition,[status(thm)],[c_12625,c_4646]) ).
tcf(c_12918,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(intersection(X0,X1),complement(X1)),X2) ),
inference(superposition,[status(thm)],[c_12625,c_4431]) ).
tcf(c_12920,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(intersection(X0,X1),complement(X1)),X2) ),
inference(superposition,[status(thm)],[c_12625,c_4430]) ).
tcf(c_12921,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X2,X1),complement(X1)),X0)
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_12625,c_4648]) ).
tcf(c_12999,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(X0,cross_product(X1,X2)),complement(cross_product(X1,X2))) = null_class,
inference(superposition,[status(thm)],[c_193,c_12688]) ).
tcf(c_13000,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(null_class,complement(X0)) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_12688]) ).
tcf(c_13001,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(cross_product(X0,X1),X2),complement(X2)) = null_class,
inference(superposition,[status(thm)],[c_193,c_12688]) ).
tcf(c_13003,plain,
intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) = null_class,
inference(superposition,[status(thm)],[c_230,c_12688]) ).
tcf(c_13009,plain,
intersection(null_class,complement(complement(cross_product(universal_class,universal_class)))) = null_class,
inference(superposition,[status(thm)],[c_11763,c_12688]) ).
tcf(c_13014,plain,
! [X0: $i] : intersection(intersection(universal_class,X0),null_class) = null_class,
inference(superposition,[status(thm)],[c_4953,c_12688]) ).
tcf(c_13015,plain,
! [X0: $i] : intersection(intersection(null_class,X0),universal_class) = null_class,
inference(superposition,[status(thm)],[c_8703,c_12688]) ).
tcf(c_13022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),intersection(X0,X1))
| subclass(intersection(intersection(intersection(X0,X1),complement(X0)),X2),X3) ),
inference(superposition,[status(thm)],[c_12688,c_4431]) ).
tcf(c_13024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),complement(X0))
| subclass(intersection(intersection(intersection(X0,X1),complement(X0)),X2),X3) ),
inference(superposition,[status(thm)],[c_12688,c_4430]) ).
tcf(c_13026,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),complement(X0))
| subclass(intersection(intersection(X0,X1),complement(X0)),X2) ),
inference(superposition,[status(thm)],[c_12688,c_4245]) ).
tcf(c_13028,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(X0,X1))
| subclass(intersection(intersection(X0,X1),complement(X0)),X2) ),
inference(superposition,[status(thm)],[c_12688,c_4224]) ).
tcf(c_13030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),intersection(X1,X2))
| subclass(intersection(X0,intersection(intersection(X1,X2),complement(X1))),X3) ),
inference(superposition,[status(thm)],[c_12688,c_4647]) ).
tcf(c_13032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),complement(X1))
| subclass(intersection(X0,intersection(intersection(X1,X2),complement(X1))),X3) ),
inference(superposition,[status(thm)],[c_12688,c_4646]) ).
tcf(c_13041,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(intersection(X0,X1),complement(X0)),X2) ),
inference(superposition,[status(thm)],[c_12688,c_4431]) ).
tcf(c_13043,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(intersection(X0,X1),complement(X0)),X2) ),
inference(superposition,[status(thm)],[c_12688,c_4430]) ).
tcf(c_13044,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X1,X2),complement(X1)),X0)
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_12688,c_4648]) ).
tcf(c_13070,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ subclass(identity_relation,X0) ),
inference(demodulation,[status(thm)],[c_11563,c_4553]) ).
tcf(c_13080,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),subset_relation)
| subclass(intersection(intersection(subset_relation,complement(cross_product(universal_class,universal_class))),X0),X1) ),
inference(superposition,[status(thm)],[c_12738,c_4431]) ).
tcf(c_13082,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(subset_relation,complement(cross_product(universal_class,universal_class))),X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_12738,c_4430]) ).
tcf(c_13084,plain,
! [X0: $i] :
( subclass(intersection(subset_relation,complement(cross_product(universal_class,universal_class))),X0)
| member(not_subclass_element(null_class,X0),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_12738,c_4245]) ).
tcf(c_13086,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),subset_relation)
| subclass(intersection(subset_relation,complement(cross_product(universal_class,universal_class))),X0) ),
inference(superposition,[status(thm)],[c_12738,c_4224]) ).
tcf(c_13088,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),subset_relation)
| subclass(intersection(X0,intersection(subset_relation,complement(cross_product(universal_class,universal_class)))),X1) ),
inference(superposition,[status(thm)],[c_12738,c_4647]) ).
tcf(c_13090,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(subset_relation,complement(cross_product(universal_class,universal_class)))),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_12738,c_4646]) ).
tcf(c_13098,plain,
! [X0: $i] :
( subclass(intersection(subset_relation,complement(cross_product(universal_class,universal_class))),X0)
| ~ member(not_subclass_element(null_class,X0),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_12738,c_4648]) ).
tcf(c_13113,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ subclass(subset_relation,X0) ),
inference(demodulation,[status(thm)],[c_12772,c_4553]) ).
tcf(c_13123,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(first(unordered_pair(X0,X1)),first(unordered_pair(X0,X1))),unordered_pair(first(unordered_pair(X0,X1)),unordered_pair(second(unordered_pair(X0,X1)),second(unordered_pair(X0,X1))))) = unordered_pair(X0,X1) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_10212,c_184]) ).
tcf(c_13124,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X1,X0))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_10212,c_246]) ).
tcf(c_13125,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_10212,c_245]) ).
tcf(c_13126,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_10212,c_248]) ).
tcf(c_13130,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ function(universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_10212,c_187]) ).
tcf(c_13131,plain,
! [X0: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_10212,c_204]) ).
tcf(c_13156,plain,
! [X0: $i] : subclass(intersection(element_relation,X0),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4224,c_4850]) ).
tcf(c_13157,plain,
! [X0: $i] : subclass(intersection(X0,element_relation),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4245,c_4850]) ).
tcf(c_13159,plain,
! [X0: $i,X1: $i] : subclass(intersection(intersection(X0,element_relation),X1),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4430,c_4850]) ).
tcf(c_13160,plain,
! [X0: $i,X1: $i] : subclass(intersection(intersection(element_relation,X0),X1),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4431,c_4850]) ).
tcf(c_13162,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,intersection(X1,element_relation)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4646,c_4850]) ).
tcf(c_13163,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,intersection(element_relation,X1)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4647,c_4850]) ).
tcf(c_13174,plain,
! [X0: $i] :
( ( X0 = universal_class )
| ~ function(universal_class)
| ~ member(not_subclass_element(universal_class,X0),X0) ),
inference(superposition,[status(thm)],[c_13126,c_254]) ).
tcf(c_13175,plain,
! [X0: $i] :
( member(not_subclass_element(universal_class,X0),universal_class)
| ( X0 = universal_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13126,c_253]) ).
tcf(c_13177,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13126,c_4342]) ).
tcf(c_13179,plain,
! [X0: $i] :
( subclass(complement(universal_class),X0)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13126,c_4264]) ).
tcf(c_13182,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(universal_class),X0),X1)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13126,c_4432]) ).
tcf(c_13183,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(universal_class)),X1)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13126,c_4648]) ).
tcf(c_13184,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ function(universal_class) ),
inference(light_normalisation,[status(thm)],[c_13179,c_4953]) ).
tcf(c_13203,plain,
! [X0: $i,X1: $i] :
( member(X1,cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ function(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_13124,c_4342]) ).
tcf(c_13228,plain,
( subclass(null_class,cross_product(universal_class,universal_class))
| ( null_class = element_relation ) ),
inference(superposition,[status(thm)],[c_223,c_13156]) ).
tcf(c_13231,plain,
! [X0: $i] :
( ( intersection(element_relation,X0) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(element_relation,X0)) ),
inference(superposition,[status(thm)],[c_13156,c_176]) ).
tcf(c_13232,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(element_relation,X1),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13156,c_250]) ).
tcf(c_13233,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(element_relation,X1)) ),
inference(superposition,[status(thm)],[c_13156,c_170]) ).
tcf(c_13244,plain,
! [X0: $i,X1: $i] : subclass(intersection(element_relation,cross_product(X0,X1)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13157]) ).
tcf(c_13246,plain,
! [X0: $i] :
( ( intersection(X0,element_relation) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(X0,element_relation)) ),
inference(superposition,[status(thm)],[c_13157,c_176]) ).
tcf(c_13247,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,element_relation),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13157,c_250]) ).
tcf(c_13248,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(X1,element_relation)) ),
inference(superposition,[status(thm)],[c_13157,c_170]) ).
tcf(c_13262,plain,
! [X0: $i] :
( ( cross_product(universal_class,universal_class) = X0 )
| ~ function(universal_class)
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),X0),X0) ),
inference(superposition,[status(thm)],[c_13177,c_254]) ).
tcf(c_13263,plain,
! [X0: $i] :
( member(not_subclass_element(cross_product(universal_class,universal_class),X0),cross_product(universal_class,universal_class))
| ( cross_product(universal_class,universal_class) = X0 )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13177,c_253]) ).
tcf(c_13267,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13177,c_184]) ).
tcf(c_13276,plain,
! [X0: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13177,c_4264]) ).
tcf(c_13277,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13177,c_4265]) ).
tcf(c_13279,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X0),X1)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13177,c_4432]) ).
tcf(c_13280,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(cross_product(universal_class,universal_class))),X1)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13177,c_4648]) ).
tcf(c_13301,plain,
! [X0: $i] :
( subclass(null_class,cross_product(universal_class,universal_class))
| ( intersection(X0,element_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_13159]) ).
tcf(c_13302,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(cross_product(X0,X1),intersection(X2,element_relation)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13159]) ).
tcf(c_13308,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(element_relation,cross_product(X0,X1)),X2),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13159]) ).
tcf(c_13309,plain,
! [X0: $i] : subclass(intersection(null_class,X0),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4553,c_13159]) ).
tcf(c_13310,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,element_relation),X1) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(intersection(X0,element_relation),X1)) ),
inference(superposition,[status(thm)],[c_13159,c_176]) ).
tcf(c_13311,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X1,element_relation),X2),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13159,c_250]) ).
tcf(c_13312,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(intersection(X1,element_relation),X2)) ),
inference(superposition,[status(thm)],[c_13159,c_170]) ).
tcf(c_13368,plain,
! [X0: $i] :
( subclass(null_class,cross_product(universal_class,universal_class))
| ( intersection(element_relation,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_13160]) ).
tcf(c_13369,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(cross_product(X0,X1),intersection(element_relation,X2)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13160]) ).
tcf(c_13374,plain,
! [X0: $i] :
( subclass(intersection(null_class,X0),cross_product(universal_class,universal_class))
| ( null_class = element_relation ) ),
inference(superposition,[status(thm)],[c_223,c_13160]) ).
tcf(c_13377,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(element_relation,X0),X1) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(intersection(element_relation,X0),X1)) ),
inference(superposition,[status(thm)],[c_13160,c_176]) ).
tcf(c_13378,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(element_relation,X1),X2),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13160,c_250]) ).
tcf(c_13379,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(intersection(element_relation,X1),X2)) ),
inference(superposition,[status(thm)],[c_13160,c_170]) ).
tcf(c_13392,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(X0,element_relation),cross_product(X1,X2)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13162]) ).
tcf(c_13397,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(X0,intersection(element_relation,cross_product(X1,X2))),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13162]) ).
tcf(c_13398,plain,
! [X0: $i] : subclass(intersection(X0,null_class),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4553,c_13162]) ).
tcf(c_13399,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,element_relation)) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(X0,intersection(X1,element_relation))) ),
inference(superposition,[status(thm)],[c_13162,c_176]) ).
tcf(c_13400,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,intersection(X2,element_relation)),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13162,c_250]) ).
tcf(c_13401,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(X1,intersection(X2,element_relation))) ),
inference(superposition,[status(thm)],[c_13162,c_170]) ).
tcf(c_13443,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(element_relation,X0),cross_product(X1,X2)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13163]) ).
tcf(c_13447,plain,
! [X0: $i] :
( subclass(intersection(X0,null_class),cross_product(universal_class,universal_class))
| ( null_class = element_relation ) ),
inference(superposition,[status(thm)],[c_223,c_13163]) ).
tcf(c_13450,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(element_relation,X1)) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(X0,intersection(element_relation,X1))) ),
inference(superposition,[status(thm)],[c_13163,c_176]) ).
tcf(c_13451,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,intersection(element_relation,X2)),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13163,c_250]) ).
tcf(c_13452,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(X1,intersection(element_relation,X2))) ),
inference(superposition,[status(thm)],[c_13163,c_170]) ).
tcf(c_13467,plain,
! [X0: $i] :
( ( complement(cross_product(universal_class,universal_class)) = X0 )
| ~ function(universal_class)
| ~ subclass(X0,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_13276,c_176]) ).
tcf(c_13468,plain,
! [X0: $i,X1: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X1)
| ~ function(universal_class)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13276,c_250]) ).
tcf(c_13469,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ function(universal_class)
| ~ member(X0,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_13276,c_170]) ).
tcf(c_13470,plain,
! [X0: $i] :
( ( intersection(X0,complement(cross_product(universal_class,universal_class))) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13276,c_5287]) ).
tcf(c_13471,plain,
! [X0: $i] :
( ( intersection(complement(cross_product(universal_class,universal_class)),X0) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13276,c_5257]) ).
tcf(c_13498,plain,
! [X0: $i] : subclass(intersection(successor_relation,X0),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4224,c_4862]) ).
tcf(c_13499,plain,
! [X0: $i] : subclass(intersection(X0,successor_relation),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4245,c_4862]) ).
tcf(c_13501,plain,
! [X0: $i,X1: $i] : subclass(intersection(intersection(X0,successor_relation),X1),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4430,c_4862]) ).
tcf(c_13502,plain,
! [X0: $i,X1: $i] : subclass(intersection(intersection(successor_relation,X0),X1),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4431,c_4862]) ).
tcf(c_13504,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,intersection(X1,successor_relation)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4646,c_4862]) ).
tcf(c_13505,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,intersection(successor_relation,X1)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_4647,c_4862]) ).
tcf(c_13532,plain,
( subclass(null_class,cross_product(universal_class,universal_class))
| ( null_class = successor_relation ) ),
inference(superposition,[status(thm)],[c_223,c_13498]) ).
tcf(c_13535,plain,
! [X0: $i] :
( ( intersection(successor_relation,X0) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(successor_relation,X0)) ),
inference(superposition,[status(thm)],[c_13498,c_176]) ).
tcf(c_13536,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(successor_relation,X1),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13498,c_250]) ).
tcf(c_13537,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(successor_relation,X1)) ),
inference(superposition,[status(thm)],[c_13498,c_170]) ).
tcf(c_13548,plain,
! [X0: $i,X1: $i] : subclass(intersection(successor_relation,cross_product(X0,X1)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13499]) ).
tcf(c_13550,plain,
! [X0: $i] :
( ( intersection(X0,successor_relation) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(X0,successor_relation)) ),
inference(superposition,[status(thm)],[c_13499,c_176]) ).
tcf(c_13551,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,successor_relation),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13499,c_250]) ).
tcf(c_13552,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(X1,successor_relation)) ),
inference(superposition,[status(thm)],[c_13499,c_170]) ).
tcf(c_13566,plain,
! [X0: $i] :
( subclass(null_class,cross_product(universal_class,universal_class))
| ( intersection(X0,successor_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_13501]) ).
tcf(c_13567,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(cross_product(X0,X1),intersection(X2,successor_relation)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13501]) ).
tcf(c_13573,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(successor_relation,cross_product(X0,X1)),X2),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13501]) ).
tcf(c_13575,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,successor_relation),X1) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(intersection(X0,successor_relation),X1)) ),
inference(superposition,[status(thm)],[c_13501,c_176]) ).
tcf(c_13576,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X1,successor_relation),X2),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13501,c_250]) ).
tcf(c_13577,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(intersection(X1,successor_relation),X2)) ),
inference(superposition,[status(thm)],[c_13501,c_170]) ).
tcf(c_13649,plain,
! [X0: $i] :
( subclass(null_class,cross_product(universal_class,universal_class))
| ( intersection(successor_relation,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_13502]) ).
tcf(c_13650,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(cross_product(X0,X1),intersection(successor_relation,X2)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13502]) ).
tcf(c_13655,plain,
! [X0: $i] :
( subclass(intersection(null_class,X0),cross_product(universal_class,universal_class))
| ( null_class = successor_relation ) ),
inference(superposition,[status(thm)],[c_223,c_13502]) ).
tcf(c_13658,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(successor_relation,X0),X1) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(intersection(successor_relation,X0),X1)) ),
inference(superposition,[status(thm)],[c_13502,c_176]) ).
tcf(c_13659,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(successor_relation,X1),X2),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13502,c_250]) ).
tcf(c_13660,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(intersection(successor_relation,X1),X2)) ),
inference(superposition,[status(thm)],[c_13502,c_170]) ).
tcf(c_13673,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(X0,successor_relation),cross_product(X1,X2)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13504]) ).
tcf(c_13678,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(X0,intersection(successor_relation,cross_product(X1,X2))),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13504]) ).
tcf(c_13680,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,successor_relation)) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(X0,intersection(X1,successor_relation))) ),
inference(superposition,[status(thm)],[c_13504,c_176]) ).
tcf(c_13681,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,intersection(X2,successor_relation)),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13504,c_250]) ).
tcf(c_13682,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(X1,intersection(X2,successor_relation))) ),
inference(superposition,[status(thm)],[c_13504,c_170]) ).
tcf(c_13708,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(intersection(successor_relation,X0),cross_product(X1,X2)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_193,c_13505]) ).
tcf(c_13712,plain,
! [X0: $i] :
( subclass(intersection(X0,null_class),cross_product(universal_class,universal_class))
| ( null_class = successor_relation ) ),
inference(superposition,[status(thm)],[c_223,c_13505]) ).
tcf(c_13715,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(successor_relation,X1)) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),intersection(X0,intersection(successor_relation,X1))) ),
inference(superposition,[status(thm)],[c_13505,c_176]) ).
tcf(c_13716,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,intersection(successor_relation,X2)),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13505,c_250]) ).
tcf(c_13717,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(X1,intersection(successor_relation,X2))) ),
inference(superposition,[status(thm)],[c_13505,c_170]) ).
tcf(c_13738,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ subclass(complement(subset_relation),X0) ),
inference(demodulation,[status(thm)],[c_11560,c_4553]) ).
tcf(c_13744,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4876,c_4388]) ).
tcf(c_13751,plain,
! [X0: $i] :
( subclass(complement(complement(universal_class)),X0)
| member(not_subclass_element(complement(null_class),X0),universal_class) ),
inference(superposition,[status(thm)],[c_4953,c_13744]) ).
tcf(c_13752,plain,
! [X0: $i] :
( subclass(complement(complement(null_class)),X0)
| member(not_subclass_element(complement(universal_class),X0),null_class) ),
inference(superposition,[status(thm)],[c_8703,c_13744]) ).
tcf(c_13755,plain,
! [X0: $i] : subclass(complement(complement(X0)),X0),
inference(superposition,[status(thm)],[c_13744,c_172]) ).
tcf(c_13756,plain,
! [X0: $i] : subclass(complement(complement(null_class)),X0),
inference(superposition,[status(thm)],[c_13744,c_256]) ).
tcf(c_13757,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_13744,c_4342]) ).
tcf(c_13758,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),universal_class) ),
inference(superposition,[status(thm)],[c_13744,c_4336]) ).
tcf(c_13759,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(complement(unordered_pair(X0,X1))),X2)
| ( not_subclass_element(complement(complement(unordered_pair(X0,X1))),X2) = X1 )
| ( not_subclass_element(complement(complement(unordered_pair(X0,X1))),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_13744,c_177]) ).
tcf(c_13760,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(complement(cross_product(X0,X1))),X2)
| ( unordered_pair(unordered_pair(first(not_subclass_element(complement(complement(cross_product(X0,X1))),X2)),first(not_subclass_element(complement(complement(cross_product(X0,X1))),X2))),unordered_pair(first(not_subclass_element(complement(complement(cross_product(X0,X1))),X2)),unordered_pair(second(not_subclass_element(complement(complement(cross_product(X0,X1))),X2)),second(not_subclass_element(complement(complement(cross_product(X0,X1))),X2))))) = not_subclass_element(complement(complement(cross_product(X0,X1))),X2) ) ),
inference(superposition,[status(thm)],[c_13744,c_184]) ).
tcf(c_13761,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(complement(intersection(X0,X1))),X2)
| member(not_subclass_element(complement(complement(intersection(X0,X1))),X2),X1) ),
inference(superposition,[status(thm)],[c_13744,c_189]) ).
tcf(c_13762,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(complement(intersection(X0,X1))),X2)
| member(not_subclass_element(complement(complement(intersection(X0,X1))),X2),X0) ),
inference(superposition,[status(thm)],[c_13744,c_188]) ).
tcf(c_13763,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(complement(X0))),X1)
| ~ member(not_subclass_element(complement(complement(complement(X0))),X1),X0) ),
inference(superposition,[status(thm)],[c_13744,c_191]) ).
tcf(c_13764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(complement(complement(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(complement(complement(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X3),not_subclass_element(complement(complement(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X3)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(complement(complement(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X3),not_subclass_element(complement(complement(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X3)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_215]) ).
tcf(c_13765,plain,
! [X0: $i] :
( subclass(complement(complement(identity_relation)),X0)
| member(not_subclass_element(complement(complement(identity_relation)),X0),subset_relation) ),
inference(superposition,[status(thm)],[c_13744,c_4293]) ).
tcf(c_13766,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(rotate(X0))),X1)
| member(not_subclass_element(complement(complement(rotate(X0))),X1),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_4338]) ).
tcf(c_13767,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(flip(X0))),X1)
| member(not_subclass_element(complement(complement(flip(X0))),X1),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_4339]) ).
tcf(c_13768,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(complement(compose(X0,X1))),X2)
| member(not_subclass_element(complement(complement(compose(X0,X1))),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_4341]) ).
tcf(c_13769,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(complement(unordered_pair(X0,X0))),X1)
| member(not_subclass_element(complement(complement(unordered_pair(X0,X0))),X1),unordered_pair(X2,X0)) ),
inference(superposition,[status(thm)],[c_13744,c_4344]) ).
tcf(c_13770,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(complement(unordered_pair(X0,X0))),X1)
| member(not_subclass_element(complement(complement(unordered_pair(X0,X0))),X1),unordered_pair(X0,X2)) ),
inference(superposition,[status(thm)],[c_13744,c_4343]) ).
tcf(c_13771,plain,
! [X0: $i] :
( subclass(complement(complement(unordered_pair(x,x))),X0)
| member(not_subclass_element(complement(complement(unordered_pair(x,x))),X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_13744,c_4346]) ).
tcf(c_13772,plain,
! [X0: $i] :
( subclass(complement(complement(unordered_pair(y,y))),X0)
| member(not_subclass_element(complement(complement(unordered_pair(y,y))),X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_13744,c_4347]) ).
tcf(c_13773,plain,
subclass(complement(complement(element_relation)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_13744,c_4850]) ).
tcf(c_13774,plain,
subclass(complement(complement(successor_relation)),cross_product(universal_class,universal_class)),
inference(superposition,[status(thm)],[c_13744,c_4862]) ).
tcf(c_13775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(complement(complement(intersection(intersection(X0,X1),X2))),X3)
| member(not_subclass_element(complement(complement(intersection(intersection(X0,X1),X2))),X3),X0) ),
inference(superposition,[status(thm)],[c_13744,c_6783]) ).
tcf(c_13776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(complement(complement(intersection(intersection(X0,X1),X2))),X3)
| member(not_subclass_element(complement(complement(intersection(intersection(X0,X1),X2))),X3),X1) ),
inference(superposition,[status(thm)],[c_13744,c_6250]) ).
tcf(c_13777,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(identity_relation,X0))),X1)
| member(not_subclass_element(complement(complement(intersection(identity_relation,X0))),X1),subset_relation) ),
inference(superposition,[status(thm)],[c_13744,c_6318]) ).
tcf(c_13778,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(subset_relation,X0))),X1)
| member(not_subclass_element(complement(complement(intersection(subset_relation,X0))),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_7274]) ).
tcf(c_13779,plain,
! [X0: $i] :
( subclass(complement(complement(complement(subset_relation))),X0)
| ~ member(not_subclass_element(complement(complement(complement(subset_relation))),X0),identity_relation) ),
inference(superposition,[status(thm)],[c_13744,c_11581]) ).
tcf(c_13780,plain,
! [X0: $i] :
( subclass(complement(complement(complement(subset_relation))),X0)
| member(not_subclass_element(complement(complement(complement(subset_relation))),X0),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_13744,c_8771]) ).
tcf(c_13781,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(complement(subset_relation),X0))),X1)
| member(not_subclass_element(complement(complement(intersection(complement(subset_relation),X0))),X1),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_13744,c_8785]) ).
tcf(c_13782,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(X0,identity_relation))),X1)
| member(not_subclass_element(complement(complement(intersection(X0,identity_relation))),X1),subset_relation) ),
inference(superposition,[status(thm)],[c_13744,c_11106]) ).
tcf(c_13785,plain,
! [X0: $i] :
( subclass(universal_class,X0)
| member(not_subclass_element(universal_class,X0),universal_class) ),
inference(light_normalisation,[status(thm)],[c_13751,c_4953,c_8703]) ).
tcf(c_13996,plain,
subclass(complement(null_class),universal_class),
inference(superposition,[status(thm)],[c_4953,c_13755]) ).
tcf(c_13997,plain,
subclass(complement(universal_class),null_class),
inference(superposition,[status(thm)],[c_8703,c_13755]) ).
tcf(c_13998,plain,
! [X0: $i] :
( ( complement(complement(X0)) = X0 )
| ~ subclass(X0,complement(complement(X0))) ),
inference(superposition,[status(thm)],[c_13755,c_176]) ).
tcf(c_13999,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(X0)),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13755,c_250]) ).
tcf(c_14000,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,complement(complement(X1))) ),
inference(superposition,[status(thm)],[c_13755,c_170]) ).
tcf(c_14001,plain,
! [X0: $i] : intersection(X0,complement(complement(null_class))) = null_class,
inference(superposition,[status(thm)],[c_13755,c_5287]) ).
tcf(c_14002,plain,
! [X0: $i] : intersection(complement(complement(null_class)),X0) = null_class,
inference(superposition,[status(thm)],[c_13755,c_5257]) ).
tcf(c_14003,plain,
complement(complement(null_class)) = null_class,
inference(superposition,[status(thm)],[c_13755,c_258]) ).
tcf(c_14005,plain,
subclass(universal_class,universal_class),
inference(light_normalisation,[status(thm)],[c_13996,c_8703]) ).
tcf(c_14021,plain,
! [X0: $i] :
( subclass(complement(null_class),X0)
| ~ subclass(universal_class,X0) ),
inference(superposition,[status(thm)],[c_4953,c_13999]) ).
tcf(c_14022,plain,
! [X0: $i] :
( subclass(complement(universal_class),X0)
| ~ subclass(null_class,X0) ),
inference(superposition,[status(thm)],[c_8703,c_13999]) ).
tcf(c_14023,plain,
! [X0: $i,X1: $i] :
( ( complement(complement(X1)) = X0 )
| ~ subclass(X1,X0)
| ~ subclass(X0,complement(complement(X1))) ),
inference(superposition,[status(thm)],[c_13999,c_176]) ).
tcf(c_14024,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(complement(X0)),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13999,c_250]) ).
tcf(c_14025,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,complement(complement(X1))) ),
inference(superposition,[status(thm)],[c_13999,c_170]) ).
tcf(c_14026,plain,
! [X0: $i,X1: $i] :
( ( intersection(X1,complement(complement(X0))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_13999,c_5287]) ).
tcf(c_14027,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(complement(X0)),X1) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_13999,c_5257]) ).
tcf(c_14028,plain,
! [X0: $i] :
( ( complement(complement(X0)) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_13999,c_258]) ).
tcf(c_14055,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,complement(complement(X0))),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0)
| ( complement(complement(X0)) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_14000]) ).
tcf(c_14056,plain,
! [X0: $i] :
( member(not_subclass_element(complement(complement(X0)),null_class),X0)
| ( complement(complement(X0)) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_14000]) ).
tcf(c_14058,plain,
! [X0: $i] :
( member(regular(complement(complement(X0))),X0)
| ( complement(complement(X0)) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_14000]) ).
tcf(c_14059,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
| ( complement(complement(X0)) = null_class )
| ~ member(complement(complement(X0)),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_14000]) ).
tcf(c_14060,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(complement(X0)),X1),X2)
| member(not_subclass_element(intersection(complement(complement(X0)),X1),X2),X0) ),
inference(superposition,[status(thm)],[c_4224,c_14000]) ).
tcf(c_14061,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(complement(complement(X0)),X1)),X0)
| ( intersection(complement(complement(X0)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_14000]) ).
tcf(c_14062,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,complement(complement(X1))),X2)
| member(not_subclass_element(intersection(X0,complement(complement(X1))),X2),X1) ),
inference(superposition,[status(thm)],[c_4245,c_14000]) ).
tcf(c_14063,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,complement(complement(X1)))),X1)
| ( intersection(X0,complement(complement(X1))) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_14000]) ).
tcf(c_14064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(complement(complement(X2)),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),complement(complement(X2))),X3),X2) ),
inference(superposition,[status(thm)],[c_4425,c_14000]) ).
tcf(c_14065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,complement(complement(X1))),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,complement(complement(X1))),X2),X3),X1) ),
inference(superposition,[status(thm)],[c_4430,c_14000]) ).
tcf(c_14066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(complement(complement(X0)),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(complement(complement(X0)),X1),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_4431,c_14000]) ).
tcf(c_14067,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(complement(complement(X1))))
| member(not_subclass_element(X0,complement(complement(complement(X1)))),X1) ),
inference(superposition,[status(thm)],[c_8328,c_14000]) ).
tcf(c_14068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),complement(complement(X0))),X3)
| member(not_subclass_element(intersection(complement(complement(X0)),cross_product(X1,X2)),X3),X0) ),
inference(superposition,[status(thm)],[c_4638,c_14000]) ).
tcf(c_14069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,complement(complement(X2)))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,complement(complement(X2)))),X3),X2) ),
inference(superposition,[status(thm)],[c_4646,c_14000]) ).
tcf(c_14070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(complement(complement(X1)),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(complement(complement(X1)),X2)),X3),X1) ),
inference(superposition,[status(thm)],[c_4647,c_14000]) ).
tcf(c_14071,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(complement(complement(X0)))),X1)
| member(not_subclass_element(complement(complement(complement(complement(X0)))),X1),X0) ),
inference(superposition,[status(thm)],[c_13744,c_14000]) ).
tcf(c_14072,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,complement(null_class)) ),
inference(superposition,[status(thm)],[c_4953,c_14000]) ).
tcf(c_14073,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_8703,c_14000]) ).
tcf(c_14219,plain,
( ( cross_product(universal_class,universal_class) = complement(complement(element_relation)) )
| ~ subclass(cross_product(universal_class,universal_class),complement(complement(element_relation))) ),
inference(superposition,[status(thm)],[c_13773,c_176]) ).
tcf(c_14220,plain,
! [X0: $i] :
( subclass(complement(complement(element_relation)),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13773,c_250]) ).
tcf(c_14221,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,complement(complement(element_relation))) ),
inference(superposition,[status(thm)],[c_13773,c_170]) ).
tcf(c_14230,plain,
( ( cross_product(universal_class,universal_class) = complement(complement(successor_relation)) )
| ~ subclass(cross_product(universal_class,universal_class),complement(complement(successor_relation))) ),
inference(superposition,[status(thm)],[c_13774,c_176]) ).
tcf(c_14231,plain,
! [X0: $i] :
( subclass(complement(complement(successor_relation)),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13774,c_250]) ).
tcf(c_14232,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,complement(complement(successor_relation))) ),
inference(superposition,[status(thm)],[c_13774,c_170]) ).
tcf(c_14256,plain,
! [X0: $i] : complement(complement(intersection(null_class,X0))) = null_class,
inference(superposition,[status(thm)],[c_4427,c_14028]) ).
tcf(c_14257,plain,
( ( complement(complement(unordered_pair(x,x))) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_4500,c_14028]) ).
tcf(c_14258,plain,
( ( complement(complement(unordered_pair(y,y))) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_4501,c_14028]) ).
tcf(c_14259,plain,
! [X0: $i,X1: $i] :
( ( complement(complement(intersection(X0,X1))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4551,c_14028]) ).
tcf(c_14260,plain,
! [X0: $i] : complement(complement(intersection(X0,null_class))) = null_class,
inference(superposition,[status(thm)],[c_4643,c_14028]) ).
tcf(c_14261,plain,
! [X0: $i,X1: $i] :
( ( complement(complement(intersection(X1,X0))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4788,c_14028]) ).
tcf(c_14262,plain,
! [X0: $i] :
( ( complement(complement(complement(complement(X0)))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_13999,c_14028]) ).
tcf(c_14263,plain,
( ( complement(complement(complement(cross_product(universal_class,universal_class)))) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13276,c_14028]) ).
tcf(c_14264,plain,
! [X0: $i,X1: $i] : complement(complement(intersection(intersection(X0,null_class),X1))) = null_class,
inference(superposition,[status(thm)],[c_6065,c_14028]) ).
tcf(c_14265,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( complement(complement(intersection(intersection(X1,X0),X2))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6249,c_14028]) ).
tcf(c_14266,plain,
! [X0: $i] :
( ( complement(complement(intersection(identity_relation,X0))) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_6317,c_14028]) ).
tcf(c_14267,plain,
! [X0: $i,X1: $i] : complement(complement(intersection(intersection(null_class,X0),X1))) = null_class,
inference(superposition,[status(thm)],[c_6583,c_14028]) ).
tcf(c_14268,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( complement(complement(intersection(intersection(X0,X1),X2))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6782,c_14028]) ).
tcf(c_14269,plain,
( ( complement(complement(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))) = null_class )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_14028]) ).
tcf(c_14270,plain,
! [X0: $i] :
( ( complement(complement(intersection(complement(subset_relation),X0))) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_8784,c_14028]) ).
tcf(c_14271,plain,
! [X0: $i,X1: $i] : complement(complement(intersection(X0,intersection(X1,null_class)))) = null_class,
inference(superposition,[status(thm)],[c_10731,c_14028]) ).
tcf(c_14272,plain,
! [X0: $i] :
( ( complement(complement(intersection(X0,identity_relation))) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_11105,c_14028]) ).
tcf(c_14273,plain,
! [X0: $i,X1: $i] : complement(complement(intersection(X0,intersection(null_class,X1)))) = null_class,
inference(superposition,[status(thm)],[c_11340,c_14028]) ).
tcf(c_14274,plain,
complement(complement(complement(complement(null_class)))) = null_class,
inference(superposition,[status(thm)],[c_13755,c_14028]) ).
tcf(c_14369,plain,
subclass(complement(cross_product(universal_class,universal_class)),complement(successor_relation)),
inference(superposition,[status(thm)],[c_8328,c_4877]) ).
tcf(c_14375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,X0),cross_product(X3,X4)),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_193,c_11018]) ).
tcf(c_14381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X2,intersection(X0,cross_product(X3,X4))),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_193,c_11018]) ).
tcf(c_14382,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,null_class),X1)
| ( X0 = null_class )
| ~ subclass(regular(X0),X1) ),
inference(superposition,[status(thm)],[c_223,c_11018]) ).
tcf(c_14383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X3,intersection(cross_product(X0,X1),X4)),X2)
| ~ subclass(cross_product(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_193,c_11018]) ).
tcf(c_14384,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,subset_relation),X0)
| ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) ),
inference(superposition,[status(thm)],[c_229,c_11018]) ).
tcf(c_14386,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,null_class),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4553,c_11018]) ).
tcf(c_14387,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ~ subclass(null_class,X0) ),
inference(superposition,[status(thm)],[c_4790,c_11018]) ).
tcf(c_14390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X3,null_class),X2)
| ~ subclass(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_11685,c_11018]) ).
tcf(c_14392,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,null_class),X1)
| ~ subclass(complement(X0),X1) ),
inference(superposition,[status(thm)],[c_12377,c_11018]) ).
tcf(c_14396,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ~ subclass(complement(cross_product(universal_class,universal_class)),X0) ),
inference(superposition,[status(thm)],[c_12738,c_11018]) ).
tcf(c_14397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(X1,intersection(X2,X3)) = X0 )
| ~ subclass(X3,X0)
| ~ subclass(X0,intersection(X1,intersection(X2,X3))) ),
inference(superposition,[status(thm)],[c_11018,c_176]) ).
tcf(c_14398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X3,intersection(X4,X0)),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11018,c_250]) ).
tcf(c_14399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X4)
| ~ subclass(X3,X4)
| ~ member(X0,intersection(X1,intersection(X2,X3))) ),
inference(superposition,[status(thm)],[c_11018,c_170]) ).
tcf(c_14400,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( complement(complement(intersection(X1,intersection(X2,X0)))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11018,c_14028]) ).
tcf(c_14401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(X1,intersection(X2,intersection(X3,X0))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11018,c_5287]) ).
tcf(c_14402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(intersection(X1,intersection(X2,X0)),X3) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11018,c_5257]) ).
tcf(c_14459,plain,
( ~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(x,x))),cross_product(z,z))
| ( unordered_pair(x,x) != null_class ) ),
inference(instantiation,[status(thm)],[c_271]) ).
tcf(c_14484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(X3,intersection(X0,intersection(X1,X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2)
| ( intersection(X0,intersection(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_251,c_11019]) ).
tcf(c_14485,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,intersection(X1,X2)),null_class),X2)
| ( intersection(X0,intersection(X1,X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_11019]) ).
tcf(c_14488,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2)
| ( intersection(X0,intersection(X1,X2)) = null_class )
| ~ member(intersection(X0,intersection(X1,X2)),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_11019]) ).
tcf(c_14490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(intersection(X0,intersection(X1,X2)),X3)),X2)
| ( intersection(intersection(X0,intersection(X1,X2)),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_11019]) ).
tcf(c_14492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(X0,intersection(X1,intersection(X2,X3)))),X3)
| ( intersection(X0,intersection(X1,intersection(X2,X3))) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_11019]) ).
tcf(c_14493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X2,intersection(X3,X4)),cross_product(X0,X1)),X5)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,X4))),X5),X4) ),
inference(superposition,[status(thm)],[c_4425,c_11019]) ).
tcf(c_14494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X0,intersection(X1,intersection(X2,X3))),X4),X5)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,intersection(X2,X3))),X4),X5),X3) ),
inference(superposition,[status(thm)],[c_4430,c_11019]) ).
tcf(c_14495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(X0,intersection(X1,X2)),X3),X4),X5)
| member(not_subclass_element(intersection(intersection(intersection(X0,intersection(X1,X2)),X3),X4),X5),X2) ),
inference(superposition,[status(thm)],[c_4431,c_11019]) ).
tcf(c_14496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X0,complement(intersection(X1,intersection(X2,X3))))
| member(not_subclass_element(X0,complement(intersection(X1,intersection(X2,X3)))),X3) ),
inference(superposition,[status(thm)],[c_8328,c_11019]) ).
tcf(c_14497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(cross_product(X3,X4),intersection(X0,intersection(X1,X2))),X5)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,X2)),cross_product(X3,X4)),X5),X2) ),
inference(superposition,[status(thm)],[c_4638,c_11019]) ).
tcf(c_14498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,intersection(X3,X4)))),X5)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,intersection(X3,X4)))),X5),X4) ),
inference(superposition,[status(thm)],[c_4646,c_11019]) ).
tcf(c_14499,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X0,intersection(intersection(X1,intersection(X2,X3)),X4)),X5)
| member(not_subclass_element(intersection(X0,intersection(intersection(X1,intersection(X2,X3)),X4)),X5),X3) ),
inference(superposition,[status(thm)],[c_4647,c_11019]) ).
tcf(c_14500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(complement(complement(intersection(X0,intersection(X1,X2)))),X3)
| member(not_subclass_element(complement(complement(intersection(X0,intersection(X1,X2)))),X3),X2) ),
inference(superposition,[status(thm)],[c_13744,c_11019]) ).
tcf(c_14502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X2)
| ~ member(X0,intersection(intersection(X1,X2),cross_product(X3,X4))) ),
inference(superposition,[status(thm)],[c_193,c_11019]) ).
tcf(c_14508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,intersection(X2,cross_product(X3,X4)))) ),
inference(superposition,[status(thm)],[c_193,c_11019]) ).
tcf(c_14510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,cross_product(X2,X3))
| ~ member(X0,intersection(X1,intersection(cross_product(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_193,c_11019]) ).
tcf(c_14511,plain,
! [X0: $i,X1: $i] :
( member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,intersection(X1,subset_relation)) ),
inference(superposition,[status(thm)],[c_229,c_11019]) ).
tcf(c_14514,plain,
! [X0: $i,X1: $i] :
( member(X0,null_class)
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_4790,c_11019]) ).
tcf(c_14528,plain,
! [X0: $i,X1: $i] : ~ member(X0,intersection(X1,null_class)),
inference(forward_subsumption_resolution,[status(thm)],[c_14514,c_256]) ).
tcf(c_14603,plain,
( ~ member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(y,y))),cross_product(z,z))
| ( unordered_pair(y,y) != null_class ) ),
inference(instantiation,[status(thm)],[c_271]) ).
tcf(c_14690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,X2),cross_product(X3,X4)),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_193,c_11629]) ).
tcf(c_14696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X3,intersection(X4,cross_product(X0,X1))),X2)
| ~ subclass(cross_product(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_193,c_11629]) ).
tcf(c_14697,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,null_class),X1)
| ( X0 = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_223,c_11629]) ).
tcf(c_14698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X2,intersection(cross_product(X3,X4),X0)),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_193,c_11629]) ).
tcf(c_14704,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ~ subclass(complement(subset_relation),X0) ),
inference(superposition,[status(thm)],[c_11311,c_11629]) ).
tcf(c_14710,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ~ subclass(identity_relation,X0) ),
inference(superposition,[status(thm)],[c_12394,c_11629]) ).
tcf(c_14711,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_12738,c_11629]) ).
tcf(c_14712,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(X1,intersection(X2,X3)) = X0 )
| ~ subclass(X2,X0)
| ~ subclass(X0,intersection(X1,intersection(X2,X3))) ),
inference(superposition,[status(thm)],[c_11629,c_176]) ).
tcf(c_14713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X3,intersection(X0,X4)),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11629,c_250]) ).
tcf(c_14714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X4)
| ~ subclass(X2,X4)
| ~ member(X0,intersection(X1,intersection(X2,X3))) ),
inference(superposition,[status(thm)],[c_11629,c_170]) ).
tcf(c_14715,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( complement(complement(intersection(X1,intersection(X0,X2)))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11629,c_14028]) ).
tcf(c_14716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(X1,intersection(X2,intersection(X0,X3))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11629,c_5287]) ).
tcf(c_14717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(intersection(X1,intersection(X0,X2)),X3) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11629,c_5257]) ).
tcf(c_14837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(X3,intersection(X0,intersection(X1,X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1)
| ( intersection(X0,intersection(X1,X2)) = X3 ) ),
inference(superposition,[status(thm)],[c_251,c_11630]) ).
tcf(c_14838,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,intersection(X1,X2)),null_class),X1)
| ( intersection(X0,intersection(X1,X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_11630]) ).
tcf(c_14841,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1)
| ( intersection(X0,intersection(X1,X2)) = null_class )
| ~ member(intersection(X0,intersection(X1,X2)),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_11630]) ).
tcf(c_14843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(intersection(X0,intersection(X1,X2)),X3)),X1)
| ( intersection(intersection(X0,intersection(X1,X2)),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_11630]) ).
tcf(c_14845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(X0,intersection(X1,intersection(X2,X3)))),X2)
| ( intersection(X0,intersection(X1,intersection(X2,X3))) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_11630]) ).
tcf(c_14846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X2,intersection(X3,X4)),cross_product(X0,X1)),X5)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,X4))),X5),X3) ),
inference(superposition,[status(thm)],[c_4425,c_11630]) ).
tcf(c_14847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X0,intersection(X1,intersection(X2,X3))),X4),X5)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,intersection(X2,X3))),X4),X5),X2) ),
inference(superposition,[status(thm)],[c_4430,c_11630]) ).
tcf(c_14848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(X0,intersection(X1,X2)),X3),X4),X5)
| member(not_subclass_element(intersection(intersection(intersection(X0,intersection(X1,X2)),X3),X4),X5),X1) ),
inference(superposition,[status(thm)],[c_4431,c_11630]) ).
tcf(c_14849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X0,complement(intersection(X1,intersection(X2,X3))))
| member(not_subclass_element(X0,complement(intersection(X1,intersection(X2,X3)))),X2) ),
inference(superposition,[status(thm)],[c_8328,c_11630]) ).
tcf(c_14850,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(cross_product(X3,X4),intersection(X0,intersection(X1,X2))),X5)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,X2)),cross_product(X3,X4)),X5),X1) ),
inference(superposition,[status(thm)],[c_4638,c_11630]) ).
tcf(c_14851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,intersection(X3,X4)))),X5)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,intersection(X3,X4)))),X5),X3) ),
inference(superposition,[status(thm)],[c_4646,c_11630]) ).
tcf(c_14852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X0,intersection(intersection(X1,intersection(X2,X3)),X4)),X5)
| member(not_subclass_element(intersection(X0,intersection(intersection(X1,intersection(X2,X3)),X4)),X5),X2) ),
inference(superposition,[status(thm)],[c_4647,c_11630]) ).
tcf(c_14853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(complement(complement(intersection(X0,intersection(X1,X2)))),X3)
| member(not_subclass_element(complement(complement(intersection(X0,intersection(X1,X2)))),X3),X1) ),
inference(superposition,[status(thm)],[c_13744,c_11630]) ).
tcf(c_14855,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X1)
| ~ member(X0,intersection(intersection(X1,X2),cross_product(X3,X4))) ),
inference(superposition,[status(thm)],[c_193,c_11630]) ).
tcf(c_14861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,cross_product(X3,X4))
| ~ member(X0,intersection(X1,intersection(X2,cross_product(X3,X4)))) ),
inference(superposition,[status(thm)],[c_193,c_11630]) ).
tcf(c_14863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X4)
| ~ member(X0,intersection(X1,intersection(cross_product(X2,X3),X4))) ),
inference(superposition,[status(thm)],[c_193,c_11630]) ).
tcf(c_14987,plain,
( ( complement(cross_product(universal_class,universal_class)) = complement(successor_relation) )
| ~ subclass(complement(successor_relation),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_14369,c_176]) ).
tcf(c_14988,plain,
! [X0: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ subclass(complement(successor_relation),X0) ),
inference(superposition,[status(thm)],[c_14369,c_250]) ).
tcf(c_14989,plain,
! [X0: $i] :
( member(X0,complement(successor_relation))
| ~ member(X0,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_14369,c_170]) ).
tcf(c_15009,plain,
! [X0: $i] : subclass(intersection(X0,subset_relation),universal_class),
inference(superposition,[status(thm)],[c_173,c_11655]) ).
tcf(c_15018,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,intersection(X0,subset_relation)),X1)
| member(not_subclass_element(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class))
| ( intersection(X0,subset_relation) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_11656]) ).
tcf(c_15019,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,subset_relation),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,subset_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_11656]) ).
tcf(c_15021,plain,
! [X0: $i] :
( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
| ( intersection(X0,subset_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_11656]) ).
tcf(c_15022,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,subset_relation),intersection(X0,subset_relation)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ( intersection(X0,subset_relation) = null_class )
| ~ member(intersection(X0,subset_relation),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_11656]) ).
tcf(c_15023,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,subset_relation),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,subset_relation),X1),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_11656]) ).
tcf(c_15024,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(X0,subset_relation),X1)),cross_product(universal_class,universal_class))
| ( intersection(intersection(X0,subset_relation),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_11656]) ).
tcf(c_15025,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,subset_relation)),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,subset_relation)),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_11656]) ).
tcf(c_15026,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(X1,subset_relation))),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(X1,subset_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_11656]) ).
tcf(c_15027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,subset_relation),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,subset_relation)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_11656]) ).
tcf(c_15028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(X1,subset_relation)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,subset_relation)),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_11656]) ).
tcf(c_15029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(X0,subset_relation),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(X0,subset_relation),X1),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_11656]) ).
tcf(c_15030,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(X1,subset_relation)))
| member(not_subclass_element(X0,complement(intersection(X1,subset_relation))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_11656]) ).
tcf(c_15031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(X0,subset_relation)),X3)
| member(not_subclass_element(intersection(intersection(X0,subset_relation),cross_product(X1,X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_11656]) ).
tcf(c_15032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,subset_relation))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,subset_relation))),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_11656]) ).
tcf(c_15033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(X1,subset_relation),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(X1,subset_relation),X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_11656]) ).
tcf(c_15034,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(X0,subset_relation))),X1)
| member(not_subclass_element(complement(complement(intersection(X0,subset_relation))),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_11656]) ).
tcf(c_15036,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(subset_relation,cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_193,c_11656]) ).
tcf(c_15156,plain,
subclass(complement(cross_product(universal_class,universal_class)),complement(element_relation)),
inference(superposition,[status(thm)],[c_8328,c_4878]) ).
tcf(c_15162,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| ~ member(not_subclass_element(intersection(X0,X1),X2),complement(X1)) ),
inference(superposition,[status(thm)],[c_171,c_11998]) ).
tcf(c_15163,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(X2,intersection(X0,X1)),X2)
| ( intersection(X0,X1) = X2 )
| ~ member(not_subclass_element(intersection(X0,X1),X2),complement(X1)) ),
inference(superposition,[status(thm)],[c_251,c_11998]) ).
tcf(c_15164,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = null_class )
| ~ member(not_subclass_element(intersection(X0,X1),null_class),complement(X1)) ),
inference(superposition,[status(thm)],[c_259,c_11998]) ).
tcf(c_15166,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = null_class )
| ~ member(regular(intersection(X0,X1)),complement(X1)) ),
inference(superposition,[status(thm)],[c_222,c_11998]) ).
tcf(c_15167,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = null_class )
| ~ member(intersection(X0,X1),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),complement(X1)) ),
inference(superposition,[status(thm)],[c_225,c_11998]) ).
tcf(c_15168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| ~ member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),complement(X1)) ),
inference(superposition,[status(thm)],[c_4224,c_11998]) ).
tcf(c_15169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,X1),X2) = null_class )
| ~ member(regular(intersection(intersection(X0,X1),X2)),complement(X1)) ),
inference(superposition,[status(thm)],[c_4225,c_11998]) ).
tcf(c_15170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| ~ member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),complement(X2)) ),
inference(superposition,[status(thm)],[c_4245,c_11998]) ).
tcf(c_15171,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(X1,X2)) = null_class )
| ~ member(regular(intersection(X0,intersection(X1,X2))),complement(X2)) ),
inference(superposition,[status(thm)],[c_4246,c_11998]) ).
tcf(c_15172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,X3),cross_product(X0,X1)),X4)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,X3)),X4),complement(X3)) ),
inference(superposition,[status(thm)],[c_4425,c_11998]) ).
tcf(c_15173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,intersection(X1,X2)),X3),X4)
| ~ member(not_subclass_element(intersection(intersection(X0,intersection(X1,X2)),X3),X4),complement(X2)) ),
inference(superposition,[status(thm)],[c_4430,c_11998]) ).
tcf(c_15174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X0,X1),X2),X3),X4)
| ~ member(not_subclass_element(intersection(intersection(intersection(X0,X1),X2),X3),X4),complement(X1)) ),
inference(superposition,[status(thm)],[c_4431,c_11998]) ).
tcf(c_15175,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,complement(intersection(X1,X2)))
| ~ member(not_subclass_element(X0,complement(intersection(X1,X2))),complement(X2)) ),
inference(superposition,[status(thm)],[c_8328,c_11998]) ).
tcf(c_15176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X2,X3),intersection(X0,X1)),X4)
| ~ member(not_subclass_element(intersection(intersection(X0,X1),cross_product(X2,X3)),X4),complement(X1)) ),
inference(superposition,[status(thm)],[c_4638,c_11998]) ).
tcf(c_15177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,X3))),X4)
| ~ member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,X3))),X4),complement(X3)) ),
inference(superposition,[status(thm)],[c_4646,c_11998]) ).
tcf(c_15178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(intersection(X1,X2),X3)),X4)
| ~ member(not_subclass_element(intersection(X0,intersection(intersection(X1,X2),X3)),X4),complement(X2)) ),
inference(superposition,[status(thm)],[c_4647,c_11998]) ).
tcf(c_15179,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(complement(intersection(X0,X1))),X2)
| ~ member(not_subclass_element(complement(complement(intersection(X0,X1))),X2),complement(X1)) ),
inference(superposition,[status(thm)],[c_13744,c_11998]) ).
tcf(c_15181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X0,complement(X1))
| ~ member(X0,intersection(X1,cross_product(X2,X3))) ),
inference(superposition,[status(thm)],[c_193,c_11998]) ).
tcf(c_15183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X0,complement(cross_product(X1,X2)))
| ~ member(X0,intersection(cross_product(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_193,c_11998]) ).
tcf(c_15184,plain,
! [X0: $i] :
( ~ member(X0,subset_relation)
| ~ member(X0,complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))) ),
inference(superposition,[status(thm)],[c_229,c_11998]) ).
tcf(c_15324,plain,
( ( complement(cross_product(universal_class,universal_class)) = complement(element_relation) )
| ~ subclass(complement(element_relation),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_15156,c_176]) ).
tcf(c_15325,plain,
! [X0: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ subclass(complement(element_relation),X0) ),
inference(superposition,[status(thm)],[c_15156,c_250]) ).
tcf(c_15326,plain,
! [X0: $i] :
( member(X0,complement(element_relation))
| ~ member(X0,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_15156,c_170]) ).
tcf(c_15405,plain,
intersection(null_class,complement(complement(domain_of(flip(cross_product(subset_relation,universal_class)))))) = null_class,
inference(superposition,[status(thm)],[c_12282,c_12688]) ).
tcf(c_15407,plain,
intersection(complement(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),null_class) = null_class,
inference(superposition,[status(thm)],[c_12282,c_11685]) ).
tcf(c_15410,plain,
! [X0: $i] : subclass(intersection(null_class,X0),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),
inference(superposition,[status(thm)],[c_12282,c_6583]) ).
tcf(c_15411,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation),X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(superposition,[status(thm)],[c_12282,c_4431]) ).
tcf(c_15413,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),identity_relation)
| subclass(intersection(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation),X0),X1) ),
inference(superposition,[status(thm)],[c_12282,c_4430]) ).
tcf(c_15415,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),identity_relation)
| subclass(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation),X0) ),
inference(superposition,[status(thm)],[c_12282,c_4245]) ).
tcf(c_15416,plain,
subclass(null_class,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),
inference(superposition,[status(thm)],[c_12282,c_4427]) ).
tcf(c_15417,plain,
! [X0: $i] :
( subclass(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation),X0)
| member(not_subclass_element(null_class,X0),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(superposition,[status(thm)],[c_12282,c_4224]) ).
tcf(c_15419,plain,
! [X0: $i] : subclass(intersection(X0,null_class),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),
inference(superposition,[status(thm)],[c_12282,c_11340]) ).
tcf(c_15420,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(superposition,[status(thm)],[c_12282,c_4647]) ).
tcf(c_15422,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),identity_relation)
| subclass(intersection(X0,intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)),X1) ),
inference(superposition,[status(thm)],[c_12282,c_4646]) ).
tcf(c_15423,plain,
! [X0: $i,X1: $i] :
( member(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_12282,c_6783]) ).
tcf(c_15425,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,identity_relation)
| ~ member(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(superposition,[status(thm)],[c_12282,c_190]) ).
tcf(c_15428,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),subset_relation)
| subclass(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation),X0) ),
inference(superposition,[status(thm)],[c_12282,c_4649]) ).
tcf(c_15431,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ~ subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) ),
inference(superposition,[status(thm)],[c_12282,c_6782]) ).
tcf(c_15433,plain,
! [X0: $i] :
( subclass(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation),X0)
| ~ member(not_subclass_element(null_class,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(superposition,[status(thm)],[c_12282,c_4432]) ).
tcf(c_15437,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ~ subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) ),
inference(superposition,[status(thm)],[c_12282,c_11629]) ).
tcf(c_15439,plain,
! [X0: $i,X1: $i] :
( member(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_12282,c_11630]) ).
tcf(c_15440,plain,
! [X0: $i,X1: $i] :
( member(X0,identity_relation)
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_12282,c_11019]) ).
tcf(c_15457,plain,
! [X0: $i] :
( ~ member(X0,identity_relation)
| ~ member(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15425,c_256]) ).
tcf(c_15462,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ member(not_subclass_element(null_class,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(light_normalisation,[status(thm)],[c_15433,c_12282]) ).
tcf(c_15463,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(light_normalisation,[status(thm)],[c_15417,c_12282]) ).
tcf(c_15474,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| ~ member(not_subclass_element(intersection(X0,X1),X2),complement(X0)) ),
inference(superposition,[status(thm)],[c_171,c_12327]) ).
tcf(c_15475,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(X2,intersection(X0,X1)),X2)
| ( intersection(X0,X1) = X2 )
| ~ member(not_subclass_element(intersection(X0,X1),X2),complement(X0)) ),
inference(superposition,[status(thm)],[c_251,c_12327]) ).
tcf(c_15476,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = null_class )
| ~ member(not_subclass_element(intersection(X0,X1),null_class),complement(X0)) ),
inference(superposition,[status(thm)],[c_259,c_12327]) ).
tcf(c_15478,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = null_class )
| ~ member(regular(intersection(X0,X1)),complement(X0)) ),
inference(superposition,[status(thm)],[c_222,c_12327]) ).
tcf(c_15479,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = null_class )
| ~ member(intersection(X0,X1),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),complement(X0)) ),
inference(superposition,[status(thm)],[c_225,c_12327]) ).
tcf(c_15480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| ~ member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),complement(X0)) ),
inference(superposition,[status(thm)],[c_4224,c_12327]) ).
tcf(c_15481,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,X1),X2) = null_class )
| ~ member(regular(intersection(intersection(X0,X1),X2)),complement(X0)) ),
inference(superposition,[status(thm)],[c_4225,c_12327]) ).
tcf(c_15482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| ~ member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),complement(X1)) ),
inference(superposition,[status(thm)],[c_4245,c_12327]) ).
tcf(c_15483,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(X1,X2)) = null_class )
| ~ member(regular(intersection(X0,intersection(X1,X2))),complement(X1)) ),
inference(superposition,[status(thm)],[c_4246,c_12327]) ).
tcf(c_15484,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,X3),cross_product(X0,X1)),X4)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,X3)),X4),complement(X2)) ),
inference(superposition,[status(thm)],[c_4425,c_12327]) ).
tcf(c_15485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,intersection(X1,X2)),X3),X4)
| ~ member(not_subclass_element(intersection(intersection(X0,intersection(X1,X2)),X3),X4),complement(X1)) ),
inference(superposition,[status(thm)],[c_4430,c_12327]) ).
tcf(c_15486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X0,X1),X2),X3),X4)
| ~ member(not_subclass_element(intersection(intersection(intersection(X0,X1),X2),X3),X4),complement(X0)) ),
inference(superposition,[status(thm)],[c_4431,c_12327]) ).
tcf(c_15487,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,complement(intersection(X1,X2)))
| ~ member(not_subclass_element(X0,complement(intersection(X1,X2))),complement(X1)) ),
inference(superposition,[status(thm)],[c_8328,c_12327]) ).
tcf(c_15488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X2,X3),intersection(X0,X1)),X4)
| ~ member(not_subclass_element(intersection(intersection(X0,X1),cross_product(X2,X3)),X4),complement(X0)) ),
inference(superposition,[status(thm)],[c_4638,c_12327]) ).
tcf(c_15489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,X3))),X4)
| ~ member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,X3))),X4),complement(X2)) ),
inference(superposition,[status(thm)],[c_4646,c_12327]) ).
tcf(c_15490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X0,intersection(intersection(X1,X2),X3)),X4)
| ~ member(not_subclass_element(intersection(X0,intersection(intersection(X1,X2),X3)),X4),complement(X1)) ),
inference(superposition,[status(thm)],[c_4647,c_12327]) ).
tcf(c_15491,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(complement(intersection(X0,X1))),X2)
| ~ member(not_subclass_element(complement(complement(intersection(X0,X1))),X2),complement(X0)) ),
inference(superposition,[status(thm)],[c_13744,c_12327]) ).
tcf(c_15493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X0,complement(cross_product(X2,X3)))
| ~ member(X0,intersection(X1,cross_product(X2,X3))) ),
inference(superposition,[status(thm)],[c_193,c_12327]) ).
tcf(c_15495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X0,complement(X3))
| ~ member(X0,intersection(cross_product(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_193,c_12327]) ).
tcf(c_15688,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(subset_relation),cross_product(X1,X2)),X0)
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_193,c_12408]) ).
tcf(c_15694,plain,
! [X0: $i,X1: $i] :
( ( intersection(X1,complement(subset_relation)) = X0 )
| ~ subclass(complement(identity_relation),X0)
| ~ subclass(X0,intersection(X1,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_12408,c_176]) ).
tcf(c_15695,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,complement(subset_relation)),X1)
| ~ subclass(X0,X1)
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_12408,c_250]) ).
tcf(c_15696,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(complement(identity_relation),X2)
| ~ member(X0,intersection(X1,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_12408,c_170]) ).
tcf(c_15697,plain,
! [X0: $i] :
( ( complement(complement(intersection(X0,complement(subset_relation)))) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_12408,c_14028]) ).
tcf(c_15698,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,complement(subset_relation))) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_12408,c_5287]) ).
tcf(c_15699,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,complement(subset_relation)),X1) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_12408,c_5257]) ).
tcf(c_15700,plain,
! [X0: $i] :
( ( intersection(X0,complement(subset_relation)) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_12408,c_258]) ).
tcf(c_15759,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,intersection(X0,complement(subset_relation))),X1)
| member(not_subclass_element(intersection(X0,complement(subset_relation)),X1),complement(identity_relation))
| ( intersection(X0,complement(subset_relation)) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_12409]) ).
tcf(c_15760,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,complement(subset_relation)),null_class),complement(identity_relation))
| ( intersection(X0,complement(subset_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_12409]) ).
tcf(c_15763,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(subset_relation)),intersection(X0,complement(subset_relation))),universal_class)),universal_class))))))),complement(identity_relation))
| ( intersection(X0,complement(subset_relation)) = null_class )
| ~ member(intersection(X0,complement(subset_relation)),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_12409]) ).
tcf(c_15765,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(X0,complement(subset_relation)),X1)),complement(identity_relation))
| ( intersection(intersection(X0,complement(subset_relation)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_12409]) ).
tcf(c_15767,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(X1,complement(subset_relation)))),complement(identity_relation))
| ( intersection(X0,intersection(X1,complement(subset_relation))) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_12409]) ).
tcf(c_15768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,complement(subset_relation)),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,complement(subset_relation))),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4425,c_12409]) ).
tcf(c_15769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(X1,complement(subset_relation))),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,complement(subset_relation))),X2),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4430,c_12409]) ).
tcf(c_15770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(X0,complement(subset_relation)),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(X0,complement(subset_relation)),X1),X2),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4431,c_12409]) ).
tcf(c_15771,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(X1,complement(subset_relation))))
| member(not_subclass_element(X0,complement(intersection(X1,complement(subset_relation)))),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_8328,c_12409]) ).
tcf(c_15772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(X0,complement(subset_relation))),X3)
| member(not_subclass_element(intersection(intersection(X0,complement(subset_relation)),cross_product(X1,X2)),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4638,c_12409]) ).
tcf(c_15773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,complement(subset_relation)))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,complement(subset_relation)))),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4646,c_12409]) ).
tcf(c_15774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(X1,complement(subset_relation)),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(X1,complement(subset_relation)),X2)),X3),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_4647,c_12409]) ).
tcf(c_15775,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(X0,complement(subset_relation)))),X1)
| member(not_subclass_element(complement(complement(intersection(X0,complement(subset_relation)))),X1),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_13744,c_12409]) ).
tcf(c_15777,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,complement(identity_relation))
| ~ member(X0,intersection(complement(subset_relation),cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_193,c_12409]) ).
tcf(c_15868,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(unordered_pair(x,x),X0),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4972,c_4342]) ).
tcf(c_15869,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(unordered_pair(x,x),X0),universal_class) ),
inference(superposition,[status(thm)],[c_4972,c_4336]) ).
tcf(c_15883,plain,
! [X0: $i] :
( member(not_subclass_element(X0,complement(cross_product(universal_class,universal_class))),X0)
| ( complement(cross_product(universal_class,universal_class)) = X0 )
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) ),
inference(superposition,[status(thm)],[c_251,c_12788]) ).
tcf(c_15887,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ member(complement(cross_product(universal_class,universal_class)),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation) ),
inference(superposition,[status(thm)],[c_225,c_12788]) ).
tcf(c_15889,plain,
! [X0: $i] :
( ( intersection(complement(cross_product(universal_class,universal_class)),X0) = null_class )
| ~ member(regular(intersection(complement(cross_product(universal_class,universal_class)),X0)),subset_relation) ),
inference(superposition,[status(thm)],[c_4225,c_12788]) ).
tcf(c_15891,plain,
! [X0: $i] :
( ( intersection(X0,complement(cross_product(universal_class,universal_class))) = null_class )
| ~ member(regular(intersection(X0,complement(cross_product(universal_class,universal_class)))),subset_relation) ),
inference(superposition,[status(thm)],[c_4246,c_12788]) ).
tcf(c_15892,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),complement(cross_product(universal_class,universal_class))),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4425,c_12788]) ).
tcf(c_15893,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),X2)
| ~ member(not_subclass_element(intersection(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4430,c_12788]) ).
tcf(c_15894,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),X2)
| ~ member(not_subclass_element(intersection(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4431,c_12788]) ).
tcf(c_15895,plain,
! [X0: $i] :
( subclass(X0,complement(complement(cross_product(universal_class,universal_class))))
| ~ member(not_subclass_element(X0,complement(complement(cross_product(universal_class,universal_class)))),subset_relation) ),
inference(superposition,[status(thm)],[c_8328,c_12788]) ).
tcf(c_15896,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),complement(cross_product(universal_class,universal_class))),X2)
| ~ member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),cross_product(X0,X1)),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4638,c_12788]) ).
tcf(c_15897,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))),X2)
| ~ member(not_subclass_element(intersection(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4646,c_12788]) ).
tcf(c_15898,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)),X2)
| ~ member(not_subclass_element(intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)),X2),subset_relation) ),
inference(superposition,[status(thm)],[c_4647,c_12788]) ).
tcf(c_15899,plain,
! [X0: $i] :
( subclass(complement(complement(complement(cross_product(universal_class,universal_class)))),X0)
| ~ member(not_subclass_element(complement(complement(complement(cross_product(universal_class,universal_class)))),X0),subset_relation) ),
inference(superposition,[status(thm)],[c_13744,c_12788]) ).
tcf(c_15997,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),identity_relation)
| subclass(intersection(intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),X0),X1) ),
inference(superposition,[status(thm)],[c_13003,c_4431]) ).
tcf(c_15999,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(superposition,[status(thm)],[c_13003,c_4430]) ).
tcf(c_16001,plain,
! [X0: $i] :
( subclass(intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),X0)
| member(not_subclass_element(null_class,X0),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(superposition,[status(thm)],[c_13003,c_4245]) ).
tcf(c_16003,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),identity_relation)
| subclass(intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),X0) ),
inference(superposition,[status(thm)],[c_13003,c_4224]) ).
tcf(c_16007,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),identity_relation)
| subclass(intersection(X0,intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))),X1) ),
inference(superposition,[status(thm)],[c_13003,c_4647]) ).
tcf(c_16009,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(superposition,[status(thm)],[c_13003,c_4646]) ).
tcf(c_16017,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),subset_relation)
| subclass(intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),X0) ),
inference(superposition,[status(thm)],[c_13003,c_4433]) ).
tcf(c_16020,plain,
! [X0: $i] :
( subclass(intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),X0)
| ~ member(not_subclass_element(null_class,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(superposition,[status(thm)],[c_13003,c_4648]) ).
tcf(c_16043,plain,
! [X0: $i] : subclass(intersection(element_relation,X0),universal_class),
inference(superposition,[status(thm)],[c_173,c_13232]) ).
tcf(c_16056,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(element_relation,X0),X1)
| member(not_subclass_element(intersection(element_relation,X0),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_13233]) ).
tcf(c_16057,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,intersection(element_relation,X0)),X1)
| member(not_subclass_element(intersection(element_relation,X0),X1),cross_product(universal_class,universal_class))
| ( intersection(element_relation,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_13233]) ).
tcf(c_16058,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(element_relation,X0),null_class),cross_product(universal_class,universal_class))
| ( intersection(element_relation,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_13233]) ).
tcf(c_16060,plain,
! [X0: $i] :
( member(regular(intersection(element_relation,X0)),cross_product(universal_class,universal_class))
| ( intersection(element_relation,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_13233]) ).
tcf(c_16061,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(element_relation,X0),intersection(element_relation,X0)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ( intersection(element_relation,X0) = null_class )
| ~ member(intersection(element_relation,X0),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_13233]) ).
tcf(c_16062,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(element_relation,X0),X1),X2)
| member(not_subclass_element(intersection(intersection(element_relation,X0),X1),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_13233]) ).
tcf(c_16063,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(element_relation,X0),X1)),cross_product(universal_class,universal_class))
| ( intersection(intersection(element_relation,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_13233]) ).
tcf(c_16064,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(element_relation,X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(element_relation,X1)),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_13233]) ).
tcf(c_16065,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(element_relation,X1))),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(element_relation,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_13233]) ).
tcf(c_16066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(element_relation,X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(element_relation,X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_13233]) ).
tcf(c_16067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(element_relation,X1)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(element_relation,X1)),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_13233]) ).
tcf(c_16068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(element_relation,X0),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(element_relation,X0),X1),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_13233]) ).
tcf(c_16069,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(element_relation,X1)))
| member(not_subclass_element(X0,complement(intersection(element_relation,X1))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_13233]) ).
tcf(c_16070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(element_relation,X0)),X3)
| member(not_subclass_element(intersection(intersection(element_relation,X0),cross_product(X1,X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_13233]) ).
tcf(c_16071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(element_relation,X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(element_relation,X2))),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_13233]) ).
tcf(c_16072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(element_relation,X1),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(element_relation,X1),X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_13233]) ).
tcf(c_16073,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(element_relation,X0))),X1)
| member(not_subclass_element(complement(complement(intersection(element_relation,X0))),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_13233]) ).
tcf(c_16173,plain,
! [X0: $i] : subclass(intersection(X0,element_relation),universal_class),
inference(superposition,[status(thm)],[c_173,c_13247]) ).
tcf(c_16181,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,element_relation),X1)
| member(not_subclass_element(intersection(X0,element_relation),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_13248]) ).
tcf(c_16182,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,intersection(X0,element_relation)),X1)
| member(not_subclass_element(intersection(X0,element_relation),X1),cross_product(universal_class,universal_class))
| ( intersection(X0,element_relation) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_13248]) ).
tcf(c_16183,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,element_relation),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,element_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_13248]) ).
tcf(c_16185,plain,
! [X0: $i] :
( member(regular(intersection(X0,element_relation)),cross_product(universal_class,universal_class))
| ( intersection(X0,element_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_13248]) ).
tcf(c_16186,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,element_relation),intersection(X0,element_relation)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ( intersection(X0,element_relation) = null_class )
| ~ member(intersection(X0,element_relation),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_13248]) ).
tcf(c_16187,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,element_relation),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,element_relation),X1),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_13248]) ).
tcf(c_16188,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(X0,element_relation),X1)),cross_product(universal_class,universal_class))
| ( intersection(intersection(X0,element_relation),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_13248]) ).
tcf(c_16189,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,element_relation)),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,element_relation)),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_13248]) ).
tcf(c_16190,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(X1,element_relation))),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(X1,element_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_13248]) ).
tcf(c_16191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,element_relation),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,element_relation)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_13248]) ).
tcf(c_16192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(X1,element_relation)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,element_relation)),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_13248]) ).
tcf(c_16193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(X0,element_relation),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(X0,element_relation),X1),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_13248]) ).
tcf(c_16194,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(X1,element_relation)))
| member(not_subclass_element(X0,complement(intersection(X1,element_relation))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_13248]) ).
tcf(c_16195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(X0,element_relation)),X3)
| member(not_subclass_element(intersection(intersection(X0,element_relation),cross_product(X1,X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_13248]) ).
tcf(c_16196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,element_relation))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,element_relation))),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_13248]) ).
tcf(c_16197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(X1,element_relation),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(X1,element_relation),X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_13248]) ).
tcf(c_16198,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(X0,element_relation))),X1)
| member(not_subclass_element(complement(complement(intersection(X0,element_relation))),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_13248]) ).
tcf(c_16200,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(element_relation,cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_193,c_13248]) ).
tcf(c_16323,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),complement(cross_product(universal_class,universal_class))),X2)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_193,c_13279]) ).
tcf(c_16329,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(cross_product(universal_class,universal_class)),X1) = X0 )
| ~ function(universal_class)
| ~ subclass(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)) ),
inference(superposition,[status(thm)],[c_13279,c_176]) ).
tcf(c_16330,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X2),X1)
| ~ function(universal_class)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13279,c_250]) ).
tcf(c_16331,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ function(universal_class)
| ~ member(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)) ),
inference(superposition,[status(thm)],[c_13279,c_170]) ).
tcf(c_16332,plain,
! [X0: $i] :
( ( complement(complement(intersection(complement(cross_product(universal_class,universal_class)),X0))) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_14028]) ).
tcf(c_16333,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_5287]) ).
tcf(c_16334,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(complement(cross_product(universal_class,universal_class)),X0),X1) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_5257]) ).
tcf(c_16374,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),cross_product(X0,X1)),X2)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_193,c_13280]) ).
tcf(c_16380,plain,
! [X0: $i,X1: $i] :
( ( intersection(X1,complement(cross_product(universal_class,universal_class))) = X0 )
| ~ function(universal_class)
| ~ subclass(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))) ),
inference(superposition,[status(thm)],[c_13280,c_176]) ).
tcf(c_16381,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,complement(cross_product(universal_class,universal_class))),X1)
| ~ function(universal_class)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13280,c_250]) ).
tcf(c_16382,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ function(universal_class)
| ~ member(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))) ),
inference(superposition,[status(thm)],[c_13280,c_170]) ).
tcf(c_16383,plain,
! [X0: $i] :
( ( complement(complement(intersection(X0,complement(cross_product(universal_class,universal_class))))) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_14028]) ).
tcf(c_16384,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_5287]) ).
tcf(c_16385,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,complement(cross_product(universal_class,universal_class))),X1) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_5257]) ).
tcf(c_16425,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(unordered_pair(x,x),regular(unordered_pair(x,x))),X0)
| ( unordered_pair(x,x) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_4976]) ).
tcf(c_16426,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(unordered_pair(x,x),null_class),X0) ),
inference(superposition,[status(thm)],[c_4790,c_4976]) ).
tcf(c_16427,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(unordered_pair(x,x),complement(unordered_pair(x,x))),X0) ),
inference(superposition,[status(thm)],[c_12377,c_4976]) ).
tcf(c_16430,plain,
! [X0: $i] : subclass(intersection(unordered_pair(x,x),X0),iPr_def_10),
inference(superposition,[status(thm)],[c_4976,c_172]) ).
tcf(c_16431,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X0),X1)
| member(not_subclass_element(intersection(unordered_pair(x,x),X0),X1),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4976,c_4342]) ).
tcf(c_16432,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X0),X1)
| member(not_subclass_element(intersection(unordered_pair(x,x),X0),X1),universal_class) ),
inference(superposition,[status(thm)],[c_4976,c_4336]) ).
tcf(c_16433,plain,
! [X0: $i] : subclass(intersection(unordered_pair(x,x),complement(iPr_def_10)),X0),
inference(superposition,[status(thm)],[c_4976,c_4648]) ).
tcf(c_16593,plain,
( subclass(null_class,iPr_def_10)
| ( unordered_pair(x,x) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_16430]) ).
tcf(c_16594,plain,
subclass(null_class,iPr_def_10),
inference(superposition,[status(thm)],[c_4790,c_16430]) ).
tcf(c_16596,plain,
! [X0: $i] :
( ( intersection(unordered_pair(x,x),X0) = iPr_def_10 )
| ~ subclass(iPr_def_10,intersection(unordered_pair(x,x),X0)) ),
inference(superposition,[status(thm)],[c_16430,c_176]) ).
tcf(c_16597,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X1),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_16430,c_250]) ).
tcf(c_16598,plain,
! [X0: $i,X1: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,intersection(unordered_pair(x,x),X1)) ),
inference(superposition,[status(thm)],[c_16430,c_170]) ).
tcf(c_16608,plain,
! [X0: $i] :
( ( intersection(unordered_pair(x,x),complement(iPr_def_10)) = X0 )
| ~ subclass(X0,intersection(unordered_pair(x,x),complement(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_16433,c_176]) ).
tcf(c_16610,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,intersection(unordered_pair(x,x),complement(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_16433,c_170]) ).
tcf(c_16611,plain,
complement(complement(intersection(unordered_pair(x,x),complement(iPr_def_10)))) = null_class,
inference(superposition,[status(thm)],[c_16433,c_14028]) ).
tcf(c_16612,plain,
! [X0: $i] : intersection(X0,intersection(unordered_pair(x,x),complement(iPr_def_10))) = null_class,
inference(superposition,[status(thm)],[c_16433,c_5287]) ).
tcf(c_16613,plain,
! [X0: $i] : intersection(intersection(unordered_pair(x,x),complement(iPr_def_10)),X0) = null_class,
inference(superposition,[status(thm)],[c_16433,c_5257]) ).
tcf(c_16614,plain,
intersection(unordered_pair(x,x),complement(iPr_def_10)) = null_class,
inference(superposition,[status(thm)],[c_16433,c_258]) ).
tcf(c_16647,plain,
intersection(null_class,complement(unordered_pair(x,x))) = null_class,
inference(superposition,[status(thm)],[c_16614,c_12688]) ).
tcf(c_16648,plain,
intersection(null_class,complement(complement(iPr_def_10))) = null_class,
inference(superposition,[status(thm)],[c_16614,c_12625]) ).
tcf(c_16649,plain,
intersection(complement(unordered_pair(x,x)),null_class) = null_class,
inference(superposition,[status(thm)],[c_16614,c_11685]) ).
tcf(c_16652,plain,
! [X0: $i] : subclass(intersection(null_class,X0),unordered_pair(x,x)),
inference(superposition,[status(thm)],[c_16614,c_6583]) ).
tcf(c_16653,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),unordered_pair(x,x))
| subclass(intersection(intersection(unordered_pair(x,x),complement(iPr_def_10)),X0),X1) ),
inference(superposition,[status(thm)],[c_16614,c_4431]) ).
tcf(c_16654,plain,
! [X0: $i] : subclass(intersection(null_class,X0),complement(iPr_def_10)),
inference(superposition,[status(thm)],[c_16614,c_6065]) ).
tcf(c_16655,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),complement(iPr_def_10))
| subclass(intersection(intersection(unordered_pair(x,x),complement(iPr_def_10)),X0),X1) ),
inference(superposition,[status(thm)],[c_16614,c_4430]) ).
tcf(c_16656,plain,
subclass(null_class,complement(iPr_def_10)),
inference(superposition,[status(thm)],[c_16614,c_4643]) ).
tcf(c_16657,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),complement(iPr_def_10))
| subclass(intersection(unordered_pair(x,x),complement(iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_16614,c_4245]) ).
tcf(c_16658,plain,
subclass(null_class,unordered_pair(x,x)),
inference(superposition,[status(thm)],[c_16614,c_4427]) ).
tcf(c_16659,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),unordered_pair(x,x))
| subclass(intersection(unordered_pair(x,x),complement(iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_16614,c_4224]) ).
tcf(c_16662,plain,
! [X0: $i] : subclass(intersection(X0,null_class),unordered_pair(x,x)),
inference(superposition,[status(thm)],[c_16614,c_11340]) ).
tcf(c_16663,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),unordered_pair(x,x))
| subclass(intersection(X0,intersection(unordered_pair(x,x),complement(iPr_def_10))),X1) ),
inference(superposition,[status(thm)],[c_16614,c_4647]) ).
tcf(c_16664,plain,
! [X0: $i] : subclass(intersection(X0,null_class),complement(iPr_def_10)),
inference(superposition,[status(thm)],[c_16614,c_10731]) ).
tcf(c_16665,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),complement(iPr_def_10))
| subclass(intersection(X0,intersection(unordered_pair(x,x),complement(iPr_def_10))),X1) ),
inference(superposition,[status(thm)],[c_16614,c_4646]) ).
tcf(c_16666,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(x,x))
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_16614,c_6783]) ).
tcf(c_16667,plain,
! [X0: $i,X1: $i] :
( member(X0,complement(iPr_def_10))
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_16614,c_6250]) ).
tcf(c_16668,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,complement(iPr_def_10))
| ~ member(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_16614,c_190]) ).
tcf(c_16671,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ~ subclass(unordered_pair(x,x),X0) ),
inference(superposition,[status(thm)],[c_16614,c_6782]) ).
tcf(c_16673,plain,
! [X0: $i] :
( subclass(intersection(unordered_pair(x,x),complement(iPr_def_10)),X0)
| ~ member(not_subclass_element(null_class,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_16614,c_4648]) ).
tcf(c_16674,plain,
intersection(complement(complement(iPr_def_10)),null_class) = null_class,
inference(superposition,[status(thm)],[c_16614,c_11228]) ).
tcf(c_16675,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ~ subclass(complement(iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_16614,c_6249]) ).
tcf(c_16678,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(unordered_pair(x,x),complement(iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_16614,c_4976]) ).
tcf(c_16679,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ~ subclass(unordered_pair(x,x),X0) ),
inference(superposition,[status(thm)],[c_16614,c_11629]) ).
tcf(c_16680,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ~ subclass(complement(iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_16614,c_11018]) ).
tcf(c_16681,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(x,x))
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_16614,c_11630]) ).
tcf(c_16682,plain,
! [X0: $i,X1: $i] :
( member(X0,complement(iPr_def_10))
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_16614,c_11019]) ).
tcf(c_16703,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_16678,c_16614]) ).
tcf(c_16704,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ member(not_subclass_element(null_class,X0),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_16673,c_16614]) ).
tcf(c_16705,plain,
! [X0: $i] :
( ~ member(X0,complement(iPr_def_10))
| ~ member(X0,unordered_pair(x,x)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16668,c_256]) ).
tcf(c_16708,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),complement(iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_16657,c_16614]) ).
tcf(c_16709,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),unordered_pair(x,x)) ),
inference(light_normalisation,[status(thm)],[c_16659,c_16614]) ).
tcf(c_16737,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ subclass(complement(iPr_def_10),X0) ),
inference(demodulation,[status(thm)],[c_16675,c_4553]) ).
tcf(c_16746,plain,
! [X0: $i] : subclass(intersection(successor_relation,X0),universal_class),
inference(superposition,[status(thm)],[c_173,c_13536]) ).
tcf(c_16755,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(successor_relation,X0),X1)
| member(not_subclass_element(intersection(successor_relation,X0),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_13537]) ).
tcf(c_16756,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,intersection(successor_relation,X0)),X1)
| member(not_subclass_element(intersection(successor_relation,X0),X1),cross_product(universal_class,universal_class))
| ( intersection(successor_relation,X0) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_13537]) ).
tcf(c_16757,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(successor_relation,X0),null_class),cross_product(universal_class,universal_class))
| ( intersection(successor_relation,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_13537]) ).
tcf(c_16759,plain,
! [X0: $i] :
( member(regular(intersection(successor_relation,X0)),cross_product(universal_class,universal_class))
| ( intersection(successor_relation,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_13537]) ).
tcf(c_16760,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(successor_relation,X0),intersection(successor_relation,X0)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ( intersection(successor_relation,X0) = null_class )
| ~ member(intersection(successor_relation,X0),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_13537]) ).
tcf(c_16761,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(successor_relation,X0),X1),X2)
| member(not_subclass_element(intersection(intersection(successor_relation,X0),X1),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_13537]) ).
tcf(c_16762,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(successor_relation,X0),X1)),cross_product(universal_class,universal_class))
| ( intersection(intersection(successor_relation,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_13537]) ).
tcf(c_16763,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(successor_relation,X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(successor_relation,X1)),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_13537]) ).
tcf(c_16764,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(successor_relation,X1))),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(successor_relation,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_13537]) ).
tcf(c_16765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(successor_relation,X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(successor_relation,X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_13537]) ).
tcf(c_16766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(successor_relation,X1)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(successor_relation,X1)),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_13537]) ).
tcf(c_16767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(successor_relation,X0),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(successor_relation,X0),X1),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_13537]) ).
tcf(c_16768,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(successor_relation,X1)))
| member(not_subclass_element(X0,complement(intersection(successor_relation,X1))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_13537]) ).
tcf(c_16769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(successor_relation,X0)),X3)
| member(not_subclass_element(intersection(intersection(successor_relation,X0),cross_product(X1,X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_13537]) ).
tcf(c_16770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(successor_relation,X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(successor_relation,X2))),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_13537]) ).
tcf(c_16771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(successor_relation,X1),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(successor_relation,X1),X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_13537]) ).
tcf(c_16772,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(successor_relation,X0))),X1)
| member(not_subclass_element(complement(complement(intersection(successor_relation,X0))),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_13537]) ).
tcf(c_16908,plain,
! [X0: $i] : subclass(intersection(X0,successor_relation),universal_class),
inference(superposition,[status(thm)],[c_173,c_13551]) ).
tcf(c_16916,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,successor_relation),X1)
| member(not_subclass_element(intersection(X0,successor_relation),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_13552]) ).
tcf(c_16917,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,intersection(X0,successor_relation)),X1)
| member(not_subclass_element(intersection(X0,successor_relation),X1),cross_product(universal_class,universal_class))
| ( intersection(X0,successor_relation) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_13552]) ).
tcf(c_16918,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,successor_relation),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,successor_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_13552]) ).
tcf(c_16920,plain,
! [X0: $i] :
( member(regular(intersection(X0,successor_relation)),cross_product(universal_class,universal_class))
| ( intersection(X0,successor_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_13552]) ).
tcf(c_16921,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,successor_relation),intersection(X0,successor_relation)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ( intersection(X0,successor_relation) = null_class )
| ~ member(intersection(X0,successor_relation),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_13552]) ).
tcf(c_16922,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,successor_relation),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,successor_relation),X1),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_13552]) ).
tcf(c_16923,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(X0,successor_relation),X1)),cross_product(universal_class,universal_class))
| ( intersection(intersection(X0,successor_relation),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_13552]) ).
tcf(c_16924,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,successor_relation)),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,successor_relation)),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_13552]) ).
tcf(c_16925,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(X1,successor_relation))),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(X1,successor_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_13552]) ).
tcf(c_16926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,successor_relation),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,successor_relation)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_13552]) ).
tcf(c_16927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(X1,successor_relation)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,successor_relation)),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_13552]) ).
tcf(c_16928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(X0,successor_relation),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(X0,successor_relation),X1),X2),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_13552]) ).
tcf(c_16929,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(X1,successor_relation)))
| member(not_subclass_element(X0,complement(intersection(X1,successor_relation))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_13552]) ).
tcf(c_16930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(X0,successor_relation)),X3)
| member(not_subclass_element(intersection(intersection(X0,successor_relation),cross_product(X1,X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_13552]) ).
tcf(c_16931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,successor_relation))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,successor_relation))),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_13552]) ).
tcf(c_16932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(X1,successor_relation),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(X1,successor_relation),X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_13552]) ).
tcf(c_16933,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(X0,successor_relation))),X1)
| member(not_subclass_element(complement(complement(intersection(X0,successor_relation))),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_13552]) ).
tcf(c_16935,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,intersection(successor_relation,cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_193,c_13552]) ).
tcf(c_17064,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(complement(unordered_pair(x,x)),unordered_pair(x,x)),X0) ),
inference(superposition,[status(thm)],[c_4169,c_4977]) ).
tcf(c_17066,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(null_class,unordered_pair(x,x)),X0) ),
inference(superposition,[status(thm)],[c_4553,c_4977]) ).
tcf(c_17069,plain,
! [X0: $i] : subclass(intersection(X0,unordered_pair(x,x)),iPr_def_10),
inference(superposition,[status(thm)],[c_4977,c_172]) ).
tcf(c_17070,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(x,x)),X1)
| member(not_subclass_element(intersection(X0,unordered_pair(x,x)),X1),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4977,c_4342]) ).
tcf(c_17071,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(x,x)),X1)
| member(not_subclass_element(intersection(X0,unordered_pair(x,x)),X1),universal_class) ),
inference(superposition,[status(thm)],[c_4977,c_4336]) ).
tcf(c_17072,plain,
! [X0: $i] : subclass(intersection(complement(iPr_def_10),unordered_pair(x,x)),X0),
inference(superposition,[status(thm)],[c_4977,c_4432]) ).
tcf(c_17094,plain,
! [X0: $i,X1: $i] : subclass(intersection(unordered_pair(x,x),cross_product(X0,X1)),iPr_def_10),
inference(superposition,[status(thm)],[c_193,c_17069]) ).
tcf(c_17096,plain,
! [X0: $i] :
( ( intersection(X0,unordered_pair(x,x)) = iPr_def_10 )
| ~ subclass(iPr_def_10,intersection(X0,unordered_pair(x,x))) ),
inference(superposition,[status(thm)],[c_17069,c_176]) ).
tcf(c_17097,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,unordered_pair(x,x)),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_17069,c_250]) ).
tcf(c_17098,plain,
! [X0: $i,X1: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,intersection(X1,unordered_pair(x,x))) ),
inference(superposition,[status(thm)],[c_17069,c_170]) ).
tcf(c_17125,plain,
! [X0: $i] :
( ( intersection(complement(iPr_def_10),unordered_pair(x,x)) = X0 )
| ~ subclass(X0,intersection(complement(iPr_def_10),unordered_pair(x,x))) ),
inference(superposition,[status(thm)],[c_17072,c_176]) ).
tcf(c_17127,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,intersection(complement(iPr_def_10),unordered_pair(x,x))) ),
inference(superposition,[status(thm)],[c_17072,c_170]) ).
tcf(c_17128,plain,
complement(complement(intersection(complement(iPr_def_10),unordered_pair(x,x)))) = null_class,
inference(superposition,[status(thm)],[c_17072,c_14028]) ).
tcf(c_17129,plain,
! [X0: $i] : intersection(X0,intersection(complement(iPr_def_10),unordered_pair(x,x))) = null_class,
inference(superposition,[status(thm)],[c_17072,c_5287]) ).
tcf(c_17130,plain,
! [X0: $i] : intersection(intersection(complement(iPr_def_10),unordered_pair(x,x)),X0) = null_class,
inference(superposition,[status(thm)],[c_17072,c_5257]) ).
tcf(c_17131,plain,
intersection(complement(iPr_def_10),unordered_pair(x,x)) = null_class,
inference(superposition,[status(thm)],[c_17072,c_258]) ).
tcf(c_17147,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),complement(iPr_def_10))
| subclass(intersection(intersection(complement(iPr_def_10),unordered_pair(x,x)),X0),X1) ),
inference(superposition,[status(thm)],[c_17131,c_4431]) ).
tcf(c_17149,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),unordered_pair(x,x))
| subclass(intersection(intersection(complement(iPr_def_10),unordered_pair(x,x)),X0),X1) ),
inference(superposition,[status(thm)],[c_17131,c_4430]) ).
tcf(c_17151,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),unordered_pair(x,x))
| subclass(intersection(complement(iPr_def_10),unordered_pair(x,x)),X0) ),
inference(superposition,[status(thm)],[c_17131,c_4245]) ).
tcf(c_17153,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),complement(iPr_def_10))
| subclass(intersection(complement(iPr_def_10),unordered_pair(x,x)),X0) ),
inference(superposition,[status(thm)],[c_17131,c_4224]) ).
tcf(c_17157,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),complement(iPr_def_10))
| subclass(intersection(X0,intersection(complement(iPr_def_10),unordered_pair(x,x))),X1) ),
inference(superposition,[status(thm)],[c_17131,c_4647]) ).
tcf(c_17159,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),unordered_pair(x,x))
| subclass(intersection(X0,intersection(complement(iPr_def_10),unordered_pair(x,x))),X1) ),
inference(superposition,[status(thm)],[c_17131,c_4646]) ).
tcf(c_17167,plain,
! [X0: $i] :
( subclass(intersection(complement(iPr_def_10),unordered_pair(x,x)),X0)
| ~ member(not_subclass_element(null_class,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_17131,c_4432]) ).
tcf(c_17172,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(complement(iPr_def_10),unordered_pair(x,x)),X0) ),
inference(superposition,[status(thm)],[c_17131,c_4977]) ).
tcf(c_17190,plain,
subclass(complement(complement(element_relation)),universal_class),
inference(superposition,[status(thm)],[c_173,c_14220]) ).
tcf(c_17198,plain,
! [X0: $i] :
( subclass(complement(complement(element_relation)),X0)
| member(not_subclass_element(complement(complement(element_relation)),X0),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_14221]) ).
tcf(c_17199,plain,
! [X0: $i] :
( member(not_subclass_element(X0,complement(complement(element_relation))),X0)
| member(not_subclass_element(complement(complement(element_relation)),X0),cross_product(universal_class,universal_class))
| ( complement(complement(element_relation)) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_14221]) ).
tcf(c_17200,plain,
( member(not_subclass_element(complement(complement(element_relation)),null_class),cross_product(universal_class,universal_class))
| ( complement(complement(element_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_14221]) ).
tcf(c_17201,plain,
! [X0: $i] :
( member(X0,complement(element_relation))
| member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_192,c_14221]) ).
tcf(c_17202,plain,
( member(regular(complement(complement(element_relation))),cross_product(universal_class,universal_class))
| ( complement(complement(element_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_14221]) ).
tcf(c_17203,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(element_relation)),complement(complement(element_relation))),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ( complement(complement(element_relation)) = null_class )
| ~ member(complement(complement(element_relation)),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_14221]) ).
tcf(c_17204,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(complement(element_relation)),X0),X1)
| member(not_subclass_element(intersection(complement(complement(element_relation)),X0),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_14221]) ).
tcf(c_17205,plain,
! [X0: $i] :
( member(regular(intersection(complement(complement(element_relation)),X0)),cross_product(universal_class,universal_class))
| ( intersection(complement(complement(element_relation)),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_14221]) ).
tcf(c_17206,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(complement(element_relation))),X1)
| member(not_subclass_element(intersection(X0,complement(complement(element_relation))),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_14221]) ).
tcf(c_17207,plain,
! [X0: $i] :
( member(regular(intersection(X0,complement(complement(element_relation)))),cross_product(universal_class,universal_class))
| ( intersection(X0,complement(complement(element_relation))) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_14221]) ).
tcf(c_17208,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(complement(element_relation)),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),complement(complement(element_relation))),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_14221]) ).
tcf(c_17209,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,complement(complement(element_relation))),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,complement(complement(element_relation))),X1),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_14221]) ).
tcf(c_17210,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(complement(complement(element_relation)),X0),X1),X2)
| member(not_subclass_element(intersection(intersection(complement(complement(element_relation)),X0),X1),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_14221]) ).
tcf(c_17211,plain,
! [X0: $i] :
( subclass(X0,complement(complement(complement(element_relation))))
| member(not_subclass_element(X0,complement(complement(complement(element_relation)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_14221]) ).
tcf(c_17212,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),complement(complement(element_relation))),X2)
| member(not_subclass_element(intersection(complement(complement(element_relation)),cross_product(X0,X1)),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_14221]) ).
tcf(c_17213,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,complement(complement(element_relation)))),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,complement(complement(element_relation)))),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_14221]) ).
tcf(c_17214,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(complement(complement(element_relation)),X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(complement(complement(element_relation)),X1)),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_14221]) ).
tcf(c_17215,plain,
! [X0: $i] :
( subclass(complement(complement(complement(complement(element_relation)))),X0)
| member(not_subclass_element(complement(complement(complement(complement(element_relation)))),X0),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_14221]) ).
tcf(c_17336,plain,
subclass(complement(complement(successor_relation)),universal_class),
inference(superposition,[status(thm)],[c_173,c_14231]) ).
tcf(c_17359,plain,
! [X0: $i] :
( subclass(complement(complement(successor_relation)),X0)
| member(not_subclass_element(complement(complement(successor_relation)),X0),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_14232]) ).
tcf(c_17360,plain,
! [X0: $i] :
( member(not_subclass_element(X0,complement(complement(successor_relation))),X0)
| member(not_subclass_element(complement(complement(successor_relation)),X0),cross_product(universal_class,universal_class))
| ( complement(complement(successor_relation)) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_14232]) ).
tcf(c_17361,plain,
( member(not_subclass_element(complement(complement(successor_relation)),null_class),cross_product(universal_class,universal_class))
| ( complement(complement(successor_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_14232]) ).
tcf(c_17362,plain,
! [X0: $i] :
( member(X0,complement(successor_relation))
| member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_192,c_14232]) ).
tcf(c_17363,plain,
( member(regular(complement(complement(successor_relation))),cross_product(universal_class,universal_class))
| ( complement(complement(successor_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_14232]) ).
tcf(c_17364,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(successor_relation)),complement(complement(successor_relation))),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ( complement(complement(successor_relation)) = null_class )
| ~ member(complement(complement(successor_relation)),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_14232]) ).
tcf(c_17365,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(complement(successor_relation)),X0),X1)
| member(not_subclass_element(intersection(complement(complement(successor_relation)),X0),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_14232]) ).
tcf(c_17366,plain,
! [X0: $i] :
( member(regular(intersection(complement(complement(successor_relation)),X0)),cross_product(universal_class,universal_class))
| ( intersection(complement(complement(successor_relation)),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_14232]) ).
tcf(c_17367,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(complement(successor_relation))),X1)
| member(not_subclass_element(intersection(X0,complement(complement(successor_relation))),X1),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_14232]) ).
tcf(c_17368,plain,
! [X0: $i] :
( member(regular(intersection(X0,complement(complement(successor_relation)))),cross_product(universal_class,universal_class))
| ( intersection(X0,complement(complement(successor_relation))) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_14232]) ).
tcf(c_17369,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(complement(successor_relation)),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),complement(complement(successor_relation))),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_14232]) ).
tcf(c_17370,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,complement(complement(successor_relation))),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,complement(complement(successor_relation))),X1),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_14232]) ).
tcf(c_17371,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(complement(complement(successor_relation)),X0),X1),X2)
| member(not_subclass_element(intersection(intersection(complement(complement(successor_relation)),X0),X1),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_14232]) ).
tcf(c_17372,plain,
! [X0: $i] :
( subclass(X0,complement(complement(complement(successor_relation))))
| member(not_subclass_element(X0,complement(complement(complement(successor_relation)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_8328,c_14232]) ).
tcf(c_17373,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),complement(complement(successor_relation))),X2)
| member(not_subclass_element(intersection(complement(complement(successor_relation)),cross_product(X0,X1)),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_14232]) ).
tcf(c_17374,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,complement(complement(successor_relation)))),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,complement(complement(successor_relation)))),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_14232]) ).
tcf(c_17375,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(complement(complement(successor_relation)),X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(complement(complement(successor_relation)),X1)),X2),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_14232]) ).
tcf(c_17376,plain,
! [X0: $i] :
( subclass(complement(complement(complement(complement(successor_relation)))),X0)
| member(not_subclass_element(complement(complement(complement(complement(successor_relation)))),X0),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_14232]) ).
tcf(c_17507,plain,
! [X0: $i] :
( ( complement(cross_product(universal_class,universal_class)) = X0 )
| ~ subclass(complement(successor_relation),X0)
| ~ subclass(X0,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_14988,c_176]) ).
tcf(c_17508,plain,
! [X0: $i,X1: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X1)
| ~ subclass(X0,X1)
| ~ subclass(complement(successor_relation),X0) ),
inference(superposition,[status(thm)],[c_14988,c_250]) ).
tcf(c_17509,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ subclass(complement(successor_relation),X1)
| ~ member(X0,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_14988,c_170]) ).
tcf(c_17510,plain,
( ( complement(complement(complement(cross_product(universal_class,universal_class)))) = null_class )
| ~ subclass(complement(successor_relation),null_class) ),
inference(superposition,[status(thm)],[c_14988,c_14028]) ).
tcf(c_17511,plain,
! [X0: $i] :
( ( intersection(X0,complement(cross_product(universal_class,universal_class))) = null_class )
| ~ subclass(complement(successor_relation),null_class) ),
inference(superposition,[status(thm)],[c_14988,c_5287]) ).
tcf(c_17512,plain,
! [X0: $i] :
( ( intersection(complement(cross_product(universal_class,universal_class)),X0) = null_class )
| ~ subclass(complement(successor_relation),null_class) ),
inference(superposition,[status(thm)],[c_14988,c_5257]) ).
tcf(c_17513,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ subclass(complement(successor_relation),null_class) ),
inference(superposition,[status(thm)],[c_14988,c_258]) ).
tcf(c_17540,plain,
! [X0: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_171,c_14989]) ).
tcf(c_17541,plain,
! [X0: $i] :
( member(not_subclass_element(X0,complement(cross_product(universal_class,universal_class))),X0)
| member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),complement(successor_relation))
| ( complement(cross_product(universal_class,universal_class)) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_14989]) ).
tcf(c_17542,plain,
( member(not_subclass_element(complement(cross_product(universal_class,universal_class)),null_class),complement(successor_relation))
| ( complement(cross_product(universal_class,universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_14989]) ).
tcf(c_17544,plain,
( member(regular(complement(cross_product(universal_class,universal_class))),complement(successor_relation))
| ( complement(cross_product(universal_class,universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_14989]) ).
tcf(c_17545,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),complement(successor_relation))
| ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ member(complement(cross_product(universal_class,universal_class)),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_14989]) ).
tcf(c_17546,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X0),X1)
| member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_4224,c_14989]) ).
tcf(c_17547,plain,
! [X0: $i] :
( member(regular(intersection(complement(cross_product(universal_class,universal_class)),X0)),complement(successor_relation))
| ( intersection(complement(cross_product(universal_class,universal_class)),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_14989]) ).
tcf(c_17548,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(cross_product(universal_class,universal_class))),X1)
| member(not_subclass_element(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_4245,c_14989]) ).
tcf(c_17549,plain,
! [X0: $i] :
( member(regular(intersection(X0,complement(cross_product(universal_class,universal_class)))),complement(successor_relation))
| ( intersection(X0,complement(cross_product(universal_class,universal_class))) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_14989]) ).
tcf(c_17550,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),complement(cross_product(universal_class,universal_class))),X2),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_4425,c_14989]) ).
tcf(c_17551,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),X2),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_4430,c_14989]) ).
tcf(c_17552,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),X2)
| member(not_subclass_element(intersection(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),X2),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_4431,c_14989]) ).
tcf(c_17553,plain,
! [X0: $i] :
( subclass(X0,complement(complement(cross_product(universal_class,universal_class))))
| member(not_subclass_element(X0,complement(complement(cross_product(universal_class,universal_class)))),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_8328,c_14989]) ).
tcf(c_17554,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),complement(cross_product(universal_class,universal_class))),X2)
| member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),cross_product(X0,X1)),X2),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_4638,c_14989]) ).
tcf(c_17555,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))),X2),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_4646,c_14989]) ).
tcf(c_17556,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)),X2),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_4647,c_14989]) ).
tcf(c_17557,plain,
! [X0: $i] :
( subclass(complement(complement(complement(cross_product(universal_class,universal_class)))),X0)
| member(not_subclass_element(complement(complement(complement(cross_product(universal_class,universal_class)))),X0),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_13744,c_14989]) ).
tcf(c_17670,plain,
! [X0: $i] :
( ( complement(cross_product(universal_class,universal_class)) = X0 )
| ~ subclass(complement(element_relation),X0)
| ~ subclass(X0,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_15325,c_176]) ).
tcf(c_17671,plain,
! [X0: $i,X1: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X1)
| ~ subclass(X0,X1)
| ~ subclass(complement(element_relation),X0) ),
inference(superposition,[status(thm)],[c_15325,c_250]) ).
tcf(c_17672,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ subclass(complement(element_relation),X1)
| ~ member(X0,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_15325,c_170]) ).
tcf(c_17673,plain,
( ( complement(complement(complement(cross_product(universal_class,universal_class)))) = null_class )
| ~ subclass(complement(element_relation),null_class) ),
inference(superposition,[status(thm)],[c_15325,c_14028]) ).
tcf(c_17674,plain,
! [X0: $i] :
( ( intersection(X0,complement(cross_product(universal_class,universal_class))) = null_class )
| ~ subclass(complement(element_relation),null_class) ),
inference(superposition,[status(thm)],[c_15325,c_5287]) ).
tcf(c_17675,plain,
! [X0: $i] :
( ( intersection(complement(cross_product(universal_class,universal_class)),X0) = null_class )
| ~ subclass(complement(element_relation),null_class) ),
inference(superposition,[status(thm)],[c_15325,c_5257]) ).
tcf(c_17676,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ subclass(complement(element_relation),null_class) ),
inference(superposition,[status(thm)],[c_15325,c_258]) ).
tcf(c_17703,plain,
! [X0: $i] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_171,c_15326]) ).
tcf(c_17704,plain,
! [X0: $i] :
( member(not_subclass_element(X0,complement(cross_product(universal_class,universal_class))),X0)
| member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),complement(element_relation))
| ( complement(cross_product(universal_class,universal_class)) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_15326]) ).
tcf(c_17705,plain,
( member(not_subclass_element(complement(cross_product(universal_class,universal_class)),null_class),complement(element_relation))
| ( complement(cross_product(universal_class,universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_15326]) ).
tcf(c_17707,plain,
( member(regular(complement(cross_product(universal_class,universal_class))),complement(element_relation))
| ( complement(cross_product(universal_class,universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_15326]) ).
tcf(c_17708,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),complement(element_relation))
| ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ member(complement(cross_product(universal_class,universal_class)),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_15326]) ).
tcf(c_17709,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X0),X1)
| member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_4224,c_15326]) ).
tcf(c_17710,plain,
! [X0: $i] :
( member(regular(intersection(complement(cross_product(universal_class,universal_class)),X0)),complement(element_relation))
| ( intersection(complement(cross_product(universal_class,universal_class)),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_15326]) ).
tcf(c_17711,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(cross_product(universal_class,universal_class))),X1)
| member(not_subclass_element(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_4245,c_15326]) ).
tcf(c_17712,plain,
! [X0: $i] :
( member(regular(intersection(X0,complement(cross_product(universal_class,universal_class)))),complement(element_relation))
| ( intersection(X0,complement(cross_product(universal_class,universal_class))) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_15326]) ).
tcf(c_17713,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),complement(cross_product(universal_class,universal_class))),X2),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_4425,c_15326]) ).
tcf(c_17714,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),X2),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_4430,c_15326]) ).
tcf(c_17715,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),X2)
| member(not_subclass_element(intersection(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),X2),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_4431,c_15326]) ).
tcf(c_17716,plain,
! [X0: $i] :
( subclass(X0,complement(complement(cross_product(universal_class,universal_class))))
| member(not_subclass_element(X0,complement(complement(cross_product(universal_class,universal_class)))),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_8328,c_15326]) ).
tcf(c_17717,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),complement(cross_product(universal_class,universal_class))),X2)
| member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),cross_product(X0,X1)),X2),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_4638,c_15326]) ).
tcf(c_17718,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))),X2),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_4646,c_15326]) ).
tcf(c_17719,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)),X2),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_4647,c_15326]) ).
tcf(c_17720,plain,
! [X0: $i] :
( subclass(complement(complement(complement(cross_product(universal_class,universal_class)))),X0)
| member(not_subclass_element(complement(complement(complement(cross_product(universal_class,universal_class)))),X0),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_13744,c_15326]) ).
tcf(c_17901,plain,
! [X0: $i,X1: $i] :
( ( intersection(unordered_pair(x,x),X1) = X0 )
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,intersection(unordered_pair(x,x),X1)) ),
inference(superposition,[status(thm)],[c_16597,c_176]) ).
tcf(c_17902,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(unordered_pair(x,x),X2),X1)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_16597,c_250]) ).
tcf(c_17903,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(iPr_def_10,X2)
| ~ member(X0,intersection(unordered_pair(x,x),X1)) ),
inference(superposition,[status(thm)],[c_16597,c_170]) ).
tcf(c_17904,plain,
! [X0: $i] :
( ( complement(complement(intersection(unordered_pair(x,x),X0))) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_16597,c_14028]) ).
tcf(c_17905,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(unordered_pair(x,x),X1)) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_16597,c_5287]) ).
tcf(c_17906,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(unordered_pair(x,x),X0),X1) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_16597,c_5257]) ).
tcf(c_17963,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(unordered_pair(y,y),X0),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4996,c_4342]) ).
tcf(c_17964,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(unordered_pair(y,y),X0),universal_class) ),
inference(superposition,[status(thm)],[c_4996,c_4336]) ).
tcf(c_17978,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(unordered_pair(x,x),X0),X1),iPr_def_10)
| member(not_subclass_element(X1,intersection(unordered_pair(x,x),X0)),X1)
| ( intersection(unordered_pair(x,x),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_16598]) ).
tcf(c_17979,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(unordered_pair(x,x),X0),null_class),iPr_def_10)
| ( intersection(unordered_pair(x,x),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_16598]) ).
tcf(c_17980,plain,
! [X0: $i,X1: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,X1)
| ~ member(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_190,c_16598]) ).
tcf(c_17982,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(x,x),X0),intersection(unordered_pair(x,x),X0)),universal_class)),universal_class))))))),iPr_def_10)
| ( intersection(unordered_pair(x,x),X0) = null_class )
| ~ member(intersection(unordered_pair(x,x),X0),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_16598]) ).
tcf(c_17984,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(unordered_pair(x,x),X0),X1)),iPr_def_10)
| ( intersection(intersection(unordered_pair(x,x),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_16598]) ).
tcf(c_17986,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(unordered_pair(x,x),X1))),iPr_def_10)
| ( intersection(X0,intersection(unordered_pair(x,x),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_16598]) ).
tcf(c_17987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(unordered_pair(x,x),X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(unordered_pair(x,x),X2)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4425,c_16598]) ).
tcf(c_17988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(unordered_pair(x,x),X1)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(unordered_pair(x,x),X1)),X2),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4430,c_16598]) ).
tcf(c_17989,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(unordered_pair(x,x),X0),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(unordered_pair(x,x),X0),X1),X2),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4431,c_16598]) ).
tcf(c_17990,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(unordered_pair(x,x),X1)))
| member(not_subclass_element(X0,complement(intersection(unordered_pair(x,x),X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8328,c_16598]) ).
tcf(c_17991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(unordered_pair(x,x),X0)),X3)
| member(not_subclass_element(intersection(intersection(unordered_pair(x,x),X0),cross_product(X1,X2)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4638,c_16598]) ).
tcf(c_17992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(unordered_pair(x,x),X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(unordered_pair(x,x),X2))),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4646,c_16598]) ).
tcf(c_17993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(unordered_pair(x,x),X1),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(unordered_pair(x,x),X1),X2)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4647,c_16598]) ).
tcf(c_17994,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(unordered_pair(x,x),X0))),X1)
| member(not_subclass_element(complement(complement(intersection(unordered_pair(x,x),X0))),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_13744,c_16598]) ).
tcf(c_18079,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ member(not_subclass_element(unordered_pair(x,x),X0),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_171,c_16705]) ).
tcf(c_18080,plain,
! [X0: $i] :
( member(not_subclass_element(X0,unordered_pair(x,x)),X0)
| ( unordered_pair(x,x) = X0 )
| ~ member(not_subclass_element(unordered_pair(x,x),X0),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_251,c_16705]) ).
tcf(c_18081,plain,
( ( unordered_pair(x,x) = null_class )
| ~ member(not_subclass_element(unordered_pair(x,x),null_class),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_259,c_16705]) ).
tcf(c_18083,plain,
( ~ member(x,universal_class)
| ~ member(x,complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_179,c_16705]) ).
tcf(c_18084,plain,
( ( unordered_pair(x,x) = null_class )
| ~ member(regular(unordered_pair(x,x)),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_222,c_16705]) ).
tcf(c_18085,plain,
( ( unordered_pair(x,x) = null_class )
| ~ member(unordered_pair(x,x),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(x,x),unordered_pair(x,x)),universal_class)),universal_class))))))),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_225,c_16705]) ).
tcf(c_18086,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X0),X1)
| ~ member(not_subclass_element(intersection(unordered_pair(x,x),X0),X1),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4224,c_16705]) ).
tcf(c_18087,plain,
! [X0: $i] :
( ( intersection(unordered_pair(x,x),X0) = null_class )
| ~ member(regular(intersection(unordered_pair(x,x),X0)),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4225,c_16705]) ).
tcf(c_18088,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(x,x)),X1)
| ~ member(not_subclass_element(intersection(X0,unordered_pair(x,x)),X1),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4245,c_16705]) ).
tcf(c_18089,plain,
! [X0: $i] :
( ( intersection(X0,unordered_pair(x,x)) = null_class )
| ~ member(regular(intersection(X0,unordered_pair(x,x))),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4246,c_16705]) ).
tcf(c_18090,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(unordered_pair(x,x),cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),unordered_pair(x,x)),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4425,c_16705]) ).
tcf(c_18091,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,unordered_pair(x,x)),X1),X2)
| ~ member(not_subclass_element(intersection(intersection(X0,unordered_pair(x,x)),X1),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4430,c_16705]) ).
tcf(c_18092,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(unordered_pair(x,x),X0),X1),X2)
| ~ member(not_subclass_element(intersection(intersection(unordered_pair(x,x),X0),X1),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4431,c_16705]) ).
tcf(c_18093,plain,
! [X0: $i] :
( subclass(X0,complement(unordered_pair(x,x)))
| ~ member(not_subclass_element(X0,complement(unordered_pair(x,x))),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_8328,c_16705]) ).
tcf(c_18094,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),unordered_pair(x,x)),X2)
| ~ member(not_subclass_element(intersection(unordered_pair(x,x),cross_product(X0,X1)),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4638,c_16705]) ).
tcf(c_18095,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,unordered_pair(x,x))),X2)
| ~ member(not_subclass_element(intersection(X0,intersection(X1,unordered_pair(x,x))),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4646,c_16705]) ).
tcf(c_18096,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(unordered_pair(x,x),X1)),X2)
| ~ member(not_subclass_element(intersection(X0,intersection(unordered_pair(x,x),X1)),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4647,c_16705]) ).
tcf(c_18097,plain,
! [X0: $i] :
( subclass(complement(complement(unordered_pair(x,x))),X0)
| ~ member(not_subclass_element(complement(complement(unordered_pair(x,x))),X0),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_13744,c_16705]) ).
tcf(c_18100,plain,
~ member(x,complement(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_18083,c_4391]) ).
tcf(c_18134,plain,
( ( unordered_pair(x,x) = null_class )
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(x,x),unordered_pair(x,x)),universal_class)),universal_class))))))),complement(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18085,c_180]) ).
tcf(c_18268,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(unordered_pair(x,x),cross_product(X1,X2)),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_193,c_17097]) ).
tcf(c_18271,plain,
! [X0: $i,X1: $i] :
( ( intersection(X1,unordered_pair(x,x)) = X0 )
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,intersection(X1,unordered_pair(x,x))) ),
inference(superposition,[status(thm)],[c_17097,c_176]) ).
tcf(c_18272,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,unordered_pair(x,x)),X1)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_17097,c_250]) ).
tcf(c_18273,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(iPr_def_10,X2)
| ~ member(X0,intersection(X1,unordered_pair(x,x))) ),
inference(superposition,[status(thm)],[c_17097,c_170]) ).
tcf(c_18274,plain,
! [X0: $i] :
( ( complement(complement(intersection(X0,unordered_pair(x,x)))) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_17097,c_14028]) ).
tcf(c_18275,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,unordered_pair(x,x))) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_17097,c_5287]) ).
tcf(c_18276,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,unordered_pair(x,x)),X1) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_17097,c_5257]) ).
tcf(c_18327,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ subclass(unordered_pair(x,x),X0) ),
inference(demodulation,[status(thm)],[c_16671,c_4553]) ).
tcf(c_18337,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,unordered_pair(x,x)),X1),iPr_def_10)
| member(not_subclass_element(X1,intersection(X0,unordered_pair(x,x))),X1)
| ( intersection(X0,unordered_pair(x,x)) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_17098]) ).
tcf(c_18338,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,unordered_pair(x,x)),null_class),iPr_def_10)
| ( intersection(X0,unordered_pair(x,x)) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_17098]) ).
tcf(c_18341,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(x,x)),intersection(X0,unordered_pair(x,x))),universal_class)),universal_class))))))),iPr_def_10)
| ( intersection(X0,unordered_pair(x,x)) = null_class )
| ~ member(intersection(X0,unordered_pair(x,x)),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_17098]) ).
tcf(c_18343,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(X0,unordered_pair(x,x)),X1)),iPr_def_10)
| ( intersection(intersection(X0,unordered_pair(x,x)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_17098]) ).
tcf(c_18345,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(X1,unordered_pair(x,x)))),iPr_def_10)
| ( intersection(X0,intersection(X1,unordered_pair(x,x))) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_17098]) ).
tcf(c_18346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,unordered_pair(x,x)),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,unordered_pair(x,x))),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4425,c_17098]) ).
tcf(c_18347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(X1,unordered_pair(x,x))),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,unordered_pair(x,x))),X2),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4430,c_17098]) ).
tcf(c_18348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(X0,unordered_pair(x,x)),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(X0,unordered_pair(x,x)),X1),X2),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4431,c_17098]) ).
tcf(c_18349,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(X1,unordered_pair(x,x))))
| member(not_subclass_element(X0,complement(intersection(X1,unordered_pair(x,x)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8328,c_17098]) ).
tcf(c_18350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(X0,unordered_pair(x,x))),X3)
| member(not_subclass_element(intersection(intersection(X0,unordered_pair(x,x)),cross_product(X1,X2)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4638,c_17098]) ).
tcf(c_18351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,unordered_pair(x,x)))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,unordered_pair(x,x)))),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4646,c_17098]) ).
tcf(c_18352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(X1,unordered_pair(x,x)),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(X1,unordered_pair(x,x)),X2)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4647,c_17098]) ).
tcf(c_18353,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(X0,unordered_pair(x,x)))),X1)
| member(not_subclass_element(complement(complement(intersection(X0,unordered_pair(x,x)))),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_13744,c_17098]) ).
tcf(c_18355,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,intersection(unordered_pair(x,x),cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_193,c_17098]) ).
tcf(c_18472,plain,
! [X0: $i] : subclass(rotate(X0),universal_class),
inference(superposition,[status(thm)],[c_173,c_4492]) ).
tcf(c_18473,plain,
! [X0: $i] :
( subclass(rotate(X0),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4571,c_4492]) ).
tcf(c_18474,plain,
! [X0: $i] :
( subclass(rotate(X0),cross_product(universal_class,universal_class))
| ~ function(cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_218,c_4492]) ).
tcf(c_18485,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(unordered_pair(y,y),regular(unordered_pair(y,y))),X0)
| ( unordered_pair(y,y) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_5000]) ).
tcf(c_18486,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(unordered_pair(y,y),null_class),X0) ),
inference(superposition,[status(thm)],[c_4790,c_5000]) ).
tcf(c_18487,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(unordered_pair(y,y),complement(unordered_pair(y,y))),X0) ),
inference(superposition,[status(thm)],[c_12377,c_5000]) ).
tcf(c_18490,plain,
! [X0: $i] : subclass(intersection(unordered_pair(y,y),X0),iPr_def_10),
inference(superposition,[status(thm)],[c_5000,c_172]) ).
tcf(c_18491,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(y,y),X0),X1)
| member(not_subclass_element(intersection(unordered_pair(y,y),X0),X1),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5000,c_4342]) ).
tcf(c_18492,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(y,y),X0),X1)
| member(not_subclass_element(intersection(unordered_pair(y,y),X0),X1),universal_class) ),
inference(superposition,[status(thm)],[c_5000,c_4336]) ).
tcf(c_18493,plain,
! [X0: $i] : subclass(intersection(unordered_pair(y,y),complement(iPr_def_10)),X0),
inference(superposition,[status(thm)],[c_5000,c_4648]) ).
tcf(c_18569,plain,
( subclass(null_class,iPr_def_10)
| ( unordered_pair(y,y) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_18490]) ).
tcf(c_18572,plain,
! [X0: $i] :
( ( intersection(unordered_pair(y,y),X0) = iPr_def_10 )
| ~ subclass(iPr_def_10,intersection(unordered_pair(y,y),X0)) ),
inference(superposition,[status(thm)],[c_18490,c_176]) ).
tcf(c_18573,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(y,y),X1),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_18490,c_250]) ).
tcf(c_18574,plain,
! [X0: $i,X1: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,intersection(unordered_pair(y,y),X1)) ),
inference(superposition,[status(thm)],[c_18490,c_170]) ).
tcf(c_18591,plain,
! [X0: $i,X1: $i] :
( ( intersection(unordered_pair(y,y),X1) = X0 )
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,intersection(unordered_pair(y,y),X1)) ),
inference(superposition,[status(thm)],[c_18573,c_176]) ).
tcf(c_18592,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(unordered_pair(y,y),X2),X1)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_18573,c_250]) ).
tcf(c_18593,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(iPr_def_10,X2)
| ~ member(X0,intersection(unordered_pair(y,y),X1)) ),
inference(superposition,[status(thm)],[c_18573,c_170]) ).
tcf(c_18594,plain,
! [X0: $i] :
( ( complement(complement(intersection(unordered_pair(y,y),X0))) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_18573,c_14028]) ).
tcf(c_18595,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(unordered_pair(y,y),X1)) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_18573,c_5287]) ).
tcf(c_18596,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(unordered_pair(y,y),X0),X1) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_18573,c_5257]) ).
tcf(c_18621,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(unordered_pair(y,y),X0),X1),iPr_def_10)
| member(not_subclass_element(X1,intersection(unordered_pair(y,y),X0)),X1)
| ( intersection(unordered_pair(y,y),X0) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_18574]) ).
tcf(c_18622,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(unordered_pair(y,y),X0),null_class),iPr_def_10)
| ( intersection(unordered_pair(y,y),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_18574]) ).
tcf(c_18623,plain,
! [X0: $i,X1: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,X1)
| ~ member(X0,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_190,c_18574]) ).
tcf(c_18625,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(y,y),X0),intersection(unordered_pair(y,y),X0)),universal_class)),universal_class))))))),iPr_def_10)
| ( intersection(unordered_pair(y,y),X0) = null_class )
| ~ member(intersection(unordered_pair(y,y),X0),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_18574]) ).
tcf(c_18627,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(unordered_pair(y,y),X0),X1)),iPr_def_10)
| ( intersection(intersection(unordered_pair(y,y),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_18574]) ).
tcf(c_18629,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(unordered_pair(y,y),X1))),iPr_def_10)
| ( intersection(X0,intersection(unordered_pair(y,y),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_18574]) ).
tcf(c_18630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(unordered_pair(y,y),X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(unordered_pair(y,y),X2)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4425,c_18574]) ).
tcf(c_18631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(unordered_pair(y,y),X1)),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(unordered_pair(y,y),X1)),X2),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4430,c_18574]) ).
tcf(c_18632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(unordered_pair(y,y),X0),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(unordered_pair(y,y),X0),X1),X2),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4431,c_18574]) ).
tcf(c_18633,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(unordered_pair(y,y),X1)))
| member(not_subclass_element(X0,complement(intersection(unordered_pair(y,y),X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8328,c_18574]) ).
tcf(c_18634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(unordered_pair(y,y),X0)),X3)
| member(not_subclass_element(intersection(intersection(unordered_pair(y,y),X0),cross_product(X1,X2)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4638,c_18574]) ).
tcf(c_18635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(unordered_pair(y,y),X2))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(unordered_pair(y,y),X2))),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4646,c_18574]) ).
tcf(c_18636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(unordered_pair(y,y),X1),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(unordered_pair(y,y),X1),X2)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4647,c_18574]) ).
tcf(c_18637,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(unordered_pair(y,y),X0))),X1)
| member(not_subclass_element(complement(complement(intersection(unordered_pair(y,y),X0))),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_13744,c_18574]) ).
tcf(c_18734,plain,
! [X0: $i] : subclass(flip(X0),universal_class),
inference(superposition,[status(thm)],[c_173,c_4493]) ).
tcf(c_18735,plain,
! [X0: $i] :
( subclass(flip(X0),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4571,c_4493]) ).
tcf(c_18736,plain,
! [X0: $i] :
( subclass(flip(X0),cross_product(universal_class,universal_class))
| ~ function(cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_218,c_4493]) ).
tcf(c_18743,plain,
! [X0: $i] :
( ( intersection(unordered_pair(y,y),complement(iPr_def_10)) = X0 )
| ~ subclass(X0,intersection(unordered_pair(y,y),complement(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_18493,c_176]) ).
tcf(c_18745,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,intersection(unordered_pair(y,y),complement(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_18493,c_170]) ).
tcf(c_18746,plain,
complement(complement(intersection(unordered_pair(y,y),complement(iPr_def_10)))) = null_class,
inference(superposition,[status(thm)],[c_18493,c_14028]) ).
tcf(c_18747,plain,
! [X0: $i] : intersection(X0,intersection(unordered_pair(y,y),complement(iPr_def_10))) = null_class,
inference(superposition,[status(thm)],[c_18493,c_5287]) ).
tcf(c_18748,plain,
! [X0: $i] : intersection(intersection(unordered_pair(y,y),complement(iPr_def_10)),X0) = null_class,
inference(superposition,[status(thm)],[c_18493,c_5257]) ).
tcf(c_18749,plain,
intersection(unordered_pair(y,y),complement(iPr_def_10)) = null_class,
inference(superposition,[status(thm)],[c_18493,c_258]) ).
tcf(c_18790,plain,
intersection(null_class,complement(unordered_pair(y,y))) = null_class,
inference(superposition,[status(thm)],[c_18749,c_12688]) ).
tcf(c_18792,plain,
intersection(complement(unordered_pair(y,y)),null_class) = null_class,
inference(superposition,[status(thm)],[c_18749,c_11685]) ).
tcf(c_18795,plain,
! [X0: $i] : subclass(intersection(null_class,X0),unordered_pair(y,y)),
inference(superposition,[status(thm)],[c_18749,c_6583]) ).
tcf(c_18796,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),unordered_pair(y,y))
| subclass(intersection(intersection(unordered_pair(y,y),complement(iPr_def_10)),X0),X1) ),
inference(superposition,[status(thm)],[c_18749,c_4431]) ).
tcf(c_18798,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),complement(iPr_def_10))
| subclass(intersection(intersection(unordered_pair(y,y),complement(iPr_def_10)),X0),X1) ),
inference(superposition,[status(thm)],[c_18749,c_4430]) ).
tcf(c_18800,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),complement(iPr_def_10))
| subclass(intersection(unordered_pair(y,y),complement(iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_18749,c_4245]) ).
tcf(c_18801,plain,
subclass(null_class,unordered_pair(y,y)),
inference(superposition,[status(thm)],[c_18749,c_4427]) ).
tcf(c_18802,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),unordered_pair(y,y))
| subclass(intersection(unordered_pair(y,y),complement(iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_18749,c_4224]) ).
tcf(c_18805,plain,
! [X0: $i] : subclass(intersection(X0,null_class),unordered_pair(y,y)),
inference(superposition,[status(thm)],[c_18749,c_11340]) ).
tcf(c_18806,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),unordered_pair(y,y))
| subclass(intersection(X0,intersection(unordered_pair(y,y),complement(iPr_def_10))),X1) ),
inference(superposition,[status(thm)],[c_18749,c_4647]) ).
tcf(c_18808,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),complement(iPr_def_10))
| subclass(intersection(X0,intersection(unordered_pair(y,y),complement(iPr_def_10))),X1) ),
inference(superposition,[status(thm)],[c_18749,c_4646]) ).
tcf(c_18809,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(y,y))
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_18749,c_6783]) ).
tcf(c_18811,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,complement(iPr_def_10))
| ~ member(X0,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_18749,c_190]) ).
tcf(c_18814,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ~ subclass(unordered_pair(y,y),X0) ),
inference(superposition,[status(thm)],[c_18749,c_6782]) ).
tcf(c_18816,plain,
! [X0: $i] :
( subclass(intersection(unordered_pair(y,y),complement(iPr_def_10)),X0)
| ~ member(not_subclass_element(null_class,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_18749,c_4648]) ).
tcf(c_18821,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(unordered_pair(y,y),complement(iPr_def_10)),X0) ),
inference(superposition,[status(thm)],[c_18749,c_5000]) ).
tcf(c_18822,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ~ subclass(unordered_pair(y,y),X0) ),
inference(superposition,[status(thm)],[c_18749,c_11629]) ).
tcf(c_18824,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(y,y))
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_18749,c_11630]) ).
tcf(c_18840,plain,
! [X0: $i] :
( ~ member(X0,complement(iPr_def_10))
| ~ member(X0,unordered_pair(y,y)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18811,c_256]) ).
tcf(c_18844,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),unordered_pair(y,y)) ),
inference(light_normalisation,[status(thm)],[c_18802,c_18749]) ).
tcf(c_18877,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ subclass(unordered_pair(y,y),X0) ),
inference(demodulation,[status(thm)],[c_18814,c_4553]) ).
tcf(c_18888,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ member(not_subclass_element(unordered_pair(y,y),X0),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_171,c_18840]) ).
tcf(c_18889,plain,
! [X0: $i] :
( member(not_subclass_element(X0,unordered_pair(y,y)),X0)
| ( unordered_pair(y,y) = X0 )
| ~ member(not_subclass_element(unordered_pair(y,y),X0),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_251,c_18840]) ).
tcf(c_18890,plain,
( ( unordered_pair(y,y) = null_class )
| ~ member(not_subclass_element(unordered_pair(y,y),null_class),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_259,c_18840]) ).
tcf(c_18892,plain,
( ~ member(y,universal_class)
| ~ member(y,complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_179,c_18840]) ).
tcf(c_18893,plain,
( ( unordered_pair(y,y) = null_class )
| ~ member(regular(unordered_pair(y,y)),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_222,c_18840]) ).
tcf(c_18894,plain,
( ( unordered_pair(y,y) = null_class )
| ~ member(unordered_pair(y,y),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(y,y),unordered_pair(y,y)),universal_class)),universal_class))))))),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_225,c_18840]) ).
tcf(c_18895,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(y,y),X0),X1)
| ~ member(not_subclass_element(intersection(unordered_pair(y,y),X0),X1),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4224,c_18840]) ).
tcf(c_18896,plain,
! [X0: $i] :
( ( intersection(unordered_pair(y,y),X0) = null_class )
| ~ member(regular(intersection(unordered_pair(y,y),X0)),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4225,c_18840]) ).
tcf(c_18897,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(y,y)),X1)
| ~ member(not_subclass_element(intersection(X0,unordered_pair(y,y)),X1),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4245,c_18840]) ).
tcf(c_18898,plain,
! [X0: $i] :
( ( intersection(X0,unordered_pair(y,y)) = null_class )
| ~ member(regular(intersection(X0,unordered_pair(y,y))),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4246,c_18840]) ).
tcf(c_18899,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(unordered_pair(y,y),cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),unordered_pair(y,y)),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4425,c_18840]) ).
tcf(c_18900,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,unordered_pair(y,y)),X1),X2)
| ~ member(not_subclass_element(intersection(intersection(X0,unordered_pair(y,y)),X1),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4430,c_18840]) ).
tcf(c_18901,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(unordered_pair(y,y),X0),X1),X2)
| ~ member(not_subclass_element(intersection(intersection(unordered_pair(y,y),X0),X1),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4431,c_18840]) ).
tcf(c_18902,plain,
! [X0: $i] :
( subclass(X0,complement(unordered_pair(y,y)))
| ~ member(not_subclass_element(X0,complement(unordered_pair(y,y))),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_8328,c_18840]) ).
tcf(c_18903,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),unordered_pair(y,y)),X2)
| ~ member(not_subclass_element(intersection(unordered_pair(y,y),cross_product(X0,X1)),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4638,c_18840]) ).
tcf(c_18904,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,unordered_pair(y,y))),X2)
| ~ member(not_subclass_element(intersection(X0,intersection(X1,unordered_pair(y,y))),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4646,c_18840]) ).
tcf(c_18905,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(unordered_pair(y,y),X1)),X2)
| ~ member(not_subclass_element(intersection(X0,intersection(unordered_pair(y,y),X1)),X2),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4647,c_18840]) ).
tcf(c_18906,plain,
! [X0: $i] :
( subclass(complement(complement(unordered_pair(y,y))),X0)
| ~ member(not_subclass_element(complement(complement(unordered_pair(y,y))),X0),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_13744,c_18840]) ).
tcf(c_18909,plain,
~ member(y,complement(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_18892,c_4392]) ).
tcf(c_18943,plain,
( ( unordered_pair(y,y) = null_class )
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(y,y),unordered_pair(y,y)),universal_class)),universal_class))))))),complement(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18894,c_180]) ).
tcf(c_18964,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(complement(unordered_pair(y,y)),unordered_pair(y,y)),X0) ),
inference(superposition,[status(thm)],[c_4169,c_5001]) ).
tcf(c_18966,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(null_class,unordered_pair(y,y)),X0) ),
inference(superposition,[status(thm)],[c_4553,c_5001]) ).
tcf(c_18969,plain,
! [X0: $i] : subclass(intersection(X0,unordered_pair(y,y)),iPr_def_10),
inference(superposition,[status(thm)],[c_5001,c_172]) ).
tcf(c_18970,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(y,y)),X1)
| member(not_subclass_element(intersection(X0,unordered_pair(y,y)),X1),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5001,c_4342]) ).
tcf(c_18971,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(y,y)),X1)
| member(not_subclass_element(intersection(X0,unordered_pair(y,y)),X1),universal_class) ),
inference(superposition,[status(thm)],[c_5001,c_4336]) ).
tcf(c_18972,plain,
! [X0: $i] : subclass(intersection(complement(iPr_def_10),unordered_pair(y,y)),X0),
inference(superposition,[status(thm)],[c_5001,c_4432]) ).
tcf(c_19007,plain,
! [X0: $i,X1: $i] : subclass(intersection(unordered_pair(y,y),cross_product(X0,X1)),iPr_def_10),
inference(superposition,[status(thm)],[c_193,c_18969]) ).
tcf(c_19009,plain,
! [X0: $i] :
( ( intersection(X0,unordered_pair(y,y)) = iPr_def_10 )
| ~ subclass(iPr_def_10,intersection(X0,unordered_pair(y,y))) ),
inference(superposition,[status(thm)],[c_18969,c_176]) ).
tcf(c_19010,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,unordered_pair(y,y)),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_18969,c_250]) ).
tcf(c_19011,plain,
! [X0: $i,X1: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,intersection(X1,unordered_pair(y,y))) ),
inference(superposition,[status(thm)],[c_18969,c_170]) ).
tcf(c_19026,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(unordered_pair(y,y),cross_product(X1,X2)),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_193,c_19010]) ).
tcf(c_19028,plain,
! [X0: $i,X1: $i] :
( ( intersection(X1,unordered_pair(y,y)) = X0 )
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,intersection(X1,unordered_pair(y,y))) ),
inference(superposition,[status(thm)],[c_19010,c_176]) ).
tcf(c_19029,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,unordered_pair(y,y)),X1)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_19010,c_250]) ).
tcf(c_19030,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(iPr_def_10,X2)
| ~ member(X0,intersection(X1,unordered_pair(y,y))) ),
inference(superposition,[status(thm)],[c_19010,c_170]) ).
tcf(c_19031,plain,
! [X0: $i] :
( ( complement(complement(intersection(X0,unordered_pair(y,y)))) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_19010,c_14028]) ).
tcf(c_19032,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,unordered_pair(y,y))) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_19010,c_5287]) ).
tcf(c_19033,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,unordered_pair(y,y)),X1) = null_class )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_19010,c_5257]) ).
tcf(c_19140,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,unordered_pair(y,y)),X1),iPr_def_10)
| member(not_subclass_element(X1,intersection(X0,unordered_pair(y,y))),X1)
| ( intersection(X0,unordered_pair(y,y)) = X1 ) ),
inference(superposition,[status(thm)],[c_251,c_19011]) ).
tcf(c_19141,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,unordered_pair(y,y)),null_class),iPr_def_10)
| ( intersection(X0,unordered_pair(y,y)) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_19011]) ).
tcf(c_19144,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(y,y)),intersection(X0,unordered_pair(y,y))),universal_class)),universal_class))))))),iPr_def_10)
| ( intersection(X0,unordered_pair(y,y)) = null_class )
| ~ member(intersection(X0,unordered_pair(y,y)),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_19011]) ).
tcf(c_19146,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(intersection(X0,unordered_pair(y,y)),X1)),iPr_def_10)
| ( intersection(intersection(X0,unordered_pair(y,y)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_19011]) ).
tcf(c_19148,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,intersection(X1,unordered_pair(y,y)))),iPr_def_10)
| ( intersection(X0,intersection(X1,unordered_pair(y,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_19011]) ).
tcf(c_19149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,unordered_pair(y,y)),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,unordered_pair(y,y))),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4425,c_19011]) ).
tcf(c_19150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,intersection(X1,unordered_pair(y,y))),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,intersection(X1,unordered_pair(y,y))),X2),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4430,c_19011]) ).
tcf(c_19151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(X0,unordered_pair(y,y)),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(intersection(X0,unordered_pair(y,y)),X1),X2),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4431,c_19011]) ).
tcf(c_19152,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(intersection(X1,unordered_pair(y,y))))
| member(not_subclass_element(X0,complement(intersection(X1,unordered_pair(y,y)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8328,c_19011]) ).
tcf(c_19153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),intersection(X0,unordered_pair(y,y))),X3)
| member(not_subclass_element(intersection(intersection(X0,unordered_pair(y,y)),cross_product(X1,X2)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4638,c_19011]) ).
tcf(c_19154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,intersection(X2,unordered_pair(y,y)))),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,unordered_pair(y,y)))),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4646,c_19011]) ).
tcf(c_19155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(intersection(X1,unordered_pair(y,y)),X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(intersection(X1,unordered_pair(y,y)),X2)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4647,c_19011]) ).
tcf(c_19156,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(intersection(X0,unordered_pair(y,y)))),X1)
| member(not_subclass_element(complement(complement(intersection(X0,unordered_pair(y,y)))),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_13744,c_19011]) ).
tcf(c_19158,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,intersection(unordered_pair(y,y),cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_193,c_19011]) ).
tcf(c_19294,plain,
! [X0: $i] :
( ( intersection(complement(iPr_def_10),unordered_pair(y,y)) = X0 )
| ~ subclass(X0,intersection(complement(iPr_def_10),unordered_pair(y,y))) ),
inference(superposition,[status(thm)],[c_18972,c_176]) ).
tcf(c_19296,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,intersection(complement(iPr_def_10),unordered_pair(y,y))) ),
inference(superposition,[status(thm)],[c_18972,c_170]) ).
tcf(c_19297,plain,
complement(complement(intersection(complement(iPr_def_10),unordered_pair(y,y)))) = null_class,
inference(superposition,[status(thm)],[c_18972,c_14028]) ).
tcf(c_19298,plain,
! [X0: $i] : intersection(X0,intersection(complement(iPr_def_10),unordered_pair(y,y))) = null_class,
inference(superposition,[status(thm)],[c_18972,c_5287]) ).
tcf(c_19299,plain,
! [X0: $i] : intersection(intersection(complement(iPr_def_10),unordered_pair(y,y)),X0) = null_class,
inference(superposition,[status(thm)],[c_18972,c_5257]) ).
tcf(c_19300,plain,
intersection(complement(iPr_def_10),unordered_pair(y,y)) = null_class,
inference(superposition,[status(thm)],[c_18972,c_258]) ).
tcf(c_19316,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),complement(iPr_def_10))
| subclass(intersection(intersection(complement(iPr_def_10),unordered_pair(y,y)),X0),X1) ),
inference(superposition,[status(thm)],[c_19300,c_4431]) ).
tcf(c_19318,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),unordered_pair(y,y))
| subclass(intersection(intersection(complement(iPr_def_10),unordered_pair(y,y)),X0),X1) ),
inference(superposition,[status(thm)],[c_19300,c_4430]) ).
tcf(c_19320,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),unordered_pair(y,y))
| subclass(intersection(complement(iPr_def_10),unordered_pair(y,y)),X0) ),
inference(superposition,[status(thm)],[c_19300,c_4245]) ).
tcf(c_19322,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),complement(iPr_def_10))
| subclass(intersection(complement(iPr_def_10),unordered_pair(y,y)),X0) ),
inference(superposition,[status(thm)],[c_19300,c_4224]) ).
tcf(c_19326,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),complement(iPr_def_10))
| subclass(intersection(X0,intersection(complement(iPr_def_10),unordered_pair(y,y))),X1) ),
inference(superposition,[status(thm)],[c_19300,c_4647]) ).
tcf(c_19328,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),unordered_pair(y,y))
| subclass(intersection(X0,intersection(complement(iPr_def_10),unordered_pair(y,y))),X1) ),
inference(superposition,[status(thm)],[c_19300,c_4646]) ).
tcf(c_19336,plain,
! [X0: $i] :
( subclass(intersection(complement(iPr_def_10),unordered_pair(y,y)),X0)
| ~ member(not_subclass_element(null_class,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_19300,c_4432]) ).
tcf(c_19341,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(complement(iPr_def_10),unordered_pair(y,y)),X0) ),
inference(superposition,[status(thm)],[c_19300,c_5001]) ).
tcf(c_19406,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| member(not_subclass_element(unordered_pair(x,x),X1),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_171,c_5056]) ).
tcf(c_19407,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,unordered_pair(x,x)),X1)
| member(not_subclass_element(unordered_pair(x,x),X1),X0)
| ( unordered_pair(x,x) = X1 )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_251,c_5056]) ).
tcf(c_19408,plain,
! [X0: $i] :
( member(not_subclass_element(unordered_pair(x,x),null_class),X0)
| ( unordered_pair(x,x) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_259,c_5056]) ).
tcf(c_19410,plain,
! [X0: $i] :
( member(x,X0)
| ~ member(x,universal_class)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_179,c_5056]) ).
tcf(c_19411,plain,
! [X0: $i] :
( member(regular(unordered_pair(x,x)),X0)
| ( unordered_pair(x,x) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_222,c_5056]) ).
tcf(c_19412,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(x,x),unordered_pair(x,x)),universal_class)),universal_class))))))),X0)
| ( unordered_pair(x,x) = null_class )
| ~ subclass(iPr_def_10,X0)
| ~ member(unordered_pair(x,x),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_5056]) ).
tcf(c_19413,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(unordered_pair(x,x),X1),X2)
| member(not_subclass_element(intersection(unordered_pair(x,x),X1),X2),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4224,c_5056]) ).
tcf(c_19414,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(unordered_pair(x,x),X1)),X0)
| ( intersection(unordered_pair(x,x),X1) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4225,c_5056]) ).
tcf(c_19415,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,unordered_pair(x,x)),X2)
| member(not_subclass_element(intersection(X1,unordered_pair(x,x)),X2),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4245,c_5056]) ).
tcf(c_19416,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X1,unordered_pair(x,x))),X0)
| ( intersection(X1,unordered_pair(x,x)) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4246,c_5056]) ).
tcf(c_19417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(unordered_pair(x,x),cross_product(X1,X2)),X3)
| member(not_subclass_element(intersection(cross_product(X1,X2),unordered_pair(x,x)),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4425,c_5056]) ).
tcf(c_19418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X1,unordered_pair(x,x)),X2),X3)
| member(not_subclass_element(intersection(intersection(X1,unordered_pair(x,x)),X2),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4430,c_5056]) ).
tcf(c_19419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(unordered_pair(x,x),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(unordered_pair(x,x),X1),X2),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4431,c_5056]) ).
tcf(c_19420,plain,
! [X0: $i,X1: $i] :
( subclass(X1,complement(unordered_pair(x,x)))
| member(not_subclass_element(X1,complement(unordered_pair(x,x))),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_8328,c_5056]) ).
tcf(c_19421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),unordered_pair(x,x)),X3)
| member(not_subclass_element(intersection(unordered_pair(x,x),cross_product(X1,X2)),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4638,c_5056]) ).
tcf(c_19422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X1,intersection(X2,unordered_pair(x,x))),X3)
| member(not_subclass_element(intersection(X1,intersection(X2,unordered_pair(x,x))),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4646,c_5056]) ).
tcf(c_19423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X1,intersection(unordered_pair(x,x),X2)),X3)
| member(not_subclass_element(intersection(X1,intersection(unordered_pair(x,x),X2)),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4647,c_5056]) ).
tcf(c_19424,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(unordered_pair(x,x))),X1)
| member(not_subclass_element(complement(complement(unordered_pair(x,x))),X1),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13744,c_5056]) ).
tcf(c_19428,plain,
! [X0: $i] :
( member(x,X0)
| ~ subclass(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19410,c_4391]) ).
tcf(c_19480,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(x,x),unordered_pair(x,x)),universal_class)),universal_class))))))),X0)
| ( unordered_pair(x,x) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19412,c_180]) ).
tcf(c_19510,plain,
! [X0: $i] :
( ( intersection(unordered_pair(x,x),X0) = unordered_pair(x,x) )
| ~ subclass(iPr_def_10,intersection(unordered_pair(x,x),X0)) ),
inference(superposition,[status(thm)],[c_4500,c_4722]) ).
tcf(c_19511,plain,
! [X0: $i] :
( ( intersection(unordered_pair(y,y),X0) = unordered_pair(y,y) )
| ~ subclass(iPr_def_10,intersection(unordered_pair(y,y),X0)) ),
inference(superposition,[status(thm)],[c_4501,c_4722]) ).
tcf(c_19512,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,X1),X2) = intersection(X0,X1) )
| ~ subclass(X0,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_4551,c_4722]) ).
tcf(c_19513,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X1,X0),X2) = intersection(X1,X0) )
| ~ subclass(X0,intersection(intersection(X1,X0),X2)) ),
inference(superposition,[status(thm)],[c_4788,c_4722]) ).
tcf(c_19514,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(complement(X0)),X1) = complement(complement(X0)) )
| ~ subclass(X0,intersection(complement(complement(X0)),X1)) ),
inference(superposition,[status(thm)],[c_13999,c_4722]) ).
tcf(c_19515,plain,
! [X0: $i] :
( ( intersection(complement(cross_product(universal_class,universal_class)),X0) = complement(cross_product(universal_class,universal_class)) )
| ~ subclass(complement(element_relation),intersection(complement(cross_product(universal_class,universal_class)),X0)) ),
inference(superposition,[status(thm)],[c_15325,c_4722]) ).
tcf(c_19516,plain,
! [X0: $i] :
( ( intersection(complement(cross_product(universal_class,universal_class)),X0) = complement(cross_product(universal_class,universal_class)) )
| ~ subclass(complement(successor_relation),intersection(complement(cross_product(universal_class,universal_class)),X0)) ),
inference(superposition,[status(thm)],[c_14988,c_4722]) ).
tcf(c_19517,plain,
! [X0: $i] :
( ( intersection(complement(cross_product(universal_class,universal_class)),X0) = complement(cross_product(universal_class,universal_class)) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13276,c_4722]) ).
tcf(c_19518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(intersection(intersection(X1,X0),X2),X3) = intersection(intersection(X1,X0),X2) )
| ~ subclass(X0,intersection(intersection(intersection(X1,X0),X2),X3)) ),
inference(superposition,[status(thm)],[c_6249,c_4722]) ).
tcf(c_19519,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(identity_relation,X0),X1) = intersection(identity_relation,X0) )
| ~ subclass(subset_relation,intersection(intersection(identity_relation,X0),X1)) ),
inference(superposition,[status(thm)],[c_6317,c_4722]) ).
tcf(c_19520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(intersection(intersection(X0,X1),X2),X3) = intersection(intersection(X0,X1),X2) )
| ~ subclass(X0,intersection(intersection(intersection(X0,X1),X2),X3)) ),
inference(superposition,[status(thm)],[c_6782,c_4722]) ).
tcf(c_19521,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(complement(cross_product(universal_class,universal_class)),X0),X1) = intersection(complement(cross_product(universal_class,universal_class)),X0) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_4722]) ).
tcf(c_19522,plain,
! [X0: $i] :
( ( intersection(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X0) = domain_of(domain_of(flip(cross_product(null_class,universal_class)))) )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_4722]) ).
tcf(c_19523,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(complement(subset_relation),X0),X1) = intersection(complement(subset_relation),X0) )
| ~ subclass(complement(identity_relation),intersection(intersection(complement(subset_relation),X0),X1)) ),
inference(superposition,[status(thm)],[c_8784,c_4722]) ).
tcf(c_19524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(intersection(X1,intersection(X2,X0)),X3) = intersection(X1,intersection(X2,X0)) )
| ~ subclass(X0,intersection(intersection(X1,intersection(X2,X0)),X3)) ),
inference(superposition,[status(thm)],[c_11018,c_4722]) ).
tcf(c_19525,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,identity_relation),X1) = intersection(X0,identity_relation) )
| ~ subclass(subset_relation,intersection(intersection(X0,identity_relation),X1)) ),
inference(superposition,[status(thm)],[c_11105,c_4722]) ).
tcf(c_19526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(intersection(X1,intersection(X0,X2)),X3) = intersection(X1,intersection(X0,X2)) )
| ~ subclass(X0,intersection(intersection(X1,intersection(X0,X2)),X3)) ),
inference(superposition,[status(thm)],[c_11629,c_4722]) ).
tcf(c_19527,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,complement(cross_product(universal_class,universal_class))),X1) = intersection(X0,complement(cross_product(universal_class,universal_class))) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_4722]) ).
tcf(c_19528,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,complement(subset_relation)),X1) = intersection(X0,complement(subset_relation)) )
| ~ subclass(complement(identity_relation),intersection(intersection(X0,complement(subset_relation)),X1)) ),
inference(superposition,[status(thm)],[c_12408,c_4722]) ).
tcf(c_19529,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(unordered_pair(x,x),X0),X1) = intersection(unordered_pair(x,x),X0) )
| ~ subclass(iPr_def_10,intersection(intersection(unordered_pair(x,x),X0),X1)) ),
inference(superposition,[status(thm)],[c_16597,c_4722]) ).
tcf(c_19530,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,unordered_pair(x,x)),X1) = intersection(X0,unordered_pair(x,x)) )
| ~ subclass(iPr_def_10,intersection(intersection(X0,unordered_pair(x,x)),X1)) ),
inference(superposition,[status(thm)],[c_17097,c_4722]) ).
tcf(c_19531,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(unordered_pair(y,y),X0),X1) = intersection(unordered_pair(y,y),X0) )
| ~ subclass(iPr_def_10,intersection(intersection(unordered_pair(y,y),X0),X1)) ),
inference(superposition,[status(thm)],[c_18573,c_4722]) ).
tcf(c_19532,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,unordered_pair(y,y)),X1) = intersection(X0,unordered_pair(y,y)) )
| ~ subclass(iPr_def_10,intersection(intersection(X0,unordered_pair(y,y)),X1)) ),
inference(superposition,[status(thm)],[c_19010,c_4722]) ).
tcf(c_19533,plain,
! [X0: $i] :
( ( intersection(complement(X0),X0) = complement(X0) )
| ~ subclass(complement(X0),null_class) ),
inference(superposition,[status(thm)],[c_4169,c_4722]) ).
tcf(c_19534,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(cross_product(X0,X1),X2) = cross_product(X0,X1) )
| ~ subclass(cross_product(X0,X1),intersection(X2,cross_product(X0,X1))) ),
inference(superposition,[status(thm)],[c_193,c_4722]) ).
tcf(c_19535,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(X0,regular(X0)) = X0 )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_223,c_4722]) ).
tcf(c_19536,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,cross_product(X1,X2)) = X0 )
| ~ subclass(X0,intersection(cross_product(X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_193,c_4722]) ).
tcf(c_19537,plain,
( ( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = cross_product(universal_class,universal_class) )
| ~ subclass(cross_product(universal_class,universal_class),subset_relation) ),
inference(superposition,[status(thm)],[c_229,c_4722]) ).
tcf(c_19538,plain,
( ( intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) = domain_of(flip(cross_product(subset_relation,universal_class))) )
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),identity_relation) ),
inference(superposition,[status(thm)],[c_230,c_4722]) ).
tcf(c_19540,plain,
! [X0: $i] :
( ( intersection(X0,null_class) = X0 )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4790,c_4722]) ).
tcf(c_19541,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(X0),intersection(X1,X0)) = complement(X0) )
| ~ subclass(complement(X0),null_class) ),
inference(superposition,[status(thm)],[c_11228,c_4722]) ).
tcf(c_19542,plain,
( ( intersection(complement(subset_relation),identity_relation) = complement(subset_relation) )
| ~ subclass(complement(subset_relation),null_class) ),
inference(superposition,[status(thm)],[c_11311,c_4722]) ).
tcf(c_19543,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(X0),intersection(X0,X1)) = complement(X0) )
| ~ subclass(complement(X0),null_class) ),
inference(superposition,[status(thm)],[c_11685,c_4722]) ).
tcf(c_19544,plain,
( ( intersection(complement(cross_product(universal_class,universal_class)),subset_relation) = complement(cross_product(universal_class,universal_class)) )
| ~ subclass(complement(cross_product(universal_class,universal_class)),null_class) ),
inference(superposition,[status(thm)],[c_11763,c_4722]) ).
tcf(c_19545,plain,
( ( intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),null_class) ),
inference(superposition,[status(thm)],[c_12282,c_4722]) ).
tcf(c_19546,plain,
! [X0: $i] :
( ( intersection(X0,complement(X0)) = X0 )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_12377,c_4722]) ).
tcf(c_19547,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,X1),complement(X1)) = intersection(X0,X1) )
| ~ subclass(intersection(X0,X1),null_class) ),
inference(superposition,[status(thm)],[c_12625,c_4722]) ).
tcf(c_19548,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,X1),complement(X0)) = intersection(X0,X1) )
| ~ subclass(intersection(X0,X1),null_class) ),
inference(superposition,[status(thm)],[c_12688,c_4722]) ).
tcf(c_19549,plain,
( ( intersection(identity_relation,complement(subset_relation)) = identity_relation )
| ~ subclass(identity_relation,null_class) ),
inference(superposition,[status(thm)],[c_12394,c_4722]) ).
tcf(c_19550,plain,
( ( intersection(subset_relation,complement(cross_product(universal_class,universal_class))) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_12738,c_4722]) ).
tcf(c_19551,plain,
( ( intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) = identity_relation )
| ~ subclass(identity_relation,null_class) ),
inference(superposition,[status(thm)],[c_13003,c_4722]) ).
tcf(c_19552,plain,
( ( intersection(unordered_pair(x,x),complement(iPr_def_10)) = unordered_pair(x,x) )
| ~ subclass(unordered_pair(x,x),null_class) ),
inference(superposition,[status(thm)],[c_16614,c_4722]) ).
tcf(c_19553,plain,
( ( intersection(complement(iPr_def_10),unordered_pair(x,x)) = complement(iPr_def_10) )
| ~ subclass(complement(iPr_def_10),null_class) ),
inference(superposition,[status(thm)],[c_17131,c_4722]) ).
tcf(c_19554,plain,
( ( intersection(unordered_pair(y,y),complement(iPr_def_10)) = unordered_pair(y,y) )
| ~ subclass(unordered_pair(y,y),null_class) ),
inference(superposition,[status(thm)],[c_18749,c_4722]) ).
tcf(c_19555,plain,
( ( intersection(complement(iPr_def_10),unordered_pair(y,y)) = complement(iPr_def_10) )
| ~ subclass(complement(iPr_def_10),null_class) ),
inference(superposition,[status(thm)],[c_19300,c_4722]) ).
tcf(c_19557,plain,
( ( null_class = identity_relation )
| ~ subclass(identity_relation,null_class) ),
inference(light_normalisation,[status(thm)],[c_19549,c_12394]) ).
tcf(c_19561,plain,
( ( null_class = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(light_normalisation,[status(thm)],[c_19550,c_12738]) ).
tcf(c_19567,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ subclass(complement(X0),null_class) ),
inference(light_normalisation,[status(thm)],[c_19533,c_4169]) ).
tcf(c_19570,plain,
( ( complement(iPr_def_10) = null_class )
| ~ subclass(complement(iPr_def_10),null_class) ),
inference(light_normalisation,[status(thm)],[c_19555,c_19300]) ).
tcf(c_19584,plain,
( ( unordered_pair(y,y) = null_class )
| ~ subclass(unordered_pair(y,y),null_class) ),
inference(light_normalisation,[status(thm)],[c_19554,c_18749]) ).
tcf(c_19587,plain,
( ( unordered_pair(x,x) = null_class )
| ~ subclass(unordered_pair(x,x),null_class) ),
inference(light_normalisation,[status(thm)],[c_19552,c_16614]) ).
tcf(c_19590,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = null_class )
| ~ subclass(intersection(X0,X1),null_class) ),
inference(light_normalisation,[status(thm)],[c_19548,c_12688]) ).
tcf(c_19608,plain,
( ( complement(cross_product(universal_class,universal_class)) = null_class )
| ~ subclass(complement(cross_product(universal_class,universal_class)),null_class) ),
inference(light_normalisation,[status(thm)],[c_19544,c_11763]) ).
tcf(c_19644,plain,
( ( complement(domain_of(flip(cross_product(subset_relation,universal_class)))) = null_class )
| ~ subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),null_class) ),
inference(light_normalisation,[status(thm)],[c_19545,c_12282]) ).
tcf(c_19790,plain,
! [X0: $i] :
( ( intersection(X0,unordered_pair(x,x)) = unordered_pair(x,x) )
| ~ subclass(iPr_def_10,intersection(X0,unordered_pair(x,x))) ),
inference(superposition,[status(thm)],[c_4500,c_4787]) ).
tcf(c_19791,plain,
! [X0: $i] :
( ( intersection(X0,unordered_pair(y,y)) = unordered_pair(y,y) )
| ~ subclass(iPr_def_10,intersection(X0,unordered_pair(y,y))) ),
inference(superposition,[status(thm)],[c_4501,c_4787]) ).
tcf(c_19792,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X1,intersection(X0,X2)) = intersection(X0,X2) )
| ~ subclass(X0,intersection(X1,intersection(X0,X2))) ),
inference(superposition,[status(thm)],[c_4551,c_4787]) ).
tcf(c_19793,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X1,intersection(X2,X0)) = intersection(X2,X0) )
| ~ subclass(X0,intersection(X1,intersection(X2,X0))) ),
inference(superposition,[status(thm)],[c_4788,c_4787]) ).
tcf(c_19794,plain,
! [X0: $i,X1: $i] :
( ( intersection(X1,complement(complement(X0))) = complement(complement(X0)) )
| ~ subclass(X0,intersection(X1,complement(complement(X0)))) ),
inference(superposition,[status(thm)],[c_13999,c_4787]) ).
tcf(c_19795,plain,
! [X0: $i] :
( ( intersection(X0,complement(cross_product(universal_class,universal_class))) = complement(cross_product(universal_class,universal_class)) )
| ~ subclass(complement(element_relation),intersection(X0,complement(cross_product(universal_class,universal_class)))) ),
inference(superposition,[status(thm)],[c_15325,c_4787]) ).
tcf(c_19796,plain,
! [X0: $i] :
( ( intersection(X0,complement(cross_product(universal_class,universal_class))) = complement(cross_product(universal_class,universal_class)) )
| ~ subclass(complement(successor_relation),intersection(X0,complement(cross_product(universal_class,universal_class)))) ),
inference(superposition,[status(thm)],[c_14988,c_4787]) ).
tcf(c_19797,plain,
! [X0: $i] :
( ( intersection(X0,complement(cross_product(universal_class,universal_class))) = complement(cross_product(universal_class,universal_class)) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13276,c_4787]) ).
tcf(c_19798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(X1,intersection(intersection(X2,X0),X3)) = intersection(intersection(X2,X0),X3) )
| ~ subclass(X0,intersection(X1,intersection(intersection(X2,X0),X3))) ),
inference(superposition,[status(thm)],[c_6249,c_4787]) ).
tcf(c_19799,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(identity_relation,X1)) = intersection(identity_relation,X1) )
| ~ subclass(subset_relation,intersection(X0,intersection(identity_relation,X1))) ),
inference(superposition,[status(thm)],[c_6317,c_4787]) ).
tcf(c_19800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(X1,intersection(intersection(X0,X2),X3)) = intersection(intersection(X0,X2),X3) )
| ~ subclass(X0,intersection(X1,intersection(intersection(X0,X2),X3))) ),
inference(superposition,[status(thm)],[c_6782,c_4787]) ).
tcf(c_19801,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)) = intersection(complement(cross_product(universal_class,universal_class)),X1) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_4787]) ).
tcf(c_19802,plain,
! [X0: $i] :
( ( intersection(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) = domain_of(domain_of(flip(cross_product(null_class,universal_class)))) )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_4787]) ).
tcf(c_19803,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(complement(subset_relation),X1)) = intersection(complement(subset_relation),X1) )
| ~ subclass(complement(identity_relation),intersection(X0,intersection(complement(subset_relation),X1))) ),
inference(superposition,[status(thm)],[c_8784,c_4787]) ).
tcf(c_19804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(X1,intersection(X2,intersection(X3,X0))) = intersection(X2,intersection(X3,X0)) )
| ~ subclass(X0,intersection(X1,intersection(X2,intersection(X3,X0)))) ),
inference(superposition,[status(thm)],[c_11018,c_4787]) ).
tcf(c_19805,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,identity_relation)) = intersection(X1,identity_relation) )
| ~ subclass(subset_relation,intersection(X0,intersection(X1,identity_relation))) ),
inference(superposition,[status(thm)],[c_11105,c_4787]) ).
tcf(c_19806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( intersection(X1,intersection(X2,intersection(X0,X3))) = intersection(X2,intersection(X0,X3)) )
| ~ subclass(X0,intersection(X1,intersection(X2,intersection(X0,X3)))) ),
inference(superposition,[status(thm)],[c_11629,c_4787]) ).
tcf(c_19807,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))) = intersection(X1,complement(cross_product(universal_class,universal_class))) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_4787]) ).
tcf(c_19808,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,complement(subset_relation))) = intersection(X1,complement(subset_relation)) )
| ~ subclass(complement(identity_relation),intersection(X0,intersection(X1,complement(subset_relation)))) ),
inference(superposition,[status(thm)],[c_12408,c_4787]) ).
tcf(c_19809,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(unordered_pair(x,x),X1)) = intersection(unordered_pair(x,x),X1) )
| ~ subclass(iPr_def_10,intersection(X0,intersection(unordered_pair(x,x),X1))) ),
inference(superposition,[status(thm)],[c_16597,c_4787]) ).
tcf(c_19810,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,unordered_pair(x,x))) = intersection(X1,unordered_pair(x,x)) )
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,unordered_pair(x,x)))) ),
inference(superposition,[status(thm)],[c_17097,c_4787]) ).
tcf(c_19811,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(unordered_pair(y,y),X1)) = intersection(unordered_pair(y,y),X1) )
| ~ subclass(iPr_def_10,intersection(X0,intersection(unordered_pair(y,y),X1))) ),
inference(superposition,[status(thm)],[c_18573,c_4787]) ).
tcf(c_19812,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,unordered_pair(y,y))) = intersection(X1,unordered_pair(y,y)) )
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,unordered_pair(y,y)))) ),
inference(superposition,[status(thm)],[c_19010,c_4787]) ).
tcf(c_19813,plain,
! [X0: $i] :
( ( intersection(complement(X0),X0) = X0 )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4169,c_4787]) ).
tcf(c_19814,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(cross_product(X1,X2),X0) = X0 )
| ~ subclass(X0,intersection(X0,cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_193,c_4787]) ).
tcf(c_19815,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(X0,regular(X0)) = regular(X0) )
| ~ subclass(regular(X0),null_class) ),
inference(superposition,[status(thm)],[c_223,c_4787]) ).
tcf(c_19816,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X2,cross_product(X0,X1)) = cross_product(X0,X1) )
| ~ subclass(cross_product(X0,X1),intersection(cross_product(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_193,c_4787]) ).
tcf(c_19817,plain,
( ( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
| ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),subset_relation) ),
inference(superposition,[status(thm)],[c_229,c_4787]) ).
tcf(c_19818,plain,
( ( intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) = subset_relation )
| ~ subclass(subset_relation,identity_relation) ),
inference(superposition,[status(thm)],[c_230,c_4787]) ).
tcf(c_19819,plain,
! [X0: $i] :
( ( intersection(null_class,X0) = X0 )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4553,c_4787]) ).
tcf(c_19821,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(X1),intersection(X0,X1)) = intersection(X0,X1) )
| ~ subclass(intersection(X0,X1),null_class) ),
inference(superposition,[status(thm)],[c_11228,c_4787]) ).
tcf(c_19822,plain,
( ( intersection(complement(subset_relation),identity_relation) = identity_relation )
| ~ subclass(identity_relation,null_class) ),
inference(superposition,[status(thm)],[c_11311,c_4787]) ).
tcf(c_19823,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(X0),intersection(X0,X1)) = intersection(X0,X1) )
| ~ subclass(intersection(X0,X1),null_class) ),
inference(superposition,[status(thm)],[c_11685,c_4787]) ).
tcf(c_19824,plain,
( ( intersection(complement(cross_product(universal_class,universal_class)),subset_relation) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_11763,c_4787]) ).
tcf(c_19825,plain,
( ( intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) = identity_relation )
| ~ subclass(identity_relation,null_class) ),
inference(superposition,[status(thm)],[c_12282,c_4787]) ).
tcf(c_19826,plain,
! [X0: $i] :
( ( intersection(X0,complement(X0)) = complement(X0) )
| ~ subclass(complement(X0),null_class) ),
inference(superposition,[status(thm)],[c_12377,c_4787]) ).
tcf(c_19827,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X1,X0),complement(X0)) = complement(X0) )
| ~ subclass(complement(X0),null_class) ),
inference(superposition,[status(thm)],[c_12625,c_4787]) ).
tcf(c_19828,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,X1),complement(X0)) = complement(X0) )
| ~ subclass(complement(X0),null_class) ),
inference(superposition,[status(thm)],[c_12688,c_4787]) ).
tcf(c_19829,plain,
( ( intersection(identity_relation,complement(subset_relation)) = complement(subset_relation) )
| ~ subclass(complement(subset_relation),null_class) ),
inference(superposition,[status(thm)],[c_12394,c_4787]) ).
tcf(c_19830,plain,
( ( intersection(subset_relation,complement(cross_product(universal_class,universal_class))) = complement(cross_product(universal_class,universal_class)) )
| ~ subclass(complement(cross_product(universal_class,universal_class)),null_class) ),
inference(superposition,[status(thm)],[c_12738,c_4787]) ).
tcf(c_19831,plain,
( ( intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),null_class) ),
inference(superposition,[status(thm)],[c_13003,c_4787]) ).
tcf(c_19832,plain,
( ( intersection(unordered_pair(x,x),complement(iPr_def_10)) = complement(iPr_def_10) )
| ~ subclass(complement(iPr_def_10),null_class) ),
inference(superposition,[status(thm)],[c_16614,c_4787]) ).
tcf(c_19833,plain,
( ( intersection(complement(iPr_def_10),unordered_pair(x,x)) = unordered_pair(x,x) )
| ~ subclass(unordered_pair(x,x),null_class) ),
inference(superposition,[status(thm)],[c_17131,c_4787]) ).
tcf(c_19834,plain,
( ( intersection(unordered_pair(y,y),complement(iPr_def_10)) = complement(iPr_def_10) )
| ~ subclass(complement(iPr_def_10),null_class) ),
inference(superposition,[status(thm)],[c_18749,c_4787]) ).
tcf(c_19835,plain,
( ( intersection(complement(iPr_def_10),unordered_pair(y,y)) = unordered_pair(y,y) )
| ~ subclass(unordered_pair(y,y),null_class) ),
inference(superposition,[status(thm)],[c_19300,c_4787]) ).
tcf(c_19839,plain,
( ( complement(subset_relation) = null_class )
| ~ subclass(complement(subset_relation),null_class) ),
inference(light_normalisation,[status(thm)],[c_19829,c_12394]) ).
tcf(c_19911,plain,
( ( intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) = subset_relation )
| ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),subset_relation) ),
inference(light_normalisation,[status(thm)],[c_19817,c_229]) ).
tcf(c_20045,plain,
member(regular(unordered_pair(x,x)),iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_4975,c_272,c_4975,c_9928,c_14459]) ).
tcf(c_20047,plain,
( member(regular(unordered_pair(x,x)),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_20045,c_4342]) ).
tcf(c_20048,plain,
member(regular(unordered_pair(x,x)),universal_class),
inference(superposition,[status(thm)],[c_20045,c_4336]) ).
tcf(c_20051,plain,
( member(regular(unordered_pair(x,x)),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_20048,c_4342]) ).
tcf(c_20061,plain,
( ( unordered_pair(unordered_pair(first(regular(unordered_pair(x,x))),first(regular(unordered_pair(x,x)))),unordered_pair(first(regular(unordered_pair(x,x))),unordered_pair(second(regular(unordered_pair(x,x))),second(regular(unordered_pair(x,x)))))) = regular(unordered_pair(x,x)) )
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_20047,c_184]) ).
tcf(c_20093,plain,
member(regular(unordered_pair(y,y)),iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_4999,c_273,c_4999,c_10079,c_14603]) ).
tcf(c_20095,plain,
( member(regular(unordered_pair(y,y)),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_20093,c_4342]) ).
tcf(c_20096,plain,
member(regular(unordered_pair(y,y)),universal_class),
inference(superposition,[status(thm)],[c_20093,c_4336]) ).
tcf(c_20099,plain,
( member(regular(unordered_pair(y,y)),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_20096,c_4342]) ).
tcf(c_20112,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| member(not_subclass_element(unordered_pair(y,y),X1),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_171,c_5077]) ).
tcf(c_20113,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,unordered_pair(y,y)),X1)
| member(not_subclass_element(unordered_pair(y,y),X1),X0)
| ( unordered_pair(y,y) = X1 )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_251,c_5077]) ).
tcf(c_20114,plain,
! [X0: $i] :
( member(not_subclass_element(unordered_pair(y,y),null_class),X0)
| ( unordered_pair(y,y) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_259,c_5077]) ).
tcf(c_20116,plain,
! [X0: $i] :
( member(y,X0)
| ~ member(y,universal_class)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_179,c_5077]) ).
tcf(c_20117,plain,
! [X0: $i] :
( member(regular(unordered_pair(y,y)),X0)
| ( unordered_pair(y,y) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_222,c_5077]) ).
tcf(c_20118,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(y,y),unordered_pair(y,y)),universal_class)),universal_class))))))),X0)
| ( unordered_pair(y,y) = null_class )
| ~ subclass(iPr_def_10,X0)
| ~ member(unordered_pair(y,y),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_5077]) ).
tcf(c_20119,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(unordered_pair(y,y),X1),X2)
| member(not_subclass_element(intersection(unordered_pair(y,y),X1),X2),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4224,c_5077]) ).
tcf(c_20120,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(unordered_pair(y,y),X1)),X0)
| ( intersection(unordered_pair(y,y),X1) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4225,c_5077]) ).
tcf(c_20121,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,unordered_pair(y,y)),X2)
| member(not_subclass_element(intersection(X1,unordered_pair(y,y)),X2),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4245,c_5077]) ).
tcf(c_20122,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X1,unordered_pair(y,y))),X0)
| ( intersection(X1,unordered_pair(y,y)) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4246,c_5077]) ).
tcf(c_20123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(unordered_pair(y,y),cross_product(X1,X2)),X3)
| member(not_subclass_element(intersection(cross_product(X1,X2),unordered_pair(y,y)),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4425,c_5077]) ).
tcf(c_20124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X1,unordered_pair(y,y)),X2),X3)
| member(not_subclass_element(intersection(intersection(X1,unordered_pair(y,y)),X2),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4430,c_5077]) ).
tcf(c_20125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(unordered_pair(y,y),X1),X2),X3)
| member(not_subclass_element(intersection(intersection(unordered_pair(y,y),X1),X2),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4431,c_5077]) ).
tcf(c_20126,plain,
! [X0: $i,X1: $i] :
( subclass(X1,complement(unordered_pair(y,y)))
| member(not_subclass_element(X1,complement(unordered_pair(y,y))),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_8328,c_5077]) ).
tcf(c_20127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),unordered_pair(y,y)),X3)
| member(not_subclass_element(intersection(unordered_pair(y,y),cross_product(X1,X2)),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4638,c_5077]) ).
tcf(c_20128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X1,intersection(X2,unordered_pair(y,y))),X3)
| member(not_subclass_element(intersection(X1,intersection(X2,unordered_pair(y,y))),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4646,c_5077]) ).
tcf(c_20129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X1,intersection(unordered_pair(y,y),X2)),X3)
| member(not_subclass_element(intersection(X1,intersection(unordered_pair(y,y),X2)),X3),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4647,c_5077]) ).
tcf(c_20130,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(unordered_pair(y,y))),X1)
| member(not_subclass_element(complement(complement(unordered_pair(y,y))),X1),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_13744,c_5077]) ).
tcf(c_20134,plain,
! [X0: $i] :
( member(y,X0)
| ~ subclass(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20116,c_4392]) ).
tcf(c_20186,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(y,y),unordered_pair(y,y)),universal_class)),universal_class))))))),X0)
| ( unordered_pair(y,y) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20118,c_180]) ).
tcf(c_20363,plain,
! [X0: $i] :
( subclass(iPr_def_10,X0)
| ( not_subclass_element(iPr_def_10,X0) = y )
| ( not_subclass_element(iPr_def_10,X0) = x ) ),
inference(superposition,[status(thm)],[c_171,c_5208]) ).
tcf(c_20364,plain,
! [X0: $i] :
( member(not_subclass_element(X0,iPr_def_10),X0)
| ( X0 = iPr_def_10 )
| ( not_subclass_element(iPr_def_10,X0) = y )
| ( not_subclass_element(iPr_def_10,X0) = x ) ),
inference(superposition,[status(thm)],[c_251,c_5208]) ).
tcf(c_20365,plain,
( ( null_class = iPr_def_10 )
| ( not_subclass_element(iPr_def_10,null_class) = y )
| ( not_subclass_element(iPr_def_10,null_class) = x ) ),
inference(superposition,[status(thm)],[c_259,c_5208]) ).
tcf(c_20366,plain,
( ( null_class = iPr_def_10 )
| ( regular(iPr_def_10) = y )
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_222,c_5208]) ).
tcf(c_20367,plain,
( ( null_class = iPr_def_10 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = y )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(iPr_def_10,universal_class) ),
inference(superposition,[status(thm)],[c_225,c_5208]) ).
tcf(c_20370,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,X0),X1)
| ( not_subclass_element(intersection(iPr_def_10,X0),X1) = y )
| ( not_subclass_element(intersection(iPr_def_10,X0),X1) = x ) ),
inference(superposition,[status(thm)],[c_4224,c_5208]) ).
tcf(c_20371,plain,
! [X0: $i] :
( ( intersection(iPr_def_10,X0) = null_class )
| ( regular(intersection(iPr_def_10,X0)) = y )
| ( regular(intersection(iPr_def_10,X0)) = x ) ),
inference(superposition,[status(thm)],[c_4225,c_5208]) ).
tcf(c_20372,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,iPr_def_10),X1)
| ( not_subclass_element(intersection(X0,iPr_def_10),X1) = y )
| ( not_subclass_element(intersection(X0,iPr_def_10),X1) = x ) ),
inference(superposition,[status(thm)],[c_4245,c_5208]) ).
tcf(c_20373,plain,
! [X0: $i] :
( ( intersection(X0,iPr_def_10) = null_class )
| ( regular(intersection(X0,iPr_def_10)) = y )
| ( regular(intersection(X0,iPr_def_10)) = x ) ),
inference(superposition,[status(thm)],[c_4246,c_5208]) ).
tcf(c_20374,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,cross_product(X0,X1)),X2)
| ( not_subclass_element(intersection(cross_product(X0,X1),iPr_def_10),X2) = y )
| ( not_subclass_element(intersection(cross_product(X0,X1),iPr_def_10),X2) = x ) ),
inference(superposition,[status(thm)],[c_4425,c_5208]) ).
tcf(c_20375,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,iPr_def_10),X1),X2)
| ( not_subclass_element(intersection(intersection(X0,iPr_def_10),X1),X2) = y )
| ( not_subclass_element(intersection(intersection(X0,iPr_def_10),X1),X2) = x ) ),
inference(superposition,[status(thm)],[c_4430,c_5208]) ).
tcf(c_20376,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(iPr_def_10,X0),X1),X2)
| ( not_subclass_element(intersection(intersection(iPr_def_10,X0),X1),X2) = y )
| ( not_subclass_element(intersection(intersection(iPr_def_10,X0),X1),X2) = x ) ),
inference(superposition,[status(thm)],[c_4431,c_5208]) ).
tcf(c_20377,plain,
! [X0: $i] :
( subclass(X0,complement(iPr_def_10))
| ( not_subclass_element(X0,complement(iPr_def_10)) = y )
| ( not_subclass_element(X0,complement(iPr_def_10)) = x ) ),
inference(superposition,[status(thm)],[c_8328,c_5208]) ).
tcf(c_20378,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),iPr_def_10),X2)
| ( not_subclass_element(intersection(iPr_def_10,cross_product(X0,X1)),X2) = y )
| ( not_subclass_element(intersection(iPr_def_10,cross_product(X0,X1)),X2) = x ) ),
inference(superposition,[status(thm)],[c_4638,c_5208]) ).
tcf(c_20379,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,iPr_def_10)),X2)
| ( not_subclass_element(intersection(X0,intersection(X1,iPr_def_10)),X2) = y )
| ( not_subclass_element(intersection(X0,intersection(X1,iPr_def_10)),X2) = x ) ),
inference(superposition,[status(thm)],[c_4646,c_5208]) ).
tcf(c_20380,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(iPr_def_10,X1)),X2)
| ( not_subclass_element(intersection(X0,intersection(iPr_def_10,X1)),X2) = y )
| ( not_subclass_element(intersection(X0,intersection(iPr_def_10,X1)),X2) = x ) ),
inference(superposition,[status(thm)],[c_4647,c_5208]) ).
tcf(c_20381,plain,
! [X0: $i] :
( subclass(complement(complement(iPr_def_10)),X0)
| ( not_subclass_element(complement(complement(iPr_def_10)),X0) = y )
| ( not_subclass_element(complement(complement(iPr_def_10)),X0) = x ) ),
inference(superposition,[status(thm)],[c_13744,c_5208]) ).
tcf(c_20382,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ( not_subclass_element(unordered_pair(x,x),X0) = y )
| ( not_subclass_element(unordered_pair(x,x),X0) = x ) ),
inference(superposition,[status(thm)],[c_4972,c_5208]) ).
tcf(c_20383,plain,
( ( regular(unordered_pair(x,x)) = y )
| ( regular(unordered_pair(x,x)) = x ) ),
inference(superposition,[status(thm)],[c_20045,c_5208]) ).
tcf(c_20384,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X0),X1)
| ( not_subclass_element(intersection(unordered_pair(x,x),X0),X1) = y )
| ( not_subclass_element(intersection(unordered_pair(x,x),X0),X1) = x ) ),
inference(superposition,[status(thm)],[c_4976,c_5208]) ).
tcf(c_20385,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(x,x)),X1)
| ( not_subclass_element(intersection(X0,unordered_pair(x,x)),X1) = y )
| ( not_subclass_element(intersection(X0,unordered_pair(x,x)),X1) = x ) ),
inference(superposition,[status(thm)],[c_4977,c_5208]) ).
tcf(c_20386,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ( not_subclass_element(unordered_pair(y,y),X0) = y )
| ( not_subclass_element(unordered_pair(y,y),X0) = x ) ),
inference(superposition,[status(thm)],[c_4996,c_5208]) ).
tcf(c_20387,plain,
( ( regular(unordered_pair(y,y)) = y )
| ( regular(unordered_pair(y,y)) = x ) ),
inference(superposition,[status(thm)],[c_20093,c_5208]) ).
tcf(c_20388,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(y,y),X0),X1)
| ( not_subclass_element(intersection(unordered_pair(y,y),X0),X1) = y )
| ( not_subclass_element(intersection(unordered_pair(y,y),X0),X1) = x ) ),
inference(superposition,[status(thm)],[c_5000,c_5208]) ).
tcf(c_20389,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(y,y)),X1)
| ( not_subclass_element(intersection(X0,unordered_pair(y,y)),X1) = y )
| ( not_subclass_element(intersection(X0,unordered_pair(y,y)),X1) = x ) ),
inference(superposition,[status(thm)],[c_5001,c_5208]) ).
tcf(c_20394,plain,
( ( regular(iPr_def_10) = y )
| ( regular(iPr_def_10) = x ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20366,c_4692]) ).
tcf(c_20400,plain,
( ( not_subclass_element(iPr_def_10,null_class) = y )
| ( not_subclass_element(iPr_def_10,null_class) = x ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20365,c_4692]) ).
tcf(c_20461,plain,
( ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = y )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20367,c_4692,c_4134]) ).
tcf(c_20572,plain,
( ( null_class = iPr_def_10 )
| ( regular(iPr_def_10) = x )
| ( intersection(iPr_def_10,y) = null_class ) ),
inference(superposition,[status(thm)],[c_20394,c_223]) ).
tcf(c_20574,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(iPr_def_10,y) = null_class ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20572,c_4692]) ).
tcf(c_20597,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(iPr_def_10,y) = iPr_def_10 )
| ~ subclass(iPr_def_10,null_class) ),
inference(superposition,[status(thm)],[c_20574,c_4722]) ).
tcf(c_20598,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(null_class,complement(iPr_def_10)) = null_class ) ),
inference(superposition,[status(thm)],[c_20574,c_12688]) ).
tcf(c_20599,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(null_class,complement(y)) = null_class ) ),
inference(superposition,[status(thm)],[c_20574,c_12625]) ).
tcf(c_20600,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(complement(iPr_def_10),null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_20574,c_11685]) ).
tcf(c_20603,plain,
! [X0: $i] :
( subclass(intersection(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_6583]) ).
tcf(c_20604,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(iPr_def_10,y),X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_4431]) ).
tcf(c_20605,plain,
! [X0: $i] :
( subclass(intersection(null_class,X0),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_6065]) ).
tcf(c_20606,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(iPr_def_10,y),X0),X1)
| member(not_subclass_element(intersection(null_class,X0),X1),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_4430]) ).
tcf(c_20607,plain,
( subclass(null_class,y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_4643]) ).
tcf(c_20608,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_4245]) ).
tcf(c_20609,plain,
( subclass(null_class,iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_4427]) ).
tcf(c_20610,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_4224]) ).
tcf(c_20613,plain,
! [X0: $i] :
( subclass(intersection(X0,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_11340]) ).
tcf(c_20614,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(iPr_def_10,y)),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_4647]) ).
tcf(c_20615,plain,
! [X0: $i] :
( subclass(intersection(X0,null_class),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_10731]) ).
tcf(c_20616,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(iPr_def_10,y)),X1)
| member(not_subclass_element(intersection(X0,null_class),X1),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_4646]) ).
tcf(c_20617,plain,
! [X0: $i,X1: $i] :
( member(X0,iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_20574,c_6783]) ).
tcf(c_20618,plain,
! [X0: $i,X1: $i] :
( member(X0,y)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_20574,c_6250]) ).
tcf(c_20619,plain,
! [X0: $i] :
( member(X0,null_class)
| ( regular(iPr_def_10) = x )
| ~ member(X0,iPr_def_10)
| ~ member(X0,y) ),
inference(superposition,[status(thm)],[c_20574,c_190]) ).
tcf(c_20622,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_20574,c_6782]) ).
tcf(c_20624,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(iPr_def_10,y) = y )
| ~ subclass(y,null_class) ),
inference(superposition,[status(thm)],[c_20574,c_4787]) ).
tcf(c_20625,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(complement(y),null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_20574,c_11228]) ).
tcf(c_20626,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(y,X0) ),
inference(superposition,[status(thm)],[c_20574,c_6249]) ).
tcf(c_20628,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_20574,c_11629]) ).
tcf(c_20629,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(y,X0) ),
inference(superposition,[status(thm)],[c_20574,c_11018]) ).
tcf(c_20630,plain,
! [X0: $i,X1: $i] :
( member(X0,iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_20574,c_11630]) ).
tcf(c_20631,plain,
! [X0: $i,X1: $i] :
( member(X0,y)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_20574,c_11019]) ).
tcf(c_20672,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ~ member(X0,iPr_def_10)
| ~ member(X0,y) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20619,c_256]) ).
tcf(c_20676,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),y)
| subclass(intersection(X0,intersection(iPr_def_10,y)),X1)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_20616,c_4790]) ).
tcf(c_20680,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),iPr_def_10)
| subclass(intersection(X0,intersection(iPr_def_10,y)),X1)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_20614,c_4790]) ).
tcf(c_20684,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),y)
| subclass(intersection(intersection(iPr_def_10,y),X0),X1)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_20606,c_4553]) ).
tcf(c_20688,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),iPr_def_10)
| subclass(intersection(intersection(iPr_def_10,y),X0),X1)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_20604,c_4553]) ).
tcf(c_20784,plain,
( ( unordered_pair(unordered_pair(first(regular(unordered_pair(y,y))),first(regular(unordered_pair(y,y)))),unordered_pair(first(regular(unordered_pair(y,y))),unordered_pair(second(regular(unordered_pair(y,y))),second(regular(unordered_pair(y,y)))))) = regular(unordered_pair(y,y)) )
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_20095,c_184]) ).
tcf(c_20787,plain,
~ subclass(iPr_def_10,null_class),
inference(global_subsumption_just,[status(thm)],[c_5344,c_3162,c_6227,c_6228]) ).
tcf(c_20795,plain,
( ( null_class = iPr_def_10 )
| ( not_subclass_element(iPr_def_10,null_class) = x )
| ~ member(y,null_class)
| ~ member(not_subclass_element(null_class,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_20400,c_254]) ).
tcf(c_20796,plain,
( member(not_subclass_element(null_class,iPr_def_10),null_class)
| ( null_class = iPr_def_10 )
| ( not_subclass_element(iPr_def_10,null_class) = x )
| ~ member(y,null_class) ),
inference(superposition,[status(thm)],[c_20400,c_253]) ).
tcf(c_20799,plain,
( subclass(iPr_def_10,null_class)
| ( not_subclass_element(iPr_def_10,null_class) = x )
| ~ member(y,null_class) ),
inference(superposition,[status(thm)],[c_20400,c_172]) ).
tcf(c_20808,plain,
( operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class)))),domain_of(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))))
| ( cross_product(domain_of(y),domain_of(y)) != y ) ),
inference(superposition,[status(thm)],[c_20461,c_234]) ).
tcf(c_20809,plain,
! [X0: $i,X1: $i] :
( compatible(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),domain_of(domain_of(X1)))
| ( domain_of(X0) != domain_of(y) ) ),
inference(superposition,[status(thm)],[c_20461,c_238]) ).
tcf(c_20810,plain,
( subclass(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class)))),domain_of(y))
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_20461,c_233]) ).
tcf(c_20811,plain,
! [X0: $i,X1: $i] :
( homomorphism(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),unordered_pair(not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),unordered_pair(not_homomorphism2(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),not_homomorphism2(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)))),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ operation(X1)
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ compatible(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1) ),
inference(superposition,[status(thm)],[c_20461,c_243]) ).
tcf(c_20812,plain,
! [X0: $i,X1: $i] :
( compatible(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0,X1)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class)))),domain_of(domain_of(X1)))
| ( domain_of(domain_of(X0)) != y ) ),
inference(superposition,[status(thm)],[c_20461,c_238]) ).
tcf(c_20813,plain,
! [X0: $i] :
( member(X0,y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(X0,X0),universal_class)) = null_class )
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_20461,c_195]) ).
tcf(c_20814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X3,X3),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) )
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),y)
| ~ homomorphism(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1) ),
inference(superposition,[status(thm)],[c_20461,c_242]) ).
tcf(c_20858,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(global_subsumption_just,[status(thm)],[c_20622,c_4501,c_18814]) ).
tcf(c_20860,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ subclass(iPr_def_10,X0) ),
inference(demodulation,[status(thm)],[c_20858,c_4553]) ).
tcf(c_20861,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(y,X0) ),
inference(demodulation,[status(thm)],[c_20626,c_4553]) ).
tcf(c_20862,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(global_subsumption_just,[status(thm)],[c_20628,c_4501,c_18822]) ).
tcf(c_20872,plain,
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3161,c_6003]) ).
tcf(c_20879,plain,
( ( cross_product(universal_class,universal_class) = unordered_pair(x,x) )
| ~ function(iPr_def_10)
| ~ subclass(cross_product(universal_class,universal_class),unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_20872,c_176]) ).
tcf(c_20880,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ function(iPr_def_10)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_20872,c_250]) ).
tcf(c_20881,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ function(iPr_def_10)
| ~ member(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_20872,c_170]) ).
tcf(c_20901,plain,
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3161,c_6026]) ).
tcf(c_20908,plain,
( ( cross_product(universal_class,universal_class) = unordered_pair(y,y) )
| ~ function(iPr_def_10)
| ~ subclass(cross_product(universal_class,universal_class),unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_20901,c_176]) ).
tcf(c_20909,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ function(iPr_def_10)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_20901,c_250]) ).
tcf(c_20910,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ function(iPr_def_10)
| ~ member(X0,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_20901,c_170]) ).
tcf(c_20936,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(complement(complement(X0)),X1),X2) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_13999,c_5346]) ).
tcf(c_20937,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(complement(cross_product(universal_class,universal_class)),X0),X1) = null_class )
| ~ subclass(complement(element_relation),null_class) ),
inference(superposition,[status(thm)],[c_15325,c_5346]) ).
tcf(c_20938,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(complement(cross_product(universal_class,universal_class)),X0),X1) = null_class )
| ~ subclass(complement(successor_relation),null_class) ),
inference(superposition,[status(thm)],[c_14988,c_5346]) ).
tcf(c_20940,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(intersection(intersection(intersection(X0,null_class),X1),X2),X3) = null_class,
inference(superposition,[status(thm)],[c_6065,c_5346]) ).
tcf(c_20941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(intersection(intersection(intersection(X1,X0),X2),X3),X4) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6249,c_5346]) ).
tcf(c_20942,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(intersection(identity_relation,X0),X1),X2) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_6317,c_5346]) ).
tcf(c_20943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(intersection(intersection(intersection(null_class,X0),X1),X2),X3) = null_class,
inference(superposition,[status(thm)],[c_6583,c_5346]) ).
tcf(c_20944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(intersection(intersection(intersection(X0,X1),X2),X3),X4) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6782,c_5346]) ).
tcf(c_20945,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(intersection(complement(cross_product(universal_class,universal_class)),X0),X1),X2) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_5346]) ).
tcf(c_20946,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X0),X1) = null_class )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_5346]) ).
tcf(c_20947,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(intersection(complement(subset_relation),X0),X1),X2) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_8784,c_5346]) ).
tcf(c_20948,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(intersection(intersection(X0,intersection(X1,null_class)),X2),X3) = null_class,
inference(superposition,[status(thm)],[c_10731,c_5346]) ).
tcf(c_20949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(intersection(intersection(X1,intersection(X2,X0)),X3),X4) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11018,c_5346]) ).
tcf(c_20950,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(intersection(X0,identity_relation),X1),X2) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_11105,c_5346]) ).
tcf(c_20951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(intersection(intersection(X0,intersection(null_class,X1)),X2),X3) = null_class,
inference(superposition,[status(thm)],[c_11340,c_5346]) ).
tcf(c_20952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(intersection(intersection(X1,intersection(X0,X2)),X3),X4) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11629,c_5346]) ).
tcf(c_20953,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(intersection(X0,complement(cross_product(universal_class,universal_class))),X1),X2) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_5346]) ).
tcf(c_20954,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(intersection(X0,complement(subset_relation)),X1),X2) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_12408,c_5346]) ).
tcf(c_20955,plain,
! [X0: $i,X1: $i] : intersection(intersection(complement(complement(null_class)),X0),X1) = null_class,
inference(superposition,[status(thm)],[c_13755,c_5346]) ).
tcf(c_21035,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X1,complement(complement(X0))),X2) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_13999,c_5348]) ).
tcf(c_21036,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,complement(cross_product(universal_class,universal_class))),X1) = null_class )
| ~ subclass(complement(element_relation),null_class) ),
inference(superposition,[status(thm)],[c_15325,c_5348]) ).
tcf(c_21037,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,complement(cross_product(universal_class,universal_class))),X1) = null_class )
| ~ subclass(complement(successor_relation),null_class) ),
inference(superposition,[status(thm)],[c_14988,c_5348]) ).
tcf(c_21039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(intersection(X0,intersection(intersection(X1,null_class),X2)),X3) = null_class,
inference(superposition,[status(thm)],[c_6065,c_5348]) ).
tcf(c_21040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(intersection(X1,intersection(intersection(X2,X0),X3)),X4) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6249,c_5348]) ).
tcf(c_21041,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,intersection(identity_relation,X1)),X2) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_6317,c_5348]) ).
tcf(c_21042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(intersection(X0,intersection(intersection(null_class,X1),X2)),X3) = null_class,
inference(superposition,[status(thm)],[c_6583,c_5348]) ).
tcf(c_21043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(intersection(X1,intersection(intersection(X0,X2),X3)),X4) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6782,c_5348]) ).
tcf(c_21044,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)),X2) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_5348]) ).
tcf(c_21045,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class))))),X1) = null_class )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_5348]) ).
tcf(c_21046,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,intersection(complement(subset_relation),X1)),X2) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_8784,c_5348]) ).
tcf(c_21047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(intersection(X0,intersection(X1,intersection(X2,null_class))),X3) = null_class,
inference(superposition,[status(thm)],[c_10731,c_5348]) ).
tcf(c_21048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(intersection(X1,intersection(X2,intersection(X3,X0))),X4) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11018,c_5348]) ).
tcf(c_21049,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,intersection(X1,identity_relation)),X2) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_11105,c_5348]) ).
tcf(c_21050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(intersection(X0,intersection(X1,intersection(null_class,X2))),X3) = null_class,
inference(superposition,[status(thm)],[c_11340,c_5348]) ).
tcf(c_21051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(intersection(X1,intersection(X2,intersection(X0,X3))),X4) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11629,c_5348]) ).
tcf(c_21052,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))),X2) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_5348]) ).
tcf(c_21053,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,intersection(X1,complement(subset_relation))),X2) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_12408,c_5348]) ).
tcf(c_21054,plain,
! [X0: $i,X1: $i] : intersection(intersection(X0,complement(complement(null_class))),X1) = null_class,
inference(superposition,[status(thm)],[c_13755,c_5348]) ).
tcf(c_21234,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),y)
| ( regular(iPr_def_10) = x )
| ( intersection(iPr_def_10,y) = X0 )
| ~ subclass(X0,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_20608,c_176]) ).
tcf(c_21235,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X0),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_20608,c_250]) ).
tcf(c_21236,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),y)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_20608,c_170]) ).
tcf(c_21237,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(iPr_def_10,y)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_20608,c_5348]) ).
tcf(c_21238,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_20608,c_5346]) ).
tcf(c_21239,plain,
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(iPr_def_10,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_20608,c_14028]) ).
tcf(c_21240,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(iPr_def_10,y)) = null_class ) ),
inference(superposition,[status(thm)],[c_20608,c_5287]) ).
tcf(c_21241,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_20608,c_5257]) ).
tcf(c_21243,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(iPr_def_10,y),X0)),y)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X0) = intersection(iPr_def_10,y) ) ),
inference(superposition,[status(thm)],[c_20608,c_4722]) ).
tcf(c_21244,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(iPr_def_10,y))),y)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(iPr_def_10,y)) = intersection(iPr_def_10,y) ) ),
inference(superposition,[status(thm)],[c_20608,c_4787]) ).
tcf(c_21313,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(iPr_def_10,y) = X0 )
| ~ subclass(X0,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_20610,c_176]) ).
tcf(c_21314,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_20610,c_250]) ).
tcf(c_21315,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_20610,c_170]) ).
tcf(c_21316,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(iPr_def_10,y)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_20610,c_5348]) ).
tcf(c_21317,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_20610,c_5346]) ).
tcf(c_21318,plain,
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(iPr_def_10,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_20610,c_14028]) ).
tcf(c_21319,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(iPr_def_10,y)) = null_class ) ),
inference(superposition,[status(thm)],[c_20610,c_5287]) ).
tcf(c_21320,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_20610,c_5257]) ).
tcf(c_21322,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(iPr_def_10,y),X0)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X0) = intersection(iPr_def_10,y) ) ),
inference(superposition,[status(thm)],[c_20610,c_4722]) ).
tcf(c_21323,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(iPr_def_10,y))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(iPr_def_10,y)) = intersection(iPr_def_10,y) ) ),
inference(superposition,[status(thm)],[c_20610,c_4787]) ).
tcf(c_21422,plain,
! [X0: $i] :
( member(X0,y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(X0,X0),universal_class)) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13126,c_20813]) ).
tcf(c_21423,plain,
! [X0: $i] :
( member(X0,y)
| ( unordered_pair(X0,X0) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(X0,X0),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4943,c_20813]) ).
tcf(c_21424,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| member(X0,y)
| ( unordered_pair(X0,X1) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(X0,X0),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_20813]) ).
tcf(c_21425,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| member(X0,y)
| ( unordered_pair(X1,X0) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(X0,X0),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_20813]) ).
tcf(c_21426,plain,
! [X0: $i,X1: $i] :
( member(X0,y)
| ( unordered_pair(X0,X1) = unordered_pair(X1,X1) )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(X0,X0),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_265,c_20813]) ).
tcf(c_21427,plain,
! [X0: $i,X1: $i] :
( member(X0,y)
| ( unordered_pair(X1,X0) = unordered_pair(X1,X1) )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(X0,X0),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_264,c_20813]) ).
tcf(c_21429,plain,
! [X0: $i] :
( subclass(universal_class,X0)
| member(not_subclass_element(universal_class,X0),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(universal_class,X0),not_subclass_element(universal_class,X0)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_171,c_20813]) ).
tcf(c_21430,plain,
! [X0: $i] :
( member(not_subclass_element(universal_class,X0),y)
| member(not_subclass_element(X0,universal_class),X0)
| ( X0 = universal_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(universal_class,X0),not_subclass_element(universal_class,X0)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_251,c_20813]) ).
tcf(c_21431,plain,
( member(not_subclass_element(universal_class,null_class),y)
| ( universal_class = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(universal_class,null_class),not_subclass_element(universal_class,null_class)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_259,c_20813]) ).
tcf(c_21432,plain,
( member(null_class,y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(null_class,null_class),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_260,c_20813]) ).
tcf(c_21433,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(X0,X1),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_180,c_20813]) ).
tcf(c_21434,plain,
( member(omega,y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(omega,omega),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_210,c_20813]) ).
tcf(c_21435,plain,
( member(regular(universal_class),y)
| ( universal_class = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(regular(universal_class),regular(universal_class)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_20813]) ).
tcf(c_21436,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class)) = null_class )
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_211,c_20813]) ).
tcf(c_21437,plain,
! [X0: $i] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class)) = null_class )
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_212,c_20813]) ).
tcf(c_21438,plain,
! [X0: $i,X1: $i] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class))))),universal_class)) = null_class )
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_221,c_20813]) ).
tcf(c_21439,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))),y)
| ( universal_class = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class)))))))),universal_class)) = null_class )
| ~ member(universal_class,universal_class) ),
inference(superposition,[status(thm)],[c_225,c_20813]) ).
tcf(c_21440,plain,
( member(iPr_def_10,y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4134,c_20813]) ).
tcf(c_21441,plain,
( member(x,y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(x,x),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4391,c_20813]) ).
tcf(c_21442,plain,
( member(y,y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(y,y),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4392,c_20813]) ).
tcf(c_21443,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(universal_class,X0),X1)
| member(not_subclass_element(intersection(universal_class,X0),X1),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),X1),not_subclass_element(intersection(universal_class,X0),X1)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4224,c_20813]) ).
tcf(c_21444,plain,
! [X0: $i] :
( member(regular(intersection(universal_class,X0)),y)
| ( intersection(universal_class,X0) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(regular(intersection(universal_class,X0)),regular(intersection(universal_class,X0))),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_20813]) ).
tcf(c_21445,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,universal_class),X1)
| member(not_subclass_element(intersection(X0,universal_class),X1),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),X1),not_subclass_element(intersection(X0,universal_class),X1)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4245,c_20813]) ).
tcf(c_21446,plain,
! [X0: $i] :
( member(regular(intersection(X0,universal_class)),y)
| ( intersection(X0,universal_class) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(regular(intersection(X0,universal_class)),regular(intersection(X0,universal_class))),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_20813]) ).
tcf(c_21447,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4388,c_20813]) ).
tcf(c_21448,plain,
! [X0: $i] :
( member(not_subclass_element(X0,null_class),y)
| ( X0 = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4389,c_20813]) ).
tcf(c_21449,plain,
! [X0: $i] :
( member(regular(X0),y)
| ( X0 = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4396,c_20813]) ).
tcf(c_21450,plain,
( member(not_subclass_element(identity_relation,null_class),y)
| ( null_class = identity_relation )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(identity_relation,null_class),not_subclass_element(identity_relation,null_class)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4400,c_20813]) ).
tcf(c_21451,plain,
( member(regular(identity_relation),y)
| ( null_class = identity_relation )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(regular(identity_relation),regular(identity_relation)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4401,c_20813]) ).
tcf(c_21452,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(universal_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),universal_class),X2),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(cross_product(X0,X1),universal_class),X2),not_subclass_element(intersection(cross_product(X0,X1),universal_class),X2)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4425,c_20813]) ).
tcf(c_21453,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,universal_class),X1),X2)
| member(not_subclass_element(intersection(intersection(X0,universal_class),X1),X2),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(intersection(X0,universal_class),X1),X2),not_subclass_element(intersection(intersection(X0,universal_class),X1),X2)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4430,c_20813]) ).
tcf(c_21454,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(universal_class,X0),X1),X2)
| member(not_subclass_element(intersection(intersection(universal_class,X0),X1),X2),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(intersection(universal_class,X0),X1),X2),not_subclass_element(intersection(intersection(universal_class,X0),X1),X2)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4431,c_20813]) ).
tcf(c_21455,plain,
! [X0: $i] :
( subclass(X0,complement(universal_class))
| member(not_subclass_element(X0,complement(universal_class)),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(X0,complement(universal_class)),not_subclass_element(X0,complement(universal_class))),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_8328,c_20813]) ).
tcf(c_21456,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),universal_class),X2)
| member(not_subclass_element(intersection(universal_class,cross_product(X0,X1)),X2),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(universal_class,cross_product(X0,X1)),X2),not_subclass_element(intersection(universal_class,cross_product(X0,X1)),X2)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4638,c_20813]) ).
tcf(c_21457,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,universal_class)),X2)
| member(not_subclass_element(intersection(X0,intersection(X1,universal_class)),X2),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(X0,intersection(X1,universal_class)),X2),not_subclass_element(intersection(X0,intersection(X1,universal_class)),X2)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4646,c_20813]) ).
tcf(c_21458,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(universal_class,X1)),X2)
| member(not_subclass_element(intersection(X0,intersection(universal_class,X1)),X2),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(X0,intersection(universal_class,X1)),X2),not_subclass_element(intersection(X0,intersection(universal_class,X1)),X2)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4647,c_20813]) ).
tcf(c_21459,plain,
! [X0: $i] :
( subclass(complement(complement(universal_class)),X0)
| member(not_subclass_element(complement(complement(universal_class)),X0),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(complement(complement(universal_class)),X0),not_subclass_element(complement(complement(universal_class)),X0)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_13744,c_20813]) ).
tcf(c_21460,plain,
( member(regular(subset_relation),y)
| ( null_class = subset_relation )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(regular(subset_relation),regular(subset_relation)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_9801,c_20813]) ).
tcf(c_21461,plain,
( member(regular(unordered_pair(x,x)),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(regular(unordered_pair(x,x)),regular(unordered_pair(x,x))),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_20048,c_20813]) ).
tcf(c_21462,plain,
( member(regular(unordered_pair(y,y)),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(regular(unordered_pair(y,y)),regular(unordered_pair(y,y))),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_20096,c_20813]) ).
tcf(c_21549,plain,
! [X0: $i] :
( subclass(X0,null_class)
| member(not_subclass_element(X0,null_class),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)),universal_class)) = null_class ) ),
inference(light_normalisation,[status(thm)],[c_21455,c_4953]) ).
tcf(c_21753,plain,
( member(x,y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class ) ),
inference(demodulation,[status(thm)],[c_21441,c_193]) ).
tcf(c_21763,plain,
( member(x,cross_product(universal_class,universal_class))
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class )
| ~ function(y) ),
inference(superposition,[status(thm)],[c_21753,c_4342]) ).
tcf(c_21775,plain,
( ( null_class = identity_relation )
| ( intersection(identity_relation,regular(identity_relation)) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_223,c_6316]) ).
tcf(c_21776,plain,
( ( intersection(identity_relation,null_class) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_4790,c_6316]) ).
tcf(c_21777,plain,
( ( intersection(identity_relation,complement(identity_relation)) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_12377,c_6316]) ).
tcf(c_21778,plain,
( ( intersection(identity_relation,complement(subset_relation)) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_12394,c_6316]) ).
tcf(c_21779,plain,
( ( intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_13003,c_6316]) ).
tcf(c_21793,plain,
( member(regular(null_class),subset_relation)
| ( null_class = identity_relation )
| ( intersection(identity_relation,regular(identity_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_6518]) ).
tcf(c_21794,plain,
( member(regular(null_class),subset_relation)
| ( intersection(identity_relation,null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_4790,c_6518]) ).
tcf(c_21795,plain,
( member(regular(null_class),subset_relation)
| ( intersection(identity_relation,complement(identity_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_12377,c_6518]) ).
tcf(c_21798,plain,
! [X0: $i] :
( member(regular(intersection(identity_relation,X0)),cross_product(universal_class,universal_class))
| ( intersection(identity_relation,X0) = null_class )
| ~ function(subset_relation) ),
inference(superposition,[status(thm)],[c_6518,c_4342]) ).
tcf(c_21799,plain,
! [X0: $i] :
( member(regular(intersection(identity_relation,X0)),universal_class)
| ( intersection(identity_relation,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_6518,c_4336]) ).
tcf(c_21888,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X1,intersection(complement(complement(X0)),X2)) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_13999,c_5371]) ).
tcf(c_21889,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)) = null_class )
| ~ subclass(complement(element_relation),null_class) ),
inference(superposition,[status(thm)],[c_15325,c_5371]) ).
tcf(c_21890,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(complement(cross_product(universal_class,universal_class)),X1)) = null_class )
| ~ subclass(complement(successor_relation),null_class) ),
inference(superposition,[status(thm)],[c_14988,c_5371]) ).
tcf(c_21892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(X0,intersection(intersection(intersection(X1,null_class),X2),X3)) = null_class,
inference(superposition,[status(thm)],[c_6065,c_5371]) ).
tcf(c_21893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(X1,intersection(intersection(intersection(X2,X0),X3),X4)) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6249,c_5371]) ).
tcf(c_21894,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(intersection(identity_relation,X1),X2)) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_6317,c_5371]) ).
tcf(c_21895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(X0,intersection(intersection(intersection(null_class,X1),X2),X3)) = null_class,
inference(superposition,[status(thm)],[c_6583,c_5371]) ).
tcf(c_21896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(X1,intersection(intersection(intersection(X0,X2),X3),X4)) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6782,c_5371]) ).
tcf(c_21897,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(intersection(complement(cross_product(universal_class,universal_class)),X1),X2)) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_5371]) ).
tcf(c_21898,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X1)) = null_class )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_5371]) ).
tcf(c_21899,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(intersection(complement(subset_relation),X1),X2)) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_8784,c_5371]) ).
tcf(c_21900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(X0,intersection(intersection(X1,intersection(X2,null_class)),X3)) = null_class,
inference(superposition,[status(thm)],[c_10731,c_5371]) ).
tcf(c_21901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(X1,intersection(intersection(X2,intersection(X3,X0)),X4)) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11018,c_5371]) ).
tcf(c_21902,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(intersection(X1,identity_relation),X2)) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_11105,c_5371]) ).
tcf(c_21903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(X0,intersection(intersection(X1,intersection(null_class,X2)),X3)) = null_class,
inference(superposition,[status(thm)],[c_11340,c_5371]) ).
tcf(c_21904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(X1,intersection(intersection(X2,intersection(X0,X3)),X4)) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11629,c_5371]) ).
tcf(c_21905,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(intersection(X1,complement(cross_product(universal_class,universal_class))),X2)) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_5371]) ).
tcf(c_21906,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(intersection(X1,complement(subset_relation)),X2)) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_12408,c_5371]) ).
tcf(c_21907,plain,
! [X0: $i,X1: $i] : intersection(X0,intersection(complement(complement(null_class)),X1)) = null_class,
inference(superposition,[status(thm)],[c_13755,c_5371]) ).
tcf(c_21912,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(iPr_def_10,y),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_20610,c_5371]) ).
tcf(c_21913,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(iPr_def_10,y),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_20608,c_5371]) ).
tcf(c_22028,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X1,intersection(X2,complement(complement(X0)))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_13999,c_5373]) ).
tcf(c_22029,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))) = null_class )
| ~ subclass(complement(element_relation),null_class) ),
inference(superposition,[status(thm)],[c_15325,c_5373]) ).
tcf(c_22030,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,complement(cross_product(universal_class,universal_class)))) = null_class )
| ~ subclass(complement(successor_relation),null_class) ),
inference(superposition,[status(thm)],[c_14988,c_5373]) ).
tcf(c_22032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(X0,intersection(X1,intersection(intersection(X2,null_class),X3))) = null_class,
inference(superposition,[status(thm)],[c_6065,c_5373]) ).
tcf(c_22033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(X1,intersection(X2,intersection(intersection(X3,X0),X4))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6249,c_5373]) ).
tcf(c_22034,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(X1,intersection(identity_relation,X2))) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_6317,c_5373]) ).
tcf(c_22035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(X0,intersection(X1,intersection(intersection(null_class,X2),X3))) = null_class,
inference(superposition,[status(thm)],[c_6583,c_5373]) ).
tcf(c_22036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(X1,intersection(X2,intersection(intersection(X0,X3),X4))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_6782,c_5373]) ).
tcf(c_22037,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(X1,intersection(complement(cross_product(universal_class,universal_class)),X2))) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_5373]) ).
tcf(c_22038,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,intersection(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))) = null_class )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_5373]) ).
tcf(c_22039,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(X1,intersection(complement(subset_relation),X2))) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_8784,c_5373]) ).
tcf(c_22040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(X0,intersection(X1,intersection(X2,intersection(X3,null_class)))) = null_class,
inference(superposition,[status(thm)],[c_10731,c_5373]) ).
tcf(c_22041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(X1,intersection(X2,intersection(X3,intersection(X4,X0)))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11018,c_5373]) ).
tcf(c_22042,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(X1,intersection(X2,identity_relation))) = null_class )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_11105,c_5373]) ).
tcf(c_22043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : intersection(X0,intersection(X1,intersection(X2,intersection(null_class,X3)))) = null_class,
inference(superposition,[status(thm)],[c_11340,c_5373]) ).
tcf(c_22044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( intersection(X1,intersection(X2,intersection(X3,intersection(X0,X4)))) = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_11629,c_5373]) ).
tcf(c_22045,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(X1,intersection(X2,complement(cross_product(universal_class,universal_class))))) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_5373]) ).
tcf(c_22046,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(X1,intersection(X2,complement(subset_relation)))) = null_class )
| ~ subclass(complement(identity_relation),null_class) ),
inference(superposition,[status(thm)],[c_12408,c_5373]) ).
tcf(c_22047,plain,
! [X0: $i,X1: $i] : intersection(X0,intersection(X1,complement(complement(null_class)))) = null_class,
inference(superposition,[status(thm)],[c_13755,c_5373]) ).
tcf(c_22052,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(iPr_def_10,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_20610,c_5373]) ).
tcf(c_22053,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(iPr_def_10,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_20608,c_5373]) ).
tcf(c_22146,plain,
( member(y,y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class ) ),
inference(demodulation,[status(thm)],[c_21442,c_193]) ).
tcf(c_22156,plain,
( member(y,cross_product(universal_class,universal_class))
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class )
| ~ function(y) ),
inference(superposition,[status(thm)],[c_22146,c_4342]) ).
tcf(c_22172,plain,
( ( unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class )
| ~ function(y) ),
inference(superposition,[status(thm)],[c_21763,c_184]) ).
tcf(c_22236,plain,
( ( unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y)))) = y )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class )
| ~ function(y) ),
inference(superposition,[status(thm)],[c_22156,c_184]) ).
tcf(c_22255,plain,
! [X0: $i] :
( compatible(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class)))),domain_of(domain_of(X0)))
| ( domain_of(y) != y ) ),
inference(superposition,[status(thm)],[c_20461,c_20809]) ).
tcf(c_22256,plain,
! [X0: $i] :
( compatible(y,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(y)
| ~ subclass(domain_of(domain_of(flip(cross_product(y,universal_class)))),domain_of(domain_of(X0))) ),
inference(equality_resolution,[status(thm)],[c_20809]) ).
tcf(c_22274,plain,
( ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class)))) = domain_of(y) )
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(domain_of(y),domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class))))) ),
inference(superposition,[status(thm)],[c_20810,c_176]) ).
tcf(c_22275,plain,
! [X0: $i] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class)))),X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(domain_of(y),X0)
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_20810,c_250]) ).
tcf(c_22276,plain,
! [X0: $i] :
( member(X0,domain_of(y))
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class))))) ),
inference(superposition,[status(thm)],[c_20810,c_170]) ).
tcf(c_22308,plain,
! [X0: $i] :
( compatible(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class)))),domain_of(domain_of(X0)))
| ( null_class != y ) ),
inference(superposition,[status(thm)],[c_5970,c_20812]) ).
tcf(c_22353,plain,
( member(not_subclass_element(complement(subset_relation),null_class),cross_product(universal_class,universal_class))
| ( complement(subset_relation) = null_class )
| ~ function(complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_8814,c_4342]) ).
tcf(c_22354,plain,
( member(not_subclass_element(complement(subset_relation),null_class),universal_class)
| ( complement(subset_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_8814,c_4336]) ).
tcf(c_22374,plain,
! [X0: $i,X1: $i] :
( homomorphism(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),unordered_pair(not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),unordered_pair(not_homomorphism2(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),not_homomorphism2(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)))),cross_product(universal_class,universal_class))
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(y)
| ~ operation(X1)
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ compatible(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1) ),
inference(superposition,[status(thm)],[c_20811,c_4342]) ).
tcf(c_22375,plain,
! [X0: $i,X1: $i] :
( homomorphism(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),unordered_pair(not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),unordered_pair(not_homomorphism2(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),not_homomorphism2(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)))),universal_class)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ operation(X1)
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ compatible(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1) ),
inference(superposition,[status(thm)],[c_20811,c_4336]) ).
tcf(c_22399,plain,
! [X0: $i] :
( subclass(y,X0)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(y,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_171,c_20672]) ).
tcf(c_22400,plain,
! [X0: $i] :
( member(not_subclass_element(X0,y),X0)
| ( X0 = y )
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(y,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_251,c_20672]) ).
tcf(c_22401,plain,
( ( null_class = y )
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(y,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_259,c_20672]) ).
tcf(c_22402,plain,
( ( null_class = y )
| ( regular(iPr_def_10) = x )
| ~ member(regular(y),iPr_def_10) ),
inference(superposition,[status(thm)],[c_222,c_20672]) ).
tcf(c_22403,plain,
( ( null_class = y )
| ( regular(iPr_def_10) = x )
| ~ member(y,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(y,y),universal_class)),universal_class))))))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_225,c_20672]) ).
tcf(c_22404,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(y,X0),X1)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(y,X0),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4224,c_20672]) ).
tcf(c_22405,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(y,X0) = null_class )
| ~ member(regular(intersection(y,X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4225,c_20672]) ).
tcf(c_22406,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,y),X1)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(X0,y),X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4245,c_20672]) ).
tcf(c_22407,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,y) = null_class )
| ~ member(regular(intersection(X0,y)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4246,c_20672]) ).
tcf(c_22408,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(y,cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),y),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4425,c_20672]) ).
tcf(c_22409,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,y),X1),X2)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(intersection(X0,y),X1),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4430,c_20672]) ).
tcf(c_22410,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(y,X0),X1),X2)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(intersection(y,X0),X1),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4431,c_20672]) ).
tcf(c_22411,plain,
! [X0: $i] :
( subclass(X0,complement(y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(X0,complement(y)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8328,c_20672]) ).
tcf(c_22412,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),y),X2)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(y,cross_product(X0,X1)),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4638,c_20672]) ).
tcf(c_22413,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,y)),X2)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(X1,y)),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4646,c_20672]) ).
tcf(c_22414,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(y,X1)),X2)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(y,X1)),X2),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4647,c_20672]) ).
tcf(c_22415,plain,
! [X0: $i] :
( subclass(complement(complement(y)),X0)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(complement(complement(y)),X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_13744,c_20672]) ).
tcf(c_22416,plain,
! [X0: $i,X1: $i] :
( homomorphism(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ operation(X1)
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ compatible(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),unordered_pair(not_homomorphism1(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),unordered_pair(not_homomorphism2(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1),not_homomorphism2(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_20811,c_20672]) ).
tcf(c_22417,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class )
| ~ member(x,iPr_def_10) ),
inference(superposition,[status(thm)],[c_21753,c_20672]) ).
tcf(c_22418,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class )
| ~ member(y,iPr_def_10) ),
inference(superposition,[status(thm)],[c_22146,c_20672]) ).
tcf(c_22468,plain,
( ( null_class = y )
| ( regular(iPr_def_10) = x )
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(y,y),universal_class)),universal_class))))))),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22403,c_4392]) ).
tcf(c_22472,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22418,c_4415]) ).
tcf(c_22476,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22417,c_4414]) ).
tcf(c_22540,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = cross_product(unordered_pair(y,y),universal_class) )
| ~ subclass(cross_product(unordered_pair(y,y),universal_class),null_class) ),
inference(superposition,[status(thm)],[c_22472,c_4722]) ).
tcf(c_22541,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(null_class,complement(cross_product(unordered_pair(y,y),universal_class))) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_12688]) ).
tcf(c_22542,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(null_class,complement(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22472,c_12625]) ).
tcf(c_22543,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(complement(cross_product(unordered_pair(y,y),universal_class)),null_class) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_11685]) ).
tcf(c_22546,plain,
! [X0: $i] :
( subclass(intersection(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_6583]) ).
tcf(c_22547,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4431]) ).
tcf(c_22548,plain,
! [X0: $i] :
( subclass(intersection(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_6065]) ).
tcf(c_22549,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4430]) ).
tcf(c_22550,plain,
( subclass(null_class,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4643]) ).
tcf(c_22551,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4245]) ).
tcf(c_22552,plain,
( subclass(null_class,cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4427]) ).
tcf(c_22553,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4224]) ).
tcf(c_22556,plain,
! [X0: $i] :
( subclass(intersection(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_11340]) ).
tcf(c_22557,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4647]) ).
tcf(c_22558,plain,
! [X0: $i] :
( subclass(intersection(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_10731]) ).
tcf(c_22559,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4646]) ).
tcf(c_22560,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_22472,c_6783]) ).
tcf(c_22561,plain,
! [X0: $i,X1: $i] :
( member(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_22472,c_6250]) ).
tcf(c_22562,plain,
! [X0: $i] :
( member(X0,null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,cross_product(unordered_pair(y,y),universal_class))
| ~ member(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22472,c_190]) ).
tcf(c_22565,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(y,y),universal_class)),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4640]) ).
tcf(c_22566,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(y,y),universal_class)),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4425]) ).
tcf(c_22567,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(cross_product(unordered_pair(y,y),universal_class),X0) ),
inference(superposition,[status(thm)],[c_22472,c_6782]) ).
tcf(c_22569,plain,
( subclass(null_class,element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_11340]) ).
tcf(c_22570,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),element_relation)
| subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4647]) ).
tcf(c_22571,plain,
( subclass(null_class,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_10731]) ).
tcf(c_22572,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_4646]) ).
tcf(c_22573,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) )
| ~ subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class) ),
inference(superposition,[status(thm)],[c_22472,c_4787]) ).
tcf(c_22574,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(complement(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_22472,c_11228]) ).
tcf(c_22575,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0) ),
inference(superposition,[status(thm)],[c_22472,c_6249]) ).
tcf(c_22577,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(cross_product(unordered_pair(y,y),universal_class),X0) ),
inference(superposition,[status(thm)],[c_22472,c_11629]) ).
tcf(c_22578,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0) ),
inference(superposition,[status(thm)],[c_22472,c_11018]) ).
tcf(c_22579,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_22472,c_11630]) ).
tcf(c_22580,plain,
! [X0: $i,X1: $i] :
( member(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_22472,c_11019]) ).
tcf(c_22585,plain,
( subclass(null_class,cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_13163]) ).
tcf(c_22626,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,cross_product(unordered_pair(y,y),universal_class))
| ~ member(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22562,c_256]) ).
tcf(c_22639,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(light_normalisation,[status(thm)],[c_22557,c_4790]) ).
tcf(c_22644,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(light_normalisation,[status(thm)],[c_22547,c_4553]) ).
tcf(c_22665,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(light_normalisation,[status(thm)],[c_22559,c_4790]) ).
tcf(c_22670,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(light_normalisation,[status(thm)],[c_22549,c_4553]) ).
tcf(c_22861,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = cross_product(unordered_pair(x,x),universal_class) )
| ~ subclass(cross_product(unordered_pair(x,x),universal_class),null_class) ),
inference(superposition,[status(thm)],[c_22476,c_4722]) ).
tcf(c_22862,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(null_class,complement(cross_product(unordered_pair(x,x),universal_class))) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_12688]) ).
tcf(c_22864,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(complement(cross_product(unordered_pair(x,x),universal_class)),null_class) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_11685]) ).
tcf(c_22867,plain,
! [X0: $i] :
( subclass(intersection(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_6583]) ).
tcf(c_22868,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_4431]) ).
tcf(c_22870,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(null_class,X0),X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_4430]) ).
tcf(c_22872,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_4245]) ).
tcf(c_22873,plain,
( subclass(null_class,cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_4427]) ).
tcf(c_22874,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_4224]) ).
tcf(c_22877,plain,
! [X0: $i] :
( subclass(intersection(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_11340]) ).
tcf(c_22878,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_4647]) ).
tcf(c_22880,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,null_class),X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_4646]) ).
tcf(c_22881,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_22476,c_6783]) ).
tcf(c_22883,plain,
! [X0: $i] :
( member(X0,null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,cross_product(unordered_pair(x,x),universal_class))
| ~ member(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22476,c_190]) ).
tcf(c_22886,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(x,x),universal_class)),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_4640]) ).
tcf(c_22887,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(x,x),universal_class)),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_4425]) ).
tcf(c_22888,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(cross_product(unordered_pair(x,x),universal_class),X0) ),
inference(superposition,[status(thm)],[c_22476,c_6782]) ).
tcf(c_22891,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),element_relation)
| subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_4647]) ).
tcf(c_22893,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_4646]) ).
tcf(c_22894,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) )
| ~ subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class) ),
inference(superposition,[status(thm)],[c_22476,c_4787]) ).
tcf(c_22898,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(cross_product(unordered_pair(x,x),universal_class),X0) ),
inference(superposition,[status(thm)],[c_22476,c_11629]) ).
tcf(c_22900,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_22476,c_11630]) ).
tcf(c_22929,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,cross_product(unordered_pair(x,x),universal_class))
| ~ member(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22883,c_256]) ).
tcf(c_22942,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(light_normalisation,[status(thm)],[c_22878,c_4790]) ).
tcf(c_22947,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(light_normalisation,[status(thm)],[c_22868,c_4553]) ).
tcf(c_22968,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(light_normalisation,[status(thm)],[c_22880,c_4790]) ).
tcf(c_22973,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(light_normalisation,[status(thm)],[c_22870,c_4553]) ).
tcf(c_23186,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(cross_product(unordered_pair(y,y),universal_class),X0) ),
inference(demodulation,[status(thm)],[c_22567,c_4553]) ).
tcf(c_23191,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),universal_class)
| subclass(intersection(cross_product(X0,X1),complement(cross_product(X0,X1))),X2) ),
inference(superposition,[status(thm)],[c_4169,c_5105]) ).
tcf(c_23192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),cross_product(X2,X3)),X4),universal_class) ),
inference(superposition,[status(thm)],[c_193,c_5105]) ).
tcf(c_23193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),X2),X3),universal_class) ),
inference(superposition,[status(thm)],[c_193,c_5105]) ).
tcf(c_23194,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),universal_class)
| subclass(intersection(cross_product(X0,X1),null_class),X2) ),
inference(superposition,[status(thm)],[c_4553,c_5105]) ).
tcf(c_23195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),X0),X3)
| member(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3),not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_5105,c_20813]) ).
tcf(c_23196,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X1,X2),X0),universal_class)
| ( intersection(X0,cross_product(X1,X2)) = universal_class )
| ~ member(not_subclass_element(universal_class,intersection(X0,cross_product(X1,X2))),intersection(X0,cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_5105,c_254]) ).
tcf(c_23197,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X1,X2),X0),universal_class)
| member(not_subclass_element(universal_class,intersection(X0,cross_product(X1,X2))),universal_class)
| ( intersection(X0,cross_product(X1,X2)) = universal_class ) ),
inference(superposition,[status(thm)],[c_5105,c_253]) ).
tcf(c_23198,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),universal_class)
| subclass(intersection(cross_product(X0,X1),X2),universal_class) ),
inference(superposition,[status(thm)],[c_5105,c_172]) ).
tcf(c_23199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),X0),X3)
| member(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_5105,c_4342]) ).
tcf(c_23201,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(universal_class),cross_product(X0,X1)),X2)
| subclass(intersection(cross_product(X0,X1),complement(universal_class)),X2) ),
inference(superposition,[status(thm)],[c_5105,c_4432]) ).
tcf(c_23206,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| subclass(intersection(cross_product(X0,X1),null_class),X2) ),
inference(light_normalisation,[status(thm)],[c_23201,c_4953]) ).
tcf(c_23238,plain,
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ function(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(superposition,[status(thm)],[c_9745,c_4342]) ).
tcf(c_23247,plain,
( ( intersection(complement(identity_relation),identity_relation) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_4169,c_11104]) ).
tcf(c_23248,plain,
! [X0: $i,X1: $i] :
( ( intersection(cross_product(X0,X1),identity_relation) = subset_relation )
| ~ subclass(subset_relation,intersection(identity_relation,cross_product(X0,X1))) ),
inference(superposition,[status(thm)],[c_193,c_11104]) ).
tcf(c_23249,plain,
( ( intersection(null_class,identity_relation) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_4553,c_11104]) ).
tcf(c_23250,plain,
( ( intersection(complement(subset_relation),identity_relation) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_11311,c_11104]) ).
tcf(c_23251,plain,
( ( intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_12282,c_11104]) ).
tcf(c_23333,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(cross_product(unordered_pair(x,x),universal_class),X0) ),
inference(demodulation,[status(thm)],[c_22888,c_4553]) ).
tcf(c_23339,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0) ),
inference(demodulation,[status(thm)],[c_22575,c_4553]) ).
tcf(c_23346,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(universal_class,X1))
| ~ function(universal_class)
| ~ member(not_subclass_element(X0,intersection(universal_class,X1)),X1) ),
inference(superposition,[status(thm)],[c_13126,c_5134]) ).
tcf(c_23347,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(universal_class,X1))
| ( unordered_pair(not_subclass_element(X0,intersection(universal_class,X1)),not_subclass_element(X0,intersection(universal_class,X1))) = null_class )
| ~ member(not_subclass_element(X0,intersection(universal_class,X1)),X1) ),
inference(superposition,[status(thm)],[c_4943,c_5134]) ).
tcf(c_23348,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,universal_class)
| subclass(X0,intersection(universal_class,X1))
| ( unordered_pair(not_subclass_element(X0,intersection(universal_class,X1)),X2) = null_class )
| ~ member(not_subclass_element(X0,intersection(universal_class,X1)),X1) ),
inference(superposition,[status(thm)],[c_266,c_5134]) ).
tcf(c_23349,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,universal_class)
| subclass(X0,intersection(universal_class,X1))
| ( unordered_pair(X2,not_subclass_element(X0,intersection(universal_class,X1))) = null_class )
| ~ member(not_subclass_element(X0,intersection(universal_class,X1)),X1) ),
inference(superposition,[status(thm)],[c_266,c_5134]) ).
tcf(c_23350,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,intersection(universal_class,X1))
| ( unordered_pair(not_subclass_element(X0,intersection(universal_class,X1)),X2) = unordered_pair(X2,X2) )
| ~ member(not_subclass_element(X0,intersection(universal_class,X1)),X1) ),
inference(superposition,[status(thm)],[c_265,c_5134]) ).
tcf(c_23351,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,intersection(universal_class,X1))
| ( unordered_pair(X2,not_subclass_element(X0,intersection(universal_class,X1))) = unordered_pair(X2,X2) )
| ~ member(not_subclass_element(X0,intersection(universal_class,X1)),X1) ),
inference(superposition,[status(thm)],[c_264,c_5134]) ).
tcf(c_23353,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(X0,X1))
| ~ member(not_subclass_element(X0,intersection(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_171,c_5134]) ).
tcf(c_23354,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(X0,X1))
| member(not_subclass_element(intersection(X0,X1),X0),intersection(X0,X1))
| ( intersection(X0,X1) = X0 )
| ~ member(not_subclass_element(X0,intersection(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_251,c_5134]) ).
tcf(c_23355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X0,intersection(intersection(X1,X2),X3))
| ~ member(not_subclass_element(X0,intersection(intersection(X1,X2),X3)),X3)
| ~ member(not_subclass_element(X0,intersection(intersection(X1,X2),X3)),X2)
| ~ member(not_subclass_element(X0,intersection(intersection(X1,X2),X3)),X1) ),
inference(superposition,[status(thm)],[c_190,c_5134]) ).
tcf(c_23356,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,intersection(complement(X1),X2))
| member(not_subclass_element(X0,intersection(complement(X1),X2)),X1)
| ~ member(not_subclass_element(X0,intersection(complement(X1),X2)),universal_class)
| ~ member(not_subclass_element(X0,intersection(complement(X1),X2)),X2) ),
inference(superposition,[status(thm)],[c_192,c_5134]) ).
tcf(c_23357,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,intersection(domain_of(X1),X2))
| ( intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,intersection(domain_of(X1),X2)),not_subclass_element(X0,intersection(domain_of(X1),X2))),universal_class)) = null_class )
| ~ member(not_subclass_element(X0,intersection(domain_of(X1),X2)),universal_class)
| ~ member(not_subclass_element(X0,intersection(domain_of(X1),X2)),X2) ),
inference(superposition,[status(thm)],[c_195,c_5134]) ).
tcf(c_23358,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),intersection(X0,X2))
| ~ member(not_subclass_element(intersection(X0,X1),intersection(X0,X2)),X2) ),
inference(superposition,[status(thm)],[c_4224,c_5134]) ).
tcf(c_23359,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),intersection(X1,X2))
| ~ member(not_subclass_element(intersection(X0,X1),intersection(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_4245,c_5134]) ).
tcf(c_23360,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X1))
| ~ member(not_subclass_element(X0,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X1)),identity_relation)
| ~ member(not_subclass_element(X0,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X1)),X1) ),
inference(superposition,[status(thm)],[c_4294,c_5134]) ).
tcf(c_23361,plain,
! [X0: $i] :
( subclass(identity_relation,intersection(subset_relation,X0))
| ~ member(not_subclass_element(identity_relation,intersection(subset_relation,X0)),X0) ),
inference(superposition,[status(thm)],[c_4305,c_5134]) ).
tcf(c_23362,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(cross_product(universal_class,universal_class),X1))
| ~ function(universal_class)
| ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),X1)),X1) ),
inference(superposition,[status(thm)],[c_13177,c_5134]) ).
tcf(c_23363,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(cross_product(universal_class,universal_class),X1))
| ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),X1)),identity_relation)
| ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),X1)),X1) ),
inference(superposition,[status(thm)],[c_7261,c_5134]) ).
tcf(c_23364,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(cross_product(universal_class,universal_class),X1))
| ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),X1)),subset_relation)
| ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),X1)),X1) ),
inference(superposition,[status(thm)],[c_6986,c_5134]) ).
tcf(c_23365,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(cross_product(universal_class,universal_class),X1))
| ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),X1)),successor_relation)
| ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),X1)),X1) ),
inference(superposition,[status(thm)],[c_4340,c_5134]) ).
tcf(c_23366,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(cross_product(universal_class,universal_class),X1))
| ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),X1)),element_relation)
| ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),X1)),X1) ),
inference(superposition,[status(thm)],[c_4337,c_5134]) ).
tcf(c_23367,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(universal_class,X1))
| ~ member(not_subclass_element(X0,intersection(universal_class,X1)),X1) ),
inference(superposition,[status(thm)],[c_4388,c_5134]) ).
tcf(c_23368,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,cross_product(X1,X2)),intersection(cross_product(X1,X2),X3))
| subclass(intersection(cross_product(X1,X2),X0),intersection(cross_product(X1,X2),X3))
| ~ member(not_subclass_element(intersection(X0,cross_product(X1,X2)),intersection(cross_product(X1,X2),X3)),X3) ),
inference(superposition,[status(thm)],[c_4424,c_5134]) ).
tcf(c_23369,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),intersection(X2,X3))
| subclass(intersection(cross_product(X0,X1),X2),intersection(X2,X3))
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),X2),intersection(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_4425,c_5134]) ).
tcf(c_23370,plain,
! [X0: $i] :
( subclass(identity_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0))
| ~ member(not_subclass_element(identity_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),X0) ),
inference(superposition,[status(thm)],[c_4447,c_5134]) ).
tcf(c_23371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,X1),X2),intersection(X1,X3))
| ~ member(not_subclass_element(intersection(intersection(X0,X1),X2),intersection(X1,X3)),X3) ),
inference(superposition,[status(thm)],[c_4430,c_5134]) ).
tcf(c_23372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,X1),X2),intersection(X0,X3))
| ~ member(not_subclass_element(intersection(intersection(X0,X1),X2),intersection(X0,X3)),X3) ),
inference(superposition,[status(thm)],[c_4431,c_5134]) ).
tcf(c_23373,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(identity_relation,X0),intersection(subset_relation,X1))
| ~ member(not_subclass_element(intersection(identity_relation,X0),intersection(subset_relation,X1)),X1) ),
inference(superposition,[status(thm)],[c_4433,c_5134]) ).
tcf(c_23374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,cross_product(X1,X2)),intersection(X0,X3))
| subclass(intersection(cross_product(X1,X2),X0),intersection(X0,X3))
| ~ member(not_subclass_element(intersection(X0,cross_product(X1,X2)),intersection(X0,X3)),X3) ),
inference(superposition,[status(thm)],[c_4638,c_5134]) ).
tcf(c_23375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),intersection(cross_product(X0,X1),X3))
| subclass(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X3))
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X3)),X3) ),
inference(superposition,[status(thm)],[c_4640,c_5134]) ).
tcf(c_23376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X3))
| ~ member(not_subclass_element(intersection(X0,intersection(X1,X2)),intersection(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_4646,c_5134]) ).
tcf(c_23377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X3))
| ~ member(not_subclass_element(intersection(X0,intersection(X1,X2)),intersection(X1,X3)),X3) ),
inference(superposition,[status(thm)],[c_4647,c_5134]) ).
tcf(c_23378,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,identity_relation),intersection(subset_relation,X1))
| ~ member(not_subclass_element(intersection(X0,identity_relation),intersection(subset_relation,X1)),X1) ),
inference(superposition,[status(thm)],[c_4649,c_5134]) ).
tcf(c_23379,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(X0)),intersection(X0,X1))
| ~ member(not_subclass_element(complement(complement(X0)),intersection(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_13744,c_5134]) ).
tcf(c_23380,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),intersection(iPr_def_10,X0))
| ~ member(not_subclass_element(unordered_pair(x,x),intersection(iPr_def_10,X0)),X0) ),
inference(superposition,[status(thm)],[c_4972,c_5134]) ).
tcf(c_23381,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X0),intersection(iPr_def_10,X1))
| ~ member(not_subclass_element(intersection(unordered_pair(x,x),X0),intersection(iPr_def_10,X1)),X1) ),
inference(superposition,[status(thm)],[c_4976,c_5134]) ).
tcf(c_23382,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(x,x)),intersection(iPr_def_10,X1))
| ~ member(not_subclass_element(intersection(X0,unordered_pair(x,x)),intersection(iPr_def_10,X1)),X1) ),
inference(superposition,[status(thm)],[c_4977,c_5134]) ).
tcf(c_23383,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),intersection(iPr_def_10,X0))
| ~ member(not_subclass_element(unordered_pair(y,y),intersection(iPr_def_10,X0)),X0) ),
inference(superposition,[status(thm)],[c_4996,c_5134]) ).
tcf(c_23384,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(y,y),X0),intersection(iPr_def_10,X1))
| ~ member(not_subclass_element(intersection(unordered_pair(y,y),X0),intersection(iPr_def_10,X1)),X1) ),
inference(superposition,[status(thm)],[c_5000,c_5134]) ).
tcf(c_23385,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,unordered_pair(y,y)),intersection(iPr_def_10,X1))
| ~ member(not_subclass_element(intersection(X0,unordered_pair(y,y)),intersection(iPr_def_10,X1)),X1) ),
inference(superposition,[status(thm)],[c_5001,c_5134]) ).
tcf(c_23386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,cross_product(X1,X2)),intersection(universal_class,X3))
| subclass(intersection(cross_product(X1,X2),X0),intersection(universal_class,X3))
| ~ member(not_subclass_element(intersection(X0,cross_product(X1,X2)),intersection(universal_class,X3)),X3) ),
inference(superposition,[status(thm)],[c_5105,c_5134]) ).
tcf(c_23387,plain,
! [X0: $i] :
( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
| ~ member(not_subclass_element(subset_relation,intersection(cross_product(universal_class,universal_class),X0)),X0) ),
inference(superposition,[status(thm)],[c_7005,c_5134]) ).
tcf(c_23388,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(complement(identity_relation),X1))
| member(not_subclass_element(X0,intersection(complement(identity_relation),X1)),subset_relation)
| ~ member(not_subclass_element(X0,intersection(complement(identity_relation),X1)),universal_class)
| ~ member(not_subclass_element(X0,intersection(complement(identity_relation),X1)),X1) ),
inference(superposition,[status(thm)],[c_8815,c_5134]) ).
tcf(c_23389,plain,
! [X0: $i] :
( subclass(complement(subset_relation),intersection(complement(identity_relation),X0))
| ~ member(not_subclass_element(complement(subset_relation),intersection(complement(identity_relation),X0)),X0) ),
inference(superposition,[status(thm)],[c_8812,c_5134]) ).
tcf(c_23390,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(complement(X1),X1))
| ~ member(not_subclass_element(X0,null_class),complement(X1))
| ~ member(not_subclass_element(X0,intersection(complement(X1),X1)),X1) ),
inference(superposition,[status(thm)],[c_4169,c_5134]) ).
tcf(c_23391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X0,intersection(cross_product(X2,X3),X1))
| ~ member(not_subclass_element(X0,intersection(cross_product(X2,X3),X1)),X1)
| ~ member(not_subclass_element(X0,intersection(X1,cross_product(X2,X3))),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_193,c_5134]) ).
tcf(c_23392,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(X1,regular(X1)))
| ( X1 = null_class )
| ~ member(not_subclass_element(X0,null_class),X1)
| ~ member(not_subclass_element(X0,intersection(X1,regular(X1))),regular(X1)) ),
inference(superposition,[status(thm)],[c_223,c_5134]) ).
tcf(c_23393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X0,intersection(X1,cross_product(X2,X3)))
| ~ member(not_subclass_element(X0,intersection(cross_product(X2,X3),X1)),X1)
| ~ member(not_subclass_element(X0,intersection(X1,cross_product(X2,X3))),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_193,c_5134]) ).
tcf(c_23394,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
| ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
inference(superposition,[status(thm)],[c_229,c_5134]) ).
tcf(c_23395,plain,
! [X0: $i] :
( subclass(X0,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation))
| ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(not_subclass_element(X0,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)),subset_relation) ),
inference(superposition,[status(thm)],[c_230,c_5134]) ).
tcf(c_23396,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(null_class,X1))
| ~ member(not_subclass_element(X0,null_class),null_class)
| ~ member(not_subclass_element(X0,intersection(null_class,X1)),X1) ),
inference(superposition,[status(thm)],[c_4553,c_5134]) ).
tcf(c_23397,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(X1,null_class))
| ~ member(not_subclass_element(X0,null_class),X1)
| ~ member(not_subclass_element(X0,intersection(X1,null_class)),null_class) ),
inference(superposition,[status(thm)],[c_4790,c_5134]) ).
tcf(c_23398,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,intersection(complement(X1),intersection(X2,X1)))
| ~ member(not_subclass_element(X0,null_class),complement(X1))
| ~ member(not_subclass_element(X0,intersection(complement(X1),intersection(X2,X1))),intersection(X2,X1)) ),
inference(superposition,[status(thm)],[c_11228,c_5134]) ).
tcf(c_23399,plain,
! [X0: $i] :
( subclass(X0,intersection(complement(subset_relation),identity_relation))
| ~ member(not_subclass_element(X0,null_class),complement(subset_relation))
| ~ member(not_subclass_element(X0,intersection(complement(subset_relation),identity_relation)),identity_relation) ),
inference(superposition,[status(thm)],[c_11311,c_5134]) ).
tcf(c_23400,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,intersection(complement(X1),intersection(X1,X2)))
| ~ member(not_subclass_element(X0,null_class),complement(X1))
| ~ member(not_subclass_element(X0,intersection(complement(X1),intersection(X1,X2))),intersection(X1,X2)) ),
inference(superposition,[status(thm)],[c_11685,c_5134]) ).
tcf(c_23401,plain,
! [X0: $i] :
( subclass(X0,intersection(complement(cross_product(universal_class,universal_class)),subset_relation))
| ~ member(not_subclass_element(X0,null_class),complement(cross_product(universal_class,universal_class)))
| ~ member(not_subclass_element(X0,intersection(complement(cross_product(universal_class,universal_class)),subset_relation)),subset_relation) ),
inference(superposition,[status(thm)],[c_11763,c_5134]) ).
tcf(c_23402,plain,
! [X0: $i] :
( subclass(X0,intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation))
| ~ member(not_subclass_element(X0,null_class),complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(not_subclass_element(X0,intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)),identity_relation) ),
inference(superposition,[status(thm)],[c_12282,c_5134]) ).
tcf(c_23403,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(X1,complement(X1)))
| ~ member(not_subclass_element(X0,null_class),X1)
| ~ member(not_subclass_element(X0,intersection(X1,complement(X1))),complement(X1)) ),
inference(superposition,[status(thm)],[c_12377,c_5134]) ).
tcf(c_23404,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,intersection(intersection(X1,X2),complement(X2)))
| ~ member(not_subclass_element(X0,null_class),intersection(X1,X2))
| ~ member(not_subclass_element(X0,intersection(intersection(X1,X2),complement(X2))),complement(X2)) ),
inference(superposition,[status(thm)],[c_12625,c_5134]) ).
tcf(c_23405,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,intersection(intersection(X1,X2),complement(X1)))
| ~ member(not_subclass_element(X0,null_class),intersection(X1,X2))
| ~ member(not_subclass_element(X0,intersection(intersection(X1,X2),complement(X1))),complement(X1)) ),
inference(superposition,[status(thm)],[c_12688,c_5134]) ).
tcf(c_23406,plain,
! [X0: $i] :
( subclass(X0,intersection(identity_relation,complement(subset_relation)))
| ~ member(not_subclass_element(X0,null_class),identity_relation)
| ~ member(not_subclass_element(X0,intersection(identity_relation,complement(subset_relation))),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_12394,c_5134]) ).
tcf(c_23407,plain,
! [X0: $i] :
( subclass(X0,intersection(subset_relation,complement(cross_product(universal_class,universal_class))))
| ~ member(not_subclass_element(X0,null_class),subset_relation)
| ~ member(not_subclass_element(X0,intersection(subset_relation,complement(cross_product(universal_class,universal_class)))),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_12738,c_5134]) ).
tcf(c_23408,plain,
! [X0: $i] :
( subclass(X0,intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))))
| ~ member(not_subclass_element(X0,null_class),identity_relation)
| ~ member(not_subclass_element(X0,intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(superposition,[status(thm)],[c_13003,c_5134]) ).
tcf(c_23409,plain,
! [X0: $i] :
( subclass(X0,intersection(unordered_pair(x,x),complement(iPr_def_10)))
| ~ member(not_subclass_element(X0,null_class),unordered_pair(x,x))
| ~ member(not_subclass_element(X0,intersection(unordered_pair(x,x),complement(iPr_def_10))),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_16614,c_5134]) ).
tcf(c_23410,plain,
! [X0: $i] :
( subclass(X0,intersection(complement(iPr_def_10),unordered_pair(x,x)))
| ~ member(not_subclass_element(X0,null_class),complement(iPr_def_10))
| ~ member(not_subclass_element(X0,intersection(complement(iPr_def_10),unordered_pair(x,x))),unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_17131,c_5134]) ).
tcf(c_23411,plain,
! [X0: $i] :
( subclass(X0,intersection(unordered_pair(y,y),complement(iPr_def_10)))
| ~ member(not_subclass_element(X0,null_class),unordered_pair(y,y))
| ~ member(not_subclass_element(X0,intersection(unordered_pair(y,y),complement(iPr_def_10))),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_18749,c_5134]) ).
tcf(c_23412,plain,
! [X0: $i] :
( subclass(X0,intersection(complement(iPr_def_10),unordered_pair(y,y)))
| ~ member(not_subclass_element(X0,null_class),complement(iPr_def_10))
| ~ member(not_subclass_element(X0,intersection(complement(iPr_def_10),unordered_pair(y,y))),unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_19300,c_5134]) ).
tcf(c_23413,plain,
! [X0: $i] :
( subclass(X0,intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(X0,null_class),iPr_def_10)
| ~ member(not_subclass_element(X0,intersection(iPr_def_10,y)),y) ),
inference(superposition,[status(thm)],[c_20574,c_5134]) ).
tcf(c_23414,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22476,c_5134]) ).
tcf(c_23415,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22472,c_5134]) ).
tcf(c_23464,plain,
! [X0: $i] :
( subclass(X0,null_class)
| ~ member(not_subclass_element(X0,null_class),identity_relation)
| ~ member(not_subclass_element(X0,null_class),complement(subset_relation)) ),
inference(light_normalisation,[status(thm)],[c_23406,c_12394]) ).
tcf(c_23512,plain,
! [X0: $i] :
( subclass(X0,null_class)
| ~ member(not_subclass_element(X0,null_class),complement(iPr_def_10))
| ~ member(not_subclass_element(X0,null_class),unordered_pair(y,y)) ),
inference(light_normalisation,[status(thm)],[c_23412,c_19300]) ).
tcf(c_23517,plain,
! [X0: $i] :
( subclass(X0,null_class)
| ~ member(not_subclass_element(X0,null_class),complement(iPr_def_10))
| ~ member(not_subclass_element(X0,null_class),unordered_pair(x,x)) ),
inference(light_normalisation,[status(thm)],[c_23410,c_17131]) ).
tcf(c_23522,plain,
! [X0: $i] :
( subclass(X0,null_class)
| ~ member(not_subclass_element(X0,null_class),subset_relation)
| ~ member(not_subclass_element(X0,null_class),complement(cross_product(universal_class,universal_class))) ),
inference(light_normalisation,[status(thm)],[c_23407,c_12738]) ).
tcf(c_23558,plain,
! [X0: $i] :
( subclass(X0,identity_relation)
| ~ member(not_subclass_element(X0,identity_relation),subset_relation)
| ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(light_normalisation,[status(thm)],[c_23395,c_230]) ).
tcf(c_23573,plain,
! [X0: $i] :
( subclass(X0,null_class)
| ~ member(not_subclass_element(X0,null_class),identity_relation)
| ~ member(not_subclass_element(X0,null_class),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(light_normalisation,[status(thm)],[c_23408,c_13003]) ).
tcf(c_23592,plain,
! [X0: $i] :
( subclass(X0,subset_relation)
| ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
| ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
inference(light_normalisation,[status(thm)],[c_23394,c_229]) ).
tcf(c_23857,plain,
( subclass(y,intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(y,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_171,c_23413]) ).
tcf(c_23858,plain,
( subclass(y,intersection(iPr_def_10,y))
| member(not_subclass_element(intersection(iPr_def_10,y),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ( intersection(iPr_def_10,y) = y )
| ~ member(not_subclass_element(y,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_251,c_23413]) ).
tcf(c_23859,plain,
! [X0: $i] :
( subclass(intersection(y,X0),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(y,X0),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4224,c_23413]) ).
tcf(c_23860,plain,
! [X0: $i] :
( subclass(intersection(X0,y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(X0,y),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4245,c_23413]) ).
tcf(c_23861,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(y,cross_product(X0,X1)),intersection(iPr_def_10,y))
| subclass(intersection(cross_product(X0,X1),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),y),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4425,c_23413]) ).
tcf(c_23862,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(X0,y),X1),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(intersection(X0,y),X1),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4430,c_23413]) ).
tcf(c_23863,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(y,X0),X1),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(intersection(y,X0),X1),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4431,c_23413]) ).
tcf(c_23864,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(y,cross_product(X0,X1)),intersection(iPr_def_10,y))
| subclass(intersection(cross_product(X0,X1),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(y,cross_product(X0,X1)),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4638,c_23413]) ).
tcf(c_23865,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(X1,y)),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(X1,y)),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4646,c_23413]) ).
tcf(c_23866,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(y,X1)),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(y,X1)),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4647,c_23413]) ).
tcf(c_23867,plain,
( subclass(complement(complement(y)),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(complement(complement(y)),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_13744,c_23413]) ).
tcf(c_23868,plain,
! [X0: $i] :
( subclass(X0,intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(X0,null_class),iPr_def_10)
| ~ member(not_subclass_element(X0,null_class),y) ),
inference(superposition,[status(thm)],[c_20574,c_23413]) ).
tcf(c_23939,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ subclass(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22570,c_176]) ).
tcf(c_23940,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),element_relation)
| subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22570,c_250]) ).
tcf(c_23941,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22570,c_170]) ).
tcf(c_23942,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22570,c_5373]) ).
tcf(c_23943,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_22570,c_5371]) ).
tcf(c_23944,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22570,c_5348]) ).
tcf(c_23945,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22570,c_5346]) ).
tcf(c_23946,plain,
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22570,c_14028]) ).
tcf(c_23947,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22570,c_5287]) ).
tcf(c_23948,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_22570,c_5257]) ).
tcf(c_23950,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22570,c_4722]) ).
tcf(c_23951,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22570,c_4787]) ).
tcf(c_24074,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ subclass(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22891,c_176]) ).
tcf(c_24075,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),element_relation)
| subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22891,c_250]) ).
tcf(c_24076,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22891,c_170]) ).
tcf(c_24077,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22891,c_5373]) ).
tcf(c_24078,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_22891,c_5371]) ).
tcf(c_24079,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22891,c_5348]) ).
tcf(c_24080,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22891,c_5346]) ).
tcf(c_24081,plain,
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22891,c_14028]) ).
tcf(c_24082,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22891,c_5287]) ).
tcf(c_24083,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_22891,c_5257]) ).
tcf(c_24085,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22891,c_4722]) ).
tcf(c_24086,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22891,c_4787]) ).
tcf(c_24174,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ subclass(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22553,c_176]) ).
tcf(c_24175,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22553,c_250]) ).
tcf(c_24176,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22553,c_170]) ).
tcf(c_24177,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22553,c_5373]) ).
tcf(c_24178,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_22553,c_5371]) ).
tcf(c_24179,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22553,c_5348]) ).
tcf(c_24180,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22553,c_5346]) ).
tcf(c_24181,plain,
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22553,c_14028]) ).
tcf(c_24182,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22553,c_5287]) ).
tcf(c_24183,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_22553,c_5257]) ).
tcf(c_24185,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22553,c_4722]) ).
tcf(c_24186,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22553,c_4787]) ).
tcf(c_24316,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(universal_class,X0)),X1)
| ~ function(universal_class)
| ~ member(not_subclass_element(complement(intersection(universal_class,X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_13126,c_5138]) ).
tcf(c_24317,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(universal_class,X0)),X1)
| ( unordered_pair(not_subclass_element(complement(intersection(universal_class,X0)),X1),not_subclass_element(complement(intersection(universal_class,X0)),X1)) = null_class )
| ~ member(not_subclass_element(complement(intersection(universal_class,X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_4943,c_5138]) ).
tcf(c_24318,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,universal_class)
| subclass(complement(intersection(universal_class,X0)),X1)
| ( unordered_pair(not_subclass_element(complement(intersection(universal_class,X0)),X1),X2) = null_class )
| ~ member(not_subclass_element(complement(intersection(universal_class,X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_266,c_5138]) ).
tcf(c_24319,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,universal_class)
| subclass(complement(intersection(universal_class,X0)),X1)
| ( unordered_pair(X2,not_subclass_element(complement(intersection(universal_class,X0)),X1)) = null_class )
| ~ member(not_subclass_element(complement(intersection(universal_class,X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_266,c_5138]) ).
tcf(c_24320,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(universal_class,X0)),X1)
| ( unordered_pair(not_subclass_element(complement(intersection(universal_class,X0)),X1),X2) = unordered_pair(X2,X2) )
| ~ member(not_subclass_element(complement(intersection(universal_class,X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_265,c_5138]) ).
tcf(c_24321,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(universal_class,X0)),X1)
| ( unordered_pair(X2,not_subclass_element(complement(intersection(universal_class,X0)),X1)) = unordered_pair(X2,X2) )
| ~ member(not_subclass_element(complement(intersection(universal_class,X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_264,c_5138]) ).
tcf(c_24322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(complement(intersection(intersection(X0,X1),X2)),X3)
| ~ member(not_subclass_element(complement(intersection(intersection(X0,X1),X2)),X3),X2)
| ~ member(not_subclass_element(complement(intersection(intersection(X0,X1),X2)),X3),X1)
| ~ member(not_subclass_element(complement(intersection(intersection(X0,X1),X2)),X3),X0) ),
inference(superposition,[status(thm)],[c_190,c_5138]) ).
tcf(c_24323,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(complement(X0),X1)),X2)
| member(not_subclass_element(complement(intersection(complement(X0),X1)),X2),X0)
| ~ member(not_subclass_element(complement(intersection(complement(X0),X1)),X2),universal_class)
| ~ member(not_subclass_element(complement(intersection(complement(X0),X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_192,c_5138]) ).
tcf(c_24324,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(domain_of(X0),X1)),X2)
| ( intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(intersection(domain_of(X0),X1)),X2),not_subclass_element(complement(intersection(domain_of(X0),X1)),X2)),universal_class)) = null_class )
| ~ member(not_subclass_element(complement(intersection(domain_of(X0),X1)),X2),universal_class)
| ~ member(not_subclass_element(complement(intersection(domain_of(X0),X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_195,c_5138]) ).
tcf(c_24325,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),X1)
| ~ member(not_subclass_element(complement(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),X1),identity_relation)
| ~ member(not_subclass_element(complement(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_4294,c_5138]) ).
tcf(c_24326,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(cross_product(universal_class,universal_class),X0)),X1)
| ~ function(universal_class)
| ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_13177,c_5138]) ).
tcf(c_24327,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(cross_product(universal_class,universal_class),X0)),X1)
| ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),X0)),X1),identity_relation)
| ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_7261,c_5138]) ).
tcf(c_24328,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(cross_product(universal_class,universal_class),X0)),X1)
| ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),X0)),X1),subset_relation)
| ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_6986,c_5138]) ).
tcf(c_24329,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(cross_product(universal_class,universal_class),X0)),X1)
| ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),X0)),X1),successor_relation)
| ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_4340,c_5138]) ).
tcf(c_24330,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(cross_product(universal_class,universal_class),X0)),X1)
| ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),X0)),X1),element_relation)
| ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_4337,c_5138]) ).
tcf(c_24331,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(universal_class,X0)),X1)
| ~ member(not_subclass_element(complement(intersection(universal_class,X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_4388,c_5138]) ).
tcf(c_24332,plain,
! [X0: $i] :
( subclass(complement(intersection(universal_class,X0)),null_class)
| ( complement(intersection(universal_class,X0)) = null_class )
| ~ member(not_subclass_element(complement(intersection(universal_class,X0)),null_class),X0) ),
inference(superposition,[status(thm)],[c_4389,c_5138]) ).
tcf(c_24333,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(X0,X1)),complement(X0))
| ~ member(not_subclass_element(complement(intersection(X0,X1)),complement(X0)),X1) ),
inference(superposition,[status(thm)],[c_8328,c_5138]) ).
tcf(c_24334,plain,
! [X0: $i] :
( subclass(complement(intersection(subset_relation,X0)),complement(identity_relation))
| ~ member(not_subclass_element(complement(intersection(subset_relation,X0)),complement(identity_relation)),X0) ),
inference(superposition,[status(thm)],[c_8344,c_5138]) ).
tcf(c_24335,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(complement(identity_relation),X0)),X1)
| member(not_subclass_element(complement(intersection(complement(identity_relation),X0)),X1),subset_relation)
| ~ member(not_subclass_element(complement(intersection(complement(identity_relation),X0)),X1),universal_class)
| ~ member(not_subclass_element(complement(intersection(complement(identity_relation),X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_8815,c_5138]) ).
tcf(c_24336,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(complement(X0),X0)),X1)
| ~ member(not_subclass_element(complement(null_class),X1),complement(X0))
| ~ member(not_subclass_element(complement(intersection(complement(X0),X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_4169,c_5138]) ).
tcf(c_24337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(complement(intersection(cross_product(X1,X2),X0)),X3)
| ~ member(not_subclass_element(complement(intersection(cross_product(X1,X2),X0)),X3),X0)
| ~ member(not_subclass_element(complement(intersection(X0,cross_product(X1,X2))),X3),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_193,c_5138]) ).
tcf(c_24338,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(X0,regular(X0))),X1)
| ( X0 = null_class )
| ~ member(not_subclass_element(complement(null_class),X1),X0)
| ~ member(not_subclass_element(complement(intersection(X0,regular(X0))),X1),regular(X0)) ),
inference(superposition,[status(thm)],[c_223,c_5138]) ).
tcf(c_24339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(complement(intersection(X0,cross_product(X1,X2))),X3)
| ~ member(not_subclass_element(complement(intersection(cross_product(X1,X2),X0)),X3),X0)
| ~ member(not_subclass_element(complement(intersection(X0,cross_product(X1,X2))),X3),cross_product(X1,X2)) ),
inference(superposition,[status(thm)],[c_193,c_5138]) ).
tcf(c_24340,plain,
! [X0: $i] :
( subclass(complement(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X0)
| ~ member(not_subclass_element(complement(subset_relation),X0),cross_product(universal_class,universal_class))
| ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
inference(superposition,[status(thm)],[c_229,c_5138]) ).
tcf(c_24341,plain,
! [X0: $i] :
( subclass(complement(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)),X0)
| ~ member(not_subclass_element(complement(identity_relation),X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(not_subclass_element(complement(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)),X0),subset_relation) ),
inference(superposition,[status(thm)],[c_230,c_5138]) ).
tcf(c_24342,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(null_class,X0)),X1)
| ~ member(not_subclass_element(complement(null_class),X1),null_class)
| ~ member(not_subclass_element(complement(intersection(null_class,X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_4553,c_5138]) ).
tcf(c_24343,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(X0,null_class)),X1)
| ~ member(not_subclass_element(complement(null_class),X1),X0)
| ~ member(not_subclass_element(complement(intersection(X0,null_class)),X1),null_class) ),
inference(superposition,[status(thm)],[c_4790,c_5138]) ).
tcf(c_24344,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(complement(X0),intersection(X1,X0))),X2)
| ~ member(not_subclass_element(complement(null_class),X2),complement(X0))
| ~ member(not_subclass_element(complement(intersection(complement(X0),intersection(X1,X0))),X2),intersection(X1,X0)) ),
inference(superposition,[status(thm)],[c_11228,c_5138]) ).
tcf(c_24345,plain,
! [X0: $i] :
( subclass(complement(intersection(complement(subset_relation),identity_relation)),X0)
| ~ member(not_subclass_element(complement(null_class),X0),complement(subset_relation))
| ~ member(not_subclass_element(complement(intersection(complement(subset_relation),identity_relation)),X0),identity_relation) ),
inference(superposition,[status(thm)],[c_11311,c_5138]) ).
tcf(c_24346,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(complement(X0),intersection(X0,X1))),X2)
| ~ member(not_subclass_element(complement(null_class),X2),complement(X0))
| ~ member(not_subclass_element(complement(intersection(complement(X0),intersection(X0,X1))),X2),intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_11685,c_5138]) ).
tcf(c_24347,plain,
! [X0: $i] :
( subclass(complement(intersection(complement(cross_product(universal_class,universal_class)),subset_relation)),X0)
| ~ member(not_subclass_element(complement(null_class),X0),complement(cross_product(universal_class,universal_class)))
| ~ member(not_subclass_element(complement(intersection(complement(cross_product(universal_class,universal_class)),subset_relation)),X0),subset_relation) ),
inference(superposition,[status(thm)],[c_11763,c_5138]) ).
tcf(c_24348,plain,
! [X0: $i] :
( subclass(complement(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)),X0)
| ~ member(not_subclass_element(complement(null_class),X0),complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(not_subclass_element(complement(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)),X0),identity_relation) ),
inference(superposition,[status(thm)],[c_12282,c_5138]) ).
tcf(c_24349,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(X0,complement(X0))),X1)
| ~ member(not_subclass_element(complement(null_class),X1),X0)
| ~ member(not_subclass_element(complement(intersection(X0,complement(X0))),X1),complement(X0)) ),
inference(superposition,[status(thm)],[c_12377,c_5138]) ).
tcf(c_24350,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(intersection(X0,X1),complement(X1))),X2)
| ~ member(not_subclass_element(complement(null_class),X2),intersection(X0,X1))
| ~ member(not_subclass_element(complement(intersection(intersection(X0,X1),complement(X1))),X2),complement(X1)) ),
inference(superposition,[status(thm)],[c_12625,c_5138]) ).
tcf(c_24351,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(intersection(X0,X1),complement(X0))),X2)
| ~ member(not_subclass_element(complement(null_class),X2),intersection(X0,X1))
| ~ member(not_subclass_element(complement(intersection(intersection(X0,X1),complement(X0))),X2),complement(X0)) ),
inference(superposition,[status(thm)],[c_12688,c_5138]) ).
tcf(c_24352,plain,
! [X0: $i] :
( subclass(complement(intersection(identity_relation,complement(subset_relation))),X0)
| ~ member(not_subclass_element(complement(null_class),X0),identity_relation)
| ~ member(not_subclass_element(complement(intersection(identity_relation,complement(subset_relation))),X0),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_12394,c_5138]) ).
tcf(c_24353,plain,
! [X0: $i] :
( subclass(complement(intersection(subset_relation,complement(cross_product(universal_class,universal_class)))),X0)
| ~ member(not_subclass_element(complement(null_class),X0),subset_relation)
| ~ member(not_subclass_element(complement(intersection(subset_relation,complement(cross_product(universal_class,universal_class)))),X0),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_12738,c_5138]) ).
tcf(c_24354,plain,
! [X0: $i] :
( subclass(complement(intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))),X0)
| ~ member(not_subclass_element(complement(null_class),X0),identity_relation)
| ~ member(not_subclass_element(complement(intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))),X0),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(superposition,[status(thm)],[c_13003,c_5138]) ).
tcf(c_24355,plain,
! [X0: $i] :
( subclass(complement(intersection(unordered_pair(x,x),complement(iPr_def_10))),X0)
| ~ member(not_subclass_element(complement(null_class),X0),unordered_pair(x,x))
| ~ member(not_subclass_element(complement(intersection(unordered_pair(x,x),complement(iPr_def_10))),X0),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_16614,c_5138]) ).
tcf(c_24356,plain,
! [X0: $i] :
( subclass(complement(intersection(complement(iPr_def_10),unordered_pair(x,x))),X0)
| ~ member(not_subclass_element(complement(null_class),X0),complement(iPr_def_10))
| ~ member(not_subclass_element(complement(intersection(complement(iPr_def_10),unordered_pair(x,x))),X0),unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_17131,c_5138]) ).
tcf(c_24357,plain,
! [X0: $i] :
( subclass(complement(intersection(unordered_pair(y,y),complement(iPr_def_10))),X0)
| ~ member(not_subclass_element(complement(null_class),X0),unordered_pair(y,y))
| ~ member(not_subclass_element(complement(intersection(unordered_pair(y,y),complement(iPr_def_10))),X0),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_18749,c_5138]) ).
tcf(c_24358,plain,
! [X0: $i] :
( subclass(complement(intersection(complement(iPr_def_10),unordered_pair(y,y))),X0)
| ~ member(not_subclass_element(complement(null_class),X0),complement(iPr_def_10))
| ~ member(not_subclass_element(complement(intersection(complement(iPr_def_10),unordered_pair(y,y))),X0),unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_19300,c_5138]) ).
tcf(c_24359,plain,
! [X0: $i] :
( subclass(complement(intersection(iPr_def_10,y)),X0)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(complement(null_class),X0),iPr_def_10)
| ~ member(not_subclass_element(complement(intersection(iPr_def_10,y)),X0),y) ),
inference(superposition,[status(thm)],[c_20574,c_5138]) ).
tcf(c_24360,plain,
! [X0: $i] :
( subclass(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(complement(null_class),X0),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22476,c_5138]) ).
tcf(c_24361,plain,
! [X0: $i] :
( subclass(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(complement(null_class),X0),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22472,c_5138]) ).
tcf(c_24371,plain,
! [X0: $i,X1: $i] :
( subclass(universal_class,X0)
| ~ member(not_subclass_element(universal_class,X0),null_class)
| ~ member(not_subclass_element(universal_class,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_24343,c_4790,c_8703]) ).
tcf(c_24379,plain,
! [X0: $i] :
( subclass(universal_class,X0)
| ~ member(not_subclass_element(universal_class,X0),identity_relation)
| ~ member(not_subclass_element(universal_class,X0),complement(subset_relation)) ),
inference(light_normalisation,[status(thm)],[c_24352,c_8703,c_12394]) ).
tcf(c_24383,plain,
! [X0: $i,X1: $i] :
( subclass(universal_class,X0)
| ~ member(not_subclass_element(universal_class,X0),X1)
| ~ member(not_subclass_element(universal_class,X0),complement(X1)) ),
inference(light_normalisation,[status(thm)],[c_24349,c_8703,c_12377]) ).
tcf(c_24389,plain,
! [X0: $i] :
( subclass(complement(intersection(iPr_def_10,y)),X0)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(universal_class,X0),iPr_def_10)
| ~ member(not_subclass_element(complement(intersection(iPr_def_10,y)),X0),y) ),
inference(light_normalisation,[status(thm)],[c_24359,c_8703]) ).
tcf(c_24400,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(X0,regular(X0))),X1)
| ( X0 = null_class )
| ~ member(not_subclass_element(universal_class,X1),X0)
| ~ member(not_subclass_element(complement(intersection(X0,regular(X0))),X1),regular(X0)) ),
inference(light_normalisation,[status(thm)],[c_24338,c_8703]) ).
tcf(c_24425,plain,
! [X0: $i] :
( subclass(universal_class,X0)
| ~ member(not_subclass_element(universal_class,X0),complement(iPr_def_10))
| ~ member(not_subclass_element(universal_class,X0),unordered_pair(y,y)) ),
inference(light_normalisation,[status(thm)],[c_24358,c_8703,c_19300]) ).
tcf(c_24430,plain,
! [X0: $i] :
( subclass(universal_class,X0)
| ~ member(not_subclass_element(universal_class,X0),complement(iPr_def_10))
| ~ member(not_subclass_element(universal_class,X0),unordered_pair(x,x)) ),
inference(light_normalisation,[status(thm)],[c_24356,c_8703,c_17131]) ).
tcf(c_24435,plain,
! [X0: $i] :
( subclass(universal_class,X0)
| ~ member(not_subclass_element(universal_class,X0),subset_relation)
| ~ member(not_subclass_element(universal_class,X0),complement(cross_product(universal_class,universal_class))) ),
inference(light_normalisation,[status(thm)],[c_24353,c_8703,c_12738]) ).
tcf(c_24439,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(universal_class,X0)
| ~ member(not_subclass_element(universal_class,X0),complement(X1))
| ~ member(not_subclass_element(universal_class,X0),intersection(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_24351,c_8703,c_12688]) ).
tcf(c_24443,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(universal_class,X0)
| ~ member(not_subclass_element(universal_class,X0),complement(X2))
| ~ member(not_subclass_element(universal_class,X0),intersection(X1,X2)) ),
inference(light_normalisation,[status(thm)],[c_24350,c_8703,c_12625]) ).
tcf(c_24459,plain,
! [X0: $i] :
( subclass(complement(identity_relation),X0)
| ~ member(not_subclass_element(complement(identity_relation),X0),subset_relation)
| ~ member(not_subclass_element(complement(identity_relation),X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(light_normalisation,[status(thm)],[c_24341,c_230]) ).
tcf(c_24474,plain,
! [X0: $i] :
( subclass(universal_class,X0)
| ~ member(not_subclass_element(universal_class,X0),identity_relation)
| ~ member(not_subclass_element(universal_class,X0),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(light_normalisation,[status(thm)],[c_24354,c_8703,c_13003]) ).
tcf(c_24487,plain,
! [X0: $i] :
( subclass(complement(subset_relation),X0)
| ~ member(not_subclass_element(complement(subset_relation),X0),cross_product(universal_class,universal_class))
| ~ member(not_subclass_element(complement(subset_relation),X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
inference(light_normalisation,[status(thm)],[c_24340,c_229]) ).
tcf(c_24491,plain,
! [X0: $i] :
( subclass(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(universal_class,X0),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(light_normalisation,[status(thm)],[c_24361,c_8703]) ).
tcf(c_24497,plain,
! [X0: $i] :
( subclass(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(universal_class,X0),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(light_normalisation,[status(thm)],[c_24360,c_8703]) ).
tcf(c_24848,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X0)
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(demodulation,[status(thm)],[c_6917,c_4169]) ).
tcf(c_24859,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ subclass(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22874,c_176]) ).
tcf(c_24860,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22874,c_250]) ).
tcf(c_24861,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22874,c_170]) ).
tcf(c_24862,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22874,c_5373]) ).
tcf(c_24863,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_22874,c_5371]) ).
tcf(c_24864,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22874,c_5348]) ).
tcf(c_24865,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22874,c_5346]) ).
tcf(c_24866,plain,
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22874,c_14028]) ).
tcf(c_24867,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22874,c_5287]) ).
tcf(c_24868,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_22874,c_5257]) ).
tcf(c_24870,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22874,c_4722]) ).
tcf(c_24871,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22874,c_4787]) ).
tcf(c_24959,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ subclass(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22572,c_176]) ).
tcf(c_24960,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22572,c_250]) ).
tcf(c_24961,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22572,c_170]) ).
tcf(c_24962,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22572,c_5373]) ).
tcf(c_24963,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_22572,c_5371]) ).
tcf(c_24964,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22572,c_5348]) ).
tcf(c_24965,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22572,c_5346]) ).
tcf(c_24966,plain,
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22572,c_14028]) ).
tcf(c_24967,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22572,c_5287]) ).
tcf(c_24968,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_22572,c_5257]) ).
tcf(c_24970,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22572,c_4722]) ).
tcf(c_24971,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22572,c_4787]) ).
tcf(c_25042,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ subclass(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22893,c_176]) ).
tcf(c_25043,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22893,c_250]) ).
tcf(c_25044,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22893,c_170]) ).
tcf(c_25045,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22893,c_5373]) ).
tcf(c_25046,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_22893,c_5371]) ).
tcf(c_25047,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22893,c_5348]) ).
tcf(c_25048,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22893,c_5346]) ).
tcf(c_25049,plain,
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22893,c_14028]) ).
tcf(c_25050,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22893,c_5287]) ).
tcf(c_25051,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_22893,c_5257]) ).
tcf(c_25053,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22893,c_4722]) ).
tcf(c_25054,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22893,c_4787]) ).
tcf(c_25162,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ subclass(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22551,c_176]) ).
tcf(c_25163,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22551,c_250]) ).
tcf(c_25164,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22551,c_170]) ).
tcf(c_25165,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22551,c_5373]) ).
tcf(c_25166,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_22551,c_5371]) ).
tcf(c_25167,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22551,c_5348]) ).
tcf(c_25168,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22551,c_5346]) ).
tcf(c_25169,plain,
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22551,c_14028]) ).
tcf(c_25170,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22551,c_5287]) ).
tcf(c_25171,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_22551,c_5257]) ).
tcf(c_25173,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22551,c_4722]) ).
tcf(c_25174,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22551,c_4787]) ).
tcf(c_25269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,X2),X3)
| member(not_subclass_element(intersection(X0,X2),X3),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_171,c_5256]) ).
tcf(c_25270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(X3,intersection(X0,X2)),X3)
| member(not_subclass_element(intersection(X0,X2),X3),X1)
| ( intersection(X0,X2) = X3 )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_251,c_5256]) ).
tcf(c_25271,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,X2),null_class),X1)
| ( intersection(X0,X2) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_259,c_5256]) ).
tcf(c_25272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| ~ subclass(X1,X3)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_190,c_5256]) ).
tcf(c_25273,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(X0,X2)),X1)
| ( intersection(X0,X2) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_5256]) ).
tcf(c_25274,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2)
| ( intersection(X0,X1) = null_class )
| ~ subclass(X0,X2)
| ~ member(intersection(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_5256]) ).
tcf(c_25275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,X2),X3),X4)
| member(not_subclass_element(intersection(intersection(X0,X2),X3),X4),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4224,c_5256]) ).
tcf(c_25276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(intersection(X0,X2),X3)),X1)
| ( intersection(intersection(X0,X2),X3) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4225,c_5256]) ).
tcf(c_25277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X2,intersection(X0,X3)),X4)
| member(not_subclass_element(intersection(X2,intersection(X0,X3)),X4),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4245,c_5256]) ).
tcf(c_25278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(X2,intersection(X0,X3))),X1)
| ( intersection(X2,intersection(X0,X3)) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4246,c_5256]) ).
tcf(c_25279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X0,X4),cross_product(X2,X3)),X5)
| member(not_subclass_element(intersection(cross_product(X2,X3),intersection(X0,X4)),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4425,c_5256]) ).
tcf(c_25280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X2,intersection(X0,X3)),X4),X5)
| member(not_subclass_element(intersection(intersection(X2,intersection(X0,X3)),X4),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4430,c_5256]) ).
tcf(c_25281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(X0,X2),X3),X4),X5)
| member(not_subclass_element(intersection(intersection(intersection(X0,X2),X3),X4),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4431,c_5256]) ).
tcf(c_25282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X2,complement(intersection(X0,X3)))
| member(not_subclass_element(X2,complement(intersection(X0,X3))),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_8328,c_5256]) ).
tcf(c_25283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(cross_product(X3,X4),intersection(X0,X2)),X5)
| member(not_subclass_element(intersection(intersection(X0,X2),cross_product(X3,X4)),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4638,c_5256]) ).
tcf(c_25284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X2,intersection(X3,intersection(X0,X4))),X5)
| member(not_subclass_element(intersection(X2,intersection(X3,intersection(X0,X4))),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4646,c_5256]) ).
tcf(c_25285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X2,intersection(intersection(X0,X3),X4)),X5)
| member(not_subclass_element(intersection(X2,intersection(intersection(X0,X3),X4)),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4647,c_5256]) ).
tcf(c_25286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(complement(complement(intersection(X0,X2))),X3)
| member(not_subclass_element(complement(complement(intersection(X0,X2))),X3),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13744,c_5256]) ).
tcf(c_25288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X4)
| ~ subclass(cross_product(X2,X3),X4)
| ~ member(X0,intersection(X1,cross_product(X2,X3))) ),
inference(superposition,[status(thm)],[c_193,c_5256]) ).
tcf(c_25289,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ( X0 = null_class )
| ~ member(X2,null_class)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_223,c_5256]) ).
tcf(c_25290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X4)
| ~ subclass(X3,X4)
| ~ member(X0,intersection(cross_product(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_193,c_5256]) ).
tcf(c_25291,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ~ member(X1,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_229,c_5256]) ).
tcf(c_25292,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ~ member(X1,identity_relation)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ),
inference(superposition,[status(thm)],[c_230,c_5256]) ).
tcf(c_25296,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ~ member(X1,null_class)
| ~ subclass(complement(subset_relation),X0) ),
inference(superposition,[status(thm)],[c_11311,c_5256]) ).
tcf(c_25297,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,null_class)
| ~ subclass(complement(X0),X1) ),
inference(superposition,[status(thm)],[c_11685,c_5256]) ).
tcf(c_25298,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ~ member(X1,null_class)
| ~ subclass(complement(cross_product(universal_class,universal_class)),X0) ),
inference(superposition,[status(thm)],[c_11763,c_5256]) ).
tcf(c_25299,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ~ member(X1,null_class)
| ~ subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) ),
inference(superposition,[status(thm)],[c_12282,c_5256]) ).
tcf(c_25300,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,null_class)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_12377,c_5256]) ).
tcf(c_25301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X2)
| ~ member(X3,null_class)
| ~ subclass(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_12625,c_5256]) ).
tcf(c_25306,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ~ member(X1,null_class)
| ~ subclass(unordered_pair(x,x),X0) ),
inference(superposition,[status(thm)],[c_16614,c_5256]) ).
tcf(c_25308,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ~ member(X1,null_class)
| ~ subclass(unordered_pair(y,y),X0) ),
inference(superposition,[status(thm)],[c_18749,c_5256]) ).
tcf(c_25309,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ~ member(X1,null_class)
| ~ subclass(complement(iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_19300,c_5256]) ).
tcf(c_25311,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X1,null_class)
| ~ subclass(cross_product(unordered_pair(x,x),universal_class),X0) ),
inference(superposition,[status(thm)],[c_22476,c_5256]) ).
tcf(c_25312,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X1,null_class)
| ~ subclass(cross_product(unordered_pair(y,y),universal_class),X0) ),
inference(superposition,[status(thm)],[c_22472,c_5256]) ).
tcf(c_25469,plain,
! [X0: $i] :
( member(not_subclass_element(universal_class,X0),universal_class)
| ( X0 = universal_class ) ),
inference(global_subsumption_just,[status(thm)],[c_13175,c_4708,c_13785]) ).
tcf(c_25475,plain,
! [X0: $i] :
( member(not_subclass_element(universal_class,X0),y)
| ( X0 = universal_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(universal_class,X0),not_subclass_element(universal_class,X0)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_25469,c_20813]) ).
tcf(c_25479,plain,
! [X0: $i] :
( member(not_subclass_element(universal_class,X0),cross_product(universal_class,universal_class))
| ( X0 = universal_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_25469,c_4342]) ).
tcf(c_25481,plain,
! [X0: $i] :
( subclass(universal_class,intersection(universal_class,X0))
| ( intersection(universal_class,X0) = universal_class )
| ~ member(not_subclass_element(universal_class,intersection(universal_class,X0)),X0) ),
inference(superposition,[status(thm)],[c_25469,c_5134]) ).
tcf(c_25498,plain,
( ( complement(complement(unordered_pair(x,x))) = unordered_pair(x,x) )
| ~ subclass(iPr_def_10,complement(complement(unordered_pair(x,x)))) ),
inference(superposition,[status(thm)],[c_4500,c_13998]) ).
tcf(c_25499,plain,
( ( complement(complement(unordered_pair(y,y))) = unordered_pair(y,y) )
| ~ subclass(iPr_def_10,complement(complement(unordered_pair(y,y)))) ),
inference(superposition,[status(thm)],[c_4501,c_13998]) ).
tcf(c_25500,plain,
! [X0: $i,X1: $i] :
( ( complement(complement(intersection(X0,X1))) = intersection(X0,X1) )
| ~ subclass(X0,complement(complement(intersection(X0,X1)))) ),
inference(superposition,[status(thm)],[c_4551,c_13998]) ).
tcf(c_25501,plain,
! [X0: $i,X1: $i] :
( ( complement(complement(intersection(X1,X0))) = intersection(X1,X0) )
| ~ subclass(X0,complement(complement(intersection(X1,X0)))) ),
inference(superposition,[status(thm)],[c_4788,c_13998]) ).
tcf(c_25502,plain,
! [X0: $i] :
( ( complement(complement(complement(complement(X0)))) = complement(complement(X0)) )
| ~ subclass(X0,complement(complement(complement(complement(X0))))) ),
inference(superposition,[status(thm)],[c_13999,c_13998]) ).
tcf(c_25503,plain,
( ( complement(complement(complement(cross_product(universal_class,universal_class)))) = complement(cross_product(universal_class,universal_class)) )
| ~ subclass(complement(element_relation),complement(complement(complement(cross_product(universal_class,universal_class))))) ),
inference(superposition,[status(thm)],[c_15325,c_13998]) ).
tcf(c_25504,plain,
( ( complement(complement(complement(cross_product(universal_class,universal_class)))) = complement(cross_product(universal_class,universal_class)) )
| ~ subclass(complement(successor_relation),complement(complement(complement(cross_product(universal_class,universal_class))))) ),
inference(superposition,[status(thm)],[c_14988,c_13998]) ).
tcf(c_25505,plain,
( ( complement(complement(complement(cross_product(universal_class,universal_class)))) = complement(cross_product(universal_class,universal_class)) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13276,c_13998]) ).
tcf(c_25506,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( complement(complement(intersection(intersection(X1,X0),X2))) = intersection(intersection(X1,X0),X2) )
| ~ subclass(X0,complement(complement(intersection(intersection(X1,X0),X2)))) ),
inference(superposition,[status(thm)],[c_6249,c_13998]) ).
tcf(c_25507,plain,
! [X0: $i] :
( ( complement(complement(intersection(identity_relation,X0))) = intersection(identity_relation,X0) )
| ~ subclass(subset_relation,complement(complement(intersection(identity_relation,X0)))) ),
inference(superposition,[status(thm)],[c_6317,c_13998]) ).
tcf(c_25508,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( complement(complement(intersection(intersection(X0,X1),X2))) = intersection(intersection(X0,X1),X2) )
| ~ subclass(X0,complement(complement(intersection(intersection(X0,X1),X2)))) ),
inference(superposition,[status(thm)],[c_6782,c_13998]) ).
tcf(c_25509,plain,
! [X0: $i] :
( ( complement(complement(intersection(complement(cross_product(universal_class,universal_class)),X0))) = intersection(complement(cross_product(universal_class,universal_class)),X0) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_13998]) ).
tcf(c_25510,plain,
( ( complement(complement(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))) = domain_of(domain_of(flip(cross_product(null_class,universal_class)))) )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_13998]) ).
tcf(c_25511,plain,
! [X0: $i] :
( ( complement(complement(intersection(complement(subset_relation),X0))) = intersection(complement(subset_relation),X0) )
| ~ subclass(complement(identity_relation),complement(complement(intersection(complement(subset_relation),X0)))) ),
inference(superposition,[status(thm)],[c_8784,c_13998]) ).
tcf(c_25512,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( complement(complement(intersection(X1,intersection(X2,X0)))) = intersection(X1,intersection(X2,X0)) )
| ~ subclass(X0,complement(complement(intersection(X1,intersection(X2,X0))))) ),
inference(superposition,[status(thm)],[c_11018,c_13998]) ).
tcf(c_25513,plain,
! [X0: $i] :
( ( complement(complement(intersection(X0,identity_relation))) = intersection(X0,identity_relation) )
| ~ subclass(subset_relation,complement(complement(intersection(X0,identity_relation)))) ),
inference(superposition,[status(thm)],[c_11105,c_13998]) ).
tcf(c_25514,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( complement(complement(intersection(X1,intersection(X0,X2)))) = intersection(X1,intersection(X0,X2)) )
| ~ subclass(X0,complement(complement(intersection(X1,intersection(X0,X2))))) ),
inference(superposition,[status(thm)],[c_11629,c_13998]) ).
tcf(c_25515,plain,
! [X0: $i] :
( ( complement(complement(intersection(X0,complement(cross_product(universal_class,universal_class))))) = intersection(X0,complement(cross_product(universal_class,universal_class))) )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_13998]) ).
tcf(c_25516,plain,
! [X0: $i] :
( ( complement(complement(intersection(X0,complement(subset_relation)))) = intersection(X0,complement(subset_relation)) )
| ~ subclass(complement(identity_relation),complement(complement(intersection(X0,complement(subset_relation))))) ),
inference(superposition,[status(thm)],[c_12408,c_13998]) ).
tcf(c_25517,plain,
! [X0: $i] :
( ( complement(complement(intersection(unordered_pair(x,x),X0))) = intersection(unordered_pair(x,x),X0) )
| ~ subclass(iPr_def_10,complement(complement(intersection(unordered_pair(x,x),X0)))) ),
inference(superposition,[status(thm)],[c_16597,c_13998]) ).
tcf(c_25518,plain,
! [X0: $i] :
( ( complement(complement(intersection(X0,unordered_pair(x,x)))) = intersection(X0,unordered_pair(x,x)) )
| ~ subclass(iPr_def_10,complement(complement(intersection(X0,unordered_pair(x,x))))) ),
inference(superposition,[status(thm)],[c_17097,c_13998]) ).
tcf(c_25519,plain,
! [X0: $i] :
( ( complement(complement(intersection(unordered_pair(y,y),X0))) = intersection(unordered_pair(y,y),X0) )
| ~ subclass(iPr_def_10,complement(complement(intersection(unordered_pair(y,y),X0)))) ),
inference(superposition,[status(thm)],[c_18573,c_13998]) ).
tcf(c_25520,plain,
! [X0: $i] :
( ( complement(complement(intersection(X0,unordered_pair(y,y)))) = intersection(X0,unordered_pair(y,y)) )
| ~ subclass(iPr_def_10,complement(complement(intersection(X0,unordered_pair(y,y))))) ),
inference(superposition,[status(thm)],[c_19010,c_13998]) ).
tcf(c_25521,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(iPr_def_10,y)))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(iPr_def_10,y))) = intersection(iPr_def_10,y) ) ),
inference(superposition,[status(thm)],[c_20610,c_13998]) ).
tcf(c_25522,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(iPr_def_10,y)))),y)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(iPr_def_10,y))) = intersection(iPr_def_10,y) ) ),
inference(superposition,[status(thm)],[c_20608,c_13998]) ).
tcf(c_25523,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22551,c_13998]) ).
tcf(c_25524,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))))),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22572,c_13998]) ).
tcf(c_25525,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))))),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22553,c_13998]) ).
tcf(c_25526,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))))),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22570,c_13998]) ).
tcf(c_25527,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))))),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22893,c_13998]) ).
tcf(c_25528,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))))),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22874,c_13998]) ).
tcf(c_25529,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))))),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22891,c_13998]) ).
tcf(c_25530,plain,
( ( complement(complement(universal_class)) = universal_class )
| ~ subclass(universal_class,complement(null_class)) ),
inference(superposition,[status(thm)],[c_4953,c_13998]) ).
tcf(c_25531,plain,
( ( complement(complement(null_class)) = null_class )
| ~ subclass(null_class,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_8703,c_13998]) ).
tcf(c_25831,plain,
( member(regular(null_class),subset_relation)
| ( intersection(complement(identity_relation),identity_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_4169,c_9850]) ).
tcf(c_25832,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(identity_relation,cross_product(X0,X1))),subset_relation)
| ( intersection(cross_product(X0,X1),identity_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_193,c_9850]) ).
tcf(c_25833,plain,
( member(regular(null_class),subset_relation)
| ( intersection(null_class,identity_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_4553,c_9850]) ).
tcf(c_25836,plain,
! [X0: $i] :
( member(regular(intersection(X0,identity_relation)),cross_product(universal_class,universal_class))
| ( intersection(X0,identity_relation) = null_class )
| ~ function(subset_relation) ),
inference(superposition,[status(thm)],[c_9850,c_4342]) ).
tcf(c_25837,plain,
! [X0: $i] :
( member(regular(intersection(X0,identity_relation)),universal_class)
| ( intersection(X0,identity_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_9850,c_4336]) ).
tcf(c_25858,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ subclass(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22872,c_176]) ).
tcf(c_25859,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22872,c_250]) ).
tcf(c_25860,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22872,c_170]) ).
tcf(c_25861,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22872,c_5373]) ).
tcf(c_25862,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_22872,c_5371]) ).
tcf(c_25863,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22872,c_5348]) ).
tcf(c_25864,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_22872,c_5346]) ).
tcf(c_25865,plain,
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22872,c_14028]) ).
tcf(c_25866,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_22872,c_5287]) ).
tcf(c_25867,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_22872,c_5257]) ).
tcf(c_25869,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22872,c_4722]) ).
tcf(c_25870,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22872,c_4787]) ).
tcf(c_25871,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_22872,c_13998]) ).
tcf(c_26007,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) )
| ~ subclass(element_relation,null_class) ),
inference(superposition,[status(thm)],[c_4551,c_22573]) ).
tcf(c_26008,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) )
| ~ subclass(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))),null_class) ),
inference(superposition,[status(thm)],[c_4788,c_22573]) ).
tcf(c_26025,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) )
| ~ subclass(element_relation,null_class) ),
inference(superposition,[status(thm)],[c_4551,c_22894]) ).
tcf(c_26026,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) )
| ~ subclass(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))),null_class) ),
inference(superposition,[status(thm)],[c_4788,c_22894]) ).
tcf(c_26046,plain,
( subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_23414]) ).
tcf(c_26047,plain,
( subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| member(not_subclass_element(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_251,c_23414]) ).
tcf(c_26048,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),element_relation)
| ~ member(not_subclass_element(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) ),
inference(superposition,[status(thm)],[c_190,c_23414]) ).
tcf(c_26049,plain,
! [X0: $i] :
( subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_23414]) ).
tcf(c_26050,plain,
! [X0: $i] :
( subclass(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_23414]) ).
tcf(c_26051,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_23414]) ).
tcf(c_26052,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_23414]) ).
tcf(c_26053,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),X1),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),X1),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_23414]) ).
tcf(c_26054,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_23414]) ).
tcf(c_26055,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(X1,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(X1,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_23414]) ).
tcf(c_26056,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_23414]) ).
tcf(c_26057,plain,
( subclass(complement(complement(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(complement(complement(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_23414]) ).
tcf(c_26058,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22476,c_23414]) ).
tcf(c_26225,plain,
! [X0: $i] :
( subclass(X0,null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22476,c_26058]) ).
tcf(c_26226,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) ),
inference(superposition,[status(thm)],[c_26058,c_176]) ).
tcf(c_26227,plain,
! [X0: $i,X1: $i] :
( subclass(X1,X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X1,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X1,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) ),
inference(superposition,[status(thm)],[c_26058,c_250]) ).
tcf(c_26228,plain,
! [X0: $i,X1: $i] :
( member(X1,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X1,X0)
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_170]) ).
tcf(c_26229,plain,
( subclass(omega,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(null_class,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),universal_class)),universal_class)))),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),universal_class)),universal_class)))),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_1547]) ).
tcf(c_26230,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = universal_class )
| ~ member(not_subclass_element(universal_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(universal_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4708]) ).
tcf(c_26231,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(universal_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(universal_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4490]) ).
tcf(c_26232,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(universal_class)
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4617]) ).
tcf(c_26233,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(X0)
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4496]) ).
tcf(c_26234,plain,
( subclass(complement(complement(successor_relation)),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_14231]) ).
tcf(c_26235,plain,
( subclass(complement(complement(element_relation)),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_14220]) ).
tcf(c_26236,plain,
! [X0: $i] :
( subclass(intersection(X0,successor_relation),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_13551]) ).
tcf(c_26237,plain,
! [X0: $i] :
( subclass(intersection(successor_relation,X0),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_13536]) ).
tcf(c_26238,plain,
! [X0: $i] :
( subclass(intersection(X0,element_relation),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_13247]) ).
tcf(c_26239,plain,
! [X0: $i] :
( subclass(intersection(element_relation,X0),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_13232]) ).
tcf(c_26240,plain,
! [X0: $i] :
( subclass(intersection(X0,subset_relation),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_11655]) ).
tcf(c_26241,plain,
! [X0: $i] :
( subclass(intersection(subset_relation,X0),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_7273]) ).
tcf(c_26242,plain,
( subclass(identity_relation,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_7260]) ).
tcf(c_26243,plain,
( subclass(subset_relation,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_6988]) ).
tcf(c_26244,plain,
! [X0: $i,X1: $i] :
( subclass(compose(X0,X1),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4495]) ).
tcf(c_26245,plain,
( subclass(successor_relation,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4494]) ).
tcf(c_26246,plain,
( subclass(element_relation,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4491]) ).
tcf(c_26247,plain,
! [X0: $i] :
( subclass(flip(X0),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4493]) ).
tcf(c_26248,plain,
! [X0: $i] :
( subclass(rotate(X0),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4492]) ).
tcf(c_26249,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(X1,X1),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(unordered_pair(X0,X1),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(unordered_pair(X0,X1),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4498]) ).
tcf(c_26250,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(X0,X0),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(unordered_pair(X0,X1),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(unordered_pair(X0,X1),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4497]) ).
tcf(c_26251,plain,
( member(y,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(iPr_def_10,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_20134]) ).
tcf(c_26252,plain,
( member(x,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(iPr_def_10,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_19428]) ).
tcf(c_26253,plain,
( subclass(identity_relation,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(subset_relation,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(subset_relation,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4502]) ).
tcf(c_26254,plain,
( subclass(identity_relation,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4592]) ).
tcf(c_26255,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = cross_product(unordered_pair(x,x),universal_class) )
| ~ member(not_subclass_element(cross_product(unordered_pair(x,x),universal_class),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(cross_product(unordered_pair(x,x),universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4722]) ).
tcf(c_26256,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_4787]) ).
tcf(c_26257,plain,
( subclass(complement(subset_relation),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(complement(identity_relation),null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(complement(identity_relation),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_8770]) ).
tcf(c_26524,plain,
( member(y,null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(iPr_def_10,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22476,c_26251]) ).
tcf(c_26539,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(iPr_def_10,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26524,c_256]) ).
tcf(c_26551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,X0),X3)
| member(not_subclass_element(intersection(X2,X0),X3),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_171,c_5286]) ).
tcf(c_26552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(X3,intersection(X2,X0)),X3)
| member(not_subclass_element(intersection(X2,X0),X3),X1)
| ( intersection(X2,X0) = X3 )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_251,c_5286]) ).
tcf(c_26553,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X2,X0),null_class),X1)
| ( intersection(X2,X0) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_259,c_5286]) ).
tcf(c_26554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| ~ subclass(X2,X3)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_190,c_5286]) ).
tcf(c_26555,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(X2,X0)),X1)
| ( intersection(X2,X0) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_5286]) ).
tcf(c_26556,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2)
| ( intersection(X0,X1) = null_class )
| ~ subclass(X1,X2)
| ~ member(intersection(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_225,c_5286]) ).
tcf(c_26557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,X0),X3),X4)
| member(not_subclass_element(intersection(intersection(X2,X0),X3),X4),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4224,c_5286]) ).
tcf(c_26558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(intersection(X2,X0),X3)),X1)
| ( intersection(intersection(X2,X0),X3) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4225,c_5286]) ).
tcf(c_26559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(X2,intersection(X3,X0)),X4)
| member(not_subclass_element(intersection(X2,intersection(X3,X0)),X4),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4245,c_5286]) ).
tcf(c_26560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(regular(intersection(X2,intersection(X3,X0))),X1)
| ( intersection(X2,intersection(X3,X0)) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4246,c_5286]) ).
tcf(c_26561,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X4,X0),cross_product(X2,X3)),X5)
| member(not_subclass_element(intersection(cross_product(X2,X3),intersection(X4,X0)),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4425,c_5286]) ).
tcf(c_26562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X2,intersection(X3,X0)),X4),X5)
| member(not_subclass_element(intersection(intersection(X2,intersection(X3,X0)),X4),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4430,c_5286]) ).
tcf(c_26563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(X2,X0),X3),X4),X5)
| member(not_subclass_element(intersection(intersection(intersection(X2,X0),X3),X4),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4431,c_5286]) ).
tcf(c_26564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X2,complement(intersection(X3,X0)))
| member(not_subclass_element(X2,complement(intersection(X3,X0))),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_8328,c_5286]) ).
tcf(c_26565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(cross_product(X3,X4),intersection(X2,X0)),X5)
| member(not_subclass_element(intersection(intersection(X2,X0),cross_product(X3,X4)),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4638,c_5286]) ).
tcf(c_26566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X2,intersection(X3,intersection(X4,X0))),X5)
| member(not_subclass_element(intersection(X2,intersection(X3,intersection(X4,X0))),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4646,c_5286]) ).
tcf(c_26567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(X2,intersection(intersection(X3,X0),X4)),X5)
| member(not_subclass_element(intersection(X2,intersection(intersection(X3,X0),X4)),X5),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4647,c_5286]) ).
tcf(c_26568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(complement(complement(intersection(X2,X0))),X3)
| member(not_subclass_element(complement(complement(intersection(X2,X0))),X3),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13744,c_5286]) ).
tcf(c_26570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X4)
| ~ subclass(X1,X4)
| ~ member(X0,intersection(X1,cross_product(X2,X3))) ),
inference(superposition,[status(thm)],[c_193,c_5286]) ).
tcf(c_26571,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ( X0 = null_class )
| ~ member(X2,null_class)
| ~ subclass(regular(X0),X1) ),
inference(superposition,[status(thm)],[c_223,c_5286]) ).
tcf(c_26572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(X0,X4)
| ~ subclass(cross_product(X1,X2),X4)
| ~ member(X0,intersection(cross_product(X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_193,c_5286]) ).
tcf(c_26573,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ~ member(X1,subset_relation)
| ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) ),
inference(superposition,[status(thm)],[c_229,c_5286]) ).
tcf(c_26574,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ subclass(subset_relation,X1)
| ~ member(X0,identity_relation) ),
inference(superposition,[status(thm)],[c_230,c_5286]) ).
tcf(c_26593,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X1,null_class)
| ~ subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0) ),
inference(superposition,[status(thm)],[c_22476,c_5286]) ).
tcf(c_26791,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_171,c_26574]) ).
tcf(c_26792,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(identity_relation,X1),X0)
| member(not_subclass_element(X1,identity_relation),X1)
| ( X1 = identity_relation )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_251,c_26574]) ).
tcf(c_26793,plain,
! [X0: $i] :
( member(not_subclass_element(identity_relation,null_class),X0)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_259,c_26574]) ).
tcf(c_26794,plain,
! [X0: $i] :
( member(regular(identity_relation),X0)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_222,c_26574]) ).
tcf(c_26795,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),X0)
| ( null_class = identity_relation )
| ~ member(identity_relation,universal_class)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_225,c_26574]) ).
tcf(c_26796,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(identity_relation,X1),X2)
| member(not_subclass_element(intersection(identity_relation,X1),X2),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4224,c_26574]) ).
tcf(c_26797,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(identity_relation,X1)),X0)
| ( intersection(identity_relation,X1) = null_class )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4225,c_26574]) ).
tcf(c_26798,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,identity_relation),X2)
| member(not_subclass_element(intersection(X1,identity_relation),X2),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4245,c_26574]) ).
tcf(c_26799,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X1,identity_relation)),X0)
| ( intersection(X1,identity_relation) = null_class )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4246,c_26574]) ).
tcf(c_26800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(identity_relation,cross_product(X1,X2)),X3)
| member(not_subclass_element(intersection(cross_product(X1,X2),identity_relation),X3),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4425,c_26574]) ).
tcf(c_26801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X1,identity_relation),X2),X3)
| member(not_subclass_element(intersection(intersection(X1,identity_relation),X2),X3),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4430,c_26574]) ).
tcf(c_26802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(identity_relation,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(identity_relation,X1),X2),X3),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4431,c_26574]) ).
tcf(c_26803,plain,
! [X0: $i,X1: $i] :
( subclass(X1,complement(identity_relation))
| member(not_subclass_element(X1,complement(identity_relation)),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_8328,c_26574]) ).
tcf(c_26804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),identity_relation),X3)
| member(not_subclass_element(intersection(identity_relation,cross_product(X1,X2)),X3),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4638,c_26574]) ).
tcf(c_26805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X1,intersection(X2,identity_relation)),X3)
| member(not_subclass_element(intersection(X1,intersection(X2,identity_relation)),X3),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4646,c_26574]) ).
tcf(c_26806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X1,intersection(identity_relation,X2)),X3)
| member(not_subclass_element(intersection(X1,intersection(identity_relation,X2)),X3),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4647,c_26574]) ).
tcf(c_26807,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(identity_relation)),X1)
| member(not_subclass_element(complement(complement(identity_relation)),X1),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_13744,c_26574]) ).
tcf(c_27093,plain,
( member(regular(complement(null_class)),universal_class)
| ( complement(complement(universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4953,c_14058]) ).
tcf(c_27094,plain,
( member(regular(complement(universal_class)),null_class)
| ( complement(complement(null_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_8703,c_14058]) ).
tcf(c_27095,plain,
( member(regular(complement(complement(universal_class))),y)
| ( complement(complement(universal_class)) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(regular(complement(complement(universal_class))),regular(complement(complement(universal_class)))),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_20813]) ).
tcf(c_27097,plain,
! [X0: $i] :
( member(regular(complement(complement(X0))),cross_product(universal_class,universal_class))
| ( complement(complement(X0)) = null_class )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_14058,c_4342]) ).
tcf(c_27098,plain,
! [X0: $i] :
( member(regular(complement(complement(X0))),universal_class)
| ( complement(complement(X0)) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_4336]) ).
tcf(c_27099,plain,
! [X0: $i,X1: $i] :
( ( complement(complement(unordered_pair(X0,X1))) = null_class )
| ( regular(complement(complement(unordered_pair(X0,X1)))) = X1 )
| ( regular(complement(complement(unordered_pair(X0,X1)))) = X0 ) ),
inference(superposition,[status(thm)],[c_14058,c_177]) ).
tcf(c_27100,plain,
! [X0: $i,X1: $i] :
( ( complement(complement(cross_product(X0,X1))) = null_class )
| ( unordered_pair(unordered_pair(first(regular(complement(complement(cross_product(X0,X1))))),first(regular(complement(complement(cross_product(X0,X1)))))),unordered_pair(first(regular(complement(complement(cross_product(X0,X1))))),unordered_pair(second(regular(complement(complement(cross_product(X0,X1))))),second(regular(complement(complement(cross_product(X0,X1)))))))) = regular(complement(complement(cross_product(X0,X1)))) ) ),
inference(superposition,[status(thm)],[c_14058,c_184]) ).
tcf(c_27101,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(complement(complement(intersection(X2,X0)))),X1)
| ( complement(complement(intersection(X2,X0))) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_14058,c_5286]) ).
tcf(c_27102,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(complement(complement(intersection(X0,X2)))),X1)
| ( complement(complement(intersection(X0,X2))) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_14058,c_5256]) ).
tcf(c_27103,plain,
! [X0: $i,X1: $i] :
( ( complement(complement(intersection(X0,X1))) = null_class )
| ~ member(regular(complement(complement(intersection(X0,X1)))),complement(X0)) ),
inference(superposition,[status(thm)],[c_14058,c_12327]) ).
tcf(c_27104,plain,
! [X0: $i,X1: $i] :
( ( complement(complement(intersection(X0,X1))) = null_class )
| ~ member(regular(complement(complement(intersection(X0,X1)))),complement(X1)) ),
inference(superposition,[status(thm)],[c_14058,c_11998]) ).
tcf(c_27105,plain,
! [X0: $i,X1: $i] :
( member(regular(complement(complement(intersection(X0,X1)))),X1)
| ( complement(complement(intersection(X0,X1))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_189]) ).
tcf(c_27106,plain,
! [X0: $i,X1: $i] :
( member(regular(complement(complement(intersection(X0,X1)))),X0)
| ( complement(complement(intersection(X0,X1))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_188]) ).
tcf(c_27107,plain,
! [X0: $i] :
( ( complement(complement(complement(X0))) = null_class )
| ~ member(regular(complement(complement(complement(X0)))),X0) ),
inference(superposition,[status(thm)],[c_14058,c_191]) ).
tcf(c_27108,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(complement(complement(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))))),regular(complement(complement(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))))),compose(X1,X2))
| ( complement(complement(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))) = null_class )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(complement(complement(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))))),regular(complement(complement(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_14058,c_215]) ).
tcf(c_27109,plain,
! [X0: $i] :
( member(regular(complement(complement(identity_relation))),X0)
| ( complement(complement(identity_relation)) = null_class )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_14058,c_26574]) ).
tcf(c_27110,plain,
( member(regular(complement(complement(identity_relation))),subset_relation)
| ( complement(complement(identity_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_4293]) ).
tcf(c_27111,plain,
! [X0: $i] :
( member(regular(complement(complement(rotate(X0)))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( complement(complement(rotate(X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_4338]) ).
tcf(c_27112,plain,
! [X0: $i] :
( member(regular(complement(complement(flip(X0)))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( complement(complement(flip(X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_4339]) ).
tcf(c_27113,plain,
! [X0: $i,X1: $i] :
( member(regular(complement(complement(compose(X0,X1)))),cross_product(universal_class,universal_class))
| ( complement(complement(compose(X0,X1))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_4341]) ).
tcf(c_27114,plain,
! [X0: $i,X1: $i] :
( member(regular(complement(complement(unordered_pair(X0,X0)))),unordered_pair(X1,X0))
| ( complement(complement(unordered_pair(X0,X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_4344]) ).
tcf(c_27115,plain,
! [X0: $i,X1: $i] :
( member(regular(complement(complement(unordered_pair(X0,X0)))),unordered_pair(X0,X1))
| ( complement(complement(unordered_pair(X0,X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_4343]) ).
tcf(c_27116,plain,
! [X0: $i] :
( member(regular(complement(complement(unordered_pair(x,x)))),X0)
| ( complement(complement(unordered_pair(x,x))) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_14058,c_5056]) ).
tcf(c_27117,plain,
( ( complement(complement(unordered_pair(x,x))) = null_class )
| ~ member(regular(complement(complement(unordered_pair(x,x)))),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_14058,c_16705]) ).
tcf(c_27118,plain,
( member(regular(complement(complement(unordered_pair(x,x)))),iPr_def_10)
| ( complement(complement(unordered_pair(x,x))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_4346]) ).
tcf(c_27119,plain,
( ( complement(complement(iPr_def_10)) = null_class )
| ( regular(complement(complement(iPr_def_10))) = y )
| ( regular(complement(complement(iPr_def_10))) = x ) ),
inference(superposition,[status(thm)],[c_14058,c_5208]) ).
tcf(c_27120,plain,
! [X0: $i] :
( member(regular(complement(complement(unordered_pair(y,y)))),X0)
| ( complement(complement(unordered_pair(y,y))) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_14058,c_5077]) ).
tcf(c_27121,plain,
( ( complement(complement(unordered_pair(y,y))) = null_class )
| ~ member(regular(complement(complement(unordered_pair(y,y)))),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_14058,c_18840]) ).
tcf(c_27122,plain,
( member(regular(complement(complement(unordered_pair(y,y)))),iPr_def_10)
| ( complement(complement(unordered_pair(y,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_4347]) ).
tcf(c_27123,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(complement(complement(intersection(intersection(X0,X1),X2)))),X0)
| ( complement(complement(intersection(intersection(X0,X1),X2))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_6783]) ).
tcf(c_27124,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(complement(complement(intersection(intersection(X0,X1),X2)))),X1)
| ( complement(complement(intersection(intersection(X0,X1),X2))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_6250]) ).
tcf(c_27125,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(identity_relation,X0)))),subset_relation)
| ( complement(complement(intersection(identity_relation,X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_6318]) ).
tcf(c_27126,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(subset_relation,X0)))),cross_product(universal_class,universal_class))
| ( complement(complement(intersection(subset_relation,X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_7274]) ).
tcf(c_27127,plain,
( ( complement(complement(complement(subset_relation))) = null_class )
| ~ member(regular(complement(complement(complement(subset_relation)))),identity_relation) ),
inference(superposition,[status(thm)],[c_14058,c_11581]) ).
tcf(c_27128,plain,
( member(regular(complement(complement(complement(subset_relation)))),complement(identity_relation))
| ( complement(complement(complement(subset_relation))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_8771]) ).
tcf(c_27129,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(complement(subset_relation),X0)))),complement(identity_relation))
| ( complement(complement(intersection(complement(subset_relation),X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_8785]) ).
tcf(c_27130,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(complement(complement(intersection(X0,intersection(X1,X2))))),X1)
| ( complement(complement(intersection(X0,intersection(X1,X2)))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_11630]) ).
tcf(c_27131,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(complement(complement(intersection(X0,intersection(X1,X2))))),X2)
| ( complement(complement(intersection(X0,intersection(X1,X2)))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_11019]) ).
tcf(c_27132,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(X0,identity_relation)))),subset_relation)
| ( complement(complement(intersection(X0,identity_relation))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_11106]) ).
tcf(c_27133,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(X0,subset_relation)))),cross_product(universal_class,universal_class))
| ( complement(complement(intersection(X0,subset_relation))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_11656]) ).
tcf(c_27134,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(X0,complement(subset_relation))))),complement(identity_relation))
| ( complement(complement(intersection(X0,complement(subset_relation)))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_12409]) ).
tcf(c_27135,plain,
( member(regular(complement(complement(complement(cross_product(universal_class,universal_class))))),complement(element_relation))
| ( complement(complement(complement(cross_product(universal_class,universal_class)))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_15326]) ).
tcf(c_27136,plain,
( member(regular(complement(complement(complement(cross_product(universal_class,universal_class))))),complement(successor_relation))
| ( complement(complement(complement(cross_product(universal_class,universal_class)))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_14989]) ).
tcf(c_27137,plain,
( ( complement(complement(complement(cross_product(universal_class,universal_class)))) = null_class )
| ~ member(regular(complement(complement(complement(cross_product(universal_class,universal_class))))),subset_relation) ),
inference(superposition,[status(thm)],[c_14058,c_12788]) ).
tcf(c_27138,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(element_relation,X0)))),cross_product(universal_class,universal_class))
| ( complement(complement(intersection(element_relation,X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_13233]) ).
tcf(c_27139,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(X0,element_relation)))),cross_product(universal_class,universal_class))
| ( complement(complement(intersection(X0,element_relation))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_13248]) ).
tcf(c_27140,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(successor_relation,X0)))),cross_product(universal_class,universal_class))
| ( complement(complement(intersection(successor_relation,X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_13537]) ).
tcf(c_27141,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(X0,successor_relation)))),cross_product(universal_class,universal_class))
| ( complement(complement(intersection(X0,successor_relation))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_13552]) ).
tcf(c_27142,plain,
! [X0: $i] :
( member(regular(complement(complement(complement(complement(X0))))),X0)
| ( complement(complement(complement(complement(X0)))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_14000]) ).
tcf(c_27143,plain,
( member(regular(complement(complement(complement(complement(element_relation))))),cross_product(universal_class,universal_class))
| ( complement(complement(complement(complement(element_relation)))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_14221]) ).
tcf(c_27144,plain,
( member(regular(complement(complement(complement(complement(successor_relation))))),cross_product(universal_class,universal_class))
| ( complement(complement(complement(complement(successor_relation)))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_14232]) ).
tcf(c_27145,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(unordered_pair(x,x),X0)))),iPr_def_10)
| ( complement(complement(intersection(unordered_pair(x,x),X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_16598]) ).
tcf(c_27146,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(X0,unordered_pair(x,x))))),iPr_def_10)
| ( complement(complement(intersection(X0,unordered_pair(x,x)))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_17098]) ).
tcf(c_27147,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(unordered_pair(y,y),X0)))),iPr_def_10)
| ( complement(complement(intersection(unordered_pair(y,y),X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_18574]) ).
tcf(c_27148,plain,
! [X0: $i] :
( member(regular(complement(complement(intersection(X0,unordered_pair(y,y))))),iPr_def_10)
| ( complement(complement(intersection(X0,unordered_pair(y,y)))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_19011]) ).
tcf(c_27149,plain,
( ( regular(iPr_def_10) = x )
| ( complement(complement(y)) = null_class )
| ~ member(regular(complement(complement(y))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_14058,c_20672]) ).
tcf(c_27151,plain,
( member(regular(universal_class),universal_class)
| ( universal_class = null_class ) ),
inference(light_normalisation,[status(thm)],[c_27093,c_4953,c_8703]) ).
tcf(c_27516,plain,
( subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_26225]) ).
tcf(c_27517,plain,
( subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class)
| member(not_subclass_element(null_class,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class)
| ( regular(iPr_def_10) = x )
| ( intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_251,c_26225]) ).
tcf(c_27518,plain,
( subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class)
| ( regular(iPr_def_10) = x )
| ( intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_259,c_26225]) ).
tcf(c_27519,plain,
! [X0: $i] :
( subclass(X0,null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),element_relation)
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X0,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) ),
inference(superposition,[status(thm)],[c_190,c_26225]) ).
tcf(c_27520,plain,
! [X0: $i] :
( subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_26225]) ).
tcf(c_27521,plain,
! [X0: $i] :
( subclass(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_26225]) ).
tcf(c_27522,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class)
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_26225]) ).
tcf(c_27523,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_26225]) ).
tcf(c_27524,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),X1),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),X1),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_26225]) ).
tcf(c_27525,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class)
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_26225]) ).
tcf(c_27526,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(X1,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(X1,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_26225]) ).
tcf(c_27527,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_26225]) ).
tcf(c_27528,plain,
( subclass(complement(complement(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(complement(complement(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_26225]) ).
tcf(c_27529,plain,
( subclass(iPr_def_10,null_class)
| ( regular(iPr_def_10) = x )
| ( not_subclass_element(iPr_def_10,null_class) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(y,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_20400,c_26225]) ).
tcf(c_27530,plain,
( ( regular(iPr_def_10) = x )
| ( not_subclass_element(iPr_def_10,null_class) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(y,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27529,c_20787]) ).
tcf(c_27636,plain,
( subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_23415]) ).
tcf(c_27637,plain,
( subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| member(not_subclass_element(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_251,c_23415]) ).
tcf(c_27638,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),element_relation)
| ~ member(not_subclass_element(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) ),
inference(superposition,[status(thm)],[c_190,c_23415]) ).
tcf(c_27639,plain,
! [X0: $i] :
( subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_23415]) ).
tcf(c_27640,plain,
! [X0: $i] :
( subclass(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_23415]) ).
tcf(c_27641,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_23415]) ).
tcf(c_27642,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_23415]) ).
tcf(c_27643,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),X1),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),X1),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_23415]) ).
tcf(c_27644,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_23415]) ).
tcf(c_27645,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(X1,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(X1,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_23415]) ).
tcf(c_27646,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_23415]) ).
tcf(c_27647,plain,
( subclass(complement(complement(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(complement(complement(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_23415]) ).
tcf(c_27648,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22472,c_23415]) ).
tcf(c_27753,plain,
! [X0: $i] :
( subclass(X0,null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22472,c_27648]) ).
tcf(c_27754,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) ),
inference(superposition,[status(thm)],[c_27648,c_176]) ).
tcf(c_27755,plain,
! [X0: $i,X1: $i] :
( subclass(X1,X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X1,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X1,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) ),
inference(superposition,[status(thm)],[c_27648,c_250]) ).
tcf(c_27756,plain,
! [X0: $i,X1: $i] :
( member(X1,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X1,X0)
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_170]) ).
tcf(c_27757,plain,
( subclass(omega,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(null_class,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),universal_class)),universal_class)))),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),universal_class)),universal_class)))),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_1547]) ).
tcf(c_27758,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = universal_class )
| ~ member(not_subclass_element(universal_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(universal_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4708]) ).
tcf(c_27759,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(universal_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(universal_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4490]) ).
tcf(c_27760,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(universal_class)
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4617]) ).
tcf(c_27761,plain,
! [X0: $i] :
( subclass(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(X0)
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4496]) ).
tcf(c_27762,plain,
( subclass(complement(complement(successor_relation)),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_14231]) ).
tcf(c_27763,plain,
( subclass(complement(complement(element_relation)),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_14220]) ).
tcf(c_27764,plain,
! [X0: $i] :
( subclass(intersection(X0,successor_relation),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_13551]) ).
tcf(c_27765,plain,
! [X0: $i] :
( subclass(intersection(successor_relation,X0),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_13536]) ).
tcf(c_27766,plain,
! [X0: $i] :
( subclass(intersection(X0,element_relation),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_13247]) ).
tcf(c_27767,plain,
! [X0: $i] :
( subclass(intersection(element_relation,X0),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_13232]) ).
tcf(c_27768,plain,
! [X0: $i] :
( subclass(intersection(X0,subset_relation),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_11655]) ).
tcf(c_27769,plain,
! [X0: $i] :
( subclass(intersection(subset_relation,X0),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_7273]) ).
tcf(c_27770,plain,
( subclass(identity_relation,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_7260]) ).
tcf(c_27771,plain,
( subclass(subset_relation,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_6988]) ).
tcf(c_27772,plain,
! [X0: $i,X1: $i] :
( subclass(compose(X0,X1),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4495]) ).
tcf(c_27773,plain,
( subclass(successor_relation,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4494]) ).
tcf(c_27774,plain,
( subclass(element_relation,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(universal_class,universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4491]) ).
tcf(c_27775,plain,
! [X0: $i] :
( subclass(flip(X0),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4493]) ).
tcf(c_27776,plain,
! [X0: $i] :
( subclass(rotate(X0),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4492]) ).
tcf(c_27777,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(X1,X1),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(unordered_pair(X0,X1),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(unordered_pair(X0,X1),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4498]) ).
tcf(c_27778,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(X0,X0),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(unordered_pair(X0,X1),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(unordered_pair(X0,X1),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4497]) ).
tcf(c_27779,plain,
( member(y,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(iPr_def_10,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_20134]) ).
tcf(c_27780,plain,
( member(x,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(iPr_def_10,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_19428]) ).
tcf(c_27781,plain,
( subclass(identity_relation,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(subset_relation,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(subset_relation,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4502]) ).
tcf(c_27782,plain,
( subclass(identity_relation,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4592]) ).
tcf(c_27783,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = cross_product(unordered_pair(y,y),universal_class) )
| ~ member(not_subclass_element(cross_product(unordered_pair(y,y),universal_class),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(cross_product(unordered_pair(y,y),universal_class),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4722]) ).
tcf(c_27784,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_4787]) ).
tcf(c_27785,plain,
( subclass(complement(subset_relation),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(complement(identity_relation),null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(complement(identity_relation),null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_8770]) ).
tcf(c_28106,plain,
( member(y,null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(iPr_def_10,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_22472,c_27779]) ).
tcf(c_28122,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(iPr_def_10,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28106,c_256]) ).
tcf(c_28168,plain,
( subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_171,c_27753]) ).
tcf(c_28169,plain,
( subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class)
| member(not_subclass_element(null_class,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class)
| ( regular(iPr_def_10) = x )
| ( intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_251,c_27753]) ).
tcf(c_28170,plain,
( subclass(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class)
| ( regular(iPr_def_10) = x )
| ( intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_259,c_27753]) ).
tcf(c_28171,plain,
! [X0: $i] :
( subclass(X0,null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),element_relation)
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X0,null_class),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))) ),
inference(superposition,[status(thm)],[c_190,c_27753]) ).
tcf(c_28172,plain,
! [X0: $i] :
( subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4224,c_27753]) ).
tcf(c_28173,plain,
! [X0: $i] :
( subclass(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4245,c_27753]) ).
tcf(c_28174,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class)
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4425,c_27753]) ).
tcf(c_28175,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4430,c_27753]) ).
tcf(c_28176,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),X1),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),X1),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4431,c_27753]) ).
tcf(c_28177,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class)
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(X0,X1)),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4638,c_27753]) ).
tcf(c_28178,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(X1,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(X1,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4646,c_27753]) ).
tcf(c_28179,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(X0,intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X1)),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4647,c_27753]) ).
tcf(c_28180,plain,
( subclass(complement(complement(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(complement(complement(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_13744,c_27753]) ).
tcf(c_28181,plain,
( subclass(iPr_def_10,null_class)
| ( regular(iPr_def_10) = x )
| ( not_subclass_element(iPr_def_10,null_class) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(y,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_20400,c_27753]) ).
tcf(c_28182,plain,
( ( regular(iPr_def_10) = x )
| ( not_subclass_element(iPr_def_10,null_class) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(iPr_def_10,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(y,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28181,c_20787]) ).
tcf(c_28281,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),y)
| subclass(intersection(intersection(iPr_def_10,y),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_193,c_20676]) ).
tcf(c_28285,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),y)
| subclass(intersection(X0,null_class),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_20676]) ).
tcf(c_28286,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),y)
| ( regular(iPr_def_10) = x )
| ( intersection(X1,intersection(iPr_def_10,y)) = X0 )
| ~ subclass(X0,intersection(X1,intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_20676,c_176]) ).
tcf(c_28287,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),y)
| subclass(intersection(X2,intersection(iPr_def_10,y)),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_20676,c_250]) ).
tcf(c_28288,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(not_subclass_element(null_class,X2),y)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(X1,intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_20676,c_170]) ).
tcf(c_28289,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(X2,intersection(iPr_def_10,y)))) = null_class ) ),
inference(superposition,[status(thm)],[c_20676,c_5373]) ).
tcf(c_28290,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(X1,intersection(iPr_def_10,y)),X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_20676,c_5371]) ).
tcf(c_28291,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(X1,intersection(iPr_def_10,y))),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_20676,c_5348]) ).
tcf(c_28292,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_20676,c_5346]) ).
tcf(c_28293,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(X0,intersection(iPr_def_10,y)))) = null_class ) ),
inference(superposition,[status(thm)],[c_20676,c_14028]) ).
tcf(c_28297,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,intersection(intersection(X0,intersection(iPr_def_10,y)),X1)),y)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(iPr_def_10,y)),X1) = intersection(X0,intersection(iPr_def_10,y)) ) ),
inference(superposition,[status(thm)],[c_20676,c_4722]) ).
tcf(c_28298,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(X1,intersection(iPr_def_10,y)))),y)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(iPr_def_10,y))) = intersection(X1,intersection(iPr_def_10,y)) ) ),
inference(superposition,[status(thm)],[c_20676,c_4787]) ).
tcf(c_28299,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,complement(complement(intersection(X0,intersection(iPr_def_10,y))))),y)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(X0,intersection(iPr_def_10,y)))) = intersection(X0,intersection(iPr_def_10,y)) ) ),
inference(superposition,[status(thm)],[c_20676,c_13998]) ).
tcf(c_28300,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),y)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_28285,c_4790]) ).
tcf(c_28487,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),iPr_def_10)
| subclass(intersection(intersection(iPr_def_10,y),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_193,c_20680]) ).
tcf(c_28491,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),iPr_def_10)
| subclass(intersection(X0,null_class),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_20680]) ).
tcf(c_28492,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(X1,intersection(iPr_def_10,y)) = X0 )
| ~ subclass(X0,intersection(X1,intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_20680,c_176]) ).
tcf(c_28493,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(X2,intersection(iPr_def_10,y)),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_20680,c_250]) ).
tcf(c_28494,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(not_subclass_element(null_class,X2),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(X1,intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_20680,c_170]) ).
tcf(c_28495,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(X2,intersection(iPr_def_10,y)))) = null_class ) ),
inference(superposition,[status(thm)],[c_20680,c_5373]) ).
tcf(c_28496,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(X1,intersection(iPr_def_10,y)),X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_20680,c_5371]) ).
tcf(c_28497,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(X1,intersection(iPr_def_10,y))),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_20680,c_5348]) ).
tcf(c_28498,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_20680,c_5346]) ).
tcf(c_28499,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(X0,intersection(iPr_def_10,y)))) = null_class ) ),
inference(superposition,[status(thm)],[c_20680,c_14028]) ).
tcf(c_28503,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,intersection(intersection(X0,intersection(iPr_def_10,y)),X1)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(iPr_def_10,y)),X1) = intersection(X0,intersection(iPr_def_10,y)) ) ),
inference(superposition,[status(thm)],[c_20680,c_4722]) ).
tcf(c_28504,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(X1,intersection(iPr_def_10,y)))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(iPr_def_10,y))) = intersection(X1,intersection(iPr_def_10,y)) ) ),
inference(superposition,[status(thm)],[c_20680,c_4787]) ).
tcf(c_28505,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,complement(complement(intersection(X0,intersection(iPr_def_10,y))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(X0,intersection(iPr_def_10,y)))) = intersection(X0,intersection(iPr_def_10,y)) ) ),
inference(superposition,[status(thm)],[c_20680,c_13998]) ).
tcf(c_28506,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_28491,c_4790]) ).
tcf(c_28564,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),y)
| subclass(intersection(cross_product(X0,X1),intersection(iPr_def_10,y)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_193,c_20684]) ).
tcf(c_28569,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),y)
| subclass(intersection(null_class,X0),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_20684]) ).
tcf(c_28570,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),y)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X1) = X0 )
| ~ subclass(X0,intersection(intersection(iPr_def_10,y),X1)) ),
inference(superposition,[status(thm)],[c_20684,c_176]) ).
tcf(c_28571,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),y)
| subclass(intersection(intersection(iPr_def_10,y),X2),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_20684,c_250]) ).
tcf(c_28572,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(not_subclass_element(null_class,X2),y)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(intersection(iPr_def_10,y),X1)) ),
inference(superposition,[status(thm)],[c_20684,c_170]) ).
tcf(c_28573,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(intersection(iPr_def_10,y),X2))) = null_class ) ),
inference(superposition,[status(thm)],[c_20684,c_5373]) ).
tcf(c_28574,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(intersection(iPr_def_10,y),X1),X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_20684,c_5371]) ).
tcf(c_28575,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(intersection(iPr_def_10,y),X1)),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_20684,c_5348]) ).
tcf(c_28576,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_20684,c_5346]) ).
tcf(c_28577,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),y)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(intersection(iPr_def_10,y),X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_20684,c_14028]) ).
tcf(c_28581,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,intersection(intersection(intersection(iPr_def_10,y),X0),X1)),y)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X0),X1) = intersection(intersection(iPr_def_10,y),X0) ) ),
inference(superposition,[status(thm)],[c_20684,c_4722]) ).
tcf(c_28582,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(intersection(iPr_def_10,y),X1))),y)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(iPr_def_10,y),X1)) = intersection(intersection(iPr_def_10,y),X1) ) ),
inference(superposition,[status(thm)],[c_20684,c_4787]) ).
tcf(c_28583,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,complement(complement(intersection(intersection(iPr_def_10,y),X0)))),y)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(intersection(iPr_def_10,y),X0))) = intersection(intersection(iPr_def_10,y),X0) ) ),
inference(superposition,[status(thm)],[c_20684,c_13998]) ).
tcf(c_28675,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),iPr_def_10)
| subclass(intersection(cross_product(X0,X1),intersection(iPr_def_10,y)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_193,c_20688]) ).
tcf(c_28680,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),iPr_def_10)
| subclass(intersection(null_class,X0),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_20688]) ).
tcf(c_28681,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X1) = X0 )
| ~ subclass(X0,intersection(intersection(iPr_def_10,y),X1)) ),
inference(superposition,[status(thm)],[c_20688,c_176]) ).
tcf(c_28682,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(intersection(iPr_def_10,y),X2),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_20688,c_250]) ).
tcf(c_28683,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(not_subclass_element(null_class,X2),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(intersection(iPr_def_10,y),X1)) ),
inference(superposition,[status(thm)],[c_20688,c_170]) ).
tcf(c_28684,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(intersection(iPr_def_10,y),X2))) = null_class ) ),
inference(superposition,[status(thm)],[c_20688,c_5373]) ).
tcf(c_28685,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(intersection(iPr_def_10,y),X1),X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_20688,c_5371]) ).
tcf(c_28686,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(intersection(iPr_def_10,y),X1)),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_20688,c_5348]) ).
tcf(c_28687,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_20688,c_5346]) ).
tcf(c_28688,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(intersection(iPr_def_10,y),X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_20688,c_14028]) ).
tcf(c_28692,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,intersection(intersection(intersection(iPr_def_10,y),X0),X1)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X0),X1) = intersection(intersection(iPr_def_10,y),X0) ) ),
inference(superposition,[status(thm)],[c_20688,c_4722]) ).
tcf(c_28693,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(intersection(iPr_def_10,y),X1))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(iPr_def_10,y),X1)) = intersection(intersection(iPr_def_10,y),X1) ) ),
inference(superposition,[status(thm)],[c_20688,c_4787]) ).
tcf(c_28694,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,complement(complement(intersection(intersection(iPr_def_10,y),X0)))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(intersection(iPr_def_10,y),X0))) = intersection(intersection(iPr_def_10,y),X0) ) ),
inference(superposition,[status(thm)],[c_20688,c_13998]) ).
tcf(c_28799,plain,
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(iPr_def_10,y))) = null_class )
| ~ function(y) ),
inference(superposition,[status(thm)],[c_21239,c_4342]) ).
tcf(c_28800,plain,
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(iPr_def_10,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_21239,c_4336]) ).
tcf(c_28801,plain,
( ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(iPr_def_10,y))) = null_class )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_21239,c_20672]) ).
tcf(c_28818,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(iPr_def_10,y)) = null_class )
| ~ function(y) ),
inference(superposition,[status(thm)],[c_21240,c_4342]) ).
tcf(c_28819,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(iPr_def_10,y)) = null_class ) ),
inference(superposition,[status(thm)],[c_21240,c_4336]) ).
tcf(c_28820,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(iPr_def_10,y)) = null_class )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_21240,c_20672]) ).
tcf(c_28840,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X0) = null_class )
| ~ function(y) ),
inference(superposition,[status(thm)],[c_21241,c_4342]) ).
tcf(c_28841,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_21241,c_4336]) ).
tcf(c_28842,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X0) = null_class )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_21241,c_20672]) ).
tcf(c_28866,plain,
( ( complement(complement(intersection(iPr_def_10,y))) = null_class )
| ( regular(iPr_def_10) = x ) ),
inference(global_subsumption_just,[status(thm)],[c_21318,c_21318,c_28801]) ).
tcf(c_28867,plain,
( ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(iPr_def_10,y))) = null_class ) ),
inference(renaming,[status(thm)],[c_28866]) ).
tcf(c_28872,plain,
( ( regular(iPr_def_10) = x )
| ( complement(complement(null_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_20574,c_28867]) ).
tcf(c_28873,plain,
( member(regular(complement(null_class)),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x )
| ( complement(complement(complement(intersection(iPr_def_10,y)))) = null_class ) ),
inference(superposition,[status(thm)],[c_28867,c_14058]) ).
tcf(c_28874,plain,
( ( regular(iPr_def_10) = x )
| ( complement(complement(complement(intersection(iPr_def_10,y)))) = complement(intersection(iPr_def_10,y)) )
| ~ subclass(complement(intersection(iPr_def_10,y)),complement(null_class)) ),
inference(superposition,[status(thm)],[c_28867,c_13998]) ).
tcf(c_28875,plain,
! [X0: $i] :
( subclass(complement(null_class),X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(intersection(iPr_def_10,y)),X0) ),
inference(superposition,[status(thm)],[c_28867,c_13999]) ).
tcf(c_28876,plain,
( subclass(complement(null_class),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_28867,c_13755]) ).
tcf(c_28877,plain,
! [X0: $i] :
( subclass(complement(complement(complement(intersection(iPr_def_10,y)))),X0)
| member(not_subclass_element(complement(null_class),X0),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_28867,c_13744]) ).
tcf(c_28878,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(complement(intersection(iPr_def_10,y)),X0),null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_28867,c_12688]) ).
tcf(c_28879,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(complement(intersection(iPr_def_10,y)),null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_28867,c_12377]) ).
tcf(c_28880,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(null_class,intersection(complement(intersection(iPr_def_10,y)),X0)) = null_class ) ),
inference(superposition,[status(thm)],[c_28867,c_11685]) ).
tcf(c_28881,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(null_class,intersection(X0,complement(intersection(iPr_def_10,y)))) = null_class ) ),
inference(superposition,[status(thm)],[c_28867,c_11228]) ).
tcf(c_28883,plain,
( member(unordered_pair(unordered_pair(complement(intersection(iPr_def_10,y)),complement(intersection(iPr_def_10,y))),unordered_pair(complement(intersection(iPr_def_10,y)),unordered_pair(complement(intersection(complement(complement(intersection(iPr_def_10,y))),complement(unordered_pair(complement(intersection(iPr_def_10,y)),complement(intersection(iPr_def_10,y)))))),complement(intersection(complement(complement(intersection(iPr_def_10,y))),complement(unordered_pair(complement(intersection(iPr_def_10,y)),complement(intersection(iPr_def_10,y))))))))),successor_relation)
| ( regular(iPr_def_10) = x )
| ~ member(unordered_pair(unordered_pair(complement(intersection(iPr_def_10,y)),complement(intersection(iPr_def_10,y))),unordered_pair(complement(intersection(iPr_def_10,y)),unordered_pair(complement(intersection(null_class,complement(unordered_pair(complement(intersection(iPr_def_10,y)),complement(intersection(iPr_def_10,y)))))),complement(intersection(null_class,complement(unordered_pair(complement(intersection(iPr_def_10,y)),complement(intersection(iPr_def_10,y))))))))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_28867,c_204]) ).
tcf(c_28884,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(complement(intersection(iPr_def_10,y))),X0),X1)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(null_class,X0),X1),complement(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_28867,c_4432]) ).
tcf(c_28885,plain,
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(null_class,universal_class)),universal_class))))),universal_class)
| ( regular(iPr_def_10) = x )
| ~ member(complement(intersection(iPr_def_10,y)),universal_class) ),
inference(superposition,[status(thm)],[c_28867,c_212]) ).
tcf(c_28887,plain,
! [X0: $i] :
( subclass(complement(complement(intersection(iPr_def_10,y))),X0)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,X0),complement(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_28867,c_4264]) ).
tcf(c_28888,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(null_class,complement(intersection(iPr_def_10,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_28867,c_4169]) ).
tcf(c_28889,plain,
! [X0: $i] :
( member(X0,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x )
| ~ member(X0,complement(null_class)) ),
inference(superposition,[status(thm)],[c_28867,c_14000]) ).
tcf(c_28890,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,complement(intersection(iPr_def_10,y))),null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_28867,c_12625]) ).
tcf(c_28891,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,complement(complement(intersection(iPr_def_10,y)))),X1)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(X0,null_class),X1),complement(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_28867,c_4648]) ).
tcf(c_28892,plain,
! [X0: $i] :
( subclass(X0,complement(complement(intersection(iPr_def_10,y))))
| member(not_subclass_element(X0,null_class),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_28867,c_8328]) ).
tcf(c_28896,plain,
( ( regular(iPr_def_10) = x )
| ( complement(complement(intersection(iPr_def_10,y))) = intersection(iPr_def_10,y) )
| ~ subclass(intersection(iPr_def_10,y),null_class) ),
inference(superposition,[status(thm)],[c_28867,c_13998]) ).
tcf(c_28898,plain,
( subclass(null_class,intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_28867,c_13755]) ).
tcf(c_28899,plain,
! [X0: $i] :
( subclass(complement(complement(intersection(iPr_def_10,y))),X0)
| member(not_subclass_element(null_class,X0),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_28867,c_13744]) ).
tcf(c_28902,plain,
( subclass(universal_class,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_28876,c_8703]) ).
tcf(c_28905,plain,
! [X0: $i] :
( member(X0,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x )
| ~ member(X0,universal_class) ),
inference(light_normalisation,[status(thm)],[c_28889,c_8703]) ).
tcf(c_28909,plain,
! [X0: $i] :
( subclass(universal_class,X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(intersection(iPr_def_10,y)),X0) ),
inference(light_normalisation,[status(thm)],[c_28875,c_8703]) ).
tcf(c_28925,plain,
! [X0: $i] :
( subclass(complement(complement(complement(intersection(iPr_def_10,y)))),X0)
| member(not_subclass_element(universal_class,X0),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_28877,c_8703]) ).
tcf(c_28929,plain,
( member(regular(universal_class),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x )
| ( complement(complement(complement(intersection(iPr_def_10,y)))) = null_class ) ),
inference(light_normalisation,[status(thm)],[c_28873,c_8703]) ).
tcf(c_28933,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,complement(complement(intersection(iPr_def_10,y)))),X0)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,X0),complement(intersection(iPr_def_10,y))) ),
inference(light_normalisation,[status(thm)],[c_28891,c_4790]) ).
tcf(c_28940,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(complement(intersection(iPr_def_10,y))),X1),X0)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,X0),complement(intersection(iPr_def_10,y))) ),
inference(light_normalisation,[status(thm)],[c_28884,c_4553]) ).
tcf(c_28944,plain,
( ( regular(iPr_def_10) = x )
| ( complement(complement(complement(intersection(iPr_def_10,y)))) = complement(intersection(iPr_def_10,y)) )
| ~ subclass(complement(intersection(iPr_def_10,y)),universal_class) ),
inference(light_normalisation,[status(thm)],[c_28874,c_8703]) ).
tcf(c_28945,plain,
( ( regular(iPr_def_10) = x )
| ( complement(complement(complement(intersection(iPr_def_10,y)))) = complement(intersection(iPr_def_10,y)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28944,c_173]) ).
tcf(c_29020,plain,
! [X0: $i] :
( ( intersection(X0,intersection(iPr_def_10,y)) = null_class )
| ( regular(iPr_def_10) = x ) ),
inference(global_subsumption_just,[status(thm)],[c_21319,c_21319,c_28820]) ).
tcf(c_29021,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(iPr_def_10,y)) = null_class ) ),
inference(renaming,[status(thm)],[c_29020]) ).
tcf(c_29029,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(X0,intersection(iPr_def_10,y))),X1)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(complement(null_class),X1),X0)
| ~ member(not_subclass_element(complement(intersection(X0,intersection(iPr_def_10,y))),X1),intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_29021,c_5138]) ).
tcf(c_29030,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(iPr_def_10,y)) = X0 )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_29021,c_4722]) ).
tcf(c_29031,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(null_class,complement(X0)) = null_class ) ),
inference(superposition,[status(thm)],[c_29021,c_12688]) ).
tcf(c_29033,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(complement(X0),null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_29021,c_11685]) ).
tcf(c_29036,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X0),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_6583]) ).
tcf(c_29037,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),X0)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4431]) ).
tcf(c_29038,plain,
! [X0: $i] :
( subclass(intersection(null_class,X0),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_6065]) ).
tcf(c_29039,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),intersection(iPr_def_10,y))
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4430]) ).
tcf(c_29041,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),intersection(iPr_def_10,y))
| subclass(intersection(X0,intersection(iPr_def_10,y)),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4245]) ).
tcf(c_29043,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),X0)
| subclass(intersection(X0,intersection(iPr_def_10,y)),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4224]) ).
tcf(c_29044,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ( regular(iPr_def_10) = x )
| ~ member(X1,null_class)
| ~ subclass(intersection(iPr_def_10,y),X0) ),
inference(superposition,[status(thm)],[c_29021,c_5286]) ).
tcf(c_29045,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ( regular(iPr_def_10) = x )
| ~ member(X2,null_class)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_29021,c_5256]) ).
tcf(c_29046,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(X1,intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(X0,null_class),X1)
| ~ member(not_subclass_element(X0,intersection(X1,intersection(iPr_def_10,y))),intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_29021,c_5134]) ).
tcf(c_29049,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,null_class),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_11340]) ).
tcf(c_29050,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,null_class),X2),X1)
| subclass(intersection(X0,intersection(X1,intersection(iPr_def_10,y))),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4647]) ).
tcf(c_29051,plain,
! [X0: $i] :
( subclass(intersection(X0,null_class),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_10731]) ).
tcf(c_29052,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,null_class),X2),intersection(iPr_def_10,y))
| subclass(intersection(X0,intersection(X1,intersection(iPr_def_10,y))),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4646]) ).
tcf(c_29054,plain,
! [X0: $i,X1: $i] :
( member(X0,intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(null_class,X1)) ),
inference(superposition,[status(thm)],[c_29021,c_6250]) ).
tcf(c_29055,plain,
! [X0: $i,X1: $i] :
( member(X0,null_class)
| ( regular(iPr_def_10) = x )
| ~ member(X0,X1)
| ~ member(X0,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_29021,c_190]) ).
tcf(c_29058,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),cross_product(X0,X1))
| subclass(intersection(intersection(iPr_def_10,y),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4640]) ).
tcf(c_29059,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(iPr_def_10,y))
| subclass(intersection(intersection(iPr_def_10,y),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4425]) ).
tcf(c_29060,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),cross_product(X0,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_29021,c_193]) ).
tcf(c_29061,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,X2),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_29021,c_6782]) ).
tcf(c_29064,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(intersection(X0,X1),intersection(iPr_def_10,y)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4431]) ).
tcf(c_29066,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(intersection(X0,X1),intersection(iPr_def_10,y)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4430]) ).
tcf(c_29067,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(X1),intersection(iPr_def_10,y)),X0)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_29021,c_4432]) ).
tcf(c_29068,plain,
( member(regular(null_class),subset_relation)
| ( regular(iPr_def_10) = x )
| ( intersection(identity_relation,intersection(iPr_def_10,y)) = null_class ) ),
inference(superposition,[status(thm)],[c_29021,c_6518]) ).
tcf(c_29069,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(identity_relation,intersection(iPr_def_10,y)) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_29021,c_6316]) ).
tcf(c_29070,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),subset_relation)
| subclass(intersection(identity_relation,intersection(iPr_def_10,y)),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4433]) ).
tcf(c_29071,plain,
( subclass(null_class,domain_of(flip(cross_product(subset_relation,universal_class))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_6777]) ).
tcf(c_29072,plain,
( subclass(null_class,subset_relation)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_6244]) ).
tcf(c_29077,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(iPr_def_10,y)) = intersection(iPr_def_10,y) )
| ~ subclass(intersection(iPr_def_10,y),null_class) ),
inference(superposition,[status(thm)],[c_29021,c_4787]) ).
tcf(c_29079,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X1),X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(intersection(iPr_def_10,y),X0) ),
inference(superposition,[status(thm)],[c_29021,c_6249]) ).
tcf(c_29082,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(unordered_pair(x,x),intersection(iPr_def_10,y)),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_4976]) ).
tcf(c_29084,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(unordered_pair(y,y),intersection(iPr_def_10,y)),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_5000]) ).
tcf(c_29085,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,null_class),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_29021,c_11629]) ).
tcf(c_29086,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X1,null_class),X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(intersection(iPr_def_10,y),X0) ),
inference(superposition,[status(thm)],[c_29021,c_11018]) ).
tcf(c_29088,plain,
! [X0: $i,X1: $i] :
( member(X0,intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(X1,null_class)) ),
inference(superposition,[status(thm)],[c_29021,c_11019]) ).
tcf(c_29094,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_29021,c_6782]) ).
tcf(c_29098,plain,
( subclass(null_class,complement(identity_relation))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_8764]) ).
tcf(c_29115,plain,
! [X0: $i] :
( subclass(intersection(null_class,X0),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_13502]) ).
tcf(c_29116,plain,
( subclass(null_class,cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_13498]) ).
tcf(c_29120,plain,
! [X0: $i] :
( subclass(intersection(X0,null_class),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_13505]) ).
tcf(c_29125,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_29049,c_4790]) ).
tcf(c_29172,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ~ member(X0,X1)
| ~ member(X0,intersection(iPr_def_10,y)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29055,c_256]) ).
tcf(c_29176,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(null_class,X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_29054,c_29172]) ).
tcf(c_29177,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(X1,null_class)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_29088,c_29172]) ).
tcf(c_29209,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(X0,intersection(X1,intersection(iPr_def_10,y))),X2)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_29050,c_4790]) ).
tcf(c_29216,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(iPr_def_10,y))
| subclass(intersection(X0,intersection(X1,intersection(iPr_def_10,y))),X2)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_29052,c_4790]) ).
tcf(c_29227,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(X0,intersection(iPr_def_10,y))),X1)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(universal_class,X1),X0)
| ~ member(not_subclass_element(complement(intersection(X0,intersection(iPr_def_10,y))),X1),intersection(iPr_def_10,y)) ),
inference(light_normalisation,[status(thm)],[c_29029,c_8703]) ).
tcf(c_29278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,cross_product(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3),universal_class) ),
inference(superposition,[status(thm)],[c_193,c_5409]) ).
tcf(c_29279,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),universal_class)
| subclass(intersection(regular(cross_product(X0,X1)),cross_product(X0,X1)),X2)
| ( cross_product(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_5409]) ).
tcf(c_29281,plain,
! [X0: $i] :
( member(not_subclass_element(subset_relation,X0),universal_class)
| subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),cross_product(universal_class,universal_class)),X0) ),
inference(superposition,[status(thm)],[c_229,c_5409]) ).
tcf(c_29282,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),universal_class)
| subclass(intersection(null_class,cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_4790,c_5409]) ).
tcf(c_29283,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),universal_class)
| subclass(intersection(complement(cross_product(X0,X1)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_12377,c_5409]) ).
tcf(c_29284,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),universal_class)
| subclass(intersection(intersection(iPr_def_10,y),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_5409]) ).
tcf(c_29285,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),universal_class)
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(x,x),universal_class)),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_5409]) ).
tcf(c_29286,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),universal_class)
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(y,y),universal_class)),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_5409]) ).
tcf(c_29287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),X2),X3),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(cross_product(X0,X1),X2),X3),not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_5409,c_20813]) ).
tcf(c_29288,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),universal_class)
| ( intersection(cross_product(X0,X1),X2) = universal_class )
| ~ member(not_subclass_element(universal_class,intersection(cross_product(X0,X1),X2)),intersection(cross_product(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_5409,c_254]) ).
tcf(c_29289,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),universal_class)
| member(not_subclass_element(universal_class,intersection(cross_product(X0,X1),X2)),universal_class)
| ( intersection(cross_product(X0,X1),X2) = universal_class ) ),
inference(superposition,[status(thm)],[c_5409,c_253]) ).
tcf(c_29291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),X2),X3),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_5409,c_4342]) ).
tcf(c_29294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X2,cross_product(X0,X1)),intersection(universal_class,X3))
| subclass(intersection(cross_product(X0,X1),X2),intersection(universal_class,X3))
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),X2),intersection(universal_class,X3)),X3) ),
inference(superposition,[status(thm)],[c_5409,c_5134]) ).
tcf(c_29373,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(identity_relation,X0),not_subclass_element(identity_relation,X0)),universal_class)) = null_class )
| ~ subclass(subset_relation,universal_class) ),
inference(superposition,[status(thm)],[c_26791,c_20813]) ).
tcf(c_29374,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ( X0 = identity_relation )
| ~ subclass(subset_relation,X0)
| ~ member(not_subclass_element(X0,identity_relation),identity_relation) ),
inference(superposition,[status(thm)],[c_26791,c_254]) ).
tcf(c_29375,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(X0,identity_relation),X0)
| ( X0 = identity_relation )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_26791,c_253]) ).
tcf(c_29377,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_26791,c_256]) ).
tcf(c_29378,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),cross_product(universal_class,universal_class))
| ~ function(X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_26791,c_4342]) ).
tcf(c_29379,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),universal_class)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_26791,c_4336]) ).
tcf(c_29380,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(identity_relation,X2)
| ( not_subclass_element(identity_relation,X2) = X1 )
| ( not_subclass_element(identity_relation,X2) = X0 )
| ~ subclass(subset_relation,unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_26791,c_177]) ).
tcf(c_29381,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(identity_relation,X2)
| ( unordered_pair(unordered_pair(first(not_subclass_element(identity_relation,X2)),first(not_subclass_element(identity_relation,X2))),unordered_pair(first(not_subclass_element(identity_relation,X2)),unordered_pair(second(not_subclass_element(identity_relation,X2)),second(not_subclass_element(identity_relation,X2))))) = not_subclass_element(identity_relation,X2) )
| ~ subclass(subset_relation,cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_26791,c_184]) ).
tcf(c_29382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(identity_relation,X3)
| member(not_subclass_element(identity_relation,X3),X2)
| ~ subclass(X1,X2)
| ~ subclass(subset_relation,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_26791,c_5286]) ).
tcf(c_29383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(identity_relation,X3)
| member(not_subclass_element(identity_relation,X3),X2)
| ~ subclass(X0,X2)
| ~ subclass(subset_relation,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_26791,c_5256]) ).
tcf(c_29384,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,intersection(X1,X2))
| ~ member(not_subclass_element(identity_relation,X0),complement(X1)) ),
inference(superposition,[status(thm)],[c_26791,c_12327]) ).
tcf(c_29385,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,intersection(X2,X1))
| ~ member(not_subclass_element(identity_relation,X0),complement(X1)) ),
inference(superposition,[status(thm)],[c_26791,c_11998]) ).
tcf(c_29386,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(identity_relation,X2)
| member(not_subclass_element(identity_relation,X2),X1)
| ~ subclass(subset_relation,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_26791,c_189]) ).
tcf(c_29387,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(identity_relation,X2)
| member(not_subclass_element(identity_relation,X2),X0)
| ~ subclass(subset_relation,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_26791,c_188]) ).
tcf(c_29388,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,complement(X1))
| ~ member(not_subclass_element(identity_relation,X0),X1) ),
inference(superposition,[status(thm)],[c_26791,c_191]) ).
tcf(c_29389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(identity_relation,X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(not_subclass_element(identity_relation,X3),not_subclass_element(identity_relation,X3)))),compose(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(not_subclass_element(identity_relation,X3),not_subclass_element(identity_relation,X3)))),cross_product(universal_class,universal_class))
| ~ subclass(subset_relation,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_26791,c_215]) ).
tcf(c_29390,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),X0)
| ~ subclass(subset_relation,identity_relation)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_26791,c_26574]) ).
tcf(c_29392,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ subclass(subset_relation,rotate(X0)) ),
inference(superposition,[status(thm)],[c_26791,c_4338]) ).
tcf(c_29393,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ subclass(subset_relation,flip(X0)) ),
inference(superposition,[status(thm)],[c_26791,c_4339]) ).
tcf(c_29394,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(identity_relation,X2)
| member(not_subclass_element(identity_relation,X2),cross_product(universal_class,universal_class))
| ~ subclass(subset_relation,compose(X0,X1)) ),
inference(superposition,[status(thm)],[c_26791,c_4341]) ).
tcf(c_29395,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),unordered_pair(X2,X0))
| ~ subclass(subset_relation,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_26791,c_4344]) ).
tcf(c_29396,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),unordered_pair(X0,X2))
| ~ subclass(subset_relation,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_26791,c_4343]) ).
tcf(c_29397,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),X0)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(subset_relation,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_26791,c_5056]) ).
tcf(c_29398,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,unordered_pair(x,x))
| ~ member(not_subclass_element(identity_relation,X0),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_26791,c_16705]) ).
tcf(c_29399,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),iPr_def_10)
| ~ subclass(subset_relation,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_26791,c_4346]) ).
tcf(c_29400,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ( not_subclass_element(identity_relation,X0) = y )
| ( not_subclass_element(identity_relation,X0) = x )
| ~ subclass(subset_relation,iPr_def_10) ),
inference(superposition,[status(thm)],[c_26791,c_5208]) ).
tcf(c_29401,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),X0)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(subset_relation,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_26791,c_5077]) ).
tcf(c_29402,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,unordered_pair(y,y))
| ~ member(not_subclass_element(identity_relation,X0),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_26791,c_18840]) ).
tcf(c_29403,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),iPr_def_10)
| ~ subclass(subset_relation,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_26791,c_4347]) ).
tcf(c_29406,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,intersection(X0,X1))
| ~ subclass(subset_relation,X0)
| ~ member(not_subclass_element(identity_relation,intersection(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_26791,c_5134]) ).
tcf(c_29407,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,domain_of(complement(cross_product(unordered_pair(not_subclass_element(identity_relation,X0),not_subclass_element(identity_relation,X0)),universal_class)))) ),
inference(superposition,[status(thm)],[c_26791,c_5852]) ).
tcf(c_29408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(identity_relation,X3)
| member(not_subclass_element(identity_relation,X3),X0)
| ~ subclass(subset_relation,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_26791,c_6783]) ).
tcf(c_29409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(identity_relation,X3)
| member(not_subclass_element(identity_relation,X3),X1)
| ~ subclass(subset_relation,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_26791,c_6250]) ).
tcf(c_29410,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),subset_relation)
| ~ subclass(subset_relation,intersection(identity_relation,X0)) ),
inference(superposition,[status(thm)],[c_26791,c_6318]) ).
tcf(c_29411,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),cross_product(universal_class,universal_class))
| ~ subclass(subset_relation,intersection(subset_relation,X0)) ),
inference(superposition,[status(thm)],[c_26791,c_7274]) ).
tcf(c_29412,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ~ subclass(subset_relation,complement(subset_relation))
| ~ member(not_subclass_element(identity_relation,X0),identity_relation) ),
inference(superposition,[status(thm)],[c_26791,c_11581]) ).
tcf(c_29413,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),complement(identity_relation))
| ~ subclass(subset_relation,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_26791,c_8771]) ).
tcf(c_29414,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),complement(identity_relation))
| ~ subclass(subset_relation,intersection(complement(subset_relation),X0)) ),
inference(superposition,[status(thm)],[c_26791,c_8785]) ).
tcf(c_29415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(identity_relation,X3)
| member(not_subclass_element(identity_relation,X3),X1)
| ~ subclass(subset_relation,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_26791,c_11630]) ).
tcf(c_29416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(identity_relation,X3)
| member(not_subclass_element(identity_relation,X3),X2)
| ~ subclass(subset_relation,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_26791,c_11019]) ).
tcf(c_29417,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),subset_relation)
| ~ subclass(subset_relation,intersection(X0,identity_relation)) ),
inference(superposition,[status(thm)],[c_26791,c_11106]) ).
tcf(c_29418,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),cross_product(universal_class,universal_class))
| ~ subclass(subset_relation,intersection(X0,subset_relation)) ),
inference(superposition,[status(thm)],[c_26791,c_11656]) ).
tcf(c_29419,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),complement(identity_relation))
| ~ subclass(subset_relation,intersection(X0,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_26791,c_12409]) ).
tcf(c_29420,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),complement(element_relation))
| ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_26791,c_15326]) ).
tcf(c_29421,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),complement(successor_relation))
| ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_26791,c_14989]) ).
tcf(c_29422,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ~ member(not_subclass_element(identity_relation,X0),subset_relation)
| ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_26791,c_12788]) ).
tcf(c_29423,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),cross_product(universal_class,universal_class))
| ~ subclass(subset_relation,intersection(element_relation,X0)) ),
inference(superposition,[status(thm)],[c_26791,c_13233]) ).
tcf(c_29424,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),cross_product(universal_class,universal_class))
| ~ subclass(subset_relation,intersection(X0,element_relation)) ),
inference(superposition,[status(thm)],[c_26791,c_13248]) ).
tcf(c_29425,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),cross_product(universal_class,universal_class))
| ~ subclass(subset_relation,intersection(successor_relation,X0)) ),
inference(superposition,[status(thm)],[c_26791,c_13537]) ).
tcf(c_29426,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),cross_product(universal_class,universal_class))
| ~ subclass(subset_relation,intersection(X0,successor_relation)) ),
inference(superposition,[status(thm)],[c_26791,c_13552]) ).
tcf(c_29427,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),X0)
| ~ subclass(subset_relation,complement(complement(X0))) ),
inference(superposition,[status(thm)],[c_26791,c_14000]) ).
tcf(c_29428,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),cross_product(universal_class,universal_class))
| ~ subclass(subset_relation,complement(complement(element_relation))) ),
inference(superposition,[status(thm)],[c_26791,c_14221]) ).
tcf(c_29429,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),cross_product(universal_class,universal_class))
| ~ subclass(subset_relation,complement(complement(successor_relation))) ),
inference(superposition,[status(thm)],[c_26791,c_14232]) ).
tcf(c_29430,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),iPr_def_10)
| ~ subclass(subset_relation,intersection(unordered_pair(x,x),X0)) ),
inference(superposition,[status(thm)],[c_26791,c_16598]) ).
tcf(c_29431,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),iPr_def_10)
| ~ subclass(subset_relation,intersection(X0,unordered_pair(x,x))) ),
inference(superposition,[status(thm)],[c_26791,c_17098]) ).
tcf(c_29432,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),iPr_def_10)
| ~ subclass(subset_relation,intersection(unordered_pair(y,y),X0)) ),
inference(superposition,[status(thm)],[c_26791,c_18574]) ).
tcf(c_29433,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(identity_relation,X1),iPr_def_10)
| ~ subclass(subset_relation,intersection(X0,unordered_pair(y,y))) ),
inference(superposition,[status(thm)],[c_26791,c_19011]) ).
tcf(c_29434,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,y)
| ~ member(not_subclass_element(identity_relation,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_26791,c_20672]) ).
tcf(c_29435,plain,
( subclass(identity_relation,intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,y)
| ~ member(not_subclass_element(identity_relation,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_26791,c_23413]) ).
tcf(c_29436,plain,
( subclass(identity_relation,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(identity_relation,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ subclass(subset_relation,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26791,c_23414]) ).
tcf(c_29437,plain,
( subclass(identity_relation,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(identity_relation,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ subclass(subset_relation,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26791,c_23415]) ).
tcf(c_29438,plain,
( subclass(identity_relation,null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(identity_relation,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ subclass(subset_relation,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26791,c_27753]) ).
tcf(c_29439,plain,
( subclass(identity_relation,null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(identity_relation,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ subclass(subset_relation,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26791,c_26225]) ).
tcf(c_29631,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(identity_relation,X0),not_subclass_element(identity_relation,X0)),universal_class)) = null_class ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29373,c_173]) ).
tcf(c_29897,plain,
( ( null_class = identity_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_26794,c_256]) ).
tcf(c_29898,plain,
! [X0: $i] :
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ function(X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_26794,c_4342]) ).
tcf(c_29900,plain,
! [X0: $i,X1: $i] :
( ( null_class = identity_relation )
| ( regular(identity_relation) = X1 )
| ( regular(identity_relation) = X0 )
| ~ subclass(subset_relation,unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_26794,c_177]) ).
tcf(c_29901,plain,
! [X0: $i,X1: $i] :
( ( null_class = identity_relation )
| ( unordered_pair(unordered_pair(first(regular(identity_relation)),first(regular(identity_relation))),unordered_pair(first(regular(identity_relation)),unordered_pair(second(regular(identity_relation)),second(regular(identity_relation))))) = regular(identity_relation) )
| ~ subclass(subset_relation,cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_26794,c_184]) ).
tcf(c_29902,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(identity_relation),X2)
| ( null_class = identity_relation )
| ~ subclass(X1,X2)
| ~ subclass(subset_relation,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_26794,c_5286]) ).
tcf(c_29903,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(identity_relation),X2)
| ( null_class = identity_relation )
| ~ subclass(X0,X2)
| ~ subclass(subset_relation,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_26794,c_5256]) ).
tcf(c_29904,plain,
! [X0: $i,X1: $i] :
( ( null_class = identity_relation )
| ~ member(regular(identity_relation),complement(X0))
| ~ subclass(subset_relation,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_26794,c_12327]) ).
tcf(c_29905,plain,
! [X0: $i,X1: $i] :
( ( null_class = identity_relation )
| ~ member(regular(identity_relation),complement(X1))
| ~ subclass(subset_relation,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_26794,c_11998]) ).
tcf(c_29906,plain,
! [X0: $i,X1: $i] :
( member(regular(identity_relation),X1)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_26794,c_189]) ).
tcf(c_29907,plain,
! [X0: $i,X1: $i] :
( member(regular(identity_relation),X0)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_26794,c_188]) ).
tcf(c_29908,plain,
! [X0: $i] :
( ( null_class = identity_relation )
| ~ subclass(subset_relation,complement(X0))
| ~ member(regular(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_26794,c_191]) ).
tcf(c_29909,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(identity_relation),regular(identity_relation)))),compose(X0,X1))
| ( null_class = identity_relation )
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(identity_relation),regular(identity_relation)))),cross_product(universal_class,universal_class))
| ~ subclass(subset_relation,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_26794,c_215]) ).
tcf(c_29910,plain,
! [X0: $i] :
( member(regular(identity_relation),X0)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,identity_relation)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_26794,c_26574]) ).
tcf(c_29912,plain,
! [X0: $i] :
( member(regular(identity_relation),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,rotate(X0)) ),
inference(superposition,[status(thm)],[c_26794,c_4338]) ).
tcf(c_29913,plain,
! [X0: $i] :
( member(regular(identity_relation),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,flip(X0)) ),
inference(superposition,[status(thm)],[c_26794,c_4339]) ).
tcf(c_29914,plain,
! [X0: $i,X1: $i] :
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,compose(X0,X1)) ),
inference(superposition,[status(thm)],[c_26794,c_4341]) ).
tcf(c_29915,plain,
! [X0: $i,X1: $i] :
( member(regular(identity_relation),unordered_pair(X1,X0))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_26794,c_4344]) ).
tcf(c_29916,plain,
! [X0: $i,X1: $i] :
( member(regular(identity_relation),unordered_pair(X0,X1))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_26794,c_4343]) ).
tcf(c_29917,plain,
! [X0: $i] :
( member(regular(identity_relation),X0)
| ( null_class = identity_relation )
| ~ subclass(iPr_def_10,X0)
| ~ subclass(subset_relation,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_26794,c_5056]) ).
tcf(c_29918,plain,
( ( null_class = identity_relation )
| ~ subclass(subset_relation,unordered_pair(x,x))
| ~ member(regular(identity_relation),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_26794,c_16705]) ).
tcf(c_29919,plain,
( member(regular(identity_relation),iPr_def_10)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_26794,c_4346]) ).
tcf(c_29920,plain,
( ( null_class = identity_relation )
| ( regular(identity_relation) = y )
| ( regular(identity_relation) = x )
| ~ subclass(subset_relation,iPr_def_10) ),
inference(superposition,[status(thm)],[c_26794,c_5208]) ).
tcf(c_29921,plain,
! [X0: $i] :
( member(regular(identity_relation),X0)
| ( null_class = identity_relation )
| ~ subclass(iPr_def_10,X0)
| ~ subclass(subset_relation,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_26794,c_5077]) ).
tcf(c_29922,plain,
( ( null_class = identity_relation )
| ~ subclass(subset_relation,unordered_pair(y,y))
| ~ member(regular(identity_relation),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_26794,c_18840]) ).
tcf(c_29923,plain,
( member(regular(identity_relation),iPr_def_10)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_26794,c_4347]) ).
tcf(c_29924,plain,
( ( null_class = identity_relation )
| ~ subclass(subset_relation,domain_of(complement(cross_product(unordered_pair(regular(identity_relation),regular(identity_relation)),universal_class)))) ),
inference(superposition,[status(thm)],[c_26794,c_5852]) ).
tcf(c_29925,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(identity_relation),X0)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_26794,c_6783]) ).
tcf(c_29926,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(identity_relation),X1)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_26794,c_6250]) ).
tcf(c_29928,plain,
! [X0: $i] :
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(subset_relation,X0)) ),
inference(superposition,[status(thm)],[c_26794,c_7274]) ).
tcf(c_29929,plain,
( ( null_class = identity_relation )
| ~ subclass(subset_relation,complement(subset_relation))
| ~ member(regular(identity_relation),identity_relation) ),
inference(superposition,[status(thm)],[c_26794,c_11581]) ).
tcf(c_29930,plain,
( member(regular(identity_relation),complement(identity_relation))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_26794,c_8771]) ).
tcf(c_29931,plain,
! [X0: $i] :
( member(regular(identity_relation),complement(identity_relation))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(complement(subset_relation),X0)) ),
inference(superposition,[status(thm)],[c_26794,c_8785]) ).
tcf(c_29932,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(identity_relation),X1)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_26794,c_11630]) ).
tcf(c_29933,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(identity_relation),X2)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_26794,c_11019]) ).
tcf(c_29935,plain,
! [X0: $i] :
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(X0,subset_relation)) ),
inference(superposition,[status(thm)],[c_26794,c_11656]) ).
tcf(c_29936,plain,
! [X0: $i] :
( member(regular(identity_relation),complement(identity_relation))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(X0,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_26794,c_12409]) ).
tcf(c_29937,plain,
( member(regular(identity_relation),complement(element_relation))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_26794,c_15326]) ).
tcf(c_29938,plain,
( member(regular(identity_relation),complement(successor_relation))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_26794,c_14989]) ).
tcf(c_29939,plain,
( ( null_class = identity_relation )
| ~ member(regular(identity_relation),subset_relation)
| ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_26794,c_12788]) ).
tcf(c_29940,plain,
! [X0: $i] :
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(element_relation,X0)) ),
inference(superposition,[status(thm)],[c_26794,c_13233]) ).
tcf(c_29941,plain,
! [X0: $i] :
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(X0,element_relation)) ),
inference(superposition,[status(thm)],[c_26794,c_13248]) ).
tcf(c_29942,plain,
! [X0: $i] :
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(successor_relation,X0)) ),
inference(superposition,[status(thm)],[c_26794,c_13537]) ).
tcf(c_29943,plain,
! [X0: $i] :
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(X0,successor_relation)) ),
inference(superposition,[status(thm)],[c_26794,c_13552]) ).
tcf(c_29944,plain,
! [X0: $i] :
( member(regular(identity_relation),X0)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,complement(complement(X0))) ),
inference(superposition,[status(thm)],[c_26794,c_14000]) ).
tcf(c_29945,plain,
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,complement(complement(element_relation))) ),
inference(superposition,[status(thm)],[c_26794,c_14221]) ).
tcf(c_29946,plain,
( member(regular(identity_relation),cross_product(universal_class,universal_class))
| ( null_class = identity_relation )
| ~ subclass(subset_relation,complement(complement(successor_relation))) ),
inference(superposition,[status(thm)],[c_26794,c_14232]) ).
tcf(c_29947,plain,
! [X0: $i] :
( member(regular(identity_relation),iPr_def_10)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(unordered_pair(x,x),X0)) ),
inference(superposition,[status(thm)],[c_26794,c_16598]) ).
tcf(c_29948,plain,
! [X0: $i] :
( member(regular(identity_relation),iPr_def_10)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(X0,unordered_pair(x,x))) ),
inference(superposition,[status(thm)],[c_26794,c_17098]) ).
tcf(c_29949,plain,
! [X0: $i] :
( member(regular(identity_relation),iPr_def_10)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(unordered_pair(y,y),X0)) ),
inference(superposition,[status(thm)],[c_26794,c_18574]) ).
tcf(c_29950,plain,
! [X0: $i] :
( member(regular(identity_relation),iPr_def_10)
| ( null_class = identity_relation )
| ~ subclass(subset_relation,intersection(X0,unordered_pair(y,y))) ),
inference(superposition,[status(thm)],[c_26794,c_19011]) ).
tcf(c_29951,plain,
( ( null_class = identity_relation )
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,y)
| ~ member(regular(identity_relation),iPr_def_10) ),
inference(superposition,[status(thm)],[c_26794,c_20672]) ).
tcf(c_30303,plain,
( subclass(universal_class,complement(null_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_28902]) ).
tcf(c_30308,plain,
! [X0: $i] :
( subclass(X0,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_28902,c_4490]) ).
tcf(c_30309,plain,
( subclass(universal_class,universal_class)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_30303,c_8703]) ).
tcf(c_30318,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),universal_class)
| subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(demodulation,[status(thm)],[c_29285,c_193]) ).
tcf(c_30332,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ subclass(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_30318,c_176]) ).
tcf(c_30333,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),universal_class)
| subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_30318,c_250]) ).
tcf(c_30334,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_30318,c_170]) ).
tcf(c_30335,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_30318,c_5373]) ).
tcf(c_30336,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_30318,c_5371]) ).
tcf(c_30337,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_30318,c_5348]) ).
tcf(c_30338,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_30318,c_5346]) ).
tcf(c_30339,plain,
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_30318,c_14028]) ).
tcf(c_30340,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_30318,c_5287]) ).
tcf(c_30341,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_30318,c_5257]) ).
tcf(c_30343,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_30318,c_4722]) ).
tcf(c_30344,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_30318,c_4787]) ).
tcf(c_30345,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))))),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_30318,c_13998]) ).
tcf(c_30503,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),universal_class)
| subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(demodulation,[status(thm)],[c_29286,c_193]) ).
tcf(c_30517,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = X0 )
| ~ subclass(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_30503,c_176]) ).
tcf(c_30518,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X0),universal_class)
| subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_30503,c_250]) ).
tcf(c_30519,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(not_subclass_element(null_class,X1),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_30503,c_170]) ).
tcf(c_30520,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_30503,c_5373]) ).
tcf(c_30521,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_30503,c_5371]) ).
tcf(c_30522,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_30503,c_5348]) ).
tcf(c_30523,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_30503,c_5346]) ).
tcf(c_30524,plain,
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_30503,c_14028]) ).
tcf(c_30525,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_30503,c_5287]) ).
tcf(c_30526,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_30503,c_5257]) ).
tcf(c_30528,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0)),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_30503,c_4722]) ).
tcf(c_30529,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_30503,c_4787]) ).
tcf(c_30530,plain,
( member(not_subclass_element(null_class,complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))))),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))) = intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_30503,c_13998]) ).
tcf(c_30616,plain,
! [X0: $i] :
( ( intersection(intersection(iPr_def_10,y),X0) = null_class )
| ( regular(iPr_def_10) = x ) ),
inference(global_subsumption_just,[status(thm)],[c_21320,c_21320,c_28842]) ).
tcf(c_30617,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X0) = null_class ) ),
inference(renaming,[status(thm)],[c_30616]) ).
tcf(c_30625,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(intersection(iPr_def_10,y),X0)),X1)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(complement(null_class),X1),intersection(iPr_def_10,y))
| ~ member(not_subclass_element(complement(intersection(intersection(iPr_def_10,y),X0)),X1),X0) ),
inference(superposition,[status(thm)],[c_30617,c_5138]) ).
tcf(c_30626,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X0) = intersection(iPr_def_10,y) )
| ~ subclass(intersection(iPr_def_10,y),null_class) ),
inference(superposition,[status(thm)],[c_30617,c_4722]) ).
tcf(c_30633,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),intersection(iPr_def_10,y))
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4431]) ).
tcf(c_30635,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(null_class,X1),X2),X0)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4430]) ).
tcf(c_30637,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),X0)
| subclass(intersection(intersection(iPr_def_10,y),X0),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4245]) ).
tcf(c_30639,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),intersection(iPr_def_10,y))
| subclass(intersection(intersection(iPr_def_10,y),X0),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4224]) ).
tcf(c_30642,plain,
! [X0: $i,X1: $i] :
( subclass(X0,intersection(intersection(iPr_def_10,y),X1))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(X0,null_class),intersection(iPr_def_10,y))
| ~ member(not_subclass_element(X0,intersection(intersection(iPr_def_10,y),X1)),X1) ),
inference(superposition,[status(thm)],[c_30617,c_5134]) ).
tcf(c_30646,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,null_class),X2),intersection(iPr_def_10,y))
| subclass(intersection(X0,intersection(intersection(iPr_def_10,y),X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4647]) ).
tcf(c_30648,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,null_class),X2),X1)
| subclass(intersection(X0,intersection(intersection(iPr_def_10,y),X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4646]) ).
tcf(c_30654,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),universal_class)
| subclass(intersection(cross_product(X0,X1),intersection(iPr_def_10,y)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_5105]) ).
tcf(c_30655,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(iPr_def_10,y))
| subclass(intersection(cross_product(X0,X1),intersection(iPr_def_10,y)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4638]) ).
tcf(c_30656,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),cross_product(X0,X1))
| subclass(intersection(cross_product(X0,X1),intersection(iPr_def_10,y)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4424]) ).
tcf(c_30657,plain,
( member(regular(null_class),subset_relation)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),identity_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_30617,c_9850]) ).
tcf(c_30658,plain,
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),identity_relation) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_30617,c_11104]) ).
tcf(c_30659,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),subset_relation)
| subclass(intersection(intersection(iPr_def_10,y),identity_relation),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4649]) ).
tcf(c_30662,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(cross_product(X0,X1),intersection(iPr_def_10,y)) = null_class ) ),
inference(superposition,[status(thm)],[c_30617,c_193]) ).
tcf(c_30663,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ~ member(X0,domain_of(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_30617,c_194]) ).
tcf(c_30664,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),compose(X1,intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x )
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_30617,c_215]) ).
tcf(c_30665,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(intersection(iPr_def_10,y),X2))
| ( regular(iPr_def_10) = x )
| ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_30617,c_215]) ).
tcf(c_30666,plain,
! [X0: $i] :
( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
| ( regular(iPr_def_10) = x )
| ~ member(X0,universal_class)
| ~ function(intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_30617,c_221]) ).
tcf(c_30667,plain,
! [X0: $i,X1: $i] :
( homomorphism(intersection(iPr_def_10,y),X1,X0)
| ( regular(iPr_def_10) = x )
| ~ operation(X1)
| ~ operation(X0)
| ~ compatible(intersection(iPr_def_10,y),X1,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_30617,c_244]) ).
tcf(c_30668,plain,
! [X0: $i,X1: $i] :
( homomorphism(intersection(iPr_def_10,y),X1,X0)
| ( regular(iPr_def_10) = x )
| ~ operation(X1)
| ~ operation(X0)
| ~ compatible(intersection(iPr_def_10,y),X1,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_30617,c_244]) ).
tcf(c_30669,plain,
! [X0: $i,X1: $i] :
( homomorphism(X0,X1,intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ operation(X1)
| ~ operation(intersection(iPr_def_10,y))
| ~ compatible(X0,X1,intersection(iPr_def_10,y))
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(iPr_def_10,y)),not_homomorphism1(X0,X1,intersection(iPr_def_10,y))),unordered_pair(not_homomorphism1(X0,X1,intersection(iPr_def_10,y)),unordered_pair(not_homomorphism2(X0,X1,intersection(iPr_def_10,y)),not_homomorphism2(X0,X1,intersection(iPr_def_10,y))))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(iPr_def_10,y)),not_homomorphism1(X0,X1,intersection(iPr_def_10,y))),unordered_pair(not_homomorphism1(X0,X1,intersection(iPr_def_10,y)),unordered_pair(not_homomorphism2(X0,X1,intersection(iPr_def_10,y)),not_homomorphism2(X0,X1,intersection(iPr_def_10,y)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(iPr_def_10,y)),not_homomorphism1(X0,X1,intersection(iPr_def_10,y))),unordered_pair(not_homomorphism1(X0,X1,intersection(iPr_def_10,y)),unordered_pair(not_homomorphism2(X0,X1,intersection(iPr_def_10,y)),not_homomorphism2(X0,X1,intersection(iPr_def_10,y))))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(iPr_def_10,y)),not_homomorphism1(X0,X1,intersection(iPr_def_10,y))),unordered_pair(not_homomorphism1(X0,X1,intersection(iPr_def_10,y)),unordered_pair(not_homomorphism2(X0,X1,intersection(iPr_def_10,y)),not_homomorphism2(X0,X1,intersection(iPr_def_10,y)))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_30617,c_244]) ).
tcf(c_30670,plain,
! [X0: $i,X1: $i] :
( homomorphism(intersection(iPr_def_10,y),X1,X0)
| ( regular(iPr_def_10) = x )
| ~ operation(X1)
| ~ operation(X0)
| ~ compatible(intersection(iPr_def_10,y),X1,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism1(intersection(iPr_def_10,y),X1,X0),not_homomorphism1(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(not_homomorphism2(intersection(iPr_def_10,y),X1,X0),not_homomorphism2(intersection(iPr_def_10,y),X1,X0)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_30617,c_244]) ).
tcf(c_30678,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(intersection(iPr_def_10,y),intersection(X0,X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4647]) ).
tcf(c_30680,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(intersection(iPr_def_10,y),intersection(X0,X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4646]) ).
tcf(c_30681,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(intersection(iPr_def_10,y),complement(X1)),X0)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_30617,c_4648]) ).
tcf(c_30682,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),X0) = X0 )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_30617,c_4787]) ).
tcf(c_30687,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(intersection(iPr_def_10,y),unordered_pair(x,x)),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_4977]) ).
tcf(c_30689,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(intersection(iPr_def_10,y),unordered_pair(y,y)),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_5001]) ).
tcf(c_30776,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(X0,intersection(intersection(iPr_def_10,y),X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_30648,c_4790]) ).
tcf(c_30790,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(iPr_def_10,y))
| subclass(intersection(X0,intersection(intersection(iPr_def_10,y),X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_30646,c_4790]) ).
tcf(c_30801,plain,
! [X0: $i,X1: $i] :
( subclass(complement(intersection(intersection(iPr_def_10,y),X0)),X1)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(universal_class,X1),intersection(iPr_def_10,y))
| ~ member(not_subclass_element(complement(intersection(intersection(iPr_def_10,y),X0)),X1),X0) ),
inference(light_normalisation,[status(thm)],[c_30625,c_8703]) ).
tcf(c_31010,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),y)
| subclass(intersection(iPr_def_10,y),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_257,c_21235]) ).
tcf(c_31011,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),universal_class)
| member(not_subclass_element(null_class,X0),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_173,c_21235]) ).
tcf(c_31012,plain,
( member(not_subclass_element(null_class,element_relation),y)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_185,c_21235]) ).
tcf(c_31013,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,rotate(X0)),y)
| subclass(intersection(iPr_def_10,y),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_196,c_21235]) ).
tcf(c_31014,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,flip(X0)),y)
| subclass(intersection(iPr_def_10,y),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_199,c_21235]) ).
tcf(c_31015,plain,
( member(not_subclass_element(null_class,successor_relation),y)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_202,c_21235]) ).
tcf(c_31016,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,compose(X0,X1)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_213,c_21235]) ).
tcf(c_31017,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),y)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4571,c_21235]) ).
tcf(c_31018,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),y)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_218,c_21235]) ).
tcf(c_31019,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),identity_relation)
| member(not_subclass_element(null_class,compose(X0,domain_of(flip(cross_product(X0,universal_class))))),y)
| ( regular(iPr_def_10) = x )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_219,c_21235]) ).
tcf(c_31020,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),domain_of(domain_of(X0)))
| member(not_subclass_element(null_class,domain_of(domain_of(flip(cross_product(X0,universal_class))))),y)
| ( regular(iPr_def_10) = x )
| ~ operation(X0) ),
inference(superposition,[status(thm)],[c_233,c_21235]) ).
tcf(c_31021,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),unordered_pair(X0,X1))
| member(not_subclass_element(null_class,unordered_pair(X0,X0)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_262,c_21235]) ).
tcf(c_31022,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),unordered_pair(X1,X0))
| member(not_subclass_element(null_class,unordered_pair(X0,X0)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_263,c_21235]) ).
tcf(c_31023,plain,
( subclass(intersection(iPr_def_10,y),omega)
| member(not_subclass_element(null_class,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_1565,c_21235]) ).
tcf(c_31024,plain,
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,unordered_pair(x,x)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4147,c_21235]) ).
tcf(c_31025,plain,
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,unordered_pair(y,y)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4149,c_21235]) ).
tcf(c_31026,plain,
( subclass(intersection(iPr_def_10,y),subset_relation)
| member(not_subclass_element(null_class,identity_relation),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4319,c_21235]) ).
tcf(c_31027,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(X0,X1)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4427,c_21235]) ).
tcf(c_31028,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,unordered_pair(x,x)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4500,c_21235]) ).
tcf(c_31029,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,unordered_pair(y,y)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4501,c_21235]) ).
tcf(c_31030,plain,
( member(not_subclass_element(null_class,identity_relation),y)
| subclass(intersection(iPr_def_10,y),domain_of(flip(cross_product(subset_relation,universal_class))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4550,c_21235]) ).
tcf(c_31031,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X0,X2)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4551,c_21235]) ).
tcf(c_31032,plain,
( member(not_subclass_element(null_class,identity_relation),y)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_7256,c_21235]) ).
tcf(c_31033,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X0,X1)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4643,c_21235]) ).
tcf(c_31034,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X2,X0)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4788,c_21235]) ).
tcf(c_31035,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,complement(complement(X0))),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13999,c_21235]) ).
tcf(c_31036,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,complement(cross_product(universal_class,universal_class))),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(element_relation),X0) ),
inference(superposition,[status(thm)],[c_15325,c_21235]) ).
tcf(c_31037,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,complement(cross_product(universal_class,universal_class))),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(successor_relation),X0) ),
inference(superposition,[status(thm)],[c_14988,c_21235]) ).
tcf(c_31038,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,complement(cross_product(universal_class,universal_class))),y)
| ( regular(iPr_def_10) = x )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13276,c_21235]) ).
tcf(c_31039,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(intersection(X0,X1),X2)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6065,c_21235]) ).
tcf(c_31040,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),subset_relation)
| member(not_subclass_element(null_class,intersection(identity_relation,X0)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6244,c_21235]) ).
tcf(c_31041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(intersection(X2,X0),X3)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6249,c_21235]) ).
tcf(c_31042,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(identity_relation,X1)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_6317,c_21235]) ).
tcf(c_31043,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(intersection(X0,X1),X2)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6583,c_21235]) ).
tcf(c_31044,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(identity_relation,X0)),y)
| subclass(intersection(iPr_def_10,y),domain_of(flip(cross_product(subset_relation,universal_class))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6777,c_21235]) ).
tcf(c_31045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(intersection(X0,X2),X3)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6782,c_21235]) ).
tcf(c_31046,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(complement(cross_product(universal_class,universal_class)),X0)),y)
| ( regular(iPr_def_10) = x )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_21235]) ).
tcf(c_31047,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(subset_relation,X0)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6976,c_21235]) ).
tcf(c_31048,plain,
( member(not_subclass_element(null_class,subset_relation),y)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6992,c_21235]) ).
tcf(c_31049,plain,
( member(not_subclass_element(null_class,subset_relation),y)
| subclass(intersection(iPr_def_10,y),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6993,c_21235]) ).
tcf(c_31050,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))),y)
| ( regular(iPr_def_10) = x )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_21235]) ).
tcf(c_31051,plain,
( member(not_subclass_element(null_class,identity_relation),y)
| subclass(intersection(iPr_def_10,y),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_8169,c_21235]) ).
tcf(c_31052,plain,
( subclass(intersection(iPr_def_10,y),complement(identity_relation))
| member(not_subclass_element(null_class,complement(subset_relation)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_8763,c_21235]) ).
tcf(c_31053,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),complement(identity_relation))
| member(not_subclass_element(null_class,intersection(complement(subset_relation),X0)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_8764,c_21235]) ).
tcf(c_31054,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(complement(subset_relation),X1)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_8784,c_21235]) ).
tcf(c_31055,plain,
( member(not_subclass_element(null_class,complement(subset_relation)),y)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_8802,c_21235]) ).
tcf(c_31056,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X2)
| member(not_subclass_element(null_class,intersection(X0,intersection(X1,X2))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_10731,c_21235]) ).
tcf(c_31057,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),subset_relation)
| member(not_subclass_element(null_class,intersection(X0,identity_relation)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_11013,c_21235]) ).
tcf(c_31058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X2,intersection(X3,X0))),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11018,c_21235]) ).
tcf(c_31059,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(X1,identity_relation)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_11105,c_21235]) ).
tcf(c_31060,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X0,intersection(X1,X2))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_11340,c_21235]) ).
tcf(c_31061,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,subset_relation)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_11622,c_21235]) ).
tcf(c_31062,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,identity_relation)),y)
| subclass(intersection(iPr_def_10,y),domain_of(flip(cross_product(subset_relation,universal_class))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_11623,c_21235]) ).
tcf(c_31063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X2,intersection(X0,X3))),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11629,c_21235]) ).
tcf(c_31064,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X0,complement(cross_product(universal_class,universal_class)))),y)
| ( regular(iPr_def_10) = x )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_21235]) ).
tcf(c_31065,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),complement(identity_relation))
| member(not_subclass_element(null_class,intersection(X0,complement(subset_relation))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_12038,c_21235]) ).
tcf(c_31066,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(X1,complement(subset_relation))),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_12408,c_21235]) ).
tcf(c_31067,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(element_relation,X0)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13156,c_21235]) ).
tcf(c_31068,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,element_relation)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13157,c_21235]) ).
tcf(c_31069,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(intersection(X0,element_relation),X1)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13159,c_21235]) ).
tcf(c_31070,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(intersection(element_relation,X0),X1)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13160,c_21235]) ).
tcf(c_31071,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,intersection(X1,element_relation))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13162,c_21235]) ).
tcf(c_31072,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,intersection(element_relation,X1))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13163,c_21235]) ).
tcf(c_31073,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(successor_relation,X0)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13498,c_21235]) ).
tcf(c_31074,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,successor_relation)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13499,c_21235]) ).
tcf(c_31075,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(intersection(X0,successor_relation),X1)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13501,c_21235]) ).
tcf(c_31076,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(intersection(successor_relation,X0),X1)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13502,c_21235]) ).
tcf(c_31077,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,intersection(X1,successor_relation))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13504,c_21235]) ).
tcf(c_31078,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,intersection(successor_relation,X1))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13505,c_21235]) ).
tcf(c_31079,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,complement(complement(X0))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13755,c_21235]) ).
tcf(c_31080,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,complement(complement(element_relation))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13773,c_21235]) ).
tcf(c_31081,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,complement(complement(successor_relation))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13774,c_21235]) ).
tcf(c_31082,plain,
( subclass(intersection(iPr_def_10,y),complement(successor_relation))
| member(not_subclass_element(null_class,complement(cross_product(universal_class,universal_class))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_14369,c_21235]) ).
tcf(c_31083,plain,
( subclass(intersection(iPr_def_10,y),complement(element_relation))
| member(not_subclass_element(null_class,complement(cross_product(universal_class,universal_class))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_15156,c_21235]) ).
tcf(c_31084,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,intersection(unordered_pair(x,x),X0)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_16430,c_21235]) ).
tcf(c_31085,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(unordered_pair(x,x),X1)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_16597,c_21235]) ).
tcf(c_31086,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,intersection(X0,unordered_pair(x,x))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_17069,c_21235]) ).
tcf(c_31087,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(X1,unordered_pair(x,x))),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_17097,c_21235]) ).
tcf(c_31088,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,intersection(unordered_pair(y,y),X0)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_18490,c_21235]) ).
tcf(c_31089,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(unordered_pair(y,y),X1)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_18573,c_21235]) ).
tcf(c_31090,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,intersection(X0,unordered_pair(y,y))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_18969,c_21235]) ).
tcf(c_31091,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(X1,unordered_pair(y,y))),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_19010,c_21235]) ).
tcf(c_31092,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X1),iPr_def_10)
| member(not_subclass_element(null_class,intersection(intersection(iPr_def_10,y),X0)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20688,c_21235]) ).
tcf(c_31093,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X1),y)
| member(not_subclass_element(null_class,intersection(intersection(iPr_def_10,y),X0)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20684,c_21235]) ).
tcf(c_31094,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),iPr_def_10)
| member(not_subclass_element(null_class,intersection(iPr_def_10,y)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20610,c_21235]) ).
tcf(c_31095,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),y)
| member(not_subclass_element(null_class,intersection(iPr_def_10,y)),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20608,c_21235]) ).
tcf(c_31096,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X1),iPr_def_10)
| member(not_subclass_element(null_class,intersection(X0,intersection(iPr_def_10,y))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20680,c_21235]) ).
tcf(c_31097,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X1),y)
| member(not_subclass_element(null_class,intersection(X0,intersection(iPr_def_10,y))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20676,c_21235]) ).
tcf(c_31098,plain,
( subclass(intersection(iPr_def_10,y),domain_of(y))
| member(not_subclass_element(null_class,domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class))))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_20810,c_21235]) ).
tcf(c_31099,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(x,x)),y)
| ( regular(iPr_def_10) = x )
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_20872,c_21235]) ).
tcf(c_31100,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(y,y)),y)
| ( regular(iPr_def_10) = x )
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_20901,c_21235]) ).
tcf(c_31101,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),universal_class)
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_30503,c_21235]) ).
tcf(c_31102,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22551,c_21235]) ).
tcf(c_31103,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22572,c_21235]) ).
tcf(c_31104,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22553,c_21235]) ).
tcf(c_31105,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),element_relation)
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22570,c_21235]) ).
tcf(c_31106,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),universal_class)
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_30318,c_21235]) ).
tcf(c_31107,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22872,c_21235]) ).
tcf(c_31108,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22893,c_21235]) ).
tcf(c_31109,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22874,c_21235]) ).
tcf(c_31110,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),element_relation)
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22891,c_21235]) ).
tcf(c_31111,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),y)
| subclass(intersection(iPr_def_10,y),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_21235]) ).
tcf(c_31112,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),y)
| subclass(intersection(iPr_def_10,y),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_21235]) ).
tcf(c_32128,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| member(not_subclass_element(null_class,X1),y) ),
inference(global_subsumption_just,[status(thm)],[c_21236,c_21236,c_29172]) ).
tcf(c_32129,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),y)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(iPr_def_10,y)) ),
inference(renaming,[status(thm)],[c_32128]) ).
tcf(c_32138,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X0),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_171,c_32129]) ).
tcf(c_32139,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),y)
| member(not_subclass_element(X0,intersection(iPr_def_10,y)),X0)
| ( regular(iPr_def_10) = x )
| ( intersection(iPr_def_10,y) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_32129]) ).
tcf(c_32144,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),y)
| subclass(intersection(intersection(iPr_def_10,y),X0),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4224,c_32129]) ).
tcf(c_32146,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),y)
| subclass(intersection(X0,intersection(iPr_def_10,y)),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4245,c_32129]) ).
tcf(c_32148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),y)
| subclass(intersection(intersection(iPr_def_10,y),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4425,c_32129]) ).
tcf(c_32149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),y)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4430,c_32129]) ).
tcf(c_32150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),y)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4431,c_32129]) ).
tcf(c_32152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),y)
| subclass(intersection(cross_product(X0,X1),intersection(iPr_def_10,y)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4638,c_32129]) ).
tcf(c_32153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),y)
| subclass(intersection(X0,intersection(X1,intersection(iPr_def_10,y))),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4646,c_32129]) ).
tcf(c_32154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),y)
| subclass(intersection(X0,intersection(intersection(iPr_def_10,y),X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4647,c_32129]) ).
tcf(c_32155,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),y)
| subclass(complement(complement(intersection(iPr_def_10,y))),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13744,c_32129]) ).
tcf(c_32157,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(null_class,X0),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_26791,c_32129]) ).
tcf(c_32158,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),y)
| ( null_class = identity_relation )
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_26794,c_32129]) ).
tcf(c_32311,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),iPr_def_10)
| subclass(intersection(iPr_def_10,y),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_257,c_21314]) ).
tcf(c_32312,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),universal_class)
| member(not_subclass_element(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_173,c_21314]) ).
tcf(c_32313,plain,
( member(not_subclass_element(null_class,element_relation),iPr_def_10)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_185,c_21314]) ).
tcf(c_32314,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,rotate(X0)),iPr_def_10)
| subclass(intersection(iPr_def_10,y),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_196,c_21314]) ).
tcf(c_32315,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,flip(X0)),iPr_def_10)
| subclass(intersection(iPr_def_10,y),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_199,c_21314]) ).
tcf(c_32316,plain,
( member(not_subclass_element(null_class,successor_relation),iPr_def_10)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_202,c_21314]) ).
tcf(c_32317,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,compose(X0,X1)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_213,c_21314]) ).
tcf(c_32318,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_4571,c_21314]) ).
tcf(c_32319,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_218,c_21314]) ).
tcf(c_32320,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),identity_relation)
| member(not_subclass_element(null_class,compose(X0,domain_of(flip(cross_product(X0,universal_class))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_219,c_21314]) ).
tcf(c_32321,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),domain_of(domain_of(X0)))
| member(not_subclass_element(null_class,domain_of(domain_of(flip(cross_product(X0,universal_class))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ operation(X0) ),
inference(superposition,[status(thm)],[c_233,c_21314]) ).
tcf(c_32322,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),unordered_pair(X0,X1))
| member(not_subclass_element(null_class,unordered_pair(X0,X0)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_262,c_21314]) ).
tcf(c_32323,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),unordered_pair(X1,X0))
| member(not_subclass_element(null_class,unordered_pair(X0,X0)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_263,c_21314]) ).
tcf(c_32324,plain,
( subclass(intersection(iPr_def_10,y),omega)
| member(not_subclass_element(null_class,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_1565,c_21314]) ).
tcf(c_32325,plain,
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,unordered_pair(x,x)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4147,c_21314]) ).
tcf(c_32326,plain,
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,unordered_pair(y,y)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4149,c_21314]) ).
tcf(c_32327,plain,
( subclass(intersection(iPr_def_10,y),subset_relation)
| member(not_subclass_element(null_class,identity_relation),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4319,c_21314]) ).
tcf(c_32328,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(X0,X1)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4427,c_21314]) ).
tcf(c_32329,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,unordered_pair(x,x)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4500,c_21314]) ).
tcf(c_32330,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,unordered_pair(y,y)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4501,c_21314]) ).
tcf(c_32331,plain,
( member(not_subclass_element(null_class,identity_relation),iPr_def_10)
| subclass(intersection(iPr_def_10,y),domain_of(flip(cross_product(subset_relation,universal_class))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4550,c_21314]) ).
tcf(c_32332,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X0,X2)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4551,c_21314]) ).
tcf(c_32333,plain,
( member(not_subclass_element(null_class,identity_relation),iPr_def_10)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_7256,c_21314]) ).
tcf(c_32334,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X0,X1)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4643,c_21314]) ).
tcf(c_32335,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X2,X0)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4788,c_21314]) ).
tcf(c_32336,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,complement(complement(X0))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13999,c_21314]) ).
tcf(c_32337,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,complement(cross_product(universal_class,universal_class))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(element_relation),X0) ),
inference(superposition,[status(thm)],[c_15325,c_21314]) ).
tcf(c_32338,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,complement(cross_product(universal_class,universal_class))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(successor_relation),X0) ),
inference(superposition,[status(thm)],[c_14988,c_21314]) ).
tcf(c_32339,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,complement(cross_product(universal_class,universal_class))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13276,c_21314]) ).
tcf(c_32340,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(intersection(X0,X1),X2)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6065,c_21314]) ).
tcf(c_32341,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),subset_relation)
| member(not_subclass_element(null_class,intersection(identity_relation,X0)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6244,c_21314]) ).
tcf(c_32342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(intersection(X2,X0),X3)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6249,c_21314]) ).
tcf(c_32343,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(identity_relation,X1)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_6317,c_21314]) ).
tcf(c_32344,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(intersection(X0,X1),X2)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6583,c_21314]) ).
tcf(c_32345,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(identity_relation,X0)),iPr_def_10)
| subclass(intersection(iPr_def_10,y),domain_of(flip(cross_product(subset_relation,universal_class))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6777,c_21314]) ).
tcf(c_32346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(intersection(X0,X2),X3)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6782,c_21314]) ).
tcf(c_32347,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(complement(cross_product(universal_class,universal_class)),X0)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13279,c_21314]) ).
tcf(c_32348,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(subset_relation,X0)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6976,c_21314]) ).
tcf(c_32349,plain,
( member(not_subclass_element(null_class,subset_relation),iPr_def_10)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6992,c_21314]) ).
tcf(c_32350,plain,
( member(not_subclass_element(null_class,subset_relation),iPr_def_10)
| subclass(intersection(iPr_def_10,y),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_6993,c_21314]) ).
tcf(c_32351,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ operation(null_class) ),
inference(superposition,[status(thm)],[c_7697,c_21314]) ).
tcf(c_32352,plain,
( member(not_subclass_element(null_class,identity_relation),iPr_def_10)
| subclass(intersection(iPr_def_10,y),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_8169,c_21314]) ).
tcf(c_32353,plain,
( subclass(intersection(iPr_def_10,y),complement(identity_relation))
| member(not_subclass_element(null_class,complement(subset_relation)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_8763,c_21314]) ).
tcf(c_32354,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),complement(identity_relation))
| member(not_subclass_element(null_class,intersection(complement(subset_relation),X0)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_8764,c_21314]) ).
tcf(c_32355,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(complement(subset_relation),X1)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_8784,c_21314]) ).
tcf(c_32356,plain,
( member(not_subclass_element(null_class,complement(subset_relation)),iPr_def_10)
| subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_8802,c_21314]) ).
tcf(c_32357,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X2)
| member(not_subclass_element(null_class,intersection(X0,intersection(X1,X2))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_10731,c_21314]) ).
tcf(c_32358,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),subset_relation)
| member(not_subclass_element(null_class,intersection(X0,identity_relation)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_11013,c_21314]) ).
tcf(c_32359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X2,intersection(X3,X0))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11018,c_21314]) ).
tcf(c_32360,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(X1,identity_relation)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_11105,c_21314]) ).
tcf(c_32361,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X0,intersection(X1,X2))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_11340,c_21314]) ).
tcf(c_32362,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,subset_relation)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_11622,c_21314]) ).
tcf(c_32363,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,intersection(X0,identity_relation)),iPr_def_10)
| subclass(intersection(iPr_def_10,y),domain_of(flip(cross_product(subset_relation,universal_class))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_11623,c_21314]) ).
tcf(c_32364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X2,intersection(X0,X3))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11629,c_21314]) ).
tcf(c_32365,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,intersection(X0,complement(cross_product(universal_class,universal_class)))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13280,c_21314]) ).
tcf(c_32366,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),complement(identity_relation))
| member(not_subclass_element(null_class,intersection(X0,complement(subset_relation))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_12038,c_21314]) ).
tcf(c_32367,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(X1,complement(subset_relation))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_12408,c_21314]) ).
tcf(c_32368,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(element_relation,X0)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13156,c_21314]) ).
tcf(c_32369,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,element_relation)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13157,c_21314]) ).
tcf(c_32370,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(intersection(X0,element_relation),X1)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13159,c_21314]) ).
tcf(c_32371,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(intersection(element_relation,X0),X1)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13160,c_21314]) ).
tcf(c_32372,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,intersection(X1,element_relation))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13162,c_21314]) ).
tcf(c_32373,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,intersection(element_relation,X1))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13163,c_21314]) ).
tcf(c_32374,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(successor_relation,X0)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13498,c_21314]) ).
tcf(c_32375,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,successor_relation)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13499,c_21314]) ).
tcf(c_32376,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(intersection(X0,successor_relation),X1)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13501,c_21314]) ).
tcf(c_32377,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(intersection(successor_relation,X0),X1)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13502,c_21314]) ).
tcf(c_32378,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,intersection(X1,successor_relation))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13504,c_21314]) ).
tcf(c_32379,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,intersection(X0,intersection(successor_relation,X1))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13505,c_21314]) ).
tcf(c_32380,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,complement(complement(X0))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13755,c_21314]) ).
tcf(c_32381,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,complement(complement(element_relation))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13773,c_21314]) ).
tcf(c_32382,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,complement(complement(successor_relation))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13774,c_21314]) ).
tcf(c_32383,plain,
( subclass(intersection(iPr_def_10,y),complement(successor_relation))
| member(not_subclass_element(null_class,complement(cross_product(universal_class,universal_class))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_14369,c_21314]) ).
tcf(c_32384,plain,
( subclass(intersection(iPr_def_10,y),complement(element_relation))
| member(not_subclass_element(null_class,complement(cross_product(universal_class,universal_class))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_15156,c_21314]) ).
tcf(c_32385,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,intersection(unordered_pair(x,x),X0)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_16430,c_21314]) ).
tcf(c_32386,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(unordered_pair(x,x),X1)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_16597,c_21314]) ).
tcf(c_32387,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,intersection(X0,unordered_pair(x,x))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_17069,c_21314]) ).
tcf(c_32388,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(X1,unordered_pair(x,x))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_17097,c_21314]) ).
tcf(c_32389,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,intersection(unordered_pair(y,y),X0)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_18490,c_21314]) ).
tcf(c_32390,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(unordered_pair(y,y),X1)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_18573,c_21314]) ).
tcf(c_32391,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),iPr_def_10)
| member(not_subclass_element(null_class,intersection(X0,unordered_pair(y,y))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_18969,c_21314]) ).
tcf(c_32392,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,intersection(X1,unordered_pair(y,y))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_19010,c_21314]) ).
tcf(c_32393,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X1),iPr_def_10)
| member(not_subclass_element(null_class,intersection(intersection(iPr_def_10,y),X0)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20688,c_21314]) ).
tcf(c_32394,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X1),y)
| member(not_subclass_element(null_class,intersection(intersection(iPr_def_10,y),X0)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20684,c_21314]) ).
tcf(c_32395,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),iPr_def_10)
| member(not_subclass_element(null_class,intersection(iPr_def_10,y)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20610,c_21314]) ).
tcf(c_32396,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),y)
| member(not_subclass_element(null_class,intersection(iPr_def_10,y)),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20608,c_21314]) ).
tcf(c_32397,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X1),iPr_def_10)
| member(not_subclass_element(null_class,intersection(X0,intersection(iPr_def_10,y))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20680,c_21314]) ).
tcf(c_32398,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X1),y)
| member(not_subclass_element(null_class,intersection(X0,intersection(iPr_def_10,y))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20676,c_21314]) ).
tcf(c_32399,plain,
( subclass(intersection(iPr_def_10,y),domain_of(y))
| member(not_subclass_element(null_class,domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_20810,c_21314]) ).
tcf(c_32400,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(x,x)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_20872,c_21314]) ).
tcf(c_32401,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(y,y)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_20901,c_21314]) ).
tcf(c_32402,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),universal_class)
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_30503,c_21314]) ).
tcf(c_32403,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22551,c_21314]) ).
tcf(c_32404,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22572,c_21314]) ).
tcf(c_32405,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22553,c_21314]) ).
tcf(c_32406,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),element_relation)
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22570,c_21314]) ).
tcf(c_32407,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),universal_class)
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_30318,c_21314]) ).
tcf(c_32408,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22872,c_21314]) ).
tcf(c_32409,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22893,c_21314]) ).
tcf(c_32410,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22874,c_21314]) ).
tcf(c_32411,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,X0),element_relation)
| member(not_subclass_element(null_class,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22891,c_21314]) ).
tcf(c_32412,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(iPr_def_10,y),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_21314]) ).
tcf(c_32413,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(iPr_def_10,y),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_21314]) ).
tcf(c_33334,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| member(not_subclass_element(null_class,X1),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_21315,c_21315,c_29172]) ).
tcf(c_33335,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ member(X0,intersection(iPr_def_10,y)) ),
inference(renaming,[status(thm)],[c_33334]) ).
tcf(c_33344,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_10,y),X1)
| member(not_subclass_element(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_171,c_33335]) ).
tcf(c_33345,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),iPr_def_10)
| member(not_subclass_element(X0,intersection(iPr_def_10,y)),X0)
| ( regular(iPr_def_10) = x )
| ( intersection(iPr_def_10,y) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_33335]) ).
tcf(c_33350,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),iPr_def_10)
| subclass(intersection(intersection(iPr_def_10,y),X0),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4224,c_33335]) ).
tcf(c_33352,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),iPr_def_10)
| subclass(intersection(X0,intersection(iPr_def_10,y)),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4245,c_33335]) ).
tcf(c_33354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),iPr_def_10)
| subclass(intersection(intersection(iPr_def_10,y),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4425,c_33335]) ).
tcf(c_33355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),iPr_def_10)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4430,c_33335]) ).
tcf(c_33356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),iPr_def_10)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4431,c_33335]) ).
tcf(c_33358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),iPr_def_10)
| subclass(intersection(cross_product(X0,X1),intersection(iPr_def_10,y)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4638,c_33335]) ).
tcf(c_33359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),iPr_def_10)
| subclass(intersection(X0,intersection(X1,intersection(iPr_def_10,y))),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4646,c_33335]) ).
tcf(c_33360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),iPr_def_10)
| subclass(intersection(X0,intersection(intersection(iPr_def_10,y),X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4647,c_33335]) ).
tcf(c_33361,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),iPr_def_10)
| subclass(complement(complement(intersection(iPr_def_10,y))),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13744,c_33335]) ).
tcf(c_33363,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X1)
| member(not_subclass_element(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_26791,c_33335]) ).
tcf(c_33364,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| ( null_class = identity_relation )
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_26794,c_33335]) ).
tcf(c_33461,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(iPr_def_10,y)),X1) = null_class )
| ~ function(y) ),
inference(superposition,[status(thm)],[c_21237,c_4342]) ).
tcf(c_33462,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(iPr_def_10,y)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_21237,c_4336]) ).
tcf(c_33463,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(iPr_def_10,y)),X1) = null_class )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_21237,c_20672]) ).
tcf(c_33514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,X1),cross_product(X2,X3)),X4)
| member(not_subclass_element(intersection(intersection(X0,X1),cross_product(X2,X3)),X4),X1) ),
inference(superposition,[status(thm)],[c_193,c_5411]) ).
tcf(c_33515,plain,
! [X0: $i] :
( member(not_subclass_element(subset_relation,X0),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| subclass(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),cross_product(universal_class,universal_class)),X0) ),
inference(superposition,[status(thm)],[c_229,c_5411]) ).
tcf(c_33517,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(x,x),universal_class)),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_5411]) ).
tcf(c_33518,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(y,y),universal_class)),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_5411]) ).
tcf(c_33519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),X0)
| subclass(intersection(intersection(complement(X0),X0),cross_product(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_4169,c_5411]) ).
tcf(c_33520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(cross_product(X3,X4),X2),cross_product(X0,X1)),X5)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,cross_product(X3,X4))),X5),X2) ),
inference(superposition,[status(thm)],[c_193,c_5411]) ).
tcf(c_33521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),regular(X0))
| subclass(intersection(intersection(X0,regular(X0)),cross_product(X1,X2)),X3)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_5411]) ).
tcf(c_33522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X4,cross_product(X2,X3)),cross_product(X0,X1)),X5)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(cross_product(X2,X3),X4)),X5),cross_product(X2,X3)) ),
inference(superposition,[status(thm)],[c_193,c_5411]) ).
tcf(c_33523,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),subset_relation),X2),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(intersection(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_229,c_5411]) ).
tcf(c_33524,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),identity_relation),X2),subset_relation)
| subclass(intersection(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_230,c_5411]) ).
tcf(c_33525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(null_class,X3),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),X3) ),
inference(superposition,[status(thm)],[c_4553,c_5411]) ).
tcf(c_33526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),null_class)
| subclass(intersection(intersection(X0,null_class),cross_product(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_4790,c_5411]) ).
tcf(c_33527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),intersection(X1,X0))
| subclass(intersection(intersection(complement(X0),intersection(X1,X0)),cross_product(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_11228,c_5411]) ).
tcf(c_33528,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),identity_relation)
| subclass(intersection(intersection(complement(subset_relation),identity_relation),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_11311,c_5411]) ).
tcf(c_33529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),intersection(X0,X1))
| subclass(intersection(intersection(complement(X0),intersection(X0,X1)),cross_product(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_11685,c_5411]) ).
tcf(c_33530,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),subset_relation)
| subclass(intersection(intersection(complement(cross_product(universal_class,universal_class)),subset_relation),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_11763,c_5411]) ).
tcf(c_33531,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),identity_relation)
| subclass(intersection(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_12282,c_5411]) ).
tcf(c_33532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),complement(X0))
| subclass(intersection(intersection(X0,complement(X0)),cross_product(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_12377,c_5411]) ).
tcf(c_33533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),complement(X1))
| subclass(intersection(intersection(intersection(X0,X1),complement(X1)),cross_product(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_12625,c_5411]) ).
tcf(c_33534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),complement(X0))
| subclass(intersection(intersection(intersection(X0,X1),complement(X0)),cross_product(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_12688,c_5411]) ).
tcf(c_33535,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(identity_relation,complement(subset_relation)),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_12394,c_5411]) ).
tcf(c_33536,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(subset_relation,complement(cross_product(universal_class,universal_class))),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_12738,c_5411]) ).
tcf(c_33537,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(superposition,[status(thm)],[c_13003,c_5411]) ).
tcf(c_33538,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(iPr_def_10))
| subclass(intersection(intersection(unordered_pair(x,x),complement(iPr_def_10)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_16614,c_5411]) ).
tcf(c_33539,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),unordered_pair(x,x))
| subclass(intersection(intersection(complement(iPr_def_10),unordered_pair(x,x)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_17131,c_5411]) ).
tcf(c_33540,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(iPr_def_10))
| subclass(intersection(intersection(unordered_pair(y,y),complement(iPr_def_10)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_18749,c_5411]) ).
tcf(c_33541,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),unordered_pair(y,y))
| subclass(intersection(intersection(complement(iPr_def_10),unordered_pair(y,y)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_19300,c_5411]) ).
tcf(c_33542,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(iPr_def_10,y),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_5411]) ).
tcf(c_33543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),X0)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),cross_product(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_5411]) ).
tcf(c_33544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),intersection(iPr_def_10,y))
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),cross_product(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_5411]) ).
tcf(c_33545,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_5411]) ).
tcf(c_33546,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_5411]) ).
tcf(c_33547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,universal_class),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,universal_class)),X3),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,universal_class)),X3),not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,universal_class)),X3)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_5411,c_20813]) ).
tcf(c_33548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X3,X0),cross_product(X1,X2)),X0)
| ( intersection(cross_product(X1,X2),intersection(X3,X0)) = X0 )
| ~ member(not_subclass_element(X0,intersection(cross_product(X1,X2),intersection(X3,X0))),intersection(cross_product(X1,X2),intersection(X3,X0))) ),
inference(superposition,[status(thm)],[c_5411,c_254]) ).
tcf(c_33549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,X3),cross_product(X0,X1)),X3)
| member(not_subclass_element(X3,intersection(cross_product(X0,X1),intersection(X2,X3))),X3)
| ( intersection(cross_product(X0,X1),intersection(X2,X3)) = X3 ) ),
inference(superposition,[status(thm)],[c_5411,c_253]) ).
tcf(c_33550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,X3),cross_product(X0,X1)),X3)
| subclass(intersection(cross_product(X0,X1),intersection(X2,X3)),X3) ),
inference(superposition,[status(thm)],[c_5411,c_172]) ).
tcf(c_33551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(X0,null_class),cross_product(X1,X2)),X3),
inference(superposition,[status(thm)],[c_5411,c_256]) ).
tcf(c_33552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X3,X0),cross_product(X1,X2)),X4)
| member(not_subclass_element(intersection(cross_product(X1,X2),intersection(X3,X0)),X4),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_5411,c_4342]) ).
tcf(c_33553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,X3)),X4),universal_class) ),
inference(superposition,[status(thm)],[c_5411,c_4336]) ).
tcf(c_33554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X2,unordered_pair(X3,X4)),cross_product(X0,X1)),X5)
| ( not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,unordered_pair(X3,X4))),X5) = X4 )
| ( not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,unordered_pair(X3,X4))),X5) = X3 ) ),
inference(superposition,[status(thm)],[c_5411,c_177]) ).
tcf(c_33555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X2,cross_product(X3,X4)),cross_product(X0,X1)),X5)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,cross_product(X3,X4))),X5)),first(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,cross_product(X3,X4))),X5))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,cross_product(X3,X4))),X5)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,cross_product(X3,X4))),X5)),second(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,cross_product(X3,X4))),X5))))) = not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,cross_product(X3,X4))),X5) ) ),
inference(superposition,[status(thm)],[c_5411,c_184]) ).
tcf(c_33556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(X4,intersection(X5,X0)),cross_product(X2,X3)),X6)
| member(not_subclass_element(intersection(cross_product(X2,X3),intersection(X4,intersection(X5,X0))),X6),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_5411,c_5286]) ).
tcf(c_33557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(X4,intersection(X0,X5)),cross_product(X2,X3)),X6)
| member(not_subclass_element(intersection(cross_product(X2,X3),intersection(X4,intersection(X0,X5))),X6),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_5411,c_5256]) ).
tcf(c_33558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X2,intersection(X3,X4)),cross_product(X0,X1)),X5)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,X4))),X5),complement(X3)) ),
inference(superposition,[status(thm)],[c_5411,c_12327]) ).
tcf(c_33559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X2,intersection(X3,X4)),cross_product(X0,X1)),X5)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,X4))),X5),complement(X4)) ),
inference(superposition,[status(thm)],[c_5411,c_11998]) ).
tcf(c_33562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,complement(X3)),cross_product(X0,X1)),X4)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,complement(X3))),X4),X3) ),
inference(superposition,[status(thm)],[c_5411,c_191]) ).
tcf(c_33563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(X3,domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),cross_product(X1,X2)),X6)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(cross_product(X1,X2),intersection(X3,domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X6),not_subclass_element(intersection(cross_product(X1,X2),intersection(X3,domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X6)))),compose(X4,X5))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(cross_product(X1,X2),intersection(X3,domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X6),not_subclass_element(intersection(cross_product(X1,X2),intersection(X3,domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))),X6)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_215]) ).
tcf(c_33564,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X3,identity_relation),cross_product(X1,X2)),X4)
| member(not_subclass_element(intersection(cross_product(X1,X2),intersection(X3,identity_relation)),X4),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_5411,c_26574]) ).
tcf(c_33566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,rotate(X3)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,rotate(X3))),X4),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_4338]) ).
tcf(c_33567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,flip(X3)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,flip(X3))),X4),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_4339]) ).
tcf(c_33568,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X2,compose(X3,X4)),cross_product(X0,X1)),X5)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,compose(X3,X4))),X5),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_4341]) ).
tcf(c_33569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X2,unordered_pair(X3,X3)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,unordered_pair(X3,X3))),X4),unordered_pair(X5,X3)) ),
inference(superposition,[status(thm)],[c_5411,c_4344]) ).
tcf(c_33570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X2,unordered_pair(X3,X3)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,unordered_pair(X3,X3))),X4),unordered_pair(X3,X5)) ),
inference(superposition,[status(thm)],[c_5411,c_4343]) ).
tcf(c_33571,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X3,unordered_pair(x,x)),cross_product(X1,X2)),X4)
| member(not_subclass_element(intersection(cross_product(X1,X2),intersection(X3,unordered_pair(x,x))),X4),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_5411,c_5056]) ).
tcf(c_33572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,unordered_pair(x,x)),cross_product(X0,X1)),X3)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,unordered_pair(x,x))),X3),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5411,c_16705]) ).
tcf(c_33574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,iPr_def_10),cross_product(X0,X1)),X3)
| ( not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,iPr_def_10)),X3) = y )
| ( not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,iPr_def_10)),X3) = x ) ),
inference(superposition,[status(thm)],[c_5411,c_5208]) ).
tcf(c_33575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X3,unordered_pair(y,y)),cross_product(X1,X2)),X4)
| member(not_subclass_element(intersection(cross_product(X1,X2),intersection(X3,unordered_pair(y,y))),X4),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_5411,c_5077]) ).
tcf(c_33576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,unordered_pair(y,y)),cross_product(X0,X1)),X3)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,unordered_pair(y,y))),X3),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5411,c_18840]) ).
tcf(c_33578,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X2,element_relation),cross_product(X0,X1)),cross_product(universal_class,universal_class))
| subclass(intersection(cross_product(X0,X1),intersection(X2,element_relation)),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_4850]) ).
tcf(c_33579,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X2,successor_relation),cross_product(X0,X1)),cross_product(universal_class,universal_class))
| subclass(intersection(cross_product(X0,X1),intersection(X2,successor_relation)),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_4862]) ).
tcf(c_33580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,X3),cross_product(X0,X1)),intersection(X3,X4))
| subclass(intersection(cross_product(X0,X1),intersection(X2,X3)),intersection(X3,X4))
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,X3)),intersection(X3,X4)),X4) ),
inference(superposition,[status(thm)],[c_5411,c_5134]) ).
tcf(c_33581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(X2,intersection(intersection(X3,X4),X5)),cross_product(X0,X1)),X6)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(intersection(X3,X4),X5))),X6),X3) ),
inference(superposition,[status(thm)],[c_5411,c_6783]) ).
tcf(c_33582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(X2,intersection(intersection(X3,X4),X5)),cross_product(X0,X1)),X6)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(intersection(X3,X4),X5))),X6),X4) ),
inference(superposition,[status(thm)],[c_5411,c_6250]) ).
tcf(c_33583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(identity_relation,X3)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(identity_relation,X3))),X4),subset_relation) ),
inference(superposition,[status(thm)],[c_5411,c_6318]) ).
tcf(c_33584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(subset_relation,X3)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(subset_relation,X3))),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_7274]) ).
tcf(c_33585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,complement(subset_relation)),cross_product(X0,X1)),X3)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,complement(subset_relation))),X3),identity_relation) ),
inference(superposition,[status(thm)],[c_5411,c_11581]) ).
tcf(c_33587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(complement(subset_relation),X3)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(complement(subset_relation),X3))),X4),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_5411,c_8785]) ).
tcf(c_33588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(X2,intersection(X3,intersection(X4,X5))),cross_product(X0,X1)),X6)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,intersection(X4,X5)))),X6),X4) ),
inference(superposition,[status(thm)],[c_5411,c_11630]) ).
tcf(c_33589,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(X2,intersection(X3,intersection(X4,X5))),cross_product(X0,X1)),X6)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,intersection(X4,X5)))),X6),X5) ),
inference(superposition,[status(thm)],[c_5411,c_11019]) ).
tcf(c_33590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(X3,identity_relation)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,identity_relation))),X4),subset_relation) ),
inference(superposition,[status(thm)],[c_5411,c_11106]) ).
tcf(c_33591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(X3,subset_relation)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,subset_relation))),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_11656]) ).
tcf(c_33592,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(X3,complement(subset_relation))),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,complement(subset_relation)))),X4),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_5411,c_12409]) ).
tcf(c_33593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,complement(cross_product(universal_class,universal_class))),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,complement(cross_product(universal_class,universal_class)))),X3),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_5411,c_15326]) ).
tcf(c_33594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,complement(cross_product(universal_class,universal_class))),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,complement(cross_product(universal_class,universal_class)))),X3),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_5411,c_14989]) ).
tcf(c_33595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,complement(cross_product(universal_class,universal_class))),cross_product(X0,X1)),X3)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,complement(cross_product(universal_class,universal_class)))),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_5411,c_12788]) ).
tcf(c_33596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(element_relation,X3)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(element_relation,X3))),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_13233]) ).
tcf(c_33597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(X3,element_relation)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,element_relation))),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_13248]) ).
tcf(c_33598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(successor_relation,X3)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(successor_relation,X3))),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_13537]) ).
tcf(c_33599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(X3,successor_relation)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,successor_relation))),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_13552]) ).
tcf(c_33600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,complement(complement(X3))),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,complement(complement(X3)))),X4),X3) ),
inference(superposition,[status(thm)],[c_5411,c_14000]) ).
tcf(c_33601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,complement(complement(element_relation))),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,complement(complement(element_relation)))),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_14221]) ).
tcf(c_33602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,complement(complement(successor_relation))),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,complement(complement(successor_relation)))),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_14232]) ).
tcf(c_33603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(unordered_pair(x,x),X3)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(unordered_pair(x,x),X3))),X4),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5411,c_16598]) ).
tcf(c_33604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(X3,unordered_pair(x,x))),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,unordered_pair(x,x)))),X4),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5411,c_17098]) ).
tcf(c_33605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(unordered_pair(y,y),X3)),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(unordered_pair(y,y),X3))),X4),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5411,c_18574]) ).
tcf(c_33606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(X3,unordered_pair(y,y))),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(X3,unordered_pair(y,y)))),X4),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5411,c_19011]) ).
tcf(c_33607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,y),cross_product(X0,X1)),X3)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,y)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5411,c_20672]) ).
tcf(c_33608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(null_class,X4),iPr_def_10)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),cross_product(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_5411,c_33335]) ).
tcf(c_33609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(null_class,X4),y)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),cross_product(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_5411,c_32129]) ).
tcf(c_33610,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X2,y),cross_product(X0,X1)),intersection(iPr_def_10,y))
| subclass(intersection(cross_product(X0,X1),intersection(X2,y)),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,y)),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5411,c_23413]) ).
tcf(c_33611,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| subclass(intersection(intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_23414]) ).
tcf(c_33612,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| subclass(intersection(intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_23415]) ).
tcf(c_33613,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class)
| subclass(intersection(intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_27753]) ).
tcf(c_33614,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class)
| subclass(intersection(intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_5411,c_26225]) ).
tcf(c_33616,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),null_class) ),
inference(light_normalisation,[status(thm)],[c_33526,c_4790]) ).
tcf(c_33623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),X3) ),
inference(light_normalisation,[status(thm)],[c_33519,c_4169]) ).
tcf(c_33631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(X3)) ),
inference(light_normalisation,[status(thm)],[c_33532,c_12377]) ).
tcf(c_33642,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),subset_relation) ),
inference(light_normalisation,[status(thm)],[c_33530,c_11763]) ).
tcf(c_33645,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_33540,c_18749]) ).
tcf(c_33659,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),unordered_pair(y,y)) ),
inference(light_normalisation,[status(thm)],[c_33541,c_19300]) ).
tcf(c_33662,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),unordered_pair(x,x)) ),
inference(light_normalisation,[status(thm)],[c_33539,c_17131]) ).
tcf(c_33666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),intersection(X3,X4)) ),
inference(light_normalisation,[status(thm)],[c_33529,c_11685]) ).
tcf(c_33679,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(cross_product(universal_class,universal_class))) ),
inference(light_normalisation,[status(thm)],[c_33536,c_12738]) ).
tcf(c_33773,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(light_normalisation,[status(thm)],[c_33537,c_13003]) ).
tcf(c_33791,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(subset_relation,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),subset_relation),X2),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
inference(light_normalisation,[status(thm)],[c_33523,c_229]) ).
tcf(c_34110,plain,
! [X0: $i] :
( subclass(domain_of(intersection(iPr_def_10,y)),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_171,c_30663]) ).
tcf(c_34111,plain,
! [X0: $i] :
( member(not_subclass_element(X0,domain_of(intersection(iPr_def_10,y))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(iPr_def_10,y)) = X0 ) ),
inference(superposition,[status(thm)],[c_251,c_30663]) ).
tcf(c_34113,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(X0,X0),universal_class)) = null_class )
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_195,c_30663]) ).
tcf(c_34114,plain,
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(iPr_def_10,y)) = null_class ) ),
inference(superposition,[status(thm)],[c_222,c_30663]) ).
tcf(c_34116,plain,
! [X0: $i,X1: $i] :
( homomorphism(X0,intersection(iPr_def_10,y),X1)
| ( regular(iPr_def_10) = x )
| ~ operation(X1)
| ~ operation(intersection(iPr_def_10,y))
| ~ compatible(X0,intersection(iPr_def_10,y),X1) ),
inference(superposition,[status(thm)],[c_243,c_30663]) ).
tcf(c_34117,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(domain_of(intersection(iPr_def_10,y)),X0),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4224,c_30663]) ).
tcf(c_34118,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(domain_of(intersection(iPr_def_10,y)),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4225,c_30663]) ).
tcf(c_34119,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,domain_of(intersection(iPr_def_10,y))),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4245,c_30663]) ).
tcf(c_34120,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,domain_of(intersection(iPr_def_10,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_4246,c_30663]) ).
tcf(c_34121,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(domain_of(intersection(iPr_def_10,y)),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4425,c_30663]) ).
tcf(c_34122,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X0,domain_of(intersection(iPr_def_10,y))),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4430,c_30663]) ).
tcf(c_34123,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(domain_of(intersection(iPr_def_10,y)),X0),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4431,c_30663]) ).
tcf(c_34124,plain,
! [X0: $i] :
( subclass(X0,complement(domain_of(intersection(iPr_def_10,y))))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_8328,c_30663]) ).
tcf(c_34125,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),domain_of(intersection(iPr_def_10,y))),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4638,c_30663]) ).
tcf(c_34126,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(X1,domain_of(intersection(iPr_def_10,y)))),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4646,c_30663]) ).
tcf(c_34127,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,intersection(domain_of(intersection(iPr_def_10,y)),X1)),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4647,c_30663]) ).
tcf(c_34128,plain,
! [X0: $i] :
( subclass(complement(complement(domain_of(intersection(iPr_def_10,y)))),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_13744,c_30663]) ).
tcf(c_34129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,domain_of(intersection(iPr_def_10,y))),cross_product(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_5411,c_30663]) ).
tcf(c_34130,plain,
( ( regular(iPr_def_10) = x )
| ( complement(complement(domain_of(intersection(iPr_def_10,y)))) = null_class ) ),
inference(superposition,[status(thm)],[c_14058,c_30663]) ).
tcf(c_34131,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,domain_of(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_26791,c_30663]) ).
tcf(c_34132,plain,
( ( null_class = identity_relation )
| ( regular(iPr_def_10) = x )
| ~ subclass(subset_relation,domain_of(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_26794,c_30663]) ).
tcf(c_34133,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ~ member(X0,domain_of(null_class)) ),
inference(superposition,[status(thm)],[c_20574,c_30663]) ).
tcf(c_34134,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ~ member(X0,null_class) ),
inference(light_normalisation,[status(thm)],[c_34133,c_5970]) ).
tcf(c_34271,plain,
! [X0: $i] :
( subclass(domain_of(null_class),X0)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_34110]) ).
tcf(c_34272,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,domain_of(intersection(iPr_def_10,y))),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_34110,c_21314]) ).
tcf(c_34273,plain,
! [X0: $i] :
( subclass(intersection(iPr_def_10,y),X0)
| member(not_subclass_element(null_class,domain_of(intersection(iPr_def_10,y))),y)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_34110,c_21235]) ).
tcf(c_34274,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(iPr_def_10,y)) = X0 )
| ~ subclass(X0,domain_of(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_34110,c_176]) ).
tcf(c_34275,plain,
! [X0: $i,X1: $i] :
( subclass(domain_of(intersection(iPr_def_10,y)),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_34110,c_250]) ).
tcf(c_34277,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,domain_of(intersection(iPr_def_10,y)))) = null_class ) ),
inference(superposition,[status(thm)],[c_34110,c_5373]) ).
tcf(c_34278,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(domain_of(intersection(iPr_def_10,y)),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_34110,c_5371]) ).
tcf(c_34279,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,domain_of(intersection(iPr_def_10,y))),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_34110,c_5348]) ).
tcf(c_34280,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(domain_of(intersection(iPr_def_10,y)),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_34110,c_5346]) ).
tcf(c_34285,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(domain_of(intersection(iPr_def_10,y)),X0) = domain_of(intersection(iPr_def_10,y)) ) ),
inference(superposition,[status(thm)],[c_34110,c_4722]) ).
tcf(c_34286,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,domain_of(intersection(iPr_def_10,y))) = domain_of(intersection(iPr_def_10,y)) ) ),
inference(superposition,[status(thm)],[c_34110,c_4787]) ).
tcf(c_34287,plain,
( ( regular(iPr_def_10) = x )
| ( complement(complement(domain_of(intersection(iPr_def_10,y)))) = domain_of(intersection(iPr_def_10,y)) ) ),
inference(superposition,[status(thm)],[c_34110,c_13998]) ).
tcf(c_34342,plain,
! [X0: $i] :
( compatible(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),intersection(iPr_def_10,y),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class)))),domain_of(domain_of(X0)))
| ( domain_of(null_class) != y ) ),
inference(superposition,[status(thm)],[c_34114,c_20812]) ).
tcf(c_34343,plain,
! [X0: $i] :
( compatible(intersection(iPr_def_10,y),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(intersection(iPr_def_10,y))
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(iPr_def_10,y),universal_class)))),domain_of(domain_of(X0)))
| ( domain_of(y) != null_class ) ),
inference(superposition,[status(thm)],[c_34114,c_20809]) ).
tcf(c_34344,plain,
( operation(intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ function(intersection(iPr_def_10,y))
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(iPr_def_10,y),universal_class)))),domain_of(domain_of(intersection(iPr_def_10,y))))
| ( cross_product(domain_of(null_class),domain_of(null_class)) != null_class ) ),
inference(superposition,[status(thm)],[c_34114,c_234]) ).
tcf(c_34345,plain,
! [X0: $i,X1: $i] :
( compatible(X0,intersection(iPr_def_10,y),X1)
| ( regular(iPr_def_10) = x )
| ~ function(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),domain_of(domain_of(X1)))
| ( domain_of(X0) != domain_of(null_class) ) ),
inference(superposition,[status(thm)],[c_34114,c_238]) ).
tcf(c_34346,plain,
( subclass(domain_of(domain_of(flip(cross_product(intersection(iPr_def_10,y),universal_class)))),domain_of(null_class))
| ( regular(iPr_def_10) = x )
| ~ operation(intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_34114,c_233]) ).
tcf(c_34347,plain,
! [X0: $i,X1: $i] :
( homomorphism(X0,intersection(iPr_def_10,y),X1)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,intersection(iPr_def_10,y),X1),not_homomorphism1(X0,intersection(iPr_def_10,y),X1)),unordered_pair(not_homomorphism1(X0,intersection(iPr_def_10,y),X1),unordered_pair(not_homomorphism2(X0,intersection(iPr_def_10,y),X1),not_homomorphism2(X0,intersection(iPr_def_10,y),X1)))),null_class)
| ( regular(iPr_def_10) = x )
| ~ operation(X1)
| ~ operation(intersection(iPr_def_10,y))
| ~ compatible(X0,intersection(iPr_def_10,y),X1) ),
inference(superposition,[status(thm)],[c_34114,c_243]) ).
tcf(c_34348,plain,
! [X0: $i,X1: $i] :
( compatible(intersection(iPr_def_10,y),X0,X1)
| ( regular(iPr_def_10) = x )
| ~ function(intersection(iPr_def_10,y))
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(iPr_def_10,y),universal_class)))),domain_of(domain_of(X1)))
| ( domain_of(domain_of(X0)) != null_class ) ),
inference(superposition,[status(thm)],[c_34114,c_238]) ).
tcf(c_34350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(iPr_def_10,y),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) )
| ~ homomorphism(X2,intersection(iPr_def_10,y),X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),null_class) ),
inference(superposition,[status(thm)],[c_34114,c_242]) ).
tcf(c_34353,plain,
( subclass(domain_of(domain_of(flip(cross_product(intersection(iPr_def_10,y),universal_class)))),null_class)
| ( regular(iPr_def_10) = x )
| ~ operation(intersection(iPr_def_10,y)) ),
inference(light_normalisation,[status(thm)],[c_34346,c_5970]) ).
tcf(c_34357,plain,
! [X0: $i,X1: $i] :
( compatible(X0,intersection(iPr_def_10,y),X1)
| ( regular(iPr_def_10) = x )
| ~ function(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(X0,universal_class)))),domain_of(domain_of(X1)))
| ( domain_of(X0) != null_class ) ),
inference(light_normalisation,[status(thm)],[c_34345,c_5970]) ).
tcf(c_34368,plain,
( operation(intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ function(intersection(iPr_def_10,y))
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(iPr_def_10,y),universal_class)))),domain_of(domain_of(intersection(iPr_def_10,y))))
| ( cross_product(null_class,null_class) != null_class ) ),
inference(light_normalisation,[status(thm)],[c_34344,c_5970]) ).
tcf(c_34381,plain,
! [X0: $i] :
( compatible(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),intersection(iPr_def_10,y),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class)))),domain_of(domain_of(X0)))
| ( null_class != y ) ),
inference(light_normalisation,[status(thm)],[c_34342,c_5970]) ).
tcf(c_34427,plain,
! [X0: $i] :
( subclass(X0,complement(null_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_30308]) ).
tcf(c_34428,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(iPr_def_10,y),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_21314]) ).
tcf(c_34429,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),y)
| subclass(intersection(iPr_def_10,y),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_21235]) ).
tcf(c_34430,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( complement(intersection(iPr_def_10,y)) = X0 )
| ~ subclass(complement(intersection(iPr_def_10,y)),X0) ),
inference(superposition,[status(thm)],[c_30308,c_176]) ).
tcf(c_34431,plain,
! [X0: $i,X1: $i] :
( subclass(X1,X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(intersection(iPr_def_10,y)),X0) ),
inference(superposition,[status(thm)],[c_30308,c_250]) ).
tcf(c_34432,plain,
! [X0: $i,X1: $i] :
( member(X0,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x )
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_30308,c_170]) ).
tcf(c_34433,plain,
( subclass(omega,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x )
| ~ member(null_class,complement(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_30308,c_1547]) ).
tcf(c_34434,plain,
( ( regular(iPr_def_10) = x )
| ( complement(intersection(iPr_def_10,y)) = universal_class ) ),
inference(superposition,[status(thm)],[c_30308,c_4708]) ).
tcf(c_34438,plain,
( subclass(complement(complement(successor_relation)),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_14231]) ).
tcf(c_34439,plain,
( subclass(complement(complement(element_relation)),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_14220]) ).
tcf(c_34440,plain,
! [X0: $i] :
( subclass(intersection(X0,successor_relation),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_13551]) ).
tcf(c_34441,plain,
! [X0: $i] :
( subclass(intersection(successor_relation,X0),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_13536]) ).
tcf(c_34442,plain,
! [X0: $i] :
( subclass(intersection(X0,element_relation),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_13247]) ).
tcf(c_34443,plain,
! [X0: $i] :
( subclass(intersection(element_relation,X0),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_13232]) ).
tcf(c_34444,plain,
! [X0: $i] :
( subclass(intersection(X0,subset_relation),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_11655]) ).
tcf(c_34445,plain,
! [X0: $i] :
( subclass(intersection(subset_relation,X0),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_7273]) ).
tcf(c_34447,plain,
( subclass(subset_relation,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_6988]) ).
tcf(c_34448,plain,
! [X0: $i,X1: $i] :
( subclass(compose(X0,X1),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_4495]) ).
tcf(c_34449,plain,
( subclass(successor_relation,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_4494]) ).
tcf(c_34450,plain,
( subclass(element_relation,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_4491]) ).
tcf(c_34451,plain,
! [X0: $i] :
( subclass(flip(X0),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_4493]) ).
tcf(c_34452,plain,
! [X0: $i] :
( subclass(rotate(X0),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_4492]) ).
tcf(c_34453,plain,
! [X0: $i] :
( subclass(unordered_pair(X0,X0),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_4498]) ).
tcf(c_34455,plain,
( member(y,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_20134]) ).
tcf(c_34456,plain,
( member(x,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_19428]) ).
tcf(c_34457,plain,
( subclass(identity_relation,complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_4502]) ).
tcf(c_34459,plain,
( subclass(complement(subset_relation),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30308,c_8770]) ).
tcf(c_34460,plain,
! [X0: $i] :
( subclass(X0,universal_class)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_34427,c_8703]) ).
tcf(c_34621,plain,
( member(y,complement(null_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_34455]) ).
tcf(c_34622,plain,
( member(y,cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(complement(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_34455,c_4342]) ).
tcf(c_34624,plain,
( ( regular(iPr_def_10) = x )
| ~ member(y,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_34455,c_191]) ).
tcf(c_34625,plain,
( member(y,universal_class)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_34621,c_8703]) ).
tcf(c_34635,plain,
( member(x,complement(null_class))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_34456]) ).
tcf(c_34636,plain,
( member(x,cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(complement(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_34456,c_4342]) ).
tcf(c_34638,plain,
( ( regular(iPr_def_10) = x )
| ~ member(x,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_34456,c_191]) ).
tcf(c_34639,plain,
( member(x,universal_class)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_34635,c_8703]) ).
tcf(c_34649,plain,
( ( regular(iPr_def_10) = x )
| ~ member(y,iPr_def_10)
| ~ member(y,y) ),
inference(superposition,[status(thm)],[c_190,c_34624]) ).
tcf(c_34650,plain,
( ( regular(iPr_def_10) = x )
| ~ member(y,null_class) ),
inference(superposition,[status(thm)],[c_20574,c_34624]) ).
tcf(c_34651,plain,
( ( regular(iPr_def_10) = x )
| ~ member(y,y) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34649,c_4415]) ).
tcf(c_34663,plain,
( ( regular(iPr_def_10) = x )
| ~ member(x,iPr_def_10)
| ~ member(x,y) ),
inference(superposition,[status(thm)],[c_190,c_34638]) ).
tcf(c_34664,plain,
( ( regular(iPr_def_10) = x )
| ~ member(x,null_class) ),
inference(superposition,[status(thm)],[c_20574,c_34638]) ).
tcf(c_34665,plain,
( ( regular(iPr_def_10) = x )
| ~ member(x,y) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34663,c_4414]) ).
tcf(c_34702,plain,
( member(y,cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(complement(null_class)) ),
inference(superposition,[status(thm)],[c_20574,c_34622]) ).
tcf(c_34703,plain,
( member(y,cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(universal_class) ),
inference(light_normalisation,[status(thm)],[c_34702,c_8703]) ).
tcf(c_34713,plain,
( member(x,cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(complement(null_class)) ),
inference(superposition,[status(thm)],[c_20574,c_34636]) ).
tcf(c_34714,plain,
( member(x,cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ~ function(universal_class) ),
inference(light_normalisation,[status(thm)],[c_34713,c_8703]) ).
tcf(c_34722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,X1),cross_product(X2,X3)),X4)
| member(not_subclass_element(intersection(intersection(X0,X1),cross_product(X2,X3)),X4),X0) ),
inference(superposition,[status(thm)],[c_193,c_5412]) ).
tcf(c_34725,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),element_relation)
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(x,x),universal_class)),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_5412]) ).
tcf(c_34726,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),element_relation)
| subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(y,y),universal_class)),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_5412]) ).
tcf(c_34727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),complement(X0))
| subclass(intersection(intersection(complement(X0),X0),cross_product(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_4169,c_5412]) ).
tcf(c_34728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(cross_product(X3,X4),X2),cross_product(X0,X1)),X5)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,cross_product(X3,X4))),X5),cross_product(X3,X4)) ),
inference(superposition,[status(thm)],[c_193,c_5412]) ).
tcf(c_34729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),X0)
| subclass(intersection(intersection(X0,regular(X0)),cross_product(X1,X2)),X3)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_223,c_5412]) ).
tcf(c_34730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X4,cross_product(X2,X3)),cross_product(X0,X1)),X5)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(cross_product(X2,X3),X4)),X5),X4) ),
inference(superposition,[status(thm)],[c_193,c_5412]) ).
tcf(c_34731,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),subset_relation),X2),cross_product(universal_class,universal_class))
| subclass(intersection(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_229,c_5412]) ).
tcf(c_34732,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),identity_relation),X2),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(superposition,[status(thm)],[c_230,c_5412]) ).
tcf(c_34733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),null_class)
| subclass(intersection(intersection(null_class,X0),cross_product(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_4553,c_5412]) ).
tcf(c_34734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X3,null_class),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),X3) ),
inference(superposition,[status(thm)],[c_4790,c_5412]) ).
tcf(c_34735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),complement(X0))
| subclass(intersection(intersection(complement(X0),intersection(X1,X0)),cross_product(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_11228,c_5412]) ).
tcf(c_34736,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(complement(subset_relation),identity_relation),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_11311,c_5412]) ).
tcf(c_34737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),complement(X0))
| subclass(intersection(intersection(complement(X0),intersection(X0,X1)),cross_product(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_11685,c_5412]) ).
tcf(c_34738,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(complement(cross_product(universal_class,universal_class)),subset_relation),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_11763,c_5412]) ).
tcf(c_34739,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
inference(superposition,[status(thm)],[c_12282,c_5412]) ).
tcf(c_34740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),X0)
| subclass(intersection(intersection(X0,complement(X0)),cross_product(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c_12377,c_5412]) ).
tcf(c_34741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),intersection(X0,X1))
| subclass(intersection(intersection(intersection(X0,X1),complement(X1)),cross_product(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_12625,c_5412]) ).
tcf(c_34742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),intersection(X0,X1))
| subclass(intersection(intersection(intersection(X0,X1),complement(X0)),cross_product(X2,X3)),X4) ),
inference(superposition,[status(thm)],[c_12688,c_5412]) ).
tcf(c_34743,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),identity_relation)
| subclass(intersection(intersection(identity_relation,complement(subset_relation)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_12394,c_5412]) ).
tcf(c_34744,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),subset_relation)
| subclass(intersection(intersection(subset_relation,complement(cross_product(universal_class,universal_class))),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_12738,c_5412]) ).
tcf(c_34745,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),identity_relation)
| subclass(intersection(intersection(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_13003,c_5412]) ).
tcf(c_34746,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),unordered_pair(x,x))
| subclass(intersection(intersection(unordered_pair(x,x),complement(iPr_def_10)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_16614,c_5412]) ).
tcf(c_34747,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(iPr_def_10))
| subclass(intersection(intersection(complement(iPr_def_10),unordered_pair(x,x)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_17131,c_5412]) ).
tcf(c_34748,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),unordered_pair(y,y))
| subclass(intersection(intersection(unordered_pair(y,y),complement(iPr_def_10)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_18749,c_5412]) ).
tcf(c_34749,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(iPr_def_10))
| subclass(intersection(intersection(complement(iPr_def_10),unordered_pair(y,y)),cross_product(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_19300,c_5412]) ).
tcf(c_34750,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(iPr_def_10,y),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),iPr_def_10)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_20574,c_5412]) ).
tcf(c_34751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),intersection(iPr_def_10,y))
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),cross_product(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_30617,c_5412]) ).
tcf(c_34752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),null_class),X3),X0)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),cross_product(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_29021,c_5412]) ).
tcf(c_34753,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_5412]) ).
tcf(c_34754,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_5412]) ).
tcf(c_34755,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(universal_class,X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(universal_class,X2)),X3),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(cross_product(X0,X1),intersection(universal_class,X2)),X3),not_subclass_element(intersection(cross_product(X0,X1),intersection(universal_class,X2)),X3)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_5412,c_20813]) ).
tcf(c_34756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,X3),cross_product(X1,X2)),X0)
| ( intersection(cross_product(X1,X2),intersection(X0,X3)) = X0 )
| ~ member(not_subclass_element(X0,intersection(cross_product(X1,X2),intersection(X0,X3))),intersection(cross_product(X1,X2),intersection(X0,X3))) ),
inference(superposition,[status(thm)],[c_5412,c_254]) ).
tcf(c_34757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,X3),cross_product(X0,X1)),X2)
| member(not_subclass_element(X2,intersection(cross_product(X0,X1),intersection(X2,X3))),X2)
| ( intersection(cross_product(X0,X1),intersection(X2,X3)) = X2 ) ),
inference(superposition,[status(thm)],[c_5412,c_253]) ).
tcf(c_34758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,X3),cross_product(X0,X1)),X2)
| subclass(intersection(cross_product(X0,X1),intersection(X2,X3)),X2) ),
inference(superposition,[status(thm)],[c_5412,c_172]) ).
tcf(c_34759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : subclass(intersection(intersection(null_class,X0),cross_product(X1,X2)),X3),
inference(superposition,[status(thm)],[c_5412,c_256]) ).
tcf(c_34760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X0,X3),cross_product(X1,X2)),X4)
| member(not_subclass_element(intersection(cross_product(X1,X2),intersection(X0,X3)),X4),cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_5412,c_4342]) ).
tcf(c_34762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(unordered_pair(X2,X3),X4),cross_product(X0,X1)),X5)
| ( not_subclass_element(intersection(cross_product(X0,X1),intersection(unordered_pair(X2,X3),X4)),X5) = X3 )
| ( not_subclass_element(intersection(cross_product(X0,X1),intersection(unordered_pair(X2,X3),X4)),X5) = X2 ) ),
inference(superposition,[status(thm)],[c_5412,c_177]) ).
tcf(c_34763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(cross_product(X2,X3),X4),cross_product(X0,X1)),X5)
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),intersection(cross_product(X2,X3),X4)),X5)),first(not_subclass_element(intersection(cross_product(X0,X1),intersection(cross_product(X2,X3),X4)),X5))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),intersection(cross_product(X2,X3),X4)),X5)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),intersection(cross_product(X2,X3),X4)),X5)),second(not_subclass_element(intersection(cross_product(X0,X1),intersection(cross_product(X2,X3),X4)),X5))))) = not_subclass_element(intersection(cross_product(X0,X1),intersection(cross_product(X2,X3),X4)),X5) ) ),
inference(superposition,[status(thm)],[c_5412,c_184]) ).
tcf(c_34764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(intersection(X4,X0),X5),cross_product(X2,X3)),X6)
| member(not_subclass_element(intersection(cross_product(X2,X3),intersection(intersection(X4,X0),X5)),X6),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_5412,c_5286]) ).
tcf(c_34765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(intersection(X0,X4),X5),cross_product(X2,X3)),X6)
| member(not_subclass_element(intersection(cross_product(X2,X3),intersection(intersection(X0,X4),X5)),X6),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_5412,c_5256]) ).
tcf(c_34766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(X2,X3),X4),cross_product(X0,X1)),X5)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,X3),X4)),X5),complement(X2)) ),
inference(superposition,[status(thm)],[c_5412,c_12327]) ).
tcf(c_34767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(X2,X3),X4),cross_product(X0,X1)),X5)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,X3),X4)),X5),complement(X3)) ),
inference(superposition,[status(thm)],[c_5412,c_11998]) ).
tcf(c_34770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(complement(X2),X3),cross_product(X0,X1)),X4)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(complement(X2),X3)),X4),X2) ),
inference(superposition,[status(thm)],[c_5412,c_191]) ).
tcf(c_34771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X5),cross_product(X1,X2)),X6)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(cross_product(X1,X2),intersection(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X5)),X6),not_subclass_element(intersection(cross_product(X1,X2),intersection(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X5)),X6)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(cross_product(X1,X2),intersection(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X5)),X6),not_subclass_element(intersection(cross_product(X1,X2),intersection(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X5)),X6)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_215]) ).
tcf(c_34772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(identity_relation,X3),cross_product(X1,X2)),X4)
| member(not_subclass_element(intersection(cross_product(X1,X2),intersection(identity_relation,X3)),X4),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_5412,c_26574]) ).
tcf(c_34774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(rotate(X2),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(rotate(X2),X3)),X4),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_4338]) ).
tcf(c_34775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(flip(X2),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(flip(X2),X3)),X4),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_4339]) ).
tcf(c_34776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(compose(X2,X3),X4),cross_product(X0,X1)),X5)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(compose(X2,X3),X4)),X5),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_4341]) ).
tcf(c_34777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(unordered_pair(X2,X2),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(unordered_pair(X2,X2),X3)),X4),unordered_pair(X5,X2)) ),
inference(superposition,[status(thm)],[c_5412,c_4344]) ).
tcf(c_34778,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(unordered_pair(X2,X2),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(unordered_pair(X2,X2),X3)),X4),unordered_pair(X2,X5)) ),
inference(superposition,[status(thm)],[c_5412,c_4343]) ).
tcf(c_34779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(unordered_pair(x,x),X3),cross_product(X1,X2)),X4)
| member(not_subclass_element(intersection(cross_product(X1,X2),intersection(unordered_pair(x,x),X3)),X4),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_5412,c_5056]) ).
tcf(c_34780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(unordered_pair(x,x),X2),cross_product(X0,X1)),X3)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(unordered_pair(x,x),X2)),X3),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5412,c_16705]) ).
tcf(c_34782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(iPr_def_10,X2),cross_product(X0,X1)),X3)
| ( not_subclass_element(intersection(cross_product(X0,X1),intersection(iPr_def_10,X2)),X3) = y )
| ( not_subclass_element(intersection(cross_product(X0,X1),intersection(iPr_def_10,X2)),X3) = x ) ),
inference(superposition,[status(thm)],[c_5412,c_5208]) ).
tcf(c_34783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(unordered_pair(y,y),X3),cross_product(X1,X2)),X4)
| member(not_subclass_element(intersection(cross_product(X1,X2),intersection(unordered_pair(y,y),X3)),X4),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_5412,c_5077]) ).
tcf(c_34784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(unordered_pair(y,y),X2),cross_product(X0,X1)),X3)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(unordered_pair(y,y),X2)),X3),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_5412,c_18840]) ).
tcf(c_34786,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(element_relation,X2),cross_product(X0,X1)),cross_product(universal_class,universal_class))
| subclass(intersection(cross_product(X0,X1),intersection(element_relation,X2)),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_4850]) ).
tcf(c_34787,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(successor_relation,X2),cross_product(X0,X1)),cross_product(universal_class,universal_class))
| subclass(intersection(cross_product(X0,X1),intersection(successor_relation,X2)),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_4862]) ).
tcf(c_34788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,X3),cross_product(X0,X1)),intersection(X2,X4))
| subclass(intersection(cross_product(X0,X1),intersection(X2,X3)),intersection(X2,X4))
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,X3)),intersection(X2,X4)),X4) ),
inference(superposition,[status(thm)],[c_5412,c_5134]) ).
tcf(c_34789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(intersection(intersection(X2,X3),X4),X5),cross_product(X0,X1)),X6)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(intersection(X2,X3),X4),X5)),X6),X2) ),
inference(superposition,[status(thm)],[c_5412,c_6783]) ).
tcf(c_34790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(intersection(intersection(X2,X3),X4),X5),cross_product(X0,X1)),X6)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(intersection(X2,X3),X4),X5)),X6),X3) ),
inference(superposition,[status(thm)],[c_5412,c_6250]) ).
tcf(c_34791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(identity_relation,X2),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(identity_relation,X2),X3)),X4),subset_relation) ),
inference(superposition,[status(thm)],[c_5412,c_6318]) ).
tcf(c_34792,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(subset_relation,X2),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(subset_relation,X2),X3)),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_7274]) ).
tcf(c_34793,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(complement(subset_relation),X2),cross_product(X0,X1)),X3)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(complement(subset_relation),X2)),X3),identity_relation) ),
inference(superposition,[status(thm)],[c_5412,c_11581]) ).
tcf(c_34795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(complement(subset_relation),X2),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(complement(subset_relation),X2),X3)),X4),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_5412,c_8785]) ).
tcf(c_34796,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(intersection(X2,intersection(X3,X4)),X5),cross_product(X0,X1)),X6)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,intersection(X3,X4)),X5)),X6),X3) ),
inference(superposition,[status(thm)],[c_5412,c_11630]) ).
tcf(c_34797,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( subclass(intersection(intersection(intersection(X2,intersection(X3,X4)),X5),cross_product(X0,X1)),X6)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,intersection(X3,X4)),X5)),X6),X4) ),
inference(superposition,[status(thm)],[c_5412,c_11019]) ).
tcf(c_34798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X2,identity_relation),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,identity_relation),X3)),X4),subset_relation) ),
inference(superposition,[status(thm)],[c_5412,c_11106]) ).
tcf(c_34799,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X2,subset_relation),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,subset_relation),X3)),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_11656]) ).
tcf(c_34800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X2,complement(subset_relation)),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,complement(subset_relation)),X3)),X4),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_5412,c_12409]) ).
tcf(c_34801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(complement(cross_product(universal_class,universal_class)),X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(complement(cross_product(universal_class,universal_class)),X2)),X3),complement(element_relation)) ),
inference(superposition,[status(thm)],[c_5412,c_15326]) ).
tcf(c_34802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(complement(cross_product(universal_class,universal_class)),X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(complement(cross_product(universal_class,universal_class)),X2)),X3),complement(successor_relation)) ),
inference(superposition,[status(thm)],[c_5412,c_14989]) ).
tcf(c_34803,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(complement(cross_product(universal_class,universal_class)),X2),cross_product(X0,X1)),X3)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(complement(cross_product(universal_class,universal_class)),X2)),X3),subset_relation) ),
inference(superposition,[status(thm)],[c_5412,c_12788]) ).
tcf(c_34804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(element_relation,X2),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(element_relation,X2),X3)),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_13233]) ).
tcf(c_34805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X2,element_relation),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,element_relation),X3)),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_13248]) ).
tcf(c_34806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(successor_relation,X2),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(successor_relation,X2),X3)),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_13537]) ).
tcf(c_34807,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X2,successor_relation),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,successor_relation),X3)),X4),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_13552]) ).
tcf(c_34808,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(complement(complement(X2)),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(complement(complement(X2)),X3)),X4),X2) ),
inference(superposition,[status(thm)],[c_5412,c_14000]) ).
tcf(c_34809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(complement(complement(element_relation)),X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(complement(complement(element_relation)),X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_14221]) ).
tcf(c_34810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(complement(complement(successor_relation)),X2),cross_product(X0,X1)),X3)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(complement(complement(successor_relation)),X2)),X3),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_14232]) ).
tcf(c_34811,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(unordered_pair(x,x),X2),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(unordered_pair(x,x),X2),X3)),X4),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5412,c_16598]) ).
tcf(c_34812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X2,unordered_pair(x,x)),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,unordered_pair(x,x)),X3)),X4),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5412,c_17098]) ).
tcf(c_34813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(unordered_pair(y,y),X2),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(unordered_pair(y,y),X2),X3)),X4),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5412,c_18574]) ).
tcf(c_34814,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X2,unordered_pair(y,y)),X3),cross_product(X0,X1)),X4)
| member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(X2,unordered_pair(y,y)),X3)),X4),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5412,c_19011]) ).
tcf(c_34815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(y,X2),cross_product(X0,X1)),X3)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(y,X2)),X3),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5412,c_20672]) ).
tcf(c_34816,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(null_class,X4),iPr_def_10)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),cross_product(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_5412,c_33335]) ).
tcf(c_34817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(null_class,X4),y)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),cross_product(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_5412,c_32129]) ).
tcf(c_34818,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(y,X2),cross_product(X0,X1)),intersection(iPr_def_10,y))
| subclass(intersection(cross_product(X0,X1),intersection(y,X2)),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(y,X2)),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5412,c_23413]) ).
tcf(c_34819,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2)),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| subclass(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2),cross_product(X0,X1)),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2)),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_23414]) ).
tcf(c_34820,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2)),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| subclass(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2),cross_product(X0,X1)),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2)),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_23415]) ).
tcf(c_34821,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2)),null_class)
| subclass(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2),cross_product(X0,X1)),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2)),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_27753]) ).
tcf(c_34822,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(cross_product(X0,X1),intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2)),null_class)
| subclass(intersection(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2),cross_product(X0,X1)),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X2)),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_5412,c_26225]) ).
tcf(c_34823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(domain_of(intersection(iPr_def_10,y)),X0),cross_product(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_5412,c_30663]) ).
tcf(c_34831,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),identity_relation) ),
inference(light_normalisation,[status(thm)],[c_34743,c_12394]) ).
tcf(c_34835,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(subset_relation)) ),
inference(light_normalisation,[status(thm)],[c_34736,c_11311]) ).
tcf(c_34922,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(identity_relation,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),identity_relation),X2),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
inference(light_normalisation,[status(thm)],[c_34732,c_230]) ).
tcf(c_34972,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(subset_relation,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),subset_relation),X2),cross_product(universal_class,universal_class)) ),
inference(light_normalisation,[status(thm)],[c_34731,c_229]) ).
tcf(c_35266,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X2,cross_product(X0,X1)),null_class),X2)
| ( intersection(cross_product(X0,X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_193,c_4282]) ).
tcf(c_35268,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),X0),null_class),cross_product(X1,X2))
| ( intersection(X0,cross_product(X1,X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_193,c_4282]) ).
tcf(c_35269,plain,
( member(not_subclass_element(subset_relation,null_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_229,c_4282]) ).
tcf(c_35270,plain,
( member(not_subclass_element(identity_relation,null_class),subset_relation)
| ( intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_230,c_4282]) ).
tcf(c_35293,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,universal_class),null_class),y)
| ( intersection(X0,universal_class) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),null_class),not_subclass_element(intersection(X0,universal_class),null_class)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_20813]) ).
tcf(c_35298,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X1,X0),null_class),cross_product(universal_class,universal_class))
| ( intersection(X1,X0) = null_class )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4282,c_4342]) ).
tcf(c_35299,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,X1),null_class),universal_class)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_4336]) ).
tcf(c_35300,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,unordered_pair(X1,X2)) = null_class )
| ( not_subclass_element(intersection(X0,unordered_pair(X1,X2)),null_class) = X2 )
| ( not_subclass_element(intersection(X0,unordered_pair(X1,X2)),null_class) = X1 ) ),
inference(superposition,[status(thm)],[c_4282,c_177]) ).
tcf(c_35301,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,cross_product(X1,X2)) = null_class )
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),null_class)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),null_class))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),null_class)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),null_class)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),null_class))))) = not_subclass_element(intersection(X0,cross_product(X1,X2)),null_class) ) ),
inference(superposition,[status(thm)],[c_4282,c_184]) ).
tcf(c_35302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X2,intersection(X3,X0)),null_class),X1)
| ( intersection(X2,intersection(X3,X0)) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4282,c_5286]) ).
tcf(c_35303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X2,intersection(X0,X3)),null_class),X1)
| ( intersection(X2,intersection(X0,X3)) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4282,c_5256]) ).
tcf(c_35304,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(X1,X2)) = null_class )
| ~ member(not_subclass_element(intersection(X0,intersection(X1,X2)),null_class),complement(X1)) ),
inference(superposition,[status(thm)],[c_4282,c_12327]) ).
tcf(c_35305,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(X0,intersection(X1,X2)) = null_class )
| ~ member(not_subclass_element(intersection(X0,intersection(X1,X2)),null_class),complement(X2)) ),
inference(superposition,[status(thm)],[c_4282,c_11998]) ).
tcf(c_35308,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,complement(X1)) = null_class )
| ~ member(not_subclass_element(intersection(X0,complement(X1)),null_class),X1) ),
inference(superposition,[status(thm)],[c_4282,c_191]) ).
tcf(c_35309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),null_class),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),null_class)))),compose(X2,X3))
| ( intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))) = null_class )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),null_class),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),null_class)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4282,c_215]) ).
tcf(c_35310,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X1,identity_relation),null_class),X0)
| ( intersection(X1,identity_relation) = null_class )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4282,c_26574]) ).
tcf(c_35312,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,rotate(X1)),null_class),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( intersection(X0,rotate(X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_4338]) ).
tcf(c_35313,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,flip(X1)),null_class),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( intersection(X0,flip(X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_4339]) ).
tcf(c_35314,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,compose(X1,X2)),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,compose(X1,X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_4341]) ).
tcf(c_35315,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,unordered_pair(X1,X1)),null_class),unordered_pair(X2,X1))
| ( intersection(X0,unordered_pair(X1,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_4344]) ).
tcf(c_35316,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X0,unordered_pair(X1,X1)),null_class),unordered_pair(X1,X2))
| ( intersection(X0,unordered_pair(X1,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_4343]) ).
tcf(c_35317,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X1,unordered_pair(x,x)),null_class),X0)
| ( intersection(X1,unordered_pair(x,x)) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4282,c_5056]) ).
tcf(c_35318,plain,
! [X0: $i] :
( ( intersection(X0,unordered_pair(x,x)) = null_class )
| ~ member(not_subclass_element(intersection(X0,unordered_pair(x,x)),null_class),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4282,c_16705]) ).
tcf(c_35320,plain,
! [X0: $i] :
( ( intersection(X0,iPr_def_10) = null_class )
| ( not_subclass_element(intersection(X0,iPr_def_10),null_class) = y )
| ( not_subclass_element(intersection(X0,iPr_def_10),null_class) = x ) ),
inference(superposition,[status(thm)],[c_4282,c_5208]) ).
tcf(c_35321,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X1,unordered_pair(y,y)),null_class),X0)
| ( intersection(X1,unordered_pair(y,y)) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4282,c_5077]) ).
tcf(c_35322,plain,
! [X0: $i] :
( ( intersection(X0,unordered_pair(y,y)) = null_class )
| ~ member(not_subclass_element(intersection(X0,unordered_pair(y,y)),null_class),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4282,c_18840]) ).
tcf(c_35325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,intersection(intersection(X1,X2),X3)),null_class),X1)
| ( intersection(X0,intersection(intersection(X1,X2),X3)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_6783]) ).
tcf(c_35326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,intersection(intersection(X1,X2),X3)),null_class),X2)
| ( intersection(X0,intersection(intersection(X1,X2),X3)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_6250]) ).
tcf(c_35327,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(identity_relation,X1)),null_class),subset_relation)
| ( intersection(X0,intersection(identity_relation,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_6318]) ).
tcf(c_35328,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(subset_relation,X1)),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(subset_relation,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_7274]) ).
tcf(c_35329,plain,
! [X0: $i] :
( ( intersection(X0,complement(subset_relation)) = null_class )
| ~ member(not_subclass_element(intersection(X0,complement(subset_relation)),null_class),identity_relation) ),
inference(superposition,[status(thm)],[c_4282,c_11581]) ).
tcf(c_35331,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(complement(subset_relation),X1)),null_class),complement(identity_relation))
| ( intersection(X0,intersection(complement(subset_relation),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_8785]) ).
tcf(c_35332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,X3))),null_class),X2)
| ( intersection(X0,intersection(X1,intersection(X2,X3))) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_11630]) ).
tcf(c_35333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,intersection(X1,intersection(X2,X3))),null_class),X3)
| ( intersection(X0,intersection(X1,intersection(X2,X3))) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_11019]) ).
tcf(c_35334,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(X1,identity_relation)),null_class),subset_relation)
| ( intersection(X0,intersection(X1,identity_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_11106]) ).
tcf(c_35335,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(X1,subset_relation)),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(X1,subset_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_11656]) ).
tcf(c_35336,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(X1,complement(subset_relation))),null_class),complement(identity_relation))
| ( intersection(X0,intersection(X1,complement(subset_relation))) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_12409]) ).
tcf(c_35337,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,complement(cross_product(universal_class,universal_class))),null_class),complement(element_relation))
| ( intersection(X0,complement(cross_product(universal_class,universal_class))) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_15326]) ).
tcf(c_35338,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,complement(cross_product(universal_class,universal_class))),null_class),complement(successor_relation))
| ( intersection(X0,complement(cross_product(universal_class,universal_class))) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_14989]) ).
tcf(c_35339,plain,
! [X0: $i] :
( ( intersection(X0,complement(cross_product(universal_class,universal_class))) = null_class )
| ~ member(not_subclass_element(intersection(X0,complement(cross_product(universal_class,universal_class))),null_class),subset_relation) ),
inference(superposition,[status(thm)],[c_4282,c_12788]) ).
tcf(c_35340,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(element_relation,X1)),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(element_relation,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_13233]) ).
tcf(c_35341,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(X1,element_relation)),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(X1,element_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_13248]) ).
tcf(c_35342,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(successor_relation,X1)),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(successor_relation,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_13537]) ).
tcf(c_35343,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(X1,successor_relation)),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,intersection(X1,successor_relation)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_13552]) ).
tcf(c_35344,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,complement(complement(X1))),null_class),X1)
| ( intersection(X0,complement(complement(X1))) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_14000]) ).
tcf(c_35345,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,complement(complement(element_relation))),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,complement(complement(element_relation))) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_14221]) ).
tcf(c_35346,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(X0,complement(complement(successor_relation))),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,complement(complement(successor_relation))) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_14232]) ).
tcf(c_35347,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(unordered_pair(x,x),X1)),null_class),iPr_def_10)
| ( intersection(X0,intersection(unordered_pair(x,x),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_16598]) ).
tcf(c_35348,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(X1,unordered_pair(x,x))),null_class),iPr_def_10)
| ( intersection(X0,intersection(X1,unordered_pair(x,x))) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_17098]) ).
tcf(c_35349,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(unordered_pair(y,y),X1)),null_class),iPr_def_10)
| ( intersection(X0,intersection(unordered_pair(y,y),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_18574]) ).
tcf(c_35350,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,intersection(X1,unordered_pair(y,y))),null_class),iPr_def_10)
| ( intersection(X0,intersection(X1,unordered_pair(y,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_19011]) ).
tcf(c_35351,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,y) = null_class )
| ~ member(not_subclass_element(intersection(X0,y),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4282,c_20672]) ).
tcf(c_35354,plain,
! [X0: $i] :
( subclass(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class )
| ~ member(not_subclass_element(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4282,c_27753]) ).
tcf(c_35355,plain,
! [X0: $i] :
( subclass(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = null_class )
| ~ member(not_subclass_element(intersection(X0,intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4282,c_26225]) ).
tcf(c_35461,plain,
( member(not_subclass_element(subset_relation,null_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ( null_class = subset_relation ) ),
inference(light_normalisation,[status(thm)],[c_35269,c_229]) ).
tcf(c_35639,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(X2,cross_product(X0,X1)),null_class),cross_product(X0,X1))
| ( intersection(cross_product(X0,X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_193,c_4283]) ).
tcf(c_35641,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(cross_product(X1,X2),X0),null_class),X0)
| ( intersection(X0,cross_product(X1,X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_193,c_4283]) ).
tcf(c_35642,plain,
( member(not_subclass_element(subset_relation,null_class),cross_product(universal_class,universal_class))
| ( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = null_class ) ),
inference(superposition,[status(thm)],[c_229,c_4283]) ).
tcf(c_35643,plain,
( member(not_subclass_element(identity_relation,null_class),domain_of(flip(cross_product(subset_relation,universal_class))))
| ( intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_230,c_4283]) ).
tcf(c_35666,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(universal_class,X0),null_class),y)
| ( intersection(universal_class,X0) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),null_class),not_subclass_element(intersection(universal_class,X0),null_class)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_20813]) ).
tcf(c_35671,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(X0,X1),null_class),cross_product(universal_class,universal_class))
| ( intersection(X0,X1) = null_class )
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4283,c_4342]) ).
tcf(c_35673,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(unordered_pair(X0,X1),X2) = null_class )
| ( not_subclass_element(intersection(unordered_pair(X0,X1),X2),null_class) = X1 )
| ( not_subclass_element(intersection(unordered_pair(X0,X1),X2),null_class) = X0 ) ),
inference(superposition,[status(thm)],[c_4283,c_177]) ).
tcf(c_35674,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(cross_product(X0,X1),X2) = null_class )
| ( unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),null_class)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),null_class))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),null_class)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),null_class)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),null_class))))) = not_subclass_element(intersection(cross_product(X0,X1),X2),null_class) ) ),
inference(superposition,[status(thm)],[c_4283,c_184]) ).
tcf(c_35675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(intersection(X2,X0),X3),null_class),X1)
| ( intersection(intersection(X2,X0),X3) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4283,c_5286]) ).
tcf(c_35676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(intersection(X0,X2),X3),null_class),X1)
| ( intersection(intersection(X0,X2),X3) = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_4283,c_5256]) ).
tcf(c_35677,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,X1),X2) = null_class )
| ~ member(not_subclass_element(intersection(intersection(X0,X1),X2),null_class),complement(X0)) ),
inference(superposition,[status(thm)],[c_4283,c_12327]) ).
tcf(c_35678,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(intersection(X0,X1),X2) = null_class )
| ~ member(not_subclass_element(intersection(intersection(X0,X1),X2),null_class),complement(X1)) ),
inference(superposition,[status(thm)],[c_4283,c_11998]) ).
tcf(c_35681,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(X0),X1) = null_class )
| ~ member(not_subclass_element(intersection(complement(X0),X1),null_class),X0) ),
inference(superposition,[status(thm)],[c_4283,c_191]) ).
tcf(c_35682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),null_class),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),null_class)))),compose(X1,X2))
| ( intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3) = null_class )
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),null_class),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),null_class)))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_4283,c_215]) ).
tcf(c_35683,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(identity_relation,X1),null_class),X0)
| ( intersection(identity_relation,X1) = null_class )
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_4283,c_26574]) ).
tcf(c_35685,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(rotate(X0),X1),null_class),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( intersection(rotate(X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_4338]) ).
tcf(c_35686,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(flip(X0),X1),null_class),cross_product(cross_product(universal_class,universal_class),universal_class))
| ( intersection(flip(X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_4339]) ).
tcf(c_35687,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(compose(X0,X1),X2),null_class),cross_product(universal_class,universal_class))
| ( intersection(compose(X0,X1),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_4341]) ).
tcf(c_35688,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(unordered_pair(X0,X0),X1),null_class),unordered_pair(X2,X0))
| ( intersection(unordered_pair(X0,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_4344]) ).
tcf(c_35689,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(intersection(unordered_pair(X0,X0),X1),null_class),unordered_pair(X0,X2))
| ( intersection(unordered_pair(X0,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_4343]) ).
tcf(c_35690,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(unordered_pair(x,x),X1),null_class),X0)
| ( intersection(unordered_pair(x,x),X1) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4283,c_5056]) ).
tcf(c_35691,plain,
! [X0: $i] :
( ( intersection(unordered_pair(x,x),X0) = null_class )
| ~ member(not_subclass_element(intersection(unordered_pair(x,x),X0),null_class),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4283,c_16705]) ).
tcf(c_35693,plain,
! [X0: $i] :
( ( intersection(iPr_def_10,X0) = null_class )
| ( not_subclass_element(intersection(iPr_def_10,X0),null_class) = y )
| ( not_subclass_element(intersection(iPr_def_10,X0),null_class) = x ) ),
inference(superposition,[status(thm)],[c_4283,c_5208]) ).
tcf(c_35694,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(unordered_pair(y,y),X1),null_class),X0)
| ( intersection(unordered_pair(y,y),X1) = null_class )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4283,c_5077]) ).
tcf(c_35695,plain,
! [X0: $i] :
( ( intersection(unordered_pair(y,y),X0) = null_class )
| ~ member(not_subclass_element(intersection(unordered_pair(y,y),X0),null_class),complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_4283,c_18840]) ).
tcf(c_35698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(intersection(intersection(X0,X1),X2),X3),null_class),X0)
| ( intersection(intersection(intersection(X0,X1),X2),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_6783]) ).
tcf(c_35699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(intersection(intersection(X0,X1),X2),X3),null_class),X1)
| ( intersection(intersection(intersection(X0,X1),X2),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_6250]) ).
tcf(c_35700,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(identity_relation,X0),X1),null_class),subset_relation)
| ( intersection(intersection(identity_relation,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_6318]) ).
tcf(c_35701,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(subset_relation,X0),X1),null_class),cross_product(universal_class,universal_class))
| ( intersection(intersection(subset_relation,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_7274]) ).
tcf(c_35702,plain,
! [X0: $i] :
( ( intersection(complement(subset_relation),X0) = null_class )
| ~ member(not_subclass_element(intersection(complement(subset_relation),X0),null_class),identity_relation) ),
inference(superposition,[status(thm)],[c_4283,c_11581]) ).
tcf(c_35704,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(complement(subset_relation),X0),X1),null_class),complement(identity_relation))
| ( intersection(intersection(complement(subset_relation),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_8785]) ).
tcf(c_35705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(intersection(X0,intersection(X1,X2)),X3),null_class),X1)
| ( intersection(intersection(X0,intersection(X1,X2)),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_11630]) ).
tcf(c_35706,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(intersection(X0,intersection(X1,X2)),X3),null_class),X2)
| ( intersection(intersection(X0,intersection(X1,X2)),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_11019]) ).
tcf(c_35707,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(X0,identity_relation),X1),null_class),subset_relation)
| ( intersection(intersection(X0,identity_relation),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_11106]) ).
tcf(c_35708,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(X0,subset_relation),X1),null_class),cross_product(universal_class,universal_class))
| ( intersection(intersection(X0,subset_relation),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_11656]) ).
tcf(c_35709,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(X0,complement(subset_relation)),X1),null_class),complement(identity_relation))
| ( intersection(intersection(X0,complement(subset_relation)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_12409]) ).
tcf(c_35710,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),X0),null_class),complement(element_relation))
| ( intersection(complement(cross_product(universal_class,universal_class)),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_15326]) ).
tcf(c_35711,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),X0),null_class),complement(successor_relation))
| ( intersection(complement(cross_product(universal_class,universal_class)),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_14989]) ).
tcf(c_35712,plain,
! [X0: $i] :
( ( intersection(complement(cross_product(universal_class,universal_class)),X0) = null_class )
| ~ member(not_subclass_element(intersection(complement(cross_product(universal_class,universal_class)),X0),null_class),subset_relation) ),
inference(superposition,[status(thm)],[c_4283,c_12788]) ).
tcf(c_35713,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(element_relation,X0),X1),null_class),cross_product(universal_class,universal_class))
| ( intersection(intersection(element_relation,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_13233]) ).
tcf(c_35714,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(X0,element_relation),X1),null_class),cross_product(universal_class,universal_class))
| ( intersection(intersection(X0,element_relation),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_13248]) ).
tcf(c_35715,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(successor_relation,X0),X1),null_class),cross_product(universal_class,universal_class))
| ( intersection(intersection(successor_relation,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_13537]) ).
tcf(c_35716,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(X0,successor_relation),X1),null_class),cross_product(universal_class,universal_class))
| ( intersection(intersection(X0,successor_relation),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_13552]) ).
tcf(c_35717,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(complement(complement(X0)),X1),null_class),X0)
| ( intersection(complement(complement(X0)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_14000]) ).
tcf(c_35718,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(complement(complement(element_relation)),X0),null_class),cross_product(universal_class,universal_class))
| ( intersection(complement(complement(element_relation)),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_14221]) ).
tcf(c_35719,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(complement(complement(successor_relation)),X0),null_class),cross_product(universal_class,universal_class))
| ( intersection(complement(complement(successor_relation)),X0) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_14232]) ).
tcf(c_35720,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(unordered_pair(x,x),X0),X1),null_class),iPr_def_10)
| ( intersection(intersection(unordered_pair(x,x),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_16598]) ).
tcf(c_35721,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(X0,unordered_pair(x,x)),X1),null_class),iPr_def_10)
| ( intersection(intersection(X0,unordered_pair(x,x)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_17098]) ).
tcf(c_35722,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(unordered_pair(y,y),X0),X1),null_class),iPr_def_10)
| ( intersection(intersection(unordered_pair(y,y),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_18574]) ).
tcf(c_35723,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(intersection(intersection(X0,unordered_pair(y,y)),X1),null_class),iPr_def_10)
| ( intersection(intersection(X0,unordered_pair(y,y)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_4283,c_19011]) ).
tcf(c_35724,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(y,X0) = null_class )
| ~ member(not_subclass_element(intersection(y,X0),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4283,c_20672]) ).
tcf(c_35727,plain,
! [X0: $i] :
( subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0) = null_class )
| ~ member(not_subclass_element(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),null_class),cross_product(unordered_pair(y,y),universal_class)) ),
inference(superposition,[status(thm)],[c_4283,c_27753]) ).
tcf(c_35728,plain,
! [X0: $i] :
( subclass(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),null_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0) = null_class )
| ~ member(not_subclass_element(intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),X0),null_class),cross_product(unordered_pair(x,x),universal_class)) ),
inference(superposition,[status(thm)],[c_4283,c_26225]) ).
tcf(c_35785,plain,
( member(not_subclass_element(identity_relation,null_class),domain_of(flip(cross_product(subset_relation,universal_class))))
| ( null_class = identity_relation ) ),
inference(light_normalisation,[status(thm)],[c_35643,c_230]) ).
tcf(c_35831,plain,
( member(not_subclass_element(subset_relation,null_class),cross_product(universal_class,universal_class))
| ( null_class = subset_relation ) ),
inference(light_normalisation,[status(thm)],[c_35642,c_229]) ).
tcf(c_36081,plain,
( member(not_subclass_element(subset_relation,null_class),universal_class)
| ( null_class = subset_relation ) ),
inference(superposition,[status(thm)],[c_35831,c_4336]) ).
tcf(c_36082,plain,
( ( null_class = subset_relation )
| ( unordered_pair(unordered_pair(first(not_subclass_element(subset_relation,null_class)),first(not_subclass_element(subset_relation,null_class))),unordered_pair(first(not_subclass_element(subset_relation,null_class)),unordered_pair(second(not_subclass_element(subset_relation,null_class)),second(not_subclass_element(subset_relation,null_class))))) = not_subclass_element(subset_relation,null_class) ) ),
inference(superposition,[status(thm)],[c_35831,c_184]) ).
tcf(c_36091,plain,
( member(not_subclass_element(subset_relation,null_class),y)
| ( null_class = subset_relation )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(subset_relation,null_class),not_subclass_element(subset_relation,null_class)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_36081,c_20813]) ).
tcf(c_36104,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(demodulation,[status(thm)],[c_34753,c_193,c_4553]) ).
tcf(c_36117,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(cross_product(X0,X1),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_193,c_36104]) ).
tcf(c_36118,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X1,X2)),X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_36104]) ).
tcf(c_36119,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X2)
| member(not_subclass_element(null_class,X2),cross_product(unordered_pair(x,x),universal_class))
| member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_36104,c_21314]) ).
tcf(c_36120,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X2)
| member(not_subclass_element(null_class,X2),cross_product(unordered_pair(x,x),universal_class))
| member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_36104,c_21235]) ).
tcf(c_36121,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)) = X0 )
| ~ subclass(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_36104,c_176]) ).
tcf(c_36122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_36104,c_250]) ).
tcf(c_36123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| member(not_subclass_element(null_class,X3),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_36104,c_170]) ).
tcf(c_36124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)))) = null_class ) ),
inference(superposition,[status(thm)],[c_36104,c_5373]) ).
tcf(c_36125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)),X3)) = null_class ) ),
inference(superposition,[status(thm)],[c_36104,c_5371]) ).
tcf(c_36126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_36104,c_5348]) ).
tcf(c_36127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_36104,c_5346]) ).
tcf(c_36128,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)))) = null_class ) ),
inference(superposition,[status(thm)],[c_36104,c_14028]) ).
tcf(c_36129,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) = null_class ) ),
inference(superposition,[status(thm)],[c_36104,c_5287]) ).
tcf(c_36130,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_36104,c_5257]) ).
tcf(c_36131,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_36104,c_258]) ).
tcf(c_36132,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2) = intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_36104,c_4722]) ).
tcf(c_36133,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)))),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) = intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_36104,c_4787]) ).
tcf(c_36134,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,complement(complement(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))))),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)))) = intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_36104,c_13998]) ).
tcf(c_36229,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(demodulation,[status(thm)],[c_36118,c_4553]) ).
tcf(c_36230,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(demodulation,[status(thm)],[c_34754,c_193,c_4553]) ).
tcf(c_36243,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(cross_product(X0,X1),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_193,c_36230]) ).
tcf(c_36244,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X1,X2)),X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22472,c_36230]) ).
tcf(c_36245,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X2)
| member(not_subclass_element(null_class,X2),cross_product(unordered_pair(y,y),universal_class))
| member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_36230,c_21314]) ).
tcf(c_36246,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X2)
| member(not_subclass_element(null_class,X2),cross_product(unordered_pair(y,y),universal_class))
| member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_36230,c_21235]) ).
tcf(c_36247,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)) = X0 )
| ~ subclass(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_36230,c_176]) ).
tcf(c_36248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_36230,c_250]) ).
tcf(c_36249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| member(not_subclass_element(null_class,X3),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_36230,c_170]) ).
tcf(c_36250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)))) = null_class ) ),
inference(superposition,[status(thm)],[c_36230,c_5373]) ).
tcf(c_36251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)),X3)) = null_class ) ),
inference(superposition,[status(thm)],[c_36230,c_5371]) ).
tcf(c_36252,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_36230,c_5348]) ).
tcf(c_36253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_36230,c_5346]) ).
tcf(c_36254,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)))) = null_class ) ),
inference(superposition,[status(thm)],[c_36230,c_14028]) ).
tcf(c_36255,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) = null_class ) ),
inference(superposition,[status(thm)],[c_36230,c_5287]) ).
tcf(c_36256,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_36230,c_5257]) ).
tcf(c_36257,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_36230,c_258]) ).
tcf(c_36258,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2) = intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_36230,c_4722]) ).
tcf(c_36259,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)))),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) = intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_36230,c_4787]) ).
tcf(c_36260,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,complement(complement(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))))),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)))) = intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_36230,c_13998]) ).
tcf(c_36404,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(demodulation,[status(thm)],[c_36244,c_4553]) ).
tcf(c_36409,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(universal_class),cross_product(X0,X1)),X2)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_13126,c_5413]) ).
tcf(c_36410,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(universal_class),cross_product(X0,X1)),X2)
| ( unordered_pair(not_subclass_element(intersection(cross_product(X0,X1),complement(universal_class)),X2),not_subclass_element(intersection(cross_product(X0,X1),complement(universal_class)),X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_4943,c_5413]) ).
tcf(c_36411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,universal_class)
| subclass(intersection(complement(universal_class),cross_product(X0,X1)),X2)
| ( unordered_pair(not_subclass_element(intersection(cross_product(X0,X1),complement(universal_class)),X2),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_5413]) ).
tcf(c_36412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,universal_class)
| subclass(intersection(complement(universal_class),cross_product(X1,X2)),X3)
| ( unordered_pair(X0,not_subclass_element(intersection(cross_product(X1,X2),complement(universal_class)),X3)) = null_class ) ),
inference(superposition,[status(thm)],[c_266,c_5413]) ).
tcf(c_36413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(complement(universal_class),cross_product(X0,X1)),X2)
| ( unordered_pair(not_subclass_element(intersection(cross_product(X0,X1),complement(universal_class)),X2),X3) = unordered_pair(X3,X3) ) ),
inference(superposition,[status(thm)],[c_265,c_5413]) ).
tcf(c_36414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(complement(universal_class),cross_product(X1,X2)),X3)
| ( unordered_pair(X0,not_subclass_element(intersection(cross_product(X1,X2),complement(universal_class)),X3)) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_264,c_5413]) ).
tcf(c_36415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(complement(intersection(X2,X3)),cross_product(X0,X1)),X4)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),complement(intersection(X2,X3))),X4),X3)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),complement(intersection(X2,X3))),X4),X2) ),
inference(superposition,[status(thm)],[c_190,c_5413]) ).
tcf(c_36417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(complement(domain_of(X2)),cross_product(X0,X1)),X3)
| ( intersection(X2,cross_product(unordered_pair(not_subclass_element(intersection(cross_product(X0,X1),complement(domain_of(X2))),X3),not_subclass_element(intersection(cross_product(X0,X1),complement(domain_of(X2))),X3)),universal_class)) = null_class )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),complement(domain_of(X2))),X3),universal_class) ),
inference(superposition,[status(thm)],[c_195,c_5413]) ).
tcf(c_36420,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),X2),identity_relation) ),
inference(superposition,[status(thm)],[c_4294,c_5413]) ).
tcf(c_36422,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),complement(cross_product(universal_class,universal_class))),X2),identity_relation) ),
inference(superposition,[status(thm)],[c_7261,c_5413]) ).
tcf(c_36424,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),complement(cross_product(universal_class,universal_class))),X2),successor_relation) ),
inference(superposition,[status(thm)],[c_4340,c_5413]) ).
tcf(c_36425,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),complement(cross_product(universal_class,universal_class))),X2),element_relation) ),
inference(superposition,[status(thm)],[c_4337,c_5413]) ).
tcf(c_36427,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(universal_class),cross_product(X0,X1)),null_class)
| ( intersection(cross_product(X0,X1),complement(universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_4389,c_5413]) ).
tcf(c_36428,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(X2),cross_product(X0,X1)),complement(X2))
| subclass(intersection(cross_product(X0,X1),complement(X2)),complement(X2)) ),
inference(superposition,[status(thm)],[c_8328,c_5413]) ).
tcf(c_36429,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(complement(cross_product(X0,X1)),cross_product(X0,X1)),X2),
inference(superposition,[status(thm)],[c_4640,c_5413]) ).
tcf(c_36430,plain,
! [X0: $i,X1: $i,X2: $i] : subclass(intersection(complement(universal_class),cross_product(X0,X1)),X2),
inference(superposition,[status(thm)],[c_5409,c_5413]) ).
tcf(c_36431,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(subset_relation),cross_product(X0,X1)),complement(identity_relation))
| subclass(intersection(cross_product(X0,X1),complement(subset_relation)),complement(identity_relation)) ),
inference(superposition,[status(thm)],[c_8344,c_5413]) ).
tcf(c_36432,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(complement(identity_relation)),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(cross_product(X0,X1),complement(complement(identity_relation))),X2),subset_relation)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),complement(complement(identity_relation))),X2),universal_class) ),
inference(superposition,[status(thm)],[c_8815,c_5413]) ).
tcf(c_36433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(complement(X0),cross_product(X1,X2)),X3)
| ~ member(not_subclass_element(intersection(complement(X0),cross_product(X1,X2)),X3),X0) ),
inference(superposition,[status(thm)],[c_193,c_5413]) ).
tcf(c_36435,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(universal_class),cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),universal_class) ),
inference(superposition,[status(thm)],[c_4953,c_5413]) ).
tcf(c_36436,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(null_class),cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),universal_class),X2),null_class) ),
inference(superposition,[status(thm)],[c_8703,c_5413]) ).
tcf(c_36437,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(complement(intersection(iPr_def_10,y))),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),complement(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_28867,c_5413]) ).
tcf(c_36439,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| ~ function(universal_class) ),
inference(light_normalisation,[status(thm)],[c_36409,c_4953]) ).
tcf(c_36442,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),null_class)
| ( intersection(cross_product(X0,X1),null_class) = null_class ) ),
inference(light_normalisation,[status(thm)],[c_36427,c_4953]) ).
tcf(c_36443,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(universal_class,cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),universal_class),X2),null_class) ),
inference(light_normalisation,[status(thm)],[c_36436,c_8703]) ).
tcf(c_36444,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),universal_class) ),
inference(light_normalisation,[status(thm)],[c_36435,c_4953]) ).
tcf(c_36455,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(null_class,cross_product(X1,X2)),X3)
| ( unordered_pair(X0,not_subclass_element(intersection(cross_product(X1,X2),null_class),X3)) = unordered_pair(X0,X0) ) ),
inference(light_normalisation,[status(thm)],[c_36414,c_4953]) ).
tcf(c_36458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| ( unordered_pair(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),X3) = unordered_pair(X3,X3) ) ),
inference(light_normalisation,[status(thm)],[c_36413,c_4953]) ).
tcf(c_36461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,universal_class)
| subclass(intersection(null_class,cross_product(X1,X2)),X3)
| ( unordered_pair(X0,not_subclass_element(intersection(cross_product(X1,X2),null_class),X3)) = null_class ) ),
inference(light_normalisation,[status(thm)],[c_36412,c_4953]) ).
tcf(c_36465,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,universal_class)
| subclass(intersection(null_class,cross_product(X0,X1)),X2)
| ( unordered_pair(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),X3) = null_class ) ),
inference(light_normalisation,[status(thm)],[c_36411,c_4953]) ).
tcf(c_36471,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X0,X1)),X2)
| ( unordered_pair(not_subclass_element(intersection(cross_product(X0,X1),null_class),X2),not_subclass_element(intersection(cross_product(X0,X1),null_class),X2)) = null_class ) ),
inference(light_normalisation,[status(thm)],[c_36410,c_4953]) ).
tcf(c_36497,plain,
member(not_subclass_element(unordered_pair(x,x),null_class),iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_4973,c_272,c_4973,c_9928,c_14459]) ).
tcf(c_36499,plain,
( member(not_subclass_element(unordered_pair(x,x),null_class),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_36497,c_4342]) ).
tcf(c_36500,plain,
member(not_subclass_element(unordered_pair(x,x),null_class),universal_class),
inference(superposition,[status(thm)],[c_36497,c_4336]) ).
tcf(c_36501,plain,
( ( not_subclass_element(unordered_pair(x,x),null_class) = y )
| ( not_subclass_element(unordered_pair(x,x),null_class) = x ) ),
inference(superposition,[status(thm)],[c_36497,c_5208]) ).
tcf(c_36510,plain,
member(not_subclass_element(unordered_pair(y,y),null_class),iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_4997,c_273,c_4997,c_10079,c_14603]) ).
tcf(c_36512,plain,
( member(not_subclass_element(unordered_pair(y,y),null_class),cross_product(universal_class,universal_class))
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_36510,c_4342]) ).
tcf(c_36513,plain,
member(not_subclass_element(unordered_pair(y,y),null_class),universal_class),
inference(superposition,[status(thm)],[c_36510,c_4336]) ).
tcf(c_36514,plain,
( ( not_subclass_element(unordered_pair(y,y),null_class) = y )
| ( not_subclass_element(unordered_pair(y,y),null_class) = x ) ),
inference(superposition,[status(thm)],[c_36510,c_5208]) ).
tcf(c_36539,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),universal_class)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_173,c_5055]) ).
tcf(c_36540,plain,
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,element_relation) ),
inference(superposition,[status(thm)],[c_185,c_5055]) ).
tcf(c_36541,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ subclass(iPr_def_10,rotate(X0)) ),
inference(superposition,[status(thm)],[c_196,c_5055]) ).
tcf(c_36542,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ subclass(iPr_def_10,flip(X0)) ),
inference(superposition,[status(thm)],[c_199,c_5055]) ).
tcf(c_36543,plain,
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,successor_relation) ),
inference(superposition,[status(thm)],[c_202,c_5055]) ).
tcf(c_36544,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,compose(X0,X1)) ),
inference(superposition,[status(thm)],[c_213,c_5055]) ).
tcf(c_36545,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4571,c_5055]) ).
tcf(c_36546,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ function(X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_218,c_5055]) ).
tcf(c_36547,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),identity_relation)
| ~ function(X0)
| ~ subclass(iPr_def_10,compose(X0,domain_of(flip(cross_product(X0,universal_class))))) ),
inference(superposition,[status(thm)],[c_219,c_5055]) ).
tcf(c_36548,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),domain_of(domain_of(X0)))
| ~ operation(X0)
| ~ subclass(iPr_def_10,domain_of(domain_of(flip(cross_product(X0,universal_class))))) ),
inference(superposition,[status(thm)],[c_233,c_5055]) ).
tcf(c_36549,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),unordered_pair(X0,X1))
| ~ subclass(iPr_def_10,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_262,c_5055]) ).
tcf(c_36550,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),unordered_pair(X1,X0))
| ~ subclass(iPr_def_10,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_263,c_5055]) ).
tcf(c_36551,plain,
( subclass(unordered_pair(x,x),omega)
| ~ subclass(iPr_def_10,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_1565,c_5055]) ).
tcf(c_36554,plain,
( subclass(unordered_pair(x,x),subset_relation)
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_4319,c_5055]) ).
tcf(c_36555,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(iPr_def_10,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_4427,c_5055]) ).
tcf(c_36558,plain,
( subclass(unordered_pair(x,x),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_4550,c_5055]) ).
tcf(c_36559,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X2)
| ~ subclass(X0,X2)
| ~ subclass(iPr_def_10,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_4551,c_5055]) ).
tcf(c_36560,plain,
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_7256,c_5055]) ).
tcf(c_36561,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(iPr_def_10,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_4643,c_5055]) ).
tcf(c_36562,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X2)
| ~ subclass(X1,X2)
| ~ subclass(iPr_def_10,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_4788,c_5055]) ).
tcf(c_36563,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(X0,X1)
| ~ subclass(iPr_def_10,complement(complement(X0))) ),
inference(superposition,[status(thm)],[c_13999,c_5055]) ).
tcf(c_36564,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(complement(element_relation),X0)
| ~ subclass(iPr_def_10,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_15325,c_5055]) ).
tcf(c_36565,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(complement(successor_relation),X0)
| ~ subclass(iPr_def_10,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_14988,c_5055]) ).
tcf(c_36566,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ function(universal_class)
| ~ subclass(iPr_def_10,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_13276,c_5055]) ).
tcf(c_36567,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(iPr_def_10,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_6065,c_5055]) ).
tcf(c_36568,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),subset_relation)
| ~ subclass(iPr_def_10,intersection(identity_relation,X0)) ),
inference(superposition,[status(thm)],[c_6244,c_5055]) ).
tcf(c_36569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(unordered_pair(x,x),X3)
| ~ subclass(X1,X3)
| ~ subclass(iPr_def_10,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_6249,c_5055]) ).
tcf(c_36570,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(subset_relation,X1)
| ~ subclass(iPr_def_10,intersection(identity_relation,X0)) ),
inference(superposition,[status(thm)],[c_6317,c_5055]) ).
tcf(c_36571,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(iPr_def_10,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_6583,c_5055]) ).
tcf(c_36572,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ subclass(iPr_def_10,intersection(identity_relation,X0)) ),
inference(superposition,[status(thm)],[c_6777,c_5055]) ).
tcf(c_36573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(unordered_pair(x,x),X3)
| ~ subclass(X0,X3)
| ~ subclass(iPr_def_10,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_6782,c_5055]) ).
tcf(c_36574,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ function(universal_class)
| ~ subclass(iPr_def_10,intersection(complement(cross_product(universal_class,universal_class)),X0)) ),
inference(superposition,[status(thm)],[c_13279,c_5055]) ).
tcf(c_36575,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(subset_relation,X0)) ),
inference(superposition,[status(thm)],[c_6976,c_5055]) ).
tcf(c_36576,plain,
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,subset_relation) ),
inference(superposition,[status(thm)],[c_6992,c_5055]) ).
tcf(c_36577,plain,
( subclass(unordered_pair(x,x),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ subclass(iPr_def_10,subset_relation) ),
inference(superposition,[status(thm)],[c_6993,c_5055]) ).
tcf(c_36578,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ operation(null_class)
| ~ subclass(iPr_def_10,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
inference(superposition,[status(thm)],[c_7697,c_5055]) ).
tcf(c_36579,plain,
( subclass(unordered_pair(x,x),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_8169,c_5055]) ).
tcf(c_36580,plain,
( subclass(unordered_pair(x,x),complement(identity_relation))
| ~ subclass(iPr_def_10,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_8763,c_5055]) ).
tcf(c_36581,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),complement(identity_relation))
| ~ subclass(iPr_def_10,intersection(complement(subset_relation),X0)) ),
inference(superposition,[status(thm)],[c_8764,c_5055]) ).
tcf(c_36582,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(complement(identity_relation),X1)
| ~ subclass(iPr_def_10,intersection(complement(subset_relation),X0)) ),
inference(superposition,[status(thm)],[c_8784,c_5055]) ).
tcf(c_36583,plain,
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ function(complement(identity_relation))
| ~ subclass(iPr_def_10,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_8802,c_5055]) ).
tcf(c_36584,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X2)
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_10731,c_5055]) ).
tcf(c_36585,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),subset_relation)
| ~ subclass(iPr_def_10,intersection(X0,identity_relation)) ),
inference(superposition,[status(thm)],[c_11013,c_5055]) ).
tcf(c_36586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(unordered_pair(x,x),X3)
| ~ subclass(X2,X3)
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_11018,c_5055]) ).
tcf(c_36587,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(subset_relation,X1)
| ~ subclass(iPr_def_10,intersection(X0,identity_relation)) ),
inference(superposition,[status(thm)],[c_11105,c_5055]) ).
tcf(c_36588,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_11340,c_5055]) ).
tcf(c_36589,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,subset_relation)) ),
inference(superposition,[status(thm)],[c_11622,c_5055]) ).
tcf(c_36590,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ subclass(iPr_def_10,intersection(X0,identity_relation)) ),
inference(superposition,[status(thm)],[c_11623,c_5055]) ).
tcf(c_36591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(unordered_pair(x,x),X3)
| ~ subclass(X1,X3)
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_11629,c_5055]) ).
tcf(c_36592,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ function(universal_class)
| ~ subclass(iPr_def_10,intersection(X0,complement(cross_product(universal_class,universal_class)))) ),
inference(superposition,[status(thm)],[c_13280,c_5055]) ).
tcf(c_36593,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),complement(identity_relation))
| ~ subclass(iPr_def_10,intersection(X0,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_12038,c_5055]) ).
tcf(c_36594,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(complement(identity_relation),X1)
| ~ subclass(iPr_def_10,intersection(X0,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_12408,c_5055]) ).
tcf(c_36595,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(element_relation,X0)) ),
inference(superposition,[status(thm)],[c_13156,c_5055]) ).
tcf(c_36596,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,element_relation)) ),
inference(superposition,[status(thm)],[c_13157,c_5055]) ).
tcf(c_36597,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(intersection(X0,element_relation),X1)) ),
inference(superposition,[status(thm)],[c_13159,c_5055]) ).
tcf(c_36598,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(intersection(element_relation,X0),X1)) ),
inference(superposition,[status(thm)],[c_13160,c_5055]) ).
tcf(c_36599,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,element_relation))) ),
inference(superposition,[status(thm)],[c_13162,c_5055]) ).
tcf(c_36600,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,intersection(element_relation,X1))) ),
inference(superposition,[status(thm)],[c_13163,c_5055]) ).
tcf(c_36601,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(successor_relation,X0)) ),
inference(superposition,[status(thm)],[c_13498,c_5055]) ).
tcf(c_36602,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,successor_relation)) ),
inference(superposition,[status(thm)],[c_13499,c_5055]) ).
tcf(c_36603,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(intersection(X0,successor_relation),X1)) ),
inference(superposition,[status(thm)],[c_13501,c_5055]) ).
tcf(c_36604,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(intersection(successor_relation,X0),X1)) ),
inference(superposition,[status(thm)],[c_13502,c_5055]) ).
tcf(c_36605,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,successor_relation))) ),
inference(superposition,[status(thm)],[c_13504,c_5055]) ).
tcf(c_36606,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,intersection(successor_relation,X1))) ),
inference(superposition,[status(thm)],[c_13505,c_5055]) ).
tcf(c_36607,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(iPr_def_10,complement(complement(X0))) ),
inference(superposition,[status(thm)],[c_13755,c_5055]) ).
tcf(c_36608,plain,
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,complement(complement(element_relation))) ),
inference(superposition,[status(thm)],[c_13773,c_5055]) ).
tcf(c_36609,plain,
( subclass(unordered_pair(x,x),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,complement(complement(successor_relation))) ),
inference(superposition,[status(thm)],[c_13774,c_5055]) ).
tcf(c_36610,plain,
( subclass(unordered_pair(x,x),complement(successor_relation))
| ~ subclass(iPr_def_10,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_14369,c_5055]) ).
tcf(c_36611,plain,
( subclass(unordered_pair(x,x),complement(element_relation))
| ~ subclass(iPr_def_10,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_15156,c_5055]) ).
tcf(c_36613,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(iPr_def_10,X1)
| ~ subclass(iPr_def_10,intersection(unordered_pair(x,x),X0)) ),
inference(superposition,[status(thm)],[c_16597,c_5055]) ).
tcf(c_36615,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(iPr_def_10,X1)
| ~ subclass(iPr_def_10,intersection(X0,unordered_pair(x,x))) ),
inference(superposition,[status(thm)],[c_17097,c_5055]) ).
tcf(c_36617,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(iPr_def_10,X1)
| ~ subclass(iPr_def_10,intersection(unordered_pair(y,y),X0)) ),
inference(superposition,[status(thm)],[c_18573,c_5055]) ).
tcf(c_36619,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| ~ subclass(iPr_def_10,X1)
| ~ subclass(iPr_def_10,intersection(X0,unordered_pair(y,y))) ),
inference(superposition,[status(thm)],[c_19010,c_5055]) ).
tcf(c_36620,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| member(not_subclass_element(null_class,X1),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(intersection(iPr_def_10,y),X0)) ),
inference(superposition,[status(thm)],[c_20688,c_5055]) ).
tcf(c_36621,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| member(not_subclass_element(null_class,X1),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(intersection(iPr_def_10,y),X0)) ),
inference(superposition,[status(thm)],[c_20684,c_5055]) ).
tcf(c_36622,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_20610,c_5055]) ).
tcf(c_36623,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_20608,c_5055]) ).
tcf(c_36624,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| member(not_subclass_element(null_class,X1),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(X0,intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_20680,c_5055]) ).
tcf(c_36625,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(x,x),X1)
| member(not_subclass_element(null_class,X1),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(X0,intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_20676,c_5055]) ).
tcf(c_36626,plain,
( subclass(unordered_pair(x,x),domain_of(y))
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(iPr_def_10,domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class))))) ),
inference(superposition,[status(thm)],[c_20810,c_5055]) ).
tcf(c_36629,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_30503,c_5055]) ).
tcf(c_36630,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22551,c_5055]) ).
tcf(c_36631,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22572,c_5055]) ).
tcf(c_36632,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22553,c_5055]) ).
tcf(c_36633,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22570,c_5055]) ).
tcf(c_36634,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_30318,c_5055]) ).
tcf(c_36635,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22872,c_5055]) ).
tcf(c_36636,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22893,c_5055]) ).
tcf(c_36637,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22874,c_5055]) ).
tcf(c_36638,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| member(not_subclass_element(null_class,X0),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22891,c_5055]) ).
tcf(c_36639,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,X0)
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_5055]) ).
tcf(c_36640,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,X0)
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_5055]) ).
tcf(c_36641,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_30308,c_5055]) ).
tcf(c_36642,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X2)
| member(not_subclass_element(null_class,X2),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))) ),
inference(superposition,[status(thm)],[c_36104,c_5055]) ).
tcf(c_36643,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X2)
| member(not_subclass_element(null_class,X2),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))) ),
inference(superposition,[status(thm)],[c_36230,c_5055]) ).
tcf(c_36644,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,domain_of(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_34110,c_5055]) ).
tcf(c_37451,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(x,x)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,element_relation) ),
inference(superposition,[status(thm)],[c_36540,c_21314]) ).
tcf(c_37452,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(x,x)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,element_relation) ),
inference(superposition,[status(thm)],[c_36540,c_21235]) ).
tcf(c_37453,plain,
( ( cross_product(universal_class,universal_class) = unordered_pair(x,x) )
| ~ subclass(iPr_def_10,element_relation)
| ~ subclass(cross_product(universal_class,universal_class),unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36540,c_176]) ).
tcf(c_37454,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(iPr_def_10,element_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_36540,c_250]) ).
tcf(c_37455,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,element_relation)
| ~ member(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36540,c_170]) ).
tcf(c_37634,plain,
( member(not_subclass_element(unordered_pair(x,x),null_class),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(unordered_pair(x,x),null_class),not_subclass_element(unordered_pair(x,x),null_class)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_36500,c_20813]) ).
tcf(c_37635,plain,
( member(not_subclass_element(unordered_pair(x,x),null_class),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_36500,c_4342]) ).
tcf(c_37642,plain,
( member(not_subclass_element(unordered_pair(y,y),null_class),y)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),cross_product(unordered_pair(not_subclass_element(unordered_pair(y,y),null_class),not_subclass_element(unordered_pair(y,y),null_class)),universal_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_36513,c_20813]) ).
tcf(c_37643,plain,
( member(not_subclass_element(unordered_pair(y,y),null_class),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_36513,c_4342]) ).
tcf(c_37655,plain,
( subclass(intersection(iPr_def_10,y),subset_relation)
| member(not_subclass_element(null_class,unordered_pair(x,x)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_36554,c_21314]) ).
tcf(c_37656,plain,
( subclass(intersection(iPr_def_10,y),subset_relation)
| member(not_subclass_element(null_class,unordered_pair(x,x)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_36554,c_21235]) ).
tcf(c_37657,plain,
( ( unordered_pair(x,x) = subset_relation )
| ~ subclass(iPr_def_10,identity_relation)
| ~ subclass(subset_relation,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36554,c_176]) ).
tcf(c_37658,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(iPr_def_10,identity_relation)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_36554,c_250]) ).
tcf(c_37659,plain,
! [X0: $i] :
( member(X0,subset_relation)
| ~ subclass(iPr_def_10,identity_relation)
| ~ member(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36554,c_170]) ).
tcf(c_37684,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(demodulation,[status(thm)],[c_33545,c_193,c_4553]) ).
tcf(c_37697,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(cross_product(X0,X1),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_193,c_37684]) ).
tcf(c_37698,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,cross_product(X1,X2)),X0)
| member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_22476,c_37684]) ).
tcf(c_37699,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X2)
| member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))) ),
inference(superposition,[status(thm)],[c_37684,c_5055]) ).
tcf(c_37700,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X2)
| member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_37684,c_21314]) ).
tcf(c_37701,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X2)
| member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_37684,c_21235]) ).
tcf(c_37702,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)) = X0 )
| ~ subclass(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_37684,c_176]) ).
tcf(c_37703,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_37684,c_250]) ).
tcf(c_37704,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| member(not_subclass_element(null_class,X3),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_37684,c_170]) ).
tcf(c_37705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)))) = null_class ) ),
inference(superposition,[status(thm)],[c_37684,c_5373]) ).
tcf(c_37706,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)),X3)) = null_class ) ),
inference(superposition,[status(thm)],[c_37684,c_5371]) ).
tcf(c_37707,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_37684,c_5348]) ).
tcf(c_37708,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_37684,c_5346]) ).
tcf(c_37709,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)))) = null_class ) ),
inference(superposition,[status(thm)],[c_37684,c_14028]) ).
tcf(c_37710,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) = null_class ) ),
inference(superposition,[status(thm)],[c_37684,c_5287]) ).
tcf(c_37711,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_37684,c_5257]) ).
tcf(c_37712,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_37684,c_258]) ).
tcf(c_37713,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2) = intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_37684,c_4722]) ).
tcf(c_37714,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) = intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_37684,c_4787]) ).
tcf(c_37715,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,complement(complement(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)))) = intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_37684,c_13998]) ).
tcf(c_37816,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(demodulation,[status(thm)],[c_37698,c_4553]) ).
tcf(c_37817,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(demodulation,[status(thm)],[c_33546,c_193,c_4553]) ).
tcf(c_37830,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(cross_product(X0,X1),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))),X2)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_193,c_37817]) ).
tcf(c_37832,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X2)
| member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))) ),
inference(superposition,[status(thm)],[c_37817,c_5055]) ).
tcf(c_37833,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X2)
| member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_37817,c_21314]) ).
tcf(c_37834,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(iPr_def_10,y),X2)
| member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| member(not_subclass_element(null_class,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))),y)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(superposition,[status(thm)],[c_37817,c_21235]) ).
tcf(c_37835,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)) = X0 )
| ~ subclass(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_37817,c_176]) ).
tcf(c_37836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_37817,c_250]) ).
tcf(c_37837,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X3)
| member(not_subclass_element(null_class,X3),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_37817,c_170]) ).
tcf(c_37838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(X1,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)))) = null_class ) ),
inference(superposition,[status(thm)],[c_37817,c_5373]) ).
tcf(c_37839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)),X3)) = null_class ) ),
inference(superposition,[status(thm)],[c_37817,c_5371]) ).
tcf(c_37840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_37817,c_5348]) ).
tcf(c_37841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2),X3) = null_class ) ),
inference(superposition,[status(thm)],[c_37817,c_5346]) ).
tcf(c_37842,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)))) = null_class ) ),
inference(superposition,[status(thm)],[c_37817,c_14028]) ).
tcf(c_37843,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) = null_class ) ),
inference(superposition,[status(thm)],[c_37817,c_5287]) ).
tcf(c_37844,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_37817,c_5257]) ).
tcf(c_37845,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_37817,c_258]) ).
tcf(c_37846,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2)),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)),X2) = intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_37817,c_4722]) ).
tcf(c_37847,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( intersection(X0,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2))) = intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_37817,c_4787]) ).
tcf(c_37848,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,complement(complement(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))))),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( complement(complement(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)))) = intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_37817,c_13998]) ).
tcf(c_37955,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X0),X1) = null_class )
| ~ function(y) ),
inference(superposition,[status(thm)],[c_21238,c_4342]) ).
tcf(c_37956,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_21238,c_4336]) ).
tcf(c_37957,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X0),X1) = null_class )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_21238,c_20672]) ).
tcf(c_37971,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(identity_relation,cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(identity_relation,cross_product(X0,X1)),X2),subset_relation) ),
inference(demodulation,[status(thm)],[c_5414,c_193]) ).
tcf(c_37977,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(x,x)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,successor_relation) ),
inference(superposition,[status(thm)],[c_36543,c_21314]) ).
tcf(c_37978,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(x,x)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,successor_relation) ),
inference(superposition,[status(thm)],[c_36543,c_21235]) ).
tcf(c_37979,plain,
( ( cross_product(universal_class,universal_class) = unordered_pair(x,x) )
| ~ subclass(iPr_def_10,successor_relation)
| ~ subclass(cross_product(universal_class,universal_class),unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36543,c_176]) ).
tcf(c_37980,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(iPr_def_10,successor_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_36543,c_250]) ).
tcf(c_37981,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,successor_relation)
| ~ member(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36543,c_170]) ).
tcf(c_38011,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),universal_class)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_173,c_5076]) ).
tcf(c_38012,plain,
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,element_relation) ),
inference(superposition,[status(thm)],[c_185,c_5076]) ).
tcf(c_38013,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ subclass(iPr_def_10,rotate(X0)) ),
inference(superposition,[status(thm)],[c_196,c_5076]) ).
tcf(c_38014,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ subclass(iPr_def_10,flip(X0)) ),
inference(superposition,[status(thm)],[c_199,c_5076]) ).
tcf(c_38015,plain,
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,successor_relation) ),
inference(superposition,[status(thm)],[c_202,c_5076]) ).
tcf(c_38016,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,compose(X0,X1)) ),
inference(superposition,[status(thm)],[c_213,c_5076]) ).
tcf(c_38017,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_4571,c_5076]) ).
tcf(c_38018,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ function(X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_218,c_5076]) ).
tcf(c_38019,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),identity_relation)
| ~ function(X0)
| ~ subclass(iPr_def_10,compose(X0,domain_of(flip(cross_product(X0,universal_class))))) ),
inference(superposition,[status(thm)],[c_219,c_5076]) ).
tcf(c_38020,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),domain_of(domain_of(X0)))
| ~ operation(X0)
| ~ subclass(iPr_def_10,domain_of(domain_of(flip(cross_product(X0,universal_class))))) ),
inference(superposition,[status(thm)],[c_233,c_5076]) ).
tcf(c_38021,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),unordered_pair(X0,X1))
| ~ subclass(iPr_def_10,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_262,c_5076]) ).
tcf(c_38022,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),unordered_pair(X1,X0))
| ~ subclass(iPr_def_10,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_263,c_5076]) ).
tcf(c_38023,plain,
( subclass(unordered_pair(y,y),omega)
| ~ subclass(iPr_def_10,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_1565,c_5076]) ).
tcf(c_38026,plain,
( subclass(unordered_pair(y,y),subset_relation)
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_4319,c_5076]) ).
tcf(c_38027,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ subclass(iPr_def_10,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_4427,c_5076]) ).
tcf(c_38030,plain,
( subclass(unordered_pair(y,y),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_4550,c_5076]) ).
tcf(c_38031,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(y,y),X2)
| ~ subclass(X0,X2)
| ~ subclass(iPr_def_10,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_4551,c_5076]) ).
tcf(c_38032,plain,
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_7256,c_5076]) ).
tcf(c_38033,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(iPr_def_10,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_4643,c_5076]) ).
tcf(c_38034,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(y,y),X2)
| ~ subclass(X1,X2)
| ~ subclass(iPr_def_10,intersection(X0,X1)) ),
inference(superposition,[status(thm)],[c_4788,c_5076]) ).
tcf(c_38035,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(X0,X1)
| ~ subclass(iPr_def_10,complement(complement(X0))) ),
inference(superposition,[status(thm)],[c_13999,c_5076]) ).
tcf(c_38036,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ subclass(complement(element_relation),X0)
| ~ subclass(iPr_def_10,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_15325,c_5076]) ).
tcf(c_38037,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ subclass(complement(successor_relation),X0)
| ~ subclass(iPr_def_10,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_14988,c_5076]) ).
tcf(c_38038,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ function(universal_class)
| ~ subclass(iPr_def_10,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_13276,c_5076]) ).
tcf(c_38039,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(iPr_def_10,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_6065,c_5076]) ).
tcf(c_38040,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),subset_relation)
| ~ subclass(iPr_def_10,intersection(identity_relation,X0)) ),
inference(superposition,[status(thm)],[c_6244,c_5076]) ).
tcf(c_38041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(unordered_pair(y,y),X3)
| ~ subclass(X1,X3)
| ~ subclass(iPr_def_10,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_6249,c_5076]) ).
tcf(c_38042,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(subset_relation,X1)
| ~ subclass(iPr_def_10,intersection(identity_relation,X0)) ),
inference(superposition,[status(thm)],[c_6317,c_5076]) ).
tcf(c_38043,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ subclass(iPr_def_10,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_6583,c_5076]) ).
tcf(c_38044,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ subclass(iPr_def_10,intersection(identity_relation,X0)) ),
inference(superposition,[status(thm)],[c_6777,c_5076]) ).
tcf(c_38045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(unordered_pair(y,y),X3)
| ~ subclass(X0,X3)
| ~ subclass(iPr_def_10,intersection(intersection(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_6782,c_5076]) ).
tcf(c_38046,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ function(universal_class)
| ~ subclass(iPr_def_10,intersection(complement(cross_product(universal_class,universal_class)),X0)) ),
inference(superposition,[status(thm)],[c_13279,c_5076]) ).
tcf(c_38047,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(subset_relation,X0)) ),
inference(superposition,[status(thm)],[c_6976,c_5076]) ).
tcf(c_38048,plain,
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,subset_relation) ),
inference(superposition,[status(thm)],[c_6992,c_5076]) ).
tcf(c_38049,plain,
( subclass(unordered_pair(y,y),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ subclass(iPr_def_10,subset_relation) ),
inference(superposition,[status(thm)],[c_6993,c_5076]) ).
tcf(c_38050,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ operation(null_class)
| ~ subclass(iPr_def_10,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
inference(superposition,[status(thm)],[c_7697,c_5076]) ).
tcf(c_38051,plain,
( subclass(unordered_pair(y,y),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_8169,c_5076]) ).
tcf(c_38052,plain,
( subclass(unordered_pair(y,y),complement(identity_relation))
| ~ subclass(iPr_def_10,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_8763,c_5076]) ).
tcf(c_38053,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),complement(identity_relation))
| ~ subclass(iPr_def_10,intersection(complement(subset_relation),X0)) ),
inference(superposition,[status(thm)],[c_8764,c_5076]) ).
tcf(c_38054,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(complement(identity_relation),X1)
| ~ subclass(iPr_def_10,intersection(complement(subset_relation),X0)) ),
inference(superposition,[status(thm)],[c_8784,c_5076]) ).
tcf(c_38055,plain,
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ function(complement(identity_relation))
| ~ subclass(iPr_def_10,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_8802,c_5076]) ).
tcf(c_38056,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(y,y),X2)
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_10731,c_5076]) ).
tcf(c_38057,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),subset_relation)
| ~ subclass(iPr_def_10,intersection(X0,identity_relation)) ),
inference(superposition,[status(thm)],[c_11013,c_5076]) ).
tcf(c_38058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(unordered_pair(y,y),X3)
| ~ subclass(X2,X3)
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_11018,c_5076]) ).
tcf(c_38059,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(subset_relation,X1)
| ~ subclass(iPr_def_10,intersection(X0,identity_relation)) ),
inference(superposition,[status(thm)],[c_11105,c_5076]) ).
tcf(c_38060,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_11340,c_5076]) ).
tcf(c_38061,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,subset_relation)) ),
inference(superposition,[status(thm)],[c_11622,c_5076]) ).
tcf(c_38062,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ subclass(iPr_def_10,intersection(X0,identity_relation)) ),
inference(superposition,[status(thm)],[c_11623,c_5076]) ).
tcf(c_38063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(unordered_pair(y,y),X3)
| ~ subclass(X1,X3)
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,X2))) ),
inference(superposition,[status(thm)],[c_11629,c_5076]) ).
tcf(c_38064,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ function(universal_class)
| ~ subclass(iPr_def_10,intersection(X0,complement(cross_product(universal_class,universal_class)))) ),
inference(superposition,[status(thm)],[c_13280,c_5076]) ).
tcf(c_38065,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),complement(identity_relation))
| ~ subclass(iPr_def_10,intersection(X0,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_12038,c_5076]) ).
tcf(c_38066,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(complement(identity_relation),X1)
| ~ subclass(iPr_def_10,intersection(X0,complement(subset_relation))) ),
inference(superposition,[status(thm)],[c_12408,c_5076]) ).
tcf(c_38067,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(element_relation,X0)) ),
inference(superposition,[status(thm)],[c_13156,c_5076]) ).
tcf(c_38068,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,element_relation)) ),
inference(superposition,[status(thm)],[c_13157,c_5076]) ).
tcf(c_38069,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(intersection(X0,element_relation),X1)) ),
inference(superposition,[status(thm)],[c_13159,c_5076]) ).
tcf(c_38070,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(intersection(element_relation,X0),X1)) ),
inference(superposition,[status(thm)],[c_13160,c_5076]) ).
tcf(c_38071,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,element_relation))) ),
inference(superposition,[status(thm)],[c_13162,c_5076]) ).
tcf(c_38072,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,intersection(element_relation,X1))) ),
inference(superposition,[status(thm)],[c_13163,c_5076]) ).
tcf(c_38073,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(successor_relation,X0)) ),
inference(superposition,[status(thm)],[c_13498,c_5076]) ).
tcf(c_38074,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,successor_relation)) ),
inference(superposition,[status(thm)],[c_13499,c_5076]) ).
tcf(c_38075,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(intersection(X0,successor_relation),X1)) ),
inference(superposition,[status(thm)],[c_13501,c_5076]) ).
tcf(c_38076,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(intersection(successor_relation,X0),X1)) ),
inference(superposition,[status(thm)],[c_13502,c_5076]) ).
tcf(c_38077,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,intersection(X1,successor_relation))) ),
inference(superposition,[status(thm)],[c_13504,c_5076]) ).
tcf(c_38078,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,intersection(X0,intersection(successor_relation,X1))) ),
inference(superposition,[status(thm)],[c_13505,c_5076]) ).
tcf(c_38079,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ subclass(iPr_def_10,complement(complement(X0))) ),
inference(superposition,[status(thm)],[c_13755,c_5076]) ).
tcf(c_38080,plain,
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,complement(complement(element_relation))) ),
inference(superposition,[status(thm)],[c_13773,c_5076]) ).
tcf(c_38081,plain,
( subclass(unordered_pair(y,y),cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,complement(complement(successor_relation))) ),
inference(superposition,[status(thm)],[c_13774,c_5076]) ).
tcf(c_38082,plain,
( subclass(unordered_pair(y,y),complement(successor_relation))
| ~ subclass(iPr_def_10,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_14369,c_5076]) ).
tcf(c_38083,plain,
( subclass(unordered_pair(y,y),complement(element_relation))
| ~ subclass(iPr_def_10,complement(cross_product(universal_class,universal_class))) ),
inference(superposition,[status(thm)],[c_15156,c_5076]) ).
tcf(c_38085,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(iPr_def_10,X1)
| ~ subclass(iPr_def_10,intersection(unordered_pair(x,x),X0)) ),
inference(superposition,[status(thm)],[c_16597,c_5076]) ).
tcf(c_38087,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(iPr_def_10,X1)
| ~ subclass(iPr_def_10,intersection(X0,unordered_pair(x,x))) ),
inference(superposition,[status(thm)],[c_17097,c_5076]) ).
tcf(c_38089,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(iPr_def_10,X1)
| ~ subclass(iPr_def_10,intersection(unordered_pair(y,y),X0)) ),
inference(superposition,[status(thm)],[c_18573,c_5076]) ).
tcf(c_38091,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| ~ subclass(iPr_def_10,X1)
| ~ subclass(iPr_def_10,intersection(X0,unordered_pair(y,y))) ),
inference(superposition,[status(thm)],[c_19010,c_5076]) ).
tcf(c_38092,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| member(not_subclass_element(null_class,X1),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(intersection(iPr_def_10,y),X0)) ),
inference(superposition,[status(thm)],[c_20688,c_5076]) ).
tcf(c_38093,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| member(not_subclass_element(null_class,X1),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(intersection(iPr_def_10,y),X0)) ),
inference(superposition,[status(thm)],[c_20684,c_5076]) ).
tcf(c_38094,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_20610,c_5076]) ).
tcf(c_38095,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(iPr_def_10,y)) ),
inference(superposition,[status(thm)],[c_20608,c_5076]) ).
tcf(c_38096,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| member(not_subclass_element(null_class,X1),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(X0,intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_20680,c_5076]) ).
tcf(c_38097,plain,
! [X0: $i,X1: $i] :
( subclass(unordered_pair(y,y),X1)
| member(not_subclass_element(null_class,X1),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,intersection(X0,intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_20676,c_5076]) ).
tcf(c_38098,plain,
( subclass(unordered_pair(y,y),domain_of(y))
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(iPr_def_10,domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class))))) ),
inference(superposition,[status(thm)],[c_20810,c_5076]) ).
tcf(c_38103,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_30503,c_5076]) ).
tcf(c_38104,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22551,c_5076]) ).
tcf(c_38105,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22572,c_5076]) ).
tcf(c_38106,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22553,c_5076]) ).
tcf(c_38107,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22570,c_5076]) ).
tcf(c_38108,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),universal_class)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_30318,c_5076]) ).
tcf(c_38109,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22872,c_5076]) ).
tcf(c_38110,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22893,c_5076]) ).
tcf(c_38111,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22874,c_5076]) ).
tcf(c_38112,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| member(not_subclass_element(null_class,X0),element_relation)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))) ),
inference(superposition,[status(thm)],[c_22891,c_5076]) ).
tcf(c_38113,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,X0)
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_26058,c_5076]) ).
tcf(c_38114,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,X0)
| ~ member(not_subclass_element(X0,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X0,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_27648,c_5076]) ).
tcf(c_38115,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),complement(intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_30308,c_5076]) ).
tcf(c_38116,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(y,y),X2)
| member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))) ),
inference(superposition,[status(thm)],[c_37684,c_5076]) ).
tcf(c_38117,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(y,y),X2)
| member(not_subclass_element(null_class,X2),cross_product(unordered_pair(x,x),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))) ),
inference(superposition,[status(thm)],[c_36104,c_5076]) ).
tcf(c_38118,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(y,y),X2)
| member(not_subclass_element(null_class,X2),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))) ),
inference(superposition,[status(thm)],[c_37817,c_5076]) ).
tcf(c_38119,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(y,y),X2)
| member(not_subclass_element(null_class,X2),cross_product(unordered_pair(y,y),universal_class))
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(iPr_def_10,intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X0,X1))) ),
inference(superposition,[status(thm)],[c_36230,c_5076]) ).
tcf(c_38120,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,domain_of(intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_34110,c_5076]) ).
tcf(c_38656,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(y,y)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,element_relation) ),
inference(superposition,[status(thm)],[c_38012,c_21314]) ).
tcf(c_38657,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(y,y)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,element_relation) ),
inference(superposition,[status(thm)],[c_38012,c_21235]) ).
tcf(c_38658,plain,
( ( cross_product(universal_class,universal_class) = unordered_pair(y,y) )
| ~ subclass(iPr_def_10,element_relation)
| ~ subclass(cross_product(universal_class,universal_class),unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_38012,c_176]) ).
tcf(c_38659,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ subclass(iPr_def_10,element_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_38012,c_250]) ).
tcf(c_38660,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,element_relation)
| ~ member(X0,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_38012,c_170]) ).
tcf(c_38734,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(y,y)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,successor_relation) ),
inference(superposition,[status(thm)],[c_38015,c_21314]) ).
tcf(c_38735,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(y,y)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,successor_relation) ),
inference(superposition,[status(thm)],[c_38015,c_21235]) ).
tcf(c_38736,plain,
( ( cross_product(universal_class,universal_class) = unordered_pair(y,y) )
| ~ subclass(iPr_def_10,successor_relation)
| ~ subclass(cross_product(universal_class,universal_class),unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_38015,c_176]) ).
tcf(c_38737,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ subclass(iPr_def_10,successor_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_38015,c_250]) ).
tcf(c_38738,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,successor_relation)
| ~ member(X0,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_38015,c_170]) ).
tcf(c_38849,plain,
( subclass(intersection(iPr_def_10,y),subset_relation)
| member(not_subclass_element(null_class,unordered_pair(y,y)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_38026,c_21314]) ).
tcf(c_38850,plain,
( subclass(intersection(iPr_def_10,y),subset_relation)
| member(not_subclass_element(null_class,unordered_pair(y,y)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_38026,c_21235]) ).
tcf(c_38851,plain,
( ( unordered_pair(y,y) = subset_relation )
| ~ subclass(iPr_def_10,identity_relation)
| ~ subclass(subset_relation,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_38026,c_176]) ).
tcf(c_38852,plain,
! [X0: $i] :
( subclass(unordered_pair(y,y),X0)
| ~ subclass(iPr_def_10,identity_relation)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_38026,c_250]) ).
tcf(c_38853,plain,
! [X0: $i] :
( member(X0,subset_relation)
| ~ subclass(iPr_def_10,identity_relation)
| ~ member(X0,unordered_pair(y,y)) ),
inference(superposition,[status(thm)],[c_38026,c_170]) ).
tcf(c_38893,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),cross_product(X1,X2))
| ~ subclass(iPr_def_10,intersection(X0,cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_193,c_36555]) ).
tcf(c_38895,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X2)
| ~ subclass(iPr_def_10,intersection(cross_product(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_193,c_36555]) ).
tcf(c_39065,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(x,x)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_36560,c_21314]) ).
tcf(c_39066,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(x,x)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,identity_relation) ),
inference(superposition,[status(thm)],[c_36560,c_21235]) ).
tcf(c_39067,plain,
( ( cross_product(universal_class,universal_class) = unordered_pair(x,x) )
| ~ subclass(iPr_def_10,identity_relation)
| ~ subclass(cross_product(universal_class,universal_class),unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36560,c_176]) ).
tcf(c_39068,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(iPr_def_10,identity_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_36560,c_250]) ).
tcf(c_39069,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,identity_relation)
| ~ member(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36560,c_170]) ).
tcf(c_39091,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(X0,intersection(iPr_def_10,y)),X1) = null_class )
| ( regular(iPr_def_10) = x ) ),
inference(global_subsumption_just,[status(thm)],[c_21316,c_21316,c_33463]) ).
tcf(c_39092,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(iPr_def_10,y)),X1) = null_class ) ),
inference(renaming,[status(thm)],[c_39091]) ).
tcf(c_39100,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),cross_product(X0,X1)),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_193,c_39092]) ).
tcf(c_39107,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,null_class),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_20574,c_39092]) ).
tcf(c_39111,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(intersection(X0,intersection(iPr_def_10,y)),X1)),X2)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(complement(null_class),X2),intersection(X0,intersection(iPr_def_10,y)))
| ~ member(not_subclass_element(complement(intersection(intersection(X0,intersection(iPr_def_10,y)),X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_39092,c_5138]) ).
tcf(c_39112,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(iPr_def_10,y)),X1) = intersection(X0,intersection(iPr_def_10,y)) )
| ~ subclass(intersection(X0,intersection(iPr_def_10,y)),null_class) ),
inference(superposition,[status(thm)],[c_39092,c_4722]) ).
tcf(c_39113,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(null_class,complement(intersection(X0,intersection(iPr_def_10,y)))) = null_class ) ),
inference(superposition,[status(thm)],[c_39092,c_12688]) ).
tcf(c_39115,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(complement(intersection(X0,intersection(iPr_def_10,y))),null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_39092,c_11685]) ).
tcf(c_39118,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X0),intersection(X1,intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_6583]) ).
tcf(c_39119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),intersection(X0,intersection(iPr_def_10,y)))
| subclass(intersection(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4431]) ).
tcf(c_39121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),X1)
| subclass(intersection(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4430]) ).
tcf(c_39123,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4245]) ).
tcf(c_39124,plain,
! [X0: $i] :
( subclass(null_class,intersection(X0,intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4427]) ).
tcf(c_39125,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(X0,intersection(iPr_def_10,y)))
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4224]) ).
tcf(c_39127,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ( regular(iPr_def_10) = x )
| ~ member(X2,null_class)
| ~ subclass(intersection(X0,intersection(iPr_def_10,y)),X1) ),
inference(superposition,[status(thm)],[c_39092,c_5256]) ).
tcf(c_39128,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,intersection(intersection(X1,intersection(iPr_def_10,y)),X2))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(X0,null_class),intersection(X1,intersection(iPr_def_10,y)))
| ~ member(not_subclass_element(X0,intersection(intersection(X1,intersection(iPr_def_10,y)),X2)),X2) ),
inference(superposition,[status(thm)],[c_39092,c_5134]) ).
tcf(c_39131,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,null_class),intersection(X1,intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_11340]) ).
tcf(c_39132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),intersection(X1,intersection(iPr_def_10,y)))
| subclass(intersection(X0,intersection(intersection(X1,intersection(iPr_def_10,y)),X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4647]) ).
tcf(c_39134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),X2)
| subclass(intersection(X0,intersection(intersection(X1,intersection(iPr_def_10,y)),X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4646]) ).
tcf(c_39137,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,null_class)
| ( regular(iPr_def_10) = x )
| ~ member(X0,X2)
| ~ member(X0,intersection(X1,intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_39092,c_190]) ).
tcf(c_39140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),universal_class)
| subclass(intersection(cross_product(X0,X1),intersection(X2,intersection(iPr_def_10,y))),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_5105]) ).
tcf(c_39141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),intersection(X2,intersection(iPr_def_10,y)))
| subclass(intersection(cross_product(X0,X1),intersection(X2,intersection(iPr_def_10,y))),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4638]) ).
tcf(c_39142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),cross_product(X0,X1))
| subclass(intersection(cross_product(X0,X1),intersection(X2,intersection(iPr_def_10,y))),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4424]) ).
tcf(c_39143,plain,
! [X0: $i] :
( member(regular(null_class),subset_relation)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(iPr_def_10,y)),identity_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_39092,c_9850]) ).
tcf(c_39144,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(X0,intersection(iPr_def_10,y)),identity_relation) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_39092,c_11104]) ).
tcf(c_39145,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),subset_relation)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),identity_relation),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4649]) ).
tcf(c_39148,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(cross_product(X0,X1),intersection(X2,intersection(iPr_def_10,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_39092,c_193]) ).
tcf(c_39149,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ~ member(X0,domain_of(intersection(X1,intersection(iPr_def_10,y)))) ),
inference(superposition,[status(thm)],[c_39092,c_194]) ).
tcf(c_39150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),compose(X1,intersection(X3,intersection(iPr_def_10,y))))
| ( regular(iPr_def_10) = x )
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_39092,c_215]) ).
tcf(c_39151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(intersection(X2,intersection(iPr_def_10,y)),X3))
| ( regular(iPr_def_10) = x )
| ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_39092,c_215]) ).
tcf(c_39152,plain,
! [X0: $i,X1: $i] :
( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
| ( regular(iPr_def_10) = x )
| ~ member(X1,universal_class)
| ~ function(intersection(X0,intersection(iPr_def_10,y))) ),
inference(superposition,[status(thm)],[c_39092,c_221]) ).
tcf(c_39153,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(intersection(X1,intersection(iPr_def_10,y)),X2,X0)
| ( regular(iPr_def_10) = x )
| ~ operation(X2)
| ~ operation(X0)
| ~ compatible(intersection(X1,intersection(iPr_def_10,y)),X2,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_39092,c_244]) ).
tcf(c_39154,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(intersection(X1,intersection(iPr_def_10,y)),X2,X0)
| ( regular(iPr_def_10) = x )
| ~ operation(X2)
| ~ operation(X0)
| ~ compatible(intersection(X1,intersection(iPr_def_10,y)),X2,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_39092,c_244]) ).
tcf(c_39155,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(X0,X1,intersection(X2,intersection(iPr_def_10,y)))
| ( regular(iPr_def_10) = x )
| ~ operation(X1)
| ~ operation(intersection(X2,intersection(iPr_def_10,y)))
| ~ compatible(X0,X1,intersection(X2,intersection(iPr_def_10,y)))
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y))),not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y)))),unordered_pair(not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y))),unordered_pair(not_homomorphism2(X0,X1,intersection(X2,intersection(iPr_def_10,y))),not_homomorphism2(X0,X1,intersection(X2,intersection(iPr_def_10,y)))))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y))),not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y)))),unordered_pair(not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y))),unordered_pair(not_homomorphism2(X0,X1,intersection(X2,intersection(iPr_def_10,y))),not_homomorphism2(X0,X1,intersection(X2,intersection(iPr_def_10,y))))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y))),not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y)))),unordered_pair(not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y))),unordered_pair(not_homomorphism2(X0,X1,intersection(X2,intersection(iPr_def_10,y))),not_homomorphism2(X0,X1,intersection(X2,intersection(iPr_def_10,y)))))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y))),not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y)))),unordered_pair(not_homomorphism1(X0,X1,intersection(X2,intersection(iPr_def_10,y))),unordered_pair(not_homomorphism2(X0,X1,intersection(X2,intersection(iPr_def_10,y))),not_homomorphism2(X0,X1,intersection(X2,intersection(iPr_def_10,y))))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_39092,c_244]) ).
tcf(c_39156,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(X1,intersection(X2,intersection(iPr_def_10,y)),X0)
| ( regular(iPr_def_10) = x )
| ~ operation(X0)
| ~ operation(intersection(X2,intersection(iPr_def_10,y)))
| ~ compatible(X1,intersection(X2,intersection(iPr_def_10,y)),X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0),not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0),not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0),not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,intersection(X2,intersection(iPr_def_10,y)),X0),not_homomorphism2(X1,intersection(X2,intersection(iPr_def_10,y)),X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,intersection(X2,intersection(iPr_def_10,y)),X0),not_homomorphism2(X1,intersection(X2,intersection(iPr_def_10,y)),X0)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0),not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0),not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0),not_homomorphism1(X1,intersection(X2,intersection(iPr_def_10,y)),X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,intersection(X2,intersection(iPr_def_10,y)),X0),not_homomorphism2(X1,intersection(X2,intersection(iPr_def_10,y)),X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,intersection(X2,intersection(iPr_def_10,y)),X0),not_homomorphism2(X1,intersection(X2,intersection(iPr_def_10,y)),X0)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_39092,c_244]) ).
tcf(c_39157,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(intersection(X1,intersection(iPr_def_10,y)),X2,X0)
| ( regular(iPr_def_10) = x )
| ~ operation(X2)
| ~ operation(X0)
| ~ compatible(intersection(X1,intersection(iPr_def_10,y)),X2,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism1(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(X1,intersection(iPr_def_10,y)),cross_product(unordered_pair(not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0),not_homomorphism2(intersection(X1,intersection(iPr_def_10,y)),X2,X0)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_39092,c_244]) ).
tcf(c_39158,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,X2),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(intersection(X0,intersection(iPr_def_10,y)),X1) ),
inference(superposition,[status(thm)],[c_39092,c_6782]) ).
tcf(c_39159,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(intersection(X0,intersection(iPr_def_10,y)),X1) ),
inference(superposition,[status(thm)],[c_39092,c_4551]) ).
tcf(c_39161,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4431]) ).
tcf(c_39163,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(iPr_def_10,y))
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4430]) ).
tcf(c_39165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),X1)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),intersection(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4647]) ).
tcf(c_39167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),X2)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),intersection(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4646]) ).
tcf(c_39168,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X2,intersection(iPr_def_10,y)),complement(X1)),X0)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_39092,c_4648]) ).
tcf(c_39169,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(X1,intersection(iPr_def_10,y)),X0) = X0 )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_39092,c_4787]) ).
tcf(c_39174,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),iPr_def_10)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),unordered_pair(x,x)),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_4977]) ).
tcf(c_39176,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),iPr_def_10)
| subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),unordered_pair(y,y)),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_5001]) ).
tcf(c_39177,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,null_class),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(intersection(X0,intersection(iPr_def_10,y)),X1) ),
inference(superposition,[status(thm)],[c_39092,c_11629]) ).
tcf(c_39179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),intersection(X0,intersection(iPr_def_10,y)))
| subclass(intersection(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),cross_product(X2,X3)),X4)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_5412]) ).
tcf(c_39180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),X1)
| subclass(intersection(intersection(intersection(X0,intersection(iPr_def_10,y)),X1),cross_product(X2,X3)),X4)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39092,c_5411]) ).
tcf(c_39220,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(null_class,X0) = null_class ) ),
inference(light_normalisation,[status(thm)],[c_39107,c_4790]) ).
tcf(c_39253,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( regular(iPr_def_10) = x )
| ~ member(X0,X2)
| ~ member(X0,intersection(X1,intersection(iPr_def_10,y))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39137,c_256]) ).
tcf(c_39281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),X2)
| subclass(intersection(X0,intersection(intersection(X1,intersection(iPr_def_10,y)),X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_39134,c_4790]) ).
tcf(c_39301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),intersection(X1,intersection(iPr_def_10,y)))
| subclass(intersection(X0,intersection(intersection(X1,intersection(iPr_def_10,y)),X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_39132,c_4790]) ).
tcf(c_39318,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(intersection(X0,intersection(iPr_def_10,y)),X1)),X2)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(universal_class,X2),intersection(X0,intersection(iPr_def_10,y)))
| ~ member(not_subclass_element(complement(intersection(intersection(X0,intersection(iPr_def_10,y)),X1)),X2),X1) ),
inference(light_normalisation,[status(thm)],[c_39111,c_8703]) ).
tcf(c_39524,plain,
! [X0: $i,X1: $i] :
( ( intersection(intersection(intersection(iPr_def_10,y),X0),X1) = null_class )
| ( regular(iPr_def_10) = x ) ),
inference(global_subsumption_just,[status(thm)],[c_21317,c_21317,c_37957]) ).
tcf(c_39525,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X0),X1) = null_class ) ),
inference(renaming,[status(thm)],[c_39524]) ).
tcf(c_39533,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(cross_product(X0,X1),intersection(iPr_def_10,y)),X2) = null_class ) ),
inference(superposition,[status(thm)],[c_193,c_39525]) ).
tcf(c_39540,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(null_class,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_20574,c_39525]) ).
tcf(c_39544,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(intersection(intersection(iPr_def_10,y),X0),X1)),X2)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(complement(null_class),X2),intersection(intersection(iPr_def_10,y),X0))
| ~ member(not_subclass_element(complement(intersection(intersection(intersection(iPr_def_10,y),X0),X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_39525,c_5138]) ).
tcf(c_39545,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X0),X1) = intersection(intersection(iPr_def_10,y),X0) )
| ~ subclass(intersection(intersection(iPr_def_10,y),X0),null_class) ),
inference(superposition,[status(thm)],[c_39525,c_4722]) ).
tcf(c_39546,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(null_class,complement(intersection(intersection(iPr_def_10,y),X0))) = null_class ) ),
inference(superposition,[status(thm)],[c_39525,c_12688]) ).
tcf(c_39548,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(complement(intersection(intersection(iPr_def_10,y),X0)),null_class) = null_class ) ),
inference(superposition,[status(thm)],[c_39525,c_11685]) ).
tcf(c_39551,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(null_class,X0),intersection(intersection(iPr_def_10,y),X1))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_6583]) ).
tcf(c_39552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),intersection(intersection(iPr_def_10,y),X0))
| subclass(intersection(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4431]) ).
tcf(c_39554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(null_class,X2),X3),X1)
| subclass(intersection(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4430]) ).
tcf(c_39556,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X1)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4245]) ).
tcf(c_39557,plain,
! [X0: $i] :
( subclass(null_class,intersection(intersection(iPr_def_10,y),X0))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4427]) ).
tcf(c_39558,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(intersection(iPr_def_10,y),X0))
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4224]) ).
tcf(c_39560,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ( regular(iPr_def_10) = x )
| ~ member(X2,null_class)
| ~ subclass(intersection(intersection(iPr_def_10,y),X0),X1) ),
inference(superposition,[status(thm)],[c_39525,c_5256]) ).
tcf(c_39561,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,intersection(intersection(intersection(iPr_def_10,y),X1),X2))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(X0,null_class),intersection(intersection(iPr_def_10,y),X1))
| ~ member(not_subclass_element(X0,intersection(intersection(intersection(iPr_def_10,y),X1),X2)),X2) ),
inference(superposition,[status(thm)],[c_39525,c_5134]) ).
tcf(c_39564,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,null_class),intersection(intersection(iPr_def_10,y),X1))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_11340]) ).
tcf(c_39565,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),intersection(intersection(iPr_def_10,y),X1))
| subclass(intersection(X0,intersection(intersection(intersection(iPr_def_10,y),X1),X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4647]) ).
tcf(c_39567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(intersection(X0,null_class),X3),X2)
| subclass(intersection(X0,intersection(intersection(intersection(iPr_def_10,y),X1),X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4646]) ).
tcf(c_39570,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,null_class)
| ( regular(iPr_def_10) = x )
| ~ member(X0,X2)
| ~ member(X0,intersection(intersection(iPr_def_10,y),X1)) ),
inference(superposition,[status(thm)],[c_39525,c_190]) ).
tcf(c_39573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),universal_class)
| subclass(intersection(cross_product(X0,X1),intersection(intersection(iPr_def_10,y),X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_5105]) ).
tcf(c_39574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),intersection(intersection(iPr_def_10,y),X2))
| subclass(intersection(cross_product(X0,X1),intersection(intersection(iPr_def_10,y),X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4638]) ).
tcf(c_39575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),cross_product(X0,X1))
| subclass(intersection(cross_product(X0,X1),intersection(intersection(iPr_def_10,y),X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4424]) ).
tcf(c_39576,plain,
! [X0: $i] :
( member(regular(null_class),subset_relation)
| ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X0),identity_relation) = null_class ) ),
inference(superposition,[status(thm)],[c_39525,c_9850]) ).
tcf(c_39577,plain,
! [X0: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X0),identity_relation) = subset_relation )
| ~ subclass(subset_relation,null_class) ),
inference(superposition,[status(thm)],[c_39525,c_11104]) ).
tcf(c_39578,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),subset_relation)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),identity_relation),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4649]) ).
tcf(c_39581,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(cross_product(X0,X1),intersection(intersection(iPr_def_10,y),X2)) = null_class ) ),
inference(superposition,[status(thm)],[c_39525,c_193]) ).
tcf(c_39582,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ~ member(X0,domain_of(intersection(intersection(iPr_def_10,y),X1))) ),
inference(superposition,[status(thm)],[c_39525,c_194]) ).
tcf(c_39583,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),compose(X1,intersection(intersection(iPr_def_10,y),X3)))
| ( regular(iPr_def_10) = x )
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class))))) ),
inference(superposition,[status(thm)],[c_39525,c_215]) ).
tcf(c_39584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(intersection(intersection(iPr_def_10,y),X2),X3))
| ( regular(iPr_def_10) = x )
| ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm)],[c_39525,c_215]) ).
tcf(c_39585,plain,
! [X0: $i,X1: $i] :
( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
| ( regular(iPr_def_10) = x )
| ~ member(X1,universal_class)
| ~ function(intersection(intersection(iPr_def_10,y),X0)) ),
inference(superposition,[status(thm)],[c_39525,c_221]) ).
tcf(c_39586,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(intersection(intersection(iPr_def_10,y),X1),X2,X0)
| ( regular(iPr_def_10) = x )
| ~ operation(X2)
| ~ operation(X0)
| ~ compatible(intersection(intersection(iPr_def_10,y),X1),X2,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_39525,c_244]) ).
tcf(c_39587,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(intersection(intersection(iPr_def_10,y),X1),X2,X0)
| ( regular(iPr_def_10) = x )
| ~ operation(X2)
| ~ operation(X0)
| ~ compatible(intersection(intersection(iPr_def_10,y),X1),X2,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)))),unordered_pair(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_39525,c_244]) ).
tcf(c_39588,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(X0,X1,intersection(intersection(iPr_def_10,y),X2))
| ( regular(iPr_def_10) = x )
| ~ operation(X1)
| ~ operation(intersection(intersection(iPr_def_10,y),X2))
| ~ compatible(X0,X1,intersection(intersection(iPr_def_10,y),X2))
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2)),not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2))),unordered_pair(not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2)),unordered_pair(not_homomorphism2(X0,X1,intersection(intersection(iPr_def_10,y),X2)),not_homomorphism2(X0,X1,intersection(intersection(iPr_def_10,y),X2))))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2)),not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2))),unordered_pair(not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2)),unordered_pair(not_homomorphism2(X0,X1,intersection(intersection(iPr_def_10,y),X2)),not_homomorphism2(X0,X1,intersection(intersection(iPr_def_10,y),X2)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2)),not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2))),unordered_pair(not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2)),unordered_pair(not_homomorphism2(X0,X1,intersection(intersection(iPr_def_10,y),X2)),not_homomorphism2(X0,X1,intersection(intersection(iPr_def_10,y),X2))))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2)),not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2))),unordered_pair(not_homomorphism1(X0,X1,intersection(intersection(iPr_def_10,y),X2)),unordered_pair(not_homomorphism2(X0,X1,intersection(intersection(iPr_def_10,y),X2)),not_homomorphism2(X0,X1,intersection(intersection(iPr_def_10,y),X2)))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_39525,c_244]) ).
tcf(c_39589,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(X1,intersection(intersection(iPr_def_10,y),X2),X0)
| ( regular(iPr_def_10) = x )
| ~ operation(X0)
| ~ operation(intersection(intersection(iPr_def_10,y),X2))
| ~ compatible(X1,intersection(intersection(iPr_def_10,y),X2),X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0),not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0),not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0),not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,intersection(intersection(iPr_def_10,y),X2),X0),not_homomorphism2(X1,intersection(intersection(iPr_def_10,y),X2),X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,intersection(intersection(iPr_def_10,y),X2),X0),not_homomorphism2(X1,intersection(intersection(iPr_def_10,y),X2),X0)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0),not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0),not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0),not_homomorphism1(X1,intersection(intersection(iPr_def_10,y),X2),X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,intersection(intersection(iPr_def_10,y),X2),X0),not_homomorphism2(X1,intersection(intersection(iPr_def_10,y),X2),X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(not_homomorphism2(X1,intersection(intersection(iPr_def_10,y),X2),X0),not_homomorphism2(X1,intersection(intersection(iPr_def_10,y),X2),X0)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),universal_class)),universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_39525,c_244]) ).
tcf(c_39590,plain,
! [X0: $i,X1: $i,X2: $i] :
( homomorphism(intersection(intersection(iPr_def_10,y),X1),X2,X0)
| ( regular(iPr_def_10) = x )
| ~ operation(X2)
| ~ operation(X0)
| ~ compatible(intersection(intersection(iPr_def_10,y),X1),X2,X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism1(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(intersection(intersection(iPr_def_10,y),X1),cross_product(unordered_pair(not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0),not_homomorphism2(intersection(intersection(iPr_def_10,y),X1),X2,X0)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(null_class,universal_class))))))) ) ),
inference(superposition,[status(thm)],[c_39525,c_244]) ).
tcf(c_39591,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(null_class,X2),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(intersection(intersection(iPr_def_10,y),X0),X1) ),
inference(superposition,[status(thm)],[c_39525,c_6782]) ).
tcf(c_39592,plain,
! [X0: $i,X1: $i] :
( subclass(null_class,X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(intersection(intersection(iPr_def_10,y),X0),X1) ),
inference(superposition,[status(thm)],[c_39525,c_4551]) ).
tcf(c_39594,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),intersection(iPr_def_10,y))
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4431]) ).
tcf(c_39596,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X2),X0)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),X1),X2)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4430]) ).
tcf(c_39598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),X1)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),intersection(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4647]) ).
tcf(c_39600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),X2)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),intersection(X1,X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4646]) ).
tcf(c_39601,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(intersection(iPr_def_10,y),X2),complement(X1)),X0)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,X0),X1) ),
inference(superposition,[status(thm)],[c_39525,c_4648]) ).
tcf(c_39602,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(intersection(intersection(iPr_def_10,y),X1),X0) = X0 )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_39525,c_4787]) ).
tcf(c_39607,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),iPr_def_10)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),unordered_pair(x,x)),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_4977]) ).
tcf(c_39609,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,X1),iPr_def_10)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X0),unordered_pair(y,y)),X1)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_5001]) ).
tcf(c_39610,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X2,null_class),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(intersection(intersection(iPr_def_10,y),X0),X1) ),
inference(superposition,[status(thm)],[c_39525,c_11629]) ).
tcf(c_39612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),intersection(intersection(iPr_def_10,y),X0))
| subclass(intersection(intersection(intersection(intersection(iPr_def_10,y),X0),X1),cross_product(X2,X3)),X4)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_5412]) ).
tcf(c_39613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(intersection(cross_product(X2,X3),null_class),X4),X1)
| subclass(intersection(intersection(intersection(intersection(iPr_def_10,y),X0),X1),cross_product(X2,X3)),X4)
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_39525,c_5411]) ).
tcf(c_39686,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( regular(iPr_def_10) = x )
| ~ member(X0,X2)
| ~ member(X0,intersection(intersection(iPr_def_10,y),X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39570,c_256]) ).
tcf(c_39714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),X2)
| subclass(intersection(X0,intersection(intersection(intersection(iPr_def_10,y),X1),X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_39567,c_4790]) ).
tcf(c_39734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X3),intersection(intersection(iPr_def_10,y),X1))
| subclass(intersection(X0,intersection(intersection(intersection(iPr_def_10,y),X1),X2)),X3)
| ( regular(iPr_def_10) = x ) ),
inference(light_normalisation,[status(thm)],[c_39565,c_4790]) ).
tcf(c_39751,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(complement(intersection(intersection(intersection(iPr_def_10,y),X0),X1)),X2)
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(universal_class,X2),intersection(intersection(iPr_def_10,y),X0))
| ~ member(not_subclass_element(complement(intersection(intersection(intersection(iPr_def_10,y),X0),X1)),X2),X1) ),
inference(light_normalisation,[status(thm)],[c_39544,c_8703]) ).
tcf(c_39979,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(iPr_def_10,y),X1)) = null_class )
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_21912,c_4342]) ).
tcf(c_39980,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(iPr_def_10,y),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_21912,c_4336]) ).
tcf(c_39981,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( not_subclass_element(null_class,null_class) = y )
| ( not_subclass_element(null_class,null_class) = x )
| ( intersection(X0,intersection(intersection(iPr_def_10,y),X1)) = null_class ) ),
inference(superposition,[status(thm)],[c_21912,c_5208]) ).
tcf(c_40002,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(iPr_def_10,y),X1)) = null_class )
| ~ function(y) ),
inference(superposition,[status(thm)],[c_21913,c_4342]) ).
tcf(c_40004,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(intersection(iPr_def_10,y),X1)) = null_class )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_21913,c_20672]) ).
tcf(c_40020,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(iPr_def_10,y))) = null_class )
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_22052,c_4342]) ).
tcf(c_40021,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(iPr_def_10,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_22052,c_4336]) ).
tcf(c_40022,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( not_subclass_element(null_class,null_class) = y )
| ( not_subclass_element(null_class,null_class) = x )
| ( intersection(X0,intersection(X1,intersection(iPr_def_10,y))) = null_class ) ),
inference(superposition,[status(thm)],[c_22052,c_5208]) ).
tcf(c_40043,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(null_class,null_class),cross_product(universal_class,universal_class))
| ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(iPr_def_10,y))) = null_class )
| ~ function(y) ),
inference(superposition,[status(thm)],[c_22053,c_4342]) ).
tcf(c_40045,plain,
! [X0: $i,X1: $i] :
( ( regular(iPr_def_10) = x )
| ( intersection(X0,intersection(X1,intersection(iPr_def_10,y))) = null_class )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_22053,c_20672]) ).
tcf(c_40075,plain,
( subclass(intersection(y,iPr_def_10),null_class)
| subclass(intersection(y,iPr_def_10),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4245,c_23859]) ).
tcf(c_40076,plain,
( subclass(intersection(y,iPr_def_10),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ( intersection(y,iPr_def_10) = null_class ) ),
inference(superposition,[status(thm)],[c_4282,c_23859]) ).
tcf(c_40077,plain,
! [X0: $i] :
( subclass(intersection(y,intersection(X0,iPr_def_10)),null_class)
| subclass(intersection(y,intersection(X0,iPr_def_10)),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4646,c_23859]) ).
tcf(c_40078,plain,
! [X0: $i] :
( subclass(intersection(y,intersection(iPr_def_10,X0)),null_class)
| subclass(intersection(y,intersection(iPr_def_10,X0)),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4647,c_23859]) ).
tcf(c_40079,plain,
( subclass(intersection(y,unordered_pair(x,x)),null_class)
| subclass(intersection(y,unordered_pair(x,x)),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4977,c_23859]) ).
tcf(c_40080,plain,
( subclass(intersection(y,unordered_pair(y,y)),null_class)
| subclass(intersection(y,unordered_pair(y,y)),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_5001,c_23859]) ).
tcf(c_40081,plain,
( subclass(intersection(y,regular(y)),intersection(iPr_def_10,y))
| ( null_class = y )
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_223,c_23859]) ).
tcf(c_40082,plain,
( subclass(intersection(y,null_class),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4790,c_23859]) ).
tcf(c_40083,plain,
( subclass(intersection(y,complement(y)),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_12377,c_23859]) ).
tcf(c_40084,plain,
( subclass(intersection(y,intersection(iPr_def_10,y)),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_29021,c_23859]) ).
tcf(c_40121,plain,
( subclass(intersection(iPr_def_10,y),null_class)
| subclass(intersection(iPr_def_10,y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4224,c_23860]) ).
tcf(c_40123,plain,
! [X0: $i] :
( subclass(intersection(intersection(X0,iPr_def_10),y),null_class)
| subclass(intersection(intersection(X0,iPr_def_10),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4430,c_23860]) ).
tcf(c_40124,plain,
! [X0: $i] :
( subclass(intersection(intersection(iPr_def_10,X0),y),null_class)
| subclass(intersection(intersection(iPr_def_10,X0),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4431,c_23860]) ).
tcf(c_40125,plain,
( subclass(intersection(unordered_pair(x,x),y),null_class)
| subclass(intersection(unordered_pair(x,x),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_4976,c_23860]) ).
tcf(c_40126,plain,
( subclass(intersection(unordered_pair(y,y),y),null_class)
| subclass(intersection(unordered_pair(y,y),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_5000,c_23860]) ).
tcf(c_40127,plain,
( subclass(intersection(complement(y),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4169,c_23860]) ).
tcf(c_40128,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(cross_product(X0,X1),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(intersection(y,cross_product(X0,X1)),null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_193,c_23860]) ).
tcf(c_40129,plain,
( subclass(intersection(null_class,y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4553,c_23860]) ).
tcf(c_40130,plain,
( subclass(intersection(iPr_def_10,y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_20574,c_23860]) ).
tcf(c_40131,plain,
( subclass(intersection(intersection(iPr_def_10,y),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_30617,c_23860]) ).
tcf(c_40132,plain,
! [X0: $i] :
( subclass(intersection(intersection(X0,intersection(iPr_def_10,y)),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_39092,c_23860]) ).
tcf(c_40133,plain,
! [X0: $i] :
( subclass(intersection(intersection(intersection(iPr_def_10,y),X0),y),intersection(iPr_def_10,y))
| ( regular(iPr_def_10) = x )
| ~ member(not_subclass_element(null_class,null_class),iPr_def_10) ),
inference(superposition,[status(thm)],[c_39525,c_23860]) ).
tcf(c_40172,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(unordered_pair(x,x),cross_product(X0,X1)),X2)
| member(not_subclass_element(intersection(unordered_pair(x,x),cross_product(X0,X1)),X2),iPr_def_10) ),
inference(demodulation,[status(thm)],[c_5415,c_193]) ).
tcf(c_40180,plain,
! [X0: $i,X1: $i] :
( subclass(regular(X0),X1)
| ( X0 = null_class )
| ~ member(not_subclass_element(regular(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_171,c_5145]) ).
tcf(c_40181,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X1,regular(X0)),X1)
| ( X0 = null_class )
| ( regular(X0) = X1 )
| ~ member(not_subclass_element(regular(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_251,c_5145]) ).
tcf(c_40182,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( regular(X0) = null_class )
| ~ member(not_subclass_element(regular(X0),null_class),X0) ),
inference(superposition,[status(thm)],[c_259,c_5145]) ).
tcf(c_40183,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( regular(X0) = null_class )
| ~ member(regular(regular(X0)),X0) ),
inference(superposition,[status(thm)],[c_222,c_5145]) ).
tcf(c_40184,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( regular(X0) = null_class )
| ~ member(regular(X0),universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),X0) ),
inference(superposition,[status(thm)],[c_225,c_5145]) ).
tcf(c_40185,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(regular(X0),X1),X2)
| ( X0 = null_class )
| ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0) ),
inference(superposition,[status(thm)],[c_4224,c_5145]) ).
tcf(c_40186,plain,
! [X0: $i,X1: $i] :
( ( X0 = null_class )
| ( intersection(regular(X0),X1) = null_class )
| ~ member(regular(intersection(regular(X0),X1)),X0) ),
inference(superposition,[status(thm)],[c_4225,c_5145]) ).
tcf(c_40187,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,regular(X1)),X2)
| ( X1 = null_class )
| ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1) ),
inference(superposition,[status(thm)],[c_4245,c_5145]) ).
tcf(c_40188,plain,
! [X0: $i,X1: $i] :
( ( X1 = null_class )
| ( intersection(X0,regular(X1)) = null_class )
| ~ member(regular(intersection(X0,regular(X1))),X1) ),
inference(superposition,[status(thm)],[c_4246,c_5145]) ).
tcf(c_40189,plain,
! [X0: $i,X1: $i] :
( ( X1 = null_class )
| ( intersection(X0,regular(X1)) = null_class )
| ~ member(not_subclass_element(intersection(X0,regular(X1)),null_class),X1) ),
inference(superposition,[status(thm)],[c_4282,c_5145]) ).
tcf(c_40190,plain,
! [X0: $i,X1: $i] :
( ( X0 = null_class )
| ( intersection(regular(X0),X1) = null_class )
| ~ member(not_subclass_element(intersection(regular(X0),X1),null_class),X0) ),
inference(superposition,[status(thm)],[c_4283,c_5145]) ).
tcf(c_40191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(regular(X2),cross_product(X0,X1)),X3)
| ( X2 = null_class )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),regular(X2)),X3),X2) ),
inference(superposition,[status(thm)],[c_4425,c_5145]) ).
tcf(c_40192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X0,regular(X1)),X2),X3)
| ( X1 = null_class )
| ~ member(not_subclass_element(intersection(intersection(X0,regular(X1)),X2),X3),X1) ),
inference(superposition,[status(thm)],[c_4430,c_5145]) ).
tcf(c_40193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(regular(X0),X1),X2),X3)
| ( X0 = null_class )
| ~ member(not_subclass_element(intersection(intersection(regular(X0),X1),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_4431,c_5145]) ).
tcf(c_40194,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(regular(X1)))
| ( X1 = null_class )
| ~ member(not_subclass_element(X0,complement(regular(X1))),X1) ),
inference(superposition,[status(thm)],[c_8328,c_5145]) ).
tcf(c_40195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(cross_product(X1,X2),regular(X0)),X3)
| ( X0 = null_class )
| ~ member(not_subclass_element(intersection(regular(X0),cross_product(X1,X2)),X3),X0) ),
inference(superposition,[status(thm)],[c_4638,c_5145]) ).
tcf(c_40196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(X1,regular(X2))),X3)
| ( X2 = null_class )
| ~ member(not_subclass_element(intersection(X0,intersection(X1,regular(X2))),X3),X2) ),
inference(superposition,[status(thm)],[c_4646,c_5145]) ).
tcf(c_40197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(X0,intersection(regular(X1),X2)),X3)
| ( X1 = null_class )
| ~ member(not_subclass_element(intersection(X0,intersection(regular(X1),X2)),X3),X1) ),
inference(superposition,[status(thm)],[c_4647,c_5145]) ).
tcf(c_40198,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(regular(X0))),X1)
| ( X0 = null_class )
| ~ member(not_subclass_element(complement(complement(regular(X0))),X1),X0) ),
inference(superposition,[status(thm)],[c_13744,c_5145]) ).
tcf(c_40199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,regular(X3)),cross_product(X0,X1)),X4)
| ( X3 = null_class )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(X2,regular(X3))),X4),X3) ),
inference(superposition,[status(thm)],[c_5411,c_5145]) ).
tcf(c_40200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(regular(X2),X3),cross_product(X0,X1)),X4)
| ( X2 = null_class )
| ~ member(not_subclass_element(intersection(cross_product(X0,X1),intersection(regular(X2),X3)),X4),X2) ),
inference(superposition,[status(thm)],[c_5412,c_5145]) ).
tcf(c_40201,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( complement(complement(regular(X0))) = null_class )
| ~ member(regular(complement(complement(regular(X0)))),X0) ),
inference(superposition,[status(thm)],[c_14058,c_5145]) ).
tcf(c_40202,plain,
! [X0: $i,X1: $i] :
( subclass(identity_relation,X0)
| ( X1 = null_class )
| ~ subclass(subset_relation,regular(X1))
| ~ member(not_subclass_element(identity_relation,X0),X1) ),
inference(superposition,[status(thm)],[c_26791,c_5145]) ).
tcf(c_40203,plain,
! [X0: $i] :
( ( null_class = identity_relation )
| ( X0 = null_class )
| ~ subclass(subset_relation,regular(X0))
| ~ member(regular(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_26794,c_5145]) ).
tcf(c_40343,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,X2),X0)
| ~ subclass(universal_class,X0) ),
inference(superposition,[status(thm)],[c_173,c_5255]) ).
tcf(c_40345,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(rotate(X1),X2),X0)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0) ),
inference(superposition,[status(thm)],[c_196,c_5255]) ).
tcf(c_40346,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(flip(X1),X2),X0)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0) ),
inference(superposition,[status(thm)],[c_199,c_5255]) ).
tcf(c_40348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(compose(X1,X2),X3),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_213,c_5255]) ).
tcf(c_40349,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,X2),X0)
| ~ function(universal_class)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_4571,c_5255]) ).
tcf(c_40350,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,X2),X0)
| ~ function(X1)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_218,c_5255]) ).
tcf(c_40351,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(compose(X1,domain_of(flip(cross_product(X1,universal_class)))),X2),X0)
| ~ function(X1)
| ~ subclass(identity_relation,X0) ),
inference(superposition,[status(thm)],[c_219,c_5255]) ).
tcf(c_40352,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(domain_of(domain_of(flip(cross_product(X0,universal_class)))),X2),X1)
| ~ operation(X0)
| ~ subclass(domain_of(domain_of(X0)),X1) ),
inference(superposition,[status(thm)],[c_233,c_5255]) ).
tcf(c_40353,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(unordered_pair(X0,X0),X3),X2)
| ~ subclass(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_262,c_5255]) ).
tcf(c_40354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(unordered_pair(X1,X1),X3),X2)
| ~ subclass(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_263,c_5255]) ).
tcf(c_40355,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))),X1),X0)
| ~ subclass(omega,X0) ),
inference(superposition,[status(thm)],[c_1565,c_5255]) ).
tcf(c_40364,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(identity_relation,X1),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_7256,c_5255]) ).
tcf(c_40367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(complement(complement(X0)),X3),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13999,c_5255]) ).
tcf(c_40368,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X2),X1)
| ~ subclass(X0,X1)
| ~ subclass(complement(element_relation),X0) ),
inference(superposition,[status(thm)],[c_15325,c_5255]) ).
tcf(c_40369,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X2),X1)
| ~ subclass(X0,X1)
| ~ subclass(complement(successor_relation),X0) ),
inference(superposition,[status(thm)],[c_14988,c_5255]) ).
tcf(c_40371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X2,X0),X3),X4),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6065,c_5255]) ).
tcf(c_40372,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(identity_relation,X1),X2),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_6244,c_5255]) ).
tcf(c_40373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(X3,X0),X4),X5),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6249,c_5255]) ).
tcf(c_40374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(identity_relation,X2),X3),X1)
| ~ subclass(subset_relation,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6317,c_5255]) ).
tcf(c_40375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(intersection(X0,X2),X3),X4),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6583,c_5255]) ).
tcf(c_40376,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(identity_relation,X1),X2),X0)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ),
inference(superposition,[status(thm)],[c_6777,c_5255]) ).
tcf(c_40377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(intersection(X0,X3),X4),X5),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_6782,c_5255]) ).
tcf(c_40378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(complement(cross_product(universal_class,universal_class)),X2),X3),X1)
| ~ function(universal_class)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13279,c_5255]) ).
tcf(c_40379,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(subset_relation,X1),X2),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_6976,c_5255]) ).
tcf(c_40381,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(subset_relation,X1),X0)
| ~ subclass(complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))),X0) ),
inference(superposition,[status(thm)],[c_6993,c_5255]) ).
tcf(c_40382,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),X1)
| ~ operation(null_class)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_7697,c_5255]) ).
tcf(c_40383,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(identity_relation,X1),X0)
| ~ subclass(complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))),X0) ),
inference(superposition,[status(thm)],[c_8169,c_5255]) ).
tcf(c_40385,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(complement(subset_relation),X1),X2),X0)
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_8764,c_5255]) ).
tcf(c_40386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(complement(subset_relation),X2),X3),X1)
| ~ subclass(X0,X1)
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_8784,c_5255]) ).
tcf(c_40387,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(subset_relation),X1),X0)
| ~ function(complement(identity_relation))
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_8802,c_5255]) ).
tcf(c_40388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(X3,X0)),X4),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_10731,c_5255]) ).
tcf(c_40389,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X1,identity_relation),X2),X0)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_11013,c_5255]) ).
tcf(c_40390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X3,intersection(X4,X0)),X5),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11018,c_5255]) ).
tcf(c_40391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,identity_relation),X3),X1)
| ~ subclass(subset_relation,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11105,c_5255]) ).
tcf(c_40392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subclass(intersection(intersection(X2,intersection(X0,X3)),X4),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11340,c_5255]) ).
tcf(c_40393,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X1,subset_relation),X2),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_11622,c_5255]) ).
tcf(c_40394,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X1,identity_relation),X2),X0)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ),
inference(superposition,[status(thm)],[c_11623,c_5255]) ).
tcf(c_40395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( subclass(intersection(intersection(X3,intersection(X0,X4)),X5),X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_11629,c_5255]) ).
tcf(c_40396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,complement(cross_product(universal_class,universal_class))),X3),X1)
| ~ function(universal_class)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13280,c_5255]) ).
tcf(c_40397,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X1,complement(subset_relation)),X2),X0)
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_12038,c_5255]) ).
tcf(c_40398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,complement(subset_relation)),X3),X1)
| ~ subclass(X0,X1)
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_12408,c_5255]) ).
tcf(c_40401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(X1,element_relation),X2),X3),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13159,c_5255]) ).
tcf(c_40402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(element_relation,X1),X2),X3),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13160,c_5255]) ).
tcf(c_40403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X1,intersection(X2,element_relation)),X3),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13162,c_5255]) ).
tcf(c_40404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X1,intersection(element_relation,X2)),X3),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13163,c_5255]) ).
tcf(c_40407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(X1,successor_relation),X2),X3),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13501,c_5255]) ).
tcf(c_40408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(intersection(successor_relation,X1),X2),X3),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13502,c_5255]) ).
tcf(c_40409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X1,intersection(X2,successor_relation)),X3),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13504,c_5255]) ).
tcf(c_40410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X1,intersection(successor_relation,X2)),X3),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13505,c_5255]) ).
tcf(c_40411,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(complement(X0)),X2),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_13755,c_5255]) ).
tcf(c_40412,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(complement(element_relation)),X1),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13773,c_5255]) ).
tcf(c_40413,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(complement(successor_relation)),X1),X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_13774,c_5255]) ).
tcf(c_40414,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X1),X0)
| ~ subclass(complement(successor_relation),X0) ),
inference(superposition,[status(thm)],[c_14369,c_5255]) ).
tcf(c_40415,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(complement(cross_product(universal_class,universal_class)),X1),X0)
| ~ subclass(complement(element_relation),X0) ),
inference(superposition,[status(thm)],[c_15156,c_5255]) ).
tcf(c_40416,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(unordered_pair(x,x),X1),X2),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_16430,c_5255]) ).
tcf(c_40417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(unordered_pair(x,x),X2),X3),X1)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_16597,c_5255]) ).
tcf(c_40418,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X1,unordered_pair(x,x)),X2),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_17069,c_5255]) ).
tcf(c_40419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,unordered_pair(x,x)),X3),X1)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_17097,c_5255]) ).
tcf(c_40420,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(unordered_pair(y,y),X1),X2),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_18490,c_5255]) ).
tcf(c_40421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(unordered_pair(y,y),X2),X3),X1)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_18573,c_5255]) ).
tcf(c_40422,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(intersection(X1,unordered_pair(y,y)),X2),X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_18969,c_5255]) ).
tcf(c_40423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(intersection(intersection(X2,unordered_pair(y,y)),X3),X1)
| ~ subclass(iPr_def_10,X0)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_19010,c_5255]) ).
tcf(c_40424,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X2),X3),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_20688,c_5255]) ).
tcf(c_40425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X0),y)
| subclass(intersection(intersection(intersection(iPr_def_10,y),X2),X3),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_20684,c_5255]) ).
tcf(c_40428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X0),iPr_def_10)
| subclass(intersection(intersection(X2,intersection(iPr_def_10,y)),X3),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_20680,c_5255]) ).
tcf(c_40429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(not_subclass_element(null_class,X0),y)
| subclass(intersection(intersection(X2,intersection(iPr_def_10,y)),X3),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_20676,c_5255]) ).
tcf(c_40430,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))),universal_class)))),X1),X0)
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(domain_of(y),X0)
| ~ operation(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) ),
inference(superposition,[status(thm)],[c_20810,c_5255]) ).
tcf(c_40431,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X1),X0)
| ~ subclass(iPr_def_10,identity_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_36560,c_5255]) ).
tcf(c_40432,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X1),X0)
| ~ subclass(iPr_def_10,successor_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_36543,c_5255]) ).
tcf(c_40433,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X1),X0)
| ~ subclass(iPr_def_10,element_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_36540,c_5255]) ).
tcf(c_40434,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X1),X0)
| ~ function(iPr_def_10)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_20872,c_5255]) ).
tcf(c_40435,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(y,y),X1),X0)
| ~ subclass(iPr_def_10,successor_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_38015,c_5255]) ).
tcf(c_40436,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(y,y),X1),X0)
| ~ subclass(iPr_def_10,element_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_38012,c_5255]) ).
tcf(c_40437,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(y,y),X1),X0)
| ~ function(iPr_def_10)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_20901,c_5255]) ).
tcf(c_40438,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),universal_class)
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X2),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_30503,c_5255]) ).
tcf(c_40439,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X2),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22551,c_5255]) ).
tcf(c_40440,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X2),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22572,c_5255]) ).
tcf(c_40441,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X2),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22553,c_5255]) ).
tcf(c_40442,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),element_relation)
| subclass(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X2),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22570,c_5255]) ).
tcf(c_40443,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),universal_class)
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X2),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_30318,c_5255]) ).
tcf(c_40444,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X2),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22872,c_5255]) ).
tcf(c_40445,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X2),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22893,c_5255]) ).
tcf(c_40446,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X2),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22874,c_5255]) ).
tcf(c_40447,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(not_subclass_element(null_class,X0),element_relation)
| subclass(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X2),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_22891,c_5255]) ).
tcf(c_40448,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,X2),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X1,null_class),cross_product(unordered_pair(x,x),universal_class))
| ~ member(not_subclass_element(X1,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) ),
inference(superposition,[status(thm)],[c_26058,c_5255]) ).
tcf(c_40449,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,X2),X0)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(not_subclass_element(X1,null_class),cross_product(unordered_pair(y,y),universal_class))
| ~ member(not_subclass_element(X1,null_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| ~ subclass(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),X0) ),
inference(superposition,[status(thm)],[c_27648,c_5255]) ).
tcf(c_40450,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X1,X2),X0)
| ( regular(iPr_def_10) = x )
| ~ subclass(complement(intersection(iPr_def_10,y)),X0) ),
inference(superposition,[status(thm)],[c_30308,c_5255]) ).
tcf(c_40451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)),X4),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_37684,c_5255]) ).
tcf(c_40452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(x,x),universal_class))
| subclass(intersection(intersection(intersection(cross_product(unordered_pair(x,x),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)),X4),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_36104,c_5255]) ).
tcf(c_40453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(null_class,X0),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))))))
| subclass(intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)),X4),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_37817,c_5255]) ).
tcf(c_40454,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( member(not_subclass_element(null_class,X0),cross_product(unordered_pair(y,y),universal_class))
| subclass(intersection(intersection(intersection(cross_product(unordered_pair(y,y),universal_class),intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))),cross_product(X2,X3)),X4),X1)
| ( regular(iPr_def_10) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_36230,c_5255]) ).
tcf(c_40455,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(domain_of(intersection(iPr_def_10,y)),X2),X1)
| ( regular(iPr_def_10) = x )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_34110,c_5255]) ).
tcf(c_40456,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X1),X0)
| ~ subclass(iPr_def_10,identity_relation)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_36554,c_5255]) ).
tcf(c_40457,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(y,y),X1),X0)
| ~ subclass(iPr_def_10,identity_relation)
| ~ subclass(subset_relation,X0) ),
inference(superposition,[status(thm)],[c_38026,c_5255]) ).
tcf(c_41174,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(iPr_def_10,intersection(X0,cross_product(X1,X2))) ),
inference(superposition,[status(thm)],[c_193,c_36561]) ).
tcf(c_41176,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(x,x),cross_product(X0,X1))
| ~ subclass(iPr_def_10,intersection(cross_product(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_193,c_36561]) ).
tcf(c_41177,plain,
( subclass(unordered_pair(x,x),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ subclass(iPr_def_10,subset_relation) ),
inference(superposition,[status(thm)],[c_229,c_36561]) ).
tcf(c_41249,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X1),X0)
| ~ subclass(iPr_def_10,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_36576,c_5255]) ).
tcf(c_41252,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(x,x)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,subset_relation) ),
inference(superposition,[status(thm)],[c_36576,c_21314]) ).
tcf(c_41253,plain,
( subclass(intersection(iPr_def_10,y),cross_product(universal_class,universal_class))
| member(not_subclass_element(null_class,unordered_pair(x,x)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,subset_relation) ),
inference(superposition,[status(thm)],[c_36576,c_21235]) ).
tcf(c_41254,plain,
( ( cross_product(universal_class,universal_class) = unordered_pair(x,x) )
| ~ subclass(iPr_def_10,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36576,c_176]) ).
tcf(c_41255,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(iPr_def_10,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X0) ),
inference(superposition,[status(thm)],[c_36576,c_250]) ).
tcf(c_41256,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ subclass(iPr_def_10,subset_relation)
| ~ member(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36576,c_170]) ).
tcf(c_41286,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(unordered_pair(x,x),X1),X0)
| ~ subclass(iPr_def_10,complement(subset_relation))
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_36580,c_5255]) ).
tcf(c_41289,plain,
( subclass(intersection(iPr_def_10,y),complement(identity_relation))
| member(not_subclass_element(null_class,unordered_pair(x,x)),iPr_def_10)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_36580,c_21314]) ).
tcf(c_41290,plain,
( subclass(intersection(iPr_def_10,y),complement(identity_relation))
| member(not_subclass_element(null_class,unordered_pair(x,x)),y)
| ( regular(iPr_def_10) = x )
| ~ subclass(iPr_def_10,complement(subset_relation)) ),
inference(superposition,[status(thm)],[c_36580,c_21235]) ).
tcf(c_41291,plain,
( ( unordered_pair(x,x) = complement(identity_relation) )
| ~ subclass(iPr_def_10,complement(subset_relation))
| ~ subclass(complement(identity_relation),unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36580,c_176]) ).
tcf(c_41292,plain,
! [X0: $i] :
( subclass(unordered_pair(x,x),X0)
| ~ subclass(iPr_def_10,complement(subset_relation))
| ~ subclass(complement(identity_relation),X0) ),
inference(superposition,[status(thm)],[c_36580,c_250]) ).
tcf(c_41293,plain,
! [X0: $i] :
( member(X0,complement(identity_relation))
| ~ subclass(iPr_def_10,complement(subset_relation))
| ~ member(X0,unordered_pair(x,x)) ),
inference(superposition,[status(thm)],[c_36580,c_170]) ).
tcf(c_41356,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_41293,c_41292,c_41291,c_41290,c_41289,c_41286,c_41256,c_41255,c_41254,c_41253,c_41252,c_41249,c_41177,c_41176,c_41174,c_40457,c_40456,c_40455,c_40454,c_40453,c_40452,c_40451,c_40450,c_40449,c_40448,c_40447,c_40446,c_40445,c_40444,c_40443,c_40442,c_40441,c_40440,c_40439,c_40438,c_40437,c_40436,c_40435,c_40434,c_40433,c_40432,c_40431,c_40430,c_40429,c_40428,c_40425,c_40424,c_40423,c_40422,c_40421,c_40420,c_40419,c_40418,c_40417,c_40416,c_40415,c_40414,c_40413,c_40412,c_40411,c_40410,c_40409,c_40408,c_40407,c_40404,c_40403,c_40402,c_40401,c_40398,c_40397,c_40396,c_40395,c_40394,c_40393,c_40392,c_40391,c_40390,c_40389,c_40388,c_40387,c_40386,c_40385,c_40383,c_40382,c_40381,c_40379,c_40378,c_40377,c_40376,c_40375,c_40374,c_40373,c_40372,c_40371,c_40369,c_40368,c_40367,c_40364,c_40355,c_40354,c_40353,c_40352,c_40351,c_40350,c_40349,c_40348,c_40346,c_40345,c_40343,c_40203,c_40202,c_40201,c_40200,c_40199,c_40198,c_40197,c_40196,c_40195,c_40194,c_40193,c_40192,c_40191,c_40190,c_40189,c_40188,c_40187,c_40186,c_40185,c_40184,c_40183,c_40182,c_40180,c_40181,c_40172,c_40133,c_40132,c_40131,c_40130,c_40129,c_40128,c_40127,c_40126,c_40125,c_40124,c_40123,c_40121,c_40084,c_40083,c_40082,c_40081,c_40080,c_40079,c_40078,c_40077,c_40076,c_40075,c_40045,c_40043,c_40022,c_40021,c_40020,c_40004,c_40002,c_39981,c_39980,c_39979,c_39751,c_39734,c_39714,c_39686,c_39613,c_39612,c_39610,c_39609,c_39607,c_39602,c_39601,c_39600,c_39598,c_39596,c_39594,c_39592,c_39591,c_39590,c_39589,c_39588,c_39587,c_39586,c_39585,c_39584,c_39583,c_39582,c_39578,c_39577,c_39576,c_39575,c_39574,c_39573,c_39570,c_39567,c_39565,c_39564,c_39561,c_39560,c_39558,c_39557,c_39556,c_39554,c_39552,c_39551,c_39548,c_39546,c_39545,c_39544,c_39540,c_39533,c_39581,c_39525,c_39318,c_39301,c_39281,c_39253,c_39180,c_39179,c_39177,c_39176,c_39174,c_39169,c_39168,c_39167,c_39165,c_39163,c_39161,c_39159,c_39158,c_39157,c_39156,c_39155,c_39154,c_39153,c_39152,c_39151,c_39150,c_39149,c_39145,c_39144,c_39143,c_39142,c_39141,c_39140,c_39137,c_39134,c_39132,c_39131,c_39128,c_39127,c_39125,c_39124,c_39123,c_39121,c_39119,c_39118,c_39115,c_39113,c_39112,c_39111,c_39107,c_39100,c_39148,c_39092,c_39069,c_39068,c_39067,c_39066,c_39065,c_38895,c_38893,c_38853,c_38852,c_38851,c_38850,c_38849,c_38738,c_38737,c_38736,c_38735,c_38734,c_38660,c_38659,c_38658,c_38657,c_38656,c_38120,c_38119,c_38118,c_38117,c_38116,c_38115,c_38114,c_38113,c_38112,c_38111,c_38110,c_38109,c_38108,c_38107,c_38106,c_38105,c_38104,c_38103,c_38098,c_38097,c_38096,c_38095,c_38094,c_38093,c_38092,c_38091,c_38089,c_38087,c_38085,c_38083,c_38082,c_38081,c_38080,c_38079,c_38078,c_38077,c_38076,c_38075,c_38074,c_38073,c_38072,c_38071,c_38070,c_38069,c_38068,c_38067,c_38066,c_38065,c_38064,c_38063,c_38062,c_38061,c_38060,c_38059,c_38058,c_38057,c_38056,c_38055,c_38054,c_38053,c_38052,c_38051,c_38050,c_38049,c_38048,c_38047,c_38046,c_38045,c_38044,c_38043,c_38042,c_38041,c_38040,c_38039,c_38038,c_38037,c_38036,c_38035,c_38034,c_38033,c_38032,c_38031,c_38030,c_38027,c_38026,c_38023,c_38022,c_38021,c_38020,c_38019,c_38018,c_38017,c_38016,c_38015,c_38014,c_38013,c_38012,c_38011,c_37981,c_37980,c_37979,c_37978,c_37977,c_37971,c_37957,c_37956,c_37955,c_37848,c_37847,c_37846,c_37845,c_37844,c_37843,c_37842,c_37841,c_37840,c_37839,c_37838,c_37837,c_37836,c_37835,c_37834,c_37833,c_37832,c_37830,c_37817,c_37816,c_37715,c_37714,c_37713,c_37712,c_37711,c_37710,c_37709,c_37708,c_37707,c_37706,c_37705,c_37704,c_37703,c_37702,c_37701,c_37700,c_37699,c_37698,c_37697,c_37684,c_37659,c_37658,c_37657,c_37656,c_37655,c_37643,c_37642,c_37635,c_37634,c_37455,c_37454,c_37453,c_37452,c_37451,c_36644,c_36643,c_36642,c_36641,c_36640,c_36639,c_36638,c_36637,c_36636,c_36635,c_36634,c_36633,c_36632,c_36631,c_36630,c_36629,c_36626,c_36625,c_36624,c_36623,c_36622,c_36621,c_36620,c_36619,c_36617,c_36615,c_36613,c_36611,c_36610,c_36609,c_36608,c_36607,c_36606,c_36605,c_36604,c_36603,c_36602,c_36601,c_36600,c_36599,c_36598,c_36597,c_36596,c_36595,c_36594,c_36593,c_36592,c_36591,c_36590,c_36589,c_36588,c_36587,c_36586,c_36585,c_36584,c_36583,c_36582,c_36581,c_36580,c_36579,c_36578,c_36577,c_36576,c_36575,c_36574,c_36573,c_36572,c_36571,c_36570,c_36569,c_36568,c_36567,c_36566,c_36565,c_36564,c_36563,c_36562,c_36561,c_36560,c_36559,c_36558,c_36555,c_36554,c_36551,c_36550,c_36549,c_36548,c_36547,c_36546,c_36545,c_36544,c_36543,c_36542,c_36541,c_36540,c_36539,c_36514,c_36513,c_36512,c_36510,c_36501,c_36500,c_36499,c_36497,c_36471,c_36465,c_36461,c_36458,c_36455,c_36444,c_36443,c_36442,c_36439,c_36437,c_36436,c_36435,c_36433,c_36432,c_36431,c_36430,c_36429,c_36428,c_36427,c_36425,c_36424,c_36422,c_36420,c_36417,c_36415,c_36414,c_36413,c_36412,c_36411,c_36410,c_36409,c_36404,c_36260,c_36259,c_36258,c_36257,c_36256,c_36255,c_36254,c_36253,c_36252,c_36251,c_36250,c_36249,c_36248,c_36247,c_36246,c_36245,c_36244,c_36243,c_36230,c_36229,c_36134,c_36133,c_36132,c_36131,c_36130,c_36129,c_36128,c_36127,c_36126,c_36125,c_36124,c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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET076-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n015.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 09:40:56 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.46
% 0.12/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.46
% 0.12/0.46 % Detected problem language: tptp
% 0.12/0.48 % Proving...
% 36.33/5.92 % SZS status Started for theBenchmark.p
% 36.33/5.92 % SZS status Unsatisfiable for theBenchmark.p
% 36.33/5.92
% 36.33/5.92 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 36.33/5.92
% 36.33/5.92 % ------ iProver source info
% 36.33/5.92
% 36.33/5.92 % git: date: 2026-07-19 20:42:38 +0200
% 36.33/5.92 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 36.33/5.92 % git: non_committed_changes: false
% 36.33/5.92
% 36.33/5.92 % ------ Parsing...% successful
% 36.33/5.92
% 36.33/5.92
% 36.33/5.92 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 36.33/5.92
% 36.33/5.92 % ------ Preprocessing... sup_sim: 0 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 %
% 36.33/5.92
% 36.33/5.92 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 36.33/5.92
% 36.33/5.92 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 36.33/5.92 % ------ Proving...
% 36.33/5.92 % ------ Problem Properties
% 36.33/5.92
% 36.33/5.92 %
% 36.33/5.92 % clauses 96
% 36.33/5.92 % conjectures 3
% 36.33/5.92 % EPR 20
% 36.33/5.92 % Horn 82
% 36.33/5.92 % unary 26
% 36.33/5.92 % binary 43
% 36.33/5.92 % lits 199
% 36.33/5.92 % lits eq 37
% 36.33/5.92 % fd_pure 0
% 36.33/5.92 % fd_pseudo 0
% 36.33/5.92 % fd_cond 5
% 36.33/5.92 % fd_pseudo_cond 8
% 36.33/5.92 % AC symbols 0
% 36.33/5.92
% 36.33/5.92 % ------ Schedule dynamic 5 is on
% 36.33/5.92
% 36.33/5.92 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 36.33/5.92
% 36.33/5.92
% 36.33/5.92 % ------
% 36.33/5.92 % Current options:
% 36.33/5.92 % ------
% 36.33/5.92
% 36.33/5.92
% 36.33/5.92 %
% 36.33/5.92
% 36.33/5.92 % ------ Proving...
% 36.33/5.92 %
% 36.33/5.92
% 36.33/5.92 % SZS status Unsatisfiable for theBenchmark.p
% 36.33/5.92
% 36.33/5.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 36.33/5.99
% 36.33/5.99
%------------------------------------------------------------------------------