%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU319+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 02:56:47 PM UTC 2026
% Result : Theorem 105.44s 17.50s
% Output : CNFRefutation 121.72s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f3532ERROR: Could not build tree for root c_211353ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
=> ~ proper_subset(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(f13,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( element(X1,X0)
=> ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_arytm_3) ).
fof(f14,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(f16,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f18,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f19,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f20,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f25,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(f27,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f28,axiom,
! [X0] :
( element(X0,omega)
=> ( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_arytm_3) ).
fof(f30,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f32,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f33,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f35,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_intersection2(X0,X1,X2) = subset_intersection2(X0,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
fof(f38,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f39,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f40,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f41,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f42,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f43,axiom,
! [X0,X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
fof(f44,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
fof(f45,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(f46,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( in(X3,the_carrier(X0))
=> ( in(X3,X2)
<=> ! [X4] :
( element(X4,powerset(the_carrier(X0)))
=> ~ ( disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_pre_topc) ).
fof(f47,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f48,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f49,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
fof(f50,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f52,axiom,
! [X0] :
( finite(X0)
<=> ? [X1] :
( in(relation_dom(X1),omega)
& relation_rng(X1) = X0
& function(X1)
& relation(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_finset_1) ).
fof(f53,axiom,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
fof(f54,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ( X1 = empty_set
=> ( ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| X0 = empty_set ) )
& ( ( X1 = empty_set
=> X0 = empty_set )
=> ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f56,axiom,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X1] :
( X1 = pair_first(X0)
<=> ! [X2,X3] :
( X0 = ordered_pair(X2,X3)
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_mcart_1) ).
fof(f57,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f58,axiom,
! [X0] :
( top_str(X0)
=> ( topological_space(X0)
<=> ( ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( ( in(X2,the_topology(X0))
& in(X1,the_topology(X0)) )
=> in(subset_intersection2(the_carrier(X0),X1,X2),the_topology(X0)) ) ) )
& ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( subset(X1,the_topology(X0))
=> in(union_of_subsets(the_carrier(X0),X1),the_topology(X0)) ) )
& in(the_carrier(X0),the_topology(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_pre_topc) ).
fof(f59,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : X1 != ordered_pair(X2,X3)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f60,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(X2,X1)
=> in(ordered_pair(X2,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
fof(f61,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
<=> subset(X2,cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
fof(f63,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f64,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = fiber(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(ordered_pair(X3,X1),X0)
& X3 != X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord1) ).
fof(f65,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = inclusion_relation(X0)
<=> ( ! [X2,X3] :
( ( in(X3,X0)
& in(X2,X0) )
=> ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) )
& relation_field(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord2) ).
fof(f66,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f67,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f69,axiom,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X1] :
( X1 = pair_second(X0)
<=> ! [X2,X3] :
( X0 = ordered_pair(X2,X3)
=> X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_mcart_1) ).
fof(f70,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f72,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
fof(f73,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f74,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X1
| X3 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f75,axiom,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> ! [X1] :
~ ( ! [X2] :
~ ( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
& X1 != empty_set
& subset(X1,relation_field(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
fof(f76,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f77,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f79,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f80,axiom,
! [X0] :
( one_sorted_str(X0)
=> cast_as_carrier_subset(X0) = the_carrier(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(f81,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
fof(f82,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f83,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
~ ( ! [X3] :
~ ( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
& X2 != empty_set
& subset(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_wellord1) ).
fof(f84,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f85,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f87,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f88,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
fof(f89,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f90,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f91,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f92,axiom,
! [X0,X1] :
( equipotent(X0,X1)
<=> ? [X2] :
( relation_rng(X2) = X1
& relation_dom(X2) = X0
& one_to_one(X2)
& function(X2)
& relation(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord2) ).
fof(f93,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f94,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f95,axiom,
! [X0] :
( X0 = omega
<=> ( ! [X1] :
( ordinal(X1)
=> ( ( being_limit_ordinal(X1)
& in(empty_set,X1) )
=> subset(X0,X1) ) )
& ordinal(X0)
& being_limit_ordinal(X0)
& in(empty_set,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_ordinal2) ).
fof(f96,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( open_subset(X1,X0)
<=> in(X1,the_topology(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_pre_topc) ).
fof(f97,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f98,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f99,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f100,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( well_orders(X0,X1)
<=> ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).
fof(f101,axiom,
! [X0] :
( being_limit_ordinal(X0)
<=> X0 = union(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_ordinal1) ).
fof(f102,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pre_topc) ).
fof(f103,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f104,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
~ ( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_2) ).
fof(f105,axiom,
! [X0] :
( relation(X0)
=> ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
fof(f106,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f107,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_isomorphism(X0,X1,X2)
<=> ( ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_dom(X2) = relation_field(X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_wellord1) ).
fof(f108,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f109,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f110,axiom,
! [X0] :
( ( latt_str(X0)
& ~ empty_carrier(X0) )
=> ( meet_absorbing(X0)
<=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> join(X0,meet(X0,X1,X2),X2) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattices) ).
fof(f111,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f112,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) )
=> in(ordered_pair(X2,X4),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
fof(f113,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f114,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f115,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> function_inverse(X0) = relation_inverse(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f116,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f121,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& join_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> element(join(X0,X1,X2),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
fof(f129,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f133,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f134,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& meet_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> element(meet(X0,X1,X2),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
fof(f138,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f140,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f145,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f149,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f150,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(f154,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f155,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
fof(f156,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(union_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(f157,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> element(subset_intersection2(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_subset_1) ).
fof(f158,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f159,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f160,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f161,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> element(subset_difference(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(f162,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f163,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f164,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f166,axiom,
! [X0] :
( meet_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f167,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f169,axiom,
! [X0] :
( join_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f170,axiom,
! [X0] :
( latt_str(X0)
=> ( join_semilatt_str(X0)
& meet_semilatt_str(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f173,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f175,axiom,
! [X0] :
( top_str(X0)
=> element(the_topology(X0),powerset(powerset(the_carrier(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
fof(f178,axiom,
? [X0] : meet_semilatt_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
fof(f179,axiom,
? [X0] : top_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
fof(f180,axiom,
? [X0] : one_sorted_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f181,axiom,
? [X0] : join_semilatt_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
fof(f182,axiom,
? [X0] : latt_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
fof(f183,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f184,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f185,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f186,axiom,
! [X0,X1] :
( finite(X1)
=> finite(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
fof(f187,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f189,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
fof(f190,axiom,
! [X0,X1] :
( finite(X0)
=> finite(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
fof(f192,axiom,
! [X0,X1] :
( ( finite(X1)
& function(X0)
& relation(X0) )
=> finite(relation_image(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
fof(f194,axiom,
! [X0] :
( finite(singleton(X0))
& ~ empty(singleton(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
fof(f196,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f197,axiom,
! [X0] : ~ empty(succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(f198,axiom,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal2) ).
fof(f200,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f201,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f202,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f209,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f211,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f213,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f224,axiom,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funct_1) ).
fof(f225,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f226,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
fof(f227,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f228,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f231,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f232,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(union(X0))
& epsilon_connected(union(X0))
& epsilon_transitive(union(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_ordinal1) ).
fof(f233,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f234,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f235,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f236,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> closed_subset(cast_as_carrier_subset(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_pre_topc) ).
fof(f237,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f238,axiom,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
fof(f239,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f240,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f241,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f242,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
fof(f243,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f244,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f246,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_intersection2(X0,X1,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
fof(f247,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f248,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f249,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f250,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f251,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f252,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f254,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f255,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f256,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l29_wellord1) ).
fof(f257,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> in(ordered_pair(X1,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
fof(f259,axiom,
! [X0,X1] :
( relation(X1)
=> ~ ( ! [X2] :
( relation(X2)
=> ~ well_orders(X2,X0) )
& equipotent(X0,relation_field(X1))
& well_ordering(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l30_wellord2) ).
fof(f262,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f263,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f264,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).
fof(f268,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f270,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f271,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f272,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f273,axiom,
! [X0,X1] :
? [X2] :
( quasi_total(X2,X0,X1)
& function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
fof(f274,axiom,
? [X0] :
( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
fof(f275,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f276,axiom,
? [X0] :
( being_limit_ordinal(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal2) ).
fof(f277,axiom,
? [X0] :
( empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
fof(f278,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f279,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f280,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f281,axiom,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(f282,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f283,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f284,axiom,
! [X0,X1] :
? [X2] :
( function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
fof(f285,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f286,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f287,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f288,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f289,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f290,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f292,axiom,
? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f294,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
fof(f295,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
fof(f299,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f300,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
fof(f301,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> union_of_subsets(X0,X1) = union(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f302,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(f304,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f305,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f306,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f307,axiom,
! [X0,X1] :
( equipotent(X0,X1)
<=> are_equipotent(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r2_wellord2) ).
fof(f308,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ordinal_subset(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(f310,axiom,
! [X0,X1] : equipotent(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_wellord2) ).
fof(f311,axiom,
! [X0,X1] :
( ( relation(X1)
& ~ empty(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X7] :
( ! [X8] :
( in(X8,X7)
=> in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( in(X6,X5)
=> in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0) )
=> X3 = X4 )
=> ? [X2] :
( ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( ? [X9] :
( ! [X10] :
( in(X10,X9)
=> in(ordered_pair(X4,X10),X1) )
& in(X4,X9)
& X3 = X9 )
& in(X3,X0)
& in(X3,X0) ) )
& function(X2)
& relation(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_1__e10_24__wellord2__1) ).
fof(f312,axiom,
! [X0] :
( ! [X1,X2,X3] :
( ( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0) )
=> X2 = X3 )
=> ? [X1] :
( ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X3 = singleton(X2)
& in(X2,X0)
& in(X2,X0) ) )
& function(X1)
& relation(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_1__e16_22__wellord2__1) ).
fof(f313,axiom,
! [X0] :
( ? [X1] :
( in(X1,X0)
& ordinal(X1) )
=> ? [X1] :
( ! [X2] :
( ordinal(X2)
=> ( in(X2,X0)
=> ordinal_subset(X1,X2) ) )
& in(X1,X0)
& ordinal(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_ordinal1__e8_6__wellord2) ).
fof(f314,axiom,
( ( ! [X3] :
( ordinal(X3)
=> ( ( ! [X10] :
( ordinal(X10)
=> ( in(X10,X3)
=> ( in(X10,omega)
=> ! [X11] :
( element(X11,powerset(powerset(X10)))
=> ~ ( ! [X12] :
~ ( ! [X13] :
( ( subset(X12,X13)
& in(X13,X11) )
=> X13 = X12 )
& in(X12,X11) )
& X11 != empty_set ) ) ) ) )
& being_limit_ordinal(X3) )
=> ( ( in(X3,omega)
=> ! [X14] :
( element(X14,powerset(powerset(X3)))
=> ~ ( ! [X15] :
~ ( ! [X16] :
( ( subset(X15,X16)
& in(X16,X14) )
=> X16 = X15 )
& in(X15,X14) )
& X14 != empty_set ) ) )
| X3 = empty_set ) ) )
& ! [X3] :
( ordinal(X3)
=> ( ( in(X3,omega)
=> ! [X4] :
( element(X4,powerset(powerset(X3)))
=> ~ ( ! [X5] :
~ ( ! [X6] :
( ( subset(X5,X6)
& in(X6,X4) )
=> X6 = X5 )
& in(X5,X4) )
& X4 != empty_set ) ) )
=> ( in(succ(X3),omega)
=> ! [X7] :
( element(X7,powerset(powerset(succ(X3))))
=> ~ ( ! [X8] :
~ ( ! [X9] :
( ( subset(X8,X9)
& in(X9,X7) )
=> X9 = X8 )
& in(X8,X7) )
& X7 != empty_set ) ) ) ) )
& ( in(empty_set,omega)
=> ! [X0] :
( element(X0,powerset(powerset(empty_set)))
=> ~ ( ! [X1] :
~ ( ! [X2] :
( ( subset(X1,X2)
& in(X2,X0) )
=> X2 = X1 )
& in(X1,X0) )
& X0 != empty_set ) ) ) )
=> ! [X3] :
( ordinal(X3)
=> ( in(X3,omega)
=> ! [X17] :
( element(X17,powerset(powerset(X3)))
=> ~ ( ! [X18] :
~ ( ! [X19] :
( ( subset(X18,X19)
& in(X19,X17) )
=> X19 = X18 )
& in(X18,X17) )
& X17 != empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_ordinal2__e18_27__finset_1) ).
fof(f315,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ? [X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& relation(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_relat_1__e6_21__wellord2) ).
fof(f316,axiom,
! [X0,X1] :
( ( relation(X1)
& ~ empty(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X7] :
( ! [X8] :
( in(X8,X7)
=> in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( in(X6,X5)
=> in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X9] :
( ! [X10] :
( in(X10,X9)
=> in(ordered_pair(X3,X10),X1) )
& in(X3,X9)
& X4 = X9 )
& in(X4,X0)
& in(X4,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__1) ).
fof(f317,axiom,
! [X0,X1] :
( ( relation(X1)
& ~ empty(X0) )
=> ! [X2] :
( ! [X3,X4,X5] :
( ( ? [X10,X11] :
( ? [X12] :
( ! [X13] :
( in(X13,X12)
=> in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& ordered_pair(X10,X11) = X5 )
& X3 = X5
& ? [X6,X7] :
( ? [X8] :
( ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X7,X9),X1) )
& in(X7,X8)
& X6 = X8 )
& in(X6,X0)
& ordered_pair(X6,X7) = X4 )
& X3 = X4 )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( ? [X14,X15] :
( ? [X16] :
( ! [X17] :
( in(X17,X16)
=> in(ordered_pair(X15,X17),X1) )
& in(X15,X16)
& X14 = X16 )
& in(X14,X0)
& ordered_pair(X14,X15) = X4 )
& X5 = X4
& in(X5,cartesian_product2(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__2) ).
fof(f318,axiom,
! [X0] :
( ! [X1,X2,X3] :
( ( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0) )
=> X2 = X3 )
=> ? [X1] :
! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = singleton(X3)
& in(X3,X0)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__1) ).
fof(f319,axiom,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 )
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X9,X10] :
( X10 = singleton(X9)
& in(X9,X0)
& ordered_pair(X9,X10) = X3 )
& X4 = X3
& in(X4,cartesian_product2(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
fof(f320,axiom,
! [X0] :
( ordinal(X0)
=> ( ! [X1,X2,X3] :
( ( ? [X8] :
( ( in(X8,omega)
=> ! [X9] :
( element(X9,powerset(powerset(X8)))
=> ~ ( ! [X10] :
~ ( ! [X11] :
( ( subset(X10,X11)
& in(X11,X9) )
=> X11 = X10 )
& in(X10,X9) )
& X9 != empty_set ) ) )
& X3 = X8
& ordinal(X8) )
& X1 = X3
& ? [X4] :
( ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( ! [X6] :
~ ( ! [X7] :
( ( subset(X6,X7)
& in(X7,X5) )
=> X7 = X6 )
& in(X6,X5) )
& X5 != empty_set ) ) )
& X2 = X4
& ordinal(X4) )
& X1 = X2 )
=> X2 = X3 )
=> ? [X1] :
! [X2] :
( in(X2,X1)
<=> ? [X3] :
( ? [X12] :
( ( in(X12,omega)
=> ! [X13] :
( element(X13,powerset(powerset(X12)))
=> ~ ( ! [X14] :
~ ( ! [X15] :
( ( subset(X14,X15)
& in(X15,X13) )
=> X15 = X14 )
& in(X14,X13) )
& X13 != empty_set ) ) )
& X2 = X12
& ordinal(X12) )
& X3 = X2
& in(X3,succ(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e18_27__finset_1__1) ).
fof(f321,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( subset(X1,X4)
& closed_subset(X6,X0)
& X6 = X4
& element(X6,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X5 = X3
& element(X5,powerset(the_carrier(X0))) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X7] :
( subset(X1,X3)
& closed_subset(X7,X0)
& X7 = X3
& element(X7,powerset(the_carrier(X0))) )
& X4 = X3
& in(X4,powerset(the_carrier(X0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e1_40__pre_topc__1) ).
fof(f322,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X4 = X3
& in(X4,powerset(the_carrier(X0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).
fof(f323,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( X4 = set_difference(X6,singleton(X0))
& in(X6,X1) )
& X2 = X4
& ? [X5] :
( X3 = set_difference(X5,singleton(X0))
& in(X5,X1) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X7] :
( X3 = set_difference(X7,singleton(X0))
& in(X7,X1) )
& X4 = X3
& in(X4,powerset(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e4_27_3_1__finset_1__1) ).
fof(f324,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ( ! [X3,X4,X5] :
( ( ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& X5 = ordered_pair(X8,X9) )
& X3 = X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& X4 = ordered_pair(X6,X7) )
& X3 = X4 )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( ? [X10,X11] :
( in(ordered_pair(apply(X2,X10),apply(X2,X11)),X1)
& X4 = ordered_pair(X10,X11) )
& X5 = X4
& in(X5,cartesian_product2(X0,X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
fof(f325,axiom,
! [X0] :
( ! [X1,X2,X3] :
( ( ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2 )
=> X2 = X3 )
=> ? [X1] :
! [X2] :
( in(X2,X1)
<=> ? [X3] :
( ordinal(X2)
& X3 = X2
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
fof(f326,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ( ! [X3,X4,X5] :
( ( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4 )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(relation_image(X2,X4),X1)
& X5 = X4
& in(X5,powerset(relation_dom(X2))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).
fof(f327,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( in(X6,X0)
& X4 = X6
& ordinal(X6) )
& X2 = X4
& ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X7] :
( in(X7,X0)
& X3 = X7
& ordinal(X7) )
& X4 = X3
& in(X4,succ(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e8_6__wellord2__1) ).
fof(f328,axiom,
! [X0,X1] :
( ( relation(X1)
& ~ empty(X0) )
=> ! [X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( ? [X7] :
( ! [X8] :
( in(X8,X7)
=> in(ordered_pair(X6,X8),X1) )
& in(X6,X7)
& X5 = X7 )
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e10_24__wellord2__1) ).
fof(f329,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4,X5] :
( X5 = singleton(X4)
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
fof(f330,axiom,
! [X0] :
( ordinal(X0)
=> ? [X1] :
! [X2] :
( in(X2,X1)
<=> ( ? [X3] :
( ( in(X3,omega)
=> ! [X4] :
( element(X4,powerset(powerset(X3)))
=> ~ ( ! [X5] :
~ ( ! [X6] :
( ( subset(X5,X6)
& in(X6,X4) )
=> X6 = X5 )
& in(X5,X4) )
& X4 != empty_set ) ) )
& X2 = X3
& ordinal(X3) )
& in(X2,succ(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e18_27__finset_1__1) ).
fof(f331,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
fof(f332,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
fof(f333,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( X3 = set_difference(X4,singleton(X0))
& in(X4,X1) )
& in(X3,powerset(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e4_27_3_1__finset_1) ).
fof(f334,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& X4 = ordered_pair(X5,X6) )
& in(X4,cartesian_product2(X0,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
fof(f335,axiom,
! [X0] :
? [X1] :
! [X2] :
( in(X2,X1)
<=> ( ordinal(X2)
& in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
fof(f336,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
fof(f337,axiom,
! [X0,X1] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( in(X4,X0)
& X3 = X4
& ordinal(X4) )
& in(X3,succ(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
fof(f338,axiom,
! [X0,X1] :
( ( relation(X1)
& ~ empty(X0) )
=> ( ( ! [X2] :
~ ( ! [X3] :
~ ? [X9] :
( ! [X10] :
( in(X10,X9)
=> in(ordered_pair(X3,X10),X1) )
& in(X3,X9)
& X2 = X9 )
& in(X2,X0) )
& ! [X2,X3,X4] :
( ( ? [X7] :
( ! [X8] :
( in(X8,X7)
=> in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& ? [X5] :
( ! [X6] :
( in(X6,X5)
=> in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0) )
=> X3 = X4 ) )
=> ? [X2] :
( ! [X3] :
( in(X3,X0)
=> ? [X11] :
( ! [X12] :
( in(X12,X11)
=> in(ordered_pair(apply(X2,X3),X12),X1) )
& in(apply(X2,X3),X11)
& X3 = X11 ) )
& relation_dom(X2) = X0
& function(X2)
& relation(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e10_24__wellord2) ).
fof(f339,axiom,
! [X0] :
( ( ! [X1] :
~ ( ! [X2] : X2 != singleton(X1)
& in(X1,X0) )
& ! [X1,X2,X3] :
( ( X3 = singleton(X1)
& X2 = singleton(X1)
& in(X1,X0) )
=> X2 = X3 ) )
=> ? [X1] :
( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = singleton(X2) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
fof(f340,axiom,
( ! [X0] :
( ordinal(X0)
=> ( ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> ( in(X1,omega)
=> ! [X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( ! [X3] :
~ ( ! [X4] :
( ( subset(X3,X4)
& in(X4,X2) )
=> X4 = X3 )
& in(X3,X2) )
& X2 != empty_set ) ) ) ) )
=> ( in(X0,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X0)))
=> ~ ( ! [X6] :
~ ( ! [X7] :
( ( subset(X6,X7)
& in(X7,X5) )
=> X7 = X6 )
& in(X6,X5) )
& X5 != empty_set ) ) ) ) )
=> ! [X0] :
( ordinal(X0)
=> ( in(X0,omega)
=> ! [X8] :
( element(X8,powerset(powerset(X0)))
=> ~ ( ! [X9] :
~ ( ! [X10] :
( ( subset(X9,X10)
& in(X10,X8) )
=> X10 = X9 )
& in(X9,X8) )
& X8 != empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_ordinal1__e18_27__finset_1__1) ).
fof(f341,axiom,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = singleton(X2) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
fof(f342,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
( ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
fof(f343,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
( ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e2_37_1_1__pre_topc) ).
fof(f344,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f345,axiom,
! [X0,X1] :
( equipotent(X0,X1)
=> equipotent(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r2_wellord2) ).
fof(f346,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f347,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f348,axiom,
! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f349,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
fof(f350,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
fof(f351,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng_restriction(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
fof(f352,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
fof(f353,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f354,axiom,
! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_relat_1) ).
fof(f355,axiom,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f357,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f358,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f359,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(f360,axiom,
! [X0,X1] :
( ( finite(X1)
& subset(X0,X1) )
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f361,axiom,
! [X0,X1,X2] :
( relation(X2)
=> relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_relat_1) ).
fof(f362,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f363,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f364,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
fof(f365,axiom,
! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
fof(f366,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(X0,relation_dom(X1))
=> subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
fof(f367,axiom,
! [X0] :
( relation(X0)
=> relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f368,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
fof(f369,axiom,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
fof(f371,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pre_topc) ).
fof(f372,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
fof(f373,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f374,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
fof(f375,axiom,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(X0,X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
fof(f376,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f377,axiom,
! [X0,X1] :
( relation(X1)
=> ~ ( relation_inverse_image(X1,X0) = empty_set
& subset(X0,relation_rng(X1))
& X0 != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
fof(f378,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( subset(X0,X1)
=> subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
fof(f380,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(f381,axiom,
! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_wellord1) ).
fof(f383,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( ! [X2] :
~ ( ! [X3] :
( ( subset(X2,X3)
& in(X3,X1) )
=> X3 = X2 )
& in(X2,X1) )
& X1 != empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finset_1) ).
fof(f384,axiom,
! [X0,X1] :
( relation(X1)
=> relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_wellord1) ).
fof(f385,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_field(relation_restriction(X2,X1)))
=> ( in(X0,X1)
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
fof(f386,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f387,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f388,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f389,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f390,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f392,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_wellord1) ).
fof(f393,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f394,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ! [X4] :
( ( function(X4)
& relation(X4) )
=> ( in(X2,X0)
=> ( apply(relation_composition(X3,X4),X2) = apply(X4,apply(X3,X2))
| X1 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_2) ).
fof(f395,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f396,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f397,axiom,
! [X0,X1,X2] :
( relation(X2)
=> subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_wellord1) ).
fof(f398,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f399,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_pre_topc) ).
fof(f400,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X1,X0)
=> ( ! [X3] :
~ ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
fof(f401,axiom,
! [X0,X1] :
( relation(X1)
=> ( reflexive(X1)
=> reflexive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_wellord1) ).
fof(f402,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f404,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f405,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ! [X3] :
~ ( ! [X4] : ~ in(ordered_pair(X4,X3),X2)
& in(X3,X1) )
<=> relation_rng_as_subset(X0,X1,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_1) ).
fof(f406,axiom,
! [X0,X1] :
( relation(X1)
=> ( connected(X1)
=> connected(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_wellord1) ).
fof(f407,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f408,axiom,
! [X0,X1] :
( relation(X1)
=> ( transitive(X1)
=> transitive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
fof(f409,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
=> ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
fof(f410,axiom,
! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord1) ).
fof(f411,axiom,
! [X0,X1] :
( relation(X1)
=> ( well_orders(X1,X0)
=> ( well_ordering(relation_restriction(X1,X0))
& relation_field(relation_restriction(X1,X0)) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord2) ).
fof(f412,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( finite(relation_dom(X0))
=> finite(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
fof(f414,axiom,
! [X0] :
? [X1] :
( well_orders(X1,X0)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_wellord2) ).
fof(f415,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f416,axiom,
! [X0] :
( ~ empty(X0)
=> ~ ( ! [X1] :
( ( function(X1)
& relation(X1) )
=> ~ ( ! [X2] :
( in(X2,X0)
=> in(apply(X1,X2),X2) )
& relation_dom(X1) = X0 ) )
& ! [X1] :
~ ( X1 = empty_set
& in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_wellord2) ).
fof(f417,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f418,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
fof(f419,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f418]) ).
fof(f420,axiom,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f422,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f423,axiom,
! [X0] : reflexive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
fof(f424,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f425,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f426,axiom,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( subset(X1,X0)
& ordinal(X1) ) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f427,axiom,
! [X0,X1] :
( relation(X1)
=> ( well_founded_relation(X1)
=> well_founded_relation(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_wellord1) ).
fof(f428,axiom,
! [X0,X1] :
( ordinal(X1)
=> ~ ( ! [X2] :
( ordinal(X2)
=> ~ ( ! [X3] :
( ordinal(X3)
=> ( in(X3,X0)
=> ordinal_subset(X2,X3) ) )
& in(X2,X0) ) )
& X0 != empty_set
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
fof(f429,axiom,
! [X0,X1] :
( relation(X1)
=> ( well_ordering(X1)
=> well_ordering(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_wellord1) ).
fof(f430,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(f431,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f432,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f433,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f434,axiom,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f435,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f436,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f437,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f438,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f439,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f440,axiom,
! [X0,X1] :
( relation(X1)
=> ( ( subset(X0,relation_field(X1))
& well_ordering(X1) )
=> relation_field(relation_restriction(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_wellord1) ).
fof(f441,axiom,
! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f442,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f443,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(f444,axiom,
! [X0,X1,X2] :
~ ( in(X2,X0)
& in(X1,X2)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(f445,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f446,axiom,
! [X0] : transitive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_wellord2) ).
fof(f447,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f448,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f449,axiom,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f450,axiom,
! [X0] :
( ordinal(X0)
=> ( being_limit_ordinal(X0)
<=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> in(succ(X1),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_ordinal1) ).
fof(f451,axiom,
! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X1] :
( X0 = succ(X1)
& ordinal(X1) ) )
& ~ ( ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) )
& ~ being_limit_ordinal(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(f452,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
fof(f453,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( in(X2,X1)
=> closed_subset(X2,X0) ) )
=> closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_pre_topc) ).
fof(f454,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
fof(f455,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( in(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( subset(X1,X3)
& closed_subset(X3,X0) )
=> in(X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pre_topc) ).
fof(f456,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
fof(f458,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( X1 != empty_set
=> ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(apply(X3,X4),X2)
& in(X4,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
fof(f459,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ( subset(X1,X3)
& closed_subset(X3,X0) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_pre_topc) ).
fof(f460,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f461,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( complements_of_subsets(X0,X1) = empty_set
& X1 != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f462,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f463,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_dom(X0),relation_rng(X1))
=> relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
fof(f464,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(f465,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).
fof(f466,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( X1 != empty_set
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f467,axiom,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f468,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_isomorphism(X0,X1,X2)
=> relation_isomorphism(X1,X0,function_inverse(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_wellord1) ).
fof(f469,axiom,
! [X0] : set_difference(empty_set,X0) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(f470,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f471,axiom,
! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_wellord2) ).
fof(f472,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f473,axiom,
! [X0] :
( X0 != empty_set
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f474,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( ( topstr_closure(X0,X1) = X1
& topological_space(X0) )
=> closed_subset(X1,X0) )
& ( closed_subset(X1,X0)
=> topstr_closure(X0,X1) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_pre_topc) ).
fof(f475,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_isomorphism(X0,X1,X2)
=> ( ( well_founded_relation(X0)
=> well_founded_relation(X1) )
& ( antisymmetric(X0)
=> antisymmetric(X1) )
& ( connected(X0)
=> connected(X1) )
& ( transitive(X0)
=> transitive(X1) )
& ( reflexive(X0)
=> reflexive(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_wellord1) ).
fof(f476,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( ( ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) )
=> ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) )
=> ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f477,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f478,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_isomorphism(X0,X1,X2)
& well_ordering(X0) )
=> well_ordering(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_wellord1) ).
fof(f479,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f480,axiom,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f481,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_rng(X1))
& one_to_one(X1) )
=> ( X0 = apply(relation_composition(function_inverse(X1),X1),X0)
& X0 = apply(X1,apply(function_inverse(X1),X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f482,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f483,axiom,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
fof(f484,axiom,
! [X0] : antisymmetric(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord2) ).
fof(f485,axiom,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f486,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f487,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
fof(f488,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f489,axiom,
! [X0] :
( relation(X0)
=> ( ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
=> X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
fof(f490,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
fof(f491,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f492,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f493,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f494,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f495,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( in(X2,X0)
=> ( in(apply(X3,X2),relation_rng(X3))
| X1 = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
fof(f496,axiom,
! [X0] :
( ordinal(X0)
=> well_founded_relation(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_wellord2) ).
fof(f497,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f498,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
fof(f499,axiom,
! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f500,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f501,axiom,
! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
fof(f502,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f503,axiom,
! [X0,X1] :
( pair_second(ordered_pair(X0,X1)) = X1
& pair_first(ordered_pair(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mcart_1) ).
fof(f504,axiom,
! [X0,X1] :
~ ( ! [X2] :
~ ( ! [X3] :
~ ( in(X3,X2)
& in(X3,X1) )
& in(X2,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
fof(f505,axiom,
! [X0] :
( ordinal(X0)
=> well_ordering(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_wellord2) ).
fof(f506,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f507,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f508,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f509,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
fof(f510,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f511,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f512,axiom,
! [X0] :
( relation(X0)
=> ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
fof(f513,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f514,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f515,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f516,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f517,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_relat_1) ).
fof(f518,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
fof(f519,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f520,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2_as_subset(X3,X0,X1)
& quasi_total(X3,X0,X1)
& function(X3) )
=> ( subset(X1,X2)
=> ( ( relation_of2_as_subset(X3,X0,X2)
& quasi_total(X3,X0,X2)
& function(X3) )
| ( X0 != empty_set
& X1 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
fof(f521,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
~ ( ! [X3] :
~ ( ! [X4] :
( subset(X4,X2)
=> in(X4,X3) )
& in(X3,X1) )
& in(X2,X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
fof(f522,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f523,plain,
! [X0,X1] :
( ( relation(X1)
& ~ empty(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X7] :
( ! [X8] :
( in(X8,X7)
=> in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( in(X6,X5)
=> in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0) )
=> X3 = X4 )
=> ? [X9] :
( ! [X10,X11] :
( in(ordered_pair(X10,X11),X9)
<=> ( ? [X12] :
( ! [X13] :
( in(X13,X12)
=> in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& in(X10,X0) ) )
& function(X9)
& relation(X9) ) ) ),
inference(rectify,[],[f311]) ).
fof(f524,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0) )
=> X2 = X3 )
=> ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) ) ),
inference(rectify,[],[f312]) ).
fof(f525,plain,
! [X0] :
( ? [X1] :
( in(X1,X0)
& ordinal(X1) )
=> ? [X2] :
( ! [X3] :
( ordinal(X3)
=> ( in(X3,X0)
=> ordinal_subset(X2,X3) ) )
& in(X2,X0)
& ordinal(X2) ) ),
inference(rectify,[],[f313]) ).
fof(f526,plain,
( ( ! [X10] :
( ordinal(X10)
=> ( ( ! [X11] :
( ordinal(X11)
=> ( in(X11,X10)
=> ( in(X11,omega)
=> ! [X12] :
( element(X12,powerset(powerset(X11)))
=> ~ ( ! [X13] :
~ ( ! [X14] :
( ( subset(X13,X14)
& in(X14,X12) )
=> X13 = X14 )
& in(X13,X12) )
& empty_set != X12 ) ) ) ) )
& being_limit_ordinal(X10) )
=> ( ( in(X10,omega)
=> ! [X15] :
( element(X15,powerset(powerset(X10)))
=> ~ ( ! [X16] :
~ ( ! [X17] :
( ( subset(X16,X17)
& in(X17,X15) )
=> X16 = X17 )
& in(X16,X15) )
& empty_set != X15 ) ) )
| empty_set = X10 ) ) )
& ! [X3] :
( ordinal(X3)
=> ( ( in(X3,omega)
=> ! [X4] :
( element(X4,powerset(powerset(X3)))
=> ~ ( ! [X5] :
~ ( ! [X6] :
( ( subset(X5,X6)
& in(X6,X4) )
=> X6 = X5 )
& in(X5,X4) )
& X4 != empty_set ) ) )
=> ( in(succ(X3),omega)
=> ! [X7] :
( element(X7,powerset(powerset(succ(X3))))
=> ~ ( ! [X8] :
~ ( ! [X9] :
( ( subset(X8,X9)
& in(X9,X7) )
=> X9 = X8 )
& in(X8,X7) )
& X7 != empty_set ) ) ) ) )
& ( in(empty_set,omega)
=> ! [X0] :
( element(X0,powerset(powerset(empty_set)))
=> ~ ( ! [X1] :
~ ( ! [X2] :
( ( subset(X1,X2)
& in(X2,X0) )
=> X2 = X1 )
& in(X1,X0) )
& X0 != empty_set ) ) ) )
=> ! [X18] :
( ordinal(X18)
=> ( in(X18,omega)
=> ! [X19] :
( element(X19,powerset(powerset(X18)))
=> ~ ( ! [X20] :
~ ( ! [X21] :
( ( subset(X20,X21)
& in(X21,X19) )
=> X20 = X21 )
& in(X20,X19) )
& empty_set != X19 ) ) ) ) ),
inference(rectify,[],[f314]) ).
fof(f527,plain,
! [X0,X1] :
( ( relation(X1)
& ~ empty(X0) )
=> ( ( ! [X9] :
~ ( ! [X10] :
~ ? [X11] :
( ! [X12] :
( in(X12,X11)
=> in(ordered_pair(X10,X12),X1) )
& in(X10,X11)
& X9 = X11 )
& in(X9,X0) )
& ! [X2,X3,X4] :
( ( ? [X7] :
( ! [X8] :
( in(X8,X7)
=> in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& ? [X5] :
( ! [X6] :
( in(X6,X5)
=> in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0) )
=> X3 = X4 ) )
=> ? [X13] :
( ! [X14] :
( in(X14,X0)
=> ? [X15] :
( ! [X16] :
( in(X16,X15)
=> in(ordered_pair(apply(X13,X14),X16),X1) )
& in(apply(X13,X14),X15)
& X14 = X15 ) )
& relation_dom(X13) = X0
& function(X13)
& relation(X13) ) ) ),
inference(rectify,[],[f338]) ).
fof(f528,plain,
! [X0] :
( ( ! [X4] :
~ ( ! [X5] : singleton(X4) != X5
& in(X4,X0) )
& ! [X1,X2,X3] :
( ( X3 = singleton(X1)
& X2 = singleton(X1)
& in(X1,X0) )
=> X2 = X3 ) )
=> ? [X6] :
( ! [X7] :
( in(X7,X0)
=> singleton(X7) = apply(X6,X7) )
& relation_dom(X6) = X0
& function(X6)
& relation(X6) ) ),
inference(rectify,[],[f339]) ).
fof(f529,plain,
( ! [X0] :
( ordinal(X0)
=> ( ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> ( in(X1,omega)
=> ! [X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( ! [X3] :
~ ( ! [X4] :
( ( subset(X3,X4)
& in(X4,X2) )
=> X4 = X3 )
& in(X3,X2) )
& X2 != empty_set ) ) ) ) )
=> ( in(X0,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X0)))
=> ~ ( ! [X6] :
~ ( ! [X7] :
( ( subset(X6,X7)
& in(X7,X5) )
=> X7 = X6 )
& in(X6,X5) )
& X5 != empty_set ) ) ) ) )
=> ! [X8] :
( ordinal(X8)
=> ( in(X8,omega)
=> ! [X9] :
( element(X9,powerset(powerset(X8)))
=> ~ ( ! [X10] :
~ ( ! [X11] :
( ( subset(X10,X11)
& in(X11,X9) )
=> X10 = X11 )
& in(X10,X9) )
& empty_set != X9 ) ) ) ) ),
inference(rectify,[],[f340]) ).
fof(f530,plain,
! [X0] :
? [X1] :
( ! [X5] :
~ ( ~ in(X5,X1)
& ~ are_equipotent(X5,X1)
& subset(X5,X1) )
& ! [X4] :
( in(X4,X1)
=> in(powerset(X4),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
inference(rectify,[],[f359]) ).
fof(f531,plain,
! [X0] :
( ~ empty(X0)
=> ~ ( ! [X2] :
( ( function(X2)
& relation(X2) )
=> ~ ( ! [X3] :
( in(X3,X0)
=> in(apply(X2,X3),X3) )
& relation_dom(X2) = X0 ) )
& ! [X1] :
~ ( X1 = empty_set
& in(X1,X0) ) ) ),
inference(rectify,[],[f416]) ).
fof(f532,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] :
( in(X3,X1)
& in(X3,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f447]) ).
fof(f533,plain,
! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X2] :
( succ(X2) = X0
& ordinal(X2) ) )
& ~ ( ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) )
& ~ being_limit_ordinal(X0) ) ) ),
inference(rectify,[],[f451]) ).
fof(f534,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] : in(X3,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f472]) ).
fof(f535,plain,
! [X0,X1] :
( ( relation(X1)
& ~ empty(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X7] :
( ! [X8] :
( in(X8,X7)
=> in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( in(X6,X5)
=> in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0) )
=> X3 = X4 )
=> ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12] :
( ! [X13] :
( in(X13,X12)
=> in(ordered_pair(X10,X13),X1) )
& in(X10,X12)
& X11 = X12 )
& in(X11,X0)
& in(X11,X0) ) ) ) ),
inference(rectify,[],[f316]) ).
fof(f536,plain,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 )
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3 )
=> X3 = X4 )
=> ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) ) ),
inference(rectify,[],[f319]) ).
fof(f537,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0) )
=> X2 = X3 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( singleton(X6) = X5
& in(X6,X0)
& in(X6,X0) ) ) ),
inference(rectify,[],[f318]) ).
fof(f538,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f244]) ).
fof(f540,plain,
! [X0] : equipotent(X0,X0),
inference(rectify,[],[f310]) ).
fof(f541,plain,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ( ! [X3,X4,X5] :
( ( ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& X5 = ordered_pair(X8,X9) )
& X3 = X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& X4 = ordered_pair(X6,X7) )
& X3 = X4 )
=> X4 = X5 )
=> ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) ) ) ),
inference(rectify,[],[f324]) ).
fof(f542,plain,
! [X0,X1] :
( ( relation(X1)
& ~ empty(X0) )
=> ! [X2] :
( ! [X3,X4,X5] :
( ( ? [X10,X11] :
( ? [X12] :
( ! [X13] :
( in(X13,X12)
=> in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& ordered_pair(X10,X11) = X5 )
& X3 = X5
& ? [X6,X7] :
( ? [X8] :
( ! [X9] :
( in(X9,X8)
=> in(ordered_pair(X7,X9),X1) )
& in(X7,X8)
& X6 = X8 )
& in(X6,X0)
& ordered_pair(X6,X7) = X4 )
& X3 = X4 )
=> X4 = X5 )
=> ? [X14] :
! [X15] :
( in(X15,X14)
<=> ? [X16] :
( ? [X17,X18] :
( ? [X19] :
( ! [X20] :
( in(X20,X19)
=> in(ordered_pair(X18,X20),X1) )
& in(X18,X19)
& X17 = X19 )
& in(X17,X0)
& ordered_pair(X17,X18) = X15 )
& X15 = X16
& in(X16,cartesian_product2(X0,X2)) ) ) ) ),
inference(rectify,[],[f317]) ).
fof(f543,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2 )
=> X2 = X3 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( ordinal(X5)
& X5 = X6
& in(X6,X0) ) ) ),
inference(rectify,[],[f325]) ).
fof(f544,plain,
! [X0] :
( ordinal(X0)
=> ( ! [X1,X2,X3] :
( ( ? [X8] :
( ( in(X8,omega)
=> ! [X9] :
( element(X9,powerset(powerset(X8)))
=> ~ ( ! [X10] :
~ ( ! [X11] :
( ( subset(X10,X11)
& in(X11,X9) )
=> X11 = X10 )
& in(X10,X9) )
& X9 != empty_set ) ) )
& X3 = X8
& ordinal(X8) )
& X1 = X3
& ? [X4] :
( ( in(X4,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X4)))
=> ~ ( ! [X6] :
~ ( ! [X7] :
( ( subset(X6,X7)
& in(X7,X5) )
=> X7 = X6 )
& in(X6,X5) )
& X5 != empty_set ) ) )
& X2 = X4
& ordinal(X4) )
& X1 = X2 )
=> X2 = X3 )
=> ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( ? [X15] :
( ( in(X15,omega)
=> ! [X16] :
( element(X16,powerset(powerset(X15)))
=> ~ ( ! [X17] :
~ ( ! [X18] :
( ( subset(X17,X18)
& in(X18,X16) )
=> X17 = X18 )
& in(X17,X16) )
& empty_set != X16 ) ) )
& X13 = X15
& ordinal(X15) )
& X13 = X14
& in(X14,succ(X0)) ) ) ) ),
inference(rectify,[],[f320]) ).
fof(f545,plain,
! [X0,X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( in(X6,X0)
& X4 = X6
& ordinal(X6) )
& X2 = X4
& ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( in(X10,X0)
& X8 = X10
& ordinal(X10) )
& X8 = X9
& in(X9,succ(X1)) ) ) ) ),
inference(rectify,[],[f327]) ).
fof(f546,plain,
! [X0,X1] :
( ( element(X1,powerset(powerset(succ(X0))))
& ordinal(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( X4 = set_difference(X6,singleton(X0))
& in(X6,X1) )
& X2 = X4
& ? [X5] :
( X3 = set_difference(X5,singleton(X0))
& in(X5,X1) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) ) ) ),
inference(rectify,[],[f323]) ).
fof(f547,plain,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3 )
=> X3 = X4 )
=> ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) ) ) ),
inference(rectify,[],[f322]) ).
fof(f548,plain,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( subset(X1,X4)
& closed_subset(X6,X0)
& X6 = X4
& element(X6,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X5 = X3
& element(X5,powerset(the_carrier(X0))) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) ) ) ),
inference(rectify,[],[f321]) ).
fof(f549,plain,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& element(X1,powerset(powerset(X0))) )
=> ( ! [X3,X4,X5] :
( ( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4 )
=> X4 = X5 )
=> ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) ) ) ),
inference(rectify,[],[f326]) ).
fof(f551,plain,
! [X0] :
? [X1] :
( ! [X7] :
~ ( ~ in(X7,X1)
& ~ are_equipotent(X7,X1)
& subset(X7,X1) )
& ! [X4] :
~ ( ! [X5] :
~ ( ! [X6] :
( subset(X6,X4)
=> in(X6,X5) )
& in(X5,X1) )
& in(X4,X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
inference(rectify,[],[f521]) ).
fof(f552,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f250]) ).
fof(f553,plain,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X4 ) ) ),
inference(rectify,[],[f56]) ).
fof(f554,plain,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X5 ) ) ),
inference(rectify,[],[f69]) ).
fof(f555,plain,
! [X0] :
( top_str(X0)
=> ( topological_space(X0)
<=> ( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( in(X3,the_topology(X0))
& in(X2,the_topology(X0)) )
=> in(subset_intersection2(the_carrier(X0),X2,X3),the_topology(X0)) ) ) )
& ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( subset(X1,the_topology(X0))
=> in(union_of_subsets(the_carrier(X0),X1),the_topology(X0)) ) )
& in(the_carrier(X0),the_topology(X0)) ) ) ),
inference(rectify,[],[f58]) ).
fof(f556,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f114]) ).
fof(f565,plain,
! [X0] :
( ~ relation(X0)
| ( reflexive(X0)
<=> ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) ) ),
inference(ennf_transformation,[],[f251]) ).
fof(f567,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f254]) ).
fof(f568,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f255]) ).
fof(f569,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ),
inference(ennf_transformation,[],[f256]) ).
fof(f570,plain,
! [X0] :
( ~ relation(X0)
| ( transitive(X0)
<=> ! [X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X1,X3),X0) ) ) ),
inference(ennf_transformation,[],[f257]) ).
fof(f571,plain,
! [X0] :
( ~ relation(X0)
| ( transitive(X0)
<=> ! [X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X1,X3),X0) ) ) ),
inference(flattening,[],[f570]) ).
fof(f572,plain,
! [X0,X1] :
( ~ relation(X1)
| ? [X2] :
( relation(X2)
& well_orders(X2,X0) )
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1) ),
inference(ennf_transformation,[],[f259]) ).
fof(f573,plain,
! [X0,X1] :
( ~ relation(X1)
| ? [X2] :
( relation(X2)
& well_orders(X2,X0) )
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1) ),
inference(flattening,[],[f572]) ).
fof(f575,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f262]) ).
fof(f576,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) ) ),
inference(flattening,[],[f575]) ).
fof(f577,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(ennf_transformation,[],[f263]) ).
fof(f578,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(flattening,[],[f577]) ).
fof(f579,plain,
! [X0] :
( ~ relation(X0)
| ( connected(X0)
<=> ! [X1,X2] :
( in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),X0)
| X1 = X2
| ~ in(X2,relation_field(X0))
| ~ in(X1,relation_field(X0)) ) ) ),
inference(ennf_transformation,[],[f264]) ).
fof(f581,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f268]) ).
fof(f584,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ? [X2,X3,X4] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 )
| ? [X9] :
( ! [X10,X11] :
( in(ordered_pair(X10,X11),X9)
<=> ( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& in(X10,X0) ) )
& function(X9)
& relation(X9) ) ),
inference(ennf_transformation,[],[f523]) ).
fof(f585,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ? [X2,X3,X4] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 )
| ? [X9] :
( ! [X10,X11] :
( in(ordered_pair(X10,X11),X9)
<=> ( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& in(X10,X0) ) )
& function(X9)
& relation(X9) ) ),
inference(flattening,[],[f584]) ).
fof(f586,plain,
! [X0] :
( ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 )
| ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) ) ),
inference(ennf_transformation,[],[f524]) ).
fof(f587,plain,
! [X0] :
( ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 )
| ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) ) ),
inference(flattening,[],[f586]) ).
fof(f588,plain,
! [X0] :
( ! [X1] :
( ~ in(X1,X0)
| ~ ordinal(X1) )
| ? [X2] :
( ! [X3] :
( ~ ordinal(X3)
| ~ in(X3,X0)
| ordinal_subset(X2,X3) )
& in(X2,X0)
& ordinal(X2) ) ),
inference(ennf_transformation,[],[f525]) ).
fof(f589,plain,
! [X0] :
( ! [X1] :
( ~ in(X1,X0)
| ~ ordinal(X1) )
| ? [X2] :
( ! [X3] :
( ~ ordinal(X3)
| ~ in(X3,X0)
| ordinal_subset(X2,X3) )
& in(X2,X0)
& ordinal(X2) ) ),
inference(flattening,[],[f588]) ).
fof(f590,plain,
( ? [X10] :
( ordinal(X10)
& ! [X11] :
( ~ ordinal(X11)
| ~ in(X11,X10)
| ~ in(X11,omega)
| ! [X12] :
( ~ element(X12,powerset(powerset(X11)))
| ? [X13] :
( ! [X14] :
( ~ subset(X13,X14)
| ~ in(X14,X12)
| X13 = X14 )
& in(X13,X12) )
| empty_set = X12 ) )
& being_limit_ordinal(X10)
& in(X10,omega)
& ? [X15] :
( element(X15,powerset(powerset(X10)))
& ! [X16] :
( ? [X17] :
( subset(X16,X17)
& in(X17,X15)
& X16 != X17 )
| ~ in(X16,X15) )
& empty_set != X15 )
& empty_set != X10 )
| ? [X3] :
( ordinal(X3)
& ( ~ in(X3,omega)
| ! [X4] :
( ~ element(X4,powerset(powerset(X3)))
| ? [X5] :
( ! [X6] :
( ~ subset(X5,X6)
| ~ in(X6,X4)
| X6 = X5 )
& in(X5,X4) )
| empty_set = X4 ) )
& in(succ(X3),omega)
& ? [X7] :
( element(X7,powerset(powerset(succ(X3))))
& ! [X8] :
( ? [X9] :
( subset(X8,X9)
& in(X9,X7)
& X8 != X9 )
| ~ in(X8,X7) )
& X7 != empty_set ) )
| ( in(empty_set,omega)
& ? [X0] :
( element(X0,powerset(powerset(empty_set)))
& ! [X1] :
( ? [X2] :
( subset(X1,X2)
& in(X2,X0)
& X1 != X2 )
| ~ in(X1,X0) )
& X0 != empty_set ) )
| ! [X18] :
( ~ ordinal(X18)
| ~ in(X18,omega)
| ! [X19] :
( ~ element(X19,powerset(powerset(X18)))
| ? [X20] :
( ! [X21] :
( ~ subset(X20,X21)
| ~ in(X21,X19)
| X20 = X21 )
& in(X20,X19) )
| empty_set = X19 ) ) ),
inference(ennf_transformation,[],[f526]) ).
fof(f591,plain,
( ? [X10] :
( ordinal(X10)
& ! [X11] :
( ~ ordinal(X11)
| ~ in(X11,X10)
| ~ in(X11,omega)
| ! [X12] :
( ~ element(X12,powerset(powerset(X11)))
| ? [X13] :
( ! [X14] :
( ~ subset(X13,X14)
| ~ in(X14,X12)
| X13 = X14 )
& in(X13,X12) )
| empty_set = X12 ) )
& being_limit_ordinal(X10)
& in(X10,omega)
& ? [X15] :
( element(X15,powerset(powerset(X10)))
& ! [X16] :
( ? [X17] :
( subset(X16,X17)
& in(X17,X15)
& X16 != X17 )
| ~ in(X16,X15) )
& empty_set != X15 )
& empty_set != X10 )
| ? [X3] :
( ordinal(X3)
& ( ~ in(X3,omega)
| ! [X4] :
( ~ element(X4,powerset(powerset(X3)))
| ? [X5] :
( ! [X6] :
( ~ subset(X5,X6)
| ~ in(X6,X4)
| X6 = X5 )
& in(X5,X4) )
| empty_set = X4 ) )
& in(succ(X3),omega)
& ? [X7] :
( element(X7,powerset(powerset(succ(X3))))
& ! [X8] :
( ? [X9] :
( subset(X8,X9)
& in(X9,X7)
& X8 != X9 )
| ~ in(X8,X7) )
& X7 != empty_set ) )
| ( in(empty_set,omega)
& ? [X0] :
( element(X0,powerset(powerset(empty_set)))
& ! [X1] :
( ? [X2] :
( subset(X1,X2)
& in(X2,X0)
& X1 != X2 )
| ~ in(X1,X0) )
& X0 != empty_set ) )
| ! [X18] :
( ~ ordinal(X18)
| ~ in(X18,omega)
| ! [X19] :
( ~ element(X19,powerset(powerset(X18)))
| ? [X20] :
( ! [X21] :
( ~ subset(X20,X21)
| ~ in(X21,X19)
| X20 = X21 )
& in(X20,X19) )
| empty_set = X19 ) ) ),
inference(flattening,[],[f590]) ).
fof(f592,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& relation(X3) ) ),
inference(ennf_transformation,[],[f315]) ).
fof(f593,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& relation(X3) ) ),
inference(flattening,[],[f592]) ).
fof(f594,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X6,X8),X1) )
& in(X6,X7)
& X5 = X7 )
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X2)) ) ) ),
inference(ennf_transformation,[],[f328]) ).
fof(f595,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X6,X8),X1) )
& in(X6,X7)
& X5 = X7 )
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X2)) ) ) ),
inference(flattening,[],[f594]) ).
fof(f596,plain,
! [X0] :
( ~ ordinal(X0)
| ? [X1] :
! [X2] :
( in(X2,X1)
<=> ( ? [X3] :
( ( ~ in(X3,omega)
| ! [X4] :
( ~ element(X4,powerset(powerset(X3)))
| ? [X5] :
( ! [X6] :
( ~ subset(X5,X6)
| ~ in(X6,X4)
| X6 = X5 )
& in(X5,X4) )
| empty_set = X4 ) )
& X2 = X3
& ordinal(X3) )
& in(X2,succ(X0)) ) ) ),
inference(ennf_transformation,[],[f330]) ).
fof(f597,plain,
! [X0] :
( ~ ordinal(X0)
| ? [X1] :
! [X2] :
( in(X2,X1)
<=> ( ? [X3] :
( ( ~ in(X3,omega)
| ! [X4] :
( ~ element(X4,powerset(powerset(X3)))
| ? [X5] :
( ! [X6] :
( ~ subset(X5,X6)
| ~ in(X6,X4)
| X6 = X5 )
& in(X5,X4) )
| empty_set = X4 ) )
& X2 = X3
& ordinal(X3) )
& in(X2,succ(X0)) ) ) ),
inference(flattening,[],[f596]) ).
fof(f598,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) ) ),
inference(ennf_transformation,[],[f331]) ).
fof(f599,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) ) ),
inference(flattening,[],[f598]) ).
fof(f600,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) ) ),
inference(ennf_transformation,[],[f332]) ).
fof(f601,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) ) ),
inference(flattening,[],[f600]) ).
fof(f602,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( X3 = set_difference(X4,singleton(X0))
& in(X4,X1) )
& in(X3,powerset(X0)) ) ) ),
inference(ennf_transformation,[],[f333]) ).
fof(f603,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( X3 = set_difference(X4,singleton(X0))
& in(X4,X1) )
& in(X3,powerset(X0)) ) ) ),
inference(flattening,[],[f602]) ).
fof(f604,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& X4 = ordered_pair(X5,X6) )
& in(X4,cartesian_product2(X0,X0)) ) ) ),
inference(ennf_transformation,[],[f334]) ).
fof(f605,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& X4 = ordered_pair(X5,X6) )
& in(X4,cartesian_product2(X0,X0)) ) ) ),
inference(flattening,[],[f604]) ).
fof(f606,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) ) ),
inference(ennf_transformation,[],[f336]) ).
fof(f607,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) ) ),
inference(flattening,[],[f606]) ).
fof(f608,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( in(X4,X0)
& X3 = X4
& ordinal(X4) )
& in(X3,succ(X1)) ) ) ),
inference(ennf_transformation,[],[f337]) ).
fof(f609,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ? [X9] :
( ! [X10,X11] :
( ? [X12] :
( in(X12,X11)
& ~ in(ordered_pair(X10,X12),X1) )
| ~ in(X10,X11)
| X9 != X11 )
& in(X9,X0) )
| ? [X2,X3,X4] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 )
| ? [X13] :
( ! [X14] :
( ~ in(X14,X0)
| ? [X15] :
( ! [X16] :
( ~ in(X16,X15)
| in(ordered_pair(apply(X13,X14),X16),X1) )
& in(apply(X13,X14),X15)
& X14 = X15 ) )
& relation_dom(X13) = X0
& function(X13)
& relation(X13) ) ),
inference(ennf_transformation,[],[f527]) ).
fof(f610,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ? [X9] :
( ! [X10,X11] :
( ? [X12] :
( in(X12,X11)
& ~ in(ordered_pair(X10,X12),X1) )
| ~ in(X10,X11)
| X9 != X11 )
& in(X9,X0) )
| ? [X2,X3,X4] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 )
| ? [X13] :
( ! [X14] :
( ~ in(X14,X0)
| ? [X15] :
( ! [X16] :
( ~ in(X16,X15)
| in(ordered_pair(apply(X13,X14),X16),X1) )
& in(apply(X13,X14),X15)
& X14 = X15 ) )
& relation_dom(X13) = X0
& function(X13)
& relation(X13) ) ),
inference(flattening,[],[f609]) ).
fof(f611,plain,
! [X0] :
( ? [X4] :
( ! [X5] : singleton(X4) != X5
& in(X4,X0) )
| ? [X1,X2,X3] :
( X3 = singleton(X1)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 )
| ? [X6] :
( ! [X7] :
( ~ in(X7,X0)
| singleton(X7) = apply(X6,X7) )
& relation_dom(X6) = X0
& function(X6)
& relation(X6) ) ),
inference(ennf_transformation,[],[f528]) ).
fof(f612,plain,
! [X0] :
( ? [X4] :
( ! [X5] : singleton(X4) != X5
& in(X4,X0) )
| ? [X1,X2,X3] :
( X3 = singleton(X1)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 )
| ? [X6] :
( ! [X7] :
( ~ in(X7,X0)
| singleton(X7) = apply(X6,X7) )
& relation_dom(X6) = X0
& function(X6)
& relation(X6) ) ),
inference(flattening,[],[f611]) ).
fof(f613,plain,
( ? [X0] :
( ordinal(X0)
& ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| ~ in(X1,omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(X1)))
| ? [X3] :
( ! [X4] :
( ~ subset(X3,X4)
| ~ in(X4,X2)
| X4 = X3 )
& in(X3,X2) )
| empty_set = X2 ) )
& in(X0,omega)
& ? [X5] :
( element(X5,powerset(powerset(X0)))
& ! [X6] :
( ? [X7] :
( subset(X6,X7)
& in(X7,X5)
& X6 != X7 )
| ~ in(X6,X5) )
& X5 != empty_set ) )
| ! [X8] :
( ~ ordinal(X8)
| ~ in(X8,omega)
| ! [X9] :
( ~ element(X9,powerset(powerset(X8)))
| ? [X10] :
( ! [X11] :
( ~ subset(X10,X11)
| ~ in(X11,X9)
| X10 = X11 )
& in(X10,X9) )
| empty_set = X9 ) ) ),
inference(ennf_transformation,[],[f529]) ).
fof(f614,plain,
( ? [X0] :
( ordinal(X0)
& ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| ~ in(X1,omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(X1)))
| ? [X3] :
( ! [X4] :
( ~ subset(X3,X4)
| ~ in(X4,X2)
| X4 = X3 )
& in(X3,X2) )
| empty_set = X2 ) )
& in(X0,omega)
& ? [X5] :
( element(X5,powerset(powerset(X0)))
& ! [X6] :
( ? [X7] :
( subset(X6,X7)
& in(X7,X5)
& X6 != X7 )
| ~ in(X6,X5) )
& X5 != empty_set ) )
| ! [X8] :
( ~ ordinal(X8)
| ~ in(X8,omega)
| ! [X9] :
( ~ element(X9,powerset(powerset(X8)))
| ? [X10] :
( ! [X11] :
( ~ subset(X10,X11)
| ~ in(X11,X9)
| X10 = X11 )
& in(X10,X9) )
| empty_set = X9 ) ) ),
inference(flattening,[],[f613]) ).
fof(f615,plain,
! [X0] :
? [X1] :
( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = singleton(X2) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f341]) ).
fof(f616,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
( ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( in(X3,X2)
<=> ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(ennf_transformation,[],[f342]) ).
fof(f617,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
( ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( in(X3,X2)
<=> ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(flattening,[],[f616]) ).
fof(f618,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
( ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( in(X3,X2)
<=> in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(ennf_transformation,[],[f343]) ).
fof(f619,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
( ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( in(X3,X2)
<=> in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(flattening,[],[f618]) ).
fof(f620,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f348]) ).
fof(f621,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f349]) ).
fof(f622,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
inference(ennf_transformation,[],[f350]) ).
fof(f623,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng_restriction(X0,X1),X1) ),
inference(ennf_transformation,[],[f351]) ).
fof(f624,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
inference(ennf_transformation,[],[f352]) ).
fof(f625,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
inference(ennf_transformation,[],[f353]) ).
fof(f626,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
inference(ennf_transformation,[],[f354]) ).
fof(f627,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(ennf_transformation,[],[f355]) ).
fof(f628,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(flattening,[],[f627]) ).
fof(f630,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
inference(ennf_transformation,[],[f357]) ).
fof(f631,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f358]) ).
fof(f632,plain,
! [X0] :
? [X1] :
( ! [X5] :
( in(X5,X1)
| are_equipotent(X5,X1)
| ~ subset(X5,X1) )
& ! [X4] :
( ~ in(X4,X1)
| in(powerset(X4),X1) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,X1)
| in(X3,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f530]) ).
fof(f633,plain,
! [X0] :
? [X1] :
( ! [X5] :
( in(X5,X1)
| are_equipotent(X5,X1)
| ~ subset(X5,X1) )
& ! [X4] :
( ~ in(X4,X1)
| in(powerset(X4),X1) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,X1)
| in(X3,X1) )
& in(X0,X1) ),
inference(flattening,[],[f632]) ).
fof(f634,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(ennf_transformation,[],[f360]) ).
fof(f635,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(flattening,[],[f634]) ).
fof(f636,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
inference(ennf_transformation,[],[f361]) ).
fof(f637,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) ) ),
inference(ennf_transformation,[],[f362]) ).
fof(f638,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(ennf_transformation,[],[f363]) ).
fof(f639,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(ennf_transformation,[],[f364]) ).
fof(f640,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(flattening,[],[f639]) ).
fof(f641,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(ennf_transformation,[],[f365]) ).
fof(f642,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_dom(X1))
| subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ),
inference(ennf_transformation,[],[f366]) ).
fof(f643,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_dom(X1))
| subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ),
inference(flattening,[],[f642]) ).
fof(f644,plain,
! [X0] :
( ~ relation(X0)
| relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
inference(ennf_transformation,[],[f367]) ).
fof(f645,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_rng(X1))
| relation_image(X1,relation_inverse_image(X1,X0)) = X0 ),
inference(ennf_transformation,[],[f368]) ).
fof(f646,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_rng(X1))
| relation_image(X1,relation_inverse_image(X1,X0)) = X0 ),
inference(flattening,[],[f645]) ).
fof(f647,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(relation_rng(X3),X1)
| relation_of2_as_subset(X3,X2,X1) ),
inference(ennf_transformation,[],[f369]) ).
fof(f648,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(relation_rng(X3),X1)
| relation_of2_as_subset(X3,X2,X1) ),
inference(flattening,[],[f647]) ).
fof(f650,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 ) ),
inference(ennf_transformation,[],[f371]) ).
fof(f651,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f372]) ).
fof(f652,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) ) ),
inference(ennf_transformation,[],[f373]) ).
fof(f653,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(ennf_transformation,[],[f374]) ).
fof(f654,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(X3,X2,X1) ),
inference(ennf_transformation,[],[f375]) ).
fof(f655,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(X3,X2,X1) ),
inference(flattening,[],[f654]) ).
fof(f656,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f376]) ).
fof(f657,plain,
! [X0,X1] :
( ~ relation(X1)
| empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0 ),
inference(ennf_transformation,[],[f377]) ).
fof(f658,plain,
! [X0,X1] :
( ~ relation(X1)
| empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0 ),
inference(flattening,[],[f657]) ).
fof(f659,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ subset(X0,X1)
| subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(ennf_transformation,[],[f378]) ).
fof(f660,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ subset(X0,X1)
| subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(flattening,[],[f659]) ).
fof(f663,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
inference(ennf_transformation,[],[f380]) ).
fof(f664,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
inference(ennf_transformation,[],[f381]) ).
fof(f665,plain,
! [X0] :
( ~ finite(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(X0)))
| ? [X2] :
( ! [X3] :
( ~ subset(X2,X3)
| ~ in(X3,X1)
| X3 = X2 )
& in(X2,X1) )
| empty_set = X1 ) ),
inference(ennf_transformation,[],[f383]) ).
fof(f666,plain,
! [X0] :
( ~ finite(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(X0)))
| ? [X2] :
( ! [X3] :
( ~ subset(X2,X3)
| ~ in(X3,X1)
| X3 = X2 )
& in(X2,X1) )
| empty_set = X1 ) ),
inference(flattening,[],[f665]) ).
fof(f667,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f384]) ).
fof(f668,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ( in(X0,X1)
& in(X0,relation_field(X2)) ) ),
inference(ennf_transformation,[],[f385]) ).
fof(f669,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ( in(X0,X1)
& in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f668]) ).
fof(f670,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f386]) ).
fof(f671,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(flattening,[],[f670]) ).
fof(f672,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f389]) ).
fof(f673,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f672]) ).
fof(f676,plain,
! [X0,X1] :
( ~ relation(X1)
| ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ) ),
inference(ennf_transformation,[],[f392]) ).
fof(f677,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
inference(ennf_transformation,[],[f393]) ).
fof(f678,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
inference(flattening,[],[f677]) ).
fof(f679,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ! [X4] :
( ~ function(X4)
| ~ relation(X4)
| ~ in(X2,X0)
| apply(relation_composition(X3,X4),X2) = apply(X4,apply(X3,X2))
| X1 = empty_set ) ),
inference(ennf_transformation,[],[f394]) ).
fof(f680,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ! [X4] :
( ~ function(X4)
| ~ relation(X4)
| ~ in(X2,X0)
| apply(relation_composition(X3,X4),X2) = apply(X4,apply(X3,X2))
| X1 = empty_set ) ),
inference(flattening,[],[f679]) ).
fof(f681,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f395]) ).
fof(f682,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ) ),
inference(flattening,[],[f681]) ).
fof(f683,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(ennf_transformation,[],[f396]) ).
fof(f684,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
inference(ennf_transformation,[],[f397]) ).
fof(f685,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ),
inference(ennf_transformation,[],[f398]) ).
fof(f686,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ),
inference(flattening,[],[f685]) ).
fof(f687,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 ) ),
inference(ennf_transformation,[],[f399]) ).
fof(f688,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X1,X0)
| ( ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
inference(ennf_transformation,[],[f400]) ).
fof(f689,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ reflexive(X1)
| reflexive(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f401]) ).
fof(f690,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ reflexive(X1)
| reflexive(relation_restriction(X1,X0)) ),
inference(flattening,[],[f689]) ).
fof(f691,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(ennf_transformation,[],[f402]) ).
fof(f692,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(flattening,[],[f691]) ).
fof(f693,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(ennf_transformation,[],[f404]) ).
fof(f694,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(flattening,[],[f693]) ).
fof(f695,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X2)
| ~ in(X3,X1) )
<=> relation_rng_as_subset(X0,X1,X2) = X1 ) ),
inference(ennf_transformation,[],[f405]) ).
fof(f696,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ connected(X1)
| connected(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f406]) ).
fof(f697,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ connected(X1)
| connected(relation_restriction(X1,X0)) ),
inference(flattening,[],[f696]) ).
fof(f698,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f407]) ).
fof(f699,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(flattening,[],[f698]) ).
fof(f700,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ transitive(X1)
| transitive(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f408]) ).
fof(f701,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ transitive(X1)
| transitive(relation_restriction(X1,X0)) ),
inference(flattening,[],[f700]) ).
fof(f702,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(X0,X1)
| ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) ) ) ),
inference(ennf_transformation,[],[f409]) ).
fof(f703,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(X0,X1)
| ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) ) ) ),
inference(flattening,[],[f702]) ).
fof(f704,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ antisymmetric(X1)
| antisymmetric(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f410]) ).
fof(f705,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ antisymmetric(X1)
| antisymmetric(relation_restriction(X1,X0)) ),
inference(flattening,[],[f704]) ).
fof(f706,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_orders(X1,X0)
| ( well_ordering(relation_restriction(X1,X0))
& relation_field(relation_restriction(X1,X0)) = X0 ) ),
inference(ennf_transformation,[],[f411]) ).
fof(f707,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_orders(X1,X0)
| ( well_ordering(relation_restriction(X1,X0))
& relation_field(relation_restriction(X1,X0)) = X0 ) ),
inference(flattening,[],[f706]) ).
fof(f708,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ finite(relation_dom(X0))
| finite(relation_rng(X0)) ),
inference(ennf_transformation,[],[f412]) ).
fof(f709,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ finite(relation_dom(X0))
| finite(relation_rng(X0)) ),
inference(flattening,[],[f708]) ).
fof(f710,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f415]) ).
fof(f711,plain,
! [X0] :
( empty(X0)
| ? [X2] :
( function(X2)
& relation(X2)
& ! [X3] :
( ~ in(X3,X0)
| in(apply(X2,X3),X3) )
& relation_dom(X2) = X0 )
| ? [X1] :
( X1 = empty_set
& in(X1,X0) ) ),
inference(ennf_transformation,[],[f531]) ).
fof(f712,plain,
! [X0] :
( empty(X0)
| ? [X2] :
( function(X2)
& relation(X2)
& ! [X3] :
( ~ in(X3,X0)
| in(apply(X2,X3),X3) )
& relation_dom(X2) = X0 )
| ? [X1] :
( X1 = empty_set
& in(X1,X0) ) ),
inference(flattening,[],[f711]) ).
fof(f713,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(ennf_transformation,[],[f417]) ).
fof(f714,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ( closed_subset(X1,X0)
<~> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f419]) ).
fof(f715,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(ennf_transformation,[],[f425]) ).
fof(f716,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f715]) ).
fof(f717,plain,
! [X0] :
( ? [X1] :
( in(X1,X0)
& ( ~ subset(X1,X0)
| ~ ordinal(X1) ) )
| ordinal(X0) ),
inference(ennf_transformation,[],[f426]) ).
fof(f718,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_founded_relation(X1)
| well_founded_relation(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f427]) ).
fof(f719,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_founded_relation(X1)
| well_founded_relation(relation_restriction(X1,X0)) ),
inference(flattening,[],[f718]) ).
fof(f720,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ? [X2] :
( ordinal(X2)
& ! [X3] :
( ~ ordinal(X3)
| ~ in(X3,X0)
| ordinal_subset(X2,X3) )
& in(X2,X0) )
| empty_set = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f428]) ).
fof(f721,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ? [X2] :
( ordinal(X2)
& ! [X3] :
( ~ ordinal(X3)
| ~ in(X3,X0)
| ordinal_subset(X2,X3) )
& in(X2,X0) )
| empty_set = X0
| ~ subset(X0,X1) ),
inference(flattening,[],[f720]) ).
fof(f722,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_ordering(X1)
| well_ordering(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f429]) ).
fof(f723,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_ordering(X1)
| well_ordering(relation_restriction(X1,X0)) ),
inference(flattening,[],[f722]) ).
fof(f724,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
inference(ennf_transformation,[],[f430]) ).
fof(f725,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(ennf_transformation,[],[f431]) ).
fof(f726,plain,
! [X0,X1,X2,X3] :
( ordered_pair(X2,X3) != ordered_pair(X0,X1)
| ( X1 = X3
& X0 = X2 ) ),
inference(ennf_transformation,[],[f432]) ).
fof(f727,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f433]) ).
fof(f728,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(flattening,[],[f727]) ).
fof(f729,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(ennf_transformation,[],[f434]) ).
fof(f730,plain,
! [X0] :
( ~ relation(X0)
| ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f436]) ).
fof(f731,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| relation_field(relation_restriction(X1,X0)) = X0 ),
inference(ennf_transformation,[],[f440]) ).
fof(f732,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| relation_field(relation_restriction(X1,X0)) = X0 ),
inference(flattening,[],[f731]) ).
fof(f733,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f444]) ).
fof(f734,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) ) )
& ( ? [X2] :
( in(X2,X1)
& in(X2,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f532]) ).
fof(f735,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(ennf_transformation,[],[f448]) ).
fof(f736,plain,
! [X0] :
( ~ ordinal(X0)
| ( being_limit_ordinal(X0)
<=> ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0) ) ) ),
inference(ennf_transformation,[],[f450]) ).
fof(f737,plain,
! [X0] :
( ~ ordinal(X0)
| ( being_limit_ordinal(X0)
<=> ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0) ) ) ),
inference(flattening,[],[f736]) ).
fof(f738,plain,
! [X0] :
( ~ ordinal(X0)
| ( ( ~ being_limit_ordinal(X0)
| ! [X2] :
( succ(X2) != X0
| ~ ordinal(X2) ) )
& ( ? [X1] :
( ordinal(X1)
& succ(X1) = X0 )
| being_limit_ordinal(X0) ) ) ),
inference(ennf_transformation,[],[f533]) ).
fof(f739,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,powerset(X0))
| ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
inference(ennf_transformation,[],[f452]) ).
fof(f740,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ? [X2] :
( element(X2,powerset(the_carrier(X0)))
& in(X2,X1)
& ~ closed_subset(X2,X0) )
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ) ),
inference(ennf_transformation,[],[f453]) ).
fof(f741,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ? [X2] :
( element(X2,powerset(the_carrier(X0)))
& in(X2,X1)
& ~ closed_subset(X2,X0) )
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ) ),
inference(flattening,[],[f740]) ).
fof(f742,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f454]) ).
fof(f743,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) ) ) ) ),
inference(ennf_transformation,[],[f455]) ).
fof(f744,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) ) ) ) ),
inference(flattening,[],[f743]) ).
fof(f745,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
inference(ennf_transformation,[],[f456]) ).
fof(f747,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| empty_set = X1
| ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(apply(X3,X4),X2)
& in(X4,X0) ) ) ),
inference(ennf_transformation,[],[f458]) ).
fof(f748,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| empty_set = X1
| ! [X4] :
( in(X4,relation_inverse_image(X3,X2))
<=> ( in(apply(X3,X4),X2)
& in(X4,X0) ) ) ),
inference(flattening,[],[f747]) ).
fof(f749,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( in(X3,X2)
<=> ( subset(X1,X3)
& closed_subset(X3,X0) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ) ),
inference(ennf_transformation,[],[f459]) ).
fof(f750,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( in(X3,X2)
<=> ( subset(X1,X3)
& closed_subset(X3,X0) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ) ),
inference(flattening,[],[f749]) ).
fof(f751,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ),
inference(ennf_transformation,[],[f460]) ).
fof(f752,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ),
inference(flattening,[],[f751]) ).
fof(f753,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set != complements_of_subsets(X0,X1)
| empty_set = X1 ),
inference(ennf_transformation,[],[f461]) ).
fof(f754,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set != complements_of_subsets(X0,X1)
| empty_set = X1 ),
inference(flattening,[],[f753]) ).
fof(f755,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(ennf_transformation,[],[f462]) ).
fof(f756,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ) ),
inference(ennf_transformation,[],[f463]) ).
fof(f757,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ) ),
inference(flattening,[],[f756]) ).
fof(f758,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ),
inference(ennf_transformation,[],[f464]) ).
fof(f759,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ),
inference(flattening,[],[f758]) ).
fof(f760,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset(X1,topstr_closure(X0,X1)) ) ),
inference(ennf_transformation,[],[f465]) ).
fof(f761,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ),
inference(ennf_transformation,[],[f466]) ).
fof(f762,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ),
inference(flattening,[],[f761]) ).
fof(f763,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| relation_isomorphism(X1,X0,function_inverse(X2)) ) ) ),
inference(ennf_transformation,[],[f468]) ).
fof(f764,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| relation_isomorphism(X1,X0,function_inverse(X2)) ) ) ),
inference(flattening,[],[f763]) ).
fof(f765,plain,
! [X0] :
( ~ ordinal(X0)
| connected(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f471]) ).
fof(f766,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( ? [X2] : in(X2,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f534]) ).
fof(f767,plain,
! [X0] :
( empty_set = X0
| ! [X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,X0)
| in(X2,X1)
| in(X2,subset_complement(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f473]) ).
fof(f768,plain,
! [X0] :
( empty_set = X0
| ! [X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,X0)
| in(X2,X1)
| in(X2,subset_complement(X0,X1)) ) ) ),
inference(flattening,[],[f767]) ).
fof(f769,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( topstr_closure(X0,X1) != X1
| ~ topological_space(X0)
| closed_subset(X1,X0) )
& ( ~ closed_subset(X1,X0)
| topstr_closure(X0,X1) = X1 ) ) ) ),
inference(ennf_transformation,[],[f474]) ).
fof(f770,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( topstr_closure(X0,X1) != X1
| ~ topological_space(X0)
| closed_subset(X1,X0) )
& ( ~ closed_subset(X1,X0)
| topstr_closure(X0,X1) = X1 ) ) ) ),
inference(flattening,[],[f769]) ).
fof(f771,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ( ( ~ well_founded_relation(X0)
| well_founded_relation(X1) )
& ( ~ antisymmetric(X0)
| antisymmetric(X1) )
& ( ~ connected(X0)
| connected(X1) )
& ( ~ transitive(X0)
| transitive(X1) )
& ( ~ reflexive(X0)
| reflexive(X1) ) ) ) ) ),
inference(ennf_transformation,[],[f475]) ).
fof(f772,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ( ( ~ well_founded_relation(X0)
| well_founded_relation(X1) )
& ( ~ antisymmetric(X0)
| antisymmetric(X1) )
& ( ~ connected(X0)
| connected(X1) )
& ( ~ transitive(X0)
| transitive(X1) )
& ( ~ reflexive(X0)
| reflexive(X1) ) ) ) ) ),
inference(flattening,[],[f771]) ).
fof(f773,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ),
inference(ennf_transformation,[],[f476]) ).
fof(f774,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ),
inference(flattening,[],[f773]) ).
fof(f775,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(ennf_transformation,[],[f477]) ).
fof(f776,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(flattening,[],[f775]) ).
fof(f777,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ well_ordering(X0)
| well_ordering(X1) ) ) ),
inference(ennf_transformation,[],[f478]) ).
fof(f778,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ well_ordering(X0)
| well_ordering(X1) ) ) ),
inference(flattening,[],[f777]) ).
fof(f779,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f479]) ).
fof(f780,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ),
inference(flattening,[],[f779]) ).
fof(f781,plain,
! [X0] :
( ~ relation(X0)
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f480]) ).
fof(f782,plain,
! [X0] :
( ~ relation(X0)
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| X0 = empty_set ),
inference(flattening,[],[f781]) ).
fof(f783,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ( X0 = apply(relation_composition(function_inverse(X1),X1),X0)
& X0 = apply(X1,apply(function_inverse(X1),X0)) ) ),
inference(ennf_transformation,[],[f481]) ).
fof(f784,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ( X0 = apply(relation_composition(function_inverse(X1),X1),X0)
& X0 = apply(X1,apply(function_inverse(X1),X0)) ) ),
inference(flattening,[],[f783]) ).
fof(f785,plain,
! [X0] :
( ~ relation(X0)
| ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f483]) ).
fof(f786,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f486]) ).
fof(f787,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| one_to_one(function_inverse(X0)) ),
inference(ennf_transformation,[],[f487]) ).
fof(f788,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| one_to_one(function_inverse(X0)) ),
inference(flattening,[],[f787]) ).
fof(f789,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(ennf_transformation,[],[f488]) ).
fof(f790,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(flattening,[],[f789]) ).
fof(f791,plain,
! [X0] :
( ~ relation(X0)
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| X0 = empty_set ),
inference(ennf_transformation,[],[f489]) ).
fof(f792,plain,
! [X0] :
( ~ relation(X0)
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| X0 = empty_set ),
inference(flattening,[],[f791]) ).
fof(f793,plain,
! [X0] :
( ~ relation(X0)
| ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
inference(ennf_transformation,[],[f490]) ).
fof(f794,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f492]) ).
fof(f795,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(flattening,[],[f794]) ).
fof(f796,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ~ in(X2,X0)
| in(apply(X3,X2),relation_rng(X3))
| X1 = empty_set ),
inference(ennf_transformation,[],[f495]) ).
fof(f797,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ~ in(X2,X0)
| in(apply(X3,X2),relation_rng(X3))
| X1 = empty_set ),
inference(flattening,[],[f796]) ).
fof(f798,plain,
! [X0] :
( ~ ordinal(X0)
| well_founded_relation(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f496]) ).
fof(f799,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(ennf_transformation,[],[f497]) ).
fof(f800,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(ennf_transformation,[],[f498]) ).
fof(f801,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(flattening,[],[f800]) ).
fof(f802,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(ennf_transformation,[],[f500]) ).
fof(f803,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(flattening,[],[f802]) ).
fof(f804,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f501]) ).
fof(f805,plain,
! [X0] :
( ~ ordinal(X0)
| well_ordering(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f505]) ).
fof(f806,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f508]) ).
fof(f807,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom_restriction(X1,X0),X1) ),
inference(ennf_transformation,[],[f509]) ).
fof(f808,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(ordered_pair(X0,X1),X2)
<=> ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) ) ),
inference(ennf_transformation,[],[f511]) ).
fof(f809,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( in(ordered_pair(X0,X1),X2)
<=> ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) ) ),
inference(flattening,[],[f808]) ).
fof(f810,plain,
! [X0] :
( ~ relation(X0)
| ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) ) ),
inference(ennf_transformation,[],[f512]) ).
fof(f811,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(ennf_transformation,[],[f513]) ).
fof(f812,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(flattening,[],[f811]) ).
fof(f813,plain,
! [X0,X1,X2] :
( singleton(X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(ennf_transformation,[],[f514]) ).
fof(f814,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
inference(ennf_transformation,[],[f515]) ).
fof(f815,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(ennf_transformation,[],[f516]) ).
fof(f816,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
inference(ennf_transformation,[],[f517]) ).
fof(f817,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
inference(ennf_transformation,[],[f518]) ).
fof(f818,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ~ subset(X1,X2)
| ( relation_of2_as_subset(X3,X0,X2)
& quasi_total(X3,X0,X2)
& function(X3) )
| ( X0 != empty_set
& X1 = empty_set ) ),
inference(ennf_transformation,[],[f520]) ).
fof(f819,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ~ subset(X1,X2)
| ( relation_of2_as_subset(X3,X0,X2)
& quasi_total(X3,X0,X2)
& function(X3) )
| ( X0 != empty_set
& X1 = empty_set ) ),
inference(flattening,[],[f818]) ).
fof(f820,plain,
! [X0,X1,X2] :
( singleton(X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(ennf_transformation,[],[f522]) ).
fof(f821,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f504]) ).
fof(f822,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f422]) ).
fof(f823,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f824,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ? [X2,X3,X4] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 )
| ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X10,X13),X1) )
& in(X10,X12)
& X11 = X12 )
& in(X11,X0)
& in(X11,X0) ) ) ),
inference(ennf_transformation,[],[f535]) ).
fof(f825,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ? [X2,X3,X4] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 )
| ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X10,X13),X1) )
& in(X10,X12)
& X11 = X12 )
& in(X11,X0)
& in(X11,X0) ) ) ),
inference(flattening,[],[f824]) ).
fof(f826,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f827,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f87]) ).
fof(f828,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( subset(X0,X1)
<=> ! [X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f829,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(ennf_transformation,[],[f72]) ).
fof(f830,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f59]) ).
fof(f831,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X2 = X3 ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f832,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X2 = X3 ) ),
inference(flattening,[],[f831]) ).
fof(f833,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(ennf_transformation,[],[f103]) ).
fof(f834,plain,
! [X0] :
( ~ relation(X0)
| ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f835,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f494]) ).
fof(f836,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 )
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3
& X3 != X4 )
| ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f536]) ).
fof(f837,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 )
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3
& X3 != X4 )
| ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) ) ),
inference(flattening,[],[f836]) ).
fof(f838,plain,
! [X0] :
( ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 )
| ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( singleton(X6) = X5
& in(X6,X0)
& in(X6,X0) ) ) ),
inference(ennf_transformation,[],[f537]) ).
fof(f839,plain,
! [X0] :
( ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 )
| ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( singleton(X6) = X5
& in(X6,X0)
& in(X6,X0) ) ) ),
inference(flattening,[],[f838]) ).
fof(f840,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(set_union2(X0,X1)) ),
inference(ennf_transformation,[],[f242]) ).
fof(f841,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(set_union2(X0,X1)) ),
inference(flattening,[],[f840]) ).
fof(f842,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(ennf_transformation,[],[f228]) ).
fof(f843,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(ennf_transformation,[],[f213]) ).
fof(f844,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_union2(X0,X1)) ),
inference(ennf_transformation,[],[f211]) ).
fof(f845,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_union2(X0,X1)) ),
inference(flattening,[],[f844]) ).
fof(f846,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(ennf_transformation,[],[f344]) ).
fof(f847,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f240]) ).
fof(f848,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f237]) ).
fof(f849,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f848]) ).
fof(f850,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f235]) ).
fof(f851,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
inference(flattening,[],[f850]) ).
fof(f852,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f164]) ).
fof(f853,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_rng_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f854,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f855,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| equipotent(X1,X0) ),
inference(ennf_transformation,[],[f345]) ).
fof(f856,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_difference(X0,X1)) ),
inference(ennf_transformation,[],[f226]) ).
fof(f857,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_difference(X0,X1)) ),
inference(flattening,[],[f856]) ).
fof(f861,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f482]) ).
fof(f862,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f470]) ).
fof(f863,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f862]) ).
fof(f864,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f279]) ).
fof(f865,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f388]) ).
fof(f866,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,X1) = union(X1) ),
inference(ennf_transformation,[],[f301]) ).
fof(f867,plain,
! [X0] :
( ~ ordinal(X0)
| ( ordinal(union(X0))
& epsilon_connected(union(X0))
& epsilon_transitive(union(X0)) ) ),
inference(ennf_transformation,[],[f232]) ).
fof(f868,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3,X4,X5] :
( ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& X5 = ordered_pair(X8,X9) )
& X3 = X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& X4 = ordered_pair(X6,X7) )
& X3 = X4
& X4 != X5 )
| ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) ) ),
inference(ennf_transformation,[],[f541]) ).
fof(f869,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3,X4,X5] :
( ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& X5 = ordered_pair(X8,X9) )
& X3 = X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& X4 = ordered_pair(X6,X7) )
& X3 = X4
& X4 != X5 )
| ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) ) ),
inference(flattening,[],[f868]) ).
fof(f870,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2] :
( ? [X3,X4,X5] :
( ? [X10,X11] :
( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& ordered_pair(X10,X11) = X5 )
& X3 = X5
& ? [X6,X7] :
( ? [X8] :
( ! [X9] :
( ~ in(X9,X8)
| in(ordered_pair(X7,X9),X1) )
& in(X7,X8)
& X6 = X8 )
& in(X6,X0)
& ordered_pair(X6,X7) = X4 )
& X3 = X4
& X4 != X5 )
| ? [X14] :
! [X15] :
( in(X15,X14)
<=> ? [X16] :
( ? [X17,X18] :
( ? [X19] :
( ! [X20] :
( ~ in(X20,X19)
| in(ordered_pair(X18,X20),X1) )
& in(X18,X19)
& X17 = X19 )
& in(X17,X0)
& ordered_pair(X17,X18) = X15 )
& X15 = X16
& in(X16,cartesian_product2(X0,X2)) ) ) ) ),
inference(ennf_transformation,[],[f542]) ).
fof(f871,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2] :
( ? [X3,X4,X5] :
( ? [X10,X11] :
( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& ordered_pair(X10,X11) = X5 )
& X3 = X5
& ? [X6,X7] :
( ? [X8] :
( ! [X9] :
( ~ in(X9,X8)
| in(ordered_pair(X7,X9),X1) )
& in(X7,X8)
& X6 = X8 )
& in(X6,X0)
& ordered_pair(X6,X7) = X4 )
& X3 = X4
& X4 != X5 )
| ? [X14] :
! [X15] :
( in(X15,X14)
<=> ? [X16] :
( ? [X17,X18] :
( ? [X19] :
( ! [X20] :
( ~ in(X20,X19)
| in(ordered_pair(X18,X20),X1) )
& in(X18,X19)
& X17 = X19 )
& in(X17,X0)
& ordered_pair(X17,X18) = X15 )
& X15 = X16
& in(X16,cartesian_product2(X0,X2)) ) ) ) ),
inference(flattening,[],[f870]) ).
fof(f872,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(ennf_transformation,[],[f234]) ).
fof(f873,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(flattening,[],[f872]) ).
fof(f874,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f173]) ).
fof(f875,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
inference(ennf_transformation,[],[f105]) ).
fof(f876,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f877,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f231]) ).
fof(f878,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f877]) ).
fof(f879,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f162]) ).
fof(f880,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f881,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f882,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f510]) ).
fof(f883,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f502]) ).
fof(f886,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( element(X1,X0)
<=> empty(X1) ) )
& ( empty(X0)
| ( element(X1,X0)
<=> in(X1,X0) ) ) ),
inference(ennf_transformation,[],[f73]) ).
fof(f887,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f888,plain,
! [X0] :
( ? [X1,X2,X3] :
( ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2
& X2 != X3 )
| ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( ordinal(X5)
& X5 = X6
& in(X6,X0) ) ) ),
inference(ennf_transformation,[],[f543]) ).
fof(f889,plain,
! [X0] :
( ? [X1,X2,X3] :
( ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2
& X2 != X3 )
| ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( ordinal(X5)
& X5 = X6
& in(X6,X0) ) ) ),
inference(flattening,[],[f888]) ).
fof(f890,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X0,X0) ),
inference(ennf_transformation,[],[f308]) ).
fof(f891,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X0,X0) ),
inference(flattening,[],[f890]) ).
fof(f892,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(ennf_transformation,[],[f306]) ).
fof(f893,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(flattening,[],[f892]) ).
fof(f894,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f895,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(flattening,[],[f894]) ).
fof(f896,plain,
! [X0] :
( ~ ordinal(X0)
| ? [X1,X2,X3] :
( ? [X8] :
( ( ~ in(X8,omega)
| ! [X9] :
( ~ element(X9,powerset(powerset(X8)))
| ? [X10] :
( ! [X11] :
( ~ subset(X10,X11)
| ~ in(X11,X9)
| X11 = X10 )
& in(X10,X9) )
| empty_set = X9 ) )
& X3 = X8
& ordinal(X8) )
& X1 = X3
& ? [X4] :
( ( ~ in(X4,omega)
| ! [X5] :
( ~ element(X5,powerset(powerset(X4)))
| ? [X6] :
( ! [X7] :
( ~ subset(X6,X7)
| ~ in(X7,X5)
| X7 = X6 )
& in(X6,X5) )
| empty_set = X5 ) )
& X2 = X4
& ordinal(X4) )
& X1 = X2
& X2 != X3 )
| ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( ? [X15] :
( ( ~ in(X15,omega)
| ! [X16] :
( ~ element(X16,powerset(powerset(X15)))
| ? [X17] :
( ! [X18] :
( ~ subset(X17,X18)
| ~ in(X18,X16)
| X17 = X18 )
& in(X17,X16) )
| empty_set = X16 ) )
& X13 = X15
& ordinal(X15) )
& X13 = X14
& in(X14,succ(X0)) ) ) ),
inference(ennf_transformation,[],[f544]) ).
fof(f897,plain,
! [X0] :
( ~ ordinal(X0)
| ? [X1,X2,X3] :
( ? [X8] :
( ( ~ in(X8,omega)
| ! [X9] :
( ~ element(X9,powerset(powerset(X8)))
| ? [X10] :
( ! [X11] :
( ~ subset(X10,X11)
| ~ in(X11,X9)
| X11 = X10 )
& in(X10,X9) )
| empty_set = X9 ) )
& X3 = X8
& ordinal(X8) )
& X1 = X3
& ? [X4] :
( ( ~ in(X4,omega)
| ! [X5] :
( ~ element(X5,powerset(powerset(X4)))
| ? [X6] :
( ! [X7] :
( ~ subset(X6,X7)
| ~ in(X7,X5)
| X7 = X6 )
& in(X6,X5) )
| empty_set = X5 ) )
& X2 = X4
& ordinal(X4) )
& X1 = X2
& X2 != X3 )
| ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( ? [X15] :
( ( ~ in(X15,omega)
| ! [X16] :
( ~ element(X16,powerset(powerset(X15)))
| ? [X17] :
( ! [X18] :
( ~ subset(X17,X18)
| ~ in(X18,X16)
| X17 = X18 )
& in(X17,X16) )
| empty_set = X16 ) )
& X13 = X15
& ordinal(X15) )
& X13 = X14
& in(X14,succ(X0)) ) ) ),
inference(flattening,[],[f896]) ).
fof(f898,plain,
! [X0] :
( X0 = omega
<=> ( ! [X1] :
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| subset(X0,X1) )
& ordinal(X0)
& being_limit_ordinal(X0)
& in(empty_set,X0) ) ),
inference(ennf_transformation,[],[f95]) ).
fof(f899,plain,
! [X0] :
( X0 = omega
<=> ( ! [X1] :
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| subset(X0,X1) )
& ordinal(X0)
& being_limit_ordinal(X0)
& in(empty_set,X0) ) ),
inference(flattening,[],[f898]) ).
fof(f900,plain,
! [X0] :
( ~ element(X0,omega)
| ( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f901,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ? [X2,X3,X4] :
( ? [X6] :
( in(X6,X0)
& X4 = X6
& ordinal(X6) )
& X2 = X4
& ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& X2 = X3
& X3 != X4 )
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( in(X10,X0)
& X8 = X10
& ordinal(X10) )
& X8 = X9
& in(X9,succ(X1)) ) ) ),
inference(ennf_transformation,[],[f545]) ).
fof(f902,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ? [X2,X3,X4] :
( ? [X6] :
( in(X6,X0)
& X4 = X6
& ordinal(X6) )
& X2 = X4
& ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& X2 = X3
& X3 != X4 )
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( in(X10,X0)
& X8 = X10
& ordinal(X10) )
& X8 = X9
& in(X9,succ(X1)) ) ) ),
inference(flattening,[],[f901]) ).
fof(f903,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ? [X2,X3,X4] :
( ? [X6] :
( X4 = set_difference(X6,singleton(X0))
& in(X6,X1) )
& X2 = X4
& ? [X5] :
( X3 = set_difference(X5,singleton(X0))
& in(X5,X1) )
& X2 = X3
& X3 != X4 )
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) ) ),
inference(ennf_transformation,[],[f546]) ).
fof(f904,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ? [X2,X3,X4] :
( ? [X6] :
( X4 = set_difference(X6,singleton(X0))
& in(X6,X1) )
& X2 = X4
& ? [X5] :
( X3 = set_difference(X5,singleton(X0))
& in(X5,X1) )
& X2 = X3
& X3 != X4 )
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) ) ),
inference(flattening,[],[f903]) ).
fof(f905,plain,
! [X0] :
( ~ ordinal(X0)
| ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
inference(ennf_transformation,[],[f225]) ).
fof(f906,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f94]) ).
fof(f907,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f906]) ).
fof(f908,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f85]) ).
fof(f909,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> X2 = empty_set ) )
& ( ~ in(X1,relation_dom(X0))
| ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
inference(flattening,[],[f908]) ).
fof(f910,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f167]) ).
fof(f911,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3
& X3 != X4 )
| ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) ) ),
inference(ennf_transformation,[],[f547]) ).
fof(f912,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3
& X3 != X4 )
| ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) ) ),
inference(flattening,[],[f911]) ).
fof(f913,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2,X3,X4] :
( ? [X6] :
( subset(X1,X4)
& closed_subset(X6,X0)
& X6 = X4
& element(X6,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X5 = X3
& element(X5,powerset(the_carrier(X0))) )
& X2 = X3
& X3 != X4 )
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) ) ),
inference(ennf_transformation,[],[f548]) ).
fof(f914,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2,X3,X4] :
( ? [X6] :
( subset(X1,X4)
& closed_subset(X6,X0)
& X6 = X4
& element(X6,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X5 = X3
& element(X5,powerset(the_carrier(X0))) )
& X2 = X3
& X3 != X4 )
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) ) ),
inference(flattening,[],[f913]) ).
fof(f915,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f295]) ).
fof(f916,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f915]) ).
fof(f917,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| closed_subset(cast_as_carrier_subset(X0),X0) ),
inference(ennf_transformation,[],[f236]) ).
fof(f918,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| closed_subset(cast_as_carrier_subset(X0),X0) ),
inference(flattening,[],[f917]) ).
fof(f920,plain,
! [X0] :
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = the_carrier(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f921,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ? [X3,X4,X5] :
( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4
& X4 != X5 )
| ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) ) ),
inference(ennf_transformation,[],[f549]) ).
fof(f922,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ? [X3,X4,X5] :
( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4
& X4 != X5 )
| ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) ) ),
inference(flattening,[],[f921]) ).
fof(f923,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ function(X0)
| ~ relation(X0)
| finite(relation_image(X0,X1)) ),
inference(ennf_transformation,[],[f192]) ).
fof(f924,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ function(X0)
| ~ relation(X0)
| finite(relation_image(X0,X1)) ),
inference(flattening,[],[f923]) ).
fof(f925,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f926,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f927,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f926]) ).
fof(f928,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f241]) ).
fof(f929,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(ennf_transformation,[],[f239]) ).
fof(f930,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(flattening,[],[f929]) ).
fof(f935,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(ennf_transformation,[],[f200]) ).
fof(f936,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(flattening,[],[f935]) ).
fof(f937,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f294]) ).
fof(f938,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f937]) ).
fof(f939,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(ennf_transformation,[],[f201]) ).
fof(f940,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(flattening,[],[f939]) ).
fof(f941,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f169]) ).
fof(f942,plain,
! [X0] :
? [X1] :
( ! [X7] :
( in(X7,X1)
| are_equipotent(X7,X1)
| ~ subset(X7,X1) )
& ! [X4] :
( ? [X5] :
( ! [X6] :
( ~ subset(X6,X4)
| in(X6,X5) )
& in(X5,X1) )
| ~ in(X4,X1) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,X1)
| in(X3,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f551]) ).
fof(f943,plain,
! [X0] :
? [X1] :
( ! [X7] :
( in(X7,X1)
| are_equipotent(X7,X1)
| ~ subset(X7,X1) )
& ! [X4] :
( ? [X5] :
( ! [X6] :
( ~ subset(X6,X4)
| in(X6,X5) )
& in(X5,X1) )
| ~ in(X4,X1) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,X1)
| in(X3,X1) )
& in(X0,X1) ),
inference(flattening,[],[f942]) ).
fof(f944,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f288]) ).
fof(f945,plain,
! [X0,X1] :
( ~ finite(X0)
| finite(set_difference(X0,X1)) ),
inference(ennf_transformation,[],[f190]) ).
fof(f947,plain,
! [X0,X1] :
( ~ finite(X1)
| finite(set_intersection2(X0,X1)) ),
inference(ennf_transformation,[],[f186]) ).
fof(f949,plain,
! [X0] :
( ~ empty(X0)
| finite(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f950,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f951,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f952,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f951]) ).
fof(f953,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
inference(ennf_transformation,[],[f302]) ).
fof(f954,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
inference(flattening,[],[f953]) ).
fof(f955,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X1) = X1 ),
inference(ennf_transformation,[],[f246]) ).
fof(f956,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X1) = X1 ),
inference(flattening,[],[f955]) ).
fof(f957,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_intersection2(X0,X1,X2),powerset(X0)) ),
inference(ennf_transformation,[],[f157]) ).
fof(f958,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_intersection2(X0,X1,X2),powerset(X0)) ),
inference(flattening,[],[f957]) ).
fof(f959,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = subset_intersection2(X0,X2,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f960,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = subset_intersection2(X0,X2,X1) ),
inference(flattening,[],[f959]) ).
fof(f961,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f243]) ).
fof(f962,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f961]) ).
fof(f963,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f196]) ).
fof(f964,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f963]) ).
fof(f965,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(ennf_transformation,[],[f187]) ).
fof(f966,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(flattening,[],[f965]) ).
fof(f967,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f154]) ).
fof(f968,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f967]) ).
fof(f969,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
inference(ennf_transformation,[],[f111]) ).
fof(f970,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f140]) ).
fof(f971,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f247]) ).
fof(f972,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f145]) ).
fof(f973,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( ~ element(X3,powerset(X0))
| ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
inference(ennf_transformation,[],[f113]) ).
fof(f974,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,X1) = set_difference(X0,X1) ),
inference(ennf_transformation,[],[f98]) ).
fof(f975,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(ennf_transformation,[],[f304]) ).
fof(f976,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(flattening,[],[f975]) ).
fof(f977,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_difference(X0,X1,X2),powerset(X0)) ),
inference(ennf_transformation,[],[f161]) ).
fof(f978,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_difference(X0,X1,X2),powerset(X0)) ),
inference(flattening,[],[f977]) ).
fof(f979,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f556]) ).
fof(f980,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(flattening,[],[f979]) ).
fof(f981,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ~ proper_subset(X1,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f982,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f70]) ).
fof(f983,plain,
! [X0] :
( ~ empty(X0)
| ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f984,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f985,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(flattening,[],[f984]) ).
fof(f986,plain,
! [X0] :
( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f987,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ element(X1,X0)
| ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f988,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
( ? [X3] :
( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
| empty_set = X2
| ~ subset(X2,X1) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f989,plain,
! [X0] :
( ~ relation(X0)
| ( well_founded_relation(X0)
<=> ! [X1] :
( ? [X2] :
( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
| empty_set = X1
| ~ subset(X1,relation_field(X0)) ) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f990,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( X2 = fiber(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(ordered_pair(X3,X1),X0)
& X3 != X1 ) ) ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f991,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(ennf_transformation,[],[f299]) ).
fof(f992,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
inference(ennf_transformation,[],[f150]) ).
fof(f993,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( ( empty_set != X1
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| X0 = empty_set )
& ( ( X1 = empty_set
& empty_set != X0 )
| ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) ) ) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f994,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( ( empty_set != X1
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| X0 = empty_set )
& ( ( X1 = empty_set
& empty_set != X0 )
| ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) ) ) ) ),
inference(flattening,[],[f993]) ).
fof(f997,plain,
! [X0] :
( ~ latt_str(X0)
| ( join_semilatt_str(X0)
& meet_semilatt_str(X0) ) ),
inference(ennf_transformation,[],[f170]) ).
fof(f998,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ( meet_absorbing(X0)
<=> ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| join(X0,meet(X0,X1,X2),X2) = X2 ) ) ) ),
inference(ennf_transformation,[],[f110]) ).
fof(f999,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ( meet_absorbing(X0)
<=> ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| join(X0,meet(X0,X1,X2),X2) = X2 ) ) ) ),
inference(flattening,[],[f998]) ).
fof(f1000,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
inference(ennf_transformation,[],[f300]) ).
fof(f1001,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
inference(ennf_transformation,[],[f155]) ).
fof(f1002,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f102]) ).
fof(f1003,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( open_subset(X1,X0)
<=> in(X1,the_topology(X0)) ) ) ),
inference(ennf_transformation,[],[f96]) ).
fof(f1004,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( ~ in(X3,the_carrier(X0))
| ( in(X3,X2)
<=> ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f1005,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( ~ in(X3,the_carrier(X0))
| ( in(X3,X2)
<=> ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) ) ) ) ) ) ),
inference(flattening,[],[f1004]) ).
fof(f1006,plain,
! [X0,X1] :
( ~ relation(X1)
| ( X1 = inclusion_relation(X0)
<=> ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) )
& relation_field(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f1007,plain,
! [X0,X1] :
( ~ relation(X1)
| ( X1 = inclusion_relation(X0)
<=> ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) )
& relation_field(X1) = X0 ) ) ),
inference(flattening,[],[f1006]) ).
fof(f1008,plain,
! [X0,X1] :
( ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f1009,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(ennf_transformation,[],[f248]) ).
fof(f1010,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f224]) ).
fof(f1011,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
inference(flattening,[],[f1010]) ).
fof(f1012,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f189]) ).
fof(f1013,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(ennf_transformation,[],[f149]) ).
fof(f1014,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(ennf_transformation,[],[f115]) ).
fof(f1015,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(flattening,[],[f1014]) ).
fof(f1016,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f106]) ).
fof(f1017,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(meet_of_subsets(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f160]) ).
fof(f1018,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f158]) ).
fof(f1019,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f1018]) ).
fof(f1020,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f249]) ).
fof(f1021,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f163]) ).
fof(f1022,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(union_of_subsets(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f156]) ).
fof(f1023,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f133]) ).
fof(f1024,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f1023]) ).
fof(f1025,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( relation_isomorphism(X0,X1,X2)
<=> ( ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_dom(X2) = relation_field(X0) ) ) ) ) ),
inference(ennf_transformation,[],[f107]) ).
fof(f1026,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( relation_isomorphism(X0,X1,X2)
<=> ( ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_dom(X2) = relation_field(X0) ) ) ) ) ),
inference(flattening,[],[f1025]) ).
fof(f1027,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f109]) ).
fof(f1028,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(flattening,[],[f1027]) ).
fof(f1029,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f1030,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
inference(flattening,[],[f1029]) ).
fof(f1031,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( well_orders(X0,X1)
<=> ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f100]) ).
fof(f1032,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X4 ) ) ),
inference(ennf_transformation,[],[f553]) ).
fof(f1033,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X5 ) ) ),
inference(ennf_transformation,[],[f554]) ).
fof(f1046,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f79]) ).
fof(f1051,plain,
! [X0] :
( ~ meet_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f166]) ).
fof(f1052,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0)
| element(meet(X0,X1,X2),the_carrier(X0)) ),
inference(ennf_transformation,[],[f134]) ).
fof(f1053,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0)
| element(meet(X0,X1,X2),the_carrier(X0)) ),
inference(flattening,[],[f1052]) ).
fof(f1054,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| element(join(X0,X1,X2),the_carrier(X0)) ),
inference(ennf_transformation,[],[f121]) ).
fof(f1055,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| element(join(X0,X1,X2),the_carrier(X0)) ),
inference(flattening,[],[f1054]) ).
fof(f1056,plain,
! [X0] :
( ~ top_str(X0)
| element(the_topology(X0),powerset(powerset(the_carrier(X0)))) ),
inference(ennf_transformation,[],[f175]) ).
fof(f1057,plain,
! [X0] :
( ~ top_str(X0)
| ( topological_space(X0)
<=> ( ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,the_topology(X0))
| ~ in(X2,the_topology(X0))
| in(subset_intersection2(the_carrier(X0),X2,X3),the_topology(X0)) ) )
& ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ subset(X1,the_topology(X0))
| in(union_of_subsets(the_carrier(X0),X1),the_topology(X0)) )
& in(the_carrier(X0),the_topology(X0)) ) ) ),
inference(ennf_transformation,[],[f555]) ).
fof(f1058,plain,
! [X0] :
( ~ top_str(X0)
| ( topological_space(X0)
<=> ( ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,the_topology(X0))
| ~ in(X2,the_topology(X0))
| in(subset_intersection2(the_carrier(X0),X2,X3),the_topology(X0)) ) )
& ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ subset(X1,the_topology(X0))
| in(union_of_subsets(the_carrier(X0),X1),the_topology(X0)) )
& in(the_carrier(X0),the_topology(X0)) ) ) ),
inference(flattening,[],[f1057]) ).
fof(f1059,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X2 = X3 ) ) ),
inference(ennf_transformation,[],[f88]) ).
fof(f1060,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X2 = X3 ) ) ),
inference(flattening,[],[f1059]) ).
fof(f1061,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f1062,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) ) ) ),
inference(ennf_transformation,[],[f104]) ).
fof(f1063,plain,
! [X0] :
( ~ relation(X0)
| ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f1064,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| in(ordered_pair(X2,X4),X0) ) ) ),
inference(ennf_transformation,[],[f112]) ).
fof(f1065,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| in(ordered_pair(X2,X4),X0) ) ) ),
inference(flattening,[],[f1064]) ).
fof(f1066,plain,
! [X0] :
( ~ relation(X0)
| ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f1067,plain,
! [X0] :
( ~ relation(X0)
| ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f116]) ).
fof(f1068,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( ~ in(X2,X1)
| in(ordered_pair(X2,X2),X0) ) ) ),
inference(ennf_transformation,[],[f60]) ).
fof(f1141,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) )
& ( ? [X1] :
( in(X1,relation_field(X0))
& ~ in(ordered_pair(X1,X1),X0) )
| reflexive(X0) ) ) ),
inference(nnf_transformation,[],[f565]) ).
fof(f1142,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X2] :
( ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ) )
& ( ? [X1] :
( in(X1,relation_field(X0))
& ~ in(ordered_pair(X1,X1),X0) )
| reflexive(X0) ) ) ),
inference(rectify,[],[f1141]) ).
fof(f1143,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X2] :
( ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ) )
& ( ( in(sK43(X0),relation_field(X0))
& ~ in(ordered_pair(sK43(X0),sK43(X0)),X0) )
| reflexive(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(X1,sK43(X0))],[f1142]) ).
fof(f1144,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ transitive(X0)
| ! [X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X1,X3),X0) ) )
& ( ? [X1,X2,X3] :
( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X1,X3),X0) )
| transitive(X0) ) ) ),
inference(nnf_transformation,[],[f571]) ).
fof(f1145,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ transitive(X0)
| ! [X4,X5,X6] :
( ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X6),X0) ) )
& ( ? [X1,X2,X3] :
( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X1,X3),X0) )
| transitive(X0) ) ) ),
inference(rectify,[],[f1144]) ).
fof(f1146,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ transitive(X0)
| ! [X4,X5,X6] :
( ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X6),X0) ) )
& ( ( in(ordered_pair(sK45(X0),sK46(X0)),X0)
& in(ordered_pair(sK44(X0),sK45(X0)),X0)
& ~ in(ordered_pair(sK44(X0),sK46(X0)),X0) )
| transitive(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44,sK45,sK46]),skolemize(X1,sK44(X0)),skolemize(X2,sK45(X0)),skolemize(X3,sK46(X0))],[f1145]) ).
fof(f1148,plain,
! [X0,X1] :
( ~ relation(X1)
| ( relation(sK47(X0))
& well_orders(sK47(X0),X0) )
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(X2,sK47(X0))],[f573]) ).
fof(f1150,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) )
& ( ? [X1,X2] :
( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0)
& X1 != X2 )
| antisymmetric(X0) ) ) ),
inference(nnf_transformation,[],[f576]) ).
fof(f1151,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| ! [X3,X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| X3 = X4 ) )
& ( ? [X1,X2] :
( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0)
& X1 != X2 )
| antisymmetric(X0) ) ) ),
inference(rectify,[],[f1150]) ).
fof(f1152,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| ! [X3,X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| X3 = X4 ) )
& ( ( in(ordered_pair(sK49(X0),sK48(X0)),X0)
& in(ordered_pair(sK48(X0),sK49(X0)),X0)
& sK48(X0) != sK49(X0) )
| antisymmetric(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48,sK49]),skolemize(X1,sK48(X0)),skolemize(X2,sK49(X0))],[f1151]) ).
fof(f1153,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ connected(X0)
| ! [X1,X2] :
( in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),X0)
| X1 = X2
| ~ in(X2,relation_field(X0))
| ~ in(X1,relation_field(X0)) ) )
& ( ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) )
| connected(X0) ) ) ),
inference(nnf_transformation,[],[f579]) ).
fof(f1154,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ connected(X0)
| ! [X3,X4] :
( in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) ) )
& ( ? [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
& ~ in(ordered_pair(X1,X2),X0)
& X1 != X2
& in(X2,relation_field(X0))
& in(X1,relation_field(X0)) )
| connected(X0) ) ) ),
inference(rectify,[],[f1153]) ).
fof(f1155,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ connected(X0)
| ! [X3,X4] :
( in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) ) )
& ( ( ~ in(ordered_pair(sK51(X0),sK50(X0)),X0)
& ~ in(ordered_pair(sK50(X0),sK51(X0)),X0)
& sK50(X0) != sK51(X0)
& in(sK51(X0),relation_field(X0))
& in(sK50(X0),relation_field(X0)) )
| connected(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50,sK51]),skolemize(X1,sK50(X0)),skolemize(X2,sK51(X0))],[f1154]) ).
fof(f1160,plain,
! [X0,X1] :
( ( in(sK52(X0,X1),X0)
& ~ in(sK52(X0,X1),X1) )
| element(X0,powerset(X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(X2,sK52(X0,X1))],[f581]) ).
fof(f1163,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ? [X2,X3,X4] :
( sP0(X2,X4,X1)
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 ) ),
inference(nnf_transformation,[],[f1077]) ).
fof(f1164,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ( sP0(sK53(X0,X1),sK55(X0,X1),X1)
& in(sK53(X0,X1),X0)
& ! [X6] :
( ~ in(X6,sK56(X0,X1))
| in(ordered_pair(sK54(X0,X1),X6),X1) )
& in(sK54(X0,X1),sK56(X0,X1))
& sK53(X0,X1) = sK56(X0,X1)
& in(sK53(X0,X1),X0)
& sK54(X0,X1) != sK55(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X2,sK53(X0,X1)),skolemize(X3,sK54(X0,X1)),skolemize(X4,sK55(X0,X1)),skolemize(X5,sK56(X0,X1))],[f1163]) ).
fof(f1165,plain,
! [X0,X1,X9] :
( ~ sP1(X0,X1,X9)
| ! [X10,X11] :
( ( ~ in(ordered_pair(X10,X11),X9)
| ( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& in(X10,X0) ) )
& ( ! [X12] :
( ? [X13] :
( in(X13,X12)
& ~ in(ordered_pair(X11,X13),X1) )
| ~ in(X11,X12)
| X10 != X12 )
| ~ in(X10,X0)
| ~ in(X10,X0)
| in(ordered_pair(X10,X11),X9) ) ) ),
inference(nnf_transformation,[],[f1076]) ).
fof(f1166,plain,
! [X0,X1,X9] :
( ~ sP1(X0,X1,X9)
| ! [X10,X11] :
( ( ~ in(ordered_pair(X10,X11),X9)
| ( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& in(X10,X0) ) )
& ( ! [X12] :
( ? [X13] :
( in(X13,X12)
& ~ in(ordered_pair(X11,X13),X1) )
| ~ in(X11,X12)
| X10 != X12 )
| ~ in(X10,X0)
| ~ in(X10,X0)
| in(ordered_pair(X10,X11),X9) ) ) ),
inference(flattening,[],[f1165]) ).
fof(f1167,plain,
! [X0,X1,X2] :
( ~ sP1(X0,X1,X2)
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X3 = X7 )
& in(X3,X0)
& in(X3,X0) ) )
& ( ! [X5] :
( ? [X6] :
( in(X6,X5)
& ~ in(ordered_pair(X4,X6),X1) )
| ~ in(X4,X5)
| X3 != X5 )
| ~ in(X3,X0)
| ~ in(X3,X0)
| in(ordered_pair(X3,X4),X2) ) ) ),
inference(rectify,[],[f1166]) ).
fof(f1168,plain,
! [X0,X1,X2] :
( ~ sP1(X0,X1,X2)
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( ! [X8] :
( ~ in(X8,sK58(X1,X3,X4))
| in(ordered_pair(X4,X8),X1) )
& in(X4,sK58(X1,X3,X4))
& sK58(X1,X3,X4) = X3
& in(X3,X0)
& in(X3,X0) ) )
& ( ! [X5] :
( ( in(sK57(X1,X4,X5),X5)
& ~ in(ordered_pair(X4,sK57(X1,X4,X5)),X1) )
| ~ in(X4,X5)
| X3 != X5 )
| ~ in(X3,X0)
| ~ in(X3,X0)
| in(ordered_pair(X3,X4),X2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57,sK58]),skolemize(X6,sK57(X1,X4,X5)),skolemize(X7,sK58(X1,X3,X4))],[f1167]) ).
fof(f1172,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| ? [X2] :
( sP1(X0,X1,X2)
& function(X2)
& relation(X2) ) ),
inference(rectify,[],[f1078]) ).
fof(f1173,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| ( sP1(X0,X1,sK60(X0,X1))
& function(sK60(X0,X1))
& relation(sK60(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(X2,sK60(X0,X1))],[f1172]) ).
fof(f1178,plain,
! [X0] :
( ( sK64(X0) = singleton(sK62(X0))
& in(sK62(X0),X0)
& sK63(X0) = singleton(sK62(X0))
& in(sK62(X0),X0)
& sK63(X0) != sK64(X0) )
| sP3(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62,sK63,sK64]),skolemize(X1,sK62(X0)),skolemize(X2,sK63(X0)),skolemize(X3,sK64(X0))],[f1080]) ).
fof(f1179,plain,
! [X0] :
( ! [X3] :
( ~ in(X3,X0)
| ~ ordinal(X3) )
| ? [X1] :
( ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| ordinal_subset(X1,X2) )
& in(X1,X0)
& ordinal(X1) ) ),
inference(rectify,[],[f589]) ).
fof(f1180,plain,
! [X0] :
( ! [X3] :
( ~ in(X3,X0)
| ~ ordinal(X3) )
| ( ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| ordinal_subset(sK65(X0),X2) )
& in(sK65(X0),X0)
& ordinal(sK65(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(X1,sK65(X0))],[f1179]) ).
fof(f1181,plain,
( ~ sP8
| ? [X3] :
( ordinal(X3)
& ( ~ in(X3,omega)
| ! [X4] :
( ~ element(X4,powerset(powerset(X3)))
| ? [X5] :
( ! [X6] :
( ~ subset(X5,X6)
| ~ in(X6,X4)
| X6 = X5 )
& in(X5,X4) )
| empty_set = X4 ) )
& in(succ(X3),omega)
& sP5(X3) ) ),
inference(nnf_transformation,[],[f1085]) ).
fof(f1182,plain,
( ~ sP8
| ? [X0] :
( ordinal(X0)
& ( ~ in(X0,omega)
| ! [X1] :
( ~ element(X1,powerset(powerset(X0)))
| ? [X2] :
( ! [X3] :
( ~ subset(X2,X3)
| ~ in(X3,X1)
| X2 = X3 )
& in(X2,X1) )
| empty_set = X1 ) )
& in(succ(X0),omega)
& sP5(X0) ) ),
inference(rectify,[],[f1181]) ).
fof(f1183,plain,
( ~ sP8
| ( ordinal(sK66)
& ( ~ in(sK66,omega)
| ! [X1] :
( ~ element(X1,powerset(powerset(sK66)))
| ( ! [X3] :
( ~ subset(sK67(X1),X3)
| ~ in(X3,X1)
| sK67(X1) = X3 )
& in(sK67(X1),X1) )
| empty_set = X1 ) )
& in(succ(sK66),omega)
& sP5(sK66) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66,sK67]),skolemize(X0,sK66),skolemize(X2,sK67(X1))],[f1182]) ).
fof(f1184,plain,
( ~ sP7
| ( in(empty_set,omega)
& ? [X0] :
( element(X0,powerset(powerset(empty_set)))
& ! [X1] :
( ? [X2] :
( subset(X1,X2)
& in(X2,X0)
& X1 != X2 )
| ~ in(X1,X0) )
& X0 != empty_set ) ) ),
inference(nnf_transformation,[],[f1084]) ).
fof(f1185,plain,
( ~ sP7
| ( in(empty_set,omega)
& element(sK68,powerset(powerset(empty_set)))
& ! [X1] :
( ( subset(X1,sK69(X1))
& in(sK69(X1),sK68)
& sK69(X1) != X1 )
| ~ in(X1,sK68) )
& empty_set != sK68 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68,sK69]),skolemize(X0,sK68),skolemize(X2,sK69(X1))],[f1184]) ).
fof(f1186,plain,
( ~ sP6
| ? [X10] :
( ordinal(X10)
& ! [X11] :
( ~ ordinal(X11)
| ~ in(X11,X10)
| ~ in(X11,omega)
| ! [X12] :
( ~ element(X12,powerset(powerset(X11)))
| ? [X13] :
( ! [X14] :
( ~ subset(X13,X14)
| ~ in(X14,X12)
| X13 = X14 )
& in(X13,X12) )
| empty_set = X12 ) )
& being_limit_ordinal(X10)
& in(X10,omega)
& sP4(X10)
& empty_set != X10 ) ),
inference(nnf_transformation,[],[f1083]) ).
fof(f1187,plain,
( ~ sP6
| ? [X0] :
( ordinal(X0)
& ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| ~ in(X1,omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(X1)))
| ? [X3] :
( ! [X4] :
( ~ subset(X3,X4)
| ~ in(X4,X2)
| X3 = X4 )
& in(X3,X2) )
| empty_set = X2 ) )
& being_limit_ordinal(X0)
& in(X0,omega)
& sP4(X0)
& empty_set != X0 ) ),
inference(rectify,[],[f1186]) ).
fof(f1188,plain,
( ~ sP6
| ( ordinal(sK70)
& ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,sK70)
| ~ in(X1,omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(X1)))
| ( ! [X4] :
( ~ subset(sK71(X2),X4)
| ~ in(X4,X2)
| sK71(X2) = X4 )
& in(sK71(X2),X2) )
| empty_set = X2 ) )
& being_limit_ordinal(sK70)
& in(sK70,omega)
& sP4(sK70)
& empty_set != sK70 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70,sK71]),skolemize(X0,sK70),skolemize(X3,sK71(X2))],[f1187]) ).
fof(f1189,plain,
! [X3] :
( ~ sP5(X3)
| ? [X7] :
( element(X7,powerset(powerset(succ(X3))))
& ! [X8] :
( ? [X9] :
( subset(X8,X9)
& in(X9,X7)
& X8 != X9 )
| ~ in(X8,X7) )
& X7 != empty_set ) ),
inference(nnf_transformation,[],[f1082]) ).
fof(f1190,plain,
! [X0] :
( ~ sP5(X0)
| ? [X1] :
( element(X1,powerset(powerset(succ(X0))))
& ! [X2] :
( ? [X3] :
( subset(X2,X3)
& in(X3,X1)
& X2 != X3 )
| ~ in(X2,X1) )
& empty_set != X1 ) ),
inference(rectify,[],[f1189]) ).
fof(f1191,plain,
! [X0] :
( ~ sP5(X0)
| ( element(sK72(X0),powerset(powerset(succ(X0))))
& ! [X2] :
( ( subset(X2,sK73(X0,X2))
& in(sK73(X0,X2),sK72(X0))
& sK73(X0,X2) != X2 )
| ~ in(X2,sK72(X0)) )
& empty_set != sK72(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72,sK73]),skolemize(X1,sK72(X0)),skolemize(X3,sK73(X0,X2))],[f1190]) ).
fof(f1195,plain,
( sP6
| sP8
| sP7
| ! [X0] :
( ~ ordinal(X0)
| ~ in(X0,omega)
| ! [X1] :
( ~ element(X1,powerset(powerset(X0)))
| ? [X2] :
( ! [X3] :
( ~ subset(X2,X3)
| ~ in(X3,X1)
| X2 = X3 )
& in(X2,X1) )
| empty_set = X1 ) ) ),
inference(rectify,[],[f1086]) ).
fof(f1196,plain,
( sP6
| sP8
| sP7
| ! [X0] :
( ~ ordinal(X0)
| ~ in(X0,omega)
| ! [X1] :
( ~ element(X1,powerset(powerset(X0)))
| ( ! [X3] :
( ~ subset(sK76(X1),X3)
| ~ in(X3,X1)
| sK76(X1) = X3 )
& in(sK76(X1),X1) )
| empty_set = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(X2,sK76(X1))],[f1195]) ).
fof(f1197,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
( ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X3)
| ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X3) ) )
& relation(X3) ) ),
inference(nnf_transformation,[],[f593]) ).
fof(f1198,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
( ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X3)
| ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X3) ) )
& relation(X3) ) ),
inference(flattening,[],[f1197]) ).
fof(f1199,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ( ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),sK77(X0,X1,X2))
| ( in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
& in(X5,X0)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),sK77(X0,X1,X2)) ) )
& relation(sK77(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(X3,sK77(X0,X1,X2))],[f1198]) ).
fof(f1200,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2] :
? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ( ? [X5,X6] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X6,X8),X1) )
& in(X6,X7)
& X5 = X7 )
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X2)) ) )
& ( ! [X5,X6] :
( ! [X7] :
( ? [X8] :
( in(X8,X7)
& ~ in(ordered_pair(X6,X8),X1) )
| ~ in(X6,X7)
| X5 != X7 )
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X2))
| in(X4,X3) ) ) ),
inference(nnf_transformation,[],[f595]) ).
fof(f1201,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2] :
? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ( ? [X5,X6] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X6,X8),X1) )
& in(X6,X7)
& X5 = X7 )
& in(X5,X0)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X2)) ) )
& ( ! [X5,X6] :
( ! [X7] :
( ? [X8] :
( in(X8,X7)
& ~ in(ordered_pair(X6,X8),X1) )
| ~ in(X6,X7)
| X5 != X7 )
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X2))
| in(X4,X3) ) ) ),
inference(flattening,[],[f1200]) ).
fof(f1202,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2] :
? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ( ? [X9,X10] :
( ? [X11] :
( ! [X12] :
( ~ in(X12,X11)
| in(ordered_pair(X10,X12),X1) )
& in(X10,X11)
& X9 = X11 )
& in(X9,X0)
& ordered_pair(X9,X10) = X4 )
& in(X4,cartesian_product2(X0,X2)) ) )
& ( ! [X5,X6] :
( ! [X7] :
( ? [X8] :
( in(X8,X7)
& ~ in(ordered_pair(X6,X8),X1) )
| ~ in(X6,X7)
| X5 != X7 )
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X2))
| in(X4,X3) ) ) ),
inference(rectify,[],[f1201]) ).
fof(f1203,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2,X4] :
( ( ~ in(X4,sK78(X0,X1,X2))
| ( ! [X12] :
( ~ in(X12,sK82(X0,X1,X4))
| in(ordered_pair(sK81(X0,X1,X4),X12),X1) )
& in(sK81(X0,X1,X4),sK82(X0,X1,X4))
& sK80(X0,X1,X4) = sK82(X0,X1,X4)
& in(sK80(X0,X1,X4),X0)
& ordered_pair(sK80(X0,X1,X4),sK81(X0,X1,X4)) = X4
& in(X4,cartesian_product2(X0,X2)) ) )
& ( ! [X5,X6] :
( ! [X7] :
( ( in(sK79(X1,X6,X7),X7)
& ~ in(ordered_pair(X6,sK79(X1,X6,X7)),X1) )
| ~ in(X6,X7)
| X5 != X7 )
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X2))
| in(X4,sK78(X0,X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78,sK79,sK80,sK81,sK82]),skolemize(X3,sK78(X0,X1,X2)),skolemize(X8,sK79(X1,X6,X7)),skolemize(X9,sK80(X0,X1,X4)),skolemize(X10,sK81(X0,X1,X4)),skolemize(X11,sK82(X0,X1,X4))],[f1202]) ).
fof(f1204,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X4,X5] :
( X5 = singleton(X4)
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) )
& ( ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1))
| in(X3,X2) ) ),
inference(nnf_transformation,[],[f329]) ).
fof(f1205,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X4,X5] :
( X5 = singleton(X4)
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) )
& ( ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1))
| in(X3,X2) ) ),
inference(flattening,[],[f1204]) ).
fof(f1206,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X6,X7] :
( singleton(X6) = X7
& in(X6,X0)
& ordered_pair(X6,X7) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) )
& ( ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1))
| in(X3,X2) ) ),
inference(rectify,[],[f1205]) ).
fof(f1207,plain,
! [X0,X1,X3] :
( ( ~ in(X3,sK83(X0,X1))
| ( sK85(X0,X3) = singleton(sK84(X0,X3))
& in(sK84(X0,X3),X0)
& ordered_pair(sK84(X0,X3),sK85(X0,X3)) = X3
& in(X3,cartesian_product2(X0,X1)) ) )
& ( ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1))
| in(X3,sK83(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83,sK84,sK85]),skolemize(X2,sK83(X0,X1)),skolemize(X6,sK84(X0,X3)),skolemize(X7,sK85(X0,X3))],[f1206]) ).
fof(f1208,plain,
! [X0] :
( ~ sP10(X0)
| ? [X1] :
! [X2] :
( ( ~ in(X2,X1)
| sP9(X0,X2) )
& ( ~ sP9(X0,X2)
| in(X2,X1) ) ) ),
inference(nnf_transformation,[],[f1088]) ).
fof(f1209,plain,
! [X0] :
( ~ sP10(X0)
| ! [X2] :
( ( ~ in(X2,sK86(X0))
| sP9(X0,X2) )
& ( ~ sP9(X0,X2)
| in(X2,sK86(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(X1,sK86(X0))],[f1208]) ).
fof(f1214,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,X2) ) ) ),
inference(nnf_transformation,[],[f599]) ).
fof(f1215,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,X2) ) ) ),
inference(flattening,[],[f1214]) ).
fof(f1216,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,X2) ) ) ),
inference(rectify,[],[f1215]) ).
fof(f1217,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ! [X3] :
( ( ~ in(X3,sK91(X0,X1))
| ( subset(X1,X3)
& closed_subset(sK92(X0,X1,X3),X0)
& sK92(X0,X1,X3) = X3
& element(sK92(X0,X1,X3),powerset(the_carrier(X0)))
& in(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,sK91(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91,sK92]),skolemize(X2,sK91(X0,X1)),skolemize(X5,sK92(X0,X1,X3))],[f1216]) ).
fof(f1218,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
& ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,X2) ) ) ),
inference(nnf_transformation,[],[f601]) ).
fof(f1219,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
& ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,X2) ) ) ),
inference(flattening,[],[f1218]) ).
fof(f1220,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ! [X3] :
( ( ~ in(X3,sK93(X0,X1))
| ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
& ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,sK93(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(X2,sK93(X0,X1))],[f1219]) ).
fof(f1221,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X4] :
( X3 = set_difference(X4,singleton(X0))
& in(X4,X1) )
& in(X3,powerset(X0)) ) )
& ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| in(X3,X2) ) ) ),
inference(nnf_transformation,[],[f603]) ).
fof(f1222,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X4] :
( X3 = set_difference(X4,singleton(X0))
& in(X4,X1) )
& in(X3,powerset(X0)) ) )
& ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| in(X3,X2) ) ) ),
inference(flattening,[],[f1221]) ).
fof(f1223,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X5] :
( set_difference(X5,singleton(X0)) = X3
& in(X5,X1) )
& in(X3,powerset(X0)) ) )
& ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| in(X3,X2) ) ) ),
inference(rectify,[],[f1222]) ).
fof(f1224,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ! [X3] :
( ( ~ in(X3,sK94(X0,X1))
| ( set_difference(sK95(X0,X1,X3),singleton(X0)) = X3
& in(sK95(X0,X1,X3),X1)
& in(X3,powerset(X0)) ) )
& ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| in(X3,sK94(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94,sK95]),skolemize(X2,sK94(X0,X1)),skolemize(X5,sK95(X0,X1,X3))],[f1223]) ).
fof(f1225,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& X4 = ordered_pair(X5,X6) )
& in(X4,cartesian_product2(X0,X0)) ) )
& ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| in(X4,X3) ) ) ),
inference(nnf_transformation,[],[f605]) ).
fof(f1226,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& X4 = ordered_pair(X5,X6) )
& in(X4,cartesian_product2(X0,X0)) ) )
& ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| in(X4,X3) ) ) ),
inference(flattening,[],[f1225]) ).
fof(f1227,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ( ? [X7,X8] :
( in(ordered_pair(apply(X2,X7),apply(X2,X8)),X1)
& ordered_pair(X7,X8) = X4 )
& in(X4,cartesian_product2(X0,X0)) ) )
& ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| in(X4,X3) ) ) ),
inference(rectify,[],[f1226]) ).
fof(f1228,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ! [X4] :
( ( ~ in(X4,sK96(X0,X1,X2))
| ( in(ordered_pair(apply(X2,sK97(X1,X2,X4)),apply(X2,sK98(X1,X2,X4))),X1)
& ordered_pair(sK97(X1,X2,X4),sK98(X1,X2,X4)) = X4
& in(X4,cartesian_product2(X0,X0)) ) )
& ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| in(X4,sK96(X0,X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96,sK97,sK98]),skolemize(X3,sK96(X0,X1,X2)),skolemize(X7,sK97(X1,X2,X4)),skolemize(X8,sK98(X1,X2,X4))],[f1227]) ).
fof(f1229,plain,
! [X0] :
? [X1] :
! [X2] :
( ( ~ in(X2,X1)
| ( ordinal(X2)
& in(X2,X0) ) )
& ( ~ ordinal(X2)
| ~ in(X2,X0)
| in(X2,X1) ) ),
inference(nnf_transformation,[],[f335]) ).
fof(f1230,plain,
! [X0] :
? [X1] :
! [X2] :
( ( ~ in(X2,X1)
| ( ordinal(X2)
& in(X2,X0) ) )
& ( ~ ordinal(X2)
| ~ in(X2,X0)
| in(X2,X1) ) ),
inference(flattening,[],[f1229]) ).
fof(f1231,plain,
! [X0,X2] :
( ( ~ in(X2,sK99(X0))
| ( ordinal(X2)
& in(X2,X0) ) )
& ( ~ ordinal(X2)
| ~ in(X2,X0)
| in(X2,sK99(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(X1,sK99(X0))],[f1230]) ).
fof(f1232,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) )
& ( ~ in(relation_image(X2,X4),X1)
| ~ in(X4,powerset(relation_dom(X2)))
| in(X4,X3) ) ) ),
inference(nnf_transformation,[],[f607]) ).
fof(f1233,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) )
& ( ~ in(relation_image(X2,X4),X1)
| ~ in(X4,powerset(relation_dom(X2)))
| in(X4,X3) ) ) ),
inference(flattening,[],[f1232]) ).
fof(f1234,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ! [X4] :
( ( ~ in(X4,sK100(X1,X2))
| ( in(relation_image(X2,X4),X1)
& in(X4,powerset(relation_dom(X2))) ) )
& ( ~ in(relation_image(X2,X4),X1)
| ~ in(X4,powerset(relation_dom(X2)))
| in(X4,sK100(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(X3,sK100(X1,X2))],[f1233]) ).
fof(f1235,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X4] :
( in(X4,X0)
& X3 = X4
& ordinal(X4) )
& in(X3,succ(X1)) ) )
& ( ! [X4] :
( ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4) )
| ~ in(X3,succ(X1))
| in(X3,X2) ) ) ),
inference(nnf_transformation,[],[f608]) ).
fof(f1236,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X4] :
( in(X4,X0)
& X3 = X4
& ordinal(X4) )
& in(X3,succ(X1)) ) )
& ( ! [X4] :
( ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4) )
| ~ in(X3,succ(X1))
| in(X3,X2) ) ) ),
inference(flattening,[],[f1235]) ).
fof(f1237,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ( ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& in(X3,succ(X1)) ) )
& ( ! [X4] :
( ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4) )
| ~ in(X3,succ(X1))
| in(X3,X2) ) ) ),
inference(rectify,[],[f1236]) ).
fof(f1238,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ! [X3] :
( ( ~ in(X3,sK101(X0,X1))
| ( in(sK102(X0,X3),X0)
& sK102(X0,X3) = X3
& ordinal(sK102(X0,X3))
& in(X3,succ(X1)) ) )
& ( ! [X4] :
( ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4) )
| ~ in(X3,succ(X1))
| in(X3,sK101(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101,sK102]),skolemize(X2,sK101(X0,X1)),skolemize(X5,sK102(X0,X3))],[f1237]) ).
fof(f1239,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| ? [X13] :
( ! [X14] :
( ~ in(X14,X0)
| ? [X15] :
( ! [X16] :
( ~ in(X16,X15)
| in(ordered_pair(apply(X13,X14),X16),X1) )
& in(apply(X13,X14),X15)
& X14 = X15 ) )
& relation_dom(X13) = X0
& function(X13)
& relation(X13) ) ),
inference(nnf_transformation,[],[f1091]) ).
fof(f1240,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| ? [X2] :
( ! [X3] :
( ~ in(X3,X0)
| ? [X4] :
( ! [X5] :
( ~ in(X5,X4)
| in(ordered_pair(apply(X2,X3),X5),X1) )
& in(apply(X2,X3),X4)
& X3 = X4 ) )
& relation_dom(X2) = X0
& function(X2)
& relation(X2) ) ),
inference(rectify,[],[f1239]) ).
fof(f1241,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| ( ! [X3] :
( ~ in(X3,X0)
| ( ! [X5] :
( ~ in(X5,sK104(X0,X1,X3))
| in(ordered_pair(apply(sK103(X0,X1),X3),X5),X1) )
& in(apply(sK103(X0,X1),X3),sK104(X0,X1,X3))
& sK104(X0,X1,X3) = X3 ) )
& relation_dom(sK103(X0,X1)) = X0
& function(sK103(X0,X1))
& relation(sK103(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103,sK104]),skolemize(X2,sK103(X0,X1)),skolemize(X4,sK104(X0,X1,X3))],[f1240]) ).
fof(f1244,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ? [X2] :
( ! [X3,X4] :
( ? [X5] :
( in(X5,X4)
& ~ in(ordered_pair(X3,X5),X1) )
| ~ in(X3,X4)
| X2 != X4 )
& in(X2,X0) )
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(rectify,[],[f1092]) ).
fof(f1245,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ( ! [X3,X4] :
( ( in(sK111(X1,X3,X4),X4)
& ~ in(ordered_pair(X3,sK111(X1,X3,X4)),X1) )
| ~ in(X3,X4)
| sK110(X0,X1) != X4 )
& in(sK110(X0,X1),X0) )
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110,sK111]),skolemize(X2,sK110(X0,X1)),skolemize(X5,sK111(X1,X3,X4))],[f1244]) ).
fof(f1248,plain,
! [X0] :
( ? [X3] :
( ! [X4] : singleton(X3) != X4
& in(X3,X0) )
| sP13(X0)
| ? [X1] :
( ! [X2] :
( ~ in(X2,X0)
| singleton(X2) = apply(X1,X2) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ) ),
inference(rectify,[],[f1094]) ).
fof(f1249,plain,
! [X0] :
( ( ! [X4] : singleton(sK116(X0)) != X4
& in(sK116(X0),X0) )
| sP13(X0)
| ( ! [X2] :
( ~ in(X2,X0)
| singleton(X2) = apply(sK115(X0),X2) )
& relation_dom(sK115(X0)) = X0
& function(sK115(X0))
& relation(sK115(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115,sK116]),skolemize(X1,sK115(X0)),skolemize(X3,sK116(X0))],[f1248]) ).
fof(f1250,plain,
( ~ sP15
| ? [X0] :
( ordinal(X0)
& ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| ~ in(X1,omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(X1)))
| ? [X3] :
( ! [X4] :
( ~ subset(X3,X4)
| ~ in(X4,X2)
| X4 = X3 )
& in(X3,X2) )
| empty_set = X2 ) )
& in(X0,omega)
& sP14(X0) ) ),
inference(nnf_transformation,[],[f1096]) ).
fof(f1251,plain,
( ~ sP15
| ( ordinal(sK117)
& ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,sK117)
| ~ in(X1,omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(X1)))
| ( ! [X4] :
( ~ subset(sK118(X2),X4)
| ~ in(X4,X2)
| sK118(X2) = X4 )
& in(sK118(X2),X2) )
| empty_set = X2 ) )
& in(sK117,omega)
& sP14(sK117) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117,sK118]),skolemize(X0,sK117),skolemize(X3,sK118(X2))],[f1250]) ).
fof(f1255,plain,
( sP15
| ! [X0] :
( ~ ordinal(X0)
| ~ in(X0,omega)
| ! [X1] :
( ~ element(X1,powerset(powerset(X0)))
| ? [X2] :
( ! [X3] :
( ~ subset(X2,X3)
| ~ in(X3,X1)
| X2 = X3 )
& in(X2,X1) )
| empty_set = X1 ) ) ),
inference(rectify,[],[f1097]) ).
fof(f1256,plain,
( sP15
| ! [X0] :
( ~ ordinal(X0)
| ~ in(X0,omega)
| ! [X1] :
( ~ element(X1,powerset(powerset(X0)))
| ( ! [X3] :
( ~ subset(sK121(X1),X3)
| ~ in(X3,X1)
| sK121(X1) = X3 )
& in(sK121(X1),X1) )
| empty_set = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(X2,sK121(X1))],[f1255]) ).
fof(f1257,plain,
! [X0] :
( ! [X2] :
( ~ in(X2,X0)
| singleton(X2) = apply(sK122(X0),X2) )
& relation_dom(sK122(X0)) = X0
& function(sK122(X0))
& relation(sK122(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(X1,sK122(X0))],[f615]) ).
fof(f1258,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
( ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( ( ~ in(X3,X2)
| ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X4 = X3
& element(X4,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| in(X3,X2) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(nnf_transformation,[],[f617]) ).
fof(f1259,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
( ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( ( ~ in(X3,X2)
| ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| in(X3,X2) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(rectify,[],[f1258]) ).
fof(f1260,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ( ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( ( ~ in(X3,sK123(X0,X1))
| ( subset(X1,X3)
& closed_subset(sK124(X0,X1,X3),X0)
& sK124(X0,X1,X3) = X3
& element(sK124(X0,X1,X3),powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| in(X3,sK123(X0,X1)) ) ) )
& element(sK123(X0,X1),powerset(powerset(the_carrier(X0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123,sK124]),skolemize(X2,sK123(X0,X1)),skolemize(X5,sK124(X0,X1,X3))],[f1259]) ).
fof(f1261,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2] :
( ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( ( ~ in(X3,X2)
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
& ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| in(X3,X2) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(nnf_transformation,[],[f619]) ).
fof(f1262,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ( ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( ( ~ in(X3,sK125(X0,X1))
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
& ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| in(X3,sK125(X0,X1)) ) ) )
& element(sK125(X0,X1),powerset(powerset(the_carrier(X0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(X2,sK125(X0,X1))],[f1261]) ).
fof(f1263,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f346]) ).
fof(f1264,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f1263]) ).
fof(f1265,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) ) ),
inference(nnf_transformation,[],[f621]) ).
fof(f1266,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) ) ),
inference(flattening,[],[f1265]) ).
fof(f1267,plain,
! [X0] :
( ! [X5] :
( in(X5,sK126(X0))
| are_equipotent(X5,sK126(X0))
| ~ subset(X5,sK126(X0)) )
& ! [X4] :
( ~ in(X4,sK126(X0))
| in(powerset(X4),sK126(X0)) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,sK126(X0))
| in(X3,sK126(X0)) )
& in(X0,sK126(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(X1,sK126(X0))],[f633]) ).
fof(f1268,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ? [X3] :
( in(X3,X1)
& in(ordered_pair(X3,X0),X2)
& in(X3,relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f637]) ).
fof(f1269,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X0),X2)
& in(X4,relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(rectify,[],[f1268]) ).
fof(f1270,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ( in(sK127(X0,X1,X2),X1)
& in(ordered_pair(sK127(X0,X1,X2),X0),X2)
& in(sK127(X0,X1,X2),relation_dom(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,relation_dom(X2)) )
| in(X0,relation_image(X2,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(X4,sK127(X0,X1,X2))],[f1269]) ).
fof(f1271,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_inverse_image(X2,X1))
| ? [X3] :
( in(X3,X1)
& in(ordered_pair(X0,X3),X2)
& in(X3,relation_rng(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f652]) ).
fof(f1272,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_inverse_image(X2,X1))
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X0,X4),X2)
& in(X4,relation_rng(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(rectify,[],[f1271]) ).
fof(f1273,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_inverse_image(X2,X1))
| ( in(sK128(X0,X1,X2),X1)
& in(ordered_pair(X0,sK128(X0,X1,X2)),X2)
& in(sK128(X0,X1,X2),relation_rng(X2)) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,relation_rng(X2)) )
| in(X0,relation_inverse_image(X2,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(X4,sK128(X0,X1,X2))],[f1272]) ).
fof(f1274,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(nnf_transformation,[],[f656]) ).
fof(f1275,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_restriction(X2,X1))
| ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
& ( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ) ) ),
inference(flattening,[],[f1274]) ).
fof(f1276,plain,
! [X0] :
( ~ finite(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(X0)))
| ( ! [X3] :
( ~ subset(sK129(X1),X3)
| ~ in(X3,X1)
| sK129(X1) = X3 )
& in(sK129(X1),X1) )
| empty_set = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(X2,sK129(X1))],[f666]) ).
fof(f1277,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ) ) ) ),
inference(nnf_transformation,[],[f678]) ).
fof(f1278,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
& ( ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ) ) ) ),
inference(flattening,[],[f1277]) ).
fof(f1279,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X1,X0)
| ( ( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) )
| relation_dom_as_subset(X1,X0,X2) = X1 )
& ( relation_dom_as_subset(X1,X0,X2) != X1
| ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) ) ) ) ),
inference(nnf_transformation,[],[f688]) ).
fof(f1280,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X1,X0)
| ( ( ? [X5] :
( ! [X6] : ~ in(ordered_pair(X5,X6),X2)
& in(X5,X1) )
| relation_dom_as_subset(X1,X0,X2) = X1 )
& ( relation_dom_as_subset(X1,X0,X2) != X1
| ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) ) ) ) ),
inference(rectify,[],[f1279]) ).
fof(f1281,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X1,X0)
| ( ( ( ! [X6] : ~ in(ordered_pair(sK131(X1,X2),X6),X2)
& in(sK131(X1,X2),X1) )
| relation_dom_as_subset(X1,X0,X2) = X1 )
& ( relation_dom_as_subset(X1,X0,X2) != X1
| ! [X3] :
( in(ordered_pair(X3,sK130(X2,X3)),X2)
| ~ in(X3,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130,sK131]),skolemize(X4,sK130(X2,X3)),skolemize(X5,sK131(X1,X2))],[f1280]) ).
fof(f1282,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( ( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X4,X3),X2)
& in(X3,X1) )
| relation_rng_as_subset(X0,X1,X2) = X1 )
& ( relation_rng_as_subset(X0,X1,X2) != X1
| ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X2)
| ~ in(X3,X1) ) ) ) ),
inference(nnf_transformation,[],[f695]) ).
fof(f1283,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( ( ? [X5] :
( ! [X6] : ~ in(ordered_pair(X6,X5),X2)
& in(X5,X1) )
| relation_rng_as_subset(X0,X1,X2) = X1 )
& ( relation_rng_as_subset(X0,X1,X2) != X1
| ! [X3] :
( ? [X4] : in(ordered_pair(X4,X3),X2)
| ~ in(X3,X1) ) ) ) ),
inference(rectify,[],[f1282]) ).
fof(f1284,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( ( ( ! [X6] : ~ in(ordered_pair(X6,sK133(X1,X2)),X2)
& in(sK133(X1,X2),X1) )
| relation_rng_as_subset(X0,X1,X2) = X1 )
& ( relation_rng_as_subset(X0,X1,X2) != X1
| ! [X3] :
( in(ordered_pair(sK132(X2,X3),X3),X2)
| ~ in(X3,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132,sK133]),skolemize(X4,sK132(X2,X3)),skolemize(X5,sK133(X1,X2))],[f1283]) ).
fof(f1285,plain,
! [X0] :
( well_orders(sK134(X0),X0)
& relation(sK134(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(X1,sK134(X0))],[f414]) ).
fof(f1286,plain,
! [X0] :
( empty(X0)
| ( function(sK136(X0))
& relation(sK136(X0))
& ! [X3] :
( ~ in(X3,X0)
| in(apply(sK136(X0),X3),X3) )
& relation_dom(sK136(X0)) = X0 )
| ( empty_set = sK135(X0)
& in(sK135(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135,sK136]),skolemize(X1,sK135(X0)),skolemize(X2,sK136(X0))],[f712]) ).
fof(f1287,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ( closed_subset(X1,X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( ~ closed_subset(X1,X0)
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(nnf_transformation,[],[f714]) ).
fof(f1288,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ( closed_subset(X1,X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( ~ closed_subset(X1,X0)
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(flattening,[],[f1287]) ).
fof(f1289,plain,
( top_str(sK137)
& element(sK138,powerset(the_carrier(sK137)))
& ( closed_subset(sK138,sK137)
| open_subset(subset_complement(the_carrier(sK137),sK138),sK137) )
& ( ~ closed_subset(sK138,sK137)
| ~ open_subset(subset_complement(the_carrier(sK137),sK138),sK137) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137,sK138]),skolemize(X0,sK137),skolemize(X1,sK138)],[f1288]) ).
fof(f1290,plain,
! [X0] :
( ( in(sK139(X0),X0)
& ( ~ subset(sK139(X0),X0)
| ~ ordinal(sK139(X0)) ) )
| ordinal(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(X1,sK139(X0))],[f717]) ).
fof(f1291,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ( ordinal(sK140(X0))
& ! [X3] :
( ~ ordinal(X3)
| ~ in(X3,X0)
| ordinal_subset(sK140(X0),X3) )
& in(sK140(X0),X0) )
| empty_set = X0
| ~ subset(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(X2,sK140(X0))],[f721]) ).
fof(f1292,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| ( ( ~ in(X0,X1)
| ordinal_subset(succ(X0),X1) )
& ( ~ ordinal_subset(succ(X0),X1)
| in(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f724]) ).
fof(f1293,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f728]) ).
fof(f1294,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f1293]) ).
fof(f1295,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f1294]) ).
fof(f1296,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK141(X0,X1),X0)
& sK141(X0,X1) != apply(X1,sK141(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(X2,sK141(X0,X1))],[f1295]) ).
fof(f1297,plain,
! [X0,X1] :
( ( empty_set != set_difference(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f437]) ).
fof(f1298,plain,
! [X0,X1] :
( ( ~ subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f438]) ).
fof(f1299,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f439]) ).
fof(f1300,plain,
! [X0,X1,X2] :
( ( ~ subset(unordered_pair(X0,X1),X2)
| ( in(X1,X2)
& in(X0,X2) ) )
& ( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f1299]) ).
fof(f1301,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f442]) ).
fof(f1302,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f1301]) ).
fof(f1303,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) ) )
& ( ( in(sK142(X0,X1),X1)
& in(sK142(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(X2,sK142(X0,X1))],[f734]) ).
fof(f1304,plain,
! [X0] :
( ~ ordinal(X0)
| ( ( ~ being_limit_ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0) ) )
& ( ? [X1] :
( ordinal(X1)
& in(X1,X0)
& ~ in(succ(X1),X0) )
| being_limit_ordinal(X0) ) ) ),
inference(nnf_transformation,[],[f737]) ).
fof(f1305,plain,
! [X0] :
( ~ ordinal(X0)
| ( ( ~ being_limit_ordinal(X0)
| ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| in(succ(X2),X0) ) )
& ( ? [X1] :
( ordinal(X1)
& in(X1,X0)
& ~ in(succ(X1),X0) )
| being_limit_ordinal(X0) ) ) ),
inference(rectify,[],[f1304]) ).
fof(f1306,plain,
! [X0] :
( ~ ordinal(X0)
| ( ( ~ being_limit_ordinal(X0)
| ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| in(succ(X2),X0) ) )
& ( ( ordinal(sK143(X0))
& in(sK143(X0),X0)
& ~ in(succ(sK143(X0)),X0) )
| being_limit_ordinal(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(X1,sK143(X0))],[f1305]) ).
fof(f1307,plain,
! [X0] :
( ~ ordinal(X0)
| ( ( ~ being_limit_ordinal(X0)
| ! [X2] :
( succ(X2) != X0
| ~ ordinal(X2) ) )
& ( ( ordinal(sK144(X0))
& succ(sK144(X0)) = X0 )
| being_limit_ordinal(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(X1,sK144(X0))],[f738]) ).
fof(f1308,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,powerset(X0))
| ( ( ~ disjoint(X1,X2)
| subset(X1,subset_complement(X0,X2)) )
& ( ~ subset(X1,subset_complement(X0,X2))
| disjoint(X1,X2) ) ) ) ),
inference(nnf_transformation,[],[f739]) ).
fof(f1309,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( element(sK145(X0,X1),powerset(the_carrier(X0)))
& in(sK145(X0,X1),X1)
& ~ closed_subset(sK145(X0,X1),X0) )
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(X2,sK145(X0,X1))],[f741]) ).
fof(f1310,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& subset(X1,X3)
& closed_subset(X3,X0)
& ~ in(X2,X3) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(nnf_transformation,[],[f744]) ).
fof(f1311,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| in(X2,X4) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& subset(X1,X3)
& closed_subset(X3,X0)
& ~ in(X2,X3) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(rectify,[],[f1310]) ).
fof(f1312,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| in(X2,X4) ) )
& ( ( element(sK146(X0,X1,X2),powerset(the_carrier(X0)))
& subset(X1,sK146(X0,X1,X2))
& closed_subset(sK146(X0,X1,X2),X0)
& ~ in(X2,sK146(X0,X1,X2)) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(X3,sK146(X0,X1,X2))],[f1311]) ).
fof(f1313,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| empty_set = X1
| ! [X4] :
( ( ~ in(X4,relation_inverse_image(X3,X2))
| ( in(apply(X3,X4),X2)
& in(X4,X0) ) )
& ( ~ in(apply(X3,X4),X2)
| ~ in(X4,X0)
| in(X4,relation_inverse_image(X3,X2)) ) ) ),
inference(nnf_transformation,[],[f748]) ).
fof(f1314,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| empty_set = X1
| ! [X4] :
( ( ~ in(X4,relation_inverse_image(X3,X2))
| ( in(apply(X3,X4),X2)
& in(X4,X0) ) )
& ( ~ in(apply(X3,X4),X2)
| ~ in(X4,X0)
| in(X4,relation_inverse_image(X3,X2)) ) ) ),
inference(flattening,[],[f1313]) ).
fof(f1315,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( ( ~ in(X3,X2)
| ( subset(X1,X3)
& closed_subset(X3,X0) ) )
& ( ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X3,X2) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ) ),
inference(nnf_transformation,[],[f750]) ).
fof(f1316,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( ( ~ in(X3,X2)
| ( subset(X1,X3)
& closed_subset(X3,X0) ) )
& ( ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X3,X2) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ) ),
inference(flattening,[],[f1315]) ).
fof(f1317,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),sK147(X0,X1))
& ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ( ( ~ in(X3,sK147(X0,X1))
| ( subset(X1,X3)
& closed_subset(X3,X0) ) )
& ( ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X3,sK147(X0,X1)) ) ) )
& element(sK147(X0,X1),powerset(powerset(the_carrier(X0)))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(X2,sK147(X0,X1))],[f1316]) ).
fof(f1318,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( in(sK148(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(X2,sK148(X0,X1))],[f766]) ).
fof(f1322,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X2,X3] :
( sP16(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP16(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_dom(X1) != relation_rng(X0)
| X1 = function_inverse(X0) ) ) ) ),
inference(nnf_transformation,[],[f1099]) ).
fof(f1323,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X2,X3] :
( sP16(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP16(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_dom(X1) != relation_rng(X0)
| X1 = function_inverse(X0) ) ) ) ),
inference(flattening,[],[f1322]) ).
fof(f1324,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X4,X5] :
( sP16(X0,X4,X5,X1)
& ( apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| ( apply(X0,X5) = X4
& in(X5,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP16(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_dom(X1) != relation_rng(X0)
| X1 = function_inverse(X0) ) ) ) ),
inference(rectify,[],[f1323]) ).
fof(f1325,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X4,X5] :
( sP16(X0,X4,X5,X1)
& ( apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| ( apply(X0,X5) = X4
& in(X5,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ~ sP16(X0,sK149(X0,X1),sK150(X0,X1),X1)
| ( sK150(X0,X1) = apply(X1,sK149(X0,X1))
& in(sK149(X0,X1),relation_rng(X0))
& ( sK149(X0,X1) != apply(X0,sK150(X0,X1))
| ~ in(sK150(X0,X1),relation_dom(X0)) ) )
| relation_dom(X1) != relation_rng(X0)
| X1 = function_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149,sK150]),skolemize(X2,sK149(X0,X1)),skolemize(X3,sK150(X0,X1))],[f1324]) ).
fof(f1326,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK151(X0),sK152(X0)),X0)
| X0 = empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151,sK152]),skolemize(X1,sK151(X0)),skolemize(X2,sK152(X0))],[f782]) ).
fof(f1327,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| is_well_founded_in(X0,relation_field(X0)) )
& ( ~ is_well_founded_in(X0,relation_field(X0))
| well_founded_relation(X0) ) ) ),
inference(nnf_transformation,[],[f785]) ).
fof(f1328,plain,
! [X0] :
( ~ relation(X0)
| ( ( relation_dom(X0) != empty_set
| relation_rng(X0) = empty_set )
& ( empty_set != relation_rng(X0)
| relation_dom(X0) = empty_set ) ) ),
inference(nnf_transformation,[],[f793]) ).
fof(f1329,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) != X0
| ~ in(X1,X0) )
& ( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ) ),
inference(nnf_transformation,[],[f491]) ).
fof(f1330,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X2,X3) != apply(X1,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f795]) ).
fof(f1331,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X2,X3) != apply(X1,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(flattening,[],[f1330]) ).
fof(f1332,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X2,X3) != apply(X1,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(rectify,[],[f1331]) ).
fof(f1333,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X2,X4) = apply(X1,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ( in(sK153(X1,X2),relation_dom(X1))
& apply(X2,sK153(X1,X2)) != apply(X1,sK153(X1,X2)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(X3,sK153(X1,X2))],[f1332]) ).
fof(f1334,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| ( ( ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) ) ),
inference(nnf_transformation,[],[f804]) ).
fof(f1335,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| ( ( ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) ) ),
inference(flattening,[],[f1334]) ).
fof(f1336,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 )
& ( set_difference(X0,X1) != X0
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f507]) ).
fof(f1337,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) ) ),
inference(nnf_transformation,[],[f806]) ).
fof(f1338,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) ) ),
inference(flattening,[],[f1337]) ).
fof(f1339,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(ordered_pair(X0,X1),X2)
| ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) )
& ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(ordered_pair(X0,X1),X2) ) ) ),
inference(nnf_transformation,[],[f809]) ).
fof(f1340,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( ~ in(ordered_pair(X0,X1),X2)
| ( X1 = apply(X2,X0)
& in(X0,relation_dom(X2)) ) )
& ( apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(ordered_pair(X0,X1),X2) ) ) ),
inference(flattening,[],[f1339]) ).
fof(f1341,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_orders(X0,relation_field(X0))
| well_ordering(X0) )
& ( ~ well_ordering(X0)
| well_orders(X0,relation_field(X0)) ) ) ),
inference(nnf_transformation,[],[f810]) ).
fof(f1342,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ in(X3,sK154(X1))
| ~ in(X3,X1) )
& in(sK154(X1),X1) )
| ~ in(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(X2,sK154(X1))],[f821]) ).
fof(f1343,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f822]) ).
fof(f1344,plain,
! [X0,X1] :
( ( ( in(sK155(X0,X1),X0)
| in(sK155(X0,X1),X1) )
& ( ~ in(sK155(X0,X1),X0)
| ~ in(sK155(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(X2,sK155(X0,X1))],[f1343]) ).
fof(f1345,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| ? [X2,X3,X4] :
( sP17(X2,X4,X1)
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 ) ),
inference(nnf_transformation,[],[f1101]) ).
fof(f1346,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| ( sP17(sK156(X0,X1),sK158(X0,X1),X1)
& in(sK156(X0,X1),X0)
& ! [X6] :
( ~ in(X6,sK159(X0,X1))
| in(ordered_pair(sK157(X0,X1),X6),X1) )
& in(sK157(X0,X1),sK159(X0,X1))
& sK156(X0,X1) = sK159(X0,X1)
& in(sK156(X0,X1),X0)
& sK157(X0,X1) != sK158(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156,sK157,sK158,sK159]),skolemize(X2,sK156(X0,X1)),skolemize(X3,sK157(X0,X1)),skolemize(X4,sK158(X0,X1)),skolemize(X5,sK159(X0,X1))],[f1345]) ).
fof(f1350,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ? [X9] :
! [X10] :
( ( ~ in(X10,X9)
| ? [X11] :
( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X10,X13),X1) )
& in(X10,X12)
& X11 = X12 )
& in(X11,X0)
& in(X11,X0) ) )
& ( ! [X11] :
( ! [X12] :
( ? [X13] :
( in(X13,X12)
& ~ in(ordered_pair(X10,X13),X1) )
| ~ in(X10,X12)
| X11 != X12 )
| ~ in(X11,X0)
| ~ in(X11,X0) )
| in(X10,X9) ) ) ),
inference(nnf_transformation,[],[f1102]) ).
fof(f1351,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ? [X7] :
( ? [X8] :
( ! [X9] :
( ~ in(X9,X8)
| in(ordered_pair(X3,X9),X1) )
& in(X3,X8)
& X7 = X8 )
& in(X7,X0)
& in(X7,X0) ) )
& ( ! [X4] :
( ! [X5] :
( ? [X6] :
( in(X6,X5)
& ~ in(ordered_pair(X3,X6),X1) )
| ~ in(X3,X5)
| X4 != X5 )
| ~ in(X4,X0)
| ~ in(X4,X0) )
| in(X3,X2) ) ) ),
inference(rectify,[],[f1350]) ).
fof(f1352,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ! [X3] :
( ( ~ in(X3,sK161(X0,X1))
| ( ! [X9] :
( ~ in(X9,sK164(X0,X1,X3))
| in(ordered_pair(X3,X9),X1) )
& in(X3,sK164(X0,X1,X3))
& sK163(X0,X1,X3) = sK164(X0,X1,X3)
& in(sK163(X0,X1,X3),X0)
& in(sK163(X0,X1,X3),X0) ) )
& ( ! [X4] :
( ! [X5] :
( ( in(sK162(X1,X3,X5),X5)
& ~ in(ordered_pair(X3,sK162(X1,X3,X5)),X1) )
| ~ in(X3,X5)
| X4 != X5 )
| ~ in(X4,X0)
| ~ in(X4,X0) )
| in(X3,sK161(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161,sK162,sK163,sK164]),skolemize(X2,sK161(X0,X1)),skolemize(X6,sK162(X1,X3,X5)),skolemize(X7,sK163(X0,X1,X3)),skolemize(X8,sK164(X0,X1,X3))],[f1351]) ).
fof(f1353,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f826]) ).
fof(f1354,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f1353]) ).
fof(f1355,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK167(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK165(X0,X1),X1)
| in(ordered_pair(sK166(X0,X1),sK165(X0,X1)),X0) )
& ( ~ in(sK165(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK165(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK165,sK166,sK167]),skolemize(X2,sK165(X0,X1)),skolemize(X4,sK166(X0,X1)),skolemize(X7,sK167(X0,X5))],[f1354]) ).
fof(f1356,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X2,X3),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(nnf_transformation,[],[f827]) ).
fof(f1357,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X5,X7),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X2,X4),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(rectify,[],[f1356]) ).
fof(f1358,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK170(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK168(X0,X1),X1)
| in(ordered_pair(sK168(X0,X1),sK169(X0,X1)),X0) )
& ( ~ in(sK168(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK168(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK168,sK169,sK170]),skolemize(X2,sK168(X0,X1)),skolemize(X4,sK169(X0,X1)),skolemize(X7,sK170(X0,X5))],[f1357]) ).
fof(f1359,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( ~ subset(X0,X1)
| ! [X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) ) )
& ( ? [X2,X3] :
( in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X2,X3),X1) )
| subset(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f828]) ).
fof(f1360,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( ~ subset(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) ) )
& ( ? [X2,X3] :
( in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X2,X3),X1) )
| subset(X0,X1) ) ) ) ),
inference(rectify,[],[f1359]) ).
fof(f1361,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( ~ subset(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) ) )
& ( ( in(ordered_pair(sK171(X0,X1),sK172(X0,X1)),X0)
& ~ in(ordered_pair(sK171(X0,X1),sK172(X0,X1)),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK171,sK172]),skolemize(X2,sK171(X0,X1)),skolemize(X3,sK172(X0,X1))],[f1360]) ).
fof(f1362,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| X0 = X1 ) ) ) ),
inference(nnf_transformation,[],[f829]) ).
fof(f1363,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) )
& ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X4,X5),X0) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| X0 = X1 ) ) ) ),
inference(rectify,[],[f1362]) ).
fof(f1364,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) )
& ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X4,X5),X0) ) ) )
& ( ( ( in(ordered_pair(sK173(X0,X1),sK174(X0,X1)),X0)
| in(ordered_pair(sK173(X0,X1),sK174(X0,X1)),X1) )
& ( ~ in(ordered_pair(sK173(X0,X1),sK174(X0,X1)),X0)
| ~ in(ordered_pair(sK173(X0,X1),sK174(X0,X1)),X1) ) )
| X0 = X1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK173,sK174]),skolemize(X2,sK173(X0,X1)),skolemize(X3,sK174(X0,X1))],[f1363]) ).
fof(f1365,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) )
& ( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
| relation(X0) ) ),
inference(nnf_transformation,[],[f830]) ).
fof(f1366,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) ) )
& ( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
| relation(X0) ) ),
inference(rectify,[],[f1365]) ).
fof(f1367,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X4] :
( ordered_pair(sK176(X4),sK177(X4)) = X4
| ~ in(X4,X0) ) )
& ( ( ! [X2,X3] : ordered_pair(X2,X3) != sK175(X0)
& in(sK175(X0),X0) )
| relation(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175,sK176,sK177]),skolemize(X1,sK175(X0)),skolemize(X5,sK176(X4)),skolemize(X6,sK177(X4))],[f1366]) ).
fof(f1368,plain,
! [X0] :
( ( ~ function(X0)
| ! [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X2 = X3 ) )
& ( ? [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0)
& X2 != X3 )
| function(X0) ) ),
inference(nnf_transformation,[],[f832]) ).
fof(f1369,plain,
! [X0] :
( ( ~ function(X0)
| ! [X4,X5,X6] :
( ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| X5 = X6 ) )
& ( ? [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0)
& X2 != X3 )
| function(X0) ) ),
inference(rectify,[],[f1368]) ).
fof(f1370,plain,
! [X0] :
( ( ~ function(X0)
| ! [X4,X5,X6] :
( ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| X5 = X6 ) )
& ( ( in(ordered_pair(sK178(X0),sK180(X0)),X0)
& in(ordered_pair(sK178(X0),sK179(X0)),X0)
& sK179(X0) != sK180(X0) )
| function(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK178,sK179,sK180]),skolemize(X1,sK178(X0)),skolemize(X2,sK179(X0)),skolemize(X3,sK180(X0))],[f1369]) ).
fof(f1371,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_ordering(X0)
| ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
& ( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ) ) ),
inference(nnf_transformation,[],[f834]) ).
fof(f1372,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_ordering(X0)
| ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
& ( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ) ) ),
inference(flattening,[],[f1371]) ).
fof(f1373,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f1374,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f1373]) ).
fof(f1375,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK181(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(X1,sK181(X0))],[f1374]) ).
fof(f1376,plain,
! [X0] :
( ~ sP20(X0)
| ? [X2,X3,X4] :
( sP19(X4,X0)
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3
& X3 != X4 ) ),
inference(nnf_transformation,[],[f1104]) ).
fof(f1377,plain,
! [X0] :
( ~ sP20(X0)
| ? [X1,X2,X3] :
( sP19(X3,X0)
& X1 = X3
& ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X2 )
& X1 = X2
& X2 != X3 ) ),
inference(rectify,[],[f1376]) ).
fof(f1378,plain,
! [X0] :
( ~ sP20(X0)
| ( sP19(sK184(X0),X0)
& sK182(X0) = sK184(X0)
& sK186(X0) = singleton(sK185(X0))
& in(sK185(X0),X0)
& sK183(X0) = ordered_pair(sK185(X0),sK186(X0))
& sK182(X0) = sK183(X0)
& sK183(X0) != sK184(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK182,sK183,sK184,sK185,sK186]),skolemize(X1,sK182(X0)),skolemize(X2,sK183(X0)),skolemize(X3,sK184(X0)),skolemize(X4,sK185(X0)),skolemize(X5,sK186(X0))],[f1377]) ).
fof(f1382,plain,
! [X0,X1] :
( sP20(X0)
| ? [X9] :
! [X10] :
( ( ~ in(X10,X9)
| ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) )
& ( ! [X11] :
( ! [X12,X13] :
( singleton(X12) != X13
| ~ in(X12,X0)
| ordered_pair(X12,X13) != X10 )
| X10 != X11
| ~ in(X11,cartesian_product2(X0,X1)) )
| in(X10,X9) ) ) ),
inference(nnf_transformation,[],[f1105]) ).
fof(f1383,plain,
! [X0,X1] :
( sP20(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ? [X7] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& X3 = X7
& in(X7,cartesian_product2(X0,X1)) ) )
& ( ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) )
| in(X3,X2) ) ) ),
inference(rectify,[],[f1382]) ).
fof(f1384,plain,
! [X0,X1] :
( sP20(X0)
| ! [X3] :
( ( ~ in(X3,sK189(X0,X1))
| ( sK192(X0,X3) = singleton(sK191(X0,X3))
& in(sK191(X0,X3),X0)
& ordered_pair(sK191(X0,X3),sK192(X0,X3)) = X3
& sK190(X0,X1,X3) = X3
& in(sK190(X0,X1,X3),cartesian_product2(X0,X1)) ) )
& ( ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) )
| in(X3,sK189(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK189,sK190,sK191,sK192]),skolemize(X2,sK189(X0,X1)),skolemize(X7,sK190(X0,X1,X3)),skolemize(X8,sK191(X0,X3)),skolemize(X9,sK192(X0,X3))],[f1383]) ).
fof(f1387,plain,
! [X0] :
( sP21(X0)
| ? [X4] :
! [X5] :
( ( ~ in(X5,X4)
| ? [X6] :
( singleton(X6) = X5
& in(X6,X0)
& in(X6,X0) ) )
& ( ! [X6] :
( singleton(X6) != X5
| ~ in(X6,X0)
| ~ in(X6,X0) )
| in(X5,X4) ) ) ),
inference(nnf_transformation,[],[f1107]) ).
fof(f1388,plain,
! [X0] :
( sP21(X0)
| ? [X1] :
! [X2] :
( ( ~ in(X2,X1)
| ? [X4] :
( singleton(X4) = X2
& in(X4,X0)
& in(X4,X0) ) )
& ( ! [X3] :
( singleton(X3) != X2
| ~ in(X3,X0)
| ~ in(X3,X0) )
| in(X2,X1) ) ) ),
inference(rectify,[],[f1387]) ).
fof(f1389,plain,
! [X0] :
( sP21(X0)
| ! [X2] :
( ( ~ in(X2,sK196(X0))
| ( singleton(sK197(X0,X2)) = X2
& in(sK197(X0,X2),X0)
& in(sK197(X0,X2),X0) ) )
& ( ! [X3] :
( singleton(X3) != X2
| ~ in(X3,X0)
| ~ in(X3,X0) )
| in(X2,sK196(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK196,sK197]),skolemize(X1,sK196(X0)),skolemize(X4,sK197(X0,X2))],[f1388]) ).
fof(f1390,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f1391,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f1390]) ).
fof(f1392,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK198(X0,X1),X1)
| sK198(X0,X1) = X0 )
& ( ~ in(sK198(X0,X1),X1)
| sK198(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(X2,sK198(X0,X1))],[f1391]) ).
fof(f1393,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f1394,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f1393]) ).
fof(f1395,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f1394]) ).
fof(f1396,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK199(X0,X1,X2),X2)
| in(sK199(X0,X1,X2),X1)
| in(sK199(X0,X1,X2),X0) )
& ( ~ in(sK199(X0,X1,X2),X2)
| ( ~ in(sK199(X0,X1,X2),X1)
& ~ in(sK199(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(X3,sK199(X0,X1,X2))],[f1395]) ).
fof(f1397,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set )
& ( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f108]) ).
fof(f1398,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f853]) ).
fof(f1399,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f1398]) ).
fof(f1400,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X1)
& in(X4,X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f1399]) ).
fof(f1401,plain,
! [X0,X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_rng_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X1)
& in(X6,X0) ) )
& ( ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),X2)
| ( in(ordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),X1)
& in(sK201(X0,X1,X2),X0) ) )
& ( ~ in(ordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),X1)
| ~ in(sK201(X0,X1,X2),X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200,sK201]),skolemize(X3,sK200(X0,X1,X2)),skolemize(X4,sK201(X0,X1,X2))],[f1400]) ).
fof(f1402,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f445]) ).
fof(f1403,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f854]) ).
fof(f1404,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f1403]) ).
fof(f1405,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK202(X0,X1),X0)
& ~ in(sK202(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(X2,sK202(X0,X1))],[f1404]) ).
fof(f1406,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| subset(X2,X0) )
& ( ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f1407,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(rectify,[],[f1406]) ).
fof(f1408,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK203(X0,X1),X1)
| subset(sK203(X0,X1),X0) )
& ( ~ in(sK203(X0,X1),X1)
| ~ subset(sK203(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(X2,sK203(X0,X1))],[f1407]) ).
fof(f1409,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f1410,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f1409]) ).
fof(f1411,plain,
! [X0,X1] :
( ( ~ equipotent(X0,X1)
| ? [X2] :
( relation_rng(X2) = X1
& relation_dom(X2) = X0
& one_to_one(X2)
& function(X2)
& relation(X2) ) )
& ( ! [X2] :
( relation_rng(X2) != X1
| relation_dom(X2) != X0
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) )
| equipotent(X0,X1) ) ),
inference(nnf_transformation,[],[f92]) ).
fof(f1412,plain,
! [X0,X1] :
( ( ~ equipotent(X0,X1)
| ? [X3] :
( relation_rng(X3) = X1
& relation_dom(X3) = X0
& one_to_one(X3)
& function(X3)
& relation(X3) ) )
& ( ! [X2] :
( relation_rng(X2) != X1
| relation_dom(X2) != X0
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) )
| equipotent(X0,X1) ) ),
inference(rectify,[],[f1411]) ).
fof(f1413,plain,
! [X0,X1] :
( ( ~ equipotent(X0,X1)
| ( relation_rng(sK204(X0,X1)) = X1
& relation_dom(sK204(X0,X1)) = X0
& one_to_one(sK204(X0,X1))
& function(sK204(X0,X1))
& relation(sK204(X0,X1)) ) )
& ( ! [X2] :
( relation_rng(X2) != X1
| relation_dom(X2) != X0
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2) )
| equipotent(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(X3,sK204(X0,X1))],[f1412]) ).
fof(f1414,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f93]) ).
fof(f1415,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(flattening,[],[f1414]) ).
fof(f1416,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(rectify,[],[f1415]) ).
fof(f1417,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK205(X0,X1,X2),X2)
| ( ~ in(sK205(X0,X1,X2),X1)
& in(sK205(X0,X1,X2),X0) ) )
& ( ~ in(sK205(X0,X1,X2),X2)
| in(sK205(X0,X1,X2),X1)
| ~ in(sK205(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(X3,sK205(X0,X1,X2))],[f1416]) ).
fof(f1418,plain,
! [X0] :
( empty(sK206(X0))
& element(sK206(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(X1,sK206(X0))],[f286]) ).
fof(f1419,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK207(X0))
& element(sK207(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(X1,sK207(X0))],[f864]) ).
fof(f1420,plain,
! [X0] : element(sK208(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(X1,sK208(X0))],[f184]) ).
fof(f1421,plain,
! [X0] :
( ( ~ being_limit_ordinal(X0)
| X0 = union(X0) )
& ( union(X0) != X0
| being_limit_ordinal(X0) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f1422,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f1423,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f1422]) ).
fof(f1424,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK211(X0,X5),X0)
& in(X5,sK211(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK209(X0,X1),X1)
| ( in(sK210(X0,X1),X0)
& in(sK209(X0,X1),sK210(X0,X1)) ) )
& ( ~ in(sK209(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK209(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK209,sK210,sK211]),skolemize(X2,sK209(X0,X1)),skolemize(X4,sK210(X0,X1)),skolemize(X7,sK211(X0,X5))],[f1423]) ).
fof(f1428,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ? [X10] :
! [X11] :
( ( ~ in(X11,X10)
| ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) )
& ( ! [X12] :
( ! [X13,X14] :
( ~ in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
| ordered_pair(X13,X14) != X11 )
| X11 != X12
| ~ in(X12,cartesian_product2(X0,X0)) )
| in(X11,X10) ) ) ),
inference(nnf_transformation,[],[f1109]) ).
fof(f1429,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ? [X8] :
( ? [X9,X10] :
( in(ordered_pair(apply(X2,X9),apply(X2,X10)),X1)
& ordered_pair(X9,X10) = X4 )
& X4 = X8
& in(X8,cartesian_product2(X0,X0)) ) )
& ( ! [X5] :
( ! [X6,X7] :
( ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X0,X0)) )
| in(X4,X3) ) ) ),
inference(rectify,[],[f1428]) ).
fof(f1430,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ! [X4] :
( ( ~ in(X4,sK219(X0,X1,X2))
| ( in(ordered_pair(apply(X2,sK221(X1,X2,X4)),apply(X2,sK222(X1,X2,X4))),X1)
& ordered_pair(sK221(X1,X2,X4),sK222(X1,X2,X4)) = X4
& sK220(X0,X1,X2,X4) = X4
& in(sK220(X0,X1,X2,X4),cartesian_product2(X0,X0)) ) )
& ( ! [X5] :
( ! [X6,X7] :
( ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X0,X0)) )
| in(X4,sK219(X0,X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK219,sK220,sK221,sK222]),skolemize(X3,sK219(X0,X1,X2)),skolemize(X8,sK220(X0,X1,X2,X4)),skolemize(X9,sK221(X1,X2,X4)),skolemize(X10,sK222(X1,X2,X4))],[f1429]) ).
fof(f1431,plain,
! [X1,X0,X2] :
( ~ sP26(X1,X0,X2)
| ? [X14] :
! [X15] :
( ( ~ in(X15,X14)
| sP25(X2,X0,X15,X1) )
& ( ~ sP25(X2,X0,X15,X1)
| in(X15,X14) ) ) ),
inference(nnf_transformation,[],[f1113]) ).
fof(f1432,plain,
! [X0,X1,X2] :
( ~ sP26(X0,X1,X2)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| sP25(X2,X1,X4,X0) )
& ( ~ sP25(X2,X1,X4,X0)
| in(X4,X3) ) ) ),
inference(rectify,[],[f1431]) ).
fof(f1433,plain,
! [X0,X1,X2] :
( ~ sP26(X0,X1,X2)
| ! [X4] :
( ( ~ in(X4,sK223(X0,X1,X2))
| sP25(X2,X1,X4,X0) )
& ( ~ sP25(X2,X1,X4,X0)
| in(X4,sK223(X0,X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(X3,sK223(X0,X1,X2))],[f1432]) ).
fof(f1434,plain,
! [X2,X0,X15,X1] :
( ( ~ sP25(X2,X0,X15,X1)
| ? [X16] :
( ? [X17,X18] :
( ? [X19] :
( ! [X20] :
( ~ in(X20,X19)
| in(ordered_pair(X18,X20),X1) )
& in(X18,X19)
& X17 = X19 )
& in(X17,X0)
& ordered_pair(X17,X18) = X15 )
& X15 = X16
& in(X16,cartesian_product2(X0,X2)) ) )
& ( ! [X16] :
( ! [X17,X18] :
( ! [X19] :
( ? [X20] :
( in(X20,X19)
& ~ in(ordered_pair(X18,X20),X1) )
| ~ in(X18,X19)
| X17 != X19 )
| ~ in(X17,X0)
| ordered_pair(X17,X18) != X15 )
| X15 != X16
| ~ in(X16,cartesian_product2(X0,X2)) )
| sP25(X2,X0,X15,X1) ) ),
inference(nnf_transformation,[],[f1112]) ).
fof(f1435,plain,
! [X0,X1,X2,X3] :
( ( ~ sP25(X0,X1,X2,X3)
| ? [X9] :
( ? [X10,X11] :
( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X11,X13),X3) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X1)
& ordered_pair(X10,X11) = X2 )
& X2 = X9
& in(X9,cartesian_product2(X1,X0)) ) )
& ( ! [X4] :
( ! [X5,X6] :
( ! [X7] :
( ? [X8] :
( in(X8,X7)
& ~ in(ordered_pair(X6,X8),X3) )
| ~ in(X6,X7)
| X5 != X7 )
| ~ in(X5,X1)
| ordered_pair(X5,X6) != X2 )
| X2 != X4
| ~ in(X4,cartesian_product2(X1,X0)) )
| sP25(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1434]) ).
fof(f1436,plain,
! [X0,X1,X2,X3] :
( ( ~ sP25(X0,X1,X2,X3)
| ( ! [X13] :
( ~ in(X13,sK228(X1,X2,X3))
| in(ordered_pair(sK227(X1,X2,X3),X13),X3) )
& in(sK227(X1,X2,X3),sK228(X1,X2,X3))
& sK226(X1,X2,X3) = sK228(X1,X2,X3)
& in(sK226(X1,X2,X3),X1)
& ordered_pair(sK226(X1,X2,X3),sK227(X1,X2,X3)) = X2
& sK225(X0,X1,X2,X3) = X2
& in(sK225(X0,X1,X2,X3),cartesian_product2(X1,X0)) ) )
& ( ! [X4] :
( ! [X5,X6] :
( ! [X7] :
( ( in(sK224(X3,X6,X7),X7)
& ~ in(ordered_pair(X6,sK224(X3,X6,X7)),X3) )
| ~ in(X6,X7)
| X5 != X7 )
| ~ in(X5,X1)
| ordered_pair(X5,X6) != X2 )
| X2 != X4
| ~ in(X4,cartesian_product2(X1,X0)) )
| sP25(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK224,sK225,sK226,sK227,sK228]),skolemize(X8,sK224(X3,X6,X7)),skolemize(X9,sK225(X0,X1,X2,X3)),skolemize(X10,sK226(X1,X2,X3)),skolemize(X11,sK227(X1,X2,X3)),skolemize(X12,sK228(X1,X2,X3))],[f1435]) ).
fof(f1437,plain,
! [X4,X0,X1] :
( ~ sP24(X4,X0,X1)
| ? [X6,X7] :
( ? [X8] :
( ! [X9] :
( ~ in(X9,X8)
| in(ordered_pair(X7,X9),X1) )
& in(X7,X8)
& X6 = X8 )
& in(X6,X0)
& ordered_pair(X6,X7) = X4 ) ),
inference(nnf_transformation,[],[f1111]) ).
fof(f1438,plain,
! [X0,X1,X2] :
( ~ sP24(X0,X1,X2)
| ? [X3,X4] :
( ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X4,X6),X2) )
& in(X4,X5)
& X3 = X5 )
& in(X3,X1)
& ordered_pair(X3,X4) = X0 ) ),
inference(rectify,[],[f1437]) ).
fof(f1439,plain,
! [X0,X1,X2] :
( ~ sP24(X0,X1,X2)
| ( ! [X6] :
( ~ in(X6,sK231(X0,X1,X2))
| in(ordered_pair(sK230(X0,X1,X2),X6),X2) )
& in(sK230(X0,X1,X2),sK231(X0,X1,X2))
& sK229(X0,X1,X2) = sK231(X0,X1,X2)
& in(sK229(X0,X1,X2),X1)
& ordered_pair(sK229(X0,X1,X2),sK230(X0,X1,X2)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK229,sK230,sK231]),skolemize(X3,sK229(X0,X1,X2)),skolemize(X4,sK230(X0,X1,X2)),skolemize(X5,sK231(X0,X1,X2))],[f1438]) ).
fof(f1443,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2] :
( ( sP23(sK237(X0,X1),X0,X1)
& sK235(X0,X1) = sK237(X0,X1)
& sP24(sK236(X0,X1),X0,X1)
& sK235(X0,X1) = sK236(X0,X1)
& sK236(X0,X1) != sK237(X0,X1) )
| sP26(X1,X0,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK235,sK236,sK237]),skolemize(X3,sK235(X0,X1)),skolemize(X4,sK236(X0,X1)),skolemize(X5,sK237(X0,X1))],[f1114]) ).
fof(f1444,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f77]) ).
fof(f1445,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(rectify,[],[f1444]) ).
fof(f1446,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ( ordered_pair(sK241(X0,X1,X8),sK242(X0,X1,X8)) = X8
& in(sK242(X0,X1,X8),X1)
& in(sK241(X0,X1,X8),X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ( ( in(sK238(X0,X1,X2),X2)
| ( sK238(X0,X1,X2) = ordered_pair(sK239(X0,X1,X2),sK240(X0,X1,X2))
& in(sK240(X0,X1,X2),X1)
& in(sK239(X0,X1,X2),X0) ) )
& ( ~ in(sK238(X0,X1,X2),X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK238(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK238,sK239,sK240,sK241,sK242]),skolemize(X3,sK238(X0,X1,X2)),skolemize(X6,sK239(X0,X1,X2)),skolemize(X7,sK240(X0,X1,X2)),skolemize(X11,sK241(X0,X1,X8)),skolemize(X12,sK242(X0,X1,X8))],[f1445]) ).
fof(f1447,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f880]) ).
fof(f1448,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(flattening,[],[f1447]) ).
fof(f1449,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(rectify,[],[f1448]) ).
fof(f1450,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ~ relation(X2)
| ( ( relation_dom_restriction(X0,X1) != X2
| ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X2)
| ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) ) )
& ( ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ) ) )
& ( ( ( in(ordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),X2)
| ( in(ordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),X0)
& in(sK243(X0,X1,X2),X1) ) )
& ( ~ in(ordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),X0)
| ~ in(sK243(X0,X1,X2),X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK243,sK244]),skolemize(X3,sK243(X0,X1,X2)),skolemize(X4,sK244(X0,X1,X2))],[f1449]) ).
fof(f1451,plain,
( function(sK245)
& empty(sK245)
& relation(sK245) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(X0,sK245)],[f282]) ).
fof(f1452,plain,
( function(sK246)
& relation(sK246) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(X0,sK246)],[f272]) ).
fof(f1453,plain,
~ empty(sK247),
inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(X0,sK247)],[f287]) ).
fof(f1454,plain,
( relation(sK248)
& ~ empty(sK248) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(X0,sK248)],[f285]) ).
fof(f1455,plain,
empty(sK249),
inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(X0,sK249)],[f280]) ).
fof(f1456,plain,
( relation(sK250)
& empty(sK250) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(X0,sK250)],[f278]) ).
fof(f1457,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( ( ~ element(X1,X0)
| empty(X1) )
& ( ~ empty(X1)
| element(X1,X0) ) ) )
& ( empty(X0)
| ( ( ~ element(X1,X0)
| in(X1,X0) )
& ( ~ in(X1,X0)
| element(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f886]) ).
fof(f1461,plain,
! [X0] :
( sP27
| ? [X4] :
! [X5] :
( ( ~ in(X5,X4)
| ? [X6] :
( ordinal(X5)
& X5 = X6
& in(X6,X0) ) )
& ( ! [X6] :
( ~ ordinal(X5)
| X5 != X6
| ~ in(X6,X0) )
| in(X5,X4) ) ) ),
inference(nnf_transformation,[],[f1116]) ).
fof(f1462,plain,
! [X0] :
( sP27
| ? [X1] :
! [X2] :
( ( ~ in(X2,X1)
| ? [X4] :
( ordinal(X2)
& X2 = X4
& in(X4,X0) ) )
& ( ! [X3] :
( ~ ordinal(X2)
| X2 != X3
| ~ in(X3,X0) )
| in(X2,X1) ) ) ),
inference(rectify,[],[f1461]) ).
fof(f1463,plain,
! [X0] :
( sP27
| ! [X2] :
( ( ~ in(X2,sK254(X0))
| ( ordinal(X2)
& sK255(X0,X2) = X2
& in(sK255(X0,X2),X0) ) )
& ( ! [X3] :
( ~ ordinal(X2)
| X2 != X3
| ~ in(X3,X0) )
| in(X2,sK254(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK254,sK255]),skolemize(X1,sK254(X0)),skolemize(X4,sK255(X0,X2))],[f1462]) ).
fof(f1464,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ( ~ ordinal_subset(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| ordinal_subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f893]) ).
fof(f1465,plain,
! [X0] :
( ~ sP30(X0)
| ? [X12] :
! [X13] :
( ( ~ in(X13,X12)
| sP29(X0,X13) )
& ( ~ sP29(X0,X13)
| in(X13,X12) ) ) ),
inference(nnf_transformation,[],[f1119]) ).
fof(f1466,plain,
! [X0] :
( ~ sP30(X0)
| ? [X1] :
! [X2] :
( ( ~ in(X2,X1)
| sP29(X0,X2) )
& ( ~ sP29(X0,X2)
| in(X2,X1) ) ) ),
inference(rectify,[],[f1465]) ).
fof(f1467,plain,
! [X0] :
( ~ sP30(X0)
| ! [X2] :
( ( ~ in(X2,sK256(X0))
| sP29(X0,X2) )
& ( ~ sP29(X0,X2)
| in(X2,sK256(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(X1,sK256(X0))],[f1466]) ).
fof(f1468,plain,
! [X0,X13] :
( ( ~ sP29(X0,X13)
| ? [X14] :
( ? [X15] :
( ( ~ in(X15,omega)
| ! [X16] :
( ~ element(X16,powerset(powerset(X15)))
| ? [X17] :
( ! [X18] :
( ~ subset(X17,X18)
| ~ in(X18,X16)
| X17 = X18 )
& in(X17,X16) )
| empty_set = X16 ) )
& X13 = X15
& ordinal(X15) )
& X13 = X14
& in(X14,succ(X0)) ) )
& ( ! [X14] :
( ! [X15] :
( ( in(X15,omega)
& ? [X16] :
( element(X16,powerset(powerset(X15)))
& ! [X17] :
( ? [X18] :
( subset(X17,X18)
& in(X18,X16)
& X17 != X18 )
| ~ in(X17,X16) )
& empty_set != X16 ) )
| X13 != X15
| ~ ordinal(X15) )
| X13 != X14
| ~ in(X14,succ(X0)) )
| sP29(X0,X13) ) ),
inference(nnf_transformation,[],[f1118]) ).
fof(f1469,plain,
! [X0,X1] :
( ( ~ sP29(X0,X1)
| ? [X7] :
( ? [X8] :
( ( ~ in(X8,omega)
| ! [X9] :
( ~ element(X9,powerset(powerset(X8)))
| ? [X10] :
( ! [X11] :
( ~ subset(X10,X11)
| ~ in(X11,X9)
| X10 = X11 )
& in(X10,X9) )
| empty_set = X9 ) )
& X1 = X8
& ordinal(X8) )
& X1 = X7
& in(X7,succ(X0)) ) )
& ( ! [X2] :
( ! [X3] :
( ( in(X3,omega)
& ? [X4] :
( element(X4,powerset(powerset(X3)))
& ! [X5] :
( ? [X6] :
( subset(X5,X6)
& in(X6,X4)
& X5 != X6 )
| ~ in(X5,X4) )
& empty_set != X4 ) )
| X1 != X3
| ~ ordinal(X3) )
| X1 != X2
| ~ in(X2,succ(X0)) )
| sP29(X0,X1) ) ),
inference(rectify,[],[f1468]) ).
fof(f1470,plain,
! [X0,X1] :
( ( ~ sP29(X0,X1)
| ( ( ~ in(sK260(X1),omega)
| ! [X9] :
( ~ element(X9,powerset(powerset(sK260(X1))))
| ( ! [X11] :
( ~ subset(sK261(X9),X11)
| ~ in(X11,X9)
| sK261(X9) = X11 )
& in(sK261(X9),X9) )
| empty_set = X9 ) )
& sK260(X1) = X1
& ordinal(sK260(X1))
& sK259(X0,X1) = X1
& in(sK259(X0,X1),succ(X0)) ) )
& ( ! [X2] :
( ! [X3] :
( ( in(X3,omega)
& element(sK257(X3),powerset(powerset(X3)))
& ! [X5] :
( ( subset(X5,sK258(X3,X5))
& in(sK258(X3,X5),sK257(X3))
& sK258(X3,X5) != X5 )
| ~ in(X5,sK257(X3)) )
& empty_set != sK257(X3) )
| X1 != X3
| ~ ordinal(X3) )
| X1 != X2
| ~ in(X2,succ(X0)) )
| sP29(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK257,sK258,sK259,sK260,sK261]),skolemize(X4,sK257(X3)),skolemize(X6,sK258(X3,X5)),skolemize(X7,sK259(X0,X1)),skolemize(X8,sK260(X1)),skolemize(X10,sK261(X9))],[f1469]) ).
fof(f1474,plain,
! [X0] :
( ~ ordinal(X0)
| ( sP28(sK266)
& sK264 = sK266
& ( ~ in(sK267,omega)
| ! [X5] :
( ~ element(X5,powerset(powerset(sK267)))
| ( ! [X7] :
( ~ subset(sK268(X5),X7)
| ~ in(X7,X5)
| sK268(X5) = X7 )
& in(sK268(X5),X5) )
| empty_set = X5 ) )
& sK265 = sK267
& ordinal(sK267)
& sK264 = sK265
& sK265 != sK266 )
| sP30(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK264,sK265,sK266,sK267,sK268]),skolemize(X1,sK264),skolemize(X2,sK265),skolemize(X3,sK266),skolemize(X4,sK267),skolemize(X6,sK268(X5))],[f1120]) ).
fof(f1475,plain,
! [X0] :
( ( omega != X0
| ( ! [X1] :
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| subset(X0,X1) )
& ordinal(X0)
& being_limit_ordinal(X0)
& in(empty_set,X0) ) )
& ( ? [X1] :
( ordinal(X1)
& being_limit_ordinal(X1)
& in(empty_set,X1)
& ~ subset(X0,X1) )
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| X0 = omega ) ),
inference(nnf_transformation,[],[f899]) ).
fof(f1476,plain,
! [X0] :
( ( omega != X0
| ( ! [X1] :
( ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(empty_set,X1)
| subset(X0,X1) )
& ordinal(X0)
& being_limit_ordinal(X0)
& in(empty_set,X0) ) )
& ( ? [X1] :
( ordinal(X1)
& being_limit_ordinal(X1)
& in(empty_set,X1)
& ~ subset(X0,X1) )
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| X0 = omega ) ),
inference(flattening,[],[f1475]) ).
fof(f1477,plain,
! [X0] :
( ( omega != X0
| ( ! [X2] :
( ~ ordinal(X2)
| ~ being_limit_ordinal(X2)
| ~ in(empty_set,X2)
| subset(X0,X2) )
& ordinal(X0)
& being_limit_ordinal(X0)
& in(empty_set,X0) ) )
& ( ? [X1] :
( ordinal(X1)
& being_limit_ordinal(X1)
& in(empty_set,X1)
& ~ subset(X0,X1) )
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| X0 = omega ) ),
inference(rectify,[],[f1476]) ).
fof(f1478,plain,
! [X0] :
( ( omega != X0
| ( ! [X2] :
( ~ ordinal(X2)
| ~ being_limit_ordinal(X2)
| ~ in(empty_set,X2)
| subset(X0,X2) )
& ordinal(X0)
& being_limit_ordinal(X0)
& in(empty_set,X0) ) )
& ( ( ordinal(sK269(X0))
& being_limit_ordinal(sK269(X0))
& in(empty_set,sK269(X0))
& ~ subset(X0,sK269(X0)) )
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| X0 = omega ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(X1,sK269(X0))],[f1477]) ).
fof(f1479,plain,
! [X0] :
( ( ~ finite(X0)
| ? [X1] :
( in(relation_dom(X1),omega)
& relation_rng(X1) = X0
& function(X1)
& relation(X1) ) )
& ( ! [X1] :
( ~ in(relation_dom(X1),omega)
| relation_rng(X1) != X0
| ~ function(X1)
| ~ relation(X1) )
| finite(X0) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f1480,plain,
! [X0] :
( ( ~ finite(X0)
| ? [X2] :
( in(relation_dom(X2),omega)
& relation_rng(X2) = X0
& function(X2)
& relation(X2) ) )
& ( ! [X1] :
( ~ in(relation_dom(X1),omega)
| relation_rng(X1) != X0
| ~ function(X1)
| ~ relation(X1) )
| finite(X0) ) ),
inference(rectify,[],[f1479]) ).
fof(f1481,plain,
! [X0] :
( ( ~ finite(X0)
| ( in(relation_dom(sK270(X0)),omega)
& relation_rng(sK270(X0)) = X0
& function(sK270(X0))
& relation(sK270(X0)) ) )
& ( ! [X1] :
( ~ in(relation_dom(X1),omega)
| relation_rng(X1) != X0
| ~ function(X1)
| ~ relation(X1) )
| finite(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(X2,sK270(X0))],[f1480]) ).
fof(f1482,plain,
! [X0] :
( ~ sP32(X0)
| ? [X2,X3,X4] :
( sP31(X4,X0)
& X2 = X4
& ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& X2 = X3
& X3 != X4 ) ),
inference(nnf_transformation,[],[f1122]) ).
fof(f1483,plain,
! [X0] :
( ~ sP32(X0)
| ? [X1,X2,X3] :
( sP31(X3,X0)
& X1 = X3
& ? [X4] :
( in(X4,X0)
& X2 = X4
& ordinal(X4) )
& X1 = X2
& X2 != X3 ) ),
inference(rectify,[],[f1482]) ).
fof(f1484,plain,
! [X0] :
( ~ sP32(X0)
| ( sP31(sK273(X0),X0)
& sK271(X0) = sK273(X0)
& in(sK274(X0),X0)
& sK272(X0) = sK274(X0)
& ordinal(sK274(X0))
& sK271(X0) = sK272(X0)
& sK272(X0) != sK273(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK271,sK272,sK273,sK274]),skolemize(X1,sK271(X0)),skolemize(X2,sK272(X0)),skolemize(X3,sK273(X0)),skolemize(X4,sK274(X0))],[f1483]) ).
fof(f1488,plain,
! [X0,X1] :
( ~ ordinal(X1)
| sP32(X0)
| ? [X7] :
! [X8] :
( ( ~ in(X8,X7)
| ? [X9] :
( ? [X10] :
( in(X10,X0)
& X8 = X10
& ordinal(X10) )
& X8 = X9
& in(X9,succ(X1)) ) )
& ( ! [X9] :
( ! [X10] :
( ~ in(X10,X0)
| X8 != X10
| ~ ordinal(X10) )
| X8 != X9
| ~ in(X9,succ(X1)) )
| in(X8,X7) ) ) ),
inference(nnf_transformation,[],[f1123]) ).
fof(f1489,plain,
! [X0,X1] :
( ~ ordinal(X1)
| sP32(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ? [X6] :
( ? [X7] :
( in(X7,X0)
& X3 = X7
& ordinal(X7) )
& X3 = X6
& in(X6,succ(X1)) ) )
& ( ! [X4] :
( ! [X5] :
( ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5) )
| X3 != X4
| ~ in(X4,succ(X1)) )
| in(X3,X2) ) ) ),
inference(rectify,[],[f1488]) ).
fof(f1490,plain,
! [X0,X1] :
( ~ ordinal(X1)
| sP32(X0)
| ! [X3] :
( ( ~ in(X3,sK276(X0,X1))
| ( in(sK278(X0,X3),X0)
& sK278(X0,X3) = X3
& ordinal(sK278(X0,X3))
& sK277(X0,X1,X3) = X3
& in(sK277(X0,X1,X3),succ(X1)) ) )
& ( ! [X4] :
( ! [X5] :
( ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5) )
| X3 != X4
| ~ in(X4,succ(X1)) )
| in(X3,sK276(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK276,sK277,sK278]),skolemize(X2,sK276(X0,X1)),skolemize(X6,sK277(X0,X1,X3)),skolemize(X7,sK278(X0,X3))],[f1489]) ).
fof(f1494,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ? [X7] :
! [X8] :
( ( ~ in(X8,X7)
| ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) )
& ( ! [X9] :
( ! [X10] :
( set_difference(X10,singleton(X0)) != X8
| ~ in(X10,X1) )
| X8 != X9
| ~ in(X9,powerset(X0)) )
| in(X8,X7) ) ) ),
inference(nnf_transformation,[],[f1125]) ).
fof(f1495,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ? [X6] :
( ? [X7] :
( set_difference(X7,singleton(X0)) = X3
& in(X7,X1) )
& X3 = X6
& in(X6,powerset(X0)) ) )
& ( ! [X4] :
( ! [X5] :
( set_difference(X5,singleton(X0)) != X3
| ~ in(X5,X1) )
| X3 != X4
| ~ in(X4,powerset(X0)) )
| in(X3,X2) ) ) ),
inference(rectify,[],[f1494]) ).
fof(f1496,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ! [X3] :
( ( ~ in(X3,sK284(X0,X1))
| ( set_difference(sK286(X0,X1,X3),singleton(X0)) = X3
& in(sK286(X0,X1,X3),X1)
& sK285(X0,X1,X3) = X3
& in(sK285(X0,X1,X3),powerset(X0)) ) )
& ( ! [X4] :
( ! [X5] :
( set_difference(X5,singleton(X0)) != X3
| ~ in(X5,X1) )
| X3 != X4
| ~ in(X4,powerset(X0)) )
| in(X3,sK284(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK284,sK285,sK286]),skolemize(X2,sK284(X0,X1)),skolemize(X6,sK285(X0,X1,X3)),skolemize(X7,sK286(X0,X1,X3))],[f1495]) ).
fof(f1497,plain,
( being_limit_ordinal(sK287)
& ordinal(sK287)
& epsilon_connected(sK287)
& epsilon_transitive(sK287) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(X0,sK287)],[f276]) ).
fof(f1498,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f907]) ).
fof(f1499,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f1498]) ).
fof(f1500,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK290(X0,X5)) = X5
& in(sK290(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK288(X0,X1),X1)
| ( sK288(X0,X1) = apply(X0,sK289(X0,X1))
& in(sK289(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK288(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK288(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK288,sK289,sK290]),skolemize(X2,sK288(X0,X1)),skolemize(X4,sK289(X0,X1)),skolemize(X7,sK290(X0,X5))],[f1499]) ).
fof(f1501,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| X2 = empty_set )
& ( empty_set != X2
| X2 = apply(X0,X1) ) ) )
& ( ~ in(X1,relation_dom(X0))
| ( ( apply(X0,X1) != X2
| in(ordered_pair(X1,X2),X0) )
& ( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f909]) ).
fof(f1502,plain,
top_str(sK291),
inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(X0,sK291)],[f179]) ).
fof(f1506,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP34(X1,X0)
| ? [X5] :
! [X6] :
( ( ~ in(X6,X5)
| ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) )
& ( ! [X7] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X6),X1)
| X6 != X7
| ~ in(X7,powerset(the_carrier(X0))) )
| in(X6,X5) ) ) ),
inference(nnf_transformation,[],[f1127]) ).
fof(f1507,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP34(X1,X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ? [X5] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X3 = X5
& in(X5,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) )
| in(X3,X2) ) ) ),
inference(rectify,[],[f1506]) ).
fof(f1508,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP34(X1,X0)
| ! [X3] :
( ( ~ in(X3,sK295(X0,X1))
| ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& sK296(X0,X1,X3) = X3
& in(sK296(X0,X1,X3),powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) )
| in(X3,sK295(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK295,sK296]),skolemize(X2,sK295(X0,X1)),skolemize(X5,sK296(X0,X1,X3))],[f1507]) ).
fof(f1509,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| ? [X2,X3,X4] :
( sP35(X0,X4,X1)
& X2 = X4
& ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X5 = X3
& element(X5,powerset(the_carrier(X0))) )
& X2 = X3
& X3 != X4 ) ),
inference(nnf_transformation,[],[f1129]) ).
fof(f1510,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| ( sP35(X0,sK299(X0,X1),X1)
& sK297(X0,X1) = sK299(X0,X1)
& subset(X1,sK298(X0,X1))
& closed_subset(sK300(X0,X1),X0)
& sK298(X0,X1) = sK300(X0,X1)
& element(sK300(X0,X1),powerset(the_carrier(X0)))
& sK297(X0,X1) = sK298(X0,X1)
& sK298(X0,X1) != sK299(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK297,sK298,sK299,sK300]),skolemize(X2,sK297(X0,X1)),skolemize(X3,sK298(X0,X1)),skolemize(X4,sK299(X0,X1)),skolemize(X5,sK300(X0,X1))],[f1509]) ).
fof(f1514,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ? [X7] :
! [X8] :
( ( ~ in(X8,X7)
| ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) )
& ( ! [X9] :
( ! [X10] :
( ~ subset(X1,X8)
| ~ closed_subset(X10,X0)
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) )
| X8 != X9
| ~ in(X9,powerset(the_carrier(X0))) )
| in(X8,X7) ) ) ),
inference(nnf_transformation,[],[f1130]) ).
fof(f1515,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ? [X6] :
( ? [X7] :
( subset(X1,X3)
& closed_subset(X7,X0)
& X3 = X7
& element(X7,powerset(the_carrier(X0))) )
& X3 = X6
& in(X6,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ! [X5] :
( ~ subset(X1,X3)
| ~ closed_subset(X5,X0)
| X3 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) )
| in(X3,X2) ) ) ),
inference(rectify,[],[f1514]) ).
fof(f1516,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ! [X3] :
( ( ~ in(X3,sK302(X0,X1))
| ( subset(X1,X3)
& closed_subset(sK304(X0,X1,X3),X0)
& sK304(X0,X1,X3) = X3
& element(sK304(X0,X1,X3),powerset(the_carrier(X0)))
& sK303(X0,X1,X3) = X3
& in(sK303(X0,X1,X3),powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ! [X5] :
( ~ subset(X1,X3)
| ~ closed_subset(X5,X0)
| X3 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) )
| in(X3,sK302(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK302,sK303,sK304]),skolemize(X2,sK302(X0,X1)),skolemize(X6,sK303(X0,X1,X3)),skolemize(X7,sK304(X0,X1,X3))],[f1515]) ).
fof(f1517,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ( closed_subset(sK305(X0),X0)
& element(sK305(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(X1,sK305(X0))],[f916]) ).
fof(f1521,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP37(X1,X2)
| ? [X6] :
! [X7] :
( ( ~ in(X7,X6)
| ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) )
& ( ! [X8] :
( ~ in(relation_image(X2,X7),X1)
| X7 != X8
| ~ in(X8,powerset(relation_dom(X2))) )
| in(X7,X6) ) ) ),
inference(nnf_transformation,[],[f1132]) ).
fof(f1522,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP37(X1,X2)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ? [X6] :
( in(relation_image(X2,X4),X1)
& X4 = X6
& in(X6,powerset(relation_dom(X2))) ) )
& ( ! [X5] :
( ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2))) )
| in(X4,X3) ) ) ),
inference(rectify,[],[f1521]) ).
fof(f1523,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP37(X1,X2)
| ! [X4] :
( ( ~ in(X4,sK309(X1,X2))
| ( in(relation_image(X2,X4),X1)
& sK310(X1,X2,X4) = X4
& in(sK310(X1,X2,X4),powerset(relation_dom(X2))) ) )
& ( ! [X5] :
( ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2))) )
| in(X4,sK309(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK309,sK310]),skolemize(X3,sK309(X1,X2)),skolemize(X6,sK310(X1,X2,X4))],[f1522]) ).
fof(f1524,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f925]) ).
fof(f1525,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X8,X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X5,X3),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f1524]) ).
fof(f1526,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK313(X0,X1,X6),X1)
& in(ordered_pair(sK313(X0,X1,X6),X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK311(X0,X1,X2),X2)
| ( in(sK312(X0,X1,X2),X1)
& in(ordered_pair(sK312(X0,X1,X2),sK311(X0,X1,X2)),X0) ) )
& ( ~ in(sK311(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK311(X0,X1,X2)),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK311,sK312,sK313]),skolemize(X3,sK311(X0,X1,X2)),skolemize(X5,sK312(X0,X1,X2)),skolemize(X8,sK313(X0,X1,X6))],[f1525]) ).
fof(f1527,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( X3 = apply(X0,X4)
& in(X4,X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f927]) ).
fof(f1528,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( apply(X0,X8) = X6
& in(X8,X1)
& in(X8,relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( apply(X0,X5) = X3
& in(X5,X1)
& in(X5,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( apply(X0,X4) != X3
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(rectify,[],[f1527]) ).
fof(f1529,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( apply(X0,sK316(X0,X1,X6)) = X6
& in(sK316(X0,X1,X6),X1)
& in(sK316(X0,X1,X6),relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ( ( in(sK314(X0,X1,X2),X2)
| ( sK314(X0,X1,X2) = apply(X0,sK315(X0,X1,X2))
& in(sK315(X0,X1,X2),X1)
& in(sK315(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK314(X0,X1,X2),X2)
| ! [X4] :
( apply(X0,X4) != sK314(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK314,sK315,sK316]),skolemize(X3,sK314(X0,X1,X2)),skolemize(X5,sK315(X0,X1,X2)),skolemize(X8,sK316(X0,X1,X6))],[f1528]) ).
fof(f1530,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f1531,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ( X1 != X3
& X0 != X3 )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f1530]) ).
fof(f1532,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| X3 = X1
| X3 = X0 )
& ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(rectify,[],[f1531]) ).
fof(f1533,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| X1 = X4
| X0 = X4 )
& ( ( X1 != X4
& X0 != X4 )
| in(X4,X2) ) ) )
& ( ( ( in(sK317(X0,X1,X2),X2)
| sK317(X0,X1,X2) = X1
| sK317(X0,X1,X2) = X0 )
& ( ~ in(sK317(X0,X1,X2),X2)
| ( sK317(X0,X1,X2) != X1
& sK317(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(X3,sK317(X0,X1,X2))],[f1532]) ).
fof(f1534,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f84]) ).
fof(f1535,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f1534]) ).
fof(f1536,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f1535]) ).
fof(f1537,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK318(X0,X1,X2),X2)
| ( in(sK318(X0,X1,X2),X1)
& in(sK318(X0,X1,X2),X0) ) )
& ( ~ in(sK318(X0,X1,X2),X2)
| ~ in(sK318(X0,X1,X2),X1)
| ~ in(sK318(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(X3,sK318(X0,X1,X2))],[f1536]) ).
fof(f1538,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( ~ empty(sK319(X0))
& element(sK319(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(X1,sK319(X0))],[f938]) ).
fof(f1539,plain,
( ~ empty_carrier(sK320)
& one_sorted_str(sK320) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(X0,sK320)],[f292]) ).
fof(f1540,plain,
one_sorted_str(sK321),
inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(X0,sK321)],[f180]) ).
fof(f1541,plain,
! [X0,X1,X2] :
( ( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
& ( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f305]) ).
fof(f1542,plain,
! [X0,X1] : relation_of2_as_subset(sK322(X0,X1),X0,X1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(X2,sK322(X0,X1))],[f185]) ).
fof(f1543,plain,
! [X0] :
( ! [X7] :
( in(X7,sK323(X0))
| are_equipotent(X7,sK323(X0))
| ~ subset(X7,sK323(X0)) )
& ! [X4] :
( ( ! [X6] :
( ~ subset(X6,X4)
| in(X6,sK324(X0,X4)) )
& in(sK324(X0,X4),sK323(X0)) )
| ~ in(X4,sK323(X0)) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,sK323(X0))
| in(X3,sK323(X0)) )
& in(X0,sK323(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK323,sK324]),skolemize(X1,sK323(X0)),skolemize(X5,sK324(X0,X4))],[f943]) ).
fof(f1544,plain,
! [X0,X1] :
( ( ~ equipotent(X0,X1)
| are_equipotent(X0,X1) )
& ( ~ are_equipotent(X0,X1)
| equipotent(X0,X1) ) ),
inference(nnf_transformation,[],[f307]) ).
fof(f1545,plain,
! [X0] :
( empty(X0)
| ( finite(sK325(X0))
& ~ empty(sK325(X0))
& element(sK325(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(X1,sK325(X0))],[f944]) ).
fof(f1546,plain,
( finite(sK326)
& ~ empty(sK326) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(X0,sK326)],[f271]) ).
fof(f1547,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f950]) ).
fof(f1548,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X5] :
( in(X5,X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f1547]) ).
fof(f1549,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK329(X0,X1,X6),X1)
& in(ordered_pair(X6,sK329(X0,X1,X6)),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK327(X0,X1,X2),X2)
| ( in(sK328(X0,X1,X2),X1)
& in(ordered_pair(sK327(X0,X1,X2),sK328(X0,X1,X2)),X0) ) )
& ( ~ in(sK327(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK327(X0,X1,X2),X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK327,sK328,sK329]),skolemize(X3,sK327(X0,X1,X2)),skolemize(X5,sK328(X0,X1,X2)),skolemize(X8,sK329(X0,X1,X6))],[f1548]) ).
fof(f1550,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(nnf_transformation,[],[f952]) ).
fof(f1551,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0))
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(flattening,[],[f1550]) ).
fof(f1552,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(apply(X0,X3),X1)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X3,X2)
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(rectify,[],[f1551]) ).
fof(f1553,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(apply(X0,X4),X1)
& in(X4,relation_dom(X0)) ) )
& ( ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ) ) )
& ( ( ( in(sK330(X0,X1,X2),X2)
| ( in(apply(X0,sK330(X0,X1,X2)),X1)
& in(sK330(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK330(X0,X1,X2),X2)
| ~ in(apply(X0,sK330(X0,X1,X2)),X1)
| ~ in(sK330(X0,X1,X2),relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(X3,sK330(X0,X1,X2))],[f1552]) ).
fof(f1554,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f969]) ).
fof(f1555,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ? [X10] :
( in(ordered_pair(X10,X8),X1)
& in(ordered_pair(X7,X10),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ? [X6] :
( in(ordered_pair(X6,X4),X1)
& in(ordered_pair(X3,X6),X0) ) )
& ( ~ in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(rectify,[],[f1554]) ).
fof(f1556,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( relation_composition(X0,X1) != X2
| ! [X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X2)
| ( in(ordered_pair(sK334(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK334(X0,X1,X7,X8)),X0) ) )
& ( ! [X9] :
( ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0) )
| in(ordered_pair(X7,X8),X2) ) ) )
& ( ( ( in(ordered_pair(sK331(X0,X1,X2),sK332(X0,X1,X2)),X2)
| ( in(ordered_pair(sK333(X0,X1,X2),sK332(X0,X1,X2)),X1)
& in(ordered_pair(sK331(X0,X1,X2),sK333(X0,X1,X2)),X0) ) )
& ( ~ in(ordered_pair(sK331(X0,X1,X2),sK332(X0,X1,X2)),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,sK332(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK331(X0,X1,X2),X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK331,sK332,sK333,sK334]),skolemize(X3,sK331(X0,X1,X2)),skolemize(X4,sK332(X0,X1,X2)),skolemize(X6,sK333(X0,X1,X2)),skolemize(X10,sK334(X0,X1,X7,X8))],[f1555]) ).
fof(f1557,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X3] :
( ~ element(X3,powerset(X0))
| ( ( ~ in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(subset_complement(X0,X3),X1)
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f973]) ).
fof(f1558,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X3] :
( ~ element(X3,powerset(X0))
| ( ( ~ in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(subset_complement(X0,X3),X1)
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(flattening,[],[f1557]) ).
fof(f1559,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X4] :
( ~ element(X4,powerset(X0))
| ( ( ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) )
& ( ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(rectify,[],[f1558]) ).
fof(f1560,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X4] :
( ~ element(X4,powerset(X0))
| ( ( ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) )
& ( ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ) ) ) )
& ( ( element(sK335(X0,X1,X2),powerset(X0))
& ( in(sK335(X0,X1,X2),X2)
| in(subset_complement(X0,sK335(X0,X1,X2)),X1) )
& ( ~ in(sK335(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK335(X0,X1,X2)),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(X3,sK335(X0,X1,X2))],[f1559]) ).
fof(f1561,plain,
! [X0,X1] :
( quasi_total(sK336(X0,X1),X0,X1)
& function(sK336(X0,X1))
& relation(sK336(X0,X1))
& relation_of2(sK336(X0,X1),X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(X2,sK336(X0,X1))],[f273]) ).
fof(f1562,plain,
( ordinal(sK337)
& epsilon_connected(sK337)
& epsilon_transitive(sK337)
& ~ empty(sK337) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(X0,sK337)],[f290]) ).
fof(f1563,plain,
( ordinal(sK338)
& epsilon_connected(sK338)
& epsilon_transitive(sK338)
& empty(sK338)
& one_to_one(sK338)
& function(sK338)
& relation(sK338) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(X0,sK338)],[f283]) ).
fof(f1564,plain,
( ordinal(sK339)
& epsilon_connected(sK339)
& epsilon_transitive(sK339) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(X0,sK339)],[f275]) ).
fof(f1567,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f982]) ).
fof(f1568,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f1567]) ).
fof(f1569,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ( in(sK340(X0),X0)
& ~ subset(sK340(X0),X0) )
| epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(X1,sK340(X0))],[f1568]) ).
fof(f1570,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_well_founded_in(X0,X1)
| ! [X2] :
( ? [X3] :
( disjoint(fiber(X0,X3),X2)
& in(X3,X2) )
| empty_set = X2
| ~ subset(X2,X1) ) )
& ( ? [X2] :
( ! [X3] :
( ~ disjoint(fiber(X0,X3),X2)
| ~ in(X3,X2) )
& empty_set != X2
& subset(X2,X1) )
| is_well_founded_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f988]) ).
fof(f1571,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_well_founded_in(X0,X1)
| ! [X4] :
( ? [X5] :
( disjoint(fiber(X0,X5),X4)
& in(X5,X4) )
| empty_set = X4
| ~ subset(X4,X1) ) )
& ( ? [X2] :
( ! [X3] :
( ~ disjoint(fiber(X0,X3),X2)
| ~ in(X3,X2) )
& empty_set != X2
& subset(X2,X1) )
| is_well_founded_in(X0,X1) ) ) ),
inference(rectify,[],[f1570]) ).
fof(f1572,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_well_founded_in(X0,X1)
| ! [X4] :
( ( disjoint(fiber(X0,sK342(X0,X4)),X4)
& in(sK342(X0,X4),X4) )
| empty_set = X4
| ~ subset(X4,X1) ) )
& ( ( ! [X3] :
( ~ disjoint(fiber(X0,X3),sK341(X0,X1))
| ~ in(X3,sK341(X0,X1)) )
& empty_set != sK341(X0,X1)
& subset(sK341(X0,X1),X1) )
| is_well_founded_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK341,sK342]),skolemize(X2,sK341(X0,X1)),skolemize(X5,sK342(X0,X4))],[f1571]) ).
fof(f1573,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| ! [X1] :
( ? [X2] :
( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
| empty_set = X1
| ~ subset(X1,relation_field(X0)) ) )
& ( ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) )
| well_founded_relation(X0) ) ) ),
inference(nnf_transformation,[],[f989]) ).
fof(f1574,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| ! [X3] :
( ? [X4] :
( disjoint(fiber(X0,X4),X3)
& in(X4,X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ) )
& ( ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) )
| well_founded_relation(X0) ) ) ),
inference(rectify,[],[f1573]) ).
fof(f1575,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| ! [X3] :
( ( disjoint(fiber(X0,sK344(X0,X3)),X3)
& in(sK344(X0,X3),X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ) )
& ( ( ! [X2] :
( ~ disjoint(fiber(X0,X2),sK343(X0))
| ~ in(X2,sK343(X0)) )
& empty_set != sK343(X0)
& subset(sK343(X0),relation_field(X0)) )
| well_founded_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK343,sK344]),skolemize(X1,sK343(X0)),skolemize(X4,sK344(X0,X3))],[f1574]) ).
fof(f1576,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( fiber(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(ordered_pair(X3,X1),X0)
& X3 != X1 ) )
& ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(ordered_pair(X3,X1),X0)
& X3 != X1 ) )
& ( ~ in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| X1 = X3 ) )
| X2 = fiber(X0,X1) ) ) ),
inference(nnf_transformation,[],[f990]) ).
fof(f1577,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( fiber(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(ordered_pair(X3,X1),X0)
& X3 != X1 ) )
& ( ~ in(ordered_pair(X3,X1),X0)
| X1 = X3
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(ordered_pair(X3,X1),X0)
& X3 != X1 ) )
& ( ~ in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| X1 = X3 ) )
| X2 = fiber(X0,X1) ) ) ),
inference(flattening,[],[f1576]) ).
fof(f1578,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( fiber(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(ordered_pair(X4,X1),X0)
& X1 != X4 ) )
& ( ~ in(ordered_pair(X4,X1),X0)
| X1 = X4
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(ordered_pair(X3,X1),X0)
& X3 != X1 ) )
& ( ~ in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| X1 = X3 ) )
| X2 = fiber(X0,X1) ) ) ),
inference(rectify,[],[f1577]) ).
fof(f1579,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( fiber(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(ordered_pair(X4,X1),X0)
& X1 != X4 ) )
& ( ~ in(ordered_pair(X4,X1),X0)
| X1 = X4
| in(X4,X2) ) ) )
& ( ( ( in(sK345(X0,X1,X2),X2)
| ( in(ordered_pair(sK345(X0,X1,X2),X1),X0)
& sK345(X0,X1,X2) != X1 ) )
& ( ~ in(sK345(X0,X1,X2),X2)
| ~ in(ordered_pair(sK345(X0,X1,X2),X1),X0)
| sK345(X0,X1,X2) = X1 ) )
| X2 = fiber(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(X3,sK345(X0,X1,X2))],[f1578]) ).
fof(f1580,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( ( empty_set != X1
| ( ( ~ quasi_total(X2,X0,X1)
| X2 = empty_set )
& ( empty_set != X2
| quasi_total(X2,X0,X1) ) )
| X0 = empty_set )
& ( ( X1 = empty_set
& empty_set != X0 )
| ( ( ~ quasi_total(X2,X0,X1)
| X0 = relation_dom_as_subset(X0,X1,X2) )
& ( relation_dom_as_subset(X0,X1,X2) != X0
| quasi_total(X2,X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f994]) ).
fof(f1582,plain,
latt_str(sK346),
inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(X0,sK346)],[f182]) ).
fof(f1583,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ( ( ~ meet_absorbing(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| join(X0,meet(X0,X1,X2),X2) = X2 ) ) )
& ( ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,the_carrier(X0))
& join(X0,meet(X0,X1,X2),X2) != X2 ) )
| meet_absorbing(X0) ) ) ),
inference(nnf_transformation,[],[f999]) ).
fof(f1584,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ( ( ~ meet_absorbing(X0)
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| join(X0,meet(X0,X3,X4),X4) = X4 ) ) )
& ( ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,the_carrier(X0))
& join(X0,meet(X0,X1,X2),X2) != X2 ) )
| meet_absorbing(X0) ) ) ),
inference(rectify,[],[f1583]) ).
fof(f1585,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ( ( ~ meet_absorbing(X0)
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| join(X0,meet(X0,X3,X4),X4) = X4 ) ) )
& ( ( element(sK347(X0),the_carrier(X0))
& element(sK348(X0),the_carrier(X0))
& sK348(X0) != join(X0,meet(X0,sK347(X0),sK348(X0)),sK348(X0)) )
| meet_absorbing(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK347,sK348]),skolemize(X1,sK347(X0)),skolemize(X2,sK348(X0))],[f1584]) ).
fof(f1586,plain,
join_semilatt_str(sK349),
inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(X0,sK349)],[f181]) ).
fof(f1587,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( ~ closed_subset(X1,X0)
| open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) )
& ( ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| closed_subset(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f1002]) ).
fof(f1588,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( ~ open_subset(X1,X0)
| in(X1,the_topology(X0)) )
& ( ~ in(X1,the_topology(X0))
| open_subset(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f1003]) ).
fof(f1589,plain,
! [X2,X1,X0] :
( ~ sP39(X2,X1,X0)
| ( ( topstr_closure(X0,X1) != X2
| sP38(X0,X1,X2) )
& ( ~ sP38(X0,X1,X2)
| X2 = topstr_closure(X0,X1) ) ) ),
inference(nnf_transformation,[],[f1134]) ).
fof(f1590,plain,
! [X0,X1,X2] :
( ~ sP39(X0,X1,X2)
| ( ( topstr_closure(X2,X1) != X0
| sP38(X2,X1,X0) )
& ( ~ sP38(X2,X1,X0)
| topstr_closure(X2,X1) = X0 ) ) ),
inference(rectify,[],[f1589]) ).
fof(f1595,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( ( ~ in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ subset(X2,X3)
| in(ordered_pair(X2,X3),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ? [X2,X3] :
( in(X3,X0)
& in(X2,X0)
& ( in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(nnf_transformation,[],[f1007]) ).
fof(f1596,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( ( ~ in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ subset(X2,X3)
| in(ordered_pair(X2,X3),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ? [X2,X3] :
( in(X3,X0)
& in(X2,X0)
& ( in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(flattening,[],[f1595]) ).
fof(f1597,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X4,X5] :
( ~ in(X5,X0)
| ~ in(X4,X0)
| ( ( ~ in(ordered_pair(X4,X5),X1)
| subset(X4,X5) )
& ( ~ subset(X4,X5)
| in(ordered_pair(X4,X5),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ? [X2,X3] :
( in(X3,X0)
& in(X2,X0)
& ( in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(rectify,[],[f1596]) ).
fof(f1598,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X4,X5] :
( ~ in(X5,X0)
| ~ in(X4,X0)
| ( ( ~ in(ordered_pair(X4,X5),X1)
| subset(X4,X5) )
& ( ~ subset(X4,X5)
| in(ordered_pair(X4,X5),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ( in(sK354(X0,X1),X0)
& in(sK353(X0,X1),X0)
& ( in(ordered_pair(sK353(X0,X1),sK354(X0,X1)),X1)
| subset(sK353(X0,X1),sK354(X0,X1)) )
& ( ~ in(ordered_pair(sK353(X0,X1),sK354(X0,X1)),X1)
| ~ subset(sK353(X0,X1),sK354(X0,X1)) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK353,sK354]),skolemize(X2,sK353(X0,X1)),skolemize(X3,sK354(X0,X1))],[f1597]) ).
fof(f1599,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( X2 != X3
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f1008]) ).
fof(f1600,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( X2 != X3
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f1599]) ).
fof(f1601,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| ( X4 = X5
& in(X4,X0) ) )
& ( X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ( X2 = X3
& in(X2,X0) ) )
& ( ~ in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f1600]) ).
fof(f1602,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| ( X4 = X5
& in(X4,X0) ) )
& ( X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ( ( in(ordered_pair(sK355(X0,X1),sK356(X0,X1)),X1)
| ( sK355(X0,X1) = sK356(X0,X1)
& in(sK355(X0,X1),X0) ) )
& ( ~ in(ordered_pair(sK355(X0,X1),sK356(X0,X1)),X1)
| sK355(X0,X1) != sK356(X0,X1)
| ~ in(sK355(X0,X1),X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK355,sK356]),skolemize(X2,sK355(X0,X1)),skolemize(X3,sK356(X0,X1))],[f1601]) ).
fof(f1603,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(nnf_transformation,[],[f1016]) ).
fof(f1604,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) )
& ( ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(rectify,[],[f1603]) ).
fof(f1605,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) )
& ( ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ( ( in(ordered_pair(sK357(X0,X1),sK358(X0,X1)),X1)
| in(ordered_pair(sK358(X0,X1),sK357(X0,X1)),X0) )
& ( ~ in(ordered_pair(sK357(X0,X1),sK358(X0,X1)),X1)
| ~ in(ordered_pair(sK358(X0,X1),sK357(X0,X1)),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK357,sK358]),skolemize(X2,sK357(X0,X1)),skolemize(X3,sK358(X0,X1))],[f1604]) ).
fof(f1606,plain,
! [X1,X0,X2] :
( ~ sP41(X1,X0,X2)
| ( ( ~ relation_isomorphism(X0,X1,X2)
| sP40(X2,X0,X1) )
& ( ~ sP40(X2,X0,X1)
| relation_isomorphism(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f1137]) ).
fof(f1607,plain,
! [X0,X1,X2] :
( ~ sP41(X0,X1,X2)
| ( ( ~ relation_isomorphism(X1,X0,X2)
| sP40(X2,X1,X0) )
& ( ~ sP40(X2,X1,X0)
| relation_isomorphism(X1,X0,X2) ) ) ),
inference(rectify,[],[f1606]) ).
fof(f1612,plain,
( one_to_one(sK361)
& function(sK361)
& relation(sK361) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK361]),skolemize(X0,sK361)],[f289]) ).
fof(f1613,plain,
( empty(sK362)
& one_to_one(sK362)
& function(sK362)
& relation(sK362) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK362]),skolemize(X0,sK362)],[f277]) ).
fof(f1614,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(nnf_transformation,[],[f1028]) ).
fof(f1615,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(rectify,[],[f1614]) ).
fof(f1616,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ( apply(X0,sK363(X0)) = apply(X0,sK364(X0))
& in(sK364(X0),relation_dom(X0))
& in(sK363(X0),relation_dom(X0))
& sK363(X0) != sK364(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK363,sK364]),skolemize(X1,sK363(X0)),skolemize(X2,sK364(X0))],[f1615]) ).
fof(f1617,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ well_orders(X0,X1)
| ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) )
& ( ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| well_orders(X0,X1) ) ) ),
inference(nnf_transformation,[],[f1031]) ).
fof(f1618,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ well_orders(X0,X1)
| ( is_well_founded_in(X0,X1)
& is_connected_in(X0,X1)
& is_antisymmetric_in(X0,X1)
& is_transitive_in(X0,X1)
& is_reflexive_in(X0,X1) ) )
& ( ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| well_orders(X0,X1) ) ) ),
inference(flattening,[],[f1617]) ).
fof(f1619,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( ( pair_first(X0) != X3
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X4 ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X0
& X3 != X4 )
| pair_first(X0) = X3 ) ) ),
inference(nnf_transformation,[],[f1032]) ).
fof(f1620,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_first(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X4 ) )
& ( ? [X2,X3] :
( ordered_pair(X2,X3) = X0
& X1 != X2 )
| pair_first(X0) = X1 ) ) ),
inference(rectify,[],[f1619]) ).
fof(f1621,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_first(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X4 ) )
& ( ( ordered_pair(sK365(X0,X1),sK366(X0,X1)) = X0
& sK365(X0,X1) != X1 )
| pair_first(X0) = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK365,sK366]),skolemize(X2,sK365(X0,X1)),skolemize(X3,sK366(X0,X1))],[f1620]) ).
fof(f1622,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( ( pair_second(X0) != X3
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X5 ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X0
& X3 != X5 )
| pair_second(X0) = X3 ) ) ),
inference(nnf_transformation,[],[f1033]) ).
fof(f1623,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_second(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X5 ) )
& ( ? [X2,X3] :
( ordered_pair(X2,X3) = X0
& X1 != X3 )
| pair_second(X0) = X1 ) ) ),
inference(rectify,[],[f1622]) ).
fof(f1624,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_second(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X5 ) )
& ( ( ordered_pair(sK367(X0,X1),sK368(X0,X1)) = X0
& sK368(X0,X1) != X1 )
| pair_second(X0) = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK367,sK368]),skolemize(X2,sK367(X0,X1)),skolemize(X3,sK368(X0,X1))],[f1623]) ).
fof(f1625,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f1046]) ).
fof(f1626,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(rectify,[],[f1625]) ).
fof(f1627,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ( ~ in(sK370(X0),sK369(X0))
& sK369(X0) != sK370(X0)
& ~ in(sK369(X0),sK370(X0))
& in(sK370(X0),X0)
& in(sK369(X0),X0) )
| epsilon_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK369,sK370]),skolemize(X1,sK369(X0)),skolemize(X2,sK370(X0))],[f1626]) ).
fof(f1628,plain,
! [X0] :
( finite(sK371(X0))
& natural(sK371(X0))
& ordinal(sK371(X0))
& epsilon_connected(sK371(X0))
& epsilon_transitive(sK371(X0))
& one_to_one(sK371(X0))
& function(sK371(X0))
& relation(sK371(X0))
& empty(sK371(X0))
& element(sK371(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK371]),skolemize(X1,sK371(X0))],[f281]) ).
fof(f1629,plain,
( natural(sK372)
& ordinal(sK372)
& epsilon_connected(sK372)
& epsilon_transitive(sK372)
& ~ empty(sK372) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK372]),skolemize(X0,sK372)],[f270]) ).
fof(f1630,plain,
! [X0,X1] :
( function(sK373(X0,X1))
& relation(sK373(X0,X1))
& relation_of2(sK373(X0,X1),X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK373]),skolemize(X2,sK373(X0,X1))],[f284]) ).
fof(f1631,plain,
! [X0,X1] : relation_of2(sK374(X0,X1),X0,X1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK374]),skolemize(X2,sK374(X0,X1))],[f183]) ).
fof(f1632,plain,
! [X0,X1,X2] :
( ( ~ relation_of2(X2,X0,X1)
| subset(X2,cartesian_product2(X0,X1)) )
& ( ~ subset(X2,cartesian_product2(X0,X1))
| relation_of2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f1633,plain,
meet_semilatt_str(sK375),
inference(skolemize,[status(esa),new_symbols(skolem,[sK375]),skolemize(X0,sK375)],[f178]) ).
fof(f1637,plain,
! [X0] :
( ~ top_str(X0)
| ( ( ~ topological_space(X0)
| ( sP42(X0)
& ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ subset(X1,the_topology(X0))
| in(union_of_subsets(the_carrier(X0),X1),the_topology(X0)) )
& in(the_carrier(X0),the_topology(X0)) ) )
& ( ~ sP42(X0)
| ? [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& subset(X1,the_topology(X0))
& ~ in(union_of_subsets(the_carrier(X0),X1),the_topology(X0)) )
| ~ in(the_carrier(X0),the_topology(X0))
| topological_space(X0) ) ) ),
inference(nnf_transformation,[],[f1140]) ).
fof(f1638,plain,
! [X0] :
( ~ top_str(X0)
| ( ( ~ topological_space(X0)
| ( sP42(X0)
& ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ subset(X1,the_topology(X0))
| in(union_of_subsets(the_carrier(X0),X1),the_topology(X0)) )
& in(the_carrier(X0),the_topology(X0)) ) )
& ( ~ sP42(X0)
| ? [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& subset(X1,the_topology(X0))
& ~ in(union_of_subsets(the_carrier(X0),X1),the_topology(X0)) )
| ~ in(the_carrier(X0),the_topology(X0))
| topological_space(X0) ) ) ),
inference(flattening,[],[f1637]) ).
fof(f1639,plain,
! [X0] :
( ~ top_str(X0)
| ( ( ~ topological_space(X0)
| ( sP42(X0)
& ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ subset(X2,the_topology(X0))
| in(union_of_subsets(the_carrier(X0),X2),the_topology(X0)) )
& in(the_carrier(X0),the_topology(X0)) ) )
& ( ~ sP42(X0)
| ? [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& subset(X1,the_topology(X0))
& ~ in(union_of_subsets(the_carrier(X0),X1),the_topology(X0)) )
| ~ in(the_carrier(X0),the_topology(X0))
| topological_space(X0) ) ) ),
inference(rectify,[],[f1638]) ).
fof(f1640,plain,
! [X0] :
( ~ top_str(X0)
| ( ( ~ topological_space(X0)
| ( sP42(X0)
& ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ subset(X2,the_topology(X0))
| in(union_of_subsets(the_carrier(X0),X2),the_topology(X0)) )
& in(the_carrier(X0),the_topology(X0)) ) )
& ( ~ sP42(X0)
| ( element(sK378(X0),powerset(powerset(the_carrier(X0))))
& subset(sK378(X0),the_topology(X0))
& ~ in(union_of_subsets(the_carrier(X0),sK378(X0)),the_topology(X0)) )
| ~ in(the_carrier(X0),the_topology(X0))
| topological_space(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK378]),skolemize(X1,sK378(X0))],[f1639]) ).
fof(f1641,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_antisymmetric_in(X0,X1)
| ! [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X2 = X3 ) )
& ( ? [X2,X3] :
( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1)
& X2 != X3 )
| is_antisymmetric_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f1060]) ).
fof(f1642,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_antisymmetric_in(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| X4 = X5 ) )
& ( ? [X2,X3] :
( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1)
& X2 != X3 )
| is_antisymmetric_in(X0,X1) ) ) ),
inference(rectify,[],[f1641]) ).
fof(f1643,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_antisymmetric_in(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| X4 = X5 ) )
& ( ( in(ordered_pair(sK380(X0,X1),sK379(X0,X1)),X0)
& in(ordered_pair(sK379(X0,X1),sK380(X0,X1)),X0)
& in(sK380(X0,X1),X1)
& in(sK379(X0,X1),X1)
& sK379(X0,X1) != sK380(X0,X1) )
| is_antisymmetric_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK379,sK380]),skolemize(X2,sK379(X0,X1)),skolemize(X3,sK380(X0,X1))],[f1642]) ).
fof(f1644,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| is_antisymmetric_in(X0,relation_field(X0)) )
& ( ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0) ) ) ),
inference(nnf_transformation,[],[f1061]) ).
fof(f1645,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_connected_in(X0,X1)
| ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
& ( ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) )
| is_connected_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f1062]) ).
fof(f1646,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_connected_in(X0,X1)
| ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) ) )
& ( ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) )
| is_connected_in(X0,X1) ) ) ),
inference(rectify,[],[f1645]) ).
fof(f1647,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_connected_in(X0,X1)
| ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) ) )
& ( ( ~ in(ordered_pair(sK382(X0,X1),sK381(X0,X1)),X0)
& ~ in(ordered_pair(sK381(X0,X1),sK382(X0,X1)),X0)
& sK381(X0,X1) != sK382(X0,X1)
& in(sK382(X0,X1),X1)
& in(sK381(X0,X1),X1) )
| is_connected_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK381,sK382]),skolemize(X2,sK381(X0,X1)),skolemize(X3,sK382(X0,X1))],[f1646]) ).
fof(f1648,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ connected(X0)
| is_connected_in(X0,relation_field(X0)) )
& ( ~ is_connected_in(X0,relation_field(X0))
| connected(X0) ) ) ),
inference(nnf_transformation,[],[f1063]) ).
fof(f1649,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_transitive_in(X0,X1)
| ! [X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| in(ordered_pair(X2,X4),X0) ) )
& ( ? [X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1)
& ~ in(ordered_pair(X2,X4),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f1065]) ).
fof(f1650,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_transitive_in(X0,X1)
| ! [X5,X6,X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| in(ordered_pair(X5,X7),X0) ) )
& ( ? [X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1)
& ~ in(ordered_pair(X2,X4),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(rectify,[],[f1649]) ).
fof(f1651,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_transitive_in(X0,X1)
| ! [X5,X6,X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| in(ordered_pair(X5,X7),X0) ) )
& ( ( in(ordered_pair(sK384(X0,X1),sK385(X0,X1)),X0)
& in(ordered_pair(sK383(X0,X1),sK384(X0,X1)),X0)
& in(sK385(X0,X1),X1)
& in(sK384(X0,X1),X1)
& in(sK383(X0,X1),X1)
& ~ in(ordered_pair(sK383(X0,X1),sK385(X0,X1)),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK383,sK384,sK385]),skolemize(X2,sK383(X0,X1)),skolemize(X3,sK384(X0,X1)),skolemize(X4,sK385(X0,X1))],[f1650]) ).
fof(f1652,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ transitive(X0)
| is_transitive_in(X0,relation_field(X0)) )
& ( ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0) ) ) ),
inference(nnf_transformation,[],[f1066]) ).
fof(f1653,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) )
& ( ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0) ) ) ),
inference(nnf_transformation,[],[f1067]) ).
fof(f1654,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_reflexive_in(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| in(ordered_pair(X2,X2),X0) ) )
& ( ? [X2] :
( in(X2,X1)
& ~ in(ordered_pair(X2,X2),X0) )
| is_reflexive_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f1068]) ).
fof(f1655,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_reflexive_in(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| in(ordered_pair(X3,X3),X0) ) )
& ( ? [X2] :
( in(X2,X1)
& ~ in(ordered_pair(X2,X2),X0) )
| is_reflexive_in(X0,X1) ) ) ),
inference(rectify,[],[f1654]) ).
fof(f1656,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_reflexive_in(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| in(ordered_pair(X3,X3),X0) ) )
& ( ( in(sK386(X0,X1),X1)
& ~ in(ordered_pair(sK386(X0,X1),sK386(X0,X1)),X0) )
| is_reflexive_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK386]),skolemize(X2,sK386(X0,X1))],[f1655]) ).
fof(f1657,plain,
( v5_membered(sK387)
& v4_membered(sK387)
& v3_membered(sK387)
& v2_membered(sK387)
& v1_membered(sK387)
& ~ empty(sK387) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK387]),skolemize(X0,sK387)],[f274]) ).
fof(f1658,plain,
! [X2,X0] :
( ~ relation(X0)
| ~ reflexive(X0)
| ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ),
inference(cnf_transformation,[],[f1143]) ).
fof(f1659,plain,
! [X0] :
( ~ relation(X0)
| in(sK43(X0),relation_field(X0))
| reflexive(X0) ),
inference(cnf_transformation,[],[f1143]) ).
fof(f1660,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK43(X0),sK43(X0)),X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f1143]) ).
fof(f1661,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f252]) ).
fof(f1663,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f567]) ).
fof(f1664,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f568]) ).
fof(f1665,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ),
inference(cnf_transformation,[],[f569]) ).
fof(f1666,plain,
! [X0,X6,X4,X5] :
( ~ relation(X0)
| ~ transitive(X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X6),X0) ),
inference(cnf_transformation,[],[f1146]) ).
fof(f1667,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK45(X0),sK46(X0)),X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f1146]) ).
fof(f1668,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK44(X0),sK45(X0)),X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f1146]) ).
fof(f1669,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK44(X0),sK46(X0)),X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f1146]) ).
fof(f1672,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(sK47(X0))
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1) ),
inference(cnf_transformation,[],[f1148]) ).
fof(f1673,plain,
! [X0,X1] :
( ~ relation(X1)
| well_orders(sK47(X0),X0)
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1) ),
inference(cnf_transformation,[],[f1148]) ).
fof(f1677,plain,
! [X3,X0,X4] :
( ~ relation(X0)
| ~ antisymmetric(X0)
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| X3 = X4 ),
inference(cnf_transformation,[],[f1152]) ).
fof(f1678,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK49(X0),sK48(X0)),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1152]) ).
fof(f1679,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK48(X0),sK49(X0)),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1152]) ).
fof(f1680,plain,
! [X0] :
( ~ relation(X0)
| sK48(X0) != sK49(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1152]) ).
fof(f1681,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(cnf_transformation,[],[f578]) ).
fof(f1682,plain,
! [X3,X0,X4] :
( ~ relation(X0)
| ~ connected(X0)
| in(ordered_pair(X4,X3),X0)
| in(ordered_pair(X3,X4),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f1155]) ).
fof(f1683,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK51(X0),sK50(X0)),X0)
| connected(X0) ),
inference(cnf_transformation,[],[f1155]) ).
fof(f1684,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK50(X0),sK51(X0)),X0)
| connected(X0) ),
inference(cnf_transformation,[],[f1155]) ).
fof(f1685,plain,
! [X0] :
( ~ relation(X0)
| sK50(X0) != sK51(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f1155]) ).
fof(f1686,plain,
! [X0] :
( ~ relation(X0)
| in(sK51(X0),relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f1155]) ).
fof(f1687,plain,
! [X0] :
( ~ relation(X0)
| in(sK50(X0),relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f1155]) ).
fof(f1695,plain,
! [X0,X1] :
( in(sK52(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1160]) ).
fof(f1696,plain,
! [X0,X1] :
( ~ in(sK52(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1160]) ).
fof(f1700,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| sP0(sK53(X0,X1),sK55(X0,X1),X1) ),
inference(cnf_transformation,[],[f1164]) ).
fof(f1701,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| in(sK53(X0,X1),X0) ),
inference(cnf_transformation,[],[f1164]) ).
fof(f1702,plain,
! [X0,X1,X6] :
( ~ sP2(X0,X1)
| ~ in(X6,sK56(X0,X1))
| in(ordered_pair(sK54(X0,X1),X6),X1) ),
inference(cnf_transformation,[],[f1164]) ).
fof(f1703,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| in(sK54(X0,X1),sK56(X0,X1)) ),
inference(cnf_transformation,[],[f1164]) ).
fof(f1704,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| sK53(X0,X1) = sK56(X0,X1) ),
inference(cnf_transformation,[],[f1164]) ).
fof(f1706,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| sK54(X0,X1) != sK55(X0,X1) ),
inference(cnf_transformation,[],[f1164]) ).
fof(f1707,plain,
! [X2,X3,X0,X1,X8,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(ordered_pair(X3,X4),X2)
| ~ in(X8,sK58(X1,X3,X4))
| in(ordered_pair(X4,X8),X1) ),
inference(cnf_transformation,[],[f1168]) ).
fof(f1708,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(ordered_pair(X3,X4),X2)
| in(X4,sK58(X1,X3,X4)) ),
inference(cnf_transformation,[],[f1168]) ).
fof(f1709,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(ordered_pair(X3,X4),X2)
| sK58(X1,X3,X4) = X3 ),
inference(cnf_transformation,[],[f1168]) ).
fof(f1710,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(ordered_pair(X3,X4),X2)
| in(X3,X0) ),
inference(cnf_transformation,[],[f1168]) ).
fof(f1717,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| sP1(X0,X1,sK60(X0,X1)) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1718,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| function(sK60(X0,X1)) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1719,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| relation(sK60(X0,X1)) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1726,plain,
! [X0] :
( sK64(X0) = singleton(sK62(X0))
| sP3(X0) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f1727,plain,
! [X0] :
( in(sK62(X0),X0)
| sP3(X0) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f1728,plain,
! [X0] :
( sK63(X0) = singleton(sK62(X0))
| sP3(X0) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f1730,plain,
! [X0] :
( sK63(X0) != sK64(X0)
| sP3(X0) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f1731,plain,
! [X2,X3,X0] :
( ~ in(X3,X0)
| ~ ordinal(X3)
| ~ ordinal(X2)
| ~ in(X2,X0)
| ordinal_subset(sK65(X0),X2) ),
inference(cnf_transformation,[],[f1180]) ).
fof(f1732,plain,
! [X3,X0] :
( ~ in(X3,X0)
| ~ ordinal(X3)
| in(sK65(X0),X0) ),
inference(cnf_transformation,[],[f1180]) ).
fof(f1733,plain,
! [X3,X0] :
( ~ in(X3,X0)
| ~ ordinal(X3)
| ordinal(sK65(X0)) ),
inference(cnf_transformation,[],[f1180]) ).
fof(f1734,plain,
( ~ sP8
| ordinal(sK66) ),
inference(cnf_transformation,[],[f1183]) ).
fof(f1735,plain,
! [X3,X1] :
( ~ sP8
| ~ in(sK66,omega)
| ~ element(X1,powerset(powerset(sK66)))
| ~ subset(sK67(X1),X3)
| ~ in(X3,X1)
| sK67(X1) = X3
| empty_set = X1 ),
inference(cnf_transformation,[],[f1183]) ).
fof(f1736,plain,
! [X1] :
( ~ sP8
| ~ in(sK66,omega)
| ~ element(X1,powerset(powerset(sK66)))
| in(sK67(X1),X1)
| empty_set = X1 ),
inference(cnf_transformation,[],[f1183]) ).
fof(f1737,plain,
( ~ sP8
| in(succ(sK66),omega) ),
inference(cnf_transformation,[],[f1183]) ).
fof(f1738,plain,
( ~ sP8
| sP5(sK66) ),
inference(cnf_transformation,[],[f1183]) ).
fof(f1740,plain,
( ~ sP7
| element(sK68,powerset(powerset(empty_set))) ),
inference(cnf_transformation,[],[f1185]) ).
fof(f1741,plain,
! [X1] :
( ~ sP7
| subset(X1,sK69(X1))
| ~ in(X1,sK68) ),
inference(cnf_transformation,[],[f1185]) ).
fof(f1742,plain,
! [X1] :
( ~ sP7
| in(sK69(X1),sK68)
| ~ in(X1,sK68) ),
inference(cnf_transformation,[],[f1185]) ).
fof(f1743,plain,
! [X1] :
( ~ sP7
| sK69(X1) != X1
| ~ in(X1,sK68) ),
inference(cnf_transformation,[],[f1185]) ).
fof(f1744,plain,
( ~ sP7
| empty_set != sK68 ),
inference(cnf_transformation,[],[f1185]) ).
fof(f1745,plain,
( ~ sP6
| ordinal(sK70) ),
inference(cnf_transformation,[],[f1188]) ).
fof(f1746,plain,
! [X2,X1,X4] :
( ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK70)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(sK71(X2),X4)
| ~ in(X4,X2)
| sK71(X2) = X4
| empty_set = X2 ),
inference(cnf_transformation,[],[f1188]) ).
fof(f1747,plain,
! [X2,X1] :
( ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK70)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| in(sK71(X2),X2)
| empty_set = X2 ),
inference(cnf_transformation,[],[f1188]) ).
fof(f1748,plain,
( ~ sP6
| being_limit_ordinal(sK70) ),
inference(cnf_transformation,[],[f1188]) ).
fof(f1749,plain,
( ~ sP6
| in(sK70,omega) ),
inference(cnf_transformation,[],[f1188]) ).
fof(f1750,plain,
( ~ sP6
| sP4(sK70) ),
inference(cnf_transformation,[],[f1188]) ).
fof(f1751,plain,
( ~ sP6
| empty_set != sK70 ),
inference(cnf_transformation,[],[f1188]) ).
fof(f1752,plain,
! [X0] :
( ~ sP5(X0)
| element(sK72(X0),powerset(powerset(succ(X0)))) ),
inference(cnf_transformation,[],[f1191]) ).
fof(f1753,plain,
! [X2,X0] :
( ~ sP5(X0)
| subset(X2,sK73(X0,X2))
| ~ in(X2,sK72(X0)) ),
inference(cnf_transformation,[],[f1191]) ).
fof(f1754,plain,
! [X2,X0] :
( ~ sP5(X0)
| in(sK73(X0,X2),sK72(X0))
| ~ in(X2,sK72(X0)) ),
inference(cnf_transformation,[],[f1191]) ).
fof(f1755,plain,
! [X2,X0] :
( ~ sP5(X0)
| sK73(X0,X2) != X2
| ~ in(X2,sK72(X0)) ),
inference(cnf_transformation,[],[f1191]) ).
fof(f1756,plain,
! [X0] :
( ~ sP5(X0)
| empty_set != sK72(X0) ),
inference(cnf_transformation,[],[f1191]) ).
fof(f1762,plain,
! [X3,X0,X1] :
( sP6
| sP8
| sP7
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| ~ subset(sK76(X1),X3)
| ~ in(X3,X1)
| sK76(X1) = X3
| empty_set = X1 ),
inference(cnf_transformation,[],[f1196]) ).
fof(f1763,plain,
! [X0,X1] :
( sP6
| sP8
| sP7
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| in(sK76(X1),X1)
| empty_set = X1 ),
inference(cnf_transformation,[],[f1196]) ).
fof(f1764,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(X4,X5),sK77(X0,X1,X2))
| in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1) ),
inference(cnf_transformation,[],[f1199]) ).
fof(f1765,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(X4,X5),sK77(X0,X1,X2))
| in(X5,X0) ),
inference(cnf_transformation,[],[f1199]) ).
fof(f1766,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(X4,X5),sK77(X0,X1,X2))
| in(X4,X0) ),
inference(cnf_transformation,[],[f1199]) ).
fof(f1767,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1)
| ~ in(X5,X0)
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),sK77(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1199]) ).
fof(f1768,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| relation(sK77(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1199]) ).
fof(f1769,plain,
! [X2,X0,X1,X4,X12] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK78(X0,X1,X2))
| ~ in(X12,sK82(X0,X1,X4))
| in(ordered_pair(sK81(X0,X1,X4),X12),X1) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1770,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK78(X0,X1,X2))
| in(sK81(X0,X1,X4),sK82(X0,X1,X4)) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1771,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK78(X0,X1,X2))
| sK80(X0,X1,X4) = sK82(X0,X1,X4) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1772,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK78(X0,X1,X2))
| in(sK80(X0,X1,X4),X0) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1773,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK78(X0,X1,X2))
| ordered_pair(sK80(X0,X1,X4),sK81(X0,X1,X4)) = X4 ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1774,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK78(X0,X1,X2))
| in(X4,cartesian_product2(X0,X2)) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1775,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ relation(X1)
| empty(X0)
| in(sK79(X1,X6,X7),X7)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X4
| ~ in(X4,cartesian_product2(X0,X2))
| in(X4,sK78(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1776,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ relation(X1)
| empty(X0)
| ~ in(ordered_pair(X6,sK79(X1,X6,X7)),X1)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X4
| ~ in(X4,cartesian_product2(X0,X2))
| in(X4,sK78(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1777,plain,
! [X3,X0,X1] :
( ~ in(X3,sK83(X0,X1))
| sK85(X0,X3) = singleton(sK84(X0,X3)) ),
inference(cnf_transformation,[],[f1207]) ).
fof(f1778,plain,
! [X3,X0,X1] :
( ~ in(X3,sK83(X0,X1))
| in(sK84(X0,X3),X0) ),
inference(cnf_transformation,[],[f1207]) ).
fof(f1779,plain,
! [X3,X0,X1] :
( ~ in(X3,sK83(X0,X1))
| ordered_pair(sK84(X0,X3),sK85(X0,X3)) = X3 ),
inference(cnf_transformation,[],[f1207]) ).
fof(f1780,plain,
! [X3,X0,X1] :
( ~ in(X3,sK83(X0,X1))
| in(X3,cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f1207]) ).
fof(f1781,plain,
! [X3,X0,X1,X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3
| ~ in(X3,cartesian_product2(X0,X1))
| in(X3,sK83(X0,X1)) ),
inference(cnf_transformation,[],[f1207]) ).
fof(f1782,plain,
! [X2,X0] :
( ~ sP10(X0)
| ~ in(X2,sK86(X0))
| sP9(X0,X2) ),
inference(cnf_transformation,[],[f1209]) ).
fof(f1783,plain,
! [X2,X0] :
( ~ sP10(X0)
| ~ sP9(X0,X2)
| in(X2,sK86(X0)) ),
inference(cnf_transformation,[],[f1209]) ).
fof(f1795,plain,
! [X0] :
( ~ ordinal(X0)
| sP10(X0) ),
inference(cnf_transformation,[],[f1089]) ).
fof(f1796,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK91(X0,X1))
| subset(X1,X3) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1797,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK91(X0,X1))
| closed_subset(sK92(X0,X1,X3),X0) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1798,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK91(X0,X1))
| sK92(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1799,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK91(X0,X1))
| element(sK92(X0,X1,X3),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1800,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK91(X0,X1))
| in(X3,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1801,plain,
! [X3,X0,X1,X4] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,sK91(X0,X1)) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1802,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK93(X0,X1))
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) ),
inference(cnf_transformation,[],[f1220]) ).
fof(f1803,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK93(X0,X1))
| in(X3,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1220]) ).
fof(f1804,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,sK93(X0,X1)) ),
inference(cnf_transformation,[],[f1220]) ).
fof(f1805,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ~ in(X3,sK94(X0,X1))
| set_difference(sK95(X0,X1,X3),singleton(X0)) = X3 ),
inference(cnf_transformation,[],[f1224]) ).
fof(f1806,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ~ in(X3,sK94(X0,X1))
| in(sK95(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f1224]) ).
fof(f1807,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ~ in(X3,sK94(X0,X1))
| in(X3,powerset(X0)) ),
inference(cnf_transformation,[],[f1224]) ).
fof(f1808,plain,
! [X3,X0,X1,X4] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1)
| ~ in(X3,powerset(X0))
| in(X3,sK94(X0,X1)) ),
inference(cnf_transformation,[],[f1224]) ).
fof(f1809,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK96(X0,X1,X2))
| in(ordered_pair(apply(X2,sK97(X1,X2,X4)),apply(X2,sK98(X1,X2,X4))),X1) ),
inference(cnf_transformation,[],[f1228]) ).
fof(f1810,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK96(X0,X1,X2))
| ordered_pair(sK97(X1,X2,X4),sK98(X1,X2,X4)) = X4 ),
inference(cnf_transformation,[],[f1228]) ).
fof(f1811,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK96(X0,X1,X2))
| in(X4,cartesian_product2(X0,X0)) ),
inference(cnf_transformation,[],[f1228]) ).
fof(f1812,plain,
! [X2,X0,X1,X6,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4
| ~ in(X4,cartesian_product2(X0,X0))
| in(X4,sK96(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1228]) ).
fof(f1813,plain,
! [X2,X0] :
( ~ in(X2,sK99(X0))
| ordinal(X2) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1814,plain,
! [X2,X0] :
( ~ in(X2,sK99(X0))
| in(X2,X0) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1815,plain,
! [X2,X0] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| in(X2,sK99(X0)) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1816,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ in(X4,sK100(X1,X2))
| in(relation_image(X2,X4),X1) ),
inference(cnf_transformation,[],[f1234]) ).
fof(f1817,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ in(X4,sK100(X1,X2))
| in(X4,powerset(relation_dom(X2))) ),
inference(cnf_transformation,[],[f1234]) ).
fof(f1818,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ in(relation_image(X2,X4),X1)
| ~ in(X4,powerset(relation_dom(X2)))
| in(X4,sK100(X1,X2)) ),
inference(cnf_transformation,[],[f1234]) ).
fof(f1819,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ in(X3,sK101(X0,X1))
| in(sK102(X0,X3),X0) ),
inference(cnf_transformation,[],[f1238]) ).
fof(f1820,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ in(X3,sK101(X0,X1))
| sK102(X0,X3) = X3 ),
inference(cnf_transformation,[],[f1238]) ).
fof(f1821,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ in(X3,sK101(X0,X1))
| ordinal(sK102(X0,X3)) ),
inference(cnf_transformation,[],[f1238]) ).
fof(f1822,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ in(X3,sK101(X0,X1))
| in(X3,succ(X1)) ),
inference(cnf_transformation,[],[f1238]) ).
fof(f1823,plain,
! [X3,X0,X1,X4] :
( ~ ordinal(X1)
| ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4)
| ~ in(X3,succ(X1))
| in(X3,sK101(X0,X1)) ),
inference(cnf_transformation,[],[f1238]) ).
fof(f1824,plain,
! [X3,X0,X1,X5] :
( ~ sP12(X0,X1)
| ~ in(X3,X0)
| ~ in(X5,sK104(X0,X1,X3))
| in(ordered_pair(apply(sK103(X0,X1),X3),X5),X1) ),
inference(cnf_transformation,[],[f1241]) ).
fof(f1825,plain,
! [X3,X0,X1] :
( ~ sP12(X0,X1)
| ~ in(X3,X0)
| in(apply(sK103(X0,X1),X3),sK104(X0,X1,X3)) ),
inference(cnf_transformation,[],[f1241]) ).
fof(f1826,plain,
! [X3,X0,X1] :
( ~ sP12(X0,X1)
| ~ in(X3,X0)
| sK104(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1241]) ).
fof(f1827,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| relation_dom(sK103(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f1241]) ).
fof(f1828,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| function(sK103(X0,X1)) ),
inference(cnf_transformation,[],[f1241]) ).
fof(f1829,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| relation(sK103(X0,X1)) ),
inference(cnf_transformation,[],[f1241]) ).
fof(f1838,plain,
! [X3,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| in(sK111(X1,X3,X4),X4)
| ~ in(X3,X4)
| sK110(X0,X1) != X4
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(cnf_transformation,[],[f1245]) ).
fof(f1839,plain,
! [X3,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(ordered_pair(X3,sK111(X1,X3,X4)),X1)
| ~ in(X3,X4)
| sK110(X0,X1) != X4
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(cnf_transformation,[],[f1245]) ).
fof(f1840,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| in(sK110(X0,X1),X0)
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(cnf_transformation,[],[f1245]) ).
fof(f1845,plain,
! [X2,X0,X4] :
( singleton(sK116(X0)) != X4
| sP13(X0)
| ~ in(X2,X0)
| singleton(X2) = apply(sK115(X0),X2) ),
inference(cnf_transformation,[],[f1249]) ).
fof(f1847,plain,
! [X0,X4] :
( singleton(sK116(X0)) != X4
| sP13(X0)
| relation_dom(sK115(X0)) = X0 ),
inference(cnf_transformation,[],[f1249]) ).
fof(f1849,plain,
! [X0,X4] :
( singleton(sK116(X0)) != X4
| sP13(X0)
| function(sK115(X0)) ),
inference(cnf_transformation,[],[f1249]) ).
fof(f1851,plain,
! [X0,X4] :
( singleton(sK116(X0)) != X4
| sP13(X0)
| relation(sK115(X0)) ),
inference(cnf_transformation,[],[f1249]) ).
fof(f1853,plain,
( ~ sP15
| ordinal(sK117) ),
inference(cnf_transformation,[],[f1251]) ).
fof(f1854,plain,
! [X2,X1,X4] :
( ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK117)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(sK118(X2),X4)
| ~ in(X4,X2)
| sK118(X2) = X4
| empty_set = X2 ),
inference(cnf_transformation,[],[f1251]) ).
fof(f1855,plain,
! [X2,X1] :
( ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK117)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| in(sK118(X2),X2)
| empty_set = X2 ),
inference(cnf_transformation,[],[f1251]) ).
fof(f1856,plain,
( ~ sP15
| in(sK117,omega) ),
inference(cnf_transformation,[],[f1251]) ).
fof(f1857,plain,
( ~ sP15
| sP14(sK117) ),
inference(cnf_transformation,[],[f1251]) ).
fof(f1863,plain,
! [X3,X0,X1] :
( sP15
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| ~ subset(sK121(X1),X3)
| ~ in(X3,X1)
| sK121(X1) = X3
| empty_set = X1 ),
inference(cnf_transformation,[],[f1256]) ).
fof(f1864,plain,
! [X0,X1] :
( sP15
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| in(sK121(X1),X1)
| empty_set = X1 ),
inference(cnf_transformation,[],[f1256]) ).
fof(f1865,plain,
! [X2,X0] :
( ~ in(X2,X0)
| singleton(X2) = apply(sK122(X0),X2) ),
inference(cnf_transformation,[],[f1257]) ).
fof(f1866,plain,
! [X0] : relation_dom(sK122(X0)) = X0,
inference(cnf_transformation,[],[f1257]) ).
fof(f1867,plain,
! [X0] : function(sK122(X0)),
inference(cnf_transformation,[],[f1257]) ).
fof(f1868,plain,
! [X0] : relation(sK122(X0)),
inference(cnf_transformation,[],[f1257]) ).
fof(f1869,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,sK123(X0,X1))
| subset(X1,X3) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f1870,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,sK123(X0,X1))
| closed_subset(sK124(X0,X1,X3),X0) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f1871,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,sK123(X0,X1))
| sK124(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1260]) ).
fof(f1872,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,sK123(X0,X1))
| element(sK124(X0,X1,X3),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f1874,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| element(sK123(X0,X1),powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f1875,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,sK125(X0,X1))
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f1876,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| in(X3,sK125(X0,X1)) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f1877,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| element(sK125(X0,X1),powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f1878,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f1264]) ).
fof(f1879,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f1264]) ).
fof(f1881,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f347]) ).
fof(f1882,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f620]) ).
fof(f1883,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f1266]) ).
fof(f1884,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f1266]) ).
fof(f1885,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f1266]) ).
fof(f1886,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
inference(cnf_transformation,[],[f622]) ).
fof(f1887,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng_restriction(X0,X1),X1) ),
inference(cnf_transformation,[],[f623]) ).
fof(f1888,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
inference(cnf_transformation,[],[f624]) ).
fof(f1889,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
inference(cnf_transformation,[],[f625]) ).
fof(f1890,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f625]) ).
fof(f1891,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
inference(cnf_transformation,[],[f626]) ).
fof(f1892,plain,
! [X2,X3,X0,X1] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(cnf_transformation,[],[f628]) ).
fof(f1894,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| subset(relation_rng(X2),X1) ),
inference(cnf_transformation,[],[f630]) ).
fof(f1895,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| subset(relation_dom(X2),X0) ),
inference(cnf_transformation,[],[f630]) ).
fof(f1896,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f631]) ).
fof(f1897,plain,
! [X0,X5] :
( in(X5,sK126(X0))
| are_equipotent(X5,sK126(X0))
| ~ subset(X5,sK126(X0)) ),
inference(cnf_transformation,[],[f1267]) ).
fof(f1898,plain,
! [X0,X4] :
( ~ in(X4,sK126(X0))
| in(powerset(X4),sK126(X0)) ),
inference(cnf_transformation,[],[f1267]) ).
fof(f1899,plain,
! [X2,X3,X0] :
( ~ subset(X3,X2)
| ~ in(X2,sK126(X0))
| in(X3,sK126(X0)) ),
inference(cnf_transformation,[],[f1267]) ).
fof(f1900,plain,
! [X0] : in(X0,sK126(X0)),
inference(cnf_transformation,[],[f1267]) ).
fof(f1901,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(cnf_transformation,[],[f635]) ).
fof(f1902,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| relation_dom_restriction(relation_rng_restriction(X0,X2),X1) = relation_rng_restriction(X0,relation_dom_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f636]) ).
fof(f1903,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(sK127(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1270]) ).
fof(f1904,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(ordered_pair(sK127(X0,X1,X2),X0),X2) ),
inference(cnf_transformation,[],[f1270]) ).
fof(f1905,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(sK127(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[],[f1270]) ).
fof(f1907,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f638]) ).
fof(f1908,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(cnf_transformation,[],[f640]) ).
fof(f1909,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(cnf_transformation,[],[f641]) ).
fof(f1910,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_dom(X1))
| subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ),
inference(cnf_transformation,[],[f643]) ).
fof(f1911,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_image(X0,relation_dom(X0)) ),
inference(cnf_transformation,[],[f644]) ).
fof(f1912,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_rng(X1))
| relation_image(X1,relation_inverse_image(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f646]) ).
fof(f1913,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(relation_rng(X3),X1)
| relation_of2_as_subset(X3,X2,X1) ),
inference(cnf_transformation,[],[f648]) ).
fof(f1915,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 ),
inference(cnf_transformation,[],[f650]) ).
fof(f1916,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ),
inference(cnf_transformation,[],[f651]) ).
fof(f1917,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(sK128(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1273]) ).
fof(f1918,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(ordered_pair(X0,sK128(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f1273]) ).
fof(f1919,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(sK128(X0,X1,X2),relation_rng(X2)) ),
inference(cnf_transformation,[],[f1273]) ).
fof(f1921,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f653]) ).
fof(f1922,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(X3,X2,X1) ),
inference(cnf_transformation,[],[f655]) ).
fof(f1923,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f1275]) ).
fof(f1924,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,X2) ),
inference(cnf_transformation,[],[f1275]) ).
fof(f1925,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f1275]) ).
fof(f1926,plain,
! [X0,X1] :
( ~ relation(X1)
| empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0 ),
inference(cnf_transformation,[],[f658]) ).
fof(f1927,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ subset(X0,X1)
| subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(cnf_transformation,[],[f660]) ).
fof(f1929,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) ),
inference(cnf_transformation,[],[f663]) ).
fof(f1930,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
inference(cnf_transformation,[],[f664]) ).
fof(f1932,plain,
! [X3,X0,X1] :
( ~ finite(X0)
| ~ element(X1,powerset(powerset(X0)))
| ~ subset(sK129(X1),X3)
| ~ in(X3,X1)
| sK129(X1) = X3
| empty_set = X1 ),
inference(cnf_transformation,[],[f1276]) ).
fof(f1933,plain,
! [X0,X1] :
( ~ finite(X0)
| ~ element(X1,powerset(powerset(X0)))
| in(sK129(X1),X1)
| empty_set = X1 ),
inference(cnf_transformation,[],[f1276]) ).
fof(f1934,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f667]) ).
fof(f1935,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f669]) ).
fof(f1936,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f669]) ).
fof(f1937,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f671]) ).
fof(f1938,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f673]) ).
fof(f1939,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f390]) ).
fof(f1942,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_field(relation_restriction(X1,X0)),X0) ),
inference(cnf_transformation,[],[f676]) ).
fof(f1943,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ),
inference(cnf_transformation,[],[f676]) ).
fof(f1944,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(apply(X2,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f1278]) ).
fof(f1945,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f1278]) ).
fof(f1946,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| in(X0,relation_dom(relation_composition(X2,X1))) ),
inference(cnf_transformation,[],[f1278]) ).
fof(f1947,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ~ function(X4)
| ~ relation(X4)
| ~ in(X2,X0)
| apply(relation_composition(X3,X4),X2) = apply(X4,apply(X3,X2))
| empty_set = X1 ),
inference(cnf_transformation,[],[f680]) ).
fof(f1948,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f682]) ).
fof(f1949,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(cnf_transformation,[],[f683]) ).
fof(f1950,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
inference(cnf_transformation,[],[f684]) ).
fof(f1951,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ),
inference(cnf_transformation,[],[f686]) ).
fof(f1952,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 ),
inference(cnf_transformation,[],[f687]) ).
fof(f1953,plain,
! [X2,X0,X1,X6] :
( ~ relation_of2_as_subset(X2,X1,X0)
| ~ in(ordered_pair(sK131(X1,X2),X6),X2)
| relation_dom_as_subset(X1,X0,X2) = X1 ),
inference(cnf_transformation,[],[f1281]) ).
fof(f1954,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X1,X0)
| in(sK131(X1,X2),X1)
| relation_dom_as_subset(X1,X0,X2) = X1 ),
inference(cnf_transformation,[],[f1281]) ).
fof(f1955,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X2,X1,X0)
| relation_dom_as_subset(X1,X0,X2) != X1
| in(ordered_pair(X3,sK130(X2,X3)),X2)
| ~ in(X3,X1) ),
inference(cnf_transformation,[],[f1281]) ).
fof(f1956,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ reflexive(X1)
| reflexive(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f690]) ).
fof(f1957,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f692]) ).
fof(f1958,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(cnf_transformation,[],[f694]) ).
fof(f1959,plain,
! [X2,X0,X1,X6] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(ordered_pair(X6,sK133(X1,X2)),X2)
| relation_rng_as_subset(X0,X1,X2) = X1 ),
inference(cnf_transformation,[],[f1284]) ).
fof(f1960,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| in(sK133(X1,X2),X1)
| relation_rng_as_subset(X0,X1,X2) = X1 ),
inference(cnf_transformation,[],[f1284]) ).
fof(f1961,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_rng_as_subset(X0,X1,X2) != X1
| in(ordered_pair(sK132(X2,X3),X3),X2)
| ~ in(X3,X1) ),
inference(cnf_transformation,[],[f1284]) ).
fof(f1962,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ connected(X1)
| connected(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f697]) ).
fof(f1963,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
inference(cnf_transformation,[],[f699]) ).
fof(f1964,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ transitive(X1)
| transitive(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f701]) ).
fof(f1965,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(X0,X1)
| subset(relation_rng(X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f703]) ).
fof(f1966,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(X0,X1)
| subset(relation_dom(X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f703]) ).
fof(f1967,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ antisymmetric(X1)
| antisymmetric(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f705]) ).
fof(f1968,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_orders(X1,X0)
| well_ordering(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f707]) ).
fof(f1969,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_orders(X1,X0)
| relation_field(relation_restriction(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f707]) ).
fof(f1970,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ finite(relation_dom(X0))
| finite(relation_rng(X0)) ),
inference(cnf_transformation,[],[f709]) ).
fof(f1971,plain,
! [X0] : well_orders(sK134(X0),X0),
inference(cnf_transformation,[],[f1285]) ).
fof(f1972,plain,
! [X0] : relation(sK134(X0)),
inference(cnf_transformation,[],[f1285]) ).
fof(f1973,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f710]) ).
fof(f1974,plain,
! [X0] :
( empty(X0)
| function(sK136(X0))
| empty_set = sK135(X0) ),
inference(cnf_transformation,[],[f1286]) ).
fof(f1975,plain,
! [X0] :
( empty(X0)
| relation(sK136(X0))
| empty_set = sK135(X0) ),
inference(cnf_transformation,[],[f1286]) ).
fof(f1976,plain,
! [X3,X0] :
( empty(X0)
| ~ in(X3,X0)
| in(apply(sK136(X0),X3),X3)
| empty_set = sK135(X0) ),
inference(cnf_transformation,[],[f1286]) ).
fof(f1977,plain,
! [X0] :
( empty(X0)
| relation_dom(sK136(X0)) = X0
| empty_set = sK135(X0) ),
inference(cnf_transformation,[],[f1286]) ).
fof(f1978,plain,
! [X0] :
( empty(X0)
| function(sK136(X0))
| in(sK135(X0),X0) ),
inference(cnf_transformation,[],[f1286]) ).
fof(f1979,plain,
! [X0] :
( empty(X0)
| relation(sK136(X0))
| in(sK135(X0),X0) ),
inference(cnf_transformation,[],[f1286]) ).
fof(f1980,plain,
! [X3,X0] :
( empty(X0)
| ~ in(X3,X0)
| in(apply(sK136(X0),X3),X3)
| in(sK135(X0),X0) ),
inference(cnf_transformation,[],[f1286]) ).
fof(f1981,plain,
! [X0] :
( empty(X0)
| relation_dom(sK136(X0)) = X0
| in(sK135(X0),X0) ),
inference(cnf_transformation,[],[f1286]) ).
fof(f1982,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f713]) ).
fof(f1983,plain,
top_str(sK137),
inference(cnf_transformation,[],[f1289]) ).
fof(f1984,plain,
element(sK138,powerset(the_carrier(sK137))),
inference(cnf_transformation,[],[f1289]) ).
fof(f1985,plain,
( closed_subset(sK138,sK137)
| open_subset(subset_complement(the_carrier(sK137),sK138),sK137) ),
inference(cnf_transformation,[],[f1289]) ).
fof(f1986,plain,
( ~ closed_subset(sK138,sK137)
| ~ open_subset(subset_complement(the_carrier(sK137),sK138),sK137) ),
inference(cnf_transformation,[],[f1289]) ).
fof(f1987,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f423]) ).
fof(f1988,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f424]) ).
fof(f1989,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_field(X2)) ),
inference(cnf_transformation,[],[f716]) ).
fof(f1990,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f716]) ).
fof(f1991,plain,
! [X0] :
( in(sK139(X0),X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f1290]) ).
fof(f1992,plain,
! [X0] :
( ~ subset(sK139(X0),X0)
| ~ ordinal(sK139(X0))
| ordinal(X0) ),
inference(cnf_transformation,[],[f1290]) ).
fof(f1993,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_founded_relation(X1)
| well_founded_relation(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f719]) ).
fof(f1994,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ordinal(sK140(X0))
| empty_set = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1291]) ).
fof(f1995,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X3)
| ~ in(X3,X0)
| ordinal_subset(sK140(X0),X3)
| empty_set = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1291]) ).
fof(f1996,plain,
! [X0,X1] :
( ~ ordinal(X1)
| in(sK140(X0),X0)
| empty_set = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1291]) ).
fof(f1997,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_ordering(X1)
| well_ordering(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f723]) ).
fof(f1998,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal_subset(succ(X0),X1) ),
inference(cnf_transformation,[],[f1292]) ).
fof(f1999,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ ordinal_subset(succ(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f1292]) ).
fof(f2000,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f725]) ).
fof(f2001,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(X0,X1)
| X1 = X3 ),
inference(cnf_transformation,[],[f726]) ).
fof(f2002,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f726]) ).
fof(f2005,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK141(X0,X1),X0)
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1296]) ).
fof(f2006,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| sK141(X0,X1) != apply(X1,sK141(X0,X1))
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1296]) ).
fof(f2007,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(cnf_transformation,[],[f729]) ).
fof(f2008,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f435]) ).
fof(f2009,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f730]) ).
fof(f2010,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f730]) ).
fof(f2011,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1297]) ).
fof(f2012,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f1297]) ).
fof(f2014,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f1298]) ).
fof(f2015,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f1300]) ).
fof(f2016,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f1300]) ).
fof(f2017,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f1300]) ).
fof(f2018,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| relation_field(relation_restriction(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f732]) ).
fof(f2019,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f441]) ).
fof(f2020,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f1302]) ).
fof(f2023,plain,
! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f733]) ).
fof(f2024,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f446]) ).
fof(f2025,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,X1)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f1303]) ).
fof(f2026,plain,
! [X0,X1] :
( in(sK142(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1303]) ).
fof(f2027,plain,
! [X0,X1] :
( in(sK142(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1303]) ).
fof(f2028,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f735]) ).
fof(f2029,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f449]) ).
fof(f2030,plain,
! [X2,X0] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X2)
| ~ in(X2,X0)
| in(succ(X2),X0) ),
inference(cnf_transformation,[],[f1306]) ).
fof(f2031,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK143(X0))
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1306]) ).
fof(f2032,plain,
! [X0] :
( ~ ordinal(X0)
| in(sK143(X0),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1306]) ).
fof(f2033,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(succ(sK143(X0)),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1306]) ).
fof(f2034,plain,
! [X2,X0] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| succ(X2) != X0
| ~ ordinal(X2) ),
inference(cnf_transformation,[],[f1307]) ).
fof(f2035,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK144(X0))
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1307]) ).
fof(f2036,plain,
! [X0] :
( ~ ordinal(X0)
| succ(sK144(X0)) = X0
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1307]) ).
fof(f2037,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| ~ disjoint(X1,X2)
| subset(X1,subset_complement(X0,X2)) ),
inference(cnf_transformation,[],[f1308]) ).
fof(f2038,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| ~ subset(X1,subset_complement(X0,X2))
| disjoint(X1,X2) ),
inference(cnf_transformation,[],[f1308]) ).
fof(f2039,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| element(sK145(X0,X1),powerset(the_carrier(X0)))
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f1309]) ).
fof(f2040,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(sK145(X0,X1),X1)
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f1309]) ).
fof(f2041,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ closed_subset(sK145(X0,X1),X0)
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f1309]) ).
fof(f2042,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ),
inference(cnf_transformation,[],[f742]) ).
fof(f2043,plain,
! [X2,X0,X1,X4] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| ~ in(X2,topstr_closure(X0,X1))
| ~ element(X4,powerset(the_carrier(X0)))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| in(X2,X4) ),
inference(cnf_transformation,[],[f1312]) ).
fof(f2044,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| element(sK146(X0,X1,X2),powerset(the_carrier(X0)))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f1312]) ).
fof(f2045,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| subset(X1,sK146(X0,X1,X2))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f1312]) ).
fof(f2046,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| closed_subset(sK146(X0,X1,X2),X0)
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f1312]) ).
fof(f2047,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| ~ in(X2,sK146(X0,X1,X2))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f1312]) ).
fof(f2048,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ),
inference(cnf_transformation,[],[f745]) ).
fof(f2050,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| empty_set = X1
| ~ in(X4,relation_inverse_image(X3,X2))
| in(apply(X3,X4),X2) ),
inference(cnf_transformation,[],[f1314]) ).
fof(f2051,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| empty_set = X1
| ~ in(X4,relation_inverse_image(X3,X2))
| in(X4,X0) ),
inference(cnf_transformation,[],[f1314]) ).
fof(f2052,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| empty_set = X1
| ~ in(apply(X3,X4),X2)
| ~ in(X4,X0)
| in(X4,relation_inverse_image(X3,X2)) ),
inference(cnf_transformation,[],[f1314]) ).
fof(f2053,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),sK147(X0,X1)) ),
inference(cnf_transformation,[],[f1317]) ).
fof(f2054,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,sK147(X0,X1))
| subset(X1,X3) ),
inference(cnf_transformation,[],[f1317]) ).
fof(f2055,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,sK147(X0,X1))
| closed_subset(X3,X0) ),
inference(cnf_transformation,[],[f1317]) ).
fof(f2056,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X3,sK147(X0,X1)) ),
inference(cnf_transformation,[],[f1317]) ).
fof(f2057,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| element(sK147(X0,X1),powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f1317]) ).
fof(f2058,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f752]) ).
fof(f2059,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set != complements_of_subsets(X0,X1)
| empty_set = X1 ),
inference(cnf_transformation,[],[f754]) ).
fof(f2060,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(cnf_transformation,[],[f755]) ).
fof(f2061,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(X0) = relation_rng(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f757]) ).
fof(f2062,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ),
inference(cnf_transformation,[],[f759]) ).
fof(f2063,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset(X1,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f760]) ).
fof(f2064,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ),
inference(cnf_transformation,[],[f762]) ).
fof(f2065,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f467]) ).
fof(f2066,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| relation_isomorphism(X1,X0,function_inverse(X2)) ),
inference(cnf_transformation,[],[f764]) ).
fof(f2067,plain,
! [X0] :
( ~ ordinal(X0)
| connected(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f765]) ).
fof(f2068,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f1318]) ).
fof(f2069,plain,
! [X0,X1] :
( in(sK148(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1318]) ).
fof(f2070,plain,
! [X2,X0,X1] :
( empty_set = X0
| ~ element(X1,powerset(X0))
| ~ element(X2,X0)
| in(X2,X1)
| in(X2,subset_complement(X0,X1)) ),
inference(cnf_transformation,[],[f768]) ).
fof(f2071,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| topstr_closure(X0,X1) != X1
| ~ topological_space(X0)
| closed_subset(X1,X0) ),
inference(cnf_transformation,[],[f770]) ).
fof(f2072,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| topstr_closure(X0,X1) = X1 ),
inference(cnf_transformation,[],[f770]) ).
fof(f2073,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ well_founded_relation(X0)
| well_founded_relation(X1) ),
inference(cnf_transformation,[],[f772]) ).
fof(f2074,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ antisymmetric(X0)
| antisymmetric(X1) ),
inference(cnf_transformation,[],[f772]) ).
fof(f2075,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ connected(X0)
| connected(X1) ),
inference(cnf_transformation,[],[f772]) ).
fof(f2076,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ transitive(X0)
| transitive(X1) ),
inference(cnf_transformation,[],[f772]) ).
fof(f2077,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ reflexive(X0)
| reflexive(X1) ),
inference(cnf_transformation,[],[f772]) ).
fof(f2083,plain,
! [X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| sP16(X0,X4,X5,X1) ),
inference(cnf_transformation,[],[f1325]) ).
fof(f2085,plain,
! [X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| in(X5,relation_dom(X0)) ),
inference(cnf_transformation,[],[f1325]) ).
fof(f2087,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ sP16(X0,sK149(X0,X1),sK150(X0,X1),X1)
| sK150(X0,X1) = apply(X1,sK149(X0,X1))
| relation_dom(X1) != relation_rng(X0)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f1325]) ).
fof(f2088,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ sP16(X0,sK149(X0,X1),sK150(X0,X1),X1)
| in(sK149(X0,X1),relation_rng(X0))
| relation_dom(X1) != relation_rng(X0)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f1325]) ).
fof(f2089,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ sP16(X0,sK149(X0,X1),sK150(X0,X1),X1)
| sK149(X0,X1) != apply(X0,sK150(X0,X1))
| ~ in(sK150(X0,X1),relation_dom(X0))
| relation_dom(X1) != relation_rng(X0)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f1325]) ).
fof(f2090,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(cnf_transformation,[],[f776]) ).
fof(f2091,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ well_ordering(X0)
| well_ordering(X1) ),
inference(cnf_transformation,[],[f778]) ).
fof(f2092,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0)) ),
inference(cnf_transformation,[],[f780]) ).
fof(f2093,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(cnf_transformation,[],[f780]) ).
fof(f2094,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK151(X0),sK152(X0)),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f1326]) ).
fof(f2095,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| apply(relation_composition(function_inverse(X1),X1),X0) = X0 ),
inference(cnf_transformation,[],[f784]) ).
fof(f2096,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| apply(X1,apply(function_inverse(X1),X0)) = X0 ),
inference(cnf_transformation,[],[f784]) ).
fof(f2097,plain,
! [X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| is_well_founded_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1327]) ).
fof(f2098,plain,
! [X0] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1327]) ).
fof(f2099,plain,
! [X0] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f484]) ).
fof(f2100,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f485]) ).
fof(f2101,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f485]) ).
fof(f2102,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f786]) ).
fof(f2103,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| one_to_one(function_inverse(X0)) ),
inference(cnf_transformation,[],[f788]) ).
fof(f2104,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(cnf_transformation,[],[f790]) ).
fof(f2105,plain,
! [X0] :
( ~ relation(X0)
| empty_set != relation_rng(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f792]) ).
fof(f2106,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) != empty_set
| empty_set = X0 ),
inference(cnf_transformation,[],[f792]) ).
fof(f2107,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) != empty_set
| empty_set = relation_rng(X0) ),
inference(cnf_transformation,[],[f1328]) ).
fof(f2108,plain,
! [X0] :
( ~ relation(X0)
| empty_set != relation_rng(X0)
| relation_dom(X0) = empty_set ),
inference(cnf_transformation,[],[f1328]) ).
fof(f2109,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) != X0
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f1329]) ).
fof(f2110,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(cnf_transformation,[],[f1329]) ).
fof(f2113,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| in(sK153(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) = X1 ),
inference(cnf_transformation,[],[f1333]) ).
fof(f2114,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| apply(X2,sK153(X1,X2)) != apply(X1,sK153(X1,X2))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) = X1 ),
inference(cnf_transformation,[],[f1333]) ).
fof(f2115,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f493]) ).
fof(f2116,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ~ in(X2,X0)
| in(apply(X3,X2),relation_rng(X3))
| empty_set = X1 ),
inference(cnf_transformation,[],[f797]) ).
fof(f2117,plain,
! [X0] :
( ~ ordinal(X0)
| well_founded_relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f798]) ).
fof(f2118,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f799]) ).
fof(f2119,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(cnf_transformation,[],[f801]) ).
fof(f2120,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f499]) ).
fof(f2121,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f499]) ).
fof(f2122,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(cnf_transformation,[],[f803]) ).
fof(f2123,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| in(ordered_pair(X0,X1),X3) ),
inference(cnf_transformation,[],[f1335]) ).
fof(f2124,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f1335]) ).
fof(f2125,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ),
inference(cnf_transformation,[],[f1335]) ).
fof(f2126,plain,
! [X0,X1] : pair_second(ordered_pair(X0,X1)) = X1,
inference(cnf_transformation,[],[f503]) ).
fof(f2127,plain,
! [X0,X1] : pair_first(ordered_pair(X0,X1)) = X0,
inference(cnf_transformation,[],[f503]) ).
fof(f2128,plain,
! [X0] :
( ~ ordinal(X0)
| well_ordering(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f805]) ).
fof(f2129,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f506]) ).
fof(f2130,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[],[f1336]) ).
fof(f2131,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1336]) ).
fof(f2132,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f1338]) ).
fof(f2133,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f1338]) ).
fof(f2134,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ),
inference(cnf_transformation,[],[f1338]) ).
fof(f2135,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom_restriction(X1,X0),X1) ),
inference(cnf_transformation,[],[f807]) ).
fof(f2136,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| apply(X2,X0) = X1 ),
inference(cnf_transformation,[],[f1340]) ).
fof(f2138,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f1340]) ).
fof(f2139,plain,
! [X0] :
( ~ relation(X0)
| ~ well_orders(X0,relation_field(X0))
| well_ordering(X0) ),
inference(cnf_transformation,[],[f1341]) ).
fof(f2140,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| well_orders(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1341]) ).
fof(f2141,plain,
! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(cnf_transformation,[],[f812]) ).
fof(f2142,plain,
! [X2,X0,X1] :
( singleton(X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f813]) ).
fof(f2143,plain,
! [X0,X1] :
( ~ relation(X1)
| set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f814]) ).
fof(f2144,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f815]) ).
fof(f2145,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
inference(cnf_transformation,[],[f816]) ).
fof(f2146,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
inference(cnf_transformation,[],[f817]) ).
fof(f2147,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f519]) ).
fof(f2149,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ~ subset(X1,X2)
| quasi_total(X3,X0,X2)
| empty_set != X0 ),
inference(cnf_transformation,[],[f819]) ).
fof(f2151,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ~ subset(X1,X2)
| relation_of2_as_subset(X3,X0,X2)
| empty_set = X1 ),
inference(cnf_transformation,[],[f819]) ).
fof(f2152,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| ~ subset(X1,X2)
| quasi_total(X3,X0,X2)
| empty_set = X1 ),
inference(cnf_transformation,[],[f819]) ).
fof(f2154,plain,
! [X2,X0,X1] :
( singleton(X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f820]) ).
fof(f2155,plain,
! [X3,X0,X1] :
( ~ in(X3,sK154(X1))
| ~ in(X3,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1342]) ).
fof(f2156,plain,
! [X0,X1] :
( in(sK154(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1342]) ).
fof(f2157,plain,
! [X0,X1] :
( in(sK155(X0,X1),X0)
| in(sK155(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1344]) ).
fof(f2158,plain,
! [X0,X1] :
( ~ in(sK155(X0,X1),X0)
| ~ in(sK155(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1344]) ).
fof(f2159,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f823]) ).
fof(f2160,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| sP17(sK156(X0,X1),sK158(X0,X1),X1) ),
inference(cnf_transformation,[],[f1346]) ).
fof(f2161,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| in(sK156(X0,X1),X0) ),
inference(cnf_transformation,[],[f1346]) ).
fof(f2162,plain,
! [X0,X1,X6] :
( ~ sP18(X0,X1)
| ~ in(X6,sK159(X0,X1))
| in(ordered_pair(sK157(X0,X1),X6),X1) ),
inference(cnf_transformation,[],[f1346]) ).
fof(f2163,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| in(sK157(X0,X1),sK159(X0,X1)) ),
inference(cnf_transformation,[],[f1346]) ).
fof(f2164,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| sK156(X0,X1) = sK159(X0,X1) ),
inference(cnf_transformation,[],[f1346]) ).
fof(f2166,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| sK157(X0,X1) != sK158(X0,X1) ),
inference(cnf_transformation,[],[f1346]) ).
fof(f2170,plain,
! [X3,X0,X1,X9] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ~ in(X3,sK161(X0,X1))
| ~ in(X9,sK164(X0,X1,X3))
| in(ordered_pair(X3,X9),X1) ),
inference(cnf_transformation,[],[f1352]) ).
fof(f2171,plain,
! [X3,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ~ in(X3,sK161(X0,X1))
| in(X3,sK164(X0,X1,X3)) ),
inference(cnf_transformation,[],[f1352]) ).
fof(f2172,plain,
! [X3,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ~ in(X3,sK161(X0,X1))
| sK163(X0,X1,X3) = sK164(X0,X1,X3) ),
inference(cnf_transformation,[],[f1352]) ).
fof(f2173,plain,
! [X3,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ~ in(X3,sK161(X0,X1))
| in(sK163(X0,X1,X3),X0) ),
inference(cnf_transformation,[],[f1352]) ).
fof(f2178,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK167(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f1355]) ).
fof(f2179,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f1355]) ).
fof(f2180,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK165(X0,X1),X1)
| in(ordered_pair(sK166(X0,X1),sK165(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f1355]) ).
fof(f2181,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK165(X0,X1),X1)
| ~ in(ordered_pair(X3,sK165(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f1355]) ).
fof(f2182,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK170(X0,X5)),X0) ),
inference(cnf_transformation,[],[f1358]) ).
fof(f2183,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f1358]) ).
fof(f2184,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK168(X0,X1),X1)
| in(ordered_pair(sK168(X0,X1),sK169(X0,X1)),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f1358]) ).
fof(f2185,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK168(X0,X1),X1)
| ~ in(ordered_pair(sK168(X0,X1),X3),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f1358]) ).
fof(f2187,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK171(X0,X1),sK172(X0,X1)),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1361]) ).
fof(f2188,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK171(X0,X1),sK172(X0,X1)),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1361]) ).
fof(f2191,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK173(X0,X1),sK174(X0,X1)),X0)
| in(ordered_pair(sK173(X0,X1),sK174(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1364]) ).
fof(f2192,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK173(X0,X1),sK174(X0,X1)),X0)
| ~ in(ordered_pair(sK173(X0,X1),sK174(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1364]) ).
fof(f2193,plain,
! [X0,X4] :
( ~ relation(X0)
| ordered_pair(sK176(X4),sK177(X4)) = X4
| ~ in(X4,X0) ),
inference(cnf_transformation,[],[f1367]) ).
fof(f2194,plain,
! [X2,X3,X0] :
( ordered_pair(X2,X3) != sK175(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f1367]) ).
fof(f2195,plain,
! [X0] :
( in(sK175(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[],[f1367]) ).
fof(f2196,plain,
! [X0,X6,X4,X5] :
( ~ function(X0)
| ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| X5 = X6 ),
inference(cnf_transformation,[],[f1370]) ).
fof(f2197,plain,
! [X0] :
( in(ordered_pair(sK178(X0),sK180(X0)),X0)
| function(X0) ),
inference(cnf_transformation,[],[f1370]) ).
fof(f2198,plain,
! [X0] :
( in(ordered_pair(sK178(X0),sK179(X0)),X0)
| function(X0) ),
inference(cnf_transformation,[],[f1370]) ).
fof(f2199,plain,
! [X0] :
( sK179(X0) != sK180(X0)
| function(X0) ),
inference(cnf_transformation,[],[f1370]) ).
fof(f2200,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f833]) ).
fof(f2201,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2202,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2203,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2204,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2205,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2206,plain,
! [X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2207,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f835]) ).
fof(f2208,plain,
relation(empty_set),
inference(cnf_transformation,[],[f233]) ).
fof(f2211,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f1375]) ).
fof(f2212,plain,
! [X0] :
( in(sK181(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f1375]) ).
fof(f2213,plain,
! [X0] :
( ~ sP20(X0)
| sP19(sK184(X0),X0) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f2214,plain,
! [X0] :
( ~ sP20(X0)
| sK182(X0) = sK184(X0) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f2215,plain,
! [X0] :
( ~ sP20(X0)
| sK186(X0) = singleton(sK185(X0)) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f2216,plain,
! [X0] :
( ~ sP20(X0)
| in(sK185(X0),X0) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f2217,plain,
! [X0] :
( ~ sP20(X0)
| sK183(X0) = ordered_pair(sK185(X0),sK186(X0)) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f2218,plain,
! [X0] :
( ~ sP20(X0)
| sK182(X0) = sK183(X0) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f2219,plain,
! [X0] :
( ~ sP20(X0)
| sK183(X0) != sK184(X0) ),
inference(cnf_transformation,[],[f1378]) ).
fof(f2223,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK189(X0,X1))
| sK192(X0,X3) = singleton(sK191(X0,X3)) ),
inference(cnf_transformation,[],[f1384]) ).
fof(f2224,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK189(X0,X1))
| in(sK191(X0,X3),X0) ),
inference(cnf_transformation,[],[f1384]) ).
fof(f2225,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK189(X0,X1))
| ordered_pair(sK191(X0,X3),sK192(X0,X3)) = X3 ),
inference(cnf_transformation,[],[f1384]) ).
fof(f2226,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK189(X0,X1))
| sK190(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1384]) ).
fof(f2227,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK189(X0,X1))
| in(sK190(X0,X1,X3),cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f1384]) ).
fof(f2228,plain,
! [X3,X0,X1,X6,X4,X5] :
( sP20(X0)
| singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1))
| in(X3,sK189(X0,X1)) ),
inference(cnf_transformation,[],[f1384]) ).
fof(f2234,plain,
! [X2,X0] :
( sP21(X0)
| ~ in(X2,sK196(X0))
| singleton(sK197(X0,X2)) = X2 ),
inference(cnf_transformation,[],[f1389]) ).
fof(f2235,plain,
! [X2,X0] :
( sP21(X0)
| ~ in(X2,sK196(X0))
| in(sK197(X0,X2),X0) ),
inference(cnf_transformation,[],[f1389]) ).
fof(f2239,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f1392]) ).
fof(f2241,plain,
! [X0,X1] :
( in(sK198(X0,X1),X1)
| sK198(X0,X1) = X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f1392]) ).
fof(f2242,plain,
! [X0,X1] :
( ~ in(sK198(X0,X1),X1)
| sK198(X0,X1) != X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f1392]) ).
fof(f2243,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f387]) ).
fof(f2244,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f538]) ).
fof(f2245,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f841]) ).
fof(f2246,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(cnf_transformation,[],[f842]) ).
fof(f2247,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f843]) ).
fof(f2248,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f845]) ).
fof(f2249,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f1396]) ).
fof(f2250,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f1396]) ).
fof(f2251,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f1396]) ).
fof(f2252,plain,
! [X2,X0,X1] :
( in(sK199(X0,X1,X2),X2)
| in(sK199(X0,X1,X2),X1)
| in(sK199(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1396]) ).
fof(f2253,plain,
! [X2,X0,X1] :
( ~ in(sK199(X0,X1,X2),X2)
| ~ in(sK199(X0,X1,X2),X1)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1396]) ).
fof(f2254,plain,
! [X2,X0,X1] :
( ~ in(sK199(X0,X1,X2),X2)
| ~ in(sK199(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1396]) ).
fof(f2255,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f57]) ).
fof(f2256,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f33]) ).
fof(f2257,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f846]) ).
fof(f2258,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f1397]) ).
fof(f2259,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1397]) ).
fof(f2260,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f847]) ).
fof(f2261,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f847]) ).
fof(f2262,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f849]) ).
fof(f2263,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| function(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f851]) ).
fof(f2265,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f852]) ).
fof(f2266,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(ordered_pair(X5,X6),X1) ),
inference(cnf_transformation,[],[f1401]) ).
fof(f2267,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(X6,X0) ),
inference(cnf_transformation,[],[f1401]) ).
fof(f2268,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X1)
| ~ in(X6,X0)
| in(ordered_pair(X5,X6),X2) ),
inference(cnf_transformation,[],[f1401]) ).
fof(f2269,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),X2)
| in(ordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),X1)
| relation_rng_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1401]) ).
fof(f2270,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),X2)
| in(sK201(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1401]) ).
fof(f2271,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),X1)
| ~ in(sK201(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1401]) ).
fof(f2272,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1402]) ).
fof(f2273,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1402]) ).
fof(f2275,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2276,plain,
! [X0,X1] :
( in(sK202(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2277,plain,
! [X0,X1] :
( ~ in(sK202(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2278,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f1408]) ).
fof(f2279,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f1408]) ).
fof(f2280,plain,
! [X0,X1] :
( in(sK203(X0,X1),X1)
| subset(sK203(X0,X1),X0)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f1408]) ).
fof(f2281,plain,
! [X0,X1] :
( ~ in(sK203(X0,X1),X1)
| ~ subset(sK203(X0,X1),X0)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f1408]) ).
fof(f2282,plain,
! [X0,X1] :
( X0 != X1
| subset(X1,X0) ),
inference(cnf_transformation,[],[f1410]) ).
fof(f2284,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1410]) ).
fof(f2285,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| equipotent(X1,X0) ),
inference(cnf_transformation,[],[f855]) ).
fof(f2286,plain,
! [X0] : equipotent(X0,X0),
inference(cnf_transformation,[],[f540]) ).
fof(f2287,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| relation_rng(sK204(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2288,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| relation_dom(sK204(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2289,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| one_to_one(sK204(X0,X1)) ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2290,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| function(sK204(X0,X1)) ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2291,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| relation(sK204(X0,X1)) ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2292,plain,
! [X2,X0,X1] :
( relation_rng(X2) != X1
| relation_dom(X2) != X0
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2)
| equipotent(X0,X1) ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2293,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f469]) ).
fof(f2294,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f443]) ).
fof(f2295,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_difference(X0,X1)) ),
inference(cnf_transformation,[],[f857]) ).
fof(f2302,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f1417]) ).
fof(f2303,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f1417]) ).
fof(f2304,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f1417]) ).
fof(f2305,plain,
! [X2,X0,X1] :
( in(sK205(X0,X1,X2),X2)
| ~ in(sK205(X0,X1,X2),X1)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1417]) ).
fof(f2306,plain,
! [X2,X0,X1] :
( in(sK205(X0,X1,X2),X2)
| in(sK205(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1417]) ).
fof(f2307,plain,
! [X2,X0,X1] :
( ~ in(sK205(X0,X1,X2),X2)
| in(sK205(X0,X1,X2),X1)
| ~ in(sK205(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1417]) ).
fof(f2308,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f861]) ).
fof(f2309,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f863]) ).
fof(f2310,plain,
! [X0] : empty(sK206(X0)),
inference(cnf_transformation,[],[f1418]) ).
fof(f2311,plain,
! [X0] : element(sK206(X0),powerset(X0)),
inference(cnf_transformation,[],[f1418]) ).
fof(f2312,plain,
! [X0] :
( empty(X0)
| ~ empty(sK207(X0)) ),
inference(cnf_transformation,[],[f1419]) ).
fof(f2313,plain,
! [X0] :
( empty(X0)
| element(sK207(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f1419]) ).
fof(f2314,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f202]) ).
fof(f2315,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f865]) ).
fof(f2316,plain,
! [X0] : element(sK208(X0),X0),
inference(cnf_transformation,[],[f1420]) ).
fof(f2317,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,X1) = union(X1) ),
inference(cnf_transformation,[],[f866]) ).
fof(f2318,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(union(X0)) ),
inference(cnf_transformation,[],[f867]) ).
fof(f2319,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(union(X0)) ),
inference(cnf_transformation,[],[f867]) ).
fof(f2320,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(union(X0)) ),
inference(cnf_transformation,[],[f867]) ).
fof(f2321,plain,
! [X0] :
( ~ being_limit_ordinal(X0)
| union(X0) = X0 ),
inference(cnf_transformation,[],[f1421]) ).
fof(f2322,plain,
! [X0] :
( union(X0) != X0
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1421]) ).
fof(f2323,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK211(X0,X5),X0) ),
inference(cnf_transformation,[],[f1424]) ).
fof(f2324,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(X5,sK211(X0,X5)) ),
inference(cnf_transformation,[],[f1424]) ).
fof(f2325,plain,
! [X0,X1,X6,X5] :
( union(X0) != X1
| ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,X1) ),
inference(cnf_transformation,[],[f1424]) ).
fof(f2326,plain,
! [X0,X1] :
( in(sK209(X0,X1),X1)
| in(sK210(X0,X1),X0)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f1424]) ).
fof(f2327,plain,
! [X0,X1] :
( in(sK209(X0,X1),X1)
| in(sK209(X0,X1),sK210(X0,X1))
| union(X0) = X1 ),
inference(cnf_transformation,[],[f1424]) ).
fof(f2328,plain,
! [X3,X0,X1] :
( ~ in(sK209(X0,X1),X1)
| ~ in(X3,X0)
| ~ in(sK209(X0,X1),X3)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f1424]) ).
fof(f2336,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ~ in(X4,sK219(X0,X1,X2))
| in(ordered_pair(apply(X2,sK221(X1,X2,X4)),apply(X2,sK222(X1,X2,X4))),X1) ),
inference(cnf_transformation,[],[f1430]) ).
fof(f2337,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ~ in(X4,sK219(X0,X1,X2))
| ordered_pair(sK221(X1,X2,X4),sK222(X1,X2,X4)) = X4 ),
inference(cnf_transformation,[],[f1430]) ).
fof(f2338,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ~ in(X4,sK219(X0,X1,X2))
| sK220(X0,X1,X2,X4) = X4 ),
inference(cnf_transformation,[],[f1430]) ).
fof(f2339,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ~ in(X4,sK219(X0,X1,X2))
| in(sK220(X0,X1,X2,X4),cartesian_product2(X0,X0)) ),
inference(cnf_transformation,[],[f1430]) ).
fof(f2340,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X0,X0))
| in(X4,sK219(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1430]) ).
fof(f2341,plain,
! [X2,X0,X1,X4] :
( ~ sP26(X0,X1,X2)
| ~ in(X4,sK223(X0,X1,X2))
| sP25(X2,X1,X4,X0) ),
inference(cnf_transformation,[],[f1433]) ).
fof(f2342,plain,
! [X2,X0,X1,X4] :
( ~ sP26(X0,X1,X2)
| ~ sP25(X2,X1,X4,X0)
| in(X4,sK223(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1433]) ).
fof(f2343,plain,
! [X2,X3,X0,X1,X13] :
( ~ sP25(X0,X1,X2,X3)
| ~ in(X13,sK228(X1,X2,X3))
| in(ordered_pair(sK227(X1,X2,X3),X13),X3) ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2344,plain,
! [X2,X3,X0,X1] :
( ~ sP25(X0,X1,X2,X3)
| in(sK227(X1,X2,X3),sK228(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2345,plain,
! [X2,X3,X0,X1] :
( ~ sP25(X0,X1,X2,X3)
| sK226(X1,X2,X3) = sK228(X1,X2,X3) ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2346,plain,
! [X2,X3,X0,X1] :
( ~ sP25(X0,X1,X2,X3)
| in(sK226(X1,X2,X3),X1) ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2347,plain,
! [X2,X3,X0,X1] :
( ~ sP25(X0,X1,X2,X3)
| ordered_pair(sK226(X1,X2,X3),sK227(X1,X2,X3)) = X2 ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2348,plain,
! [X2,X3,X0,X1] :
( ~ sP25(X0,X1,X2,X3)
| sK225(X0,X1,X2,X3) = X2 ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2349,plain,
! [X2,X3,X0,X1] :
( ~ sP25(X0,X1,X2,X3)
| in(sK225(X0,X1,X2,X3),cartesian_product2(X1,X0)) ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2350,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( in(sK224(X3,X6,X7),X7)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X1)
| ordered_pair(X5,X6) != X2
| X2 != X4
| ~ in(X4,cartesian_product2(X1,X0))
| sP25(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2351,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ in(ordered_pair(X6,sK224(X3,X6,X7)),X3)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X1)
| ordered_pair(X5,X6) != X2
| X2 != X4
| ~ in(X4,cartesian_product2(X1,X0))
| sP25(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2352,plain,
! [X2,X0,X1,X6] :
( ~ sP24(X0,X1,X2)
| ~ in(X6,sK231(X0,X1,X2))
| in(ordered_pair(sK230(X0,X1,X2),X6),X2) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2353,plain,
! [X2,X0,X1] :
( ~ sP24(X0,X1,X2)
| in(sK230(X0,X1,X2),sK231(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2354,plain,
! [X2,X0,X1] :
( ~ sP24(X0,X1,X2)
| sK229(X0,X1,X2) = sK231(X0,X1,X2) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2355,plain,
! [X2,X0,X1] :
( ~ sP24(X0,X1,X2)
| in(sK229(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2356,plain,
! [X2,X0,X1] :
( ~ sP24(X0,X1,X2)
| ordered_pair(sK229(X0,X1,X2),sK230(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2362,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP23(sK237(X0,X1),X0,X1)
| sP26(X1,X0,X2) ),
inference(cnf_transformation,[],[f1443]) ).
fof(f2363,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sK235(X0,X1) = sK237(X0,X1)
| sP26(X1,X0,X2) ),
inference(cnf_transformation,[],[f1443]) ).
fof(f2364,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP24(sK236(X0,X1),X0,X1)
| sP26(X1,X0,X2) ),
inference(cnf_transformation,[],[f1443]) ).
fof(f2365,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sK235(X0,X1) = sK236(X0,X1)
| sP26(X1,X0,X2) ),
inference(cnf_transformation,[],[f1443]) ).
fof(f2366,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sK236(X0,X1) != sK237(X0,X1)
| sP26(X1,X0,X2) ),
inference(cnf_transformation,[],[f1443]) ).
fof(f2367,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f873]) ).
fof(f2368,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f874]) ).
fof(f2369,plain,
! [X0,X1] :
( ~ relation(X0)
| relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f875]) ).
fof(f2370,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| ordered_pair(sK241(X0,X1,X8),sK242(X0,X1,X8)) = X8 ),
inference(cnf_transformation,[],[f1446]) ).
fof(f2371,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK242(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f1446]) ).
fof(f2372,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK241(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f1446]) ).
fof(f2373,plain,
! [X2,X10,X0,X1,X8,X9] :
( cartesian_product2(X0,X1) != X2
| ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(X8,X2) ),
inference(cnf_transformation,[],[f1446]) ).
fof(f2374,plain,
! [X2,X0,X1] :
( in(sK238(X0,X1,X2),X2)
| sK238(X0,X1,X2) = ordered_pair(sK239(X0,X1,X2),sK240(X0,X1,X2))
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1446]) ).
fof(f2375,plain,
! [X2,X0,X1] :
( in(sK238(X0,X1,X2),X2)
| in(sK240(X0,X1,X2),X1)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1446]) ).
fof(f2376,plain,
! [X2,X0,X1] :
( in(sK238(X0,X1,X2),X2)
| in(sK239(X0,X1,X2),X0)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1446]) ).
fof(f2377,plain,
! [X2,X0,X1,X4,X5] :
( ~ in(sK238(X0,X1,X2),X2)
| ordered_pair(X4,X5) != sK238(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1446]) ).
fof(f2378,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f876]) ).
fof(f2379,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f878]) ).
fof(f2381,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f879]) ).
fof(f2382,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(ordered_pair(X5,X6),X0) ),
inference(cnf_transformation,[],[f1450]) ).
fof(f2383,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X2)
| in(X5,X1) ),
inference(cnf_transformation,[],[f1450]) ).
fof(f2384,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| in(ordered_pair(X5,X6),X2) ),
inference(cnf_transformation,[],[f1450]) ).
fof(f2385,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(ordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),X2)
| in(ordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),X0)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1450]) ).
fof(f2386,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(ordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),X2)
| in(sK243(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1450]) ).
fof(f2387,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| ~ in(ordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),X0)
| ~ in(sK243(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1450]) ).
fof(f2388,plain,
function(sK245),
inference(cnf_transformation,[],[f1451]) ).
fof(f2389,plain,
empty(sK245),
inference(cnf_transformation,[],[f1451]) ).
fof(f2390,plain,
relation(sK245),
inference(cnf_transformation,[],[f1451]) ).
fof(f2391,plain,
function(sK246),
inference(cnf_transformation,[],[f1452]) ).
fof(f2392,plain,
relation(sK246),
inference(cnf_transformation,[],[f1452]) ).
fof(f2393,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f881]) ).
fof(f2394,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f882]) ).
fof(f2395,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f883]) ).
fof(f2397,plain,
~ empty(sK247),
inference(cnf_transformation,[],[f1453]) ).
fof(f2398,plain,
relation(sK248),
inference(cnf_transformation,[],[f1454]) ).
fof(f2399,plain,
~ empty(sK248),
inference(cnf_transformation,[],[f1454]) ).
fof(f2400,plain,
empty(sK249),
inference(cnf_transformation,[],[f1455]) ).
fof(f2401,plain,
relation(sK250),
inference(cnf_transformation,[],[f1456]) ).
fof(f2402,plain,
empty(sK250),
inference(cnf_transformation,[],[f1456]) ).
fof(f2403,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ element(X1,X0)
| empty(X1) ),
inference(cnf_transformation,[],[f1457]) ).
fof(f2404,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| element(X1,X0) ),
inference(cnf_transformation,[],[f1457]) ).
fof(f2405,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| in(X1,X0) ),
inference(cnf_transformation,[],[f1457]) ).
fof(f2407,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f887]) ).
fof(f2413,plain,
! [X2,X0] :
( sP27
| ~ in(X2,sK254(X0))
| ordinal(X2) ),
inference(cnf_transformation,[],[f1463]) ).
fof(f2414,plain,
! [X2,X0] :
( sP27
| ~ in(X2,sK254(X0))
| sK255(X0,X2) = X2 ),
inference(cnf_transformation,[],[f1463]) ).
fof(f2415,plain,
! [X2,X0] :
( sP27
| ~ in(X2,sK254(X0))
| in(sK255(X0,X2),X0) ),
inference(cnf_transformation,[],[f1463]) ).
fof(f2416,plain,
! [X2,X3,X0] :
( sP27
| ~ ordinal(X2)
| X2 != X3
| ~ in(X3,X0)
| in(X2,sK254(X0)) ),
inference(cnf_transformation,[],[f1463]) ).
fof(f2417,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X0,X0) ),
inference(cnf_transformation,[],[f891]) ).
fof(f2418,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1464]) ).
fof(f2419,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ subset(X0,X1)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f1464]) ).
fof(f2420,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f895]) ).
fof(f2421,plain,
! [X2,X0] :
( ~ sP30(X0)
| ~ in(X2,sK256(X0))
| sP29(X0,X2) ),
inference(cnf_transformation,[],[f1467]) ).
fof(f2422,plain,
! [X2,X0] :
( ~ sP30(X0)
| ~ sP29(X0,X2)
| in(X2,sK256(X0)) ),
inference(cnf_transformation,[],[f1467]) ).
fof(f2423,plain,
! [X0,X11,X1,X9] :
( ~ sP29(X0,X1)
| ~ in(sK260(X1),omega)
| ~ element(X9,powerset(powerset(sK260(X1))))
| ~ subset(sK261(X9),X11)
| ~ in(X11,X9)
| sK261(X9) = X11
| empty_set = X9 ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2424,plain,
! [X0,X1,X9] :
( ~ sP29(X0,X1)
| ~ in(sK260(X1),omega)
| ~ element(X9,powerset(powerset(sK260(X1))))
| in(sK261(X9),X9)
| empty_set = X9 ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2425,plain,
! [X0,X1] :
( ~ sP29(X0,X1)
| sK260(X1) = X1 ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2426,plain,
! [X0,X1] :
( ~ sP29(X0,X1)
| ordinal(sK260(X1)) ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2427,plain,
! [X0,X1] :
( ~ sP29(X0,X1)
| sK259(X0,X1) = X1 ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2428,plain,
! [X0,X1] :
( ~ sP29(X0,X1)
| in(sK259(X0,X1),succ(X0)) ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2429,plain,
! [X2,X3,X0,X1] :
( in(X3,omega)
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP29(X0,X1) ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2430,plain,
! [X2,X3,X0,X1] :
( element(sK257(X3),powerset(powerset(X3)))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP29(X0,X1) ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2431,plain,
! [X2,X3,X0,X1,X5] :
( subset(X5,sK258(X3,X5))
| ~ in(X5,sK257(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP29(X0,X1) ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2432,plain,
! [X2,X3,X0,X1,X5] :
( in(sK258(X3,X5),sK257(X3))
| ~ in(X5,sK257(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP29(X0,X1) ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2433,plain,
! [X2,X3,X0,X1,X5] :
( sK258(X3,X5) != X5
| ~ in(X5,sK257(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP29(X0,X1) ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2434,plain,
! [X2,X3,X0,X1] :
( empty_set != sK257(X3)
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP29(X0,X1) ),
inference(cnf_transformation,[],[f1470]) ).
fof(f2439,plain,
! [X0] :
( ~ ordinal(X0)
| sP28(sK266)
| sP30(X0) ),
inference(cnf_transformation,[],[f1474]) ).
fof(f2440,plain,
! [X0] :
( ~ ordinal(X0)
| sK264 = sK266
| sP30(X0) ),
inference(cnf_transformation,[],[f1474]) ).
fof(f2441,plain,
! [X0,X7,X5] :
( ~ ordinal(X0)
| ~ in(sK267,omega)
| ~ element(X5,powerset(powerset(sK267)))
| ~ subset(sK268(X5),X7)
| ~ in(X7,X5)
| sK268(X5) = X7
| empty_set = X5
| sP30(X0) ),
inference(cnf_transformation,[],[f1474]) ).
fof(f2442,plain,
! [X0,X5] :
( ~ ordinal(X0)
| ~ in(sK267,omega)
| ~ element(X5,powerset(powerset(sK267)))
| in(sK268(X5),X5)
| empty_set = X5
| sP30(X0) ),
inference(cnf_transformation,[],[f1474]) ).
fof(f2443,plain,
! [X0] :
( ~ ordinal(X0)
| sK265 = sK267
| sP30(X0) ),
inference(cnf_transformation,[],[f1474]) ).
fof(f2444,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK267)
| sP30(X0) ),
inference(cnf_transformation,[],[f1474]) ).
fof(f2445,plain,
! [X0] :
( ~ ordinal(X0)
| sK264 = sK265
| sP30(X0) ),
inference(cnf_transformation,[],[f1474]) ).
fof(f2446,plain,
! [X0] :
( ~ ordinal(X0)
| sK265 != sK266
| sP30(X0) ),
inference(cnf_transformation,[],[f1474]) ).
fof(f2447,plain,
~ empty(omega),
inference(cnf_transformation,[],[f198]) ).
fof(f2449,plain,
epsilon_connected(omega),
inference(cnf_transformation,[],[f198]) ).
fof(f2450,plain,
epsilon_transitive(omega),
inference(cnf_transformation,[],[f198]) ).
fof(f2451,plain,
! [X2,X0] :
( omega != X0
| ~ ordinal(X2)
| ~ being_limit_ordinal(X2)
| ~ in(empty_set,X2)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f1478]) ).
fof(f2452,plain,
! [X0] :
( omega != X0
| ordinal(X0) ),
inference(cnf_transformation,[],[f1478]) ).
fof(f2453,plain,
! [X0] :
( omega != X0
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1478]) ).
fof(f2454,plain,
! [X0] :
( omega != X0
| in(empty_set,X0) ),
inference(cnf_transformation,[],[f1478]) ).
fof(f2455,plain,
! [X0] :
( ordinal(sK269(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| omega = X0 ),
inference(cnf_transformation,[],[f1478]) ).
fof(f2456,plain,
! [X0] :
( being_limit_ordinal(sK269(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| omega = X0 ),
inference(cnf_transformation,[],[f1478]) ).
fof(f2457,plain,
! [X0] :
( in(empty_set,sK269(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| omega = X0 ),
inference(cnf_transformation,[],[f1478]) ).
fof(f2458,plain,
! [X0] :
( ~ subset(X0,sK269(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| omega = X0 ),
inference(cnf_transformation,[],[f1478]) ).
fof(f2459,plain,
! [X0] :
( ~ finite(X0)
| in(relation_dom(sK270(X0)),omega) ),
inference(cnf_transformation,[],[f1481]) ).
fof(f2460,plain,
! [X0] :
( ~ finite(X0)
| relation_rng(sK270(X0)) = X0 ),
inference(cnf_transformation,[],[f1481]) ).
fof(f2461,plain,
! [X0] :
( ~ finite(X0)
| function(sK270(X0)) ),
inference(cnf_transformation,[],[f1481]) ).
fof(f2462,plain,
! [X0] :
( ~ finite(X0)
| relation(sK270(X0)) ),
inference(cnf_transformation,[],[f1481]) ).
fof(f2463,plain,
! [X0,X1] :
( ~ in(relation_dom(X1),omega)
| relation_rng(X1) != X0
| ~ function(X1)
| ~ relation(X1)
| finite(X0) ),
inference(cnf_transformation,[],[f1481]) ).
fof(f2465,plain,
! [X0] :
( ~ element(X0,omega)
| ordinal(X0) ),
inference(cnf_transformation,[],[f900]) ).
fof(f2466,plain,
! [X0] :
( ~ element(X0,omega)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f900]) ).
fof(f2467,plain,
! [X0] :
( ~ element(X0,omega)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f900]) ).
fof(f2468,plain,
! [X0] :
( ~ sP32(X0)
| sP31(sK273(X0),X0) ),
inference(cnf_transformation,[],[f1484]) ).
fof(f2469,plain,
! [X0] :
( ~ sP32(X0)
| sK271(X0) = sK273(X0) ),
inference(cnf_transformation,[],[f1484]) ).
fof(f2470,plain,
! [X0] :
( ~ sP32(X0)
| in(sK274(X0),X0) ),
inference(cnf_transformation,[],[f1484]) ).
fof(f2471,plain,
! [X0] :
( ~ sP32(X0)
| sK272(X0) = sK274(X0) ),
inference(cnf_transformation,[],[f1484]) ).
fof(f2472,plain,
! [X0] :
( ~ sP32(X0)
| ordinal(sK274(X0)) ),
inference(cnf_transformation,[],[f1484]) ).
fof(f2473,plain,
! [X0] :
( ~ sP32(X0)
| sK271(X0) = sK272(X0) ),
inference(cnf_transformation,[],[f1484]) ).
fof(f2474,plain,
! [X0] :
( ~ sP32(X0)
| sK272(X0) != sK273(X0) ),
inference(cnf_transformation,[],[f1484]) ).
fof(f2478,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP32(X0)
| ~ in(X3,sK276(X0,X1))
| in(sK278(X0,X3),X0) ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2479,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP32(X0)
| ~ in(X3,sK276(X0,X1))
| sK278(X0,X3) = X3 ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2480,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP32(X0)
| ~ in(X3,sK276(X0,X1))
| ordinal(sK278(X0,X3)) ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2481,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP32(X0)
| ~ in(X3,sK276(X0,X1))
| sK277(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2482,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP32(X0)
| ~ in(X3,sK276(X0,X1))
| in(sK277(X0,X1,X3),succ(X1)) ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2483,plain,
! [X3,X0,X1,X4,X5] :
( ~ ordinal(X1)
| sP32(X0)
| ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5)
| X3 != X4
| ~ in(X4,succ(X1))
| in(X3,sK276(X0,X1)) ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2491,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ~ in(X3,sK284(X0,X1))
| set_difference(sK286(X0,X1,X3),singleton(X0)) = X3 ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2492,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ~ in(X3,sK284(X0,X1))
| in(sK286(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2493,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ~ in(X3,sK284(X0,X1))
| sK285(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2494,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ~ in(X3,sK284(X0,X1))
| in(sK285(X0,X1,X3),powerset(X0)) ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2495,plain,
! [X3,X0,X1,X4,X5] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP33(X1,X0)
| set_difference(X5,singleton(X0)) != X3
| ~ in(X5,X1)
| X3 != X4
| ~ in(X4,powerset(X0))
| in(X3,sK284(X0,X1)) ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2496,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(succ(X0)) ),
inference(cnf_transformation,[],[f905]) ).
fof(f2497,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(succ(X0)) ),
inference(cnf_transformation,[],[f905]) ).
fof(f2498,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(succ(X0)) ),
inference(cnf_transformation,[],[f905]) ).
fof(f2500,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[],[f197]) ).
fof(f2501,plain,
being_limit_ordinal(sK287),
inference(cnf_transformation,[],[f1497]) ).
fof(f2502,plain,
ordinal(sK287),
inference(cnf_transformation,[],[f1497]) ).
fof(f2503,plain,
epsilon_connected(sK287),
inference(cnf_transformation,[],[f1497]) ).
fof(f2504,plain,
epsilon_transitive(sK287),
inference(cnf_transformation,[],[f1497]) ).
fof(f2505,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| apply(X0,sK290(X0,X5)) = X5 ),
inference(cnf_transformation,[],[f1500]) ).
fof(f2506,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(sK290(X0,X5),relation_dom(X0)) ),
inference(cnf_transformation,[],[f1500]) ).
fof(f2507,plain,
! [X0,X1,X6,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| in(X5,X1) ),
inference(cnf_transformation,[],[f1500]) ).
fof(f2508,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK288(X0,X1),X1)
| sK288(X0,X1) = apply(X0,sK289(X0,X1))
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f1500]) ).
fof(f2509,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK288(X0,X1),X1)
| in(sK289(X0,X1),relation_dom(X0))
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f1500]) ).
fof(f2510,plain,
! [X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK288(X0,X1),X1)
| apply(X0,X3) != sK288(X0,X1)
| ~ in(X3,relation_dom(X0))
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f1500]) ).
fof(f2511,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| empty_set = X2 ),
inference(cnf_transformation,[],[f1501]) ).
fof(f2515,plain,
top_str(sK291),
inference(cnf_transformation,[],[f1502]) ).
fof(f2516,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f910]) ).
fof(f2522,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP34(X1,X0)
| ~ in(X3,sK295(X0,X1))
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) ),
inference(cnf_transformation,[],[f1508]) ).
fof(f2523,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP34(X1,X0)
| ~ in(X3,sK295(X0,X1))
| sK296(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1508]) ).
fof(f2524,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP34(X1,X0)
| ~ in(X3,sK295(X0,X1))
| in(sK296(X0,X1,X3),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1508]) ).
fof(f2525,plain,
! [X3,X0,X1,X4] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP34(X1,X0)
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0)))
| in(X3,sK295(X0,X1)) ),
inference(cnf_transformation,[],[f1508]) ).
fof(f2526,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| sP35(X0,sK299(X0,X1),X1) ),
inference(cnf_transformation,[],[f1510]) ).
fof(f2527,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| sK297(X0,X1) = sK299(X0,X1) ),
inference(cnf_transformation,[],[f1510]) ).
fof(f2528,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| subset(X1,sK298(X0,X1)) ),
inference(cnf_transformation,[],[f1510]) ).
fof(f2529,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| closed_subset(sK300(X0,X1),X0) ),
inference(cnf_transformation,[],[f1510]) ).
fof(f2530,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| sK298(X0,X1) = sK300(X0,X1) ),
inference(cnf_transformation,[],[f1510]) ).
fof(f2531,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| element(sK300(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1510]) ).
fof(f2532,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| sK297(X0,X1) = sK298(X0,X1) ),
inference(cnf_transformation,[],[f1510]) ).
fof(f2533,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| sK298(X0,X1) != sK299(X0,X1) ),
inference(cnf_transformation,[],[f1510]) ).
fof(f2538,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ~ in(X3,sK302(X0,X1))
| subset(X1,X3) ),
inference(cnf_transformation,[],[f1516]) ).
fof(f2539,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ~ in(X3,sK302(X0,X1))
| closed_subset(sK304(X0,X1,X3),X0) ),
inference(cnf_transformation,[],[f1516]) ).
fof(f2540,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ~ in(X3,sK302(X0,X1))
| sK304(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1516]) ).
fof(f2541,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ~ in(X3,sK302(X0,X1))
| element(sK304(X0,X1,X3),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1516]) ).
fof(f2542,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ~ in(X3,sK302(X0,X1))
| sK303(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1516]) ).
fof(f2543,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ~ in(X3,sK302(X0,X1))
| in(sK303(X0,X1,X3),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1516]) ).
fof(f2544,plain,
! [X3,X0,X1,X4,X5] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ~ subset(X1,X3)
| ~ closed_subset(X5,X0)
| X3 != X5
| ~ element(X5,powerset(the_carrier(X0)))
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0)))
| in(X3,sK302(X0,X1)) ),
inference(cnf_transformation,[],[f1516]) ).
fof(f2545,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| closed_subset(sK305(X0),X0) ),
inference(cnf_transformation,[],[f1517]) ).
fof(f2546,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| element(sK305(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1517]) ).
fof(f2547,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| closed_subset(cast_as_carrier_subset(X0),X0) ),
inference(cnf_transformation,[],[f918]) ).
fof(f2549,plain,
! [X0] :
( ~ one_sorted_str(X0)
| the_carrier(X0) = cast_as_carrier_subset(X0) ),
inference(cnf_transformation,[],[f920]) ).
fof(f2555,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP37(X1,X2)
| ~ in(X4,sK309(X1,X2))
| in(relation_image(X2,X4),X1) ),
inference(cnf_transformation,[],[f1523]) ).
fof(f2556,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP37(X1,X2)
| ~ in(X4,sK309(X1,X2))
| sK310(X1,X2,X4) = X4 ),
inference(cnf_transformation,[],[f1523]) ).
fof(f2557,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP37(X1,X2)
| ~ in(X4,sK309(X1,X2))
| in(sK310(X1,X2,X4),powerset(relation_dom(X2))) ),
inference(cnf_transformation,[],[f1523]) ).
fof(f2558,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP37(X1,X2)
| ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2)))
| in(X4,sK309(X1,X2)) ),
inference(cnf_transformation,[],[f1523]) ).
fof(f2559,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ function(X0)
| ~ relation(X0)
| finite(relation_image(X0,X1)) ),
inference(cnf_transformation,[],[f924]) ).
fof(f2560,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK313(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2561,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(sK313(X0,X1,X6),X6),X0) ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2562,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2563,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK311(X0,X1,X2),X2)
| in(sK312(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2564,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK311(X0,X1,X2),X2)
| in(ordered_pair(sK312(X0,X1,X2),sK311(X0,X1,X2)),X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2565,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK311(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK311(X0,X1,X2)),X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2566,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| apply(X0,sK316(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f1529]) ).
fof(f2567,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK316(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f1529]) ).
fof(f2568,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK316(X0,X1,X6),relation_dom(X0)) ),
inference(cnf_transformation,[],[f1529]) ).
fof(f2569,plain,
! [X2,X0,X1,X6,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f1529]) ).
fof(f2570,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK314(X0,X1,X2),X2)
| sK314(X0,X1,X2) = apply(X0,sK315(X0,X1,X2))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1529]) ).
fof(f2571,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK314(X0,X1,X2),X2)
| in(sK315(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1529]) ).
fof(f2572,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK314(X0,X1,X2),X2)
| in(sK315(X0,X1,X2),relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1529]) ).
fof(f2573,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK314(X0,X1,X2),X2)
| apply(X0,X4) != sK314(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1529]) ).
fof(f2574,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f227]) ).
fof(f2575,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f99]) ).
fof(f2576,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| ~ in(X4,X2)
| X1 = X4
| X0 = X4 ),
inference(cnf_transformation,[],[f1533]) ).
fof(f2577,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X1 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f1533]) ).
fof(f2578,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f1533]) ).
fof(f2579,plain,
! [X2,X0,X1] :
( in(sK317(X0,X1,X2),X2)
| sK317(X0,X1,X2) = X1
| sK317(X0,X1,X2) = X0
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1533]) ).
fof(f2580,plain,
! [X2,X0,X1] :
( ~ in(sK317(X0,X1,X2),X2)
| sK317(X0,X1,X2) != X1
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1533]) ).
fof(f2581,plain,
! [X2,X0,X1] :
( ~ in(sK317(X0,X1,X2),X2)
| sK317(X0,X1,X2) != X0
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1533]) ).
fof(f2582,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f32]) ).
fof(f2583,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_rng(X0)) ),
inference(cnf_transformation,[],[f928]) ).
fof(f2584,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f928]) ).
fof(f2585,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f930]) ).
fof(f2586,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f420]) ).
fof(f2594,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f936]) ).
fof(f2595,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f1537]) ).
fof(f2597,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f1537]) ).
fof(f2598,plain,
! [X2,X0,X1] :
( in(sK318(X0,X1,X2),X2)
| in(sK318(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1537]) ).
fof(f2599,plain,
! [X2,X0,X1] :
( in(sK318(X0,X1,X2),X2)
| in(sK318(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1537]) ).
fof(f2600,plain,
! [X2,X0,X1] :
( ~ in(sK318(X0,X1,X2),X2)
| ~ in(sK318(X0,X1,X2),X1)
| ~ in(sK318(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1537]) ).
fof(f2601,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f35]) ).
fof(f2602,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(sK319(X0)) ),
inference(cnf_transformation,[],[f1538]) ).
fof(f2603,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| element(sK319(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1538]) ).
fof(f2604,plain,
~ empty_carrier(sK320),
inference(cnf_transformation,[],[f1539]) ).
fof(f2605,plain,
one_sorted_str(sK320),
inference(cnf_transformation,[],[f1539]) ).
fof(f2606,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f940]) ).
fof(f2607,plain,
one_sorted_str(sK321),
inference(cnf_transformation,[],[f1540]) ).
fof(f2608,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f941]) ).
fof(f2609,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f1541]) ).
fof(f2610,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f1541]) ).
fof(f2611,plain,
! [X0,X1] : relation_of2_as_subset(sK322(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1542]) ).
fof(f2612,plain,
! [X0,X7] :
( in(X7,sK323(X0))
| are_equipotent(X7,sK323(X0))
| ~ subset(X7,sK323(X0)) ),
inference(cnf_transformation,[],[f1543]) ).
fof(f2613,plain,
! [X0,X6,X4] :
( ~ subset(X6,X4)
| in(X6,sK324(X0,X4))
| ~ in(X4,sK323(X0)) ),
inference(cnf_transformation,[],[f1543]) ).
fof(f2614,plain,
! [X0,X4] :
( in(sK324(X0,X4),sK323(X0))
| ~ in(X4,sK323(X0)) ),
inference(cnf_transformation,[],[f1543]) ).
fof(f2615,plain,
! [X2,X3,X0] :
( ~ subset(X3,X2)
| ~ in(X2,sK323(X0))
| in(X3,sK323(X0)) ),
inference(cnf_transformation,[],[f1543]) ).
fof(f2616,plain,
! [X0] : in(X0,sK323(X0)),
inference(cnf_transformation,[],[f1543]) ).
fof(f2617,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| are_equipotent(X0,X1) ),
inference(cnf_transformation,[],[f1544]) ).
fof(f2618,plain,
! [X0,X1] :
( ~ are_equipotent(X0,X1)
| equipotent(X0,X1) ),
inference(cnf_transformation,[],[f1544]) ).
fof(f2619,plain,
! [X0] :
( empty(X0)
| finite(sK325(X0)) ),
inference(cnf_transformation,[],[f1545]) ).
fof(f2620,plain,
! [X0] :
( empty(X0)
| ~ empty(sK325(X0)) ),
inference(cnf_transformation,[],[f1545]) ).
fof(f2621,plain,
! [X0] :
( empty(X0)
| element(sK325(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f1545]) ).
fof(f2622,plain,
finite(sK326),
inference(cnf_transformation,[],[f1546]) ).
fof(f2623,plain,
~ empty(sK326),
inference(cnf_transformation,[],[f1546]) ).
fof(f2624,plain,
! [X0] : finite(singleton(X0)),
inference(cnf_transformation,[],[f194]) ).
fof(f2626,plain,
! [X0,X1] :
( ~ finite(X0)
| finite(set_difference(X0,X1)) ),
inference(cnf_transformation,[],[f945]) ).
fof(f2628,plain,
! [X0,X1] :
( ~ finite(X1)
| finite(set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f947]) ).
fof(f2630,plain,
! [X0] :
( ~ empty(X0)
| finite(X0) ),
inference(cnf_transformation,[],[f949]) ).
fof(f2631,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK329(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f1549]) ).
fof(f2632,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(X6,sK329(X0,X1,X6)),X0) ),
inference(cnf_transformation,[],[f1549]) ).
fof(f2633,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f1549]) ).
fof(f2634,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK327(X0,X1,X2),X2)
| in(sK328(X0,X1,X2),X1)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1549]) ).
fof(f2635,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK327(X0,X1,X2),X2)
| in(ordered_pair(sK327(X0,X1,X2),sK328(X0,X1,X2)),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1549]) ).
fof(f2636,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK327(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(ordered_pair(sK327(X0,X1,X2),X4),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1549]) ).
fof(f2637,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(apply(X0,X4),X1) ),
inference(cnf_transformation,[],[f1553]) ).
fof(f2638,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,relation_dom(X0)) ),
inference(cnf_transformation,[],[f1553]) ).
fof(f2639,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,X2) ),
inference(cnf_transformation,[],[f1553]) ).
fof(f2640,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK330(X0,X1,X2),X2)
| in(apply(X0,sK330(X0,X1,X2)),X1)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1553]) ).
fof(f2641,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK330(X0,X1,X2),X2)
| in(sK330(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1553]) ).
fof(f2642,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK330(X0,X1,X2),X2)
| ~ in(apply(X0,sK330(X0,X1,X2)),X1)
| ~ in(sK330(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1553]) ).
fof(f2643,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
inference(cnf_transformation,[],[f954]) ).
fof(f2644,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X1) = X1 ),
inference(cnf_transformation,[],[f956]) ).
fof(f2645,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_intersection2(X0,X1,X2),powerset(X0)) ),
inference(cnf_transformation,[],[f958]) ).
fof(f2646,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = subset_intersection2(X0,X2,X1) ),
inference(cnf_transformation,[],[f960]) ).
fof(f2647,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f962]) ).
fof(f2648,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| empty(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f962]) ).
fof(f2649,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f964]) ).
fof(f2650,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f964]) ).
fof(f2651,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f966]) ).
fof(f2652,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| empty(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f966]) ).
fof(f2653,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f968]) ).
fof(f2654,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X7,X8),X2)
| in(ordered_pair(sK334(X0,X1,X7,X8),X8),X1) ),
inference(cnf_transformation,[],[f1556]) ).
fof(f2655,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X7,X8),X2)
| in(ordered_pair(X7,sK334(X0,X1,X7,X8)),X0) ),
inference(cnf_transformation,[],[f1556]) ).
fof(f2656,plain,
! [X2,X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(ordered_pair(X9,X8),X1)
| ~ in(ordered_pair(X7,X9),X0)
| in(ordered_pair(X7,X8),X2) ),
inference(cnf_transformation,[],[f1556]) ).
fof(f2657,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK331(X0,X1,X2),sK332(X0,X1,X2)),X2)
| in(ordered_pair(sK333(X0,X1,X2),sK332(X0,X1,X2)),X1)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1556]) ).
fof(f2658,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK331(X0,X1,X2),sK332(X0,X1,X2)),X2)
| in(ordered_pair(sK331(X0,X1,X2),sK333(X0,X1,X2)),X0)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1556]) ).
fof(f2659,plain,
! [X2,X0,X1,X5] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sK331(X0,X1,X2),sK332(X0,X1,X2)),X2)
| ~ in(ordered_pair(X5,sK332(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK331(X0,X1,X2),X5),X0)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1556]) ).
fof(f2660,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f970]) ).
fof(f2661,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f971]) ).
fof(f2662,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f972]) ).
fof(f2663,plain,
! [X2,X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) != X2
| ~ element(X4,powerset(X0))
| ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) ),
inference(cnf_transformation,[],[f1560]) ).
fof(f2664,plain,
! [X2,X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) != X2
| ~ element(X4,powerset(X0))
| ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f1560]) ).
fof(f2665,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| element(sK335(X0,X1,X2),powerset(X0))
| complements_of_subsets(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1560]) ).
fof(f2666,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| in(sK335(X0,X1,X2),X2)
| in(subset_complement(X0,sK335(X0,X1,X2)),X1)
| complements_of_subsets(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1560]) ).
fof(f2667,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| ~ in(sK335(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK335(X0,X1,X2)),X1)
| complements_of_subsets(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1560]) ).
fof(f2668,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) ),
inference(cnf_transformation,[],[f974]) ).
fof(f2669,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(cnf_transformation,[],[f976]) ).
fof(f2670,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_difference(X0,X1,X2),powerset(X0)) ),
inference(cnf_transformation,[],[f978]) ).
fof(f2671,plain,
! [X0,X1] : quasi_total(sK336(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1561]) ).
fof(f2672,plain,
! [X0,X1] : function(sK336(X0,X1)),
inference(cnf_transformation,[],[f1561]) ).
fof(f2673,plain,
! [X0,X1] : relation(sK336(X0,X1)),
inference(cnf_transformation,[],[f1561]) ).
fof(f2674,plain,
! [X0,X1] : relation_of2(sK336(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1561]) ).
fof(f2675,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f552]) ).
fof(f2676,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f980]) ).
fof(f2677,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ~ proper_subset(X1,X0) ),
inference(cnf_transformation,[],[f981]) ).
fof(f2678,plain,
ordinal(sK337),
inference(cnf_transformation,[],[f1562]) ).
fof(f2679,plain,
epsilon_connected(sK337),
inference(cnf_transformation,[],[f1562]) ).
fof(f2680,plain,
epsilon_transitive(sK337),
inference(cnf_transformation,[],[f1562]) ).
fof(f2681,plain,
~ empty(sK337),
inference(cnf_transformation,[],[f1562]) ).
fof(f2682,plain,
ordinal(sK338),
inference(cnf_transformation,[],[f1563]) ).
fof(f2683,plain,
epsilon_connected(sK338),
inference(cnf_transformation,[],[f1563]) ).
fof(f2684,plain,
epsilon_transitive(sK338),
inference(cnf_transformation,[],[f1563]) ).
fof(f2685,plain,
empty(sK338),
inference(cnf_transformation,[],[f1563]) ).
fof(f2686,plain,
one_to_one(sK338),
inference(cnf_transformation,[],[f1563]) ).
fof(f2687,plain,
function(sK338),
inference(cnf_transformation,[],[f1563]) ).
fof(f2688,plain,
relation(sK338),
inference(cnf_transformation,[],[f1563]) ).
fof(f2689,plain,
ordinal(sK339),
inference(cnf_transformation,[],[f1564]) ).
fof(f2690,plain,
epsilon_connected(sK339),
inference(cnf_transformation,[],[f1564]) ).
fof(f2691,plain,
epsilon_transitive(sK339),
inference(cnf_transformation,[],[f1564]) ).
fof(f2695,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f1569]) ).
fof(f2696,plain,
! [X0] :
( in(sK340(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f1569]) ).
fof(f2697,plain,
! [X0] :
( ~ subset(sK340(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f1569]) ).
fof(f2698,plain,
! [X0] :
( ~ empty(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f983]) ).
fof(f2699,plain,
! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f983]) ).
fof(f2700,plain,
! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f983]) ).
fof(f2701,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f985]) ).
fof(f2702,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f986]) ).
fof(f2703,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f986]) ).
fof(f2704,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ element(X1,X0)
| ordinal(X1) ),
inference(cnf_transformation,[],[f987]) ).
fof(f2705,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ element(X1,X0)
| epsilon_connected(X1) ),
inference(cnf_transformation,[],[f987]) ).
fof(f2706,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ element(X1,X0)
| epsilon_transitive(X1) ),
inference(cnf_transformation,[],[f987]) ).
fof(f2707,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| disjoint(fiber(X0,sK342(X0,X4)),X4)
| empty_set = X4
| ~ subset(X4,X1) ),
inference(cnf_transformation,[],[f1572]) ).
fof(f2708,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| in(sK342(X0,X4),X4)
| empty_set = X4
| ~ subset(X4,X1) ),
inference(cnf_transformation,[],[f1572]) ).
fof(f2709,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ disjoint(fiber(X0,X3),sK341(X0,X1))
| ~ in(X3,sK341(X0,X1))
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f1572]) ).
fof(f2710,plain,
! [X0,X1] :
( ~ relation(X0)
| empty_set != sK341(X0,X1)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f1572]) ).
fof(f2711,plain,
! [X0,X1] :
( ~ relation(X0)
| subset(sK341(X0,X1),X1)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f1572]) ).
fof(f2712,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| disjoint(fiber(X0,sK344(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f1575]) ).
fof(f2713,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| in(sK344(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f1575]) ).
fof(f2714,plain,
! [X2,X0] :
( ~ relation(X0)
| ~ disjoint(fiber(X0,X2),sK343(X0))
| ~ in(X2,sK343(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1575]) ).
fof(f2715,plain,
! [X0] :
( ~ relation(X0)
| empty_set != sK343(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1575]) ).
fof(f2716,plain,
! [X0] :
( ~ relation(X0)
| subset(sK343(X0),relation_field(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1575]) ).
fof(f2717,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| fiber(X0,X1) != X2
| ~ in(X4,X2)
| in(ordered_pair(X4,X1),X0) ),
inference(cnf_transformation,[],[f1579]) ).
fof(f2718,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| fiber(X0,X1) != X2
| ~ in(X4,X2)
| X1 != X4 ),
inference(cnf_transformation,[],[f1579]) ).
fof(f2719,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| fiber(X0,X1) != X2
| ~ in(ordered_pair(X4,X1),X0)
| X1 = X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f1579]) ).
fof(f2720,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK345(X0,X1,X2),X2)
| in(ordered_pair(sK345(X0,X1,X2),X1),X0)
| fiber(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1579]) ).
fof(f2721,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK345(X0,X1,X2),X2)
| sK345(X0,X1,X2) != X1
| fiber(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1579]) ).
fof(f2722,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ in(sK345(X0,X1,X2),X2)
| ~ in(ordered_pair(sK345(X0,X1,X2),X1),X0)
| sK345(X0,X1,X2) = X1
| fiber(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1579]) ).
fof(f2723,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(cnf_transformation,[],[f991]) ).
fof(f2724,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
inference(cnf_transformation,[],[f992]) ).
fof(f2725,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set != X1
| ~ quasi_total(X2,X0,X1)
| empty_set = X2
| empty_set = X0 ),
inference(cnf_transformation,[],[f1580]) ).
fof(f2726,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set != X1
| empty_set != X2
| quasi_total(X2,X0,X1)
| empty_set = X0 ),
inference(cnf_transformation,[],[f1580]) ).
fof(f2727,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set = X1
| ~ quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f1580]) ).
fof(f2728,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set != X0
| ~ quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f1580]) ).
fof(f2729,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set = X1
| relation_dom_as_subset(X0,X1,X2) != X0
| quasi_total(X2,X0,X1) ),
inference(cnf_transformation,[],[f1580]) ).
fof(f2730,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| empty_set != X0
| relation_dom_as_subset(X0,X1,X2) != X0
| quasi_total(X2,X0,X1) ),
inference(cnf_transformation,[],[f1580]) ).
fof(f2733,plain,
latt_str(sK346),
inference(cnf_transformation,[],[f1582]) ).
fof(f2734,plain,
! [X0] :
( ~ latt_str(X0)
| join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f997]) ).
fof(f2735,plain,
! [X0] :
( ~ latt_str(X0)
| meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f997]) ).
fof(f2736,plain,
! [X3,X0,X4] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ~ meet_absorbing(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X4,the_carrier(X0))
| join(X0,meet(X0,X3,X4),X4) = X4 ),
inference(cnf_transformation,[],[f1585]) ).
fof(f2737,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| element(sK347(X0),the_carrier(X0))
| meet_absorbing(X0) ),
inference(cnf_transformation,[],[f1585]) ).
fof(f2738,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| element(sK348(X0),the_carrier(X0))
| meet_absorbing(X0) ),
inference(cnf_transformation,[],[f1585]) ).
fof(f2739,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| sK348(X0) != join(X0,meet(X0,sK347(X0),sK348(X0)),sK348(X0))
| meet_absorbing(X0) ),
inference(cnf_transformation,[],[f1585]) ).
fof(f2740,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_rng(X2) = relation_rng_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1000]) ).
fof(f2741,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f1001]) ).
fof(f2742,plain,
join_semilatt_str(sK349),
inference(cnf_transformation,[],[f1586]) ).
fof(f2743,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ),
inference(cnf_transformation,[],[f1587]) ).
fof(f2744,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| closed_subset(X1,X0) ),
inference(cnf_transformation,[],[f1587]) ).
fof(f2745,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(X1,X0)
| in(X1,the_topology(X0)) ),
inference(cnf_transformation,[],[f1588]) ).
fof(f2746,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,the_topology(X0))
| open_subset(X1,X0) ),
inference(cnf_transformation,[],[f1588]) ).
fof(f2747,plain,
! [X2,X0,X1] :
( ~ sP39(X0,X1,X2)
| topstr_closure(X2,X1) != X0
| sP38(X2,X1,X0) ),
inference(cnf_transformation,[],[f1590]) ).
fof(f2748,plain,
! [X2,X0,X1] :
( ~ sP39(X0,X1,X2)
| ~ sP38(X2,X1,X0)
| topstr_closure(X2,X1) = X0 ),
inference(cnf_transformation,[],[f1590]) ).
fof(f2760,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(the_carrier(X0)))
| sP39(X2,X1,X0) ),
inference(cnf_transformation,[],[f1135]) ).
fof(f2761,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f129]) ).
fof(f2762,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ in(ordered_pair(X4,X5),X1)
| subset(X4,X5) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2763,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ subset(X4,X5)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2764,plain,
! [X0,X1] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| relation_field(X1) = X0 ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2765,plain,
! [X0,X1] :
( ~ relation(X1)
| in(sK354(X0,X1),X0)
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2766,plain,
! [X0,X1] :
( ~ relation(X1)
| in(sK353(X0,X1),X0)
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2767,plain,
! [X0,X1] :
( ~ relation(X1)
| in(ordered_pair(sK353(X0,X1),sK354(X0,X1)),X1)
| subset(sK353(X0,X1),sK354(X0,X1))
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2768,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(ordered_pair(sK353(X0,X1),sK354(X0,X1)),X1)
| ~ subset(sK353(X0,X1),sK354(X0,X1))
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2769,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f209]) ).
fof(f2770,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f209]) ).
fof(f2771,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f159]) ).
fof(f2772,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| X4 = X5 ),
inference(cnf_transformation,[],[f1602]) ).
fof(f2773,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f1602]) ).
fof(f2774,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| X4 != X5
| ~ in(X4,X0)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f1602]) ).
fof(f2775,plain,
! [X0,X1] :
( ~ relation(X1)
| in(ordered_pair(sK355(X0,X1),sK356(X0,X1)),X1)
| sK355(X0,X1) = sK356(X0,X1)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1602]) ).
fof(f2776,plain,
! [X0,X1] :
( ~ relation(X1)
| in(ordered_pair(sK355(X0,X1),sK356(X0,X1)),X1)
| in(sK355(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1602]) ).
fof(f2777,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(ordered_pair(sK355(X0,X1),sK356(X0,X1)),X1)
| sK355(X0,X1) != sK356(X0,X1)
| ~ in(sK355(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1602]) ).
fof(f2778,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(cnf_transformation,[],[f1009]) ).
fof(f2779,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| function(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1011]) ).
fof(f2781,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f2782,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f2783,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1013]) ).
fof(f2784,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_inverse(X0) = function_inverse(X0) ),
inference(cnf_transformation,[],[f1015]) ).
fof(f2785,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) ),
inference(cnf_transformation,[],[f1605]) ).
fof(f2786,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f1605]) ).
fof(f2787,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK357(X0,X1),sK358(X0,X1)),X1)
| in(ordered_pair(sK358(X0,X1),sK357(X0,X1)),X0)
| relation_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f1605]) ).
fof(f2788,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK357(X0,X1),sK358(X0,X1)),X1)
| ~ in(ordered_pair(sK358(X0,X1),sK357(X0,X1)),X0)
| relation_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f1605]) ).
fof(f2789,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(meet_of_subsets(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f1017]) ).
fof(f2790,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1019]) ).
fof(f2791,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f1020]) ).
fof(f2792,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1021]) ).
fof(f2793,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(union_of_subsets(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f1022]) ).
fof(f2794,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f138]) ).
fof(f2795,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f89]) ).
fof(f2796,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f1024]) ).
fof(f2797,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f1024]) ).
fof(f2798,plain,
! [X2,X0,X1] :
( ~ sP41(X0,X1,X2)
| ~ relation_isomorphism(X1,X0,X2)
| sP40(X2,X1,X0) ),
inference(cnf_transformation,[],[f1607]) ).
fof(f2799,plain,
! [X2,X0,X1] :
( ~ sP41(X0,X1,X2)
| ~ sP40(X2,X1,X0)
| relation_isomorphism(X1,X0,X2) ),
inference(cnf_transformation,[],[f1607]) ).
fof(f2811,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| sP41(X1,X0,X2) ),
inference(cnf_transformation,[],[f1138]) ).
fof(f2812,plain,
one_to_one(sK361),
inference(cnf_transformation,[],[f1612]) ).
fof(f2813,plain,
function(sK361),
inference(cnf_transformation,[],[f1612]) ).
fof(f2814,plain,
relation(sK361),
inference(cnf_transformation,[],[f1612]) ).
fof(f2815,plain,
empty(sK362),
inference(cnf_transformation,[],[f1613]) ).
fof(f2816,plain,
one_to_one(sK362),
inference(cnf_transformation,[],[f1613]) ).
fof(f2817,plain,
function(sK362),
inference(cnf_transformation,[],[f1613]) ).
fof(f2818,plain,
relation(sK362),
inference(cnf_transformation,[],[f1613]) ).
fof(f2819,plain,
! [X3,X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| apply(X0,X4) != apply(X0,X3)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ),
inference(cnf_transformation,[],[f1616]) ).
fof(f2820,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK363(X0)) = apply(X0,sK364(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1616]) ).
fof(f2821,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK364(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1616]) ).
fof(f2822,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK363(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1616]) ).
fof(f2823,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK363(X0) != sK364(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1616]) ).
fof(f2824,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1030]) ).
fof(f2827,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f1618]) ).
fof(f2828,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1618]) ).
fof(f2829,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1618]) ).
fof(f2830,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1618]) ).
fof(f2831,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f1618]) ).
fof(f2832,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| well_orders(X0,X1) ),
inference(cnf_transformation,[],[f1618]) ).
fof(f2833,plain,
! [X0,X1,X6,X7,X4,X5] :
( ordered_pair(X6,X7) != X0
| pair_first(X0) != X1
| ordered_pair(X4,X5) != X0
| X1 = X4 ),
inference(cnf_transformation,[],[f1621]) ).
fof(f2834,plain,
! [X0,X1,X6,X7] :
( ordered_pair(X6,X7) != X0
| ordered_pair(sK365(X0,X1),sK366(X0,X1)) = X0
| pair_first(X0) = X1 ),
inference(cnf_transformation,[],[f1621]) ).
fof(f2835,plain,
! [X0,X1,X6,X7] :
( ordered_pair(X6,X7) != X0
| sK365(X0,X1) != X1
| pair_first(X0) = X1 ),
inference(cnf_transformation,[],[f1621]) ).
fof(f2836,plain,
! [X0,X1,X6,X7,X4,X5] :
( ordered_pair(X6,X7) != X0
| pair_second(X0) != X1
| ordered_pair(X4,X5) != X0
| X1 = X5 ),
inference(cnf_transformation,[],[f1624]) ).
fof(f2837,plain,
! [X0,X1,X6,X7] :
( ordered_pair(X6,X7) != X0
| ordered_pair(sK367(X0,X1),sK368(X0,X1)) = X0
| pair_second(X0) = X1 ),
inference(cnf_transformation,[],[f1624]) ).
fof(f2838,plain,
! [X0,X1,X6,X7] :
( ordered_pair(X6,X7) != X0
| sK368(X0,X1) != X1
| pair_second(X0) = X1 ),
inference(cnf_transformation,[],[f1624]) ).
fof(f2870,plain,
! [X3,X0,X4] :
( ~ epsilon_connected(X0)
| in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f1627]) ).
fof(f2871,plain,
! [X0] :
( ~ in(sK370(X0),sK369(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1627]) ).
fof(f2872,plain,
! [X0] :
( sK369(X0) != sK370(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1627]) ).
fof(f2873,plain,
! [X0] :
( ~ in(sK369(X0),sK370(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1627]) ).
fof(f2874,plain,
! [X0] :
( in(sK370(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1627]) ).
fof(f2875,plain,
! [X0] :
( in(sK369(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1627]) ).
fof(f2876,plain,
! [X0] : finite(sK371(X0)),
inference(cnf_transformation,[],[f1628]) ).
fof(f2878,plain,
! [X0] : ordinal(sK371(X0)),
inference(cnf_transformation,[],[f1628]) ).
fof(f2879,plain,
! [X0] : epsilon_connected(sK371(X0)),
inference(cnf_transformation,[],[f1628]) ).
fof(f2880,plain,
! [X0] : epsilon_transitive(sK371(X0)),
inference(cnf_transformation,[],[f1628]) ).
fof(f2881,plain,
! [X0] : one_to_one(sK371(X0)),
inference(cnf_transformation,[],[f1628]) ).
fof(f2882,plain,
! [X0] : function(sK371(X0)),
inference(cnf_transformation,[],[f1628]) ).
fof(f2883,plain,
! [X0] : relation(sK371(X0)),
inference(cnf_transformation,[],[f1628]) ).
fof(f2884,plain,
! [X0] : empty(sK371(X0)),
inference(cnf_transformation,[],[f1628]) ).
fof(f2885,plain,
! [X0] : element(sK371(X0),powerset(X0)),
inference(cnf_transformation,[],[f1628]) ).
fof(f2887,plain,
ordinal(sK372),
inference(cnf_transformation,[],[f1629]) ).
fof(f2888,plain,
epsilon_connected(sK372),
inference(cnf_transformation,[],[f1629]) ).
fof(f2889,plain,
epsilon_transitive(sK372),
inference(cnf_transformation,[],[f1629]) ).
fof(f2890,plain,
~ empty(sK372),
inference(cnf_transformation,[],[f1629]) ).
fof(f2900,plain,
! [X0,X1] : function(sK373(X0,X1)),
inference(cnf_transformation,[],[f1630]) ).
fof(f2901,plain,
! [X0,X1] : relation(sK373(X0,X1)),
inference(cnf_transformation,[],[f1630]) ).
fof(f2902,plain,
! [X0,X1] : relation_of2(sK373(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1630]) ).
fof(f2903,plain,
! [X0,X1] : relation_of2(sK374(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1631]) ).
fof(f2904,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| subset(X2,cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f1632]) ).
fof(f2905,plain,
! [X2,X0,X1] :
( ~ subset(X2,cartesian_product2(X0,X1))
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f1632]) ).
fof(f2906,plain,
meet_semilatt_str(sK375),
inference(cnf_transformation,[],[f1633]) ).
fof(f2907,plain,
! [X0] :
( ~ meet_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f1051]) ).
fof(f2908,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| empty_carrier(X0)
| element(meet(X0,X1,X2),the_carrier(X0)) ),
inference(cnf_transformation,[],[f1053]) ).
fof(f2909,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| element(join(X0,X1,X2),the_carrier(X0)) ),
inference(cnf_transformation,[],[f1055]) ).
fof(f2910,plain,
! [X0] :
( ~ top_str(X0)
| element(the_topology(X0),powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f1056]) ).
fof(f2917,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| sP42(X0) ),
inference(cnf_transformation,[],[f1640]) ).
fof(f2918,plain,
! [X2,X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ subset(X2,the_topology(X0))
| in(union_of_subsets(the_carrier(X0),X2),the_topology(X0)) ),
inference(cnf_transformation,[],[f1640]) ).
fof(f2919,plain,
! [X0] :
( ~ top_str(X0)
| ~ topological_space(X0)
| in(the_carrier(X0),the_topology(X0)) ),
inference(cnf_transformation,[],[f1640]) ).
fof(f2920,plain,
! [X0] :
( ~ top_str(X0)
| ~ sP42(X0)
| element(sK378(X0),powerset(powerset(the_carrier(X0))))
| ~ in(the_carrier(X0),the_topology(X0))
| topological_space(X0) ),
inference(cnf_transformation,[],[f1640]) ).
fof(f2921,plain,
! [X0] :
( ~ top_str(X0)
| ~ sP42(X0)
| subset(sK378(X0),the_topology(X0))
| ~ in(the_carrier(X0),the_topology(X0))
| topological_space(X0) ),
inference(cnf_transformation,[],[f1640]) ).
fof(f2922,plain,
! [X0] :
( ~ top_str(X0)
| ~ sP42(X0)
| ~ in(union_of_subsets(the_carrier(X0),sK378(X0)),the_topology(X0))
| ~ in(the_carrier(X0),the_topology(X0))
| topological_space(X0) ),
inference(cnf_transformation,[],[f1640]) ).
fof(f2923,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| X4 = X5 ),
inference(cnf_transformation,[],[f1643]) ).
fof(f2924,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK380(X0,X1),sK379(X0,X1)),X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1643]) ).
fof(f2925,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK379(X0,X1),sK380(X0,X1)),X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1643]) ).
fof(f2926,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK380(X0,X1),X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1643]) ).
fof(f2927,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK379(X0,X1),X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1643]) ).
fof(f2928,plain,
! [X0,X1] :
( ~ relation(X0)
| sK379(X0,X1) != sK380(X0,X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1643]) ).
fof(f2929,plain,
! [X0] :
( ~ relation(X0)
| ~ antisymmetric(X0)
| is_antisymmetric_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1644]) ).
fof(f2930,plain,
! [X0] :
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1644]) ).
fof(f2931,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ is_connected_in(X0,X1)
| in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f1647]) ).
fof(f2932,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK382(X0,X1),sK381(X0,X1)),X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1647]) ).
fof(f2933,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK381(X0,X1),sK382(X0,X1)),X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1647]) ).
fof(f2934,plain,
! [X0,X1] :
( ~ relation(X0)
| sK381(X0,X1) != sK382(X0,X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1647]) ).
fof(f2935,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK382(X0,X1),X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1647]) ).
fof(f2936,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK381(X0,X1),X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1647]) ).
fof(f2937,plain,
! [X0] :
( ~ relation(X0)
| ~ connected(X0)
| is_connected_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1648]) ).
fof(f2938,plain,
! [X0] :
( ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f1648]) ).
fof(f2939,plain,
! [X0,X1,X6,X7,X5] :
( ~ relation(X0)
| ~ is_transitive_in(X0,X1)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| in(ordered_pair(X5,X7),X0) ),
inference(cnf_transformation,[],[f1651]) ).
fof(f2940,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK384(X0,X1),sK385(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
fof(f2941,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK383(X0,X1),sK384(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
fof(f2942,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK385(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
fof(f2943,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK384(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
fof(f2944,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK383(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
fof(f2945,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK383(X0,X1),sK385(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
fof(f2946,plain,
! [X0] :
( ~ relation(X0)
| ~ transitive(X0)
| is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1652]) ).
fof(f2947,plain,
! [X0] :
( ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0) ),
inference(cnf_transformation,[],[f1652]) ).
fof(f2948,plain,
! [X0] :
( ~ relation(X0)
| ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1653]) ).
fof(f2949,plain,
! [X0] :
( ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0) ),
inference(cnf_transformation,[],[f1653]) ).
fof(f2950,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ is_reflexive_in(X0,X1)
| ~ in(X3,X1)
| in(ordered_pair(X3,X3),X0) ),
inference(cnf_transformation,[],[f1656]) ).
fof(f2951,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK386(X0,X1),X1)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f1656]) ).
fof(f2952,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK386(X0,X1),sK386(X0,X1)),X0)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f1656]) ).
fof(f2958,plain,
~ empty(sK387),
inference(cnf_transformation,[],[f1657]) ).
fof(f2964,plain,
empty(empty_set),
inference(cnf_transformation,[],[f238]) ).
fof(f2991,plain,
! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f2255,f2115]) ).
fof(f2992,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f2575,f2115]) ).
fof(f2993,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK43(X0),sK43(X0)),unordered_pair(sK43(X0),sK43(X0))),X0)
| reflexive(X0) ),
inference(definition_unfolding,[],[f1660,f2992]) ).
fof(f2994,plain,
! [X2,X0] :
( ~ relation(X0)
| ~ reflexive(X0)
| ~ in(X2,relation_field(X0))
| in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X2)),X0) ),
inference(definition_unfolding,[],[f1658,f2992]) ).
fof(f2995,plain,
! [X0] : empty_set != unordered_pair(X0,X0),
inference(definition_unfolding,[],[f1661,f2115]) ).
fof(f2997,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f1663,f2115]) ).
fof(f2998,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f1664,f2115]) ).
fof(f2999,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK44(X0),sK46(X0)),unordered_pair(sK44(X0),sK44(X0))),X0)
| transitive(X0) ),
inference(definition_unfolding,[],[f1669,f2992]) ).
fof(f3000,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK44(X0),sK45(X0)),unordered_pair(sK44(X0),sK44(X0))),X0)
| transitive(X0) ),
inference(definition_unfolding,[],[f1668,f2992]) ).
fof(f3001,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK45(X0),sK46(X0)),unordered_pair(sK45(X0),sK45(X0))),X0)
| transitive(X0) ),
inference(definition_unfolding,[],[f1667,f2992]) ).
fof(f3002,plain,
! [X0,X6,X4,X5] :
( ~ relation(X0)
| ~ transitive(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| in(unordered_pair(unordered_pair(X4,X6),unordered_pair(X4,X4)),X0) ),
inference(definition_unfolding,[],[f1666,f2992,f2992,f2992]) ).
fof(f3005,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK48(X0),sK49(X0)),unordered_pair(sK48(X0),sK48(X0))),X0)
| antisymmetric(X0) ),
inference(definition_unfolding,[],[f1679,f2992]) ).
fof(f3006,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK49(X0),sK48(X0)),unordered_pair(sK49(X0),sK49(X0))),X0)
| antisymmetric(X0) ),
inference(definition_unfolding,[],[f1678,f2992]) ).
fof(f3007,plain,
! [X3,X0,X4] :
( ~ relation(X0)
| ~ antisymmetric(X0)
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X0)
| X3 = X4 ),
inference(definition_unfolding,[],[f1677,f2992,f2992]) ).
fof(f3008,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0) ),
inference(definition_unfolding,[],[f1681,f2115]) ).
fof(f3009,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK50(X0),sK51(X0)),unordered_pair(sK50(X0),sK50(X0))),X0)
| connected(X0) ),
inference(definition_unfolding,[],[f1684,f2992]) ).
fof(f3010,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK51(X0),sK50(X0)),unordered_pair(sK51(X0),sK51(X0))),X0)
| connected(X0) ),
inference(definition_unfolding,[],[f1683,f2992]) ).
fof(f3011,plain,
! [X3,X0,X4] :
( ~ relation(X0)
| ~ connected(X0)
| in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X0)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) ),
inference(definition_unfolding,[],[f1682,f2992,f2992]) ).
fof(f3018,plain,
! [X0,X1,X6] :
( ~ sP2(X0,X1)
| ~ in(X6,sK56(X0,X1))
| in(unordered_pair(unordered_pair(sK54(X0,X1),X6),unordered_pair(sK54(X0,X1),sK54(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1702,f2992]) ).
fof(f3022,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X2)
| in(X3,X0) ),
inference(definition_unfolding,[],[f1710,f2992]) ).
fof(f3023,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X2)
| sK58(X1,X3,X4) = X3 ),
inference(definition_unfolding,[],[f1709,f2992]) ).
fof(f3024,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X2)
| in(X4,sK58(X1,X3,X4)) ),
inference(definition_unfolding,[],[f1708,f2992]) ).
fof(f3025,plain,
! [X2,X3,X0,X1,X8,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X2)
| ~ in(X8,sK58(X1,X3,X4))
| in(unordered_pair(unordered_pair(X4,X8),unordered_pair(X4,X4)),X1) ),
inference(definition_unfolding,[],[f1707,f2992,f2992]) ).
fof(f3031,plain,
! [X0] :
( sK63(X0) = unordered_pair(sK62(X0),sK62(X0))
| sP3(X0) ),
inference(definition_unfolding,[],[f1728,f2115]) ).
fof(f3032,plain,
! [X0] :
( sK64(X0) = unordered_pair(sK62(X0),sK62(X0))
| sP3(X0) ),
inference(definition_unfolding,[],[f1726,f2115]) ).
fof(f3033,plain,
( ~ sP8
| in(set_union2(sK66,unordered_pair(sK66,sK66)),omega) ),
inference(definition_unfolding,[],[f1737,f2991]) ).
fof(f3034,plain,
! [X0] :
( ~ sP5(X0)
| element(sK72(X0),powerset(powerset(set_union2(X0,unordered_pair(X0,X0))))) ),
inference(definition_unfolding,[],[f1752,f2991]) ).
fof(f3035,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(apply(X2,X4),apply(X2,X5)),unordered_pair(apply(X2,X4),apply(X2,X4))),X1)
| ~ in(X5,X0)
| ~ in(X4,X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK77(X0,X1,X2)) ),
inference(definition_unfolding,[],[f1767,f2992,f2992]) ).
fof(f3036,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK77(X0,X1,X2))
| in(X4,X0) ),
inference(definition_unfolding,[],[f1766,f2992]) ).
fof(f3037,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK77(X0,X1,X2))
| in(X5,X0) ),
inference(definition_unfolding,[],[f1765,f2992]) ).
fof(f3038,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK77(X0,X1,X2))
| in(unordered_pair(unordered_pair(apply(X2,X4),apply(X2,X5)),unordered_pair(apply(X2,X4),apply(X2,X4))),X1) ),
inference(definition_unfolding,[],[f1764,f2992,f2992]) ).
fof(f3039,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ relation(X1)
| empty(X0)
| ~ in(unordered_pair(unordered_pair(X6,sK79(X1,X6,X7)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X0)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X4,cartesian_product2(X0,X2))
| in(X4,sK78(X0,X1,X2)) ),
inference(definition_unfolding,[],[f1776,f2992,f2992]) ).
fof(f3040,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ relation(X1)
| empty(X0)
| in(sK79(X1,X6,X7),X7)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X0)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X4,cartesian_product2(X0,X2))
| in(X4,sK78(X0,X1,X2)) ),
inference(definition_unfolding,[],[f1775,f2992]) ).
fof(f3041,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK78(X0,X1,X2))
| unordered_pair(unordered_pair(sK80(X0,X1,X4),sK81(X0,X1,X4)),unordered_pair(sK80(X0,X1,X4),sK80(X0,X1,X4))) = X4 ),
inference(definition_unfolding,[],[f1773,f2992]) ).
fof(f3042,plain,
! [X2,X0,X1,X4,X12] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK78(X0,X1,X2))
| ~ in(X12,sK82(X0,X1,X4))
| in(unordered_pair(unordered_pair(sK81(X0,X1,X4),X12),unordered_pair(sK81(X0,X1,X4),sK81(X0,X1,X4))),X1) ),
inference(definition_unfolding,[],[f1769,f2992]) ).
fof(f3043,plain,
! [X3,X0,X1,X4,X5] :
( unordered_pair(X4,X4) != X5
| ~ in(X4,X0)
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != X3
| ~ in(X3,cartesian_product2(X0,X1))
| in(X3,sK83(X0,X1)) ),
inference(definition_unfolding,[],[f1781,f2992,f2115]) ).
fof(f3044,plain,
! [X3,X0,X1] :
( ~ in(X3,sK83(X0,X1))
| unordered_pair(unordered_pair(sK84(X0,X3),sK85(X0,X3)),unordered_pair(sK84(X0,X3),sK84(X0,X3))) = X3 ),
inference(definition_unfolding,[],[f1779,f2992]) ).
fof(f3045,plain,
! [X3,X0,X1] :
( ~ in(X3,sK83(X0,X1))
| sK85(X0,X3) = unordered_pair(sK84(X0,X3),sK84(X0,X3)) ),
inference(definition_unfolding,[],[f1777,f2115]) ).
fof(f3053,plain,
! [X3,X0,X1,X4] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| set_difference(X4,unordered_pair(X0,X0)) != X3
| ~ in(X4,X1)
| ~ in(X3,powerset(X0))
| in(X3,sK94(X0,X1)) ),
inference(definition_unfolding,[],[f1808,f2115,f2991]) ).
fof(f3054,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| ~ in(X3,sK94(X0,X1))
| in(X3,powerset(X0)) ),
inference(definition_unfolding,[],[f1807,f2991]) ).
fof(f3055,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| ~ in(X3,sK94(X0,X1))
| in(sK95(X0,X1,X3),X1) ),
inference(definition_unfolding,[],[f1806,f2991]) ).
fof(f3056,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| ~ in(X3,sK94(X0,X1))
| set_difference(sK95(X0,X1,X3),unordered_pair(X0,X0)) = X3 ),
inference(definition_unfolding,[],[f1805,f2115,f2991]) ).
fof(f3057,plain,
! [X2,X0,X1,X6,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(apply(X2,X5),apply(X2,X6)),unordered_pair(apply(X2,X5),apply(X2,X5))),X1)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X4,cartesian_product2(X0,X0))
| in(X4,sK96(X0,X1,X2)) ),
inference(definition_unfolding,[],[f1812,f2992,f2992]) ).
fof(f3058,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK96(X0,X1,X2))
| unordered_pair(unordered_pair(sK97(X1,X2,X4),sK98(X1,X2,X4)),unordered_pair(sK97(X1,X2,X4),sK97(X1,X2,X4))) = X4 ),
inference(definition_unfolding,[],[f1810,f2992]) ).
fof(f3059,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK96(X0,X1,X2))
| in(unordered_pair(unordered_pair(apply(X2,sK97(X1,X2,X4)),apply(X2,sK98(X1,X2,X4))),unordered_pair(apply(X2,sK97(X1,X2,X4)),apply(X2,sK97(X1,X2,X4)))),X1) ),
inference(definition_unfolding,[],[f1809,f2992]) ).
fof(f3060,plain,
! [X3,X0,X1,X4] :
( ~ ordinal(X1)
| ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4)
| ~ in(X3,set_union2(X1,unordered_pair(X1,X1)))
| in(X3,sK101(X0,X1)) ),
inference(definition_unfolding,[],[f1823,f2991]) ).
fof(f3061,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ in(X3,sK101(X0,X1))
| in(X3,set_union2(X1,unordered_pair(X1,X1))) ),
inference(definition_unfolding,[],[f1822,f2991]) ).
fof(f3062,plain,
! [X3,X0,X1,X5] :
( ~ sP12(X0,X1)
| ~ in(X3,X0)
| ~ in(X5,sK104(X0,X1,X3))
| in(unordered_pair(unordered_pair(apply(sK103(X0,X1),X3),X5),unordered_pair(apply(sK103(X0,X1),X3),apply(sK103(X0,X1),X3))),X1) ),
inference(definition_unfolding,[],[f1824,f2992]) ).
fof(f3065,plain,
! [X3,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(unordered_pair(unordered_pair(X3,sK111(X1,X3,X4)),unordered_pair(X3,X3)),X1)
| ~ in(X3,X4)
| sK110(X0,X1) != X4
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(definition_unfolding,[],[f1839,f2992]) ).
fof(f3068,plain,
! [X0,X4] :
( unordered_pair(sK116(X0),sK116(X0)) != X4
| sP13(X0)
| relation(sK115(X0)) ),
inference(definition_unfolding,[],[f1851,f2115]) ).
fof(f3069,plain,
! [X0,X4] :
( unordered_pair(sK116(X0),sK116(X0)) != X4
| sP13(X0)
| function(sK115(X0)) ),
inference(definition_unfolding,[],[f1849,f2115]) ).
fof(f3070,plain,
! [X0,X4] :
( unordered_pair(sK116(X0),sK116(X0)) != X4
| sP13(X0)
| relation_dom(sK115(X0)) = X0 ),
inference(definition_unfolding,[],[f1847,f2115]) ).
fof(f3072,plain,
! [X2,X0,X4] :
( unordered_pair(sK116(X0),sK116(X0)) != X4
| sP13(X0)
| ~ in(X2,X0)
| apply(sK115(X0),X2) = unordered_pair(X2,X2) ),
inference(definition_unfolding,[],[f1845,f2115,f2115]) ).
fof(f3073,plain,
! [X2,X0] :
( ~ in(X2,X0)
| apply(sK122(X0),X2) = unordered_pair(X2,X2) ),
inference(definition_unfolding,[],[f1865,f2115]) ).
fof(f3075,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f1879,f2992]) ).
fof(f3076,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f1878,f2992]) ).
fof(f3077,plain,
! [X0] : in(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f1881,f2991]) ).
fof(f3078,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_difference(relation_rng(X1),set_difference(relation_rng(X1),X0)) ),
inference(definition_unfolding,[],[f1891,f2065]) ).
fof(f3080,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(unordered_pair(unordered_pair(sK127(X0,X1,X2),X0),unordered_pair(sK127(X0,X1,X2),sK127(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1904,f2992]) ).
fof(f3081,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_image(X1,X0) = relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0))) ),
inference(definition_unfolding,[],[f1909,f2065]) ).
fof(f3084,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(unordered_pair(unordered_pair(X0,sK128(X0,X1,X2)),unordered_pair(X0,X0)),X2) ),
inference(definition_unfolding,[],[f1918,f2992]) ).
fof(f3086,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(definition_unfolding,[],[f1937,f2065]) ).
fof(f3087,plain,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f1939,f2115]) ).
fof(f3090,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X2,X1,X0)
| relation_dom_as_subset(X1,X0,X2) != X1
| in(unordered_pair(unordered_pair(X3,sK130(X2,X3)),unordered_pair(X3,X3)),X2)
| ~ in(X3,X1) ),
inference(definition_unfolding,[],[f1955,f2992]) ).
fof(f3091,plain,
! [X2,X0,X1,X6] :
( ~ relation_of2_as_subset(X2,X1,X0)
| ~ in(unordered_pair(unordered_pair(sK131(X1,X2),X6),unordered_pair(sK131(X1,X2),sK131(X1,X2))),X2)
| relation_dom_as_subset(X1,X0,X2) = X1 ),
inference(definition_unfolding,[],[f1953,f2992]) ).
fof(f3092,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_rng_as_subset(X0,X1,X2) != X1
| in(unordered_pair(unordered_pair(sK132(X2,X3),X3),unordered_pair(sK132(X2,X3),sK132(X2,X3))),X2)
| ~ in(X3,X1) ),
inference(definition_unfolding,[],[f1961,f2992]) ).
fof(f3093,plain,
! [X2,X0,X1,X6] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(unordered_pair(unordered_pair(X6,sK133(X1,X2)),unordered_pair(X6,X6)),X2)
| relation_rng_as_subset(X0,X1,X2) = X1 ),
inference(definition_unfolding,[],[f1959,f2992]) ).
fof(f3094,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2))) ),
inference(definition_unfolding,[],[f1973,f2065,f2065]) ).
fof(f3095,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,set_difference(X0,X1)) = X0 ),
inference(definition_unfolding,[],[f1982,f2065]) ).
fof(f3096,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X0,relation_field(X2)) ),
inference(definition_unfolding,[],[f1990,f2992]) ).
fof(f3097,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X1,relation_field(X2)) ),
inference(definition_unfolding,[],[f1989,f2992]) ).
fof(f3098,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f1999,f2991]) ).
fof(f3099,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1) ),
inference(definition_unfolding,[],[f1998,f2991]) ).
fof(f3100,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X0 = X2 ),
inference(definition_unfolding,[],[f2002,f2992,f2992]) ).
fof(f3101,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| X1 = X3 ),
inference(definition_unfolding,[],[f2001,f2992,f2992]) ).
fof(f3102,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f2014,f2115]) ).
fof(f3106,plain,
! [X0,X1] :
( ~ subset(X0,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = X0
| empty_set = X0 ),
inference(definition_unfolding,[],[f2020,f2115,f2115]) ).
fof(f3107,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(set_union2(sK143(X0),unordered_pair(sK143(X0),sK143(X0))),X0)
| being_limit_ordinal(X0) ),
inference(definition_unfolding,[],[f2033,f2991]) ).
fof(f3108,plain,
! [X2,X0] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X2)
| ~ in(X2,X0)
| in(set_union2(X2,unordered_pair(X2,X2)),X0) ),
inference(definition_unfolding,[],[f2030,f2991]) ).
fof(f3109,plain,
! [X0] :
( ~ ordinal(X0)
| set_union2(sK144(X0),unordered_pair(sK144(X0),sK144(X0))) = X0
| being_limit_ordinal(X0) ),
inference(definition_unfolding,[],[f2036,f2991]) ).
fof(f3110,plain,
! [X2,X0] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| set_union2(X2,unordered_pair(X2,X2)) != X0
| ~ ordinal(X2) ),
inference(definition_unfolding,[],[f2034,f2991]) ).
fof(f3111,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(unordered_pair(X0,X0),X1) = X1 ),
inference(definition_unfolding,[],[f2060,f2115]) ).
fof(f3112,plain,
! [X0,X1] :
( in(sK148(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f2069,f2065]) ).
fof(f3113,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f2068,f2065]) ).
fof(f3114,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK151(X0),sK152(X0)),unordered_pair(sK151(X0),sK151(X0))),X0)
| empty_set = X0 ),
inference(definition_unfolding,[],[f2094,f2992]) ).
fof(f3115,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) = X0 ),
inference(definition_unfolding,[],[f2110,f2115]) ).
fof(f3116,plain,
! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) != X0
| ~ in(X1,X0) ),
inference(definition_unfolding,[],[f2109,f2115]) ).
fof(f3117,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| apply(X2,sK153(X1,X2)) != apply(X1,sK153(X1,X2))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| relation_dom_restriction(X2,X0) = X1 ),
inference(definition_unfolding,[],[f2114,f2065]) ).
fof(f3118,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| in(sK153(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_difference(relation_dom(X2),set_difference(relation_dom(X2),X0))
| relation_dom_restriction(X2,X0) = X1 ),
inference(definition_unfolding,[],[f2113,f2065]) ).
fof(f3120,plain,
! [X0,X1] :
( ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1))
| X0 = X1 ),
inference(definition_unfolding,[],[f2118,f2115,f2115]) ).
fof(f3121,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3)) ),
inference(definition_unfolding,[],[f2125,f2992,f2992]) ).
fof(f3122,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f2124,f2992]) ).
fof(f3123,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3) ),
inference(definition_unfolding,[],[f2123,f2992,f2992]) ).
fof(f3124,plain,
! [X0,X1] : pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0,
inference(definition_unfolding,[],[f2127,f2992]) ).
fof(f3125,plain,
! [X0,X1] : pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1,
inference(definition_unfolding,[],[f2126,f2992]) ).
fof(f3126,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| apply(X2,X0) != X1
| ~ in(X0,relation_dom(X2))
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(definition_unfolding,[],[f2138,f2992]) ).
fof(f3128,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| apply(X2,X0) = X1 ),
inference(definition_unfolding,[],[f2136,f2992]) ).
fof(f3129,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(definition_unfolding,[],[f2142,f2115]) ).
fof(f3130,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)) ),
inference(definition_unfolding,[],[f2143,f2065]) ).
fof(f3131,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(definition_unfolding,[],[f2154,f2115]) ).
fof(f3132,plain,
! [X0,X1,X6] :
( ~ sP18(X0,X1)
| ~ in(X6,sK159(X0,X1))
| in(unordered_pair(unordered_pair(sK157(X0,X1),X6),unordered_pair(sK157(X0,X1),sK157(X0,X1))),X1) ),
inference(definition_unfolding,[],[f2162,f2992]) ).
fof(f3135,plain,
! [X3,X0,X1,X9] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ~ in(X3,sK161(X0,X1))
| ~ in(X9,sK164(X0,X1,X3))
| in(unordered_pair(unordered_pair(X3,X9),unordered_pair(X3,X3)),X1) ),
inference(definition_unfolding,[],[f2170,f2992]) ).
fof(f3137,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK165(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(X3,sK165(X0,X1)),unordered_pair(X3,X3)),X0)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f2181,f2992]) ).
fof(f3138,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK165(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK166(X0,X1),sK165(X0,X1)),unordered_pair(sK166(X0,X1),sK166(X0,X1))),X0)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f2180,f2992]) ).
fof(f3139,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(unordered_pair(unordered_pair(X6,X5),unordered_pair(X6,X6)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f2179,f2992]) ).
fof(f3140,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK167(X0,X5),X5),unordered_pair(sK167(X0,X5),sK167(X0,X5))),X0) ),
inference(definition_unfolding,[],[f2178,f2992]) ).
fof(f3141,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK168(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(sK168(X0,X1),X3),unordered_pair(sK168(X0,X1),sK168(X0,X1))),X0)
| relation_dom(X0) = X1 ),
inference(definition_unfolding,[],[f2185,f2992]) ).
fof(f3142,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK168(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK168(X0,X1),sK169(X0,X1)),unordered_pair(sK168(X0,X1),sK168(X0,X1))),X0)
| relation_dom(X0) = X1 ),
inference(definition_unfolding,[],[f2184,f2992]) ).
fof(f3143,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| in(X5,X1) ),
inference(definition_unfolding,[],[f2183,f2992]) ).
fof(f3144,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,sK170(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f2182,f2992]) ).
fof(f3145,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK171(X0,X1),sK172(X0,X1)),unordered_pair(sK171(X0,X1),sK171(X0,X1))),X1)
| subset(X0,X1) ),
inference(definition_unfolding,[],[f2188,f2992]) ).
fof(f3146,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK171(X0,X1),sK172(X0,X1)),unordered_pair(sK171(X0,X1),sK171(X0,X1))),X0)
| subset(X0,X1) ),
inference(definition_unfolding,[],[f2187,f2992]) ).
fof(f3148,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK173(X0,X1),sK174(X0,X1)),unordered_pair(sK173(X0,X1),sK173(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK173(X0,X1),sK174(X0,X1)),unordered_pair(sK173(X0,X1),sK173(X0,X1))),X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f2192,f2992,f2992]) ).
fof(f3149,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK173(X0,X1),sK174(X0,X1)),unordered_pair(sK173(X0,X1),sK173(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK173(X0,X1),sK174(X0,X1)),unordered_pair(sK173(X0,X1),sK173(X0,X1))),X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f2191,f2992,f2992]) ).
fof(f3152,plain,
! [X2,X3,X0] :
( sK175(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| relation(X0) ),
inference(definition_unfolding,[],[f2194,f2992]) ).
fof(f3153,plain,
! [X0,X4] :
( ~ relation(X0)
| unordered_pair(unordered_pair(sK176(X4),sK177(X4)),unordered_pair(sK176(X4),sK176(X4))) = X4
| ~ in(X4,X0) ),
inference(definition_unfolding,[],[f2193,f2992]) ).
fof(f3154,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK178(X0),sK179(X0)),unordered_pair(sK178(X0),sK178(X0))),X0)
| function(X0) ),
inference(definition_unfolding,[],[f2198,f2992]) ).
fof(f3155,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK178(X0),sK180(X0)),unordered_pair(sK178(X0),sK178(X0))),X0)
| function(X0) ),
inference(definition_unfolding,[],[f2197,f2992]) ).
fof(f3156,plain,
! [X0,X6,X4,X5] :
( ~ function(X0)
| ~ in(unordered_pair(unordered_pair(X4,X6),unordered_pair(X4,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| X5 = X6 ),
inference(definition_unfolding,[],[f2196,f2992,f2992]) ).
fof(f3157,plain,
! [X0] :
( ~ sP20(X0)
| sK183(X0) = unordered_pair(unordered_pair(sK185(X0),sK186(X0)),unordered_pair(sK185(X0),sK185(X0))) ),
inference(definition_unfolding,[],[f2217,f2992]) ).
fof(f3158,plain,
! [X0] :
( ~ sP20(X0)
| sK186(X0) = unordered_pair(sK185(X0),sK185(X0)) ),
inference(definition_unfolding,[],[f2215,f2115]) ).
fof(f3161,plain,
! [X3,X0,X1,X6,X4,X5] :
( sP20(X0)
| unordered_pair(X5,X5) != X6
| ~ in(X5,X0)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X3
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1))
| in(X3,sK189(X0,X1)) ),
inference(definition_unfolding,[],[f2228,f2992,f2115]) ).
fof(f3162,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK189(X0,X1))
| unordered_pair(unordered_pair(sK191(X0,X3),sK192(X0,X3)),unordered_pair(sK191(X0,X3),sK191(X0,X3))) = X3 ),
inference(definition_unfolding,[],[f2225,f2992]) ).
fof(f3163,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK189(X0,X1))
| sK192(X0,X3) = unordered_pair(sK191(X0,X3),sK191(X0,X3)) ),
inference(definition_unfolding,[],[f2223,f2115]) ).
fof(f3167,plain,
! [X2,X0] :
( sP21(X0)
| ~ in(X2,sK196(X0))
| unordered_pair(sK197(X0,X2),sK197(X0,X2)) = X2 ),
inference(definition_unfolding,[],[f2234,f2115]) ).
fof(f3169,plain,
! [X0,X1] :
( ~ in(sK198(X0,X1),X1)
| sK198(X0,X1) != X0
| unordered_pair(X0,X0) = X1 ),
inference(definition_unfolding,[],[f2242,f2115]) ).
fof(f3170,plain,
! [X0,X1] :
( in(sK198(X0,X1),X1)
| sK198(X0,X1) = X0
| unordered_pair(X0,X0) = X1 ),
inference(definition_unfolding,[],[f2241,f2115]) ).
fof(f3172,plain,
! [X3,X0,X1] :
( unordered_pair(X0,X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(definition_unfolding,[],[f2239,f2115]) ).
fof(f3173,plain,
! [X0,X1] :
( empty_set != set_difference(X0,set_difference(X0,X1))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f2259,f2065]) ).
fof(f3174,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| empty_set = set_difference(X0,set_difference(X0,X1)) ),
inference(definition_unfolding,[],[f2258,f2065]) ).
fof(f3175,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),unordered_pair(sK200(X0,X1,X2),sK200(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),unordered_pair(sK200(X0,X1,X2),sK200(X0,X1,X2))),X1)
| ~ in(sK201(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2271,f2992,f2992]) ).
fof(f3176,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),unordered_pair(sK200(X0,X1,X2),sK200(X0,X1,X2))),X2)
| in(sK201(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2270,f2992]) ).
fof(f3177,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),unordered_pair(sK200(X0,X1,X2),sK200(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),unordered_pair(sK200(X0,X1,X2),sK200(X0,X1,X2))),X1)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2269,f2992,f2992]) ).
fof(f3178,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| ~ in(X6,X0)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2) ),
inference(definition_unfolding,[],[f2268,f2992,f2992]) ).
fof(f3179,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(X6,X0) ),
inference(definition_unfolding,[],[f2267,f2992]) ).
fof(f3180,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1) ),
inference(definition_unfolding,[],[f2266,f2992,f2992]) ).
fof(f3185,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ~ in(unordered_pair(unordered_pair(apply(X2,X6),apply(X2,X7)),unordered_pair(apply(X2,X6),apply(X2,X6))),X1)
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X0,X0))
| in(X4,sK219(X0,X1,X2)) ),
inference(definition_unfolding,[],[f2340,f2992,f2992]) ).
fof(f3186,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ~ in(X4,sK219(X0,X1,X2))
| unordered_pair(unordered_pair(sK221(X1,X2,X4),sK222(X1,X2,X4)),unordered_pair(sK221(X1,X2,X4),sK221(X1,X2,X4))) = X4 ),
inference(definition_unfolding,[],[f2337,f2992]) ).
fof(f3187,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ~ in(X4,sK219(X0,X1,X2))
| in(unordered_pair(unordered_pair(apply(X2,sK221(X1,X2,X4)),apply(X2,sK222(X1,X2,X4))),unordered_pair(apply(X2,sK221(X1,X2,X4)),apply(X2,sK221(X1,X2,X4)))),X1) ),
inference(definition_unfolding,[],[f2336,f2992]) ).
fof(f3188,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ in(unordered_pair(unordered_pair(X6,sK224(X3,X6,X7)),unordered_pair(X6,X6)),X3)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X1)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X2
| X2 != X4
| ~ in(X4,cartesian_product2(X1,X0))
| sP25(X0,X1,X2,X3) ),
inference(definition_unfolding,[],[f2351,f2992,f2992]) ).
fof(f3189,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( in(sK224(X3,X6,X7),X7)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X1)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X2
| X2 != X4
| ~ in(X4,cartesian_product2(X1,X0))
| sP25(X0,X1,X2,X3) ),
inference(definition_unfolding,[],[f2350,f2992]) ).
fof(f3190,plain,
! [X2,X3,X0,X1] :
( ~ sP25(X0,X1,X2,X3)
| unordered_pair(unordered_pair(sK226(X1,X2,X3),sK227(X1,X2,X3)),unordered_pair(sK226(X1,X2,X3),sK226(X1,X2,X3))) = X2 ),
inference(definition_unfolding,[],[f2347,f2992]) ).
fof(f3191,plain,
! [X2,X3,X0,X1,X13] :
( ~ sP25(X0,X1,X2,X3)
| ~ in(X13,sK228(X1,X2,X3))
| in(unordered_pair(unordered_pair(sK227(X1,X2,X3),X13),unordered_pair(sK227(X1,X2,X3),sK227(X1,X2,X3))),X3) ),
inference(definition_unfolding,[],[f2343,f2992]) ).
fof(f3192,plain,
! [X2,X0,X1] :
( ~ sP24(X0,X1,X2)
| unordered_pair(unordered_pair(sK229(X0,X1,X2),sK230(X0,X1,X2)),unordered_pair(sK229(X0,X1,X2),sK229(X0,X1,X2))) = X0 ),
inference(definition_unfolding,[],[f2356,f2992]) ).
fof(f3193,plain,
! [X2,X0,X1,X6] :
( ~ sP24(X0,X1,X2)
| ~ in(X6,sK231(X0,X1,X2))
| in(unordered_pair(unordered_pair(sK230(X0,X1,X2),X6),unordered_pair(sK230(X0,X1,X2),sK230(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f2352,f2992]) ).
fof(f3196,plain,
! [X0,X1] :
( ~ relation(X0)
| relation_restriction(X0,X1) = set_difference(X0,set_difference(X0,cartesian_product2(X1,X1))) ),
inference(definition_unfolding,[],[f2369,f2065]) ).
fof(f3197,plain,
! [X2,X0,X1,X4,X5] :
( ~ in(sK238(X0,X1,X2),X2)
| sK238(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X1)
| ~ in(X4,X0)
| cartesian_product2(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2377,f2992]) ).
fof(f3198,plain,
! [X2,X0,X1] :
( in(sK238(X0,X1,X2),X2)
| sK238(X0,X1,X2) = unordered_pair(unordered_pair(sK239(X0,X1,X2),sK240(X0,X1,X2)),unordered_pair(sK239(X0,X1,X2),sK239(X0,X1,X2)))
| cartesian_product2(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2374,f2992]) ).
fof(f3199,plain,
! [X2,X10,X0,X1,X8,X9] :
( cartesian_product2(X0,X1) != X2
| unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(X8,X2) ),
inference(definition_unfolding,[],[f2373,f2992]) ).
fof(f3200,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| unordered_pair(unordered_pair(sK241(X0,X1,X8),sK242(X0,X1,X8)),unordered_pair(sK241(X0,X1,X8),sK241(X0,X1,X8))) = X8 ),
inference(definition_unfolding,[],[f2370,f2992]) ).
fof(f3201,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),unordered_pair(sK243(X0,X1,X2),sK243(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),unordered_pair(sK243(X0,X1,X2),sK243(X0,X1,X2))),X0)
| ~ in(sK243(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2387,f2992,f2992]) ).
fof(f3202,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),unordered_pair(sK243(X0,X1,X2),sK243(X0,X1,X2))),X2)
| in(sK243(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2386,f2992]) ).
fof(f3203,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),unordered_pair(sK243(X0,X1,X2),sK243(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),unordered_pair(sK243(X0,X1,X2),sK243(X0,X1,X2))),X0)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2385,f2992,f2992]) ).
fof(f3204,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2) ),
inference(definition_unfolding,[],[f2384,f2992,f2992]) ).
fof(f3205,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(X5,X1) ),
inference(definition_unfolding,[],[f2383,f2992]) ).
fof(f3206,plain,
! [X2,X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(X2)
| relation_dom_restriction(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f2382,f2992,f2992]) ).
fof(f3207,plain,
! [X2,X3,X0,X1] :
( empty_set != sK257(X3)
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X1) ),
inference(definition_unfolding,[],[f2434,f2991]) ).
fof(f3208,plain,
! [X2,X3,X0,X1,X5] :
( sK258(X3,X5) != X5
| ~ in(X5,sK257(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X1) ),
inference(definition_unfolding,[],[f2433,f2991]) ).
fof(f3209,plain,
! [X2,X3,X0,X1,X5] :
( in(sK258(X3,X5),sK257(X3))
| ~ in(X5,sK257(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X1) ),
inference(definition_unfolding,[],[f2432,f2991]) ).
fof(f3210,plain,
! [X2,X3,X0,X1,X5] :
( subset(X5,sK258(X3,X5))
| ~ in(X5,sK257(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X1) ),
inference(definition_unfolding,[],[f2431,f2991]) ).
fof(f3211,plain,
! [X2,X3,X0,X1] :
( element(sK257(X3),powerset(powerset(X3)))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X1) ),
inference(definition_unfolding,[],[f2430,f2991]) ).
fof(f3212,plain,
! [X2,X3,X0,X1] :
( in(X3,omega)
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X1) ),
inference(definition_unfolding,[],[f2429,f2991]) ).
fof(f3213,plain,
! [X0,X1] :
( ~ sP29(X0,X1)
| in(sK259(X0,X1),set_union2(X0,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f2428,f2991]) ).
fof(f3214,plain,
! [X3,X0,X1,X4,X5] :
( ~ ordinal(X1)
| sP32(X0)
| ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5)
| X3 != X4
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1)))
| in(X3,sK276(X0,X1)) ),
inference(definition_unfolding,[],[f2483,f2991]) ).
fof(f3215,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP32(X0)
| ~ in(X3,sK276(X0,X1))
| in(sK277(X0,X1,X3),set_union2(X1,unordered_pair(X1,X1))) ),
inference(definition_unfolding,[],[f2482,f2991]) ).
fof(f3218,plain,
! [X3,X0,X1,X4,X5] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP33(X1,X0)
| set_difference(X5,unordered_pair(X0,X0)) != X3
| ~ in(X5,X1)
| X3 != X4
| ~ in(X4,powerset(X0))
| in(X3,sK284(X0,X1)) ),
inference(definition_unfolding,[],[f2495,f2115,f2991]) ).
fof(f3219,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ~ in(X3,sK284(X0,X1))
| in(sK285(X0,X1,X3),powerset(X0)) ),
inference(definition_unfolding,[],[f2494,f2991]) ).
fof(f3220,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ~ in(X3,sK284(X0,X1))
| sK285(X0,X1,X3) = X3 ),
inference(definition_unfolding,[],[f2493,f2991]) ).
fof(f3221,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ~ in(X3,sK284(X0,X1))
| in(sK286(X0,X1,X3),X1) ),
inference(definition_unfolding,[],[f2492,f2991]) ).
fof(f3222,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ~ in(X3,sK284(X0,X1))
| set_difference(sK286(X0,X1,X3),unordered_pair(X0,X0)) = X3 ),
inference(definition_unfolding,[],[f2491,f2115,f2991]) ).
fof(f3224,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(set_union2(X0,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f2498,f2991]) ).
fof(f3225,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(set_union2(X0,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f2497,f2991]) ).
fof(f3226,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f2496,f2991]) ).
fof(f3227,plain,
! [X0] : ~ empty(set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f2500,f2991]) ).
fof(f3230,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK311(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(X4,sK311(X0,X1,X2)),unordered_pair(X4,X4)),X0)
| relation_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2565,f2992]) ).
fof(f3231,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK311(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK312(X0,X1,X2),sK311(X0,X1,X2)),unordered_pair(sK312(X0,X1,X2),sK312(X0,X1,X2))),X0)
| relation_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2564,f2992]) ).
fof(f3232,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f2562,f2992]) ).
fof(f3233,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(unordered_pair(unordered_pair(sK313(X0,X1,X6),X6),unordered_pair(sK313(X0,X1,X6),sK313(X0,X1,X6))),X0) ),
inference(definition_unfolding,[],[f2561,f2992]) ).
fof(f3234,plain,
! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)),
inference(definition_unfolding,[],[f2586,f2065]) ).
fof(f3242,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f2594,f2065]) ).
fof(f3243,plain,
! [X2,X0,X1] :
( ~ in(sK318(X0,X1,X2),X2)
| ~ in(sK318(X0,X1,X2),X1)
| ~ in(sK318(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f2600,f2065]) ).
fof(f3244,plain,
! [X2,X0,X1] :
( in(sK318(X0,X1,X2),X2)
| in(sK318(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f2599,f2065]) ).
fof(f3245,plain,
! [X2,X0,X1] :
( in(sK318(X0,X1,X2),X2)
| in(sK318(X0,X1,X2),X1)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f2598,f2065]) ).
fof(f3246,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,set_difference(X0,X1)) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(definition_unfolding,[],[f2597,f2065]) ).
fof(f3248,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,set_difference(X0,X1)) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(definition_unfolding,[],[f2595,f2065]) ).
fof(f3249,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f2601,f2065,f2065]) ).
fof(f3251,plain,
! [X0] : finite(unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f2624,f2115]) ).
fof(f3253,plain,
! [X0,X1] :
( ~ finite(X1)
| finite(set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f2628,f2065]) ).
fof(f3254,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK327(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(sK327(X0,X1,X2),X4),unordered_pair(sK327(X0,X1,X2),sK327(X0,X1,X2))),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2636,f2992]) ).
fof(f3255,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK327(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK327(X0,X1,X2),sK328(X0,X1,X2)),unordered_pair(sK327(X0,X1,X2),sK327(X0,X1,X2))),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2635,f2992]) ).
fof(f3256,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| in(X6,X2) ),
inference(definition_unfolding,[],[f2633,f2992]) ).
fof(f3257,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(unordered_pair(unordered_pair(X6,sK329(X0,X1,X6)),unordered_pair(X6,X6)),X0) ),
inference(definition_unfolding,[],[f2632,f2992]) ).
fof(f3258,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_difference(X1,set_difference(X1,X2)) ),
inference(definition_unfolding,[],[f2643,f2065]) ).
fof(f3259,plain,
! [X2,X0,X1,X5] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(sK331(X0,X1,X2),sK332(X0,X1,X2)),unordered_pair(sK331(X0,X1,X2),sK331(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(X5,sK332(X0,X1,X2)),unordered_pair(X5,X5)),X1)
| ~ in(unordered_pair(unordered_pair(sK331(X0,X1,X2),X5),unordered_pair(sK331(X0,X1,X2),sK331(X0,X1,X2))),X0)
| relation_composition(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2659,f2992,f2992,f2992]) ).
fof(f3260,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK331(X0,X1,X2),sK332(X0,X1,X2)),unordered_pair(sK331(X0,X1,X2),sK331(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK331(X0,X1,X2),sK333(X0,X1,X2)),unordered_pair(sK331(X0,X1,X2),sK331(X0,X1,X2))),X0)
| relation_composition(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2658,f2992,f2992]) ).
fof(f3261,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK331(X0,X1,X2),sK332(X0,X1,X2)),unordered_pair(sK331(X0,X1,X2),sK331(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK333(X0,X1,X2),sK332(X0,X1,X2)),unordered_pair(sK333(X0,X1,X2),sK333(X0,X1,X2))),X1)
| relation_composition(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2657,f2992,f2992]) ).
fof(f3262,plain,
! [X2,X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2) ),
inference(definition_unfolding,[],[f2656,f2992,f2992,f2992]) ).
fof(f3263,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| in(unordered_pair(unordered_pair(X7,sK334(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0) ),
inference(definition_unfolding,[],[f2655,f2992,f2992]) ).
fof(f3264,plain,
! [X2,X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| in(unordered_pair(unordered_pair(sK334(X0,X1,X7,X8),X8),unordered_pair(sK334(X0,X1,X7,X8),sK334(X0,X1,X7,X8))),X1) ),
inference(definition_unfolding,[],[f2654,f2992,f2992]) ).
fof(f3265,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ in(sK345(X0,X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(sK345(X0,X1,X2),X1),unordered_pair(sK345(X0,X1,X2),sK345(X0,X1,X2))),X0)
| sK345(X0,X1,X2) = X1
| fiber(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2722,f2992]) ).
fof(f3266,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK345(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK345(X0,X1,X2),X1),unordered_pair(sK345(X0,X1,X2),sK345(X0,X1,X2))),X0)
| fiber(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2720,f2992]) ).
fof(f3267,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| fiber(X0,X1) != X2
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0)
| X1 = X4
| in(X4,X2) ),
inference(definition_unfolding,[],[f2719,f2992]) ).
fof(f3268,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| fiber(X0,X1) != X2
| ~ in(X4,X2)
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0) ),
inference(definition_unfolding,[],[f2717,f2992]) ).
fof(f3269,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK353(X0,X1),sK354(X0,X1)),unordered_pair(sK353(X0,X1),sK353(X0,X1))),X1)
| ~ subset(sK353(X0,X1),sK354(X0,X1))
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(definition_unfolding,[],[f2768,f2992]) ).
fof(f3270,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK353(X0,X1),sK354(X0,X1)),unordered_pair(sK353(X0,X1),sK353(X0,X1))),X1)
| subset(sK353(X0,X1),sK354(X0,X1))
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(definition_unfolding,[],[f2767,f2992]) ).
fof(f3271,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ subset(X4,X5)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1) ),
inference(definition_unfolding,[],[f2763,f2992]) ).
fof(f3272,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| subset(X4,X5) ),
inference(definition_unfolding,[],[f2762,f2992]) ).
fof(f3273,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK355(X0,X1),sK356(X0,X1)),unordered_pair(sK355(X0,X1),sK355(X0,X1))),X1)
| sK355(X0,X1) != sK356(X0,X1)
| ~ in(sK355(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f2777,f2992]) ).
fof(f3274,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK355(X0,X1),sK356(X0,X1)),unordered_pair(sK355(X0,X1),sK355(X0,X1))),X1)
| in(sK355(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f2776,f2992]) ).
fof(f3275,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK355(X0,X1),sK356(X0,X1)),unordered_pair(sK355(X0,X1),sK355(X0,X1))),X1)
| sK355(X0,X1) = sK356(X0,X1)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f2775,f2992]) ).
fof(f3276,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| X4 != X5
| ~ in(X4,X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1) ),
inference(definition_unfolding,[],[f2774,f2992]) ).
fof(f3277,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| in(X4,X0) ),
inference(definition_unfolding,[],[f2773,f2992]) ).
fof(f3278,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| X4 = X5 ),
inference(definition_unfolding,[],[f2772,f2992]) ).
fof(f3279,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK357(X0,X1),sK358(X0,X1)),unordered_pair(sK357(X0,X1),sK357(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK358(X0,X1),sK357(X0,X1)),unordered_pair(sK358(X0,X1),sK358(X0,X1))),X0)
| relation_inverse(X0) = X1 ),
inference(definition_unfolding,[],[f2788,f2992,f2992]) ).
fof(f3280,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK357(X0,X1),sK358(X0,X1)),unordered_pair(sK357(X0,X1),sK357(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK358(X0,X1),sK357(X0,X1)),unordered_pair(sK358(X0,X1),sK358(X0,X1))),X0)
| relation_inverse(X0) = X1 ),
inference(definition_unfolding,[],[f2787,f2992,f2992]) ).
fof(f3281,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1) ),
inference(definition_unfolding,[],[f2786,f2992,f2992]) ).
fof(f3282,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f2785,f2992,f2992]) ).
fof(f3291,plain,
! [X0,X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| sK365(X0,X1) != X1
| pair_first(X0) = X1 ),
inference(definition_unfolding,[],[f2835,f2992]) ).
fof(f3292,plain,
! [X0,X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| unordered_pair(unordered_pair(sK365(X0,X1),sK366(X0,X1)),unordered_pair(sK365(X0,X1),sK365(X0,X1))) = X0
| pair_first(X0) = X1 ),
inference(definition_unfolding,[],[f2834,f2992,f2992]) ).
fof(f3293,plain,
! [X0,X1,X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| pair_first(X0) != X1
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != X0
| X1 = X4 ),
inference(definition_unfolding,[],[f2833,f2992,f2992]) ).
fof(f3294,plain,
! [X0,X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| sK368(X0,X1) != X1
| pair_second(X0) = X1 ),
inference(definition_unfolding,[],[f2838,f2992]) ).
fof(f3295,plain,
! [X0,X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| unordered_pair(unordered_pair(sK367(X0,X1),sK368(X0,X1)),unordered_pair(sK367(X0,X1),sK367(X0,X1))) = X0
| pair_second(X0) = X1 ),
inference(definition_unfolding,[],[f2837,f2992,f2992]) ).
fof(f3296,plain,
! [X0,X1,X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| pair_second(X0) != X1
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != X0
| X1 = X5 ),
inference(definition_unfolding,[],[f2836,f2992,f2992]) ).
fof(f3316,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK379(X0,X1),sK380(X0,X1)),unordered_pair(sK379(X0,X1),sK379(X0,X1))),X0)
| is_antisymmetric_in(X0,X1) ),
inference(definition_unfolding,[],[f2925,f2992]) ).
fof(f3317,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK380(X0,X1),sK379(X0,X1)),unordered_pair(sK380(X0,X1),sK380(X0,X1))),X0)
| is_antisymmetric_in(X0,X1) ),
inference(definition_unfolding,[],[f2924,f2992]) ).
fof(f3318,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| X4 = X5 ),
inference(definition_unfolding,[],[f2923,f2992,f2992]) ).
fof(f3319,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK381(X0,X1),sK382(X0,X1)),unordered_pair(sK381(X0,X1),sK381(X0,X1))),X0)
| is_connected_in(X0,X1) ),
inference(definition_unfolding,[],[f2933,f2992]) ).
fof(f3320,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK382(X0,X1),sK381(X0,X1)),unordered_pair(sK382(X0,X1),sK382(X0,X1))),X0)
| is_connected_in(X0,X1) ),
inference(definition_unfolding,[],[f2932,f2992]) ).
fof(f3321,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ is_connected_in(X0,X1)
| in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) ),
inference(definition_unfolding,[],[f2931,f2992,f2992]) ).
fof(f3322,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK383(X0,X1),sK385(X0,X1)),unordered_pair(sK383(X0,X1),sK383(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f2945,f2992]) ).
fof(f3323,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK383(X0,X1),sK384(X0,X1)),unordered_pair(sK383(X0,X1),sK383(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f2941,f2992]) ).
fof(f3324,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK384(X0,X1),sK385(X0,X1)),unordered_pair(sK384(X0,X1),sK384(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f2940,f2992]) ).
fof(f3325,plain,
! [X0,X1,X6,X7,X5] :
( ~ relation(X0)
| ~ is_transitive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X7),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f2939,f2992,f2992,f2992]) ).
fof(f3326,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK386(X0,X1),sK386(X0,X1)),unordered_pair(sK386(X0,X1),sK386(X0,X1))),X0)
| is_reflexive_in(X0,X1) ),
inference(definition_unfolding,[],[f2952,f2992]) ).
fof(f3327,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ is_reflexive_in(X0,X1)
| ~ in(X3,X1)
| in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X3)),X0) ),
inference(definition_unfolding,[],[f2950,f2992]) ).
fof(f3343,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ relation(X1)
| empty(X0)
| ~ in(unordered_pair(unordered_pair(X6,sK79(X1,X6,X7)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),cartesian_product2(X0,X2))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),sK78(X0,X1,X2)) ),
inference(equality_resolution,[],[f3039]) ).
fof(f3344,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X1)
| empty(X0)
| ~ in(unordered_pair(unordered_pair(X6,sK79(X1,X6,X7)),unordered_pair(X6,X6)),X1)
| ~ in(X6,X7)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),cartesian_product2(X0,X2))
| in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),sK78(X0,X1,X2)) ),
inference(equality_resolution,[],[f3343]) ).
fof(f3345,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ relation(X1)
| empty(X0)
| in(sK79(X1,X6,X7),X7)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),cartesian_product2(X0,X2))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),sK78(X0,X1,X2)) ),
inference(equality_resolution,[],[f3040]) ).
fof(f3346,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X1)
| empty(X0)
| in(sK79(X1,X6,X7),X7)
| ~ in(X6,X7)
| ~ in(X7,X0)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),cartesian_product2(X0,X2))
| in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),sK78(X0,X1,X2)) ),
inference(equality_resolution,[],[f3345]) ).
fof(f3347,plain,
! [X0,X1,X4,X5] :
( unordered_pair(X4,X4) != X5
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),cartesian_product2(X0,X1))
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK83(X0,X1)) ),
inference(equality_resolution,[],[f3043]) ).
fof(f3348,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,unordered_pair(X4,X4)),unordered_pair(X4,X4)),cartesian_product2(X0,X1))
| in(unordered_pair(unordered_pair(X4,unordered_pair(X4,X4)),unordered_pair(X4,X4)),sK83(X0,X1)) ),
inference(equality_resolution,[],[f3347]) ).
fof(f3355,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,powerset(the_carrier(X0)))
| in(X4,sK91(X0,X1)) ),
inference(equality_resolution,[],[f1801]) ).
fof(f3356,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| ~ in(X4,X1)
| ~ in(set_difference(X4,unordered_pair(X0,X0)),powerset(X0))
| in(set_difference(X4,unordered_pair(X0,X0)),sK94(X0,X1)) ),
inference(equality_resolution,[],[f3053]) ).
fof(f3357,plain,
! [X2,X0,X1,X6,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(apply(X2,X5),apply(X2,X6)),unordered_pair(apply(X2,X5),apply(X2,X5))),X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),cartesian_product2(X0,X0))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),sK96(X0,X1,X2)) ),
inference(equality_resolution,[],[f3057]) ).
fof(f3358,plain,
! [X0,X1,X4] :
( ~ ordinal(X1)
| ~ in(X4,X0)
| ~ ordinal(X4)
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1)))
| in(X4,sK101(X0,X1)) ),
inference(equality_resolution,[],[f3060]) ).
fof(f3359,plain,
! [X3,X0,X1] :
( ~ relation(X1)
| empty(X0)
| ~ in(unordered_pair(unordered_pair(X3,sK111(X1,X3,sK110(X0,X1))),unordered_pair(X3,X3)),X1)
| ~ in(X3,sK110(X0,X1))
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(equality_resolution,[],[f3065]) ).
fof(f3360,plain,
! [X3,X0,X1] :
( ~ relation(X1)
| empty(X0)
| in(sK111(X1,X3,sK110(X0,X1)),sK110(X0,X1))
| ~ in(X3,sK110(X0,X1))
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(equality_resolution,[],[f1838]) ).
fof(f3361,plain,
! [X0] :
( sP13(X0)
| relation(sK115(X0)) ),
inference(equality_resolution,[],[f3068]) ).
fof(f3362,plain,
! [X0] :
( sP13(X0)
| function(sK115(X0)) ),
inference(equality_resolution,[],[f3069]) ).
fof(f3363,plain,
! [X0] :
( sP13(X0)
| relation_dom(sK115(X0)) = X0 ),
inference(equality_resolution,[],[f3070]) ).
fof(f3364,plain,
! [X2,X0] :
( sP13(X0)
| ~ in(X2,X0)
| apply(sK115(X0),X2) = unordered_pair(X2,X2) ),
inference(equality_resolution,[],[f3072]) ).
fof(f3366,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| sK141(relation_dom(X1),X1) != apply(X1,sK141(relation_dom(X1),X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f2006]) ).
fof(f3367,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK141(relation_dom(X1),X1),relation_dom(X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f2005]) ).
fof(f3372,plain,
! [X2] :
( ~ ordinal(set_union2(X2,unordered_pair(X2,X2)))
| ~ being_limit_ordinal(set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2) ),
inference(equality_resolution,[],[f3110]) ).
fof(f3377,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| ~ in(X4,relation_rng(X0))
| in(apply(X1,X4),relation_dom(X0)) ),
inference(equality_resolution,[],[f2085]) ).
fof(f3378,plain,
! [X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ in(X4,relation_rng(X0))
| in(apply(function_inverse(X0),X4),relation_dom(X0)) ),
inference(equality_resolution,[],[f3377]) ).
fof(f3381,plain,
! [X0,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| sP16(X0,X4,X5,function_inverse(X0)) ),
inference(equality_resolution,[],[f2083]) ).
fof(f3384,plain,
! [X2,X0] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| in(unordered_pair(unordered_pair(X0,apply(X2,X0)),unordered_pair(X0,X0)),X2) ),
inference(equality_resolution,[],[f3126]) ).
fof(f3386,plain,
! [X2,X3,X1] :
( ~ relation_of2_as_subset(X3,empty_set,X1)
| ~ quasi_total(X3,empty_set,X1)
| ~ function(X3)
| ~ subset(X1,X2)
| quasi_total(X3,empty_set,X2) ),
inference(equality_resolution,[],[f2149]) ).
fof(f3390,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X6,X5),unordered_pair(X6,X6)),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f3139]) ).
fof(f3391,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK167(X0,X5),X5),unordered_pair(sK167(X0,X5),sK167(X0,X5))),X0) ),
inference(equality_resolution,[],[f3140]) ).
fof(f3392,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f3143]) ).
fof(f3393,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK170(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f3144]) ).
fof(f3396,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f2211]) ).
fof(f3397,plain,
! [X0,X1,X6,X4,X5] :
( sP20(X0)
| unordered_pair(X5,X5) != X6
| ~ in(X5,X0)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X4,cartesian_product2(X0,X1))
| in(X4,sK189(X0,X1)) ),
inference(equality_resolution,[],[f3161]) ).
fof(f3398,plain,
! [X0,X1,X6,X5] :
( sP20(X0)
| unordered_pair(X5,X5) != X6
| ~ in(X5,X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),cartesian_product2(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),sK189(X0,X1)) ),
inference(equality_resolution,[],[f3397]) ).
fof(f3399,plain,
! [X0,X1,X5] :
( sP20(X0)
| ~ in(X5,X0)
| ~ in(unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)),cartesian_product2(X0,X1))
| in(unordered_pair(unordered_pair(X5,unordered_pair(X5,X5)),unordered_pair(X5,X5)),sK189(X0,X1)) ),
inference(equality_resolution,[],[f3398]) ).
fof(f3403,plain,
! [X3,X0] :
( ~ in(X3,unordered_pair(X0,X0))
| X0 = X3 ),
inference(equality_resolution,[],[f3172]) ).
fof(f3404,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f2251]) ).
fof(f3405,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f2250]) ).
fof(f3406,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f2249]) ).
fof(f3407,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| ~ in(X6,X0)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1)) ),
inference(equality_resolution,[],[f3178]) ).
fof(f3408,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1))
| in(X6,X0) ),
inference(equality_resolution,[],[f3179]) ).
fof(f3409,plain,
! [X0,X1,X6,X5] :
( ~ relation(X1)
| ~ relation(relation_rng_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_rng_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1) ),
inference(equality_resolution,[],[f3180]) ).
fof(f3410,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f2279]) ).
fof(f3411,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f2278]) ).
fof(f3413,plain,
! [X1] : subset(X1,X1),
inference(equality_resolution,[],[f2282]) ).
fof(f3414,plain,
! [X2,X1] :
( relation_rng(X2) != X1
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2)
| equipotent(relation_dom(X2),X1) ),
inference(equality_resolution,[],[f2292]) ).
fof(f3415,plain,
! [X2] :
( ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2)
| equipotent(relation_dom(X2),relation_rng(X2)) ),
inference(equality_resolution,[],[f3414]) ).
fof(f3416,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f2304]) ).
fof(f3417,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f2303]) ).
fof(f3418,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f2302]) ).
fof(f3419,plain,
! [X0,X6,X5] :
( ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,union(X0)) ),
inference(equality_resolution,[],[f2325]) ).
fof(f3420,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(X5,sK211(X0,X5)) ),
inference(equality_resolution,[],[f2324]) ).
fof(f3421,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK211(X0,X5),X0) ),
inference(equality_resolution,[],[f2323]) ).
fof(f3422,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ~ in(unordered_pair(unordered_pair(apply(X2,X6),apply(X2,X7)),unordered_pair(apply(X2,X6),apply(X2,X6))),X1)
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X5
| ~ in(X5,cartesian_product2(X0,X0))
| in(X5,sK219(X0,X1,X2)) ),
inference(equality_resolution,[],[f3185]) ).
fof(f3423,plain,
! [X2,X0,X1,X6,X7] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ~ in(unordered_pair(unordered_pair(apply(X2,X6),apply(X2,X7)),unordered_pair(apply(X2,X6),apply(X2,X6))),X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),cartesian_product2(X0,X0))
| in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),sK219(X0,X1,X2)) ),
inference(equality_resolution,[],[f3422]) ).
fof(f3424,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( ~ in(unordered_pair(unordered_pair(X6,sK224(X3,X6,X7)),unordered_pair(X6,X6)),X3)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X1)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X4,cartesian_product2(X1,X0))
| sP25(X0,X1,X4,X3) ),
inference(equality_resolution,[],[f3188]) ).
fof(f3425,plain,
! [X3,X0,X1,X6,X7,X5] :
( ~ in(unordered_pair(unordered_pair(X6,sK224(X3,X6,X7)),unordered_pair(X6,X6)),X3)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),cartesian_product2(X1,X0))
| sP25(X0,X1,unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X3) ),
inference(equality_resolution,[],[f3424]) ).
fof(f3426,plain,
! [X3,X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X6,sK224(X3,X6,X7)),unordered_pair(X6,X6)),X3)
| ~ in(X6,X7)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),cartesian_product2(X1,X0))
| sP25(X0,X1,unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X3) ),
inference(equality_resolution,[],[f3425]) ).
fof(f3427,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( in(sK224(X3,X6,X7),X7)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X1)
| unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)) != X4
| ~ in(X4,cartesian_product2(X1,X0))
| sP25(X0,X1,X4,X3) ),
inference(equality_resolution,[],[f3189]) ).
fof(f3428,plain,
! [X3,X0,X1,X6,X7,X5] :
( in(sK224(X3,X6,X7),X7)
| ~ in(X6,X7)
| X5 != X7
| ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),cartesian_product2(X1,X0))
| sP25(X0,X1,unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X3) ),
inference(equality_resolution,[],[f3427]) ).
fof(f3429,plain,
! [X3,X0,X1,X6,X7] :
( in(sK224(X3,X6,X7),X7)
| ~ in(X6,X7)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),cartesian_product2(X1,X0))
| sP25(X0,X1,unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X3) ),
inference(equality_resolution,[],[f3428]) ).
fof(f3430,plain,
! [X2,X10,X0,X1,X9] :
( cartesian_product2(X0,X1) != X2
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2) ),
inference(equality_resolution,[],[f3199]) ).
fof(f3431,plain,
! [X10,X0,X1,X9] :
( ~ in(X10,X1)
| ~ in(X9,X0)
| in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f3430]) ).
fof(f3432,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK241(X0,X1,X8),X0) ),
inference(equality_resolution,[],[f2372]) ).
fof(f3433,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK242(X0,X1,X8),X1) ),
inference(equality_resolution,[],[f2371]) ).
fof(f3434,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(sK241(X0,X1,X8),sK242(X0,X1,X8)),unordered_pair(sK241(X0,X1,X8),sK241(X0,X1,X8))) = X8 ),
inference(equality_resolution,[],[f3200]) ).
fof(f3435,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1)) ),
inference(equality_resolution,[],[f3204]) ).
fof(f3436,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1))
| in(X5,X1) ),
inference(equality_resolution,[],[f3205]) ).
fof(f3437,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),relation_dom_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f3206]) ).
fof(f3438,plain,
! [X3,X0] :
( sP27
| ~ ordinal(X3)
| ~ in(X3,X0)
| in(X3,sK254(X0)) ),
inference(equality_resolution,[],[f2416]) ).
fof(f3439,plain,
! [X2,X3,X0] :
( empty_set != sK257(X3)
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X2) ),
inference(equality_resolution,[],[f3207]) ).
fof(f3440,plain,
! [X3,X0] :
( empty_set != sK257(X3)
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X3) ),
inference(equality_resolution,[],[f3439]) ).
fof(f3441,plain,
! [X2,X3,X0,X5] :
( sK258(X3,X5) != X5
| ~ in(X5,sK257(X3))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X2) ),
inference(equality_resolution,[],[f3208]) ).
fof(f3442,plain,
! [X3,X0,X5] :
( sK258(X3,X5) != X5
| ~ in(X5,sK257(X3))
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X3) ),
inference(equality_resolution,[],[f3441]) ).
fof(f3443,plain,
! [X2,X3,X0,X5] :
( in(sK258(X3,X5),sK257(X3))
| ~ in(X5,sK257(X3))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X2) ),
inference(equality_resolution,[],[f3209]) ).
fof(f3444,plain,
! [X3,X0,X5] :
( in(sK258(X3,X5),sK257(X3))
| ~ in(X5,sK257(X3))
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X3) ),
inference(equality_resolution,[],[f3443]) ).
fof(f3445,plain,
! [X2,X3,X0,X5] :
( subset(X5,sK258(X3,X5))
| ~ in(X5,sK257(X3))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X2) ),
inference(equality_resolution,[],[f3210]) ).
fof(f3446,plain,
! [X3,X0,X5] :
( subset(X5,sK258(X3,X5))
| ~ in(X5,sK257(X3))
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X3) ),
inference(equality_resolution,[],[f3445]) ).
fof(f3447,plain,
! [X2,X3,X0] :
( element(sK257(X3),powerset(powerset(X3)))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X2) ),
inference(equality_resolution,[],[f3211]) ).
fof(f3448,plain,
! [X3,X0] :
( element(sK257(X3),powerset(powerset(X3)))
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X3) ),
inference(equality_resolution,[],[f3447]) ).
fof(f3449,plain,
! [X2,X3,X0] :
( in(X3,omega)
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X2) ),
inference(equality_resolution,[],[f3212]) ).
fof(f3450,plain,
! [X3,X0] :
( in(X3,omega)
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP29(X0,X3) ),
inference(equality_resolution,[],[f3449]) ).
fof(f3451,plain,
in(empty_set,omega),
inference(equality_resolution,[],[f2454]) ).
fof(f3452,plain,
being_limit_ordinal(omega),
inference(equality_resolution,[],[f2453]) ).
fof(f3453,plain,
ordinal(omega),
inference(equality_resolution,[],[f2452]) ).
fof(f3454,plain,
! [X2] :
( ~ ordinal(X2)
| ~ being_limit_ordinal(X2)
| ~ in(empty_set,X2)
| subset(omega,X2) ),
inference(equality_resolution,[],[f2451]) ).
fof(f3455,plain,
! [X1] :
( ~ in(relation_dom(X1),omega)
| ~ function(X1)
| ~ relation(X1)
| finite(relation_rng(X1)) ),
inference(equality_resolution,[],[f2463]) ).
fof(f3456,plain,
! [X0,X1,X4,X5] :
( ~ ordinal(X1)
| sP32(X0)
| ~ in(X5,X0)
| X4 != X5
| ~ ordinal(X5)
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1)))
| in(X4,sK276(X0,X1)) ),
inference(equality_resolution,[],[f3214]) ).
fof(f3457,plain,
! [X0,X1,X5] :
( ~ ordinal(X1)
| sP32(X0)
| ~ in(X5,X0)
| ~ ordinal(X5)
| ~ in(X5,set_union2(X1,unordered_pair(X1,X1)))
| in(X5,sK276(X0,X1)) ),
inference(equality_resolution,[],[f3456]) ).
fof(f3458,plain,
! [X0,X1,X4,X5] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP33(X1,X0)
| set_difference(X5,unordered_pair(X0,X0)) != X4
| ~ in(X5,X1)
| ~ in(X4,powerset(X0))
| in(X4,sK284(X0,X1)) ),
inference(equality_resolution,[],[f3218]) ).
fof(f3459,plain,
! [X0,X1,X5] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ~ in(X5,X1)
| ~ in(set_difference(X5,unordered_pair(X0,X0)),powerset(X0))
| in(set_difference(X5,unordered_pair(X0,X0)),sK284(X0,X1)) ),
inference(equality_resolution,[],[f3458]) ).
fof(f3460,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),X1) ),
inference(equality_resolution,[],[f2507]) ).
fof(f3461,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f3460]) ).
fof(f3462,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(sK290(X0,X5),relation_dom(X0)) ),
inference(equality_resolution,[],[f2506]) ).
fof(f3463,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| apply(X0,sK290(X0,X5)) = X5 ),
inference(equality_resolution,[],[f2505]) ).
fof(f3466,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| empty_set = apply(X0,X1) ),
inference(equality_resolution,[],[f2511]) ).
fof(f3467,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP34(X1,X0)
| ~ in(set_difference(cast_as_carrier_subset(X0),X4),X1)
| ~ in(X4,powerset(the_carrier(X0)))
| in(X4,sK295(X0,X1)) ),
inference(equality_resolution,[],[f2525]) ).
fof(f3468,plain,
! [X0,X1,X4,X5] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ~ subset(X1,X4)
| ~ closed_subset(X5,X0)
| X4 != X5
| ~ element(X5,powerset(the_carrier(X0)))
| ~ in(X4,powerset(the_carrier(X0)))
| in(X4,sK302(X0,X1)) ),
inference(equality_resolution,[],[f2544]) ).
fof(f3469,plain,
! [X0,X1,X5] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ~ subset(X1,X5)
| ~ closed_subset(X5,X0)
| ~ element(X5,powerset(the_carrier(X0)))
| ~ in(X5,powerset(the_carrier(X0)))
| in(X5,sK302(X0,X1)) ),
inference(equality_resolution,[],[f3468]) ).
fof(f3470,plain,
! [X2,X0,X1,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP37(X1,X2)
| ~ in(relation_image(X2,X5),X1)
| ~ in(X5,powerset(relation_dom(X2)))
| in(X5,sK309(X1,X2)) ),
inference(equality_resolution,[],[f2558]) ).
fof(f3471,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X0)
| in(X6,relation_image(X0,X1)) ),
inference(equality_resolution,[],[f3232]) ).
fof(f3472,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(unordered_pair(unordered_pair(sK313(X0,X1,X6),X6),unordered_pair(sK313(X0,X1,X6),sK313(X0,X1,X6))),X0) ),
inference(equality_resolution,[],[f3233]) ).
fof(f3473,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK313(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f2560]) ).
fof(f3474,plain,
! [X2,X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),X2) ),
inference(equality_resolution,[],[f2569]) ).
fof(f3475,plain,
! [X0,X1,X7] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0))
| in(apply(X0,X7),relation_image(X0,X1)) ),
inference(equality_resolution,[],[f3474]) ).
fof(f3476,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK316(X0,X1,X6),relation_dom(X0)) ),
inference(equality_resolution,[],[f2568]) ).
fof(f3477,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK316(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f2567]) ).
fof(f3478,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| apply(X0,sK316(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f2566]) ).
fof(f3479,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f2578]) ).
fof(f3480,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f3479]) ).
fof(f3481,plain,
! [X2,X0,X4] :
( unordered_pair(X0,X4) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f2577]) ).
fof(f3482,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f3481]) ).
fof(f3483,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f2576]) ).
fof(f3484,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,set_difference(X0,X1))) ),
inference(equality_resolution,[],[f3246]) ).
fof(f3486,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,set_difference(X0,X1)))
| in(X4,X1) ),
inference(equality_resolution,[],[f3248]) ).
fof(f3487,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X0)
| in(X6,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f3256]) ).
fof(f3488,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(unordered_pair(unordered_pair(X6,sK329(X0,X1,X6)),unordered_pair(X6,X6)),X0) ),
inference(equality_resolution,[],[f3257]) ).
fof(f3489,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(sK329(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f2631]) ).
fof(f3490,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(apply(X0,X4),X1)
| ~ in(X4,relation_dom(X0))
| in(X4,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f2639]) ).
fof(f3491,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f2638]) ).
fof(f3492,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f2637]) ).
fof(f3493,plain,
! [X0,X1,X8,X9,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X0)
| in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f3262]) ).
fof(f3494,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(X7,sK334(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0) ),
inference(equality_resolution,[],[f3263]) ).
fof(f3495,plain,
! [X0,X1,X8,X7] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(sK334(X0,X1,X7,X8),X8),unordered_pair(sK334(X0,X1,X7,X8),sK334(X0,X1,X7,X8))),X1) ),
inference(equality_resolution,[],[f3264]) ).
fof(f3496,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X4,powerset(X0))
| ~ in(subset_complement(X0,X4),X1)
| in(X4,complements_of_subsets(X0,X1)) ),
inference(equality_resolution,[],[f2664]) ).
fof(f3497,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X4,powerset(X0))
| ~ in(X4,complements_of_subsets(X0,X1))
| in(subset_complement(X0,X4),X1) ),
inference(equality_resolution,[],[f2663]) ).
fof(f3498,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0)
| X1 = X4
| in(X4,fiber(X0,X1)) ),
inference(equality_resolution,[],[f3267]) ).
fof(f3499,plain,
! [X2,X0,X4] :
( ~ relation(X0)
| fiber(X0,X4) != X2
| ~ in(X4,X2) ),
inference(equality_resolution,[],[f2718]) ).
fof(f3500,plain,
! [X0,X4] :
( ~ relation(X0)
| ~ in(X4,fiber(X0,X4)) ),
inference(equality_resolution,[],[f3499]) ).
fof(f3501,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ in(X4,fiber(X0,X1))
| in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X0) ),
inference(equality_resolution,[],[f3268]) ).
fof(f3502,plain,
! [X2,X1] :
( ~ relation_of2_as_subset(X2,empty_set,X1)
| empty_set != relation_dom_as_subset(empty_set,X1,X2)
| quasi_total(X2,empty_set,X1) ),
inference(equality_resolution,[],[f2730]) ).
fof(f3503,plain,
! [X2,X1] :
( ~ relation_of2_as_subset(X2,empty_set,X1)
| ~ quasi_total(X2,empty_set,X1)
| empty_set = relation_dom_as_subset(empty_set,X1,X2) ),
inference(equality_resolution,[],[f2728]) ).
fof(f3504,plain,
! [X0,X1] :
( ~ relation_of2_as_subset(empty_set,X0,X1)
| empty_set != X1
| quasi_total(empty_set,X0,X1)
| empty_set = X0 ),
inference(equality_resolution,[],[f2726]) ).
fof(f3505,plain,
! [X0] :
( ~ relation_of2_as_subset(empty_set,X0,empty_set)
| quasi_total(empty_set,X0,empty_set)
| empty_set = X0 ),
inference(equality_resolution,[],[f3504]) ).
fof(f3506,plain,
! [X2,X0] :
( ~ relation_of2_as_subset(X2,X0,empty_set)
| ~ quasi_total(X2,X0,empty_set)
| empty_set = X2
| empty_set = X0 ),
inference(equality_resolution,[],[f2725]) ).
fof(f3507,plain,
! [X2,X1] :
( ~ sP39(topstr_closure(X2,X1),X1,X2)
| sP38(X2,X1,topstr_closure(X2,X1)) ),
inference(equality_resolution,[],[f2747]) ).
fof(f3508,plain,
! [X1] :
( ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK353(relation_field(X1),X1),sK354(relation_field(X1),X1)),unordered_pair(sK353(relation_field(X1),X1),sK353(relation_field(X1),X1))),X1)
| ~ subset(sK353(relation_field(X1),X1),sK354(relation_field(X1),X1))
| inclusion_relation(relation_field(X1)) = X1 ),
inference(equality_resolution,[],[f3269]) ).
fof(f3509,plain,
! [X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK353(relation_field(X1),X1),sK354(relation_field(X1),X1)),unordered_pair(sK353(relation_field(X1),X1),sK353(relation_field(X1),X1))),X1)
| subset(sK353(relation_field(X1),X1),sK354(relation_field(X1),X1))
| inclusion_relation(relation_field(X1)) = X1 ),
inference(equality_resolution,[],[f3270]) ).
fof(f3510,plain,
! [X1] :
( ~ relation(X1)
| in(sK353(relation_field(X1),X1),relation_field(X1))
| inclusion_relation(relation_field(X1)) = X1 ),
inference(equality_resolution,[],[f2766]) ).
fof(f3511,plain,
! [X1] :
( ~ relation(X1)
| in(sK354(relation_field(X1),X1),relation_field(X1))
| inclusion_relation(relation_field(X1)) = X1 ),
inference(equality_resolution,[],[f2765]) ).
fof(f3512,plain,
! [X0] :
( ~ relation(inclusion_relation(X0))
| relation_field(inclusion_relation(X0)) = X0 ),
inference(equality_resolution,[],[f2764]) ).
fof(f3513,plain,
! [X0,X4,X5] :
( ~ relation(inclusion_relation(X0))
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ subset(X4,X5)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),inclusion_relation(X0)) ),
inference(equality_resolution,[],[f3271]) ).
fof(f3514,plain,
! [X0,X4,X5] :
( ~ relation(inclusion_relation(X0))
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),inclusion_relation(X0))
| subset(X4,X5) ),
inference(equality_resolution,[],[f3272]) ).
fof(f3515,plain,
! [X0,X1,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X5,X0)
| in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1) ),
inference(equality_resolution,[],[f3276]) ).
fof(f3516,plain,
! [X0,X5] :
( ~ relation(identity_relation(X0))
| ~ in(X5,X0)
| in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),identity_relation(X0)) ),
inference(equality_resolution,[],[f3515]) ).
fof(f3517,plain,
! [X0,X4,X5] :
( ~ relation(identity_relation(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),identity_relation(X0))
| in(X4,X0) ),
inference(equality_resolution,[],[f3277]) ).
fof(f3518,plain,
! [X0,X4,X5] :
( ~ relation(identity_relation(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),identity_relation(X0))
| X4 = X5 ),
inference(equality_resolution,[],[f3278]) ).
fof(f3519,plain,
! [X0,X4,X5] :
( ~ relation(X0)
| ~ relation(relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0)) ),
inference(equality_resolution,[],[f3281]) ).
fof(f3520,plain,
! [X0,X4,X5] :
( ~ relation(X0)
| ~ relation(relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f3282]) ).
fof(f3521,plain,
! [X1,X6,X7] :
( sK365(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1) != X1
| pair_first(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))) = X1 ),
inference(equality_resolution,[],[f3291]) ).
fof(f3522,plain,
! [X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) = unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK366(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)),unordered_pair(sK365(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK365(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)))
| pair_first(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))) = X1 ),
inference(equality_resolution,[],[f3292]) ).
fof(f3523,plain,
! [X1,X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))
| pair_first(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) != X1
| X1 = X4 ),
inference(equality_resolution,[],[f3293]) ).
fof(f3524,plain,
! [X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))
| pair_first(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) = X4 ),
inference(equality_resolution,[],[f3523]) ).
fof(f3525,plain,
! [X1,X6,X7] :
( sK368(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1) != X1
| pair_second(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))) = X1 ),
inference(equality_resolution,[],[f3294]) ).
fof(f3526,plain,
! [X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) = unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK368(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)),unordered_pair(sK367(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK367(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)))
| pair_second(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))) = X1 ),
inference(equality_resolution,[],[f3295]) ).
fof(f3527,plain,
! [X1,X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))
| pair_second(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) != X1
| X1 = X5 ),
inference(equality_resolution,[],[f3296]) ).
fof(f3528,plain,
! [X6,X7,X4,X5] :
( unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6))
| pair_second(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) = X5 ),
inference(equality_resolution,[],[f3527]) ).
tcf(c_49,plain,
! [X0: $i] :
( reflexive(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK43(X0),sK43(X0)),unordered_pair(sK43(X0),sK43(X0))),X0) ),
inference(cnf_transformation,[],[f2993]) ).
tcf(c_50,plain,
! [X0: $i] :
( reflexive(X0)
| in(sK43(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1659]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ reflexive(X1)
| ~ in(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f2994]) ).
tcf(c_52,plain,
! [X0: $i] : unordered_pair(X0,X0) != empty_set,
inference(cnf_transformation,[],[f2995]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(cnf_transformation,[],[f2997]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| disjoint(unordered_pair(X0,X0),X1) ),
inference(cnf_transformation,[],[f2998]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_rng_restriction(X1,X0)),relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1665]) ).
tcf(c_57,plain,
! [X0: $i] :
( transitive(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK44(X0),sK46(X0)),unordered_pair(sK44(X0),sK44(X0))),X0) ),
inference(cnf_transformation,[],[f2999]) ).
tcf(c_58,plain,
! [X0: $i] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK44(X0),sK45(X0)),unordered_pair(sK44(X0),sK44(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3000]) ).
tcf(c_59,plain,
! [X0: $i] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK45(X0),sK46(X0)),unordered_pair(sK45(X0),sK45(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3001]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),X2)
| ~ transitive(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3002]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( well_orders(sK47(X0),X0)
| ~ well_ordering(X1)
| ~ relation(X1)
| ~ equipotent(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f1673]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( relation(sK47(X0))
| ~ well_ordering(X1)
| ~ relation(X1)
| ~ equipotent(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f1672]) ).
tcf(c_68,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ relation(X0)
| ( sK48(X0) != sK49(X0) ) ),
inference(cnf_transformation,[],[f1680]) ).
tcf(c_69,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK48(X0),sK49(X0)),unordered_pair(sK48(X0),sK48(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3005]) ).
tcf(c_70,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK49(X0),sK48(X0)),unordered_pair(sK49(X0),sK49(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3006]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ antisymmetric(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3007]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3008]) ).
tcf(c_73,plain,
! [X0: $i] :
( connected(X0)
| in(sK50(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1687]) ).
tcf(c_74,plain,
! [X0: $i] :
( connected(X0)
| in(sK51(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1686]) ).
tcf(c_75,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ( sK50(X0) != sK51(X0) ) ),
inference(cnf_transformation,[],[f1685]) ).
tcf(c_76,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK50(X0),sK51(X0)),unordered_pair(sK50(X0),sK50(X0))),X0) ),
inference(cnf_transformation,[],[f3009]) ).
tcf(c_77,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK51(X0),sK50(X0)),unordered_pair(sK51(X0),sK51(X0))),X0) ),
inference(cnf_transformation,[],[f3010]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1)
| in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1)
| ( X0 = X2 )
| ~ connected(X1)
| ~ relation(X1)
| ~ in(X2,relation_field(X1))
| ~ in(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f3011]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ in(sK52(X0,X1),X1) ),
inference(cnf_transformation,[],[f1696]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| in(sK52(X0,X1),X0) ),
inference(cnf_transformation,[],[f1695]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( ~ sP2(X0,X1)
| ( sK54(X0,X1) != sK55(X0,X1) ) ),
inference(cnf_transformation,[],[f1706]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( ( sK53(X0,X1) = sK56(X0,X1) )
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1704]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( in(sK54(X0,X1),sK56(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1703]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK54(X1,X2),X0),unordered_pair(sK54(X1,X2),sK54(X1,X2))),X2)
| ~ sP2(X1,X2)
| ~ in(X0,sK56(X1,X2)) ),
inference(cnf_transformation,[],[f3018]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( in(sK53(X0,X1),X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1701]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( sP0(sK53(X0,X1),sK55(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1700]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X4)
| ~ in(X2,X3)
| ~ in(X0,X2)
| ~ sP1(X3,X1,X4)
| ~ in(unordered_pair(unordered_pair(X0,sK57(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3529]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK57(X1,X3,X4),X4)
| in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X2)
| ~ in(X4,X0)
| ~ in(X3,X4)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f3530]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,X3)
| ~ sP1(X3,X4,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3022]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK58(X4,X0,X1) = X0 )
| ~ sP1(X3,X4,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3023]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X1,sK58(X4,X0,X1))
| ~ sP1(X3,X4,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3024]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4)
| ~ sP1(X5,X4,X2)
| ~ in(X3,sK58(X4,X0,X1))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3025]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| sP2(X1,X0)
| relation(sK60(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1719]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| sP2(X1,X0)
| function(sK60(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1718]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| sP2(X1,X0)
| sP1(X1,X0,sK60(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1717]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK61(X1))
| ~ sP3(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3531]) ).
tcf(c_117,plain,
! [X0: $i] :
( sP3(X0)
| ( sK63(X0) != sK64(X0) ) ),
inference(cnf_transformation,[],[f1730]) ).
tcf(c_119,plain,
! [X0: $i] :
( sP3(X0)
| ( unordered_pair(sK62(X0),sK62(X0)) = sK63(X0) ) ),
inference(cnf_transformation,[],[f3031]) ).
tcf(c_120,plain,
! [X0: $i] :
( sP3(X0)
| in(sK62(X0),X0) ),
inference(cnf_transformation,[],[f1727]) ).
tcf(c_121,plain,
! [X0: $i] :
( sP3(X0)
| ( unordered_pair(sK62(X0),sK62(X0)) = sK64(X0) ) ),
inference(cnf_transformation,[],[f3032]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( ordinal(sK65(X1))
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1733]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( in(sK65(X1),X1)
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1732]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK65(X1),X0)
| ~ ordinal(X2)
| ~ ordinal(X0)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1731]) ).
tcf(c_125,plain,
( sP5(sK66)
| ~ sP8 ),
inference(cnf_transformation,[],[f1738]) ).
tcf(c_126,plain,
( in(set_union2(sK66,unordered_pair(sK66,sK66)),omega)
| ~ sP8 ),
inference(cnf_transformation,[],[f3033]) ).
tcf(c_127,plain,
! [X0: $i] :
( in(sK67(X0),X0)
| ( X0 = empty_set )
| ~ sP8
| ~ in(sK66,omega)
| ~ element(X0,powerset(powerset(sK66))) ),
inference(cnf_transformation,[],[f1736]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( sK67(X0) = X1 )
| ~ sP8
| ~ in(sK66,omega)
| ~ in(X1,X0)
| ~ subset(sK67(X0),X1)
| ~ element(X0,powerset(powerset(sK66))) ),
inference(cnf_transformation,[],[f1735]) ).
tcf(c_129,plain,
( ordinal(sK66)
| ~ sP8 ),
inference(cnf_transformation,[],[f1734]) ).
tcf(c_130,plain,
( ~ sP7
| ( empty_set != sK68 ) ),
inference(cnf_transformation,[],[f1744]) ).
tcf(c_131,plain,
! [X0: $i] :
( ~ sP7
| ~ in(X0,sK68)
| ( sK69(X0) != X0 ) ),
inference(cnf_transformation,[],[f1743]) ).
tcf(c_132,plain,
! [X0: $i] :
( in(sK69(X0),sK68)
| ~ sP7
| ~ in(X0,sK68) ),
inference(cnf_transformation,[],[f1742]) ).
tcf(c_133,plain,
! [X0: $i] :
( subset(X0,sK69(X0))
| ~ sP7
| ~ in(X0,sK68) ),
inference(cnf_transformation,[],[f1741]) ).
tcf(c_134,plain,
( element(sK68,powerset(powerset(empty_set)))
| ~ sP7 ),
inference(cnf_transformation,[],[f1740]) ).
tcf(c_136,plain,
( ~ sP6
| ( empty_set != sK70 ) ),
inference(cnf_transformation,[],[f1751]) ).
tcf(c_137,plain,
( sP4(sK70)
| ~ sP6 ),
inference(cnf_transformation,[],[f1750]) ).
tcf(c_138,plain,
( in(sK70,omega)
| ~ sP6 ),
inference(cnf_transformation,[],[f1749]) ).
tcf(c_139,plain,
( being_limit_ordinal(sK70)
| ~ sP6 ),
inference(cnf_transformation,[],[f1748]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( in(sK71(X0),X0)
| ( X0 = empty_set )
| ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK70)
| ~ in(X1,omega)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1747]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( sK71(X0) = X2 )
| ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK70)
| ~ in(X1,omega)
| ~ in(X2,X0)
| ~ subset(sK71(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1746]) ).
tcf(c_142,plain,
( ordinal(sK70)
| ~ sP6 ),
inference(cnf_transformation,[],[f1745]) ).
tcf(c_143,plain,
! [X0: $i] :
( ~ sP5(X0)
| ( sK72(X0) != empty_set ) ),
inference(cnf_transformation,[],[f1756]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( ~ sP5(X0)
| ~ in(X1,sK72(X0))
| ( sK73(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f1755]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( in(sK73(X1,X0),sK72(X1))
| ~ sP5(X1)
| ~ in(X0,sK72(X1)) ),
inference(cnf_transformation,[],[f1754]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK73(X1,X0))
| ~ sP5(X1)
| ~ in(X0,sK72(X1)) ),
inference(cnf_transformation,[],[f1753]) ).
tcf(c_147,plain,
! [X0: $i] :
( element(sK72(X0),powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f3034]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( sP6
| sP7
| sP8
| in(sK76(X0),X0)
| ( X0 = empty_set )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1763]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP6
| sP7
| sP8
| ( X0 = empty_set )
| ( sK76(X0) = X2 )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ in(X2,X0)
| ~ subset(sK76(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1762]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(sK77(X2,X1,X0))
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1768]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK77(X4,X3,X0))
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ in(unordered_pair(unordered_pair(apply(X0,X1),apply(X0,X2)),unordered_pair(apply(X0,X1),apply(X0,X1))),X3) ),
inference(cnf_transformation,[],[f3035]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,X2)
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK77(X2,X3,X4)) ),
inference(cnf_transformation,[],[f3036]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X1,X2)
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK77(X2,X3,X4)) ),
inference(cnf_transformation,[],[f3037]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(apply(X4,X0),apply(X4,X1)),unordered_pair(apply(X4,X0),apply(X4,X0))),X3)
| ~ function(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK77(X2,X3,X4)) ),
inference(cnf_transformation,[],[f3038]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( empty(X3)
| in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),sK78(X3,X1,X4))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),cartesian_product2(X3,X4))
| ~ in(unordered_pair(unordered_pair(X0,sK79(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3344]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( empty(X2)
| in(sK79(X4,X1,X0),X0)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK78(X2,X4,X3))
| ~ relation(X4)
| ~ in(X1,X0)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f3346]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| in(X0,cartesian_product2(X1,X3))
| ~ relation(X2)
| ~ in(X0,sK78(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1774]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| ( unordered_pair(unordered_pair(sK80(X1,X2,X0),sK81(X1,X2,X0)),unordered_pair(sK80(X1,X2,X0),sK80(X1,X2,X0))) = X0 )
| ~ relation(X2)
| ~ in(X0,sK78(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3041]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| in(sK80(X1,X2,X0),X1)
| ~ relation(X2)
| ~ in(X0,sK78(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1772]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| ( sK80(X1,X2,X0) = sK82(X1,X2,X0) )
| ~ relation(X2)
| ~ in(X0,sK78(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1771]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| in(sK81(X1,X2,X0),sK82(X1,X2,X0))
| ~ relation(X2)
| ~ in(X0,sK78(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1770]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( empty(X1)
| in(unordered_pair(unordered_pair(sK81(X1,X2,X0),X4),unordered_pair(sK81(X1,X2,X0),sK81(X1,X2,X0))),X2)
| ~ relation(X2)
| ~ in(X4,sK82(X1,X2,X0))
| ~ in(X0,sK78(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3042]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK83(X1,X2))
| ~ in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f3348]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,cartesian_product2(X1,X2))
| ~ in(X0,sK83(X1,X2)) ),
inference(cnf_transformation,[],[f1780]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK84(X1,X0),sK85(X1,X0)),unordered_pair(sK84(X1,X0),sK84(X1,X0))) = X0 )
| ~ in(X0,sK83(X1,X2)) ),
inference(cnf_transformation,[],[f3044]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK84(X1,X0),X1)
| ~ in(X0,sK83(X1,X2)) ),
inference(cnf_transformation,[],[f1778]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(sK84(X1,X0),sK84(X1,X0)) = sK85(X1,X0) )
| ~ in(X0,sK83(X1,X2)) ),
inference(cnf_transformation,[],[f3045]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] :
( in(X1,sK86(X0))
| ~ sP10(X0)
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f1783]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] :
( sP9(X1,X0)
| ~ sP10(X1)
| ~ in(X0,sK86(X1)) ),
inference(cnf_transformation,[],[f1782]) ).
tcf(c_186,plain,
! [X0: $i] :
( sP10(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1795]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK91(X1,X2))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ closed_subset(X0,X1)
| ~ subset(X2,X0)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f3355]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK91(X1,X2)) ),
inference(cnf_transformation,[],[f1800]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK92(X1,X2,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK91(X1,X2)) ),
inference(cnf_transformation,[],[f1799]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK92(X1,X2,X0) = X0 )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK91(X1,X2)) ),
inference(cnf_transformation,[],[f1798]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(sK92(X1,X2,X0),X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK91(X1,X2)) ),
inference(cnf_transformation,[],[f1797]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK91(X1,X2)) ),
inference(cnf_transformation,[],[f1796]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK93(X0,X2))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2) ),
inference(cnf_transformation,[],[f1804]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X2,sK93(X1,X0))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f1803]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_difference(cast_as_carrier_subset(X1),X2),X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X2,sK93(X1,X0))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f1802]) ).
tcf(c_196,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_difference(X2,unordered_pair(X1,X1)),sK94(X1,X0))
| ~ ordinal(X1)
| ~ in(X2,X0)
| ~ in(set_difference(X2,unordered_pair(X1,X1)),powerset(X1))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3356]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,powerset(X1))
| ~ ordinal(X1)
| ~ in(X2,sK94(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3054]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK95(X1,X0,X2),X0)
| ~ ordinal(X1)
| ~ in(X2,sK94(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3055]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(sK95(X1,X0,X2),unordered_pair(X1,X1)) = X2 )
| ~ ordinal(X1)
| ~ in(X2,sK94(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3056]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK96(X4,X3,X0))
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),cartesian_product2(X4,X4))
| ~ in(unordered_pair(unordered_pair(apply(X0,X1),apply(X0,X2)),unordered_pair(apply(X0,X1),apply(X0,X1))),X3) ),
inference(cnf_transformation,[],[f3357]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,cartesian_product2(X1,X1))
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK96(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1811]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK97(X2,X3,X0),sK98(X2,X3,X0)),unordered_pair(sK97(X2,X3,X0),sK97(X2,X3,X0))) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK96(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3058]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(apply(X3,sK97(X2,X3,X0)),apply(X3,sK98(X2,X3,X0))),unordered_pair(apply(X3,sK97(X2,X3,X0)),apply(X3,sK97(X2,X3,X0)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK96(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3059]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i] :
( in(X0,sK99(X1))
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1815]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,sK99(X1)) ),
inference(cnf_transformation,[],[f1814]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ in(X0,sK99(X1)) ),
inference(cnf_transformation,[],[f1813]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,sK100(X2,X0))
| ~ function(X0)
| ~ relation(X0)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X1,powerset(relation_dom(X0)))
| ~ in(relation_image(X0,X1),X2) ),
inference(cnf_transformation,[],[f1818]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,powerset(relation_dom(X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X3)))
| ~ in(X0,sK100(X1,X2)) ),
inference(cnf_transformation,[],[f1817]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(relation_image(X2,X0),X1)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X3)))
| ~ in(X0,sK100(X1,X2)) ),
inference(cnf_transformation,[],[f1816]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK101(X2,X1))
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X2)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3358]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X0,sK101(X1,X2)) ),
inference(cnf_transformation,[],[f3061]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK102(X1,X0))
| ~ ordinal(X2)
| ~ in(X0,sK101(X1,X2)) ),
inference(cnf_transformation,[],[f1821]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK102(X1,X0) = X0 )
| ~ ordinal(X2)
| ~ in(X0,sK101(X1,X2)) ),
inference(cnf_transformation,[],[f1820]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK102(X1,X0),X1)
| ~ ordinal(X2)
| ~ in(X0,sK101(X1,X2)) ),
inference(cnf_transformation,[],[f1819]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] :
( relation(sK103(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f1829]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i] :
( function(sK103(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f1828]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK103(X0,X1)) = X0 )
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f1827]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK104(X1,X2,X0) = X0 )
| ~ sP12(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1826]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK103(X1,X2),X0),sK104(X1,X2,X0))
| ~ sP12(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1825]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(apply(sK103(X1,X2),X3),X0),unordered_pair(apply(sK103(X1,X2),X3),apply(sK103(X1,X2),X3))),X2)
| ~ sP12(X1,X2)
| ~ in(X3,X1)
| ~ in(X0,sK104(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3062]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| sP11(X1,X0)
| sP12(X1,X0)
| in(sK110(X1,X0),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1840]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| sP11(X2,X1)
| sP12(X2,X1)
| ~ relation(X1)
| ~ in(X0,sK110(X2,X1))
| ~ in(unordered_pair(unordered_pair(X0,sK111(X1,X0,sK110(X2,X1))),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3359]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP11(X1,X2)
| sP12(X1,X2)
| in(sK111(X2,X0,sK110(X1,X2)),sK110(X1,X2))
| ~ relation(X2)
| ~ in(X0,sK110(X1,X2)) ),
inference(cnf_transformation,[],[f3360]) ).
tcf(c_237,plain,
! [X0: $i] :
( sP13(X0)
| relation(sK115(X0)) ),
inference(cnf_transformation,[],[f3361]) ).
tcf(c_239,plain,
! [X0: $i] :
( sP13(X0)
| function(sK115(X0)) ),
inference(cnf_transformation,[],[f3362]) ).
tcf(c_241,plain,
! [X0: $i] :
( sP13(X0)
| ( relation_dom(sK115(X0)) = X0 ) ),
inference(cnf_transformation,[],[f3363]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] :
( sP13(X1)
| ( apply(sK115(X1),X0) = unordered_pair(X0,X0) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3364]) ).
tcf(c_244,plain,
( sP14(sK117)
| ~ sP15 ),
inference(cnf_transformation,[],[f1857]) ).
tcf(c_245,plain,
( in(sK117,omega)
| ~ sP15 ),
inference(cnf_transformation,[],[f1856]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] :
( in(sK118(X0),X0)
| ( X0 = empty_set )
| ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK117)
| ~ in(X1,omega)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1855]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( sK118(X0) = X2 )
| ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK117)
| ~ in(X1,omega)
| ~ in(X2,X0)
| ~ subset(sK118(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1854]) ).
tcf(c_248,plain,
( ordinal(sK117)
| ~ sP15 ),
inference(cnf_transformation,[],[f1853]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] :
( sP15
| in(sK121(X0),X0)
| ( X0 = empty_set )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1864]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP15
| ( X0 = empty_set )
| ( sK121(X0) = X2 )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ in(X2,X0)
| ~ subset(sK121(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1863]) ).
tcf(c_256,plain,
! [X0: $i] : relation(sK122(X0)),
inference(cnf_transformation,[],[f1868]) ).
tcf(c_257,plain,
! [X0: $i] : function(sK122(X0)),
inference(cnf_transformation,[],[f1867]) ).
tcf(c_258,plain,
! [X0: $i] : relation_dom(sK122(X0)) = X0,
inference(cnf_transformation,[],[f1866]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] :
( ( apply(sK122(X1),X0) = unordered_pair(X0,X0) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3073]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i] :
( element(sK123(X1,X0),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f1874]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK123(X1,X0))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ closed_subset(X2,X1)
| ~ subset(X0,X2)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f3532]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK124(X1,X2,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK123(X1,X2)) ),
inference(cnf_transformation,[],[f1872]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK124(X1,X2,X0) = X0 )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK123(X1,X2)) ),
inference(cnf_transformation,[],[f1871]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(sK124(X1,X2,X0),X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK123(X1,X2)) ),
inference(cnf_transformation,[],[f1870]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK123(X1,X2)) ),
inference(cnf_transformation,[],[f1869]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] :
( element(sK125(X1,X0),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f1877]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK125(X0,X2))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2) ),
inference(cnf_transformation,[],[f1876]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_difference(cast_as_carrier_subset(X1),X2),X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X2,sK125(X1,X0))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f1875]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f3075]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f3076]) ).
tcf(c_272,plain,
! [X0: $i] : in(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(cnf_transformation,[],[f3077]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( X0 = X2 )
| ( unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
inference(cnf_transformation,[],[f1882]) ).
tcf(c_274,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_rng(relation_rng_restriction(X2,X1)))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f1885]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f1884]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f1883]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1886]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng_restriction(X1,X0),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1887]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1888]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1890]) ).
tcf(c_281,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1889]) ).
tcf(c_282,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(X0),set_difference(relation_rng(X0),X1)) = relation_rng(relation_rng_restriction(X1,X0)) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3078]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1892]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1895]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(X0),X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1894]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1896]) ).
tcf(c_288,plain,
! [X0: $i] : in(X0,sK126(X0)),
inference(cnf_transformation,[],[f1900]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK126(X1))
| ~ subset(X2,X0)
| ~ in(X0,sK126(X1)) ),
inference(cnf_transformation,[],[f1899]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i] :
( in(powerset(X0),sK126(X1))
| ~ in(X0,sK126(X1)) ),
inference(cnf_transformation,[],[f1898]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i] :
( are_equipotent(X0,sK126(X1))
| in(X0,sK126(X1))
| ~ subset(X0,sK126(X1)) ),
inference(cnf_transformation,[],[f1897]) ).
tcf(c_292,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1901]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_restriction(X1,relation_dom_restriction(X0,X2)) = relation_dom_restriction(relation_rng_restriction(X1,X0),X2) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1902]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK127(X0,X2,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f1905]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK127(X0,X2,X1),X0),unordered_pair(sK127(X0,X2,X1),sK127(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3080]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK127(X0,X2,X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f1903]) ).
tcf(c_298,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(X0,X1),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1907]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(X0,relation_inverse_image(X0,X1)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1908]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X0,set_difference(relation_dom(X0),set_difference(relation_dom(X0),X1))) = relation_image(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3081]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i] :
( subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
| ~ relation(X1)
| ~ subset(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f1910]) ).
tcf(c_302,plain,
! [X0: $i] :
( ( relation_image(X0,relation_dom(X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1911]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,relation_inverse_image(X1,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f1912]) ).
tcf(c_304,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2_as_subset(X0,X1,X3)
| ~ subset(relation_rng(X0),X3)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1913]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i] :
( ( subset_intersection2(the_carrier(X1),X0,cast_as_carrier_subset(X1)) = X0 )
| ~ one_sorted_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f1915]) ).
tcf(c_307,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,relation_rng(X0)) = relation_rng(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1916]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK128(X0,X2,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f1919]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK128(X0,X2,X1)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f3084]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK128(X0,X2,X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f1917]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(X0,X1),relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1921]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2_as_subset(X0,X1,X3)
| ~ subset(X2,X3)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1922]) ).
tcf(c_314,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_restriction(X2,X1))
| ~ relation(X2)
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f1925]) ).
tcf(c_315,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(X1)
| ~ in(X0,relation_restriction(X1,X2)) ),
inference(cnf_transformation,[],[f1924]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,cartesian_product2(X2,X2))
| ~ relation(X1)
| ~ in(X0,relation_restriction(X1,X2)) ),
inference(cnf_transformation,[],[f1923]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ~ relation(X0)
| ~ subset(X1,relation_rng(X0))
| ( relation_inverse_image(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f1926]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
| ~ relation(X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1927]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X0) = subset_complement(the_carrier(X1),X0) )
| ~ one_sorted_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f1929]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,X0),X1) = relation_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1930]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i] :
( in(sK129(X0),X0)
| ( X0 = empty_set )
| ~ finite(X1)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1933]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( sK129(X0) = X2 )
| ~ finite(X1)
| ~ in(X2,X0)
| ~ subset(sK129(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f1932]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X1,relation_dom_restriction(X0,X1)) = relation_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1934]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X1))
| ~ relation(X1)
| ~ in(X0,relation_field(relation_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f1936]) ).
tcf(c_327,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_field(relation_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f1935]) ).
tcf(c_328,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_difference(X2,set_difference(X2,X1)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3086]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1938]) ).
tcf(c_330,plain,
unordered_pair(empty_set,empty_set) = powerset(empty_set),
inference(cnf_transformation,[],[f3087]) ).
tcf(c_333,plain,
! [X0: $i,X1: $i] :
( subset(relation_field(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1943]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i] :
( subset(relation_field(relation_restriction(X0,X1)),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1942]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_dom(relation_composition(X0,X2)))
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),relation_dom(X2)) ),
inference(cnf_transformation,[],[f1946]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f1945]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_dom(X2))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f1944]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = empty_set )
| ( apply(relation_composition(X0,X4),X3) = apply(X4,apply(X0,X3)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ in(X3,X1)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1947]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ epsilon_transitive(X0)
| ~ ordinal(X1)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f1948]) ).
tcf(c_340,plain,
! [X0: $i] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1949]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(fiber(relation_restriction(X0,X1),X2),fiber(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1950]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf_transformation,[],[f1951]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X0)) = X0 )
| ~ one_sorted_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f1952]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X3,sK130(X2,X3)),unordered_pair(X3,X3)),X2)
| ~ in(X3,X0)
| ~ relation_of2_as_subset(X2,X0,X1)
| ( relation_dom_as_subset(X0,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f3090]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK131(X1,X0),X1)
| ( relation_dom_as_subset(X1,X2,X0) = X1 )
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1954]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_dom_as_subset(X0,X3,X1) = X0 )
| ~ relation_of2_as_subset(X1,X0,X3)
| ~ in(unordered_pair(unordered_pair(sK131(X0,X1),X2),unordered_pair(sK131(X0,X1),sK131(X0,X1))),X1) ),
inference(cnf_transformation,[],[f3091]) ).
tcf(c_347,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ reflexive(X0) ),
inference(cnf_transformation,[],[f1956]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) )
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f1957]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1958]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK132(X2,X3),X3),unordered_pair(sK132(X2,X3),sK132(X2,X3))),X2)
| ~ in(X3,X1)
| ~ relation_of2_as_subset(X2,X0,X1)
| ( relation_rng_as_subset(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f3092]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK133(X2,X0),X2)
| ( relation_rng_as_subset(X1,X2,X0) = X2 )
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1960]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_rng_as_subset(X3,X1,X2) = X1 )
| ~ relation_of2_as_subset(X2,X3,X1)
| ~ in(unordered_pair(unordered_pair(X0,sK133(X1,X2)),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3093]) ).
tcf(c_353,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1962]) ).
tcf(c_354,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1963]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i] :
( transitive(relation_restriction(X0,X1))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1964]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1966]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1965]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i] :
( antisymmetric(relation_restriction(X0,X1))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1967]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i] :
( ( relation_field(relation_restriction(X0,X1)) = X1 )
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f1969]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i] :
( well_ordering(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f1968]) ).
tcf(c_361,plain,
! [X0: $i] :
( finite(relation_rng(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ finite(relation_dom(X0)) ),
inference(cnf_transformation,[],[f1970]) ).
tcf(c_362,plain,
! [X0: $i] : relation(sK134(X0)),
inference(cnf_transformation,[],[f1972]) ).
tcf(c_363,plain,
! [X0: $i] : well_orders(sK134(X0),X0),
inference(cnf_transformation,[],[f1971]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3094]) ).
tcf(c_365,plain,
! [X0: $i] :
( empty(X0)
| in(sK135(X0),X0)
| ( relation_dom(sK136(X0)) = X0 ) ),
inference(cnf_transformation,[],[f1981]) ).
tcf(c_366,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK135(X1),X1)
| in(apply(sK136(X1),X0),X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1980]) ).
tcf(c_367,plain,
! [X0: $i] :
( empty(X0)
| relation(sK136(X0))
| in(sK135(X0),X0) ),
inference(cnf_transformation,[],[f1979]) ).
tcf(c_368,plain,
! [X0: $i] :
( empty(X0)
| function(sK136(X0))
| in(sK135(X0),X0) ),
inference(cnf_transformation,[],[f1978]) ).
tcf(c_369,plain,
! [X0: $i] :
( empty(X0)
| ( sK135(X0) = empty_set )
| ( relation_dom(sK136(X0)) = X0 ) ),
inference(cnf_transformation,[],[f1977]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(apply(sK136(X1),X0),X0)
| ( sK135(X1) = empty_set )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1976]) ).
tcf(c_371,plain,
! [X0: $i] :
( empty(X0)
| relation(sK136(X0))
| ( sK135(X0) = empty_set ) ),
inference(cnf_transformation,[],[f1975]) ).
tcf(c_372,plain,
! [X0: $i] :
( empty(X0)
| function(sK136(X0))
| ( sK135(X0) = empty_set ) ),
inference(cnf_transformation,[],[f1974]) ).
tcf(c_373,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X0 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3095]) ).
tcf(c_374,negated_conjecture,
( ~ closed_subset(sK138,sK137)
| ~ open_subset(subset_complement(the_carrier(sK137),sK138),sK137) ),
inference(cnf_transformation,[],[f1986]) ).
tcf(c_375,negated_conjecture,
( closed_subset(sK138,sK137)
| open_subset(subset_complement(the_carrier(sK137),sK138),sK137) ),
inference(cnf_transformation,[],[f1985]) ).
tcf(c_376,negated_conjecture,
element(sK138,powerset(the_carrier(sK137))),
inference(cnf_transformation,[],[f1984]) ).
tcf(c_377,negated_conjecture,
top_str(sK137),
inference(cnf_transformation,[],[f1983]) ).
tcf(c_378,plain,
! [X0: $i] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f1987]) ).
tcf(c_379,plain,
! [X0: $i] : subset(empty_set,X0),
inference(cnf_transformation,[],[f1988]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3096]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3097]) ).
tcf(c_382,plain,
! [X0: $i] :
( ordinal(X0)
| ~ ordinal(sK139(X0))
| ~ subset(sK139(X0),X0) ),
inference(cnf_transformation,[],[f1992]) ).
tcf(c_383,plain,
! [X0: $i] :
( ordinal(X0)
| in(sK139(X0),X0) ),
inference(cnf_transformation,[],[f1991]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(relation_restriction(X0,X1))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1993]) ).
tcf(c_385,plain,
! [X0: $i,X1: $i] :
( in(sK140(X0),X0)
| ( X0 = empty_set )
| ~ ordinal(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1996]) ).
tcf(c_386,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK140(X1),X0)
| ( X1 = empty_set )
| ~ ordinal(X2)
| ~ ordinal(X0)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1995]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] :
( ordinal(sK140(X0))
| ( X0 = empty_set )
| ~ ordinal(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1994]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] :
( well_ordering(relation_restriction(X0,X1))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1997]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3098]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3099]) ).
tcf(c_391,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2000]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(cnf_transformation,[],[f3100]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(cnf_transformation,[],[f3101]) ).
tcf(c_394,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0)
| ( apply(X0,sK141(relation_dom(X0),X0)) != sK141(relation_dom(X0),X0) ) ),
inference(cnf_transformation,[],[f3366]) ).
tcf(c_395,plain,
! [X0: $i] :
( in(sK141(relation_dom(X0),X0),relation_dom(X0))
| ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3367]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2007]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f2008]) ).
tcf(c_400,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2010]) ).
tcf(c_401,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(X0)) = relation_dom(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2009]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2012]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f2011]) ).
tcf(c_404,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3102]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X0,X2),X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2017]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f2016]) ).
tcf(c_408,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f2015]) ).
tcf(c_409,plain,
! [X0: $i,X1: $i] :
( ( relation_field(relation_restriction(X1,X0)) = X0 )
| ~ well_ordering(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f2018]) ).
tcf(c_410,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(cnf_transformation,[],[f2019]) ).
tcf(c_413,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(X1,X1) = X0 )
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f3106]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2023]) ).
tcf(c_415,plain,
! [X0: $i] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f2024]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK142(X0,X1),X0) ),
inference(cnf_transformation,[],[f2027]) ).
tcf(c_417,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK142(X0,X1),X1) ),
inference(cnf_transformation,[],[f2026]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2025]) ).
tcf(c_419,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f2028]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[],[f2029]) ).
tcf(c_421,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(set_union2(sK143(X0),unordered_pair(sK143(X0),sK143(X0))),X0) ),
inference(cnf_transformation,[],[f3107]) ).
tcf(c_422,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| in(sK143(X0),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2032]) ).
tcf(c_423,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ordinal(sK143(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2031]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i] :
( in(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3108]) ).
tcf(c_425,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ( set_union2(sK144(X0),unordered_pair(sK144(X0),sK144(X0))) = X0 )
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f3109]) ).
tcf(c_426,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ordinal(sK144(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2035]) ).
tcf(c_427,plain,
! [X0: $i] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(cnf_transformation,[],[f3372]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1))
| ~ subset(X0,subset_complement(X1,X2)) ),
inference(cnf_transformation,[],[f2038]) ).
tcf(c_429,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,subset_complement(X1,X0))
| ~ disjoint(X2,X0)
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2037]) ).
tcf(c_430,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(X1),X0),X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ closed_subset(sK145(X1,X0),X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f2041]) ).
tcf(c_431,plain,
! [X0: $i,X1: $i] :
( in(sK145(X1,X0),X0)
| closed_subset(meet_of_subsets(the_carrier(X1),X0),X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f2040]) ).
tcf(c_432,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(X1),X0),X1)
| element(sK145(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f2039]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2042]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,topstr_closure(X1,X2))
| ~ top_str(X1)
| ~ in(X0,the_carrier(X1))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK146(X1,X2,X0)) ),
inference(cnf_transformation,[],[f2047]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X1,X0))
| closed_subset(sK146(X1,X0,X2),X1)
| ~ top_str(X1)
| ~ in(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2046]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X1,X0))
| subset(X0,sK146(X1,X0,X2))
| ~ top_str(X1)
| ~ in(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2045]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X1,X0))
| element(sK146(X1,X0,X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ in(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2044]) ).
tcf(c_438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ top_str(X1)
| ~ closed_subset(X3,X1)
| ~ subset(X2,X3)
| ~ in(X0,the_carrier(X1))
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,topstr_closure(X1,X2)) ),
inference(cnf_transformation,[],[f2043]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2048]) ).
tcf(c_441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X1,relation_inverse_image(X0,X2))
| ( X4 = empty_set )
| ~ function(X0)
| ~ in(X1,X3)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ in(apply(X0,X1),X2) ),
inference(cnf_transformation,[],[f2052]) ).
tcf(c_442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,X3)
| ( X4 = empty_set )
| ~ function(X1)
| ~ quasi_total(X1,X3,X4)
| ~ relation_of2_as_subset(X1,X3,X4)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f2051]) ).
tcf(c_443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,X0),X2)
| ( X4 = empty_set )
| ~ function(X1)
| ~ quasi_total(X1,X3,X4)
| ~ relation_of2_as_subset(X1,X3,X4)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f2050]) ).
tcf(c_444,plain,
! [X0: $i,X1: $i] :
( element(sK147(X1,X0),powerset(powerset(the_carrier(X1))))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2057]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK147(X1,X0))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ closed_subset(X2,X1)
| ~ subset(X0,X2)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2056]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(X0,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK147(X1,X2)) ),
inference(cnf_transformation,[],[f2055]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK147(X1,X2)) ),
inference(cnf_transformation,[],[f2054]) ).
tcf(c_448,plain,
! [X0: $i,X1: $i] :
( ( meet_of_subsets(the_carrier(X1),sK147(X1,X0)) = topstr_closure(X1,X0) )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2053]) ).
tcf(c_449,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(X0,X1)) = relation_dom(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_rng(X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f2058]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ~ element(X1,powerset(powerset(X0)))
| ( complements_of_subsets(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f2059]) ).
tcf(c_451,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(X0,X0),X1) = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3111]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X1,X0)) = relation_rng(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f2061]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X0)) = meet_of_subsets(X1,complements_of_subsets(X1,X0)) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2062]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i] :
( subset(X0,topstr_closure(X1,X0))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2063]) ).
tcf(c_455,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X0)) = union_of_subsets(X1,complements_of_subsets(X1,X0)) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2064]) ).
tcf(c_456,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_isomorphism(X1,X0,function_inverse(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation_isomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f2066]) ).
tcf(c_457,plain,
! [X0: $i] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2067]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK148(X0,X1),set_difference(X0,set_difference(X0,X1))) ),
inference(cnf_transformation,[],[f3112]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(cnf_transformation,[],[f3113]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X2,subset_complement(X1,X0))
| ( X1 = empty_set )
| ~ element(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2070]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(X1,X0) = X0 )
| ~ top_str(X1)
| ~ closed_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2072]) ).
tcf(c_462,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( topstr_closure(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f2071]) ).
tcf(c_463,plain,
! [X0: $i,X1: $i,X2: $i] :
( reflexive(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ reflexive(X0)
| ~ relation_isomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f2077]) ).
tcf(c_464,plain,
! [X0: $i,X1: $i,X2: $i] :
( transitive(X1)
| ~ function(X2)
| ~ transitive(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation_isomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f2076]) ).
tcf(c_465,plain,
! [X0: $i,X1: $i,X2: $i] :
( connected(X1)
| ~ function(X2)
| ~ connected(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation_isomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f2075]) ).
tcf(c_466,plain,
! [X0: $i,X1: $i,X2: $i] :
( antisymmetric(X1)
| ~ function(X2)
| ~ antisymmetric(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation_isomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f2074]) ).
tcf(c_467,plain,
! [X0: $i,X1: $i,X2: $i] :
( well_founded_relation(X1)
| ~ well_founded_relation(X0)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation_isomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f2073]) ).
tcf(c_473,plain,
! [X0: $i,X1: $i] :
( ( function_inverse(X0) = X1 )
| ~ one_to_one(X0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK150(X0,X1),relation_dom(X0))
| ~ sP16(X0,sK149(X0,X1),sK150(X0,X1),X1)
| ( relation_dom(X1) != relation_rng(X0) )
| ( apply(X0,sK150(X0,X1)) != sK149(X0,X1) ) ),
inference(cnf_transformation,[],[f2089]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i] :
( in(sK149(X1,X0),relation_rng(X1))
| ( function_inverse(X1) = X0 )
| ~ one_to_one(X1)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ sP16(X1,sK149(X1,X0),sK150(X1,X0),X0)
| ( relation_dom(X0) != relation_rng(X1) ) ),
inference(cnf_transformation,[],[f2088]) ).
tcf(c_475,plain,
! [X0: $i,X1: $i] :
( ( function_inverse(X1) = X0 )
| ( apply(X0,sK149(X1,X0)) = sK150(X1,X0) )
| ~ one_to_one(X1)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ sP16(X1,sK149(X1,X0),sK150(X1,X0),X0)
| ( relation_dom(X0) != relation_rng(X1) ) ),
inference(cnf_transformation,[],[f2087]) ).
tcf(c_477,plain,
! [X0: $i,X1: $i] :
( in(apply(function_inverse(X1),X0),relation_dom(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(function_inverse(X1))
| ~ relation(function_inverse(X1))
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f3378]) ).
tcf(c_479,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP16(X0,X1,X2,function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f3381]) ).
tcf(c_480,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ element(X2,powerset(X1))
| ~ in(X0,subset_complement(X1,X2)) ),
inference(cnf_transformation,[],[f2090]) ).
tcf(c_481,plain,
! [X0: $i,X1: $i,X2: $i] :
( well_ordering(X1)
| ~ function(X2)
| ~ well_ordering(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation_isomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f2091]) ).
tcf(c_482,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(X0)) = relation_rng(X0) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2093]) ).
tcf(c_483,plain,
! [X0: $i] :
( ( relation_rng(function_inverse(X0)) = relation_dom(X0) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2092]) ).
tcf(c_484,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK151(X0),sK152(X0)),unordered_pair(sK151(X0),sK151(X0))),X0)
| ( X0 = empty_set )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3114]) ).
tcf(c_485,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f2096]) ).
tcf(c_486,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0 )
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f2095]) ).
tcf(c_487,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2098]) ).
tcf(c_488,plain,
! [X0: $i] :
( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2097]) ).
tcf(c_489,plain,
! [X0: $i] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f2099]) ).
tcf(c_490,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[],[f2101]) ).
tcf(c_491,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[],[f2100]) ).
tcf(c_492,plain,
! [X0: $i,X1: $i] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2102]) ).
tcf(c_493,plain,
! [X0: $i] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2103]) ).
tcf(c_494,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X1)
| ~ subset(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f2104]) ).
tcf(c_495,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ relation(X0)
| ( relation_dom(X0) != empty_set ) ),
inference(cnf_transformation,[],[f2106]) ).
tcf(c_496,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ relation(X0)
| ( relation_rng(X0) != empty_set ) ),
inference(cnf_transformation,[],[f2105]) ).
tcf(c_497,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ relation(X0)
| ( relation_rng(X0) != empty_set ) ),
inference(cnf_transformation,[],[f2108]) ).
tcf(c_498,plain,
! [X0: $i] :
( ( relation_rng(X0) = empty_set )
| ~ relation(X0)
| ( relation_dom(X0) != empty_set ) ),
inference(cnf_transformation,[],[f2107]) ).
tcf(c_499,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( set_difference(X0,unordered_pair(X1,X1)) = X0 ) ),
inference(cnf_transformation,[],[f3115]) ).
tcf(c_500,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ( set_difference(X0,unordered_pair(X1,X1)) != X0 ) ),
inference(cnf_transformation,[],[f3116]) ).
tcf(c_501,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(X1,X2) = X0 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ( apply(X0,sK153(X0,X1)) != apply(X1,sK153(X0,X1)) )
| ( set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2)) != relation_dom(X0) ) ),
inference(cnf_transformation,[],[f3117]) ).
tcf(c_502,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK153(X2,X0),relation_dom(X2))
| ( relation_dom_restriction(X0,X1) = X2 )
| ~ function(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X0)
| ( set_difference(relation_dom(X0),set_difference(relation_dom(X0),X1)) != relation_dom(X2) ) ),
inference(cnf_transformation,[],[f3118]) ).
tcf(c_505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,X3),relation_rng(X0))
| ( X2 = empty_set )
| ~ function(X0)
| ~ in(X3,X1)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f2116]) ).
tcf(c_506,plain,
! [X0: $i] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2117]) ).
tcf(c_507,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f3120]) ).
tcf(c_508,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f2119]) ).
tcf(c_509,plain,
! [X0: $i] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f2121]) ).
tcf(c_510,plain,
! [X0: $i] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f2120]) ).
tcf(c_511,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X2,X1),X0) = apply(X2,X0) )
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2122]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X3),X2))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3121]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3)) ),
inference(cnf_transformation,[],[f3122]) ).
tcf(c_514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3)) ),
inference(cnf_transformation,[],[f3123]) ).
tcf(c_515,plain,
! [X0: $i,X1: $i] : pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0,
inference(cnf_transformation,[],[f3124]) ).
tcf(c_516,plain,
! [X0: $i,X1: $i] : pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1,
inference(cnf_transformation,[],[f3125]) ).
tcf(c_517,plain,
! [X0: $i] :
( well_ordering(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2128]) ).
tcf(c_518,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f2129]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f2131]) ).
tcf(c_520,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f2130]) ).
tcf(c_521,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f2134]) ).
tcf(c_522,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f2133]) ).
tcf(c_523,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f2132]) ).
tcf(c_524,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom_restriction(X0,X1),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2135]) ).
tcf(c_525,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,apply(X1,X0)),unordered_pair(X0,X0)),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f3384]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,X0) = X1 )
| ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3128]) ).
tcf(c_528,plain,
! [X0: $i] :
( well_orders(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2140]) ).
tcf(c_529,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ relation(X0)
| ~ well_orders(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2139]) ).
tcf(c_530,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2141]) ).
tcf(c_531,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(cnf_transformation,[],[f3129]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom(X0),set_difference(relation_dom(X0),X1)) = relation_dom(relation_dom_restriction(X0,X1)) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3130]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2144]) ).
tcf(c_534,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),X0) = relation_dom_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2145]) ).
tcf(c_535,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(X0,X1)),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2146]) ).
tcf(c_536,plain,
! [X0: $i] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f2147]) ).
tcf(c_537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( quasi_total(X0,X1,X3)
| ( X2 = empty_set )
| ~ function(X0)
| ~ subset(X2,X3)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f2152]) ).
tcf(c_538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2_as_subset(X0,X1,X3)
| ( X2 = empty_set )
| ~ function(X0)
| ~ subset(X2,X3)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f2151]) ).
tcf(c_539,plain,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(X0,empty_set,X2)
| ~ function(X0)
| ~ subset(X1,X2)
| ~ quasi_total(X0,empty_set,X1)
| ~ relation_of2_as_subset(X0,empty_set,X1) ),
inference(cnf_transformation,[],[f3386]) ).
tcf(c_541,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(cnf_transformation,[],[f3131]) ).
tcf(c_542,plain,
! [X0: $i,X1: $i] :
( in(sK154(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2156]) ).
tcf(c_543,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(X0,X1)
| ~ in(X0,sK154(X1)) ),
inference(cnf_transformation,[],[f2155]) ).
tcf(c_544,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK155(X0,X1),X1)
| ~ in(sK155(X0,X1),X0) ),
inference(cnf_transformation,[],[f2158]) ).
tcf(c_545,plain,
! [X0: $i,X1: $i] :
( in(sK155(X0,X1),X1)
| in(sK155(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f2157]) ).
tcf(c_546,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2159]) ).
tcf(c_547,plain,
! [X0: $i,X1: $i] :
( ~ sP18(X0,X1)
| ( sK157(X0,X1) != sK158(X0,X1) ) ),
inference(cnf_transformation,[],[f2166]) ).
tcf(c_549,plain,
! [X0: $i,X1: $i] :
( ( sK156(X0,X1) = sK159(X0,X1) )
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f2164]) ).
tcf(c_550,plain,
! [X0: $i,X1: $i] :
( in(sK157(X0,X1),sK159(X0,X1))
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f2163]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK157(X1,X2),X0),unordered_pair(sK157(X1,X2),sK157(X1,X2))),X2)
| ~ sP18(X1,X2)
| ~ in(X0,sK159(X1,X2)) ),
inference(cnf_transformation,[],[f3132]) ).
tcf(c_552,plain,
! [X0: $i,X1: $i] :
( in(sK156(X0,X1),X0)
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f2161]) ).
tcf(c_553,plain,
! [X0: $i,X1: $i] :
( sP17(sK156(X0,X1),sK158(X0,X1),X1)
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f2160]) ).
tcf(c_557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X3)
| sP18(X3,X1)
| in(X0,sK161(X3,X1))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,sK162(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3533]) ).
tcf(c_558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| sP18(X1,X3)
| in(X2,sK161(X1,X3))
| in(sK162(X3,X2,X0),X0)
| ~ relation(X3)
| ~ in(X2,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3534]) ).
tcf(c_560,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP18(X1,X2)
| in(sK163(X1,X2,X0),X1)
| ~ relation(X2)
| ~ in(X0,sK161(X1,X2)) ),
inference(cnf_transformation,[],[f2173]) ).
tcf(c_561,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP18(X1,X2)
| ( sK163(X1,X2,X0) = sK164(X1,X2,X0) )
| ~ relation(X2)
| ~ in(X0,sK161(X1,X2)) ),
inference(cnf_transformation,[],[f2172]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP18(X1,X2)
| in(X0,sK164(X1,X2,X0))
| ~ relation(X2)
| ~ in(X0,sK161(X1,X2)) ),
inference(cnf_transformation,[],[f2171]) ).
tcf(c_563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| sP18(X1,X2)
| in(unordered_pair(unordered_pair(X3,X0),unordered_pair(X3,X3)),X2)
| ~ relation(X2)
| ~ in(X3,sK161(X1,X2))
| ~ in(X0,sK164(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3135]) ).
tcf(c_565,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(X1) = X2 )
| ~ relation(X1)
| ~ in(sK165(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X0,sK165(X1,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3137]) ).
tcf(c_566,plain,
! [X0: $i,X1: $i] :
( in(sK165(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK166(X0,X1),sK165(X0,X1)),unordered_pair(sK166(X0,X1),sK166(X0,X1))),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3138]) ).
tcf(c_567,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3390]) ).
tcf(c_568,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK167(X1,X0),X0),unordered_pair(sK167(X1,X0),sK167(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f3391]) ).
tcf(c_569,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X0) = X1 )
| ~ relation(X0)
| ~ in(sK168(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(sK168(X0,X1),X2),unordered_pair(sK168(X0,X1),sK168(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3141]) ).
tcf(c_570,plain,
! [X0: $i,X1: $i] :
( in(sK168(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK168(X0,X1),sK169(X0,X1)),unordered_pair(sK168(X0,X1),sK168(X0,X1))),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3142]) ).
tcf(c_571,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3392]) ).
tcf(c_572,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK170(X1,X0)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f3393]) ).
tcf(c_573,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK171(X0,X1),sK172(X0,X1)),unordered_pair(sK171(X0,X1),sK171(X0,X1))),X1) ),
inference(cnf_transformation,[],[f3145]) ).
tcf(c_574,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK171(X0,X1),sK172(X0,X1)),unordered_pair(sK171(X0,X1),sK171(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3146]) ).
tcf(c_576,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK173(X0,X1),sK174(X0,X1)),unordered_pair(sK173(X0,X1),sK173(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK173(X0,X1),sK174(X0,X1)),unordered_pair(sK173(X0,X1),sK173(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3148]) ).
tcf(c_577,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK173(X0,X1),sK174(X0,X1)),unordered_pair(sK173(X0,X1),sK173(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK173(X0,X1),sK174(X0,X1)),unordered_pair(sK173(X0,X1),sK173(X0,X1))),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3149]) ).
tcf(c_580,plain,
! [X0: $i] :
( relation(X0)
| in(sK175(X0),X0) ),
inference(cnf_transformation,[],[f2195]) ).
tcf(c_581,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X2)
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != sK175(X2) ) ),
inference(cnf_transformation,[],[f3152]) ).
tcf(c_582,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK176(X0),sK177(X0)),unordered_pair(sK176(X0),sK176(X0))) = X0 )
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3153]) ).
tcf(c_583,plain,
! [X0: $i] :
( function(X0)
| ( sK179(X0) != sK180(X0) ) ),
inference(cnf_transformation,[],[f2199]) ).
tcf(c_584,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK178(X0),sK179(X0)),unordered_pair(sK178(X0),sK178(X0))),X0) ),
inference(cnf_transformation,[],[f3154]) ).
tcf(c_585,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK178(X0),sK180(X0)),unordered_pair(sK178(X0),sK178(X0))),X0) ),
inference(cnf_transformation,[],[f3155]) ).
tcf(c_586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ function(X2)
| ~ in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3156]) ).
tcf(c_587,plain,
! [X0: $i] :
( ( set_union2(relation_dom(X0),relation_rng(X0)) = relation_field(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2200]) ).
tcf(c_588,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ relation(X0)
| ~ reflexive(X0) ),
inference(cnf_transformation,[],[f2206]) ).
tcf(c_589,plain,
! [X0: $i] :
( reflexive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2205]) ).
tcf(c_590,plain,
! [X0: $i] :
( transitive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2204]) ).
tcf(c_591,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2203]) ).
tcf(c_592,plain,
! [X0: $i] :
( connected(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2202]) ).
tcf(c_593,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2201]) ).
tcf(c_594,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2207]) ).
tcf(c_596,plain,
relation(empty_set),
inference(cnf_transformation,[],[f2208]) ).
tcf(c_598,plain,
! [X0: $i] :
( in(sK181(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f2212]) ).
tcf(c_599,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f3396]) ).
tcf(c_600,plain,
! [X0: $i] :
( ~ sP20(X0)
| ( sK183(X0) != sK184(X0) ) ),
inference(cnf_transformation,[],[f2219]) ).
tcf(c_601,plain,
! [X0: $i] :
( ( sK183(X0) = sK182(X0) )
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f2218]) ).
tcf(c_602,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK185(X0),sK186(X0)),unordered_pair(sK185(X0),sK185(X0))) = sK183(X0) )
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f3157]) ).
tcf(c_603,plain,
! [X0: $i] :
( in(sK185(X0),X0)
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f2216]) ).
tcf(c_604,plain,
! [X0: $i] :
( ( unordered_pair(sK185(X0),sK185(X0)) = sK186(X0) )
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f3158]) ).
tcf(c_605,plain,
! [X0: $i] :
( ( sK184(X0) = sK182(X0) )
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f2214]) ).
tcf(c_606,plain,
! [X0: $i] :
( sP19(sK184(X0),X0)
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f2213]) ).
tcf(c_610,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK189(X1,X2))
| ~ in(X0,X1)
| ~ in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f3399]) ).
tcf(c_611,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| in(sK190(X1,X2,X0),cartesian_product2(X1,X2))
| ~ in(X0,sK189(X1,X2)) ),
inference(cnf_transformation,[],[f2227]) ).
tcf(c_612,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| ( sK190(X1,X2,X0) = X0 )
| ~ in(X0,sK189(X1,X2)) ),
inference(cnf_transformation,[],[f2226]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| ( unordered_pair(unordered_pair(sK191(X1,X0),sK192(X1,X0)),unordered_pair(sK191(X1,X0),sK191(X1,X0))) = X0 )
| ~ in(X0,sK189(X1,X2)) ),
inference(cnf_transformation,[],[f3162]) ).
tcf(c_614,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| in(sK191(X1,X0),X1)
| ~ in(X0,sK189(X1,X2)) ),
inference(cnf_transformation,[],[f2224]) ).
tcf(c_615,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| ( unordered_pair(sK191(X1,X0),sK191(X1,X0)) = sK192(X1,X0) )
| ~ in(X0,sK189(X1,X2)) ),
inference(cnf_transformation,[],[f3163]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i] :
( sP21(X1)
| in(unordered_pair(X0,X0),sK196(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3537]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i] :
( sP21(X1)
| in(sK197(X1,X0),X1)
| ~ in(X0,sK196(X1)) ),
inference(cnf_transformation,[],[f2235]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i] :
( sP21(X1)
| ( unordered_pair(sK197(X1,X0),sK197(X1,X0)) = X0 )
| ~ in(X0,sK196(X1)) ),
inference(cnf_transformation,[],[f3167]) ).
tcf(c_626,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = X1 )
| ~ in(sK198(X0,X1),X1)
| ( sK198(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f3169]) ).
tcf(c_627,plain,
! [X0: $i,X1: $i] :
( in(sK198(X0,X1),X1)
| ( sK198(X0,X1) = X0 )
| ( unordered_pair(X0,X0) = X1 ) ),
inference(cnf_transformation,[],[f3170]) ).
tcf(c_629,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f3403]) ).
tcf(c_630,plain,
! [X0: $i] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f2243]) ).
tcf(c_631,plain,
! [X0: $i] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f2244]) ).
tcf(c_632,plain,
! [X0: $i,X1: $i] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2245]) ).
tcf(c_633,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f2246]) ).
tcf(c_634,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f2247]) ).
tcf(c_635,plain,
! [X0: $i,X1: $i] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2248]) ).
tcf(c_636,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK199(X0,X1,X2),X2)
| ~ in(sK199(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f2254]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK199(X0,X1,X2),X2)
| ~ in(sK199(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f2253]) ).
tcf(c_638,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK199(X0,X1,X2),X2)
| in(sK199(X0,X1,X2),X1)
| in(sK199(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f2252]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3404]) ).
tcf(c_640,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3405]) ).
tcf(c_641,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f3406]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2256]) ).
tcf(c_643,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f2257]) ).
tcf(c_644,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,set_difference(X0,X1)) != empty_set ) ),
inference(cnf_transformation,[],[f3173]) ).
tcf(c_645,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = empty_set )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f3174]) ).
tcf(c_646,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2261]) ).
tcf(c_647,plain,
! [X0: $i] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2260]) ).
tcf(c_648,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f2262]) ).
tcf(c_650,plain,
! [X0: $i,X1: $i] :
( function(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2263]) ).
tcf(c_651,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2265]) ).
tcf(c_652,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ in(sK201(X0,X1,X2),X0)
| ~ in(unordered_pair(unordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),unordered_pair(sK200(X0,X1,X2),sK200(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2)),unordered_pair(sK200(X0,X1,X2),sK200(X0,X1,X2))),X1) ),
inference(cnf_transformation,[],[f3175]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK201(X2,X1,X0),X2)
| in(unordered_pair(unordered_pair(sK200(X2,X1,X0),sK201(X2,X1,X0)),unordered_pair(sK200(X2,X1,X0),sK200(X2,X1,X0))),X0)
| ( relation_rng_restriction(X2,X1) = X0 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3176]) ).
tcf(c_654,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK200(X2,X1,X0),sK201(X2,X1,X0)),unordered_pair(sK200(X2,X1,X0),sK200(X2,X1,X0))),X1)
| in(unordered_pair(unordered_pair(sK200(X2,X1,X0),sK201(X2,X1,X0)),unordered_pair(sK200(X2,X1,X0),sK200(X2,X1,X0))),X0)
| ( relation_rng_restriction(X2,X1) = X0 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3177]) ).
tcf(c_655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ relation(relation_rng_restriction(X3,X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3407]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ relation(X3)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f3408]) ).
tcf(c_657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ relation(X3)
| ~ relation(relation_rng_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f3409]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2273]) ).
tcf(c_659,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2272]) ).
tcf(c_661,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK202(X0,X1),X1) ),
inference(cnf_transformation,[],[f2277]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK202(X0,X1),X0) ),
inference(cnf_transformation,[],[f2276]) ).
tcf(c_663,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2275]) ).
tcf(c_664,plain,
! [X0: $i,X1: $i] :
( ( powerset(X0) = X1 )
| ~ subset(sK203(X0,X1),X0)
| ~ in(sK203(X0,X1),X1) ),
inference(cnf_transformation,[],[f2281]) ).
tcf(c_665,plain,
! [X0: $i,X1: $i] :
( subset(sK203(X0,X1),X0)
| in(sK203(X0,X1),X1)
| ( powerset(X0) = X1 ) ),
inference(cnf_transformation,[],[f2280]) ).
tcf(c_666,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3410]) ).
tcf(c_667,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f3411]) ).
tcf(c_668,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2284]) ).
tcf(c_670,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f3413]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i] :
( equipotent(X1,X0)
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2285]) ).
tcf(c_672,plain,
! [X0: $i] : equipotent(X0,X0),
inference(cnf_transformation,[],[f2286]) ).
tcf(c_673,plain,
! [X0: $i] :
( equipotent(relation_dom(X0),relation_rng(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3415]) ).
tcf(c_674,plain,
! [X0: $i,X1: $i] :
( relation(sK204(X0,X1))
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2291]) ).
tcf(c_675,plain,
! [X0: $i,X1: $i] :
( function(sK204(X0,X1))
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2290]) ).
tcf(c_676,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK204(X0,X1))
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2289]) ).
tcf(c_677,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK204(X0,X1)) = X0 )
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2288]) ).
tcf(c_678,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK204(X0,X1)) = X1 )
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2287]) ).
tcf(c_679,plain,
! [X0: $i] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[],[f2293]) ).
tcf(c_680,plain,
! [X0: $i] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f2294]) ).
tcf(c_681,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2295]) ).
tcf(c_688,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK205(X0,X1,X2),X1)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK205(X0,X1,X2),X2)
| ~ in(sK205(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f2307]) ).
tcf(c_689,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK205(X0,X1,X2),X2)
| in(sK205(X0,X1,X2),X0)
| ( set_difference(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f2306]) ).
tcf(c_690,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK205(X0,X1,X2),X2)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK205(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f2305]) ).
tcf(c_691,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3416]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f3417]) ).
tcf(c_693,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f3418]) ).
tcf(c_694,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2308]) ).
tcf(c_695,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2309]) ).
tcf(c_696,plain,
! [X0: $i] : element(sK206(X0),powerset(X0)),
inference(cnf_transformation,[],[f2311]) ).
tcf(c_697,plain,
! [X0: $i] : empty(sK206(X0)),
inference(cnf_transformation,[],[f2310]) ).
tcf(c_698,plain,
! [X0: $i] :
( empty(X0)
| element(sK207(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f2313]) ).
tcf(c_699,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK207(X0)) ),
inference(cnf_transformation,[],[f2312]) ).
tcf(c_700,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f2314]) ).
tcf(c_701,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2315]) ).
tcf(c_702,plain,
! [X0: $i] : element(sK208(X0),X0),
inference(cnf_transformation,[],[f2316]) ).
tcf(c_703,plain,
! [X0: $i,X1: $i] :
( ( union_of_subsets(X1,X0) = union(X0) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2317]) ).
tcf(c_704,plain,
! [X0: $i] :
( epsilon_transitive(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2320]) ).
tcf(c_705,plain,
! [X0: $i] :
( epsilon_connected(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2319]) ).
tcf(c_706,plain,
! [X0: $i] :
( ordinal(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2318]) ).
tcf(c_707,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ( union(X0) != X0 ) ),
inference(cnf_transformation,[],[f2322]) ).
tcf(c_708,plain,
! [X0: $i] :
( ( union(X0) = X0 )
| ~ being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f2321]) ).
tcf(c_709,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( union(X0) = X1 )
| ~ in(X2,X0)
| ~ in(sK209(X0,X1),X2)
| ~ in(sK209(X0,X1),X1) ),
inference(cnf_transformation,[],[f2328]) ).
tcf(c_710,plain,
! [X0: $i,X1: $i] :
( in(sK209(X0,X1),X1)
| in(sK209(X0,X1),sK210(X0,X1))
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f2327]) ).
tcf(c_711,plain,
! [X0: $i,X1: $i] :
( in(sK210(X0,X1),X0)
| in(sK209(X0,X1),X1)
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f2326]) ).
tcf(c_712,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,union(X1))
| ~ in(X2,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3419]) ).
tcf(c_713,plain,
! [X0: $i,X1: $i] :
( in(X0,sK211(X1,X0))
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f3420]) ).
tcf(c_714,plain,
! [X0: $i,X1: $i] :
( in(sK211(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f3421]) ).
tcf(c_722,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP22(X3,X0)
| in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK219(X4,X3,X0))
| ~ function(X0)
| ~ relation(X3)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),cartesian_product2(X4,X4))
| ~ in(unordered_pair(unordered_pair(apply(X0,X1),apply(X0,X2)),unordered_pair(apply(X0,X1),apply(X0,X1))),X3) ),
inference(cnf_transformation,[],[f3423]) ).
tcf(c_723,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP22(X2,X3)
| in(sK220(X1,X2,X3,X0),cartesian_product2(X1,X1))
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK219(X1,X2,X3)) ),
inference(cnf_transformation,[],[f2339]) ).
tcf(c_724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP22(X2,X3)
| ( sK220(X1,X2,X3,X0) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK219(X1,X2,X3)) ),
inference(cnf_transformation,[],[f2338]) ).
tcf(c_725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP22(X2,X3)
| ( unordered_pair(unordered_pair(sK221(X2,X3,X0),sK222(X2,X3,X0)),unordered_pair(sK221(X2,X3,X0),sK221(X2,X3,X0))) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK219(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3186]) ).
tcf(c_726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP22(X2,X3)
| in(unordered_pair(unordered_pair(apply(X3,sK221(X2,X3,X0)),apply(X3,sK222(X2,X3,X0))),unordered_pair(apply(X3,sK221(X2,X3,X0)),apply(X3,sK221(X2,X3,X0)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK219(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3187]) ).
tcf(c_727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,sK223(X3,X1,X0))
| ~ sP26(X3,X1,X0)
| ~ sP25(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2342]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP25(X3,X2,X0,X1)
| ~ sP26(X1,X2,X3)
| ~ in(X0,sK223(X1,X2,X3)) ),
inference(cnf_transformation,[],[f2341]) ).
tcf(c_729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP25(X4,X3,unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1)
| ~ in(X2,X3)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),cartesian_product2(X3,X4))
| ~ in(unordered_pair(unordered_pair(X0,sK224(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3426]) ).
tcf(c_730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK224(X4,X1,X0),X0)
| sP25(X3,X2,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)
| ~ in(X1,X0)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f3429]) ).
tcf(c_731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK225(X0,X1,X2,X3),cartesian_product2(X1,X0))
| ~ sP25(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2349]) ).
tcf(c_732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK225(X0,X1,X2,X3) = X2 )
| ~ sP25(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2348]) ).
tcf(c_733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK226(X1,X2,X3),sK227(X1,X2,X3)),unordered_pair(sK226(X1,X2,X3),sK226(X1,X2,X3))) = X2 )
| ~ sP25(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3190]) ).
tcf(c_734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK226(X1,X2,X3),X1)
| ~ sP25(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2346]) ).
tcf(c_735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK226(X1,X2,X3) = sK228(X1,X2,X3) )
| ~ sP25(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2345]) ).
tcf(c_736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK227(X1,X2,X3),sK228(X1,X2,X3))
| ~ sP25(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2344]) ).
tcf(c_737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(sK227(X1,X2,X3),X0),unordered_pair(sK227(X1,X2,X3),sK227(X1,X2,X3))),X3)
| ~ sP25(X4,X1,X2,X3)
| ~ in(X0,sK228(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3191]) ).
tcf(c_738,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK229(X0,X1,X2),sK230(X0,X1,X2)),unordered_pair(sK229(X0,X1,X2),sK229(X0,X1,X2))) = X0 )
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f3192]) ).
tcf(c_739,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK229(X0,X1,X2),X1)
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f2355]) ).
tcf(c_740,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK229(X0,X1,X2) = sK231(X0,X1,X2) )
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f2354]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK230(X0,X1,X2),sK231(X0,X1,X2))
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f2353]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK230(X1,X2,X3),X0),unordered_pair(sK230(X1,X2,X3),sK230(X1,X2,X3))),X3)
| ~ sP24(X1,X2,X3)
| ~ in(X0,sK231(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3193]) ).
tcf(c_748,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| sP26(X1,X0,X2)
| ~ relation(X1)
| ( sK236(X0,X1) != sK237(X0,X1) ) ),
inference(cnf_transformation,[],[f2366]) ).
tcf(c_749,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP26(X0,X1,X2)
| ( sK236(X1,X0) = sK235(X1,X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2365]) ).
tcf(c_750,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP26(X0,X1,X2)
| sP24(sK236(X1,X0),X1,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2364]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP26(X0,X1,X2)
| ( sK237(X1,X0) = sK235(X1,X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2363]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP26(X0,X1,X2)
| sP23(sK237(X1,X0),X1,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2362]) ).
tcf(c_753,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f2367]) ).
tcf(c_754,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f2368]) ).
tcf(c_755,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,cartesian_product2(X1,X1))) = relation_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3196]) ).
tcf(c_756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(sK238(X2,X3,X4),X4)
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != sK238(X2,X3,X4) ) ),
inference(cnf_transformation,[],[f3197]) ).
tcf(c_757,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK239(X0,X1,X2),X0)
| in(sK238(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f2376]) ).
tcf(c_758,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK240(X0,X1,X2),X1)
| in(sK238(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f2375]) ).
tcf(c_759,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK238(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK239(X0,X1,X2),sK240(X0,X1,X2)),unordered_pair(sK239(X0,X1,X2),sK239(X0,X1,X2))) = sK238(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f3198]) ).
tcf(c_760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3431]) ).
tcf(c_761,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK241(X1,X2,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f3432]) ).
tcf(c_762,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK242(X1,X2,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f3433]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK241(X1,X2,X0),sK242(X1,X2,X0)),unordered_pair(sK241(X1,X2,X0),sK241(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f3434]) ).
tcf(c_764,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f2378]) ).
tcf(c_766,plain,
! [X0: $i,X1: $i] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2379]) ).
tcf(c_767,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2381]) ).
tcf(c_768,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK243(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),unordered_pair(sK243(X0,X1,X2),sK243(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2)),unordered_pair(sK243(X0,X1,X2),sK243(X0,X1,X2))),X0) ),
inference(cnf_transformation,[],[f3201]) ).
tcf(c_769,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK243(X0,X2,X1),X2)
| in(unordered_pair(unordered_pair(sK243(X0,X2,X1),sK244(X0,X2,X1)),unordered_pair(sK243(X0,X2,X1),sK243(X0,X2,X1))),X1)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3202]) ).
tcf(c_770,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK243(X0,X2,X1),sK244(X0,X2,X1)),unordered_pair(sK243(X0,X2,X1),sK243(X0,X2,X1))),X1)
| in(unordered_pair(unordered_pair(sK243(X0,X2,X1),sK244(X0,X2,X1)),unordered_pair(sK243(X0,X2,X1),sK243(X0,X2,X1))),X0)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3203]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3435]) ).
tcf(c_772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f3436]) ).
tcf(c_773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(cnf_transformation,[],[f3437]) ).
tcf(c_774,plain,
relation(sK245),
inference(cnf_transformation,[],[f2390]) ).
tcf(c_775,plain,
empty(sK245),
inference(cnf_transformation,[],[f2389]) ).
tcf(c_776,plain,
function(sK245),
inference(cnf_transformation,[],[f2388]) ).
tcf(c_777,plain,
relation(sK246),
inference(cnf_transformation,[],[f2392]) ).
tcf(c_778,plain,
function(sK246),
inference(cnf_transformation,[],[f2391]) ).
tcf(c_779,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2393]) ).
tcf(c_780,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2394]) ).
tcf(c_781,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2395]) ).
tcf(c_783,plain,
~ empty(sK247),
inference(cnf_transformation,[],[f2397]) ).
tcf(c_784,plain,
~ empty(sK248),
inference(cnf_transformation,[],[f2399]) ).
tcf(c_785,plain,
relation(sK248),
inference(cnf_transformation,[],[f2398]) ).
tcf(c_786,plain,
empty(sK249),
inference(cnf_transformation,[],[f2400]) ).
tcf(c_787,plain,
empty(sK250),
inference(cnf_transformation,[],[f2402]) ).
tcf(c_788,plain,
relation(sK250),
inference(cnf_transformation,[],[f2401]) ).
tcf(c_790,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f2405]) ).
tcf(c_791,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2404]) ).
tcf(c_792,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f2403]) ).
tcf(c_793,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2407]) ).
tcf(c_799,plain,
! [X0: $i,X1: $i] :
( sP27
| in(X0,sK254(X1))
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3438]) ).
tcf(c_800,plain,
! [X0: $i,X1: $i] :
( sP27
| in(sK255(X1,X0),X1)
| ~ in(X0,sK254(X1)) ),
inference(cnf_transformation,[],[f2415]) ).
tcf(c_801,plain,
! [X0: $i,X1: $i] :
( sP27
| ( sK255(X1,X0) = X0 )
| ~ in(X0,sK254(X1)) ),
inference(cnf_transformation,[],[f2414]) ).
tcf(c_802,plain,
! [X0: $i,X1: $i] :
( sP27
| ordinal(X0)
| ~ in(X0,sK254(X1)) ),
inference(cnf_transformation,[],[f2413]) ).
tcf(c_803,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2417]) ).
tcf(c_804,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2419]) ).
tcf(c_805,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f2418]) ).
tcf(c_806,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2420]) ).
tcf(c_807,plain,
! [X0: $i,X1: $i] :
( in(X1,sK256(X0))
| ~ sP30(X0)
| ~ sP29(X0,X1) ),
inference(cnf_transformation,[],[f2422]) ).
tcf(c_808,plain,
! [X0: $i,X1: $i] :
( sP29(X1,X0)
| ~ sP30(X1)
| ~ in(X0,sK256(X1)) ),
inference(cnf_transformation,[],[f2421]) ).
tcf(c_809,plain,
! [X0: $i,X1: $i] :
( sP29(X1,X0)
| ~ ordinal(X0)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1)))
| ( sK257(X0) != empty_set ) ),
inference(cnf_transformation,[],[f3440]) ).
tcf(c_810,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP29(X2,X0)
| ~ ordinal(X0)
| ~ in(X1,sK257(X0))
| ~ in(X0,set_union2(X2,unordered_pair(X2,X2)))
| ( sK258(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f3442]) ).
tcf(c_811,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP29(X1,X0)
| in(sK258(X0,X2),sK257(X0))
| ~ ordinal(X0)
| ~ in(X2,sK257(X0))
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3444]) ).
tcf(c_812,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP29(X1,X0)
| subset(X2,sK258(X0,X2))
| ~ ordinal(X0)
| ~ in(X2,sK257(X0))
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3446]) ).
tcf(c_813,plain,
! [X0: $i,X1: $i] :
( sP29(X1,X0)
| element(sK257(X0),powerset(powerset(X0)))
| ~ ordinal(X0)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3448]) ).
tcf(c_814,plain,
! [X0: $i,X1: $i] :
( in(X0,omega)
| sP29(X1,X0)
| ~ ordinal(X0)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3450]) ).
tcf(c_815,plain,
! [X0: $i,X1: $i] :
( in(sK259(X0,X1),set_union2(X0,unordered_pair(X0,X0)))
| ~ sP29(X0,X1) ),
inference(cnf_transformation,[],[f3213]) ).
tcf(c_816,plain,
! [X0: $i,X1: $i] :
( ( sK259(X0,X1) = X1 )
| ~ sP29(X0,X1) ),
inference(cnf_transformation,[],[f2427]) ).
tcf(c_817,plain,
! [X0: $i,X1: $i] :
( ordinal(sK260(X1))
| ~ sP29(X0,X1) ),
inference(cnf_transformation,[],[f2426]) ).
tcf(c_818,plain,
! [X0: $i,X1: $i] :
( ( sK260(X1) = X1 )
| ~ sP29(X0,X1) ),
inference(cnf_transformation,[],[f2425]) ).
tcf(c_819,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK261(X0),X0)
| ( X0 = empty_set )
| ~ sP29(X2,X1)
| ~ in(sK260(X1),omega)
| ~ element(X0,powerset(powerset(sK260(X1)))) ),
inference(cnf_transformation,[],[f2424]) ).
tcf(c_820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = empty_set )
| ( sK261(X0) = X2 )
| ~ sP29(X3,X1)
| ~ in(X2,X0)
| ~ in(sK260(X1),omega)
| ~ subset(sK261(X0),X2)
| ~ element(X0,powerset(powerset(sK260(X1)))) ),
inference(cnf_transformation,[],[f2423]) ).
tcf(c_825,plain,
! [X0: $i] :
( sP30(X0)
| ~ ordinal(X0)
| ( sK265 != sK266 ) ),
inference(cnf_transformation,[],[f2446]) ).
tcf(c_826,plain,
! [X0: $i] :
( sP30(X0)
| ( sK265 = sK264 )
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2445]) ).
tcf(c_827,plain,
! [X0: $i] :
( ordinal(sK267)
| sP30(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2444]) ).
tcf(c_828,plain,
! [X0: $i] :
( sP30(X0)
| ( sK265 = sK267 )
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2443]) ).
tcf(c_829,plain,
! [X0: $i,X1: $i] :
( sP30(X1)
| in(sK268(X0),X0)
| ( X0 = empty_set )
| ~ ordinal(X1)
| ~ in(sK267,omega)
| ~ element(X0,powerset(powerset(sK267))) ),
inference(cnf_transformation,[],[f2442]) ).
tcf(c_830,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP30(X2)
| ( X0 = empty_set )
| ( sK268(X0) = X1 )
| ~ ordinal(X2)
| ~ in(sK267,omega)
| ~ in(X1,X0)
| ~ subset(sK268(X0),X1)
| ~ element(X0,powerset(powerset(sK267))) ),
inference(cnf_transformation,[],[f2441]) ).
tcf(c_831,plain,
! [X0: $i] :
( sP30(X0)
| ( sK266 = sK264 )
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2440]) ).
tcf(c_832,plain,
! [X0: $i] :
( sP28(sK266)
| sP30(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2439]) ).
tcf(c_833,plain,
epsilon_transitive(omega),
inference(cnf_transformation,[],[f2450]) ).
tcf(c_834,plain,
epsilon_connected(omega),
inference(cnf_transformation,[],[f2449]) ).
tcf(c_836,plain,
~ empty(omega),
inference(cnf_transformation,[],[f2447]) ).
tcf(c_837,plain,
! [X0: $i] :
( ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(empty_set,X0)
| ~ subset(X0,sK269(X0)) ),
inference(cnf_transformation,[],[f2458]) ).
tcf(c_838,plain,
! [X0: $i] :
( in(empty_set,sK269(X0))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(empty_set,X0) ),
inference(cnf_transformation,[],[f2457]) ).
tcf(c_839,plain,
! [X0: $i] :
( being_limit_ordinal(sK269(X0))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(empty_set,X0) ),
inference(cnf_transformation,[],[f2456]) ).
tcf(c_840,plain,
! [X0: $i] :
( ordinal(sK269(X0))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(empty_set,X0) ),
inference(cnf_transformation,[],[f2455]) ).
tcf(c_841,plain,
in(empty_set,omega),
inference(cnf_transformation,[],[f3451]) ).
tcf(c_842,plain,
being_limit_ordinal(omega),
inference(cnf_transformation,[],[f3452]) ).
tcf(c_843,plain,
ordinal(omega),
inference(cnf_transformation,[],[f3453]) ).
tcf(c_844,plain,
! [X0: $i] :
( subset(omega,X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(empty_set,X0) ),
inference(cnf_transformation,[],[f3454]) ).
tcf(c_845,plain,
! [X0: $i] :
( finite(relation_rng(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),omega) ),
inference(cnf_transformation,[],[f3455]) ).
tcf(c_846,plain,
! [X0: $i] :
( relation(sK270(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2462]) ).
tcf(c_847,plain,
! [X0: $i] :
( function(sK270(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2461]) ).
tcf(c_848,plain,
! [X0: $i] :
( ( relation_rng(sK270(X0)) = X0 )
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2460]) ).
tcf(c_849,plain,
! [X0: $i] :
( in(relation_dom(sK270(X0)),omega)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2459]) ).
tcf(c_850,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ element(X0,omega) ),
inference(cnf_transformation,[],[f2467]) ).
tcf(c_851,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ element(X0,omega) ),
inference(cnf_transformation,[],[f2466]) ).
tcf(c_852,plain,
! [X0: $i] :
( ordinal(X0)
| ~ element(X0,omega) ),
inference(cnf_transformation,[],[f2465]) ).
tcf(c_854,plain,
! [X0: $i] :
( ~ sP32(X0)
| ( sK272(X0) != sK273(X0) ) ),
inference(cnf_transformation,[],[f2474]) ).
tcf(c_855,plain,
! [X0: $i] :
( ( sK272(X0) = sK271(X0) )
| ~ sP32(X0) ),
inference(cnf_transformation,[],[f2473]) ).
tcf(c_856,plain,
! [X0: $i] :
( ordinal(sK274(X0))
| ~ sP32(X0) ),
inference(cnf_transformation,[],[f2472]) ).
tcf(c_857,plain,
! [X0: $i] :
( ( sK272(X0) = sK274(X0) )
| ~ sP32(X0) ),
inference(cnf_transformation,[],[f2471]) ).
tcf(c_858,plain,
! [X0: $i] :
( in(sK274(X0),X0)
| ~ sP32(X0) ),
inference(cnf_transformation,[],[f2470]) ).
tcf(c_859,plain,
! [X0: $i] :
( ( sK273(X0) = sK271(X0) )
| ~ sP32(X0) ),
inference(cnf_transformation,[],[f2469]) ).
tcf(c_860,plain,
! [X0: $i] :
( sP31(sK273(X0),X0)
| ~ sP32(X0) ),
inference(cnf_transformation,[],[f2468]) ).
tcf(c_864,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP32(X2)
| in(X0,sK276(X2,X1))
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X2)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3457]) ).
tcf(c_865,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP32(X1)
| in(sK277(X1,X2,X0),set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X0,sK276(X1,X2)) ),
inference(cnf_transformation,[],[f3215]) ).
tcf(c_866,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP32(X1)
| ( sK277(X1,X2,X0) = X0 )
| ~ ordinal(X2)
| ~ in(X0,sK276(X1,X2)) ),
inference(cnf_transformation,[],[f2481]) ).
tcf(c_867,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP32(X1)
| ordinal(sK278(X1,X0))
| ~ ordinal(X2)
| ~ in(X0,sK276(X1,X2)) ),
inference(cnf_transformation,[],[f2480]) ).
tcf(c_868,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP32(X1)
| ( sK278(X1,X0) = X0 )
| ~ ordinal(X2)
| ~ in(X0,sK276(X1,X2)) ),
inference(cnf_transformation,[],[f2479]) ).
tcf(c_869,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP32(X1)
| in(sK278(X1,X0),X1)
| ~ ordinal(X2)
| ~ in(X0,sK276(X1,X2)) ),
inference(cnf_transformation,[],[f2478]) ).
tcf(c_877,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP33(X0,X1)
| in(set_difference(X2,unordered_pair(X1,X1)),sK284(X1,X0))
| ~ ordinal(X1)
| ~ in(X2,X0)
| ~ in(set_difference(X2,unordered_pair(X1,X1)),powerset(X1))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3459]) ).
tcf(c_878,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP33(X0,X1)
| in(sK285(X1,X0,X2),powerset(X1))
| ~ ordinal(X1)
| ~ in(X2,sK284(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3219]) ).
tcf(c_879,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP33(X0,X1)
| ( sK285(X1,X0,X2) = X2 )
| ~ ordinal(X1)
| ~ in(X2,sK284(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3220]) ).
tcf(c_880,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP33(X0,X1)
| in(sK286(X1,X0,X2),X0)
| ~ ordinal(X1)
| ~ in(X2,sK284(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3221]) ).
tcf(c_881,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP33(X0,X1)
| ( set_difference(sK286(X1,X0,X2),unordered_pair(X1,X1)) = X2 )
| ~ ordinal(X1)
| ~ in(X2,sK284(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3222]) ).
tcf(c_883,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f3224]) ).
tcf(c_884,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f3225]) ).
tcf(c_885,plain,
! [X0: $i] :
( ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f3226]) ).
tcf(c_886,plain,
! [X0: $i] : ~ empty(set_union2(X0,unordered_pair(X0,X0))),
inference(cnf_transformation,[],[f3227]) ).
tcf(c_887,plain,
epsilon_transitive(sK287),
inference(cnf_transformation,[],[f2504]) ).
tcf(c_888,plain,
epsilon_connected(sK287),
inference(cnf_transformation,[],[f2503]) ).
tcf(c_889,plain,
ordinal(sK287),
inference(cnf_transformation,[],[f2502]) ).
tcf(c_890,plain,
being_limit_ordinal(sK287),
inference(cnf_transformation,[],[f2501]) ).
tcf(c_891,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(X0) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(sK288(X0,X2),X2)
| ( apply(X0,X1) != sK288(X0,X2) ) ),
inference(cnf_transformation,[],[f2510]) ).
tcf(c_892,plain,
! [X0: $i,X1: $i] :
( in(sK288(X0,X1),X1)
| in(sK289(X0,X1),relation_dom(X0))
| ( relation_rng(X0) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2509]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i] :
( in(sK288(X0,X1),X1)
| ( relation_rng(X0) = X1 )
| ( apply(X0,sK289(X0,X1)) = sK288(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2508]) ).
tcf(c_894,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f3461]) ).
tcf(c_895,plain,
! [X0: $i,X1: $i] :
( in(sK290(X1,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f3462]) ).
tcf(c_896,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK290(X1,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f3463]) ).
tcf(c_900,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(X0))
| ( apply(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3466]) ).
tcf(c_901,plain,
top_str(sK291),
inference(cnf_transformation,[],[f2515]) ).
tcf(c_902,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f2516]) ).
tcf(c_908,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X2,X0)
| in(X1,sK295(X0,X2))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2) ),
inference(cnf_transformation,[],[f3467]) ).
tcf(c_909,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X0,X1)
| in(sK296(X1,X0,X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X2,sK295(X1,X0))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f2524]) ).
tcf(c_910,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X0,X1)
| ( sK296(X1,X0,X2) = X2 )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X2,sK295(X1,X0))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f2523]) ).
tcf(c_911,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X0,X1)
| in(set_difference(cast_as_carrier_subset(X1),X2),X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X2,sK295(X1,X0))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f2522]) ).
tcf(c_912,plain,
! [X0: $i,X1: $i] :
( ~ sP36(X0,X1)
| ( sK298(X0,X1) != sK299(X0,X1) ) ),
inference(cnf_transformation,[],[f2533]) ).
tcf(c_913,plain,
! [X0: $i,X1: $i] :
( ( sK298(X0,X1) = sK297(X0,X1) )
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f2532]) ).
tcf(c_914,plain,
! [X0: $i,X1: $i] :
( element(sK300(X0,X1),powerset(the_carrier(X0)))
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f2531]) ).
tcf(c_915,plain,
! [X0: $i,X1: $i] :
( ( sK298(X0,X1) = sK300(X0,X1) )
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f2530]) ).
tcf(c_916,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK300(X0,X1),X0)
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f2529]) ).
tcf(c_917,plain,
! [X0: $i,X1: $i] :
( subset(X1,sK298(X0,X1))
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f2528]) ).
tcf(c_918,plain,
! [X0: $i,X1: $i] :
( ( sK299(X0,X1) = sK297(X0,X1) )
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f2527]) ).
tcf(c_919,plain,
! [X0: $i,X1: $i] :
( sP35(X0,sK299(X0,X1),X1)
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f2526]) ).
tcf(c_924,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X1,X2)
| in(X0,sK302(X1,X2))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ closed_subset(X0,X1)
| ~ subset(X2,X0)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f3469]) ).
tcf(c_925,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X1,X2)
| in(sK303(X1,X2,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK302(X1,X2)) ),
inference(cnf_transformation,[],[f2543]) ).
tcf(c_926,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X1,X2)
| ( sK303(X1,X2,X0) = X0 )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK302(X1,X2)) ),
inference(cnf_transformation,[],[f2542]) ).
tcf(c_927,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X1,X2)
| element(sK304(X1,X2,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK302(X1,X2)) ),
inference(cnf_transformation,[],[f2541]) ).
tcf(c_928,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X1,X2)
| ( sK304(X1,X2,X0) = X0 )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK302(X1,X2)) ),
inference(cnf_transformation,[],[f2540]) ).
tcf(c_929,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X1,X2)
| closed_subset(sK304(X1,X2,X0),X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK302(X1,X2)) ),
inference(cnf_transformation,[],[f2539]) ).
tcf(c_930,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X1,X2)
| subset(X2,X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK302(X1,X2)) ),
inference(cnf_transformation,[],[f2538]) ).
tcf(c_931,plain,
! [X0: $i] :
( element(sK305(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f2546]) ).
tcf(c_932,plain,
! [X0: $i] :
( closed_subset(sK305(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f2545]) ).
tcf(c_933,plain,
! [X0: $i] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f2547]) ).
tcf(c_935,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f2549]) ).
tcf(c_941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP37(X2,X0)
| in(X1,sK309(X2,X0))
| ~ function(X0)
| ~ relation(X0)
| ~ element(X2,powerset(powerset(X3)))
| ~ in(X1,powerset(relation_dom(X0)))
| ~ in(relation_image(X0,X1),X2) ),
inference(cnf_transformation,[],[f3470]) ).
tcf(c_942,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP37(X1,X2)
| in(sK310(X1,X2,X0),powerset(relation_dom(X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X3)))
| ~ in(X0,sK309(X1,X2)) ),
inference(cnf_transformation,[],[f2557]) ).
tcf(c_943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP37(X1,X2)
| ( sK310(X1,X2,X0) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X3)))
| ~ in(X0,sK309(X1,X2)) ),
inference(cnf_transformation,[],[f2556]) ).
tcf(c_944,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP37(X1,X2)
| in(relation_image(X2,X0),X1)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X3)))
| ~ in(X0,sK309(X1,X2)) ),
inference(cnf_transformation,[],[f2555]) ).
tcf(c_945,plain,
! [X0: $i,X1: $i] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2559]) ).
tcf(c_946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,X2) = X3 )
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(sK311(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(X0,sK311(X1,X2,X3)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3230]) ).
tcf(c_947,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK311(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK312(X0,X1,X2),sK311(X0,X1,X2)),unordered_pair(sK312(X0,X1,X2),sK312(X0,X1,X2))),X0)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3231]) ).
tcf(c_948,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK312(X0,X1,X2),X1)
| in(sK311(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2563]) ).
tcf(c_949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,relation_image(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3471]) ).
tcf(c_950,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK313(X1,X2,X0),X0),unordered_pair(sK313(X1,X2,X0),sK313(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3472]) ).
tcf(c_951,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK313(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3473]) ).
tcf(c_952,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(X3,relation_dom(X0))
| ~ in(sK314(X0,X1,X2),X2)
| ( sK314(X0,X1,X2) != apply(X0,X3) ) ),
inference(cnf_transformation,[],[f2573]) ).
tcf(c_953,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK314(X0,X1,X2),X2)
| in(sK315(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2572]) ).
tcf(c_954,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK315(X0,X1,X2),X1)
| in(sK314(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2571]) ).
tcf(c_955,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK314(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK315(X0,X1,X2)) = sK314(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2570]) ).
tcf(c_956,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),relation_image(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f3475]) ).
tcf(c_957,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK316(X1,X2,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3476]) ).
tcf(c_958,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK316(X1,X2,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3477]) ).
tcf(c_959,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK316(X1,X2,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3478]) ).
tcf(c_960,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f2574]) ).
tcf(c_961,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X1) = X2 )
| ~ in(sK317(X0,X1,X2),X2)
| ( sK317(X0,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2581]) ).
tcf(c_962,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X1) = X2 )
| ~ in(sK317(X0,X1,X2),X2)
| ( sK317(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f2580]) ).
tcf(c_963,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK317(X0,X1,X2),X2)
| ( unordered_pair(X0,X1) = X2 )
| ( sK317(X0,X1,X2) = X1 )
| ( sK317(X0,X1,X2) = X0 ) ),
inference(cnf_transformation,[],[f2579]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f3480]) ).
tcf(c_965,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f3482]) ).
tcf(c_966,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f3483]) ).
tcf(c_967,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2582]) ).
tcf(c_968,plain,
! [X0: $i] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2584]) ).
tcf(c_969,plain,
! [X0: $i] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2583]) ).
tcf(c_970,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f2585]) ).
tcf(c_971,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = empty_set,
inference(cnf_transformation,[],[f3234]) ).
tcf(c_979,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3242]) ).
tcf(c_980,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ in(sK318(X0,X1,X2),X2)
| ~ in(sK318(X0,X1,X2),X1)
| ~ in(sK318(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f3243]) ).
tcf(c_981,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,X1,X2),X2)
| in(sK318(X0,X1,X2),X0)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f3244]) ).
tcf(c_982,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,X1,X2),X2)
| in(sK318(X0,X1,X2),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f3245]) ).
tcf(c_983,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_difference(X1,set_difference(X1,X2)))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3484]) ).
tcf(c_985,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(cnf_transformation,[],[f3486]) ).
tcf(c_986,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(cnf_transformation,[],[f3249]) ).
tcf(c_987,plain,
! [X0: $i] :
( empty_carrier(X0)
| element(sK319(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f2603]) ).
tcf(c_988,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(sK319(X0)) ),
inference(cnf_transformation,[],[f2602]) ).
tcf(c_989,plain,
one_sorted_str(sK320),
inference(cnf_transformation,[],[f2605]) ).
tcf(c_990,plain,
~ empty_carrier(sK320),
inference(cnf_transformation,[],[f2604]) ).
tcf(c_991,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f2606]) ).
tcf(c_992,plain,
one_sorted_str(sK321),
inference(cnf_transformation,[],[f2607]) ).
tcf(c_993,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f2608]) ).
tcf(c_994,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f2610]) ).
tcf(c_995,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f2609]) ).
tcf(c_996,plain,
! [X0: $i,X1: $i] : relation_of2_as_subset(sK322(X0,X1),X0,X1),
inference(cnf_transformation,[],[f2611]) ).
tcf(c_997,plain,
! [X0: $i] : in(X0,sK323(X0)),
inference(cnf_transformation,[],[f2616]) ).
tcf(c_998,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK323(X1))
| ~ subset(X2,X0)
| ~ in(X0,sK323(X1)) ),
inference(cnf_transformation,[],[f2615]) ).
tcf(c_999,plain,
! [X0: $i,X1: $i] :
( in(sK324(X1,X0),sK323(X1))
| ~ in(X0,sK323(X1)) ),
inference(cnf_transformation,[],[f2614]) ).
tcf(c_1000,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK324(X1,X0))
| ~ subset(X2,X0)
| ~ in(X0,sK323(X1)) ),
inference(cnf_transformation,[],[f2613]) ).
tcf(c_1001,plain,
! [X0: $i,X1: $i] :
( are_equipotent(X0,sK323(X1))
| in(X0,sK323(X1))
| ~ subset(X0,sK323(X1)) ),
inference(cnf_transformation,[],[f2612]) ).
tcf(c_1002,plain,
! [X0: $i,X1: $i] :
( equipotent(X0,X1)
| ~ are_equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2618]) ).
tcf(c_1003,plain,
! [X0: $i,X1: $i] :
( are_equipotent(X0,X1)
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2617]) ).
tcf(c_1004,plain,
! [X0: $i] :
( empty(X0)
| element(sK325(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f2621]) ).
tcf(c_1005,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK325(X0)) ),
inference(cnf_transformation,[],[f2620]) ).
tcf(c_1006,plain,
! [X0: $i] :
( empty(X0)
| finite(sK325(X0)) ),
inference(cnf_transformation,[],[f2619]) ).
tcf(c_1007,plain,
~ empty(sK326),
inference(cnf_transformation,[],[f2623]) ).
tcf(c_1008,plain,
finite(sK326),
inference(cnf_transformation,[],[f2622]) ).
tcf(c_1010,plain,
! [X0: $i] : finite(unordered_pair(X0,X0)),
inference(cnf_transformation,[],[f3251]) ).
tcf(c_1011,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2626]) ).
tcf(c_1013,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(X1,set_difference(X1,X0)))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f3253]) ).
tcf(c_1015,plain,
! [X0: $i] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2630]) ).
tcf(c_1016,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(sK327(X0,X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(sK327(X0,X1,X2),X3),unordered_pair(sK327(X0,X1,X2),sK327(X0,X1,X2))),X0) ),
inference(cnf_transformation,[],[f3254]) ).
tcf(c_1017,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK327(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK327(X0,X1,X2),sK328(X0,X1,X2)),unordered_pair(sK327(X0,X1,X2),sK327(X0,X1,X2))),X0)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3255]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK328(X0,X1,X2),X1)
| in(sK327(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2634]) ).
tcf(c_1019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3487]) ).
tcf(c_1020,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK329(X1,X2,X0)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f3488]) ).
tcf(c_1021,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK329(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f3489]) ).
tcf(c_1022,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK330(X0,X1,X2),X2)
| ~ in(sK330(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK330(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f2642]) ).
tcf(c_1023,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK330(X0,X1,X2),X2)
| in(sK330(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2641]) ).
tcf(c_1024,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK330(X0,X1,X2),X2)
| in(apply(X0,sK330(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2640]) ).
tcf(c_1025,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_inverse_image(X0,X2))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(apply(X0,X1),X2) ),
inference(cnf_transformation,[],[f3490]) ).
tcf(c_1026,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f3491]) ).
tcf(c_1027,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X1,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f3492]) ).
tcf(c_1028,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X2,set_difference(X2,X0)) = subset_intersection2(X1,X2,X0) )
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f3258]) ).
tcf(c_1029,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_intersection2(X1,X2,X2) = X2 )
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2644]) ).
tcf(c_1030,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subset_intersection2(X1,X2,X0),powerset(X1))
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2645]) ).
tcf(c_1031,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_intersection2(X1,X0,X2) = subset_intersection2(X1,X2,X0) )
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2646]) ).
tcf(c_1032,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2648]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2647]) ).
tcf(c_1034,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2650]) ).
tcf(c_1035,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2649]) ).
tcf(c_1036,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2652]) ).
tcf(c_1037,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2651]) ).
tcf(c_1038,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2653]) ).
tcf(c_1039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X3,sK332(X0,X1,X2)),unordered_pair(X3,X3)),X1)
| ~ in(unordered_pair(unordered_pair(sK331(X0,X1,X2),X3),unordered_pair(sK331(X0,X1,X2),sK331(X0,X1,X2))),X0)
| ~ in(unordered_pair(unordered_pair(sK331(X0,X1,X2),sK332(X0,X1,X2)),unordered_pair(sK331(X0,X1,X2),sK331(X0,X1,X2))),X2) ),
inference(cnf_transformation,[],[f3259]) ).
tcf(c_1040,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK331(X0,X2,X1),sK333(X0,X2,X1)),unordered_pair(sK331(X0,X2,X1),sK331(X0,X2,X1))),X0)
| in(unordered_pair(unordered_pair(sK331(X0,X2,X1),sK332(X0,X2,X1)),unordered_pair(sK331(X0,X2,X1),sK331(X0,X2,X1))),X1)
| ( relation_composition(X0,X2) = X1 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3260]) ).
tcf(c_1041,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK333(X0,X2,X1),sK332(X0,X2,X1)),unordered_pair(sK333(X0,X2,X1),sK333(X0,X2,X1))),X2)
| in(unordered_pair(unordered_pair(sK331(X0,X2,X1),sK332(X0,X2,X1)),unordered_pair(sK331(X0,X2,X1),sK331(X0,X2,X1))),X1)
| ( relation_composition(X0,X2) = X1 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3261]) ).
tcf(c_1042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X4))
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3493]) ).
tcf(c_1043,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,sK334(X2,X3,X0,X1)),unordered_pair(X0,X0)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f3494]) ).
tcf(c_1044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK334(X2,X3,X0,X1),X1),unordered_pair(sK334(X2,X3,X0,X1),sK334(X2,X3,X0,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(relation_composition(X2,X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(cnf_transformation,[],[f3495]) ).
tcf(c_1045,plain,
! [X0: $i,X1: $i] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2660]) ).
tcf(c_1046,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2661]) ).
tcf(c_1047,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2662]) ).
tcf(c_1048,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( complements_of_subsets(X0,X1) = X2 )
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(sK335(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK335(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f2667]) ).
tcf(c_1049,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK335(X1,X2,X0),X0)
| in(subset_complement(X1,sK335(X1,X2,X0)),X2)
| ( complements_of_subsets(X1,X2) = X0 )
| ~ element(X2,powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2666]) ).
tcf(c_1050,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK335(X1,X2,X0),powerset(X1))
| ( complements_of_subsets(X1,X2) = X0 )
| ~ element(X2,powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2665]) ).
tcf(c_1051,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,complements_of_subsets(X0,X1))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(subset_complement(X0,X2),X1)
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f3496]) ).
tcf(c_1052,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X0,X2),X1)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(X2,complements_of_subsets(X0,X1))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f3497]) ).
tcf(c_1053,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2668]) ).
tcf(c_1054,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_difference(X1,X2,X0) = set_difference(X2,X0) )
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2669]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subset_difference(X1,X2,X0),powerset(X1))
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2670]) ).
tcf(c_1056,plain,
! [X0: $i,X1: $i] : relation_of2(sK336(X0,X1),X0,X1),
inference(cnf_transformation,[],[f2674]) ).
tcf(c_1057,plain,
! [X0: $i,X1: $i] : relation(sK336(X0,X1)),
inference(cnf_transformation,[],[f2673]) ).
tcf(c_1058,plain,
! [X0: $i,X1: $i] : function(sK336(X0,X1)),
inference(cnf_transformation,[],[f2672]) ).
tcf(c_1059,plain,
! [X0: $i,X1: $i] : quasi_total(sK336(X0,X1),X0,X1),
inference(cnf_transformation,[],[f2671]) ).
tcf(c_1060,plain,
! [X0: $i] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f2675]) ).
tcf(c_1061,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,X1)
| ( X0 = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2676]) ).
tcf(c_1062,plain,
! [X0: $i,X1: $i] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f2677]) ).
tcf(c_1063,plain,
~ empty(sK337),
inference(cnf_transformation,[],[f2681]) ).
tcf(c_1064,plain,
epsilon_transitive(sK337),
inference(cnf_transformation,[],[f2680]) ).
tcf(c_1065,plain,
epsilon_connected(sK337),
inference(cnf_transformation,[],[f2679]) ).
tcf(c_1066,plain,
ordinal(sK337),
inference(cnf_transformation,[],[f2678]) ).
tcf(c_1067,plain,
relation(sK338),
inference(cnf_transformation,[],[f2688]) ).
tcf(c_1068,plain,
function(sK338),
inference(cnf_transformation,[],[f2687]) ).
tcf(c_1069,plain,
one_to_one(sK338),
inference(cnf_transformation,[],[f2686]) ).
tcf(c_1070,plain,
empty(sK338),
inference(cnf_transformation,[],[f2685]) ).
tcf(c_1071,plain,
epsilon_transitive(sK338),
inference(cnf_transformation,[],[f2684]) ).
tcf(c_1072,plain,
epsilon_connected(sK338),
inference(cnf_transformation,[],[f2683]) ).
tcf(c_1073,plain,
ordinal(sK338),
inference(cnf_transformation,[],[f2682]) ).
tcf(c_1074,plain,
epsilon_transitive(sK339),
inference(cnf_transformation,[],[f2691]) ).
tcf(c_1075,plain,
epsilon_connected(sK339),
inference(cnf_transformation,[],[f2690]) ).
tcf(c_1076,plain,
ordinal(sK339),
inference(cnf_transformation,[],[f2689]) ).
tcf(c_1080,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK340(X0),X0) ),
inference(cnf_transformation,[],[f2697]) ).
tcf(c_1081,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK340(X0),X0) ),
inference(cnf_transformation,[],[f2696]) ).
tcf(c_1082,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2695]) ).
tcf(c_1083,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2700]) ).
tcf(c_1084,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2699]) ).
tcf(c_1085,plain,
! [X0: $i] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2698]) ).
tcf(c_1086,plain,
! [X0: $i] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f2701]) ).
tcf(c_1087,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2703]) ).
tcf(c_1088,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2702]) ).
tcf(c_1089,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f2706]) ).
tcf(c_1090,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| ~ ordinal(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f2705]) ).
tcf(c_1091,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f2704]) ).
tcf(c_1092,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(X0,X1)
| subset(sK341(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2711]) ).
tcf(c_1093,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(X0,X1)
| ~ relation(X0)
| ( sK341(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f2710]) ).
tcf(c_1094,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_well_founded_in(X0,X2)
| ~ relation(X0)
| ~ in(X1,sK341(X0,X2))
| ~ disjoint(fiber(X0,X1),sK341(X0,X2)) ),
inference(cnf_transformation,[],[f2709]) ).
tcf(c_1095,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK342(X2,X0),X0)
| ( X0 = empty_set )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2708]) ).
tcf(c_1096,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X2,sK342(X2,X0)),X0)
| ( X0 = empty_set )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2707]) ).
tcf(c_1097,plain,
! [X0: $i] :
( well_founded_relation(X0)
| subset(sK343(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2716]) ).
tcf(c_1098,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ( sK343(X0) != empty_set ) ),
inference(cnf_transformation,[],[f2715]) ).
tcf(c_1099,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ~ in(X1,sK343(X0))
| ~ disjoint(fiber(X0,X1),sK343(X0)) ),
inference(cnf_transformation,[],[f2714]) ).
tcf(c_1100,plain,
! [X0: $i,X1: $i] :
( in(sK344(X1,X0),X0)
| ( X0 = empty_set )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f2713]) ).
tcf(c_1101,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X1,sK344(X1,X0)),X0)
| ( X0 = empty_set )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f2712]) ).
tcf(c_1102,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( fiber(X0,X1) = X2 )
| ( sK345(X0,X1,X2) = X1 )
| ~ relation(X0)
| ~ in(sK345(X0,X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(sK345(X0,X1,X2),X1),unordered_pair(sK345(X0,X1,X2),sK345(X0,X1,X2))),X0) ),
inference(cnf_transformation,[],[f3265]) ).
tcf(c_1103,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK345(X0,X1,X2),X2)
| ( fiber(X0,X1) = X2 )
| ~ relation(X0)
| ( sK345(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f2721]) ).
tcf(c_1104,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK345(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK345(X0,X1,X2),X1),unordered_pair(sK345(X0,X1,X2),sK345(X0,X1,X2))),X0)
| ( fiber(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3266]) ).
tcf(c_1105,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,fiber(X2,X1))
| ( X0 = X1 )
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3498]) ).
tcf(c_1106,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ in(X0,fiber(X1,X0)) ),
inference(cnf_transformation,[],[f3500]) ).
tcf(c_1107,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,fiber(X1,X2)) ),
inference(cnf_transformation,[],[f3501]) ).
tcf(c_1108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_as_subset(X1,X2,X0) = relation_dom(X0) )
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f2723]) ).
tcf(c_1109,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(relation_dom_as_subset(X1,X2,X0),powerset(X1))
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f2724]) ).
tcf(c_1110,plain,
! [X0: $i,X1: $i] :
( quasi_total(X1,empty_set,X0)
| ~ relation_of2_as_subset(X1,empty_set,X0)
| ( relation_dom_as_subset(empty_set,X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f3502]) ).
tcf(c_1111,plain,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(X2,X0,X1)
| ( X1 = empty_set )
| ~ relation_of2_as_subset(X2,X0,X1)
| ( relation_dom_as_subset(X0,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2729]) ).
tcf(c_1112,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_as_subset(empty_set,X1,X0) = empty_set )
| ~ quasi_total(X0,empty_set,X1)
| ~ relation_of2_as_subset(X0,empty_set,X1) ),
inference(cnf_transformation,[],[f3503]) ).
tcf(c_1113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = empty_set )
| ( relation_dom_as_subset(X1,X2,X0) = X1 )
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f2727]) ).
tcf(c_1114,plain,
! [X0: $i] :
( quasi_total(empty_set,X0,empty_set)
| ( X0 = empty_set )
| ~ relation_of2_as_subset(empty_set,X0,empty_set) ),
inference(cnf_transformation,[],[f3505]) ).
tcf(c_1115,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( X0 = empty_set )
| ~ quasi_total(X0,X1,empty_set)
| ~ relation_of2_as_subset(X0,X1,empty_set) ),
inference(cnf_transformation,[],[f3506]) ).
tcf(c_1118,plain,
latt_str(sK346),
inference(cnf_transformation,[],[f2733]) ).
tcf(c_1119,plain,
! [X0: $i] :
( meet_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f2735]) ).
tcf(c_1120,plain,
! [X0: $i] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f2734]) ).
tcf(c_1121,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| ( join(X0,meet(X0,sK347(X0),sK348(X0)),sK348(X0)) != sK348(X0) ) ),
inference(cnf_transformation,[],[f2739]) ).
tcf(c_1122,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| element(sK348(X0),the_carrier(X0))
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f2738]) ).
tcf(c_1123,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| element(sK347(X0),the_carrier(X0))
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f2737]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| ( join(X1,meet(X1,X2,X0),X0) = X0 )
| ~ meet_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f2736]) ).
tcf(c_1125,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_as_subset(X1,X2,X0) = relation_rng(X0) )
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f2740]) ).
tcf(c_1126,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(relation_rng_as_subset(X1,X2,X0),powerset(X2))
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f2741]) ).
tcf(c_1127,plain,
join_semilatt_str(sK349),
inference(cnf_transformation,[],[f2742]) ).
tcf(c_1128,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ),
inference(cnf_transformation,[],[f2744]) ).
tcf(c_1129,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X0),X1)
| ~ top_str(X1)
| ~ closed_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2743]) ).
tcf(c_1130,plain,
! [X0: $i,X1: $i] :
( open_subset(X0,X1)
| ~ top_str(X1)
| ~ in(X0,the_topology(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2746]) ).
tcf(c_1131,plain,
! [X0: $i,X1: $i] :
( in(X0,the_topology(X1))
| ~ top_str(X1)
| ~ open_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2745]) ).
tcf(c_1132,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( topstr_closure(X0,X1) = X2 )
| ~ sP39(X2,X1,X0)
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f2748]) ).
tcf(c_1133,plain,
! [X0: $i,X1: $i] :
( sP38(X0,X1,topstr_closure(X0,X1))
| ~ sP39(topstr_closure(X0,X1),X1,X0) ),
inference(cnf_transformation,[],[f3507]) ).
tcf(c_1145,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP39(X0,X2,X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2760]) ).
tcf(c_1146,plain,
! [X0: $i] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f2761]) ).
tcf(c_1147,plain,
! [X0: $i] :
( ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0)
| ~ subset(sK353(relation_field(X0),X0),sK354(relation_field(X0),X0))
| ~ in(unordered_pair(unordered_pair(sK353(relation_field(X0),X0),sK354(relation_field(X0),X0)),unordered_pair(sK353(relation_field(X0),X0),sK353(relation_field(X0),X0))),X0) ),
inference(cnf_transformation,[],[f3508]) ).
tcf(c_1148,plain,
! [X0: $i] :
( subset(sK353(relation_field(X0),X0),sK354(relation_field(X0),X0))
| in(unordered_pair(unordered_pair(sK353(relation_field(X0),X0),sK354(relation_field(X0),X0)),unordered_pair(sK353(relation_field(X0),X0),sK353(relation_field(X0),X0))),X0)
| ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3509]) ).
tcf(c_1149,plain,
! [X0: $i] :
( in(sK353(relation_field(X0),X0),relation_field(X0))
| ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3510]) ).
tcf(c_1150,plain,
! [X0: $i] :
( in(sK354(relation_field(X0),X0),relation_field(X0))
| ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3511]) ).
tcf(c_1151,plain,
! [X0: $i] :
( ( relation_field(inclusion_relation(X0)) = X0 )
| ~ relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f3512]) ).
tcf(c_1152,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),inclusion_relation(X1))
| ~ relation(inclusion_relation(X1))
| ~ subset(X0,X2)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3513]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| ~ relation(inclusion_relation(X2))
| ~ in(X1,X2)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),inclusion_relation(X2)) ),
inference(cnf_transformation,[],[f3514]) ).
tcf(c_1154,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f2770]) ).
tcf(c_1155,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f2769]) ).
tcf(c_1156,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f2771]) ).
tcf(c_1157,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ~ relation(X1)
| ~ in(sK355(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK355(X0,X1),sK356(X0,X1)),unordered_pair(sK355(X0,X1),sK355(X0,X1))),X1)
| ( sK355(X0,X1) != sK356(X0,X1) ) ),
inference(cnf_transformation,[],[f3273]) ).
tcf(c_1158,plain,
! [X0: $i,X1: $i] :
( in(sK355(X1,X0),X1)
| in(unordered_pair(unordered_pair(sK355(X1,X0),sK356(X1,X0)),unordered_pair(sK355(X1,X0),sK355(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3274]) ).
tcf(c_1159,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK355(X1,X0),sK356(X1,X0)),unordered_pair(sK355(X1,X0),sK355(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ( sK355(X1,X0) = sK356(X1,X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3275]) ).
tcf(c_1160,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3516]) ).
tcf(c_1161,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(identity_relation(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(cnf_transformation,[],[f3517]) ).
tcf(c_1162,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ relation(identity_relation(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(cnf_transformation,[],[f3518]) ).
tcf(c_1163,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2778]) ).
tcf(c_1165,plain,
! [X0: $i] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2779]) ).
tcf(c_1166,plain,
! [X0: $i] :
( empty(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2782]) ).
tcf(c_1167,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2781]) ).
tcf(c_1168,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2783]) ).
tcf(c_1169,plain,
! [X0: $i] :
( ( relation_inverse(X0) = function_inverse(X0) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2784]) ).
tcf(c_1170,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK357(X0,X1),sK358(X0,X1)),unordered_pair(sK357(X0,X1),sK357(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK358(X0,X1),sK357(X0,X1)),unordered_pair(sK358(X0,X1),sK358(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3279]) ).
tcf(c_1171,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK357(X0,X1),sK358(X0,X1)),unordered_pair(sK357(X0,X1),sK357(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK358(X0,X1),sK357(X0,X1)),unordered_pair(sK358(X0,X1),sK358(X0,X1))),X0)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3280]) ).
tcf(c_1172,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),relation_inverse(X2))
| ~ relation(X2)
| ~ relation(relation_inverse(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3519]) ).
tcf(c_1173,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2)
| ~ relation(X2)
| ~ relation(relation_inverse(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_inverse(X2)) ),
inference(cnf_transformation,[],[f3520]) ).
tcf(c_1174,plain,
! [X0: $i,X1: $i] :
( element(meet_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2789]) ).
tcf(c_1175,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2790]) ).
tcf(c_1176,plain,
! [X0: $i,X1: $i] :
( ( complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2791]) ).
tcf(c_1177,plain,
! [X0: $i,X1: $i] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2792]) ).
tcf(c_1178,plain,
! [X0: $i,X1: $i] :
( element(union_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2793]) ).
tcf(c_1179,plain,
! [X0: $i] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f2794]) ).
tcf(c_1180,plain,
! [X0: $i] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f2795]) ).
tcf(c_1181,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2797]) ).
tcf(c_1182,plain,
! [X0: $i] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2796]) ).
tcf(c_1183,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_isomorphism(X1,X2,X0)
| ~ sP41(X2,X1,X0)
| ~ sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f2799]) ).
tcf(c_1184,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP40(X2,X0,X1)
| ~ sP41(X1,X0,X2)
| ~ relation_isomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f2798]) ).
tcf(c_1196,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP41(X2,X0,X1)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2811]) ).
tcf(c_1197,plain,
relation(sK361),
inference(cnf_transformation,[],[f2814]) ).
tcf(c_1198,plain,
function(sK361),
inference(cnf_transformation,[],[f2813]) ).
tcf(c_1199,plain,
one_to_one(sK361),
inference(cnf_transformation,[],[f2812]) ).
tcf(c_1200,plain,
relation(sK362),
inference(cnf_transformation,[],[f2818]) ).
tcf(c_1201,plain,
function(sK362),
inference(cnf_transformation,[],[f2817]) ).
tcf(c_1202,plain,
one_to_one(sK362),
inference(cnf_transformation,[],[f2816]) ).
tcf(c_1203,plain,
empty(sK362),
inference(cnf_transformation,[],[f2815]) ).
tcf(c_1204,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( sK363(X0) != sK364(X0) ) ),
inference(cnf_transformation,[],[f2823]) ).
tcf(c_1205,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK363(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2822]) ).
tcf(c_1206,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK364(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2821]) ).
tcf(c_1207,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK363(X0)) = apply(X0,sK364(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2820]) ).
tcf(c_1208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| ( apply(X0,X1) != apply(X0,X2) ) ),
inference(cnf_transformation,[],[f2819]) ).
tcf(c_1209,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2824]) ).
tcf(c_1210,plain,
! [X0: $i,X1: $i] :
( well_orders(X0,X1)
| ~ relation(X0)
| ~ is_connected_in(X0,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ is_reflexive_in(X0,X1)
| ~ is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f2832]) ).
tcf(c_1211,plain,
! [X0: $i,X1: $i] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f2831]) ).
tcf(c_1212,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f2830]) ).
tcf(c_1213,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f2829]) ).
tcf(c_1214,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f2828]) ).
tcf(c_1215,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f2827]) ).
tcf(c_1216,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(cnf_transformation,[],[f3521]) ).
tcf(c_1217,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(cnf_transformation,[],[f3522]) ).
tcf(c_1218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(cnf_transformation,[],[f3524]) ).
tcf(c_1219,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(cnf_transformation,[],[f3525]) ).
tcf(c_1220,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(cnf_transformation,[],[f3526]) ).
tcf(c_1221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(cnf_transformation,[],[f3528]) ).
tcf(c_1253,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK369(X0),X0) ),
inference(cnf_transformation,[],[f2875]) ).
tcf(c_1254,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK370(X0),X0) ),
inference(cnf_transformation,[],[f2874]) ).
tcf(c_1255,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK369(X0),sK370(X0)) ),
inference(cnf_transformation,[],[f2873]) ).
tcf(c_1256,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK369(X0) != sK370(X0) ) ),
inference(cnf_transformation,[],[f2872]) ).
tcf(c_1257,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK370(X0),sK369(X0)) ),
inference(cnf_transformation,[],[f2871]) ).
tcf(c_1258,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X0,X2)
| ( X0 = X2 )
| ~ epsilon_connected(X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2870]) ).
tcf(c_1259,plain,
! [X0: $i] : element(sK371(X0),powerset(X0)),
inference(cnf_transformation,[],[f2885]) ).
tcf(c_1260,plain,
! [X0: $i] : empty(sK371(X0)),
inference(cnf_transformation,[],[f2884]) ).
tcf(c_1261,plain,
! [X0: $i] : relation(sK371(X0)),
inference(cnf_transformation,[],[f2883]) ).
tcf(c_1262,plain,
! [X0: $i] : function(sK371(X0)),
inference(cnf_transformation,[],[f2882]) ).
tcf(c_1263,plain,
! [X0: $i] : one_to_one(sK371(X0)),
inference(cnf_transformation,[],[f2881]) ).
tcf(c_1264,plain,
! [X0: $i] : epsilon_transitive(sK371(X0)),
inference(cnf_transformation,[],[f2880]) ).
tcf(c_1265,plain,
! [X0: $i] : epsilon_connected(sK371(X0)),
inference(cnf_transformation,[],[f2879]) ).
tcf(c_1266,plain,
! [X0: $i] : ordinal(sK371(X0)),
inference(cnf_transformation,[],[f2878]) ).
tcf(c_1268,plain,
! [X0: $i] : finite(sK371(X0)),
inference(cnf_transformation,[],[f2876]) ).
tcf(c_1269,plain,
~ empty(sK372),
inference(cnf_transformation,[],[f2890]) ).
tcf(c_1270,plain,
epsilon_transitive(sK372),
inference(cnf_transformation,[],[f2889]) ).
tcf(c_1271,plain,
epsilon_connected(sK372),
inference(cnf_transformation,[],[f2888]) ).
tcf(c_1272,plain,
ordinal(sK372),
inference(cnf_transformation,[],[f2887]) ).
tcf(c_1282,plain,
! [X0: $i,X1: $i] : relation_of2(sK373(X0,X1),X0,X1),
inference(cnf_transformation,[],[f2902]) ).
tcf(c_1283,plain,
! [X0: $i,X1: $i] : relation(sK373(X0,X1)),
inference(cnf_transformation,[],[f2901]) ).
tcf(c_1284,plain,
! [X0: $i,X1: $i] : function(sK373(X0,X1)),
inference(cnf_transformation,[],[f2900]) ).
tcf(c_1285,plain,
! [X0: $i,X1: $i] : relation_of2(sK374(X0,X1),X0,X1),
inference(cnf_transformation,[],[f2903]) ).
tcf(c_1286,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f2905]) ).
tcf(c_1287,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,cartesian_product2(X1,X2))
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f2904]) ).
tcf(c_1288,plain,
meet_semilatt_str(sK375),
inference(cnf_transformation,[],[f2906]) ).
tcf(c_1289,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f2907]) ).
tcf(c_1290,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| element(meet(X1,X2,X0),the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f2908]) ).
tcf(c_1291,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| element(join(X1,X2,X0),the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f2909]) ).
tcf(c_1292,plain,
! [X0: $i] :
( element(the_topology(X0),powerset(powerset(the_carrier(X0))))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f2910]) ).
tcf(c_1299,plain,
! [X0: $i] :
( topological_space(X0)
| ~ sP42(X0)
| ~ top_str(X0)
| ~ in(the_carrier(X0),the_topology(X0))
| ~ in(union_of_subsets(the_carrier(X0),sK378(X0)),the_topology(X0)) ),
inference(cnf_transformation,[],[f2922]) ).
tcf(c_1300,plain,
! [X0: $i] :
( topological_space(X0)
| subset(sK378(X0),the_topology(X0))
| ~ sP42(X0)
| ~ top_str(X0)
| ~ in(the_carrier(X0),the_topology(X0)) ),
inference(cnf_transformation,[],[f2921]) ).
tcf(c_1301,plain,
! [X0: $i] :
( topological_space(X0)
| element(sK378(X0),powerset(powerset(the_carrier(X0))))
| ~ sP42(X0)
| ~ top_str(X0)
| ~ in(the_carrier(X0),the_topology(X0)) ),
inference(cnf_transformation,[],[f2920]) ).
tcf(c_1302,plain,
! [X0: $i] :
( in(the_carrier(X0),the_topology(X0))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f2919]) ).
tcf(c_1303,plain,
! [X0: $i,X1: $i] :
( in(union_of_subsets(the_carrier(X1),X0),the_topology(X1))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ subset(X0,the_topology(X1))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f2918]) ).
tcf(c_1304,plain,
! [X0: $i] :
( sP42(X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f2917]) ).
tcf(c_1305,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| ~ relation(X0)
| ( sK379(X0,X1) != sK380(X0,X1) ) ),
inference(cnf_transformation,[],[f2928]) ).
tcf(c_1306,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(sK379(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2927]) ).
tcf(c_1307,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(sK380(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2926]) ).
tcf(c_1308,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK379(X0,X1),sK380(X0,X1)),unordered_pair(sK379(X0,X1),sK379(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3316]) ).
tcf(c_1309,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK380(X0,X1),sK379(X0,X1)),unordered_pair(sK380(X0,X1),sK380(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3317]) ).
tcf(c_1310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ~ relation(X2)
| ~ is_antisymmetric_in(X2,X3)
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3318]) ).
tcf(c_1311,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2930]) ).
tcf(c_1312,plain,
! [X0: $i] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2929]) ).
tcf(c_1313,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| in(sK381(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2936]) ).
tcf(c_1314,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| in(sK382(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2935]) ).
tcf(c_1315,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ( sK381(X0,X1) != sK382(X0,X1) ) ),
inference(cnf_transformation,[],[f2934]) ).
tcf(c_1316,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK381(X0,X1),sK382(X0,X1)),unordered_pair(sK381(X0,X1),sK381(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3319]) ).
tcf(c_1317,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK382(X0,X1),sK381(X0,X1)),unordered_pair(sK382(X0,X1),sK382(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3320]) ).
tcf(c_1318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X3)
| in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X3)
| ( X0 = X2 )
| ~ relation(X3)
| ~ is_connected_in(X3,X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3321]) ).
tcf(c_1319,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2938]) ).
tcf(c_1320,plain,
! [X0: $i] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2937]) ).
tcf(c_1321,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK383(X0,X1),sK385(X0,X1)),unordered_pair(sK383(X0,X1),sK383(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3322]) ).
tcf(c_1322,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(sK383(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2944]) ).
tcf(c_1323,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(sK384(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2943]) ).
tcf(c_1324,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(sK385(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2942]) ).
tcf(c_1325,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK383(X0,X1),sK384(X0,X1)),unordered_pair(sK383(X0,X1),sK383(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3323]) ).
tcf(c_1326,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK384(X0,X1),sK385(X0,X1)),unordered_pair(sK384(X0,X1),sK384(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3324]) ).
tcf(c_1327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2)
| ~ relation(X2)
| ~ is_transitive_in(X2,X4)
| ~ in(X3,X4)
| ~ in(X1,X4)
| ~ in(X0,X4)
| ~ in(unordered_pair(unordered_pair(X3,X0),unordered_pair(X3,X3)),X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3325]) ).
tcf(c_1328,plain,
! [X0: $i] :
( transitive(X0)
| ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2947]) ).
tcf(c_1329,plain,
! [X0: $i] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2946]) ).
tcf(c_1330,plain,
! [X0: $i] :
( reflexive(X0)
| ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2949]) ).
tcf(c_1331,plain,
! [X0: $i] :
( is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0)
| ~ reflexive(X0) ),
inference(cnf_transformation,[],[f2948]) ).
tcf(c_1332,plain,
! [X0: $i,X1: $i] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK386(X0,X1),sK386(X0,X1)),unordered_pair(sK386(X0,X1),sK386(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3326]) ).
tcf(c_1333,plain,
! [X0: $i,X1: $i] :
( is_reflexive_in(X0,X1)
| in(sK386(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2951]) ).
tcf(c_1334,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ is_reflexive_in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3327]) ).
tcf(c_1335,plain,
~ empty(sK387),
inference(cnf_transformation,[],[f2958]) ).
tcf(c_1341,plain,
empty(empty_set),
inference(cnf_transformation,[],[f2964]) ).
tcf(c_1414,plain,
( ordinal(empty_set)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_1085]) ).
tcf(c_2259,plain,
! [X0: $i] : relation_field(inclusion_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_1151,c_1146,c_1151]) ).
tcf(c_2268,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1209,c_793,c_779,c_1209]) ).
tcf(c_2285,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1034,c_1038]) ).
tcf(c_2287,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| in(apply(sK136(X1),X0),X0)
| in(sK135(X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_366,c_781,c_366]) ).
tcf(c_2288,plain,
! [X0: $i,X1: $i] :
( in(sK135(X1),X1)
| in(apply(sK136(X1),X0),X0)
| ~ in(X0,X1) ),
inference(renaming,[status(thm)],[c_2287]) ).
tcf(c_2291,plain,
! [X0: $i] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(global_subsumption_just,[status(thm)],[c_427,c_885,c_427]) ).
tcf(c_2294,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_390,c_349,c_390]) ).
tcf(c_2296,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ( sK135(X1) = empty_set )
| in(apply(sK136(X1),X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_370,c_781,c_370]) ).
tcf(c_2297,plain,
! [X0: $i,X1: $i] :
( in(apply(sK136(X1),X0),X0)
| ( sK135(X1) = empty_set )
| ~ in(X0,X1) ),
inference(renaming,[status(thm)],[c_2296]) ).
tcf(c_2306,plain,
! [X0: $i,X1: $i] :
( in(set_union2(X0,unordered_pair(X0,X0)),X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_424,c_349,c_424]) ).
tcf(c_2310,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP16(X0,X1,X2,function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_479,c_1182,c_1181,c_479]) ).
tcf(c_2315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2_as_subset(X0,X1,X3)
| ~ subset(X2,X3)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_538,c_313]) ).
tcf(c_2319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X0,X1)
| ~ in(X2,X0)
| ~ relation(X3)
| in(sK162(X3,X2,X0),X0)
| in(X2,sK161(X1,X3))
| sP18(X1,X3) ),
inference(global_subsumption_just,[status(thm)],[c_558,c_781,c_558]) ).
tcf(c_2320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP18(X1,X3)
| in(X2,sK161(X1,X3))
| in(sK162(X3,X2,X0),X0)
| ~ relation(X3)
| ~ in(X2,X0)
| ~ in(X0,X1) ),
inference(renaming,[status(thm)],[c_2319]) ).
tcf(c_2325,plain,
! [X0: $i,X1: $i] : pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1,
inference(global_subsumption_just,[status(thm)],[c_1221,c_516]) ).
tcf(c_2327,plain,
! [X0: $i,X1: $i] : pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0,
inference(global_subsumption_just,[status(thm)],[c_1218,c_515]) ).
tcf(c_2335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK224(X4,X1,X0),X0)
| sP25(X3,X2,unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)
| ~ in(X1,X0)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_730,c_270,c_730]) ).
tcf(c_2337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( empty(X2)
| in(sK79(X4,X1,X0),X0)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK78(X2,X4,X3))
| ~ relation(X4)
| ~ in(X1,X0)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_161,c_270,c_161]) ).
tcf(c_2353,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_658]) ).
tcf(c_2357,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_994]) ).
tcf(c_2427,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_767]) ).
tcf(c_2439,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_651]) ).
tcf(c_2447,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_1168]) ).
tcf(c_2459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(prop_impl_just,[status(thm)],[c_270]) ).
tcf(c_2460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(renaming,[status(thm)],[c_2459]) ).
tcf(c_2481,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_781]) ).
tcf(c_2483,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_701]) ).
tcf(c_2509,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_658,c_1046]) ).
tcf(c_2511,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_658,c_1047]) ).
tcf(c_2513,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_658,c_1053]) ).
tcf(c_2515,plain,
! [X0: $i,X1: $i] :
( ~ in(sK52(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_659,c_86]) ).
tcf(c_2516,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK52(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_2515]) ).
tcf(c_2517,plain,
! [X0: $i,X1: $i] :
( in(sK52(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_659,c_87]) ).
tcf(c_2518,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK52(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_2517]) ).
tcf(c_2605,plain,
! [X0: $i] :
( sP10(X0)
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_186]) ).
tcf(c_2639,plain,
( sP5(sK66)
| ~ sP8 ),
inference(prop_impl_just,[status(thm)],[c_125]) ).
tcf(c_2655,plain,
( sP4(sK70)
| ~ sP6 ),
inference(prop_impl_just,[status(thm)],[c_137]) ).
tcf(c_2669,plain,
! [X0: $i,X1: $i] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(prop_impl_just,[status(thm)],[c_1177]) ).
tcf(c_2673,plain,
! [X0: $i] :
( ( sK72(X0) != empty_set )
| ~ sP5(X0) ),
inference(prop_impl_just,[status(thm)],[c_143]) ).
tcf(c_2674,plain,
! [X0: $i] :
( ~ sP5(X0)
| ( sK72(X0) != empty_set ) ),
inference(renaming,[status(thm)],[c_2673]) ).
tcf(c_2675,plain,
! [X0: $i] :
( element(sK72(X0),powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ sP5(X0) ),
inference(prop_impl_just,[status(thm)],[c_147]) ).
tcf(c_2687,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK178(X0),sK179(X0)),unordered_pair(sK178(X0),sK178(X0))),X0)
| function(X0) ),
inference(prop_impl_just,[status(thm)],[c_584]) ).
tcf(c_2688,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK178(X0),sK179(X0)),unordered_pair(sK178(X0),sK178(X0))),X0) ),
inference(renaming,[status(thm)],[c_2687]) ).
tcf(c_2689,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK178(X0),sK180(X0)),unordered_pair(sK178(X0),sK178(X0))),X0)
| function(X0) ),
inference(prop_impl_just,[status(thm)],[c_585]) ).
tcf(c_2690,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK178(X0),sK180(X0)),unordered_pair(sK178(X0),sK178(X0))),X0) ),
inference(renaming,[status(thm)],[c_2689]) ).
tcf(c_2695,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK84(X1,X0),sK85(X1,X0)),unordered_pair(sK84(X1,X0),sK84(X1,X0))) = X0 )
| ~ in(X0,sK83(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_170]) ).
tcf(c_2705,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK241(X1,X2,X0),sK242(X1,X2,X0)),unordered_pair(sK241(X1,X2,X0),sK241(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_763]) ).
tcf(c_2717,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_902]) ).
tcf(c_2719,plain,
! [X0: $i] :
( element(the_topology(X0),powerset(powerset(the_carrier(X0))))
| ~ top_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_1292]) ).
tcf(c_2761,plain,
( sP14(sK117)
| ~ sP15 ),
inference(prop_impl_just,[status(thm)],[c_244]) ).
tcf(c_2775,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ~ one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_935]) ).
tcf(c_2781,plain,
! [X0: $i] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_993]) ).
tcf(c_2782,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(renaming,[status(thm)],[c_2781]) ).
tcf(c_2783,plain,
! [X0: $i] :
( ~ meet_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_1289]) ).
tcf(c_2784,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ meet_semilatt_str(X0) ),
inference(renaming,[status(thm)],[c_2783]) ).
tcf(c_2903,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK185(X0),sK186(X0)),unordered_pair(sK185(X0),sK185(X0))) = sK183(X0) )
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_602]) ).
tcf(c_2911,plain,
! [X0: $i] :
( sP19(sK184(X0),X0)
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_606]) ).
tcf(c_3025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK226(X1,X2,X3),sK227(X1,X2,X3)),unordered_pair(sK226(X1,X2,X3),sK226(X1,X2,X3))) = X2 )
| ~ sP25(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_733]) ).
tcf(c_3033,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK229(X0,X1,X2),sK230(X0,X1,X2)),unordered_pair(sK229(X0,X1,X2),sK229(X0,X1,X2))) = X0 )
| ~ sP24(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_738]) ).
tcf(c_3053,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation_of2(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_994,c_754]) ).
tcf(c_3054,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_3053]) ).
tcf(c_3103,plain,
! [X0: $i] :
( sP31(sK273(X0),X0)
| ~ sP32(X0) ),
inference(prop_impl_just,[status(thm)],[c_860]) ).
tcf(c_3157,plain,
! [X0: $i,X1: $i] :
( sP35(X0,sK299(X0,X1),X1)
| ~ sP36(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_919]) ).
tcf(c_3183,plain,
! [X0: $i] :
( ~ latt_str(X0)
| join_semilatt_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_1120]) ).
tcf(c_3184,plain,
! [X0: $i] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(renaming,[status(thm)],[c_3183]) ).
tcf(c_3185,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_994,c_285]) ).
tcf(c_3187,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(X0),X2)
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_994,c_286]) ).
tcf(c_3201,plain,
! [X0: $i,X1: $i] :
( equipotent(X1,X0)
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_1002,c_671]) ).
tcf(c_3203,plain,
! [X0: $i,X1: $i] :
( relation(sK204(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_1002,c_674]) ).
tcf(c_3205,plain,
! [X0: $i,X1: $i] :
( function(sK204(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_1002,c_675]) ).
tcf(c_3207,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK204(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_1002,c_676]) ).
tcf(c_3209,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK204(X0,X1)) = X0 )
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_1002,c_677]) ).
tcf(c_3211,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK204(X0,X1)) = X1 )
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_1002,c_678]) ).
tcf(c_3239,plain,
! [X0: $i] :
( meet_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_1119]) ).
tcf(c_3243,plain,
! [X0: $i,X1: $i] :
( sP38(X0,X1,topstr_closure(X0,X1))
| ~ sP39(topstr_closure(X0,X1),X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_1133]) ).
tcf(c_3255,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(prop_impl_just,[status(thm)],[c_1216]) ).
tcf(c_3257,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(prop_impl_just,[status(thm)],[c_1219]) ).
tcf(c_3923,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) )
| ( pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 ) ),
inference(prop_impl_just,[status(thm)],[c_1220]) ).
tcf(c_3924,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(renaming,[status(thm)],[c_3923]) ).
tcf(c_3927,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) )
| ( pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 ) ),
inference(prop_impl_just,[status(thm)],[c_1217]) ).
tcf(c_3928,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(renaming,[status(thm)],[c_3927]) ).
tcf(c_5689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2_as_subset(X0,X1,X3)
| ~ subset(relation_rng(X0),X3)
| ~ relation_of2(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_304,c_2357]) ).
tcf(c_5690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2_as_subset(X0,X1,X3)
| ~ subset(X2,X3)
| ~ relation_of2(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_2315,c_2357]) ).
tcf(c_5691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = empty_set )
| ( apply(relation_composition(X0,X4),X3) = apply(X4,apply(X0,X3)) )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ in(X3,X1)
| ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_338,c_2357]) ).
tcf(c_5692,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK131(X1,X0),X1)
| ( relation_dom_as_subset(X1,X2,X0) = X1 )
| ~ relation_of2(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_345,c_2357]) ).
tcf(c_5693,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK133(X2,X0),X2)
| ( relation_rng_as_subset(X1,X2,X0) = X2 )
| ~ relation_of2(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_351,c_2357]) ).
tcf(c_5694,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ subset(X0,X1)
| ~ element(X2,powerset(X1))
| ~ subset(X0,subset_complement(X1,X2)) ),
inference(bin_hyper_res,[status(thm)],[c_428,c_2353]) ).
tcf(c_5695,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,subset_complement(X1,X2))
| ~ subset(X2,X1)
| ~ disjoint(X0,X2)
| ~ element(X0,powerset(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_429,c_2353]) ).
tcf(c_5696,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X2,subset_complement(X1,X0))
| ( X1 = empty_set )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_460,c_2353]) ).
tcf(c_5697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,X3),relation_rng(X0))
| ( X2 = empty_set )
| ~ function(X0)
| ~ in(X3,X1)
| ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_505,c_2357]) ).
tcf(c_5698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( quasi_total(X0,X1,X3)
| ( X2 = empty_set )
| ~ function(X0)
| ~ subset(X2,X3)
| ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_537,c_2357]) ).
tcf(c_5699,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_694,c_2353]) ).
tcf(c_5700,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_695,c_2353]) ).
tcf(c_5702,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X2)) = subset_intersection2(X1,X0,X2) )
| ~ subset(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_1028,c_2353]) ).
tcf(c_5703,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_intersection2(X1,X0,X0) = X0 )
| ~ subset(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_1029,c_2353]) ).
tcf(c_5704,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subset_intersection2(X1,X0,X2),powerset(X1))
| ~ subset(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_1030,c_2353]) ).
tcf(c_5705,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_intersection2(X1,X2,X0) = subset_intersection2(X1,X0,X2) )
| ~ subset(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_1031,c_2353]) ).
tcf(c_5706,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_difference(X1,X0,X2) = set_difference(X0,X2) )
| ~ subset(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_1054,c_2353]) ).
tcf(c_5707,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subset_difference(X1,X0,X2),powerset(X1))
| ~ subset(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(bin_hyper_res,[status(thm)],[c_1055,c_2353]) ).
tcf(c_5708,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = empty_set )
| ( relation_dom_as_subset(X1,X2,X0) = X1 )
| ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_1113,c_2357]) ).
tcf(c_5895,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| ~ in(X1,X2)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),inclusion_relation(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1153,c_1146]) ).
tcf(c_5896,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),inclusion_relation(X1))
| ~ subset(X0,X2)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1152,c_1146]) ).
tcf(c_5899,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1162,c_1154]) ).
tcf(c_5900,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1161,c_1154]) ).
tcf(c_5901,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1160,c_1154]) ).
tcf(c_6192,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_inverse(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1173,c_2447]) ).
tcf(c_6193,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),relation_inverse(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1172,c_2447]) ).
tcf(c_6336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_772,c_2427]) ).
tcf(c_6337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_773,c_2427]) ).
tcf(c_6338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_dom_restriction(X2,X3))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_771,c_2427]) ).
tcf(c_6345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_656,c_2439]) ).
tcf(c_6346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_657,c_2439]) ).
tcf(c_6347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_rng_restriction(X3,X2))
| ~ relation(X2)
| ~ in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_655,c_2439]) ).
tcf(c_6358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),sK78(X3,X1,X4))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),cartesian_product2(X3,X4))
| ~ in(unordered_pair(unordered_pair(X0,sK79(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_160,c_2481]) ).
tcf(c_6359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP18(X3,X1)
| in(X0,sK161(X3,X1))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,sK162(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_557,c_2481]) ).
tcf(c_6364,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK91(X1,X2))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ closed_subset(X0,X1)
| ~ subset(X2,X0)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,powerset(the_carrier(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_187,c_2483]) ).
tcf(c_6365,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X1,X2)
| in(X0,sK302(X1,X2))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ closed_subset(X0,X1)
| ~ subset(X2,X0)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,powerset(the_carrier(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_924,c_2483]) ).
tcf(c_7414,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X1,X0),X2)
| ~ element(X0,powerset(X1))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1052,c_2669]) ).
tcf(c_7415,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,complements_of_subsets(X0,X2))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(powerset(X0)))
| ~ in(subset_complement(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1051,c_2669]) ).
tcf(c_7522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP25(X4,X3,unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),cartesian_product2(X3,X4))
| ~ in(unordered_pair(unordered_pair(X0,sK224(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_729,c_2460]) ).
tcf(c_7523,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK189(X1,X2))
| ~ in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),cartesian_product2(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_610,c_2460]) ).
tcf(c_7524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),sK78(X3,X1,X4))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),cartesian_product2(X3,X4))
| ~ in(unordered_pair(unordered_pair(X0,sK79(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6358,c_2460]) ).
tcf(c_7525,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK83(X1,X2))
| ~ in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),cartesian_product2(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_168,c_2460]) ).
tcf(c_7860,plain,
! [X0: $i,X1: $i] :
( in(apply(function_inverse(X1),X0),relation_dom(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(function_inverse(X1))
| ~ in(X0,relation_rng(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_477,c_1181]) ).
tcf(c_7868,plain,
! [X0: $i,X1: $i] :
( in(apply(function_inverse(X1),X0),relation_dom(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_7860,c_1182]) ).
tcf(c_8248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,sK334(X2,X3,X0,X1)),unordered_pair(X0,X0)),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1043,c_2285]) ).
tcf(c_8249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK334(X2,X3,X0,X1),X1),unordered_pair(sK334(X2,X3,X0,X1),sK334(X2,X3,X0,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1044,c_2285]) ).
tcf(c_8250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X0,X3),unordered_pair(X0,X0)),relation_composition(X2,X4))
| ~ relation(X4)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1042,c_2285]) ).
tcf(c_13308,plain,
! [X0: $i] : element(X0,powerset(X0)),
inference(light_normalisation,[status(thm)],[c_1179,c_1180]) ).
tcf(c_13761,plain,
! [X0: $i] : set_difference(X0,X0) = empty_set,
inference(light_normalisation,[status(thm)],[c_971,c_680]) ).
tcf(c_16098,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK178(X0),sK178(X0)),unordered_pair(sK178(X0),sK180(X0))),X0) ),
inference(demodulation,[status(thm)],[c_2690,c_967]) ).
tcf(c_16105,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK178(X0),sK178(X0)),unordered_pair(sK178(X0),sK179(X0))),X0) ),
inference(demodulation,[status(thm)],[c_2688,c_967]) ).
tcf(c_16798,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK185(X0),sK185(X0)),unordered_pair(sK185(X0),sK186(X0))) = sK183(X0) )
| ~ sP20(X0) ),
inference(demodulation,[status(thm)],[c_2903,c_967]) ).
tcf(c_16877,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK48(X0),sK49(X0)),unordered_pair(sK49(X0),sK49(X0))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_70,c_967]) ).
tcf(c_16887,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK48(X0),sK48(X0)),unordered_pair(sK48(X0),sK49(X0))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_69,c_967]) ).
tcf(c_16897,plain,
! [X0: $i] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK45(X0),sK45(X0)),unordered_pair(sK45(X0),sK46(X0))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_59,c_967]) ).
tcf(c_16907,plain,
! [X0: $i] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK44(X0),sK44(X0)),unordered_pair(sK44(X0),sK45(X0))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_58,c_967]) ).
tcf(c_17021,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK170(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_572,c_967]) ).
tcf(c_17075,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sK61(X1))
| ~ sP3(X1)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_113,c_967]) ).
tcf(c_17091,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK50(X0),sK51(X0)),unordered_pair(sK51(X0),sK51(X0))),X0) ),
inference(demodulation,[status(thm)],[c_77,c_967]) ).
tcf(c_17101,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK50(X0),sK50(X0)),unordered_pair(sK50(X0),sK51(X0))),X0) ),
inference(demodulation,[status(thm)],[c_76,c_967]) ).
tcf(c_17111,plain,
! [X0: $i] :
( transitive(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK44(X0),sK44(X0)),unordered_pair(sK44(X0),sK46(X0))),X0) ),
inference(demodulation,[status(thm)],[c_57,c_967]) ).
tcf(c_17273,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK151(X0),sK151(X0)),unordered_pair(sK151(X0),sK152(X0))),X0)
| ( X0 = empty_set )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_484,c_967]) ).
tcf(c_17427,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK329(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_1020,c_967]) ).
tcf(c_17489,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK176(X0),sK176(X0)),unordered_pair(sK176(X0),sK177(X0))) = X0 )
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_582,c_967]) ).
tcf(c_17545,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK128(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_310,c_967]) ).
tcf(c_17752,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,apply(X1,X0))),X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_525,c_967]) ).
tcf(c_17921,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK384(X0,X1),sK384(X0,X1)),unordered_pair(sK384(X0,X1),sK385(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1326,c_967]) ).
tcf(c_17931,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK383(X0,X1),sK383(X0,X1)),unordered_pair(sK383(X0,X1),sK384(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1325,c_967]) ).
tcf(c_17941,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK379(X0,X1),sK380(X0,X1)),unordered_pair(sK380(X0,X1),sK380(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1309,c_967]) ).
tcf(c_17951,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK379(X0,X1),sK379(X0,X1)),unordered_pair(sK379(X0,X1),sK380(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1308,c_967]) ).
tcf(c_18001,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK167(X1,X0)),unordered_pair(sK167(X1,X0),sK167(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(demodulation,[status(thm)],[c_568,c_967]) ).
tcf(c_18131,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK383(X0,X1),sK383(X0,X1)),unordered_pair(sK383(X0,X1),sK385(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_1321,c_967]) ).
tcf(c_18141,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK381(X0,X1),sK382(X0,X1)),unordered_pair(sK382(X0,X1),sK382(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_1317,c_967]) ).
tcf(c_18151,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK381(X0,X1),sK381(X0,X1)),unordered_pair(sK381(X0,X1),sK382(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_1316,c_967]) ).
tcf(c_18161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(light_normalisation,[status(thm)],[c_3257,c_2325]) ).
tcf(c_18168,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(light_normalisation,[status(thm)],[c_3255,c_2327]) ).
tcf(c_18249,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( subset_difference(X1,X1,meet_of_subsets(X1,X0)) = union_of_subsets(X1,complements_of_subsets(X1,X0)) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(demodulation,[status(thm)],[c_455,c_1180]) ).
tcf(c_18259,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( subset_difference(X1,X1,union_of_subsets(X1,X0)) = meet_of_subsets(X1,complements_of_subsets(X1,X0)) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(demodulation,[status(thm)],[c_453,c_1180]) ).
tcf(c_18325,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK84(X1,X0),sK84(X1,X0)),unordered_pair(sK84(X1,X0),sK85(X1,X0))) = X0 )
| ~ in(X0,sK83(X1,X2)) ),
inference(demodulation,[status(thm)],[c_2695,c_967]) ).
tcf(c_18642,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| ( unordered_pair(unordered_pair(sK191(X1,X0),sK191(X1,X0)),unordered_pair(sK191(X1,X0),sK192(X1,X0))) = X0 )
| ~ in(X0,sK189(X1,X2)) ),
inference(demodulation,[status(thm)],[c_613,c_967]) ).
tcf(c_18652,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK171(X0,X1),sK171(X0,X1)),unordered_pair(sK171(X0,X1),sK172(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_574,c_967]) ).
tcf(c_18725,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sK83(X1,X2))
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),cartesian_product2(X1,X2)) ),
inference(demodulation,[status(thm)],[c_7525,c_967]) ).
tcf(c_18768,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK313(X1,X2,X0)),unordered_pair(sK313(X1,X2,X0),sK313(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_950,c_967]) ).
tcf(c_18797,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK229(X0,X1,X2),sK229(X0,X1,X2)),unordered_pair(sK229(X0,X1,X2),sK230(X0,X1,X2))) = X0 )
| ~ sP24(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_3033,c_967]) ).
tcf(c_18824,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK171(X0,X1),sK171(X0,X1)),unordered_pair(sK171(X0,X1),sK172(X0,X1))),X1) ),
inference(demodulation,[status(thm)],[c_573,c_967]) ).
tcf(c_18883,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK127(X0,X2,X1)),unordered_pair(sK127(X0,X2,X1),sK127(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_296,c_967]) ).
tcf(c_19031,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK241(X1,X2,X0),sK241(X1,X2,X0)),unordered_pair(sK241(X1,X2,X0),sK242(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(demodulation,[status(thm)],[c_2705,c_967]) ).
tcf(c_19038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK226(X1,X2,X3),sK226(X1,X2,X3)),unordered_pair(sK226(X1,X2,X3),sK227(X1,X2,X3))) = X2 )
| ~ sP25(X0,X1,X2,X3) ),
inference(demodulation,[status(thm)],[c_3025,c_967]) ).
tcf(c_19075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,sK130(X2,X3))),X2)
| ~ in(X3,X0)
| ~ relation_of2_as_subset(X2,X0,X1)
| ( relation_dom_as_subset(X0,X1,X2) != X0 ) ),
inference(demodulation,[status(thm)],[c_344,c_967]) ).
tcf(c_19098,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sK189(X1,X2))
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),cartesian_product2(X1,X2)) ),
inference(demodulation,[status(thm)],[c_7523,c_967]) ).
tcf(c_19230,plain,
! [X0: $i,X1: $i] :
( in(sK355(X1,X0),X1)
| in(unordered_pair(unordered_pair(sK355(X1,X0),sK355(X1,X0)),unordered_pair(sK355(X1,X0),sK356(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1158,c_967]) ).
tcf(c_19277,plain,
! [X0: $i,X1: $i] :
( in(sK168(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK168(X0,X1),sK168(X0,X1)),unordered_pair(sK168(X0,X1),sK169(X0,X1))),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_570,c_967]) ).
tcf(c_19298,plain,
! [X0: $i,X1: $i] :
( in(sK165(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK165(X0,X1),sK166(X0,X1)),unordered_pair(sK166(X0,X1),sK166(X0,X1))),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_566,c_967]) ).
tcf(c_19381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK334(X2,X3,X0,X1))),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(demodulation,[status(thm)],[c_8248,c_967]) ).
tcf(c_19534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP18(X3,X1)
| in(X0,sK161(X3,X1))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK162(X1,X0,X2))),X1) ),
inference(demodulation,[status(thm)],[c_6359,c_967]) ).
tcf(c_19625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X3,sK132(X2,X3)),unordered_pair(sK132(X2,X3),sK132(X2,X3))),X2)
| ~ in(X3,X1)
| ~ relation_of2_as_subset(X2,X0,X1)
| ( relation_rng_as_subset(X0,X1,X2) != X1 ) ),
inference(demodulation,[status(thm)],[c_350,c_967]) ).
tcf(c_19666,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| sP11(X2,X1)
| sP12(X2,X1)
| ~ relation(X1)
| ~ in(X0,sK110(X2,X1))
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK111(X1,X0,sK110(X2,X1)))),X1) ),
inference(demodulation,[status(thm)],[c_230,c_967]) ).
tcf(c_19705,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK355(X1,X0),sK355(X1,X0)),unordered_pair(sK355(X1,X0),sK356(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ( sK355(X1,X0) = sK356(X1,X0) )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1159,c_967]) ).
tcf(c_19718,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK345(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(X1,sK345(X0,X1,X2)),unordered_pair(sK345(X0,X1,X2),sK345(X0,X1,X2))),X0)
| ( fiber(X0,X1) = X2 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1104,c_967]) ).
tcf(c_19849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| ( unordered_pair(unordered_pair(sK80(X1,X2,X0),sK80(X1,X2,X0)),unordered_pair(sK80(X1,X2,X0),sK81(X1,X2,X0))) = X0 )
| ~ relation(X2)
| ~ in(X0,sK78(X1,X2,X3)) ),
inference(demodulation,[status(thm)],[c_163,c_967]) ).
tcf(c_19902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X4)
| ~ in(X2,X3)
| ~ in(X0,X2)
| ~ sP1(X3,X1,X4)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK57(X1,X0,X2))),X1) ),
inference(demodulation,[status(thm)],[c_98,c_967]) ).
tcf(c_19940,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK327(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK327(X0,X1,X2),sK327(X0,X1,X2)),unordered_pair(sK327(X0,X1,X2),sK328(X0,X1,X2))),X0)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1017,c_967]) ).
tcf(c_19953,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK311(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK311(X0,X1,X2),sK312(X0,X1,X2)),unordered_pair(sK312(X0,X1,X2),sK312(X0,X1,X2))),X0)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_947,c_967]) ).
tcf(c_20012,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK238(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK239(X0,X1,X2),sK239(X0,X1,X2)),unordered_pair(sK239(X0,X1,X2),sK240(X0,X1,X2))) = sK238(X0,X1,X2) ) ),
inference(demodulation,[status(thm)],[c_759,c_967]) ).
tcf(c_20110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK97(X2,X3,X0),sK97(X2,X3,X0)),unordered_pair(sK97(X2,X3,X0),sK98(X2,X3,X0))) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK96(X1,X2,X3)) ),
inference(demodulation,[status(thm)],[c_202,c_967]) ).
tcf(c_20140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X1,sK334(X2,X3,X0,X1)),unordered_pair(sK334(X2,X3,X0,X1),sK334(X2,X3,X0,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(X2,X3)) ),
inference(demodulation,[status(thm)],[c_8249,c_967]) ).
tcf(c_20195,plain,
! [X0: $i] :
( subset(sK353(relation_field(X0),X0),sK354(relation_field(X0),X0))
| in(unordered_pair(unordered_pair(sK353(relation_field(X0),X0),sK353(relation_field(X0),X0)),unordered_pair(sK353(relation_field(X0),X0),sK354(relation_field(X0),X0))),X0)
| ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1148,c_967]) ).
tcf(c_20218,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK243(X0,X2,X1),X2)
| in(unordered_pair(unordered_pair(sK243(X0,X2,X1),sK243(X0,X2,X1)),unordered_pair(sK243(X0,X2,X1),sK244(X0,X2,X1))),X1)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_769,c_967]) ).
tcf(c_20234,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK201(X2,X1,X0),X2)
| in(unordered_pair(unordered_pair(sK200(X2,X1,X0),sK200(X2,X1,X0)),unordered_pair(sK200(X2,X1,X0),sK201(X2,X1,X0))),X0)
| ( relation_rng_restriction(X2,X1) = X0 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_653,c_967]) ).
tcf(c_20260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP25(X4,X3,unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),cartesian_product2(X3,X4))
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK224(X1,X0,X2))),X1) ),
inference(demodulation,[status(thm)],[c_7522,c_967]) ).
tcf(c_20273,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ~ relation(X1)
| ~ in(sK355(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK355(X0,X1),sK355(X0,X1)),unordered_pair(sK355(X0,X1),sK356(X0,X1))),X1)
| ( sK355(X0,X1) != sK356(X0,X1) ) ),
inference(demodulation,[status(thm)],[c_1157,c_967]) ).
tcf(c_20289,plain,
! [X0: $i] :
( ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0)
| ~ subset(sK353(relation_field(X0),X0),sK354(relation_field(X0),X0))
| ~ in(unordered_pair(unordered_pair(sK353(relation_field(X0),X0),sK353(relation_field(X0),X0)),unordered_pair(sK353(relation_field(X0),X0),sK354(relation_field(X0),X0))),X0) ),
inference(demodulation,[status(thm)],[c_1147,c_967]) ).
tcf(c_20302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP22(X2,X3)
| ( unordered_pair(unordered_pair(sK221(X2,X3,X0),sK221(X2,X3,X0)),unordered_pair(sK221(X2,X3,X0),sK222(X2,X3,X0))) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK219(X1,X2,X3)) ),
inference(demodulation,[status(thm)],[c_725,c_967]) ).
tcf(c_20331,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( fiber(X1,X0) = X2 )
| ( sK345(X1,X0,X2) = X0 )
| ~ relation(X1)
| ~ in(sK345(X1,X0,X2),X2)
| ~ in(unordered_pair(unordered_pair(X0,sK345(X1,X0,X2)),unordered_pair(sK345(X1,X0,X2),sK345(X1,X0,X2))),X1) ),
inference(demodulation,[status(thm)],[c_1102,c_967]) ).
tcf(c_20379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),sK78(X3,X1,X4))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),cartesian_product2(X3,X4))
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK79(X1,X0,X2))),X1) ),
inference(demodulation,[status(thm)],[c_7524,c_967]) ).
tcf(c_20395,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK173(X0,X1),sK173(X0,X1)),unordered_pair(sK173(X0,X1),sK174(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK173(X0,X1),sK173(X0,X1)),unordered_pair(sK173(X0,X1),sK174(X0,X1))),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_577,c_967]) ).
tcf(c_20411,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK358(X0,X1),sK357(X0,X1)),unordered_pair(sK357(X0,X1),sK357(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK358(X0,X1),sK358(X0,X1)),unordered_pair(sK358(X0,X1),sK357(X0,X1))),X0)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1171,c_967]) ).
tcf(c_20427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(apply(X3,sK97(X2,X3,X0)),apply(X3,sK97(X2,X3,X0))),unordered_pair(apply(X3,sK97(X2,X3,X0)),apply(X3,sK98(X2,X3,X0)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK96(X1,X2,X3)) ),
inference(demodulation,[status(thm)],[c_203,c_967]) ).
tcf(c_20443,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK173(X0,X1),sK173(X0,X1)),unordered_pair(sK173(X0,X1),sK174(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK173(X0,X1),sK173(X0,X1)),unordered_pair(sK173(X0,X1),sK174(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_576,c_967]) ).
tcf(c_20459,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK358(X0,X1),sK357(X0,X1)),unordered_pair(sK357(X0,X1),sK357(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK358(X0,X1),sK358(X0,X1)),unordered_pair(sK358(X0,X1),sK357(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_1170,c_967]) ).
tcf(c_20523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP22(X2,X3)
| in(unordered_pair(unordered_pair(apply(X3,sK221(X2,X3,X0)),apply(X3,sK221(X2,X3,X0))),unordered_pair(apply(X3,sK221(X2,X3,X0)),apply(X3,sK222(X2,X3,X0)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK219(X1,X2,X3)) ),
inference(demodulation,[status(thm)],[c_726,c_967]) ).
tcf(c_20592,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK243(X0,X2,X1),sK243(X0,X2,X1)),unordered_pair(sK243(X0,X2,X1),sK244(X0,X2,X1))),X1)
| in(unordered_pair(unordered_pair(sK243(X0,X2,X1),sK243(X0,X2,X1)),unordered_pair(sK243(X0,X2,X1),sK244(X0,X2,X1))),X0)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_770,c_967]) ).
tcf(c_20622,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK200(X2,X1,X0),sK200(X2,X1,X0)),unordered_pair(sK200(X2,X1,X0),sK201(X2,X1,X0))),X1)
| in(unordered_pair(unordered_pair(sK200(X2,X1,X0),sK200(X2,X1,X0)),unordered_pair(sK200(X2,X1,X0),sK201(X2,X1,X0))),X0)
| ( relation_rng_restriction(X2,X1) = X0 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_654,c_967]) ).
tcf(c_20658,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK332(X0,X2,X1),sK333(X0,X2,X1)),unordered_pair(sK333(X0,X2,X1),sK333(X0,X2,X1))),X2)
| in(unordered_pair(unordered_pair(sK331(X0,X2,X1),sK331(X0,X2,X1)),unordered_pair(sK331(X0,X2,X1),sK332(X0,X2,X1))),X1)
| ( relation_composition(X0,X2) = X1 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1041,c_967]) ).
tcf(c_20677,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK331(X0,X2,X1),sK331(X0,X2,X1)),unordered_pair(sK331(X0,X2,X1),sK333(X0,X2,X1))),X0)
| in(unordered_pair(unordered_pair(sK331(X0,X2,X1),sK331(X0,X2,X1)),unordered_pair(sK331(X0,X2,X1),sK332(X0,X2,X1))),X1)
| ( relation_composition(X0,X2) = X1 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1040,c_967]) ).
tcf(c_20696,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(light_normalisation,[status(thm)],[c_3924,c_2325]) ).
tcf(c_20697,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(demodulation,[status(thm)],[c_20696,c_967]) ).
tcf(c_20704,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(light_normalisation,[status(thm)],[c_3928,c_2327]) ).
tcf(c_20705,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(demodulation,[status(thm)],[c_20704,c_967]) ).
tcf(c_20712,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK243(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK243(X0,X1,X2),sK243(X0,X1,X2)),unordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK243(X0,X1,X2),sK243(X0,X1,X2)),unordered_pair(sK243(X0,X1,X2),sK244(X0,X1,X2))),X0) ),
inference(demodulation,[status(thm)],[c_768,c_967]) ).
tcf(c_20731,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ in(sK201(X0,X1,X2),X0)
| ~ in(unordered_pair(unordered_pair(sK200(X0,X1,X2),sK200(X0,X1,X2)),unordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK200(X0,X1,X2),sK200(X0,X1,X2)),unordered_pair(sK200(X0,X1,X2),sK201(X0,X1,X2))),X1) ),
inference(demodulation,[status(thm)],[c_652,c_967]) ).
tcf(c_20750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_composition(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X3,sK332(X0,X1,X2)),unordered_pair(X3,X3)),X1)
| ~ in(unordered_pair(unordered_pair(sK331(X0,X1,X2),X3),unordered_pair(sK331(X0,X1,X2),sK331(X0,X1,X2))),X0)
| ~ in(unordered_pair(unordered_pair(sK331(X0,X1,X2),sK331(X0,X1,X2)),unordered_pair(sK331(X0,X1,X2),sK332(X0,X1,X2))),X2) ),
inference(demodulation,[status(thm)],[c_1039,c_967]) ).
tcf(c_20998,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK86(X1))
| ~ ordinal(X0)
| ~ sP9(X1,X2)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2605,c_173]) ).
tcf(c_20999,plain,
! [X0: $i,X1: $i] :
( in(X1,sK86(X0))
| ~ ordinal(X0)
| ~ sP9(X0,X1) ),
inference(unflattening,[status(thm)],[c_20998]) ).
tcf(c_21010,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP9(X1,X2)
| ~ ordinal(X0)
| ~ in(X2,sK86(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2605,c_174]) ).
tcf(c_21011,plain,
! [X0: $i,X1: $i] :
( sP9(X1,X0)
| ~ ordinal(X1)
| ~ in(X0,sK86(X1)) ),
inference(unflattening,[status(thm)],[c_21010]) ).
tcf(c_21212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( topstr_closure(X3,X5) = X1 )
| ~ top_str(X2)
| ~ sP38(X3,X5,X1)
| ~ element(X4,powerset(the_carrier(X2)))
| ~ element(X0,powerset(the_carrier(X2)))
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1145,c_1132]) ).
tcf(c_21213,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( topstr_closure(X1,X2) = X0 )
| ~ top_str(X1)
| ~ sP38(X1,X2,X0)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(unflattening,[status(thm)],[c_21212]) ).
tcf(c_21230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP38(X0,X1,topstr_closure(X0,X1))
| ~ top_str(X3)
| ~ element(X4,powerset(the_carrier(X3)))
| ~ element(X2,powerset(the_carrier(X3)))
| ( X1 != X4 )
| ( X0 != X3 )
| ( topstr_closure(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_1145,c_3243]) ).
tcf(c_21231,plain,
! [X0: $i,X1: $i] :
( sP38(X0,X1,topstr_closure(X0,X1))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(unflattening,[status(thm)],[c_21230]) ).
tcf(c_21241,plain,
! [X0: $i,X1: $i] :
( sP38(X1,X0,topstr_closure(X1,X0))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21231,c_1175]) ).
tcf(c_21373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( relation_isomorphism(X2,X4,X0)
| ~ function(X1)
| ~ relation(X5)
| ~ relation(X3)
| ~ relation(X1)
| ~ sP40(X0,X2,X4)
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1183,c_1196]) ).
tcf(c_21374,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_isomorphism(X1,X2,X0)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ sP40(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_21373]) ).
tcf(c_21394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sP40(X4,X0,X2)
| ~ function(X5)
| ~ relation(X5)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation_isomorphism(X0,X2,X4)
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1184,c_1196]) ).
tcf(c_21395,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP40(X2,X0,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation_isomorphism(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_21394]) ).
tcf(c_21427,plain,
! [X0: $i] :
( element(sK72(X0),powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ sP8
| ( X0 != sK66 ) ),
inference(resolution_lifted,[status(thm)],[c_2639,c_2675]) ).
tcf(c_21428,plain,
( element(sK72(sK66),powerset(powerset(set_union2(sK66,unordered_pair(sK66,sK66)))))
| ~ sP8 ),
inference(unflattening,[status(thm)],[c_21427]) ).
tcf(c_21435,plain,
! [X0: $i,X1: $i] :
( ~ sP8
| ~ in(X1,sK72(X0))
| ( X0 != sK66 )
| ( sK73(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2639,c_144]) ).
tcf(c_21436,plain,
! [X0: $i] :
( ~ sP8
| ~ in(X0,sK72(sK66))
| ( sK73(sK66,X0) != X0 ) ),
inference(unflattening,[status(thm)],[c_21435]) ).
tcf(c_21447,plain,
! [X0: $i] :
( ~ sP8
| ( X0 != sK66 )
| ( sK72(X0) != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_2639,c_2674]) ).
tcf(c_21448,plain,
( ~ sP8
| ( sK72(sK66) != empty_set ) ),
inference(unflattening,[status(thm)],[c_21447]) ).
tcf(c_21455,plain,
! [X0: $i,X1: $i] :
( subset(X1,sK73(X0,X1))
| ~ sP8
| ~ in(X1,sK72(X0))
| ( X0 != sK66 ) ),
inference(resolution_lifted,[status(thm)],[c_2639,c_146]) ).
tcf(c_21456,plain,
! [X0: $i] :
( subset(X0,sK73(sK66,X0))
| ~ sP8
| ~ in(X0,sK72(sK66)) ),
inference(unflattening,[status(thm)],[c_21455]) ).
tcf(c_21467,plain,
! [X0: $i,X1: $i] :
( in(sK73(X0,X1),sK72(X0))
| ~ sP8
| ~ in(X1,sK72(X0))
| ( X0 != sK66 ) ),
inference(resolution_lifted,[status(thm)],[c_2639,c_145]) ).
tcf(c_21468,plain,
! [X0: $i] :
( in(sK73(sK66,X0),sK72(sK66))
| ~ sP8
| ~ in(X0,sK72(sK66)) ),
inference(unflattening,[status(thm)],[c_21467]) ).
tcf(c_21622,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| element(sK347(X0),the_carrier(X0))
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_1118,c_1123]) ).
tcf(c_21623,plain,
( meet_absorbing(sK346)
| empty_carrier(sK346)
| element(sK347(sK346),the_carrier(sK346)) ),
inference(unflattening,[status(thm)],[c_21622]) ).
tcf(c_21633,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| element(sK348(X0),the_carrier(X0))
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_1118,c_1122]) ).
tcf(c_21634,plain,
( meet_absorbing(sK346)
| empty_carrier(sK346)
| element(sK348(sK346),the_carrier(sK346)) ),
inference(unflattening,[status(thm)],[c_21633]) ).
tcf(c_21644,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| ( X0 != sK346 )
| ( join(X0,meet(X0,sK347(X0),sK348(X0)),sK348(X0)) != sK348(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_1118,c_1121]) ).
tcf(c_21645,plain,
( meet_absorbing(sK346)
| empty_carrier(sK346)
| ( join(sK346,meet(sK346,sK347(sK346),sK348(sK346)),sK348(sK346)) != sK348(sK346) ) ),
inference(unflattening,[status(thm)],[c_21644]) ).
tcf(c_21655,plain,
! [X0: $i] :
( join_semilatt_str(X0)
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_1118,c_3184]) ).
tcf(c_21656,plain,
join_semilatt_str(sK346),
inference(unflattening,[status(thm)],[c_21655]) ).
tcf(c_21660,plain,
! [X0: $i] :
( meet_semilatt_str(X0)
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_1118,c_3239]) ).
tcf(c_21661,plain,
meet_semilatt_str(sK346),
inference(unflattening,[status(thm)],[c_21660]) ).
tcf(c_21665,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| ( join(X0,meet(X0,X2,X1),X1) = X1 )
| ~ meet_absorbing(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_1118,c_1124]) ).
tcf(c_21666,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK346)
| ( join(sK346,meet(sK346,X1,X0),X0) = X0 )
| ~ meet_absorbing(sK346)
| ~ element(X1,the_carrier(sK346))
| ~ element(X0,the_carrier(sK346)) ),
inference(unflattening,[status(thm)],[c_21665]) ).
tcf(c_21699,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK349 ) ),
inference(resolution_lifted,[status(thm)],[c_2782,c_1127]) ).
tcf(c_21700,plain,
one_sorted_str(sK349),
inference(unflattening,[status(thm)],[c_21699]) ).
tcf(c_21704,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_2782,c_21656]) ).
tcf(c_21705,plain,
one_sorted_str(sK346),
inference(unflattening,[status(thm)],[c_21704]) ).
tcf(c_21709,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| element(join(X0,X2,X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X0 != sK349 ) ),
inference(resolution_lifted,[status(thm)],[c_1127,c_1291]) ).
tcf(c_21710,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK349)
| element(join(sK349,X1,X0),the_carrier(sK349))
| ~ element(X1,the_carrier(sK349))
| ~ element(X0,the_carrier(sK349)) ),
inference(unflattening,[status(thm)],[c_21709]) ).
tcf(c_21723,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| element(join(X0,X2,X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_1291,c_21656]) ).
tcf(c_21724,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK346)
| element(join(sK346,X1,X0),the_carrier(sK346))
| ~ element(X1,the_carrier(sK346))
| ~ element(X0,the_carrier(sK346)) ),
inference(unflattening,[status(thm)],[c_21723]) ).
tcf(c_21748,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK375 ) ),
inference(resolution_lifted,[status(thm)],[c_2784,c_1288]) ).
tcf(c_21749,plain,
one_sorted_str(sK375),
inference(unflattening,[status(thm)],[c_21748]) ).
tcf(c_21755,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| element(meet(X0,X2,X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X0 != sK375 ) ),
inference(resolution_lifted,[status(thm)],[c_1288,c_1290]) ).
tcf(c_21756,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK375)
| element(meet(sK375,X1,X0),the_carrier(sK375))
| ~ element(X1,the_carrier(sK375))
| ~ element(X0,the_carrier(sK375)) ),
inference(unflattening,[status(thm)],[c_21755]) ).
tcf(c_21769,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| element(meet(X0,X2,X1),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_1290,c_21661]) ).
tcf(c_21770,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK346)
| element(meet(sK346,X1,X0),the_carrier(sK346))
| ~ element(X1,the_carrier(sK346))
| ~ element(X0,the_carrier(sK346)) ),
inference(unflattening,[status(thm)],[c_21769]) ).
tcf(c_22138,plain,
! [X0: $i] :
( ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0))
| ( X0 != sK320 ) ),
inference(resolution_lifted,[status(thm)],[c_991,c_990]) ).
tcf(c_22139,plain,
( ~ one_sorted_str(sK320)
| ~ empty(the_carrier(sK320)) ),
inference(unflattening,[status(thm)],[c_22138]) ).
tcf(c_22140,plain,
~ empty(the_carrier(sK320)),
inference(global_subsumption_just,[status(thm)],[c_22139,c_989,c_22139]) ).
tcf(c_22145,plain,
! [X0: $i] :
( ~ one_sorted_str(X0)
| ~ empty(sK319(X0))
| ( X0 != sK320 ) ),
inference(resolution_lifted,[status(thm)],[c_988,c_990]) ).
tcf(c_22146,plain,
( ~ one_sorted_str(sK320)
| ~ empty(sK319(sK320)) ),
inference(unflattening,[status(thm)],[c_22145]) ).
tcf(c_22147,plain,
~ empty(sK319(sK320)),
inference(global_subsumption_just,[status(thm)],[c_22146,c_989,c_22146]) ).
tcf(c_22152,plain,
! [X0: $i] :
( element(sK319(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| ( X0 != sK320 ) ),
inference(resolution_lifted,[status(thm)],[c_987,c_990]) ).
tcf(c_22153,plain,
( element(sK319(sK320),powerset(the_carrier(sK320)))
| ~ one_sorted_str(sK320) ),
inference(unflattening,[status(thm)],[c_22152]) ).
tcf(c_22154,plain,
element(sK319(sK320),powerset(the_carrier(sK320))),
inference(global_subsumption_just,[status(thm)],[c_22153,c_989,c_22153]) ).
tcf(c_22159,plain,
! [X0: $i,X1: $i] :
( element(join(sK349,X1,X0),the_carrier(sK349))
| ~ element(X1,the_carrier(sK349))
| ~ element(X0,the_carrier(sK349))
| ( sK320 != sK349 ) ),
inference(resolution_lifted,[status(thm)],[c_990,c_21710]) ).
tcf(c_22173,plain,
! [X0: $i,X1: $i] :
( element(meet(sK375,X1,X0),the_carrier(sK375))
| ~ element(X1,the_carrier(sK375))
| ~ element(X0,the_carrier(sK375))
| ( sK320 != sK375 ) ),
inference(resolution_lifted,[status(thm)],[c_990,c_21756]) ).
tcf(c_22187,plain,
! [X0: $i,X1: $i] :
( element(meet(sK346,X1,X0),the_carrier(sK346))
| ~ element(X1,the_carrier(sK346))
| ~ element(X0,the_carrier(sK346))
| ( sK320 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_990,c_21770]) ).
tcf(c_22201,plain,
! [X0: $i,X1: $i] :
( element(join(sK346,X1,X0),the_carrier(sK346))
| ~ element(X1,the_carrier(sK346))
| ~ element(X0,the_carrier(sK346))
| ( sK320 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_990,c_21724]) ).
tcf(c_22215,plain,
! [X0: $i,X1: $i] :
( ( join(sK346,meet(sK346,X1,X0),X0) = X0 )
| ~ meet_absorbing(sK346)
| ~ element(X1,the_carrier(sK346))
| ~ element(X0,the_carrier(sK346))
| ( sK320 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_990,c_21666]) ).
tcf(c_22232,plain,
( meet_absorbing(sK346)
| ( sK320 != sK346 )
| ( join(sK346,meet(sK346,sK347(sK346),sK348(sK346)),sK348(sK346)) != sK348(sK346) ) ),
inference(resolution_lifted,[status(thm)],[c_990,c_21645]) ).
tcf(c_22242,plain,
( meet_absorbing(sK346)
| element(sK348(sK346),the_carrier(sK346))
| ( sK320 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_990,c_21634]) ).
tcf(c_22252,plain,
( meet_absorbing(sK346)
| element(sK347(sK346),the_carrier(sK346))
| ( sK320 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_990,c_21623]) ).
tcf(c_23669,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK320 ) ),
inference(resolution_lifted,[status(thm)],[c_343,c_989]) ).
tcf(c_23670,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK320),cast_as_carrier_subset(sK320),subset_difference(the_carrier(sK320),cast_as_carrier_subset(sK320),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(unflattening,[status(thm)],[c_23669]) ).
tcf(c_23678,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK320 ) ),
inference(resolution_lifted,[status(thm)],[c_320,c_989]) ).
tcf(c_23679,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK320),cast_as_carrier_subset(sK320),X0) = subset_complement(the_carrier(sK320),X0) )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(unflattening,[status(thm)],[c_23678]) ).
tcf(c_23687,plain,
! [X0: $i,X1: $i] :
( ( subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK320 ) ),
inference(resolution_lifted,[status(thm)],[c_306,c_989]) ).
tcf(c_23688,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK320),X0,cast_as_carrier_subset(sK320)) = X0 )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(unflattening,[status(thm)],[c_23687]) ).
tcf(c_23696,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK321 ) ),
inference(resolution_lifted,[status(thm)],[c_343,c_992]) ).
tcf(c_23697,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK321),cast_as_carrier_subset(sK321),subset_difference(the_carrier(sK321),cast_as_carrier_subset(sK321),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(unflattening,[status(thm)],[c_23696]) ).
tcf(c_23705,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK321 ) ),
inference(resolution_lifted,[status(thm)],[c_320,c_992]) ).
tcf(c_23706,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK321),cast_as_carrier_subset(sK321),X0) = subset_complement(the_carrier(sK321),X0) )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(unflattening,[status(thm)],[c_23705]) ).
tcf(c_23714,plain,
! [X0: $i,X1: $i] :
( ( subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK321 ) ),
inference(resolution_lifted,[status(thm)],[c_306,c_992]) ).
tcf(c_23715,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK321),X0,cast_as_carrier_subset(sK321)) = X0 )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(unflattening,[status(thm)],[c_23714]) ).
tcf(c_23723,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK349 ) ),
inference(resolution_lifted,[status(thm)],[c_343,c_21700]) ).
tcf(c_23724,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK349),cast_as_carrier_subset(sK349),subset_difference(the_carrier(sK349),cast_as_carrier_subset(sK349),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(unflattening,[status(thm)],[c_23723]) ).
tcf(c_23732,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK349 ) ),
inference(resolution_lifted,[status(thm)],[c_320,c_21700]) ).
tcf(c_23733,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK349),cast_as_carrier_subset(sK349),X0) = subset_complement(the_carrier(sK349),X0) )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(unflattening,[status(thm)],[c_23732]) ).
tcf(c_23741,plain,
! [X0: $i,X1: $i] :
( ( subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK349 ) ),
inference(resolution_lifted,[status(thm)],[c_306,c_21700]) ).
tcf(c_23742,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK349),X0,cast_as_carrier_subset(sK349)) = X0 )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(unflattening,[status(thm)],[c_23741]) ).
tcf(c_23750,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK375 ) ),
inference(resolution_lifted,[status(thm)],[c_343,c_21749]) ).
tcf(c_23751,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK375),cast_as_carrier_subset(sK375),subset_difference(the_carrier(sK375),cast_as_carrier_subset(sK375),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(unflattening,[status(thm)],[c_23750]) ).
tcf(c_23759,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK375 ) ),
inference(resolution_lifted,[status(thm)],[c_320,c_21749]) ).
tcf(c_23760,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK375),cast_as_carrier_subset(sK375),X0) = subset_complement(the_carrier(sK375),X0) )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(unflattening,[status(thm)],[c_23759]) ).
tcf(c_23768,plain,
! [X0: $i,X1: $i] :
( ( subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK375 ) ),
inference(resolution_lifted,[status(thm)],[c_306,c_21749]) ).
tcf(c_23769,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK375),X0,cast_as_carrier_subset(sK375)) = X0 )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(unflattening,[status(thm)],[c_23768]) ).
tcf(c_23777,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_343,c_21705]) ).
tcf(c_23778,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK346),cast_as_carrier_subset(sK346),subset_difference(the_carrier(sK346),cast_as_carrier_subset(sK346),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(unflattening,[status(thm)],[c_23777]) ).
tcf(c_23786,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_320,c_21705]) ).
tcf(c_23787,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK346),cast_as_carrier_subset(sK346),X0) = subset_complement(the_carrier(sK346),X0) )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(unflattening,[status(thm)],[c_23786]) ).
tcf(c_23795,plain,
! [X0: $i,X1: $i] :
( ( subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_306,c_21705]) ).
tcf(c_23796,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK346),X0,cast_as_carrier_subset(sK346)) = X0 )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(unflattening,[status(thm)],[c_23795]) ).
tcf(c_47394,plain,
! [X0: $i] :
( sP42(X0)
| ~ topological_space(X0)
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_1304,c_377]) ).
tcf(c_47395,plain,
( sP42(sK137)
| ~ topological_space(sK137) ),
inference(unflattening,[status(thm)],[c_47394]) ).
tcf(c_47402,plain,
! [X0: $i] :
( in(the_carrier(X0),the_topology(X0))
| ~ topological_space(X0)
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_1302,c_377]) ).
tcf(c_47403,plain,
( in(the_carrier(sK137),the_topology(sK137))
| ~ topological_space(sK137) ),
inference(unflattening,[status(thm)],[c_47402]) ).
tcf(c_47410,plain,
! [X0: $i] :
( topological_space(X0)
| element(sK378(X0),powerset(powerset(the_carrier(X0))))
| ~ sP42(X0)
| ~ in(the_carrier(X0),the_topology(X0))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_1301,c_377]) ).
tcf(c_47411,plain,
( topological_space(sK137)
| element(sK378(sK137),powerset(powerset(the_carrier(sK137))))
| ~ sP42(sK137)
| ~ in(the_carrier(sK137),the_topology(sK137)) ),
inference(unflattening,[status(thm)],[c_47410]) ).
tcf(c_47424,plain,
! [X0: $i] :
( topological_space(X0)
| subset(sK378(X0),the_topology(X0))
| ~ sP42(X0)
| ~ in(the_carrier(X0),the_topology(X0))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_1300,c_377]) ).
tcf(c_47425,plain,
( topological_space(sK137)
| subset(sK378(sK137),the_topology(sK137))
| ~ sP42(sK137)
| ~ in(the_carrier(sK137),the_topology(sK137)) ),
inference(unflattening,[status(thm)],[c_47424]) ).
tcf(c_47438,plain,
! [X0: $i] :
( topological_space(X0)
| ~ sP42(X0)
| ~ in(the_carrier(X0),the_topology(X0))
| ~ in(union_of_subsets(the_carrier(X0),sK378(X0)),the_topology(X0))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_1299,c_377]) ).
tcf(c_47439,plain,
( topological_space(sK137)
| ~ sP42(sK137)
| ~ in(the_carrier(sK137),the_topology(sK137))
| ~ in(union_of_subsets(the_carrier(sK137),sK378(sK137)),the_topology(sK137)) ),
inference(unflattening,[status(thm)],[c_47438]) ).
tcf(c_47452,plain,
! [X0: $i] :
( element(the_topology(X0),powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_2719,c_377]) ).
tcf(c_47453,plain,
element(the_topology(sK137),powerset(powerset(the_carrier(sK137)))),
inference(unflattening,[status(thm)],[c_47452]) ).
tcf(c_47457,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_1128,c_377]) ).
tcf(c_47458,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ open_subset(subset_difference(the_carrier(sK137),cast_as_carrier_subset(sK137),X0),sK137) ),
inference(unflattening,[status(thm)],[c_47457]) ).
tcf(c_47469,plain,
! [X0: $i] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ topological_space(X0)
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_933,c_377]) ).
tcf(c_47470,plain,
( closed_subset(cast_as_carrier_subset(sK137),sK137)
| ~ topological_space(sK137) ),
inference(unflattening,[status(thm)],[c_47469]) ).
tcf(c_47477,plain,
! [X0: $i] :
( closed_subset(sK305(X0),X0)
| ~ topological_space(X0)
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_932,c_377]) ).
tcf(c_47478,plain,
( closed_subset(sK305(sK137),sK137)
| ~ topological_space(sK137) ),
inference(unflattening,[status(thm)],[c_47477]) ).
tcf(c_47485,plain,
! [X0: $i] :
( element(sK305(X0),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_931,c_377]) ).
tcf(c_47486,plain,
( element(sK305(sK137),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(unflattening,[status(thm)],[c_47485]) ).
tcf(c_47493,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X2,X0)
| in(X1,sK295(X0,X2))
| ~ topological_space(X0)
| ~ in(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2)
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_908,c_377]) ).
tcf(c_47494,plain,
! [X0: $i,X1: $i] :
( sP34(X1,sK137)
| in(X0,sK295(sK137,X1))
| ~ topological_space(sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(set_difference(cast_as_carrier_subset(sK137),X0),X1) ),
inference(unflattening,[status(thm)],[c_47493]) ).
tcf(c_47514,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_2717,c_377]) ).
tcf(c_47515,plain,
one_sorted_str(sK137),
inference(unflattening,[status(thm)],[c_47514]) ).
tcf(c_47519,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 )
| ( topstr_closure(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_462,c_377]) ).
tcf(c_47520,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,X0) != X0 ) ),
inference(unflattening,[status(thm)],[c_47519]) ).
tcf(c_47534,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK125(X0,X2))
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2)
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_267,c_377]) ).
tcf(c_47535,plain,
! [X0: $i,X1: $i] :
( in(X0,sK125(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(set_difference(cast_as_carrier_subset(sK137),X0),X1) ),
inference(unflattening,[status(thm)],[c_47534]) ).
tcf(c_47552,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK93(X0,X2))
| ~ topological_space(X0)
| ~ in(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2)
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_193,c_377]) ).
tcf(c_47553,plain,
! [X0: $i,X1: $i] :
( in(X0,sK93(sK137,X1))
| ~ topological_space(sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(set_difference(cast_as_carrier_subset(sK137),X0),X1) ),
inference(unflattening,[status(thm)],[c_47552]) ).
tcf(c_47570,plain,
! [X0: $i] :
( sP42(X0)
| ~ topological_space(X0)
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_1304,c_901]) ).
tcf(c_47571,plain,
( sP42(sK291)
| ~ topological_space(sK291) ),
inference(unflattening,[status(thm)],[c_47570]) ).
tcf(c_47578,plain,
! [X0: $i] :
( in(the_carrier(X0),the_topology(X0))
| ~ topological_space(X0)
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_1302,c_901]) ).
tcf(c_47579,plain,
( in(the_carrier(sK291),the_topology(sK291))
| ~ topological_space(sK291) ),
inference(unflattening,[status(thm)],[c_47578]) ).
tcf(c_47586,plain,
! [X0: $i] :
( topological_space(X0)
| element(sK378(X0),powerset(powerset(the_carrier(X0))))
| ~ sP42(X0)
| ~ in(the_carrier(X0),the_topology(X0))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_1301,c_901]) ).
tcf(c_47587,plain,
( topological_space(sK291)
| element(sK378(sK291),powerset(powerset(the_carrier(sK291))))
| ~ sP42(sK291)
| ~ in(the_carrier(sK291),the_topology(sK291)) ),
inference(unflattening,[status(thm)],[c_47586]) ).
tcf(c_47600,plain,
! [X0: $i] :
( topological_space(X0)
| subset(sK378(X0),the_topology(X0))
| ~ sP42(X0)
| ~ in(the_carrier(X0),the_topology(X0))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_1300,c_901]) ).
tcf(c_47601,plain,
( topological_space(sK291)
| subset(sK378(sK291),the_topology(sK291))
| ~ sP42(sK291)
| ~ in(the_carrier(sK291),the_topology(sK291)) ),
inference(unflattening,[status(thm)],[c_47600]) ).
tcf(c_47614,plain,
! [X0: $i] :
( topological_space(X0)
| ~ sP42(X0)
| ~ in(the_carrier(X0),the_topology(X0))
| ~ in(union_of_subsets(the_carrier(X0),sK378(X0)),the_topology(X0))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_1299,c_901]) ).
tcf(c_47615,plain,
( topological_space(sK291)
| ~ sP42(sK291)
| ~ in(the_carrier(sK291),the_topology(sK291))
| ~ in(union_of_subsets(the_carrier(sK291),sK378(sK291)),the_topology(sK291)) ),
inference(unflattening,[status(thm)],[c_47614]) ).
tcf(c_47628,plain,
! [X0: $i] :
( element(the_topology(X0),powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_2719,c_901]) ).
tcf(c_47629,plain,
element(the_topology(sK291),powerset(powerset(the_carrier(sK291)))),
inference(unflattening,[status(thm)],[c_47628]) ).
tcf(c_47633,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_1128,c_901]) ).
tcf(c_47634,plain,
! [X0: $i] :
( closed_subset(X0,sK291)
| ~ element(X0,powerset(the_carrier(sK291)))
| ~ open_subset(subset_difference(the_carrier(sK291),cast_as_carrier_subset(sK291),X0),sK291) ),
inference(unflattening,[status(thm)],[c_47633]) ).
tcf(c_47645,plain,
! [X0: $i] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ topological_space(X0)
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_933,c_901]) ).
tcf(c_47646,plain,
( closed_subset(cast_as_carrier_subset(sK291),sK291)
| ~ topological_space(sK291) ),
inference(unflattening,[status(thm)],[c_47645]) ).
tcf(c_47653,plain,
! [X0: $i] :
( closed_subset(sK305(X0),X0)
| ~ topological_space(X0)
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_932,c_901]) ).
tcf(c_47654,plain,
( closed_subset(sK305(sK291),sK291)
| ~ topological_space(sK291) ),
inference(unflattening,[status(thm)],[c_47653]) ).
tcf(c_47661,plain,
! [X0: $i] :
( element(sK305(X0),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_931,c_901]) ).
tcf(c_47662,plain,
( element(sK305(sK291),powerset(the_carrier(sK291)))
| ~ topological_space(sK291) ),
inference(unflattening,[status(thm)],[c_47661]) ).
tcf(c_47669,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X2,X0)
| in(X1,sK295(X0,X2))
| ~ topological_space(X0)
| ~ in(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2)
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_908,c_901]) ).
tcf(c_47670,plain,
! [X0: $i,X1: $i] :
( sP34(X1,sK291)
| in(X0,sK295(sK291,X1))
| ~ topological_space(sK291)
| ~ in(X0,powerset(the_carrier(sK291)))
| ~ element(X1,powerset(powerset(the_carrier(sK291))))
| ~ in(set_difference(cast_as_carrier_subset(sK291),X0),X1) ),
inference(unflattening,[status(thm)],[c_47669]) ).
tcf(c_47690,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_2717,c_901]) ).
tcf(c_47691,plain,
one_sorted_str(sK291),
inference(unflattening,[status(thm)],[c_47690]) ).
tcf(c_47695,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 )
| ( topstr_closure(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_462,c_901]) ).
tcf(c_47696,plain,
! [X0: $i] :
( closed_subset(X0,sK291)
| ~ topological_space(sK291)
| ~ element(X0,powerset(the_carrier(sK291)))
| ( topstr_closure(sK291,X0) != X0 ) ),
inference(unflattening,[status(thm)],[c_47695]) ).
tcf(c_47710,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK125(X0,X2))
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2)
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_267,c_901]) ).
tcf(c_47711,plain,
! [X0: $i,X1: $i] :
( in(X0,sK125(sK291,X1))
| ~ topological_space(sK291)
| ~ element(X0,powerset(the_carrier(sK291)))
| ~ element(X1,powerset(powerset(the_carrier(sK291))))
| ~ in(set_difference(cast_as_carrier_subset(sK291),X0),X1) ),
inference(unflattening,[status(thm)],[c_47710]) ).
tcf(c_47728,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK93(X0,X2))
| ~ topological_space(X0)
| ~ in(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2)
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_193,c_901]) ).
tcf(c_47729,plain,
! [X0: $i,X1: $i] :
( in(X0,sK93(sK291,X1))
| ~ topological_space(sK291)
| ~ in(X0,powerset(the_carrier(sK291)))
| ~ element(X1,powerset(powerset(the_carrier(sK291))))
| ~ in(set_difference(cast_as_carrier_subset(sK291),X0),X1) ),
inference(unflattening,[status(thm)],[c_47728]) ).
tcf(c_47746,plain,
! [X0: $i,X1: $i] :
( sP38(X0,X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_21241,c_377]) ).
tcf(c_47747,plain,
! [X0: $i] :
( sP38(sK137,X0,topstr_closure(sK137,X0))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_47746]) ).
tcf(c_47755,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( topstr_closure(X0,X2) = X1 )
| ~ sP38(X0,X2,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_21213,c_377]) ).
tcf(c_47756,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(sK137,X1) = X0 )
| ~ sP38(sK137,X1,X0)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_47755]) ).
tcf(c_47770,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| in(X1,sK302(X0,X2))
| ~ topological_space(X0)
| ~ closed_subset(X1,X0)
| ~ subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_6365,c_377]) ).
tcf(c_47771,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| in(X0,sK302(sK137,X1))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(X1,X0)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_47770]) ).
tcf(c_47794,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK91(X0,X2))
| ~ topological_space(X0)
| ~ closed_subset(X1,X0)
| ~ subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_6364,c_377]) ).
tcf(c_47795,plain,
! [X0: $i,X1: $i] :
( in(X0,sK91(sK137,X1))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(X1,X0)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_47794]) ).
tcf(c_47815,plain,
! [X0: $i,X1: $i] :
( in(union_of_subsets(the_carrier(X0),X1),the_topology(X0))
| ~ topological_space(X0)
| ~ subset(X1,the_topology(X0))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_1303,c_377]) ).
tcf(c_47816,plain,
! [X0: $i] :
( in(union_of_subsets(the_carrier(sK137),X0),the_topology(sK137))
| ~ topological_space(sK137)
| ~ subset(X0,the_topology(sK137))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(unflattening,[status(thm)],[c_47815]) ).
tcf(c_47830,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_1175,c_377]) ).
tcf(c_47831,plain,
! [X0: $i] :
( element(topstr_closure(sK137,X0),powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_47830]) ).
tcf(c_47839,plain,
! [X0: $i,X1: $i] :
( in(X1,the_topology(X0))
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_1131,c_377]) ).
tcf(c_47840,plain,
! [X0: $i] :
( in(X0,the_topology(sK137))
| ~ open_subset(X0,sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_47839]) ).
tcf(c_47851,plain,
! [X0: $i,X1: $i] :
( open_subset(X1,X0)
| ~ in(X1,the_topology(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_1130,c_377]) ).
tcf(c_47852,plain,
! [X0: $i] :
( open_subset(X0,sK137)
| ~ in(X0,the_topology(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_47851]) ).
tcf(c_47863,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_1129,c_377]) ).
tcf(c_47864,plain,
! [X0: $i] :
( open_subset(subset_difference(the_carrier(sK137),cast_as_carrier_subset(sK137),X0),sK137)
| ~ closed_subset(X0,sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_47863]) ).
tcf(c_47875,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| subset(X2,X1)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_930,c_377]) ).
tcf(c_47876,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| subset(X1,X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_47875]) ).
tcf(c_47892,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| closed_subset(sK304(X0,X2,X1),X0)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_929,c_377]) ).
tcf(c_47893,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| closed_subset(sK304(sK137,X1,X0),sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_47892]) ).
tcf(c_47910,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| ( sK304(X0,X2,X1) = X1 )
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_928,c_377]) ).
tcf(c_47911,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ( sK304(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_47910]) ).
tcf(c_47928,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| element(sK304(X0,X2,X1),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_927,c_377]) ).
tcf(c_47929,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| element(sK304(sK137,X1,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_47928]) ).
tcf(c_47946,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| ( sK303(X0,X2,X1) = X1 )
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_926,c_377]) ).
tcf(c_47947,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ( sK303(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_47946]) ).
tcf(c_47964,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| in(sK303(X0,X2,X1),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_925,c_377]) ).
tcf(c_47965,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| in(sK303(sK137,X1,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_47964]) ).
tcf(c_47982,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X1,X0)
| in(set_difference(cast_as_carrier_subset(X0),X2),X1)
| ~ topological_space(X0)
| ~ in(X2,sK295(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_911,c_377]) ).
tcf(c_47983,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK137)
| in(set_difference(cast_as_carrier_subset(sK137),X1),X0)
| ~ topological_space(sK137)
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(unflattening,[status(thm)],[c_47982]) ).
tcf(c_48000,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X1,X0)
| ( sK296(X0,X1,X2) = X2 )
| ~ topological_space(X0)
| ~ in(X2,sK295(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_910,c_377]) ).
tcf(c_48001,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK137)
| ( sK296(sK137,X0,X1) = X1 )
| ~ topological_space(sK137)
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(unflattening,[status(thm)],[c_48000]) ).
tcf(c_48018,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X1,X0)
| in(sK296(X0,X1,X2),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ in(X2,sK295(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_909,c_377]) ).
tcf(c_48019,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK137)
| in(sK296(sK137,X0,X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(unflattening,[status(thm)],[c_48018]) ).
tcf(c_48036,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(X0,X1) = X1 )
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_461,c_377]) ).
tcf(c_48037,plain,
! [X0: $i] :
( ( topstr_closure(sK137,X0) = X0 )
| ~ closed_subset(X0,sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_48036]) ).
tcf(c_48048,plain,
! [X0: $i,X1: $i] :
( subset(X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_454,c_377]) ).
tcf(c_48049,plain,
! [X0: $i] :
( subset(X0,topstr_closure(sK137,X0))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_48048]) ).
tcf(c_48057,plain,
! [X0: $i,X1: $i] :
( ( meet_of_subsets(the_carrier(X0),sK147(X0,X1)) = topstr_closure(X0,X1) )
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_448,c_377]) ).
tcf(c_48058,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,X0)) = topstr_closure(sK137,X0) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_48057]) ).
tcf(c_48069,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK147(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_447,c_377]) ).
tcf(c_48070,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48069]) ).
tcf(c_48086,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(X1,X0)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK147(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_446,c_377]) ).
tcf(c_48087,plain,
! [X0: $i,X1: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48086]) ).
tcf(c_48104,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK147(X0,X1))
| ~ topological_space(X0)
| ~ closed_subset(X2,X0)
| ~ subset(X1,X2)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_445,c_377]) ).
tcf(c_48105,plain,
! [X0: $i,X1: $i] :
( in(X1,sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(X1,sK137)
| ~ subset(X0,X1)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_48104]) ).
tcf(c_48125,plain,
! [X0: $i,X1: $i] :
( element(sK147(X0,X1),powerset(powerset(the_carrier(X0))))
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_444,c_377]) ).
tcf(c_48126,plain,
! [X0: $i] :
( element(sK147(sK137,X0),powerset(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_48125]) ).
tcf(c_48137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X2,X3)
| ~ in(X1,the_carrier(X0))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,topstr_closure(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_438,c_377]) ).
tcf(c_48138,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ closed_subset(X2,sK137)
| ~ subset(X1,X2)
| ~ in(X0,the_carrier(sK137))
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48137]) ).
tcf(c_48161,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X0,X1))
| element(sK146(X0,X1,X2),powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_437,c_377]) ).
tcf(c_48162,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| element(sK146(sK137,X0,X1),powerset(the_carrier(sK137)))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_48161]) ).
tcf(c_48176,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X0,X1))
| subset(X1,sK146(X0,X1,X2))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_436,c_377]) ).
tcf(c_48177,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| subset(X0,sK146(sK137,X0,X1))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_48176]) ).
tcf(c_48191,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X0,X1))
| closed_subset(sK146(X0,X1,X2),X0)
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_435,c_377]) ).
tcf(c_48192,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| closed_subset(sK146(sK137,X0,X1),sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_48191]) ).
tcf(c_48206,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,topstr_closure(X0,X2))
| ~ in(X1,the_carrier(X0))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK146(X0,X2,X1))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_434,c_377]) ).
tcf(c_48207,plain,
! [X0: $i,X1: $i] :
( in(X0,topstr_closure(sK137,X1))
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK146(sK137,X1,X0)) ),
inference(unflattening,[status(thm)],[c_48206]) ).
tcf(c_48221,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| element(sK145(X0,X1),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_432,c_377]) ).
tcf(c_48222,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| element(sK145(sK137,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(unflattening,[status(thm)],[c_48221]) ).
tcf(c_48236,plain,
! [X0: $i,X1: $i] :
( in(sK145(X0,X1),X1)
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_431,c_377]) ).
tcf(c_48237,plain,
! [X0: $i] :
( in(sK145(sK137,X0),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(unflattening,[status(thm)],[c_48236]) ).
tcf(c_48251,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ~ topological_space(X0)
| ~ closed_subset(sK145(X0,X1),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_430,c_377]) ).
tcf(c_48252,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,X0),sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(unflattening,[status(thm)],[c_48251]) ).
tcf(c_48266,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_difference(cast_as_carrier_subset(X0),X2),X1)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X2,sK125(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_268,c_377]) ).
tcf(c_48267,plain,
! [X0: $i,X1: $i] :
( in(set_difference(cast_as_carrier_subset(sK137),X1),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X1,sK125(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(unflattening,[status(thm)],[c_48266]) ).
tcf(c_48284,plain,
! [X0: $i,X1: $i] :
( element(sK125(X0,X1),powerset(powerset(the_carrier(X0))))
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_266,c_377]) ).
tcf(c_48285,plain,
! [X0: $i] :
( element(sK125(sK137,X0),powerset(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(unflattening,[status(thm)],[c_48284]) ).
tcf(c_48296,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK123(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_265,c_377]) ).
tcf(c_48297,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48296]) ).
tcf(c_48313,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(sK124(X0,X2,X1),X0)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK123(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_264,c_377]) ).
tcf(c_48314,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK124(sK137,X1,X0),sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48313]) ).
tcf(c_48331,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK124(X0,X2,X1) = X1 )
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK123(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_263,c_377]) ).
tcf(c_48332,plain,
! [X0: $i,X1: $i] :
( ( sK124(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48331]) ).
tcf(c_48349,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK124(X0,X2,X1),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK123(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_262,c_377]) ).
tcf(c_48350,plain,
! [X0: $i,X1: $i] :
( element(sK124(sK137,X1,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48349]) ).
tcf(c_48367,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK123(X0,X1))
| ~ topological_space(X0)
| ~ closed_subset(X2,X0)
| ~ subset(X1,X2)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_261,c_377]) ).
tcf(c_48368,plain,
! [X0: $i,X1: $i] :
( in(X1,sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(X1,sK137)
| ~ subset(X0,X1)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_48367]) ).
tcf(c_48388,plain,
! [X0: $i,X1: $i] :
( element(sK123(X0,X1),powerset(powerset(the_carrier(X0))))
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_260,c_377]) ).
tcf(c_48389,plain,
! [X0: $i] :
( element(sK123(sK137,X0),powerset(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_48388]) ).
tcf(c_48400,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_difference(cast_as_carrier_subset(X0),X2),X1)
| ~ topological_space(X0)
| ~ in(X2,sK93(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_195,c_377]) ).
tcf(c_48401,plain,
! [X0: $i,X1: $i] :
( in(set_difference(cast_as_carrier_subset(sK137),X1),X0)
| ~ topological_space(sK137)
| ~ in(X1,sK93(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(unflattening,[status(thm)],[c_48400]) ).
tcf(c_48415,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ in(X2,sK93(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_194,c_377]) ).
tcf(c_48416,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X1,sK93(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(unflattening,[status(thm)],[c_48415]) ).
tcf(c_48430,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK91(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_192,c_377]) ).
tcf(c_48431,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48430]) ).
tcf(c_48444,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(sK92(X0,X2,X1),X0)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK91(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_191,c_377]) ).
tcf(c_48445,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK92(sK137,X1,X0),sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48444]) ).
tcf(c_48459,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK92(X0,X2,X1) = X1 )
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK91(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_190,c_377]) ).
tcf(c_48460,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48459]) ).
tcf(c_48474,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK92(X0,X2,X1),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK91(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_189,c_377]) ).
tcf(c_48475,plain,
! [X0: $i,X1: $i] :
( element(sK92(sK137,X1,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48474]) ).
tcf(c_48489,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK91(X0,X2))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_188,c_377]) ).
tcf(c_48490,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(unflattening,[status(thm)],[c_48489]) ).
tcf(c_48504,plain,
! [X0: $i,X1: $i] :
( sP38(X0,X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_21241,c_901]) ).
tcf(c_48505,plain,
! [X0: $i] :
( sP38(sK291,X0,topstr_closure(sK291,X0))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48504]) ).
tcf(c_48513,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( topstr_closure(X0,X2) = X1 )
| ~ sP38(X0,X2,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_21213,c_901]) ).
tcf(c_48514,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(sK291,X1) = X0 )
| ~ sP38(sK291,X1,X0)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48513]) ).
tcf(c_48528,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| in(X1,sK302(X0,X2))
| ~ topological_space(X0)
| ~ closed_subset(X1,X0)
| ~ subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_6365,c_901]) ).
tcf(c_48529,plain,
! [X0: $i,X1: $i] :
( sP36(sK291,X1)
| in(X0,sK302(sK291,X1))
| ~ topological_space(sK291)
| ~ closed_subset(X0,sK291)
| ~ subset(X1,X0)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48528]) ).
tcf(c_48552,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK91(X0,X2))
| ~ topological_space(X0)
| ~ closed_subset(X1,X0)
| ~ subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_6364,c_901]) ).
tcf(c_48553,plain,
! [X0: $i,X1: $i] :
( in(X0,sK91(sK291,X1))
| ~ topological_space(sK291)
| ~ closed_subset(X0,sK291)
| ~ subset(X1,X0)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48552]) ).
tcf(c_48573,plain,
! [X0: $i,X1: $i] :
( in(union_of_subsets(the_carrier(X0),X1),the_topology(X0))
| ~ topological_space(X0)
| ~ subset(X1,the_topology(X0))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_1303,c_901]) ).
tcf(c_48574,plain,
! [X0: $i] :
( in(union_of_subsets(the_carrier(sK291),X0),the_topology(sK291))
| ~ topological_space(sK291)
| ~ subset(X0,the_topology(sK291))
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(unflattening,[status(thm)],[c_48573]) ).
tcf(c_48588,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_1175,c_901]) ).
tcf(c_48589,plain,
! [X0: $i] :
( element(topstr_closure(sK291,X0),powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48588]) ).
tcf(c_48597,plain,
! [X0: $i,X1: $i] :
( in(X1,the_topology(X0))
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_1131,c_901]) ).
tcf(c_48598,plain,
! [X0: $i] :
( in(X0,the_topology(sK291))
| ~ open_subset(X0,sK291)
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48597]) ).
tcf(c_48609,plain,
! [X0: $i,X1: $i] :
( open_subset(X1,X0)
| ~ in(X1,the_topology(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_1130,c_901]) ).
tcf(c_48610,plain,
! [X0: $i] :
( open_subset(X0,sK291)
| ~ in(X0,the_topology(sK291))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48609]) ).
tcf(c_48621,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_1129,c_901]) ).
tcf(c_48622,plain,
! [X0: $i] :
( open_subset(subset_difference(the_carrier(sK291),cast_as_carrier_subset(sK291),X0),sK291)
| ~ closed_subset(X0,sK291)
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48621]) ).
tcf(c_48633,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| subset(X2,X1)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_930,c_901]) ).
tcf(c_48634,plain,
! [X0: $i,X1: $i] :
( sP36(sK291,X1)
| subset(X1,X0)
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK302(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_48633]) ).
tcf(c_48650,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| closed_subset(sK304(X0,X2,X1),X0)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_929,c_901]) ).
tcf(c_48651,plain,
! [X0: $i,X1: $i] :
( sP36(sK291,X1)
| closed_subset(sK304(sK291,X1,X0),sK291)
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK302(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_48650]) ).
tcf(c_48668,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| ( sK304(X0,X2,X1) = X1 )
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_928,c_901]) ).
tcf(c_48669,plain,
! [X0: $i,X1: $i] :
( sP36(sK291,X1)
| ( sK304(sK291,X1,X0) = X0 )
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK302(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_48668]) ).
tcf(c_48686,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| element(sK304(X0,X2,X1),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_927,c_901]) ).
tcf(c_48687,plain,
! [X0: $i,X1: $i] :
( sP36(sK291,X1)
| element(sK304(sK291,X1,X0),powerset(the_carrier(sK291)))
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK302(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_48686]) ).
tcf(c_48704,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| ( sK303(X0,X2,X1) = X1 )
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_926,c_901]) ).
tcf(c_48705,plain,
! [X0: $i,X1: $i] :
( sP36(sK291,X1)
| ( sK303(sK291,X1,X0) = X0 )
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK302(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_48704]) ).
tcf(c_48722,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(X0,X2)
| in(sK303(X0,X2,X1),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK302(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_925,c_901]) ).
tcf(c_48723,plain,
! [X0: $i,X1: $i] :
( sP36(sK291,X1)
| in(sK303(sK291,X1,X0),powerset(the_carrier(sK291)))
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK302(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_48722]) ).
tcf(c_48740,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X1,X0)
| in(set_difference(cast_as_carrier_subset(X0),X2),X1)
| ~ topological_space(X0)
| ~ in(X2,sK295(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_911,c_901]) ).
tcf(c_48741,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK291)
| in(set_difference(cast_as_carrier_subset(sK291),X1),X0)
| ~ topological_space(sK291)
| ~ in(X1,sK295(sK291,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(unflattening,[status(thm)],[c_48740]) ).
tcf(c_48758,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X1,X0)
| ( sK296(X0,X1,X2) = X2 )
| ~ topological_space(X0)
| ~ in(X2,sK295(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_910,c_901]) ).
tcf(c_48759,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK291)
| ( sK296(sK291,X0,X1) = X1 )
| ~ topological_space(sK291)
| ~ in(X1,sK295(sK291,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(unflattening,[status(thm)],[c_48758]) ).
tcf(c_48776,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X1,X0)
| in(sK296(X0,X1,X2),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ in(X2,sK295(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_909,c_901]) ).
tcf(c_48777,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK291)
| in(sK296(sK291,X0,X1),powerset(the_carrier(sK291)))
| ~ topological_space(sK291)
| ~ in(X1,sK295(sK291,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(unflattening,[status(thm)],[c_48776]) ).
tcf(c_48794,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(X0,X1) = X1 )
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_461,c_901]) ).
tcf(c_48795,plain,
! [X0: $i] :
( ( topstr_closure(sK291,X0) = X0 )
| ~ closed_subset(X0,sK291)
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48794]) ).
tcf(c_48806,plain,
! [X0: $i,X1: $i] :
( subset(X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_454,c_901]) ).
tcf(c_48807,plain,
! [X0: $i] :
( subset(X0,topstr_closure(sK291,X0))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48806]) ).
tcf(c_48815,plain,
! [X0: $i,X1: $i] :
( ( meet_of_subsets(the_carrier(X0),sK147(X0,X1)) = topstr_closure(X0,X1) )
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_448,c_901]) ).
tcf(c_48816,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK291),sK147(sK291,X0)) = topstr_closure(sK291,X0) )
| ~ topological_space(sK291)
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48815]) ).
tcf(c_48827,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK147(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_447,c_901]) ).
tcf(c_48828,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291)))
| ~ in(X0,sK147(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_48827]) ).
tcf(c_48844,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(X1,X0)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK147(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_446,c_901]) ).
tcf(c_48845,plain,
! [X0: $i,X1: $i] :
( closed_subset(X0,sK291)
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291)))
| ~ in(X0,sK147(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_48844]) ).
tcf(c_48862,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK147(X0,X1))
| ~ topological_space(X0)
| ~ closed_subset(X2,X0)
| ~ subset(X1,X2)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_445,c_901]) ).
tcf(c_48863,plain,
! [X0: $i,X1: $i] :
( in(X1,sK147(sK291,X0))
| ~ topological_space(sK291)
| ~ closed_subset(X1,sK291)
| ~ subset(X0,X1)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48862]) ).
tcf(c_48883,plain,
! [X0: $i,X1: $i] :
( element(sK147(X0,X1),powerset(powerset(the_carrier(X0))))
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_444,c_901]) ).
tcf(c_48884,plain,
! [X0: $i] :
( element(sK147(sK291,X0),powerset(powerset(the_carrier(sK291))))
| ~ topological_space(sK291)
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48883]) ).
tcf(c_48895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X2,X3)
| ~ in(X1,the_carrier(X0))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,topstr_closure(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_438,c_901]) ).
tcf(c_48896,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ closed_subset(X2,sK291)
| ~ subset(X1,X2)
| ~ in(X0,the_carrier(sK291))
| ~ element(X2,powerset(the_carrier(sK291)))
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,topstr_closure(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_48895]) ).
tcf(c_48919,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X0,X1))
| element(sK146(X0,X1,X2),powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_437,c_901]) ).
tcf(c_48920,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK291,X0))
| element(sK146(sK291,X0,X1),powerset(the_carrier(sK291)))
| ~ in(X1,the_carrier(sK291))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48919]) ).
tcf(c_48934,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X0,X1))
| subset(X1,sK146(X0,X1,X2))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_436,c_901]) ).
tcf(c_48935,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK291,X0))
| subset(X0,sK146(sK291,X0,X1))
| ~ in(X1,the_carrier(sK291))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48934]) ).
tcf(c_48949,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X0,X1))
| closed_subset(sK146(X0,X1,X2),X0)
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_435,c_901]) ).
tcf(c_48950,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK291,X0))
| closed_subset(sK146(sK291,X0,X1),sK291)
| ~ in(X1,the_carrier(sK291))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_48949]) ).
tcf(c_48964,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,topstr_closure(X0,X2))
| ~ in(X1,the_carrier(X0))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK146(X0,X2,X1))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_434,c_901]) ).
tcf(c_48965,plain,
! [X0: $i,X1: $i] :
( in(X0,topstr_closure(sK291,X1))
| ~ in(X0,the_carrier(sK291))
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK146(sK291,X1,X0)) ),
inference(unflattening,[status(thm)],[c_48964]) ).
tcf(c_48979,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| element(sK145(X0,X1),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_432,c_901]) ).
tcf(c_48980,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK291),X0),sK291)
| element(sK145(sK291,X0),powerset(the_carrier(sK291)))
| ~ topological_space(sK291)
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(unflattening,[status(thm)],[c_48979]) ).
tcf(c_48994,plain,
! [X0: $i,X1: $i] :
( in(sK145(X0,X1),X1)
| closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_431,c_901]) ).
tcf(c_48995,plain,
! [X0: $i] :
( in(sK145(sK291,X0),X0)
| closed_subset(meet_of_subsets(the_carrier(sK291),X0),sK291)
| ~ topological_space(sK291)
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(unflattening,[status(thm)],[c_48994]) ).
tcf(c_49009,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(X0),X1),X0)
| ~ topological_space(X0)
| ~ closed_subset(sK145(X0,X1),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_430,c_901]) ).
tcf(c_49010,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK291),X0),sK291)
| ~ topological_space(sK291)
| ~ closed_subset(sK145(sK291,X0),sK291)
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(unflattening,[status(thm)],[c_49009]) ).
tcf(c_49024,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_difference(cast_as_carrier_subset(X0),X2),X1)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X2,sK125(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_268,c_901]) ).
tcf(c_49025,plain,
! [X0: $i,X1: $i] :
( in(set_difference(cast_as_carrier_subset(sK291),X1),X0)
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X1,sK125(sK291,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(unflattening,[status(thm)],[c_49024]) ).
tcf(c_49042,plain,
! [X0: $i,X1: $i] :
( element(sK125(X0,X1),powerset(powerset(the_carrier(X0))))
| ~ topological_space(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_266,c_901]) ).
tcf(c_49043,plain,
! [X0: $i] :
( element(sK125(sK291,X0),powerset(powerset(the_carrier(sK291))))
| ~ topological_space(sK291)
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(unflattening,[status(thm)],[c_49042]) ).
tcf(c_49054,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK123(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_265,c_901]) ).
tcf(c_49055,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291)))
| ~ in(X0,sK123(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_49054]) ).
tcf(c_49071,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(sK124(X0,X2,X1),X0)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK123(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_264,c_901]) ).
tcf(c_49072,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK124(sK291,X1,X0),sK291)
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291)))
| ~ in(X0,sK123(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_49071]) ).
tcf(c_49089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK124(X0,X2,X1) = X1 )
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK123(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_263,c_901]) ).
tcf(c_49090,plain,
! [X0: $i,X1: $i] :
( ( sK124(sK291,X1,X0) = X0 )
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291)))
| ~ in(X0,sK123(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_49089]) ).
tcf(c_49107,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK124(X0,X2,X1),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X1,sK123(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_262,c_901]) ).
tcf(c_49108,plain,
! [X0: $i,X1: $i] :
( element(sK124(sK291,X1,X0),powerset(the_carrier(sK291)))
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291)))
| ~ in(X0,sK123(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_49107]) ).
tcf(c_49125,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK123(X0,X1))
| ~ topological_space(X0)
| ~ closed_subset(X2,X0)
| ~ subset(X1,X2)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_261,c_901]) ).
tcf(c_49126,plain,
! [X0: $i,X1: $i] :
( in(X1,sK123(sK291,X0))
| ~ topological_space(sK291)
| ~ closed_subset(X1,sK291)
| ~ subset(X0,X1)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_49125]) ).
tcf(c_49146,plain,
! [X0: $i,X1: $i] :
( element(sK123(X0,X1),powerset(powerset(the_carrier(X0))))
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_260,c_901]) ).
tcf(c_49147,plain,
! [X0: $i] :
( element(sK123(sK291,X0),powerset(powerset(the_carrier(sK291))))
| ~ topological_space(sK291)
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_49146]) ).
tcf(c_49158,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_difference(cast_as_carrier_subset(X0),X2),X1)
| ~ topological_space(X0)
| ~ in(X2,sK93(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_195,c_901]) ).
tcf(c_49159,plain,
! [X0: $i,X1: $i] :
( in(set_difference(cast_as_carrier_subset(sK291),X1),X0)
| ~ topological_space(sK291)
| ~ in(X1,sK93(sK291,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(unflattening,[status(thm)],[c_49158]) ).
tcf(c_49173,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ in(X2,sK93(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_194,c_901]) ).
tcf(c_49174,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(the_carrier(sK291)))
| ~ topological_space(sK291)
| ~ in(X1,sK93(sK291,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(unflattening,[status(thm)],[c_49173]) ).
tcf(c_49188,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK91(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_192,c_901]) ).
tcf(c_49189,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK91(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_49188]) ).
tcf(c_49202,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(sK92(X0,X2,X1),X0)
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK91(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_191,c_901]) ).
tcf(c_49203,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK92(sK291,X1,X0),sK291)
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK91(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_49202]) ).
tcf(c_49217,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK92(X0,X2,X1) = X1 )
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK91(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_190,c_901]) ).
tcf(c_49218,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK291,X1,X0) = X0 )
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK91(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_49217]) ).
tcf(c_49232,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK92(X0,X2,X1),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK91(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_189,c_901]) ).
tcf(c_49233,plain,
! [X0: $i,X1: $i] :
( element(sK92(sK291,X1,X0),powerset(the_carrier(sK291)))
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK91(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_49232]) ).
tcf(c_49247,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK91(X0,X2))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_188,c_901]) ).
tcf(c_49248,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK291)))
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X0,sK91(sK291,X1)) ),
inference(unflattening,[status(thm)],[c_49247]) ).
tcf(c_49773,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ( X0 != sK320 ) ),
inference(resolution_lifted,[status(thm)],[c_2775,c_989]) ).
tcf(c_49774,plain,
the_carrier(sK320) = cast_as_carrier_subset(sK320),
inference(unflattening,[status(thm)],[c_49773]) ).
tcf(c_49783,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ( X0 != sK321 ) ),
inference(resolution_lifted,[status(thm)],[c_2775,c_992]) ).
tcf(c_49784,plain,
the_carrier(sK321) = cast_as_carrier_subset(sK321),
inference(unflattening,[status(thm)],[c_49783]) ).
tcf(c_49793,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ( X0 != sK349 ) ),
inference(resolution_lifted,[status(thm)],[c_2775,c_21700]) ).
tcf(c_49794,plain,
the_carrier(sK349) = cast_as_carrier_subset(sK349),
inference(unflattening,[status(thm)],[c_49793]) ).
tcf(c_49803,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ( X0 != sK375 ) ),
inference(resolution_lifted,[status(thm)],[c_2775,c_21749]) ).
tcf(c_49804,plain,
the_carrier(sK375) = cast_as_carrier_subset(sK375),
inference(unflattening,[status(thm)],[c_49803]) ).
tcf(c_49813,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ( X0 != sK346 ) ),
inference(resolution_lifted,[status(thm)],[c_2775,c_21705]) ).
tcf(c_49814,plain,
the_carrier(sK346) = cast_as_carrier_subset(sK346),
inference(unflattening,[status(thm)],[c_49813]) ).
tcf(c_49823,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_2775,c_47515]) ).
tcf(c_49824,plain,
the_carrier(sK137) = cast_as_carrier_subset(sK137),
inference(unflattening,[status(thm)],[c_49823]) ).
tcf(c_49833,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_2775,c_47691]) ).
tcf(c_49834,plain,
the_carrier(sK291) = cast_as_carrier_subset(sK291),
inference(unflattening,[status(thm)],[c_49833]) ).
tcf(c_49958,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_343,c_47515]) ).
tcf(c_49959,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK137),cast_as_carrier_subset(sK137),subset_difference(the_carrier(sK137),cast_as_carrier_subset(sK137),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_49958]) ).
tcf(c_49967,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_320,c_47515]) ).
tcf(c_49968,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK137),cast_as_carrier_subset(sK137),X0) = subset_complement(the_carrier(sK137),X0) )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_49967]) ).
tcf(c_49976,plain,
! [X0: $i,X1: $i] :
( ( subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK137 ) ),
inference(resolution_lifted,[status(thm)],[c_306,c_47515]) ).
tcf(c_49977,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK137),X0,cast_as_carrier_subset(sK137)) = X0 )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(unflattening,[status(thm)],[c_49976]) ).
tcf(c_49985,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_343,c_47691]) ).
tcf(c_49986,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK291),cast_as_carrier_subset(sK291),subset_difference(the_carrier(sK291),cast_as_carrier_subset(sK291),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_49985]) ).
tcf(c_49994,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_320,c_47691]) ).
tcf(c_49995,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK291),cast_as_carrier_subset(sK291),X0) = subset_complement(the_carrier(sK291),X0) )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_49994]) ).
tcf(c_50003,plain,
! [X0: $i,X1: $i] :
( ( subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK291 ) ),
inference(resolution_lifted,[status(thm)],[c_306,c_47691]) ).
tcf(c_50004,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK291),X0,cast_as_carrier_subset(sK291)) = X0 )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(unflattening,[status(thm)],[c_50003]) ).
tcf(c_58021,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_658]) ).
tcf(c_59331,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK320),cast_as_carrier_subset(sK320),subset_difference(the_carrier(sK320),cast_as_carrier_subset(sK320),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(prop_impl_just,[status(thm)],[c_23670]) ).
tcf(c_59333,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK320),cast_as_carrier_subset(sK320),X0) = subset_complement(the_carrier(sK320),X0) )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(prop_impl_just,[status(thm)],[c_23679]) ).
tcf(c_59335,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK320),X0,cast_as_carrier_subset(sK320)) = X0 )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(prop_impl_just,[status(thm)],[c_23688]) ).
tcf(c_59343,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK321),cast_as_carrier_subset(sK321),subset_difference(the_carrier(sK321),cast_as_carrier_subset(sK321),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(prop_impl_just,[status(thm)],[c_23697]) ).
tcf(c_59345,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK321),cast_as_carrier_subset(sK321),X0) = subset_complement(the_carrier(sK321),X0) )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(prop_impl_just,[status(thm)],[c_23706]) ).
tcf(c_59347,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK321),X0,cast_as_carrier_subset(sK321)) = X0 )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(prop_impl_just,[status(thm)],[c_23715]) ).
tcf(c_59355,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK349),cast_as_carrier_subset(sK349),subset_difference(the_carrier(sK349),cast_as_carrier_subset(sK349),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(prop_impl_just,[status(thm)],[c_23724]) ).
tcf(c_59357,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK349),cast_as_carrier_subset(sK349),X0) = subset_complement(the_carrier(sK349),X0) )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(prop_impl_just,[status(thm)],[c_23733]) ).
tcf(c_59359,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK349),X0,cast_as_carrier_subset(sK349)) = X0 )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(prop_impl_just,[status(thm)],[c_23742]) ).
tcf(c_59367,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK375),cast_as_carrier_subset(sK375),subset_difference(the_carrier(sK375),cast_as_carrier_subset(sK375),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(prop_impl_just,[status(thm)],[c_23751]) ).
tcf(c_59369,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK375),cast_as_carrier_subset(sK375),X0) = subset_complement(the_carrier(sK375),X0) )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(prop_impl_just,[status(thm)],[c_23760]) ).
tcf(c_59371,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK375),X0,cast_as_carrier_subset(sK375)) = X0 )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(prop_impl_just,[status(thm)],[c_23769]) ).
tcf(c_59379,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK346),cast_as_carrier_subset(sK346),subset_difference(the_carrier(sK346),cast_as_carrier_subset(sK346),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(prop_impl_just,[status(thm)],[c_23778]) ).
tcf(c_59381,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK346),cast_as_carrier_subset(sK346),X0) = subset_complement(the_carrier(sK346),X0) )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(prop_impl_just,[status(thm)],[c_23787]) ).
tcf(c_59383,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK346),X0,cast_as_carrier_subset(sK346)) = X0 )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(prop_impl_just,[status(thm)],[c_23796]) ).
tcf(c_59397,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK137),cast_as_carrier_subset(sK137),subset_difference(the_carrier(sK137),cast_as_carrier_subset(sK137),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(prop_impl_just,[status(thm)],[c_49959]) ).
tcf(c_59399,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK137),cast_as_carrier_subset(sK137),X0) = subset_complement(the_carrier(sK137),X0) )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(prop_impl_just,[status(thm)],[c_49968]) ).
tcf(c_59401,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK137),X0,cast_as_carrier_subset(sK137)) = X0 )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(prop_impl_just,[status(thm)],[c_49977]) ).
tcf(c_59407,plain,
( closed_subset(cast_as_carrier_subset(sK137),sK137)
| ~ topological_space(sK137) ),
inference(prop_impl_just,[status(thm)],[c_47470]) ).
tcf(c_59427,plain,
( closed_subset(cast_as_carrier_subset(sK291),sK291)
| ~ topological_space(sK291) ),
inference(prop_impl_just,[status(thm)],[c_47646]) ).
tcf(c_59443,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK291),cast_as_carrier_subset(sK291),subset_difference(the_carrier(sK291),cast_as_carrier_subset(sK291),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(prop_impl_just,[status(thm)],[c_49986]) ).
tcf(c_59445,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK291),cast_as_carrier_subset(sK291),X0) = subset_complement(the_carrier(sK291),X0) )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(prop_impl_just,[status(thm)],[c_49995]) ).
tcf(c_59447,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK291),X0,cast_as_carrier_subset(sK291)) = X0 )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(prop_impl_just,[status(thm)],[c_50004]) ).
tcf(c_61221,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,subset_complement(X2,X1))
| ~ subset(X1,X2)
| ~ subset(X0,X2)
| ~ disjoint(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_5695,c_58021]) ).
tcf(c_61222,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X2)) = subset_intersection2(X1,X0,X2) )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_5702,c_58021]) ).
tcf(c_61223,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_intersection2(X1,X0,X0) = X0 )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_5703,c_58021]) ).
tcf(c_61224,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subset_intersection2(X1,X0,X2),powerset(X1))
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_5704,c_58021]) ).
tcf(c_61225,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_intersection2(X1,X2,X0) = subset_intersection2(X1,X0,X2) )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_5705,c_58021]) ).
tcf(c_61226,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_difference(X1,X0,X2) = set_difference(X0,X2) )
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_5706,c_58021]) ).
tcf(c_61227,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subset_difference(X1,X0,X2),powerset(X1))
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_5707,c_58021]) ).
tcf(c_61228,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X1,X0),X2)
| ~ subset(X0,X1)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(bin_hyper_res,[status(thm)],[c_7414,c_58021]) ).
tcf(c_68972,plain,
( closed_subset(the_carrier(sK291),sK291)
| ~ topological_space(sK291) ),
inference(light_normalisation,[status(thm)],[c_59427,c_49834]) ).
tcf(c_68983,plain,
( closed_subset(the_carrier(sK137),sK137)
| ~ topological_space(sK137) ),
inference(light_normalisation,[status(thm)],[c_59407,c_49824]) ).
tcf(c_71230,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK291),X0,the_carrier(sK291)) = X0 )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(light_normalisation,[status(thm)],[c_59447,c_49834]) ).
tcf(c_71237,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK137),X0,the_carrier(sK137)) = X0 )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(light_normalisation,[status(thm)],[c_59401,c_49824]) ).
tcf(c_71244,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK346),X0,the_carrier(sK346)) = X0 )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(light_normalisation,[status(thm)],[c_59383,c_49814]) ).
tcf(c_71251,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK375),X0,the_carrier(sK375)) = X0 )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(light_normalisation,[status(thm)],[c_59371,c_49804]) ).
tcf(c_71258,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK349),X0,the_carrier(sK349)) = X0 )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(light_normalisation,[status(thm)],[c_59359,c_49794]) ).
tcf(c_71265,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK321),X0,the_carrier(sK321)) = X0 )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(light_normalisation,[status(thm)],[c_59347,c_49784]) ).
tcf(c_71272,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK320),X0,the_carrier(sK320)) = X0 )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(light_normalisation,[status(thm)],[c_59335,c_49774]) ).
tcf(c_71997,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK291),the_carrier(sK291),X0) = subset_complement(the_carrier(sK291),X0) )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(light_normalisation,[status(thm)],[c_59445,c_49834]) ).
tcf(c_72004,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK137),the_carrier(sK137),X0) = subset_complement(the_carrier(sK137),X0) )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(light_normalisation,[status(thm)],[c_59399,c_49824]) ).
tcf(c_72025,plain,
! [X0: $i] :
( open_subset(subset_difference(the_carrier(sK291),the_carrier(sK291),X0),sK291)
| ~ closed_subset(X0,sK291)
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(light_normalisation,[status(thm)],[c_48622,c_49834]) ).
tcf(c_72049,plain,
! [X0: $i] :
( open_subset(subset_difference(the_carrier(sK137),the_carrier(sK137),X0),sK137)
| ~ closed_subset(X0,sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(light_normalisation,[status(thm)],[c_47864,c_49824]) ).
tcf(c_72059,plain,
! [X0: $i] :
( closed_subset(X0,sK291)
| ~ element(X0,powerset(the_carrier(sK291)))
| ~ open_subset(subset_difference(the_carrier(sK291),the_carrier(sK291),X0),sK291) ),
inference(light_normalisation,[status(thm)],[c_47634,c_49834]) ).
tcf(c_72077,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ open_subset(subset_difference(the_carrier(sK137),the_carrier(sK137),X0),sK137) ),
inference(light_normalisation,[status(thm)],[c_47458,c_49824]) ).
tcf(c_72095,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK346),the_carrier(sK346),X0) = subset_complement(the_carrier(sK346),X0) )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(light_normalisation,[status(thm)],[c_59381,c_49814]) ).
tcf(c_72102,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK375),the_carrier(sK375),X0) = subset_complement(the_carrier(sK375),X0) )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(light_normalisation,[status(thm)],[c_59369,c_49804]) ).
tcf(c_72109,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK349),the_carrier(sK349),X0) = subset_complement(the_carrier(sK349),X0) )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(light_normalisation,[status(thm)],[c_59357,c_49794]) ).
tcf(c_72116,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK321),the_carrier(sK321),X0) = subset_complement(the_carrier(sK321),X0) )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(light_normalisation,[status(thm)],[c_59345,c_49784]) ).
tcf(c_72123,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK320),the_carrier(sK320),X0) = subset_complement(the_carrier(sK320),X0) )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(light_normalisation,[status(thm)],[c_59333,c_49774]) ).
tcf(c_72502,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK291),the_carrier(sK291),subset_difference(the_carrier(sK291),the_carrier(sK291),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(light_normalisation,[status(thm)],[c_59443,c_49834]) ).
tcf(c_72509,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK137),the_carrier(sK137),subset_difference(the_carrier(sK137),the_carrier(sK137),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(light_normalisation,[status(thm)],[c_59397,c_49824]) ).
tcf(c_72560,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK346),the_carrier(sK346),subset_difference(the_carrier(sK346),the_carrier(sK346),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(light_normalisation,[status(thm)],[c_59379,c_49814]) ).
tcf(c_72567,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK375),the_carrier(sK375),subset_difference(the_carrier(sK375),the_carrier(sK375),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(light_normalisation,[status(thm)],[c_59367,c_49804]) ).
tcf(c_72574,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK349),the_carrier(sK349),subset_difference(the_carrier(sK349),the_carrier(sK349),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(light_normalisation,[status(thm)],[c_59355,c_49794]) ).
tcf(c_72581,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK321),the_carrier(sK321),subset_difference(the_carrier(sK321),the_carrier(sK321),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(light_normalisation,[status(thm)],[c_59343,c_49784]) ).
tcf(c_72588,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK320),the_carrier(sK320),subset_difference(the_carrier(sK320),the_carrier(sK320),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(light_normalisation,[status(thm)],[c_59331,c_49774]) ).
tcf(c_73081,plain,
! [X0: $i,X1: $i] :
( in(set_difference(the_carrier(sK291),X1),X0)
| ~ topological_space(sK291)
| ~ in(X1,sK93(sK291,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(light_normalisation,[status(thm)],[c_49159,c_49834]) ).
tcf(c_73134,plain,
! [X0: $i,X1: $i] :
( in(set_difference(the_carrier(sK137),X1),X0)
| ~ topological_space(sK137)
| ~ in(X1,sK93(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(light_normalisation,[status(thm)],[c_48401,c_49824]) ).
tcf(c_73915,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK291)
| in(set_difference(the_carrier(sK291),X1),X0)
| ~ topological_space(sK291)
| ~ in(X1,sK295(sK291,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(light_normalisation,[status(thm)],[c_48741,c_49834]) ).
tcf(c_73951,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK137)
| in(set_difference(the_carrier(sK137),X1),X0)
| ~ topological_space(sK137)
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(light_normalisation,[status(thm)],[c_47983,c_49824]) ).
tcf(c_74519,plain,
! [X0: $i,X1: $i] :
( in(set_difference(the_carrier(sK291),X1),X0)
| ~ topological_space(sK291)
| ~ element(X1,powerset(the_carrier(sK291)))
| ~ in(X1,sK125(sK291,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK291)))) ),
inference(light_normalisation,[status(thm)],[c_49025,c_49834]) ).
tcf(c_74581,plain,
! [X0: $i,X1: $i] :
( in(set_difference(the_carrier(sK137),X1),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X1,sK125(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(light_normalisation,[status(thm)],[c_48267,c_49824]) ).
tcf(c_74621,plain,
! [X0: $i,X1: $i] :
( in(X0,sK93(sK291,X1))
| ~ topological_space(sK291)
| ~ in(X0,powerset(the_carrier(sK291)))
| ~ element(X1,powerset(powerset(the_carrier(sK291))))
| ~ in(set_difference(the_carrier(sK291),X0),X1) ),
inference(light_normalisation,[status(thm)],[c_47729,c_49834]) ).
tcf(c_74637,plain,
! [X0: $i,X1: $i] :
( in(X0,sK125(sK291,X1))
| ~ topological_space(sK291)
| ~ element(X0,powerset(the_carrier(sK291)))
| ~ element(X1,powerset(powerset(the_carrier(sK291))))
| ~ in(set_difference(the_carrier(sK291),X0),X1) ),
inference(light_normalisation,[status(thm)],[c_47711,c_49834]) ).
tcf(c_74653,plain,
! [X0: $i,X1: $i] :
( in(X0,sK93(sK137,X1))
| ~ topological_space(sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(set_difference(the_carrier(sK137),X0),X1) ),
inference(light_normalisation,[status(thm)],[c_47553,c_49824]) ).
tcf(c_74669,plain,
! [X0: $i,X1: $i] :
( in(X0,sK125(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(set_difference(the_carrier(sK137),X0),X1) ),
inference(light_normalisation,[status(thm)],[c_47535,c_49824]) ).
tcf(c_75035,plain,
! [X0: $i,X1: $i] :
( sP34(X1,sK291)
| in(X0,sK295(sK291,X1))
| ~ topological_space(sK291)
| ~ in(X0,powerset(the_carrier(sK291)))
| ~ element(X1,powerset(powerset(the_carrier(sK291))))
| ~ in(set_difference(the_carrier(sK291),X0),X1) ),
inference(light_normalisation,[status(thm)],[c_47670,c_49834]) ).
tcf(c_75054,plain,
! [X0: $i,X1: $i] :
( sP34(X1,sK137)
| in(X0,sK295(sK137,X1))
| ~ topological_space(sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(set_difference(the_carrier(sK137),X0),X1) ),
inference(light_normalisation,[status(thm)],[c_47494,c_49824]) ).
tcf(c_104831,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2))
| in(X0,X2) ),
inference(prop_impl_just,[status(thm)],[c_5900]) ).
tcf(c_104832,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(renaming,[status(thm)],[c_104831]) ).
tcf(c_104855,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_5901]) ).
tcf(c_104879,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2509]) ).
tcf(c_104881,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2511]) ).
tcf(c_104883,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2513]) ).
tcf(c_104885,plain,
! [X0: $i,X1: $i] :
( ~ in(sK52(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2516]) ).
tcf(c_104886,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK52(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_104885]) ).
tcf(c_104887,plain,
! [X0: $i,X1: $i] :
( in(sK52(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2518]) ).
tcf(c_104888,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK52(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_104887]) ).
tcf(c_104931,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0) ),
inference(prop_impl_just,[status(thm)],[c_2268]) ).
tcf(c_104967,plain,
! [X0: $i] :
( ~ being_limit_ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_2291]) ).
tcf(c_104968,plain,
! [X0: $i] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(renaming,[status(thm)],[c_104967]) ).
tcf(c_104999,plain,
( element(sK72(sK66),powerset(powerset(set_union2(sK66,unordered_pair(sK66,sK66)))))
| ~ sP8 ),
inference(prop_impl_just,[status(thm)],[c_21428]) ).
tcf(c_105001,plain,
( ( sK72(sK66) != empty_set )
| ~ sP8 ),
inference(prop_impl_just,[status(thm)],[c_21448]) ).
tcf(c_105002,plain,
( ~ sP8
| ( sK72(sK66) != empty_set ) ),
inference(renaming,[status(thm)],[c_105001]) ).
tcf(c_105037,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK178(X0),sK178(X0)),unordered_pair(sK178(X0),sK180(X0))),X0)
| function(X0) ),
inference(prop_impl_just,[status(thm)],[c_16098]) ).
tcf(c_105038,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK178(X0),sK178(X0)),unordered_pair(sK178(X0),sK180(X0))),X0) ),
inference(renaming,[status(thm)],[c_105037]) ).
tcf(c_105039,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK178(X0),sK178(X0)),unordered_pair(sK178(X0),sK179(X0))),X0)
| function(X0) ),
inference(prop_impl_just,[status(thm)],[c_16105]) ).
tcf(c_105040,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK178(X0),sK178(X0)),unordered_pair(sK178(X0),sK179(X0))),X0) ),
inference(renaming,[status(thm)],[c_105039]) ).
tcf(c_105047,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK84(X1,X0),sK84(X1,X0)),unordered_pair(sK84(X1,X0),sK85(X1,X0))) = X0 )
| ~ in(X0,sK83(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_18325]) ).
tcf(c_105053,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK241(X1,X2,X0),sK241(X1,X2,X0)),unordered_pair(sK241(X1,X2,X0),sK242(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_19031]) ).
tcf(c_105231,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK185(X0),sK185(X0)),unordered_pair(sK185(X0),sK186(X0))) = sK183(X0) )
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_16798]) ).
tcf(c_105299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK226(X1,X2,X3),sK226(X1,X2,X3)),unordered_pair(sK226(X1,X2,X3),sK227(X1,X2,X3))) = X2 )
| ~ sP25(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_19038]) ).
tcf(c_105307,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK229(X0,X1,X2),sK229(X0,X1,X2)),unordered_pair(sK229(X0,X1,X2),sK230(X0,X1,X2))) = X0 )
| ~ sP24(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_18797]) ).
tcf(c_105321,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation_of2(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_3054]) ).
tcf(c_105322,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_105321]) ).
tcf(c_105439,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_3185]) ).
tcf(c_105441,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(X0),X2)
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_3187]) ).
tcf(c_105455,plain,
! [X0: $i,X1: $i] :
( equipotent(X1,X0)
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3201]) ).
tcf(c_105457,plain,
! [X0: $i,X1: $i] :
( relation(sK204(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3203]) ).
tcf(c_105459,plain,
! [X0: $i,X1: $i] :
( function(sK204(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3205]) ).
tcf(c_105461,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK204(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3207]) ).
tcf(c_105463,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK204(X0,X1)) = X0 )
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3209]) ).
tcf(c_105465,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK204(X0,X1)) = X1 )
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3211]) ).
tcf(c_105493,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),identity_relation(X2)) ),
inference(prop_impl_just,[status(thm)],[c_5899]) ).
tcf(c_105505,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(prop_impl_just,[status(thm)],[c_18168]) ).
tcf(c_105507,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(prop_impl_just,[status(thm)],[c_18161]) ).
tcf(c_105911,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) )
| ( X1 = X2 ) ),
inference(prop_impl_just,[status(thm)],[c_20697]) ).
tcf(c_105912,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(renaming,[status(thm)],[c_105911]) ).
tcf(c_105925,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) )
| ( X0 = X2 ) ),
inference(prop_impl_just,[status(thm)],[c_20705]) ).
tcf(c_105926,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(renaming,[status(thm)],[c_105925]) ).
tcf(c_105977,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sK83(X1,X2))
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),cartesian_product2(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_18725]) ).
tcf(c_106029,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK320),X0,the_carrier(sK320)) = X0 )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(prop_impl_just,[status(thm)],[c_71272]) ).
tcf(c_106031,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK320),the_carrier(sK320),X0) = subset_complement(the_carrier(sK320),X0) )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(prop_impl_just,[status(thm)],[c_72123]) ).
tcf(c_106033,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK320),the_carrier(sK320),subset_difference(the_carrier(sK320),the_carrier(sK320),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK320))) ),
inference(prop_impl_just,[status(thm)],[c_72588]) ).
tcf(c_106035,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK321),X0,the_carrier(sK321)) = X0 )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(prop_impl_just,[status(thm)],[c_71265]) ).
tcf(c_106037,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK321),the_carrier(sK321),X0) = subset_complement(the_carrier(sK321),X0) )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(prop_impl_just,[status(thm)],[c_72116]) ).
tcf(c_106039,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK321),the_carrier(sK321),subset_difference(the_carrier(sK321),the_carrier(sK321),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK321))) ),
inference(prop_impl_just,[status(thm)],[c_72581]) ).
tcf(c_106041,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK349),X0,the_carrier(sK349)) = X0 )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(prop_impl_just,[status(thm)],[c_71258]) ).
tcf(c_106043,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK349),the_carrier(sK349),X0) = subset_complement(the_carrier(sK349),X0) )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(prop_impl_just,[status(thm)],[c_72109]) ).
tcf(c_106045,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK349),the_carrier(sK349),subset_difference(the_carrier(sK349),the_carrier(sK349),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK349))) ),
inference(prop_impl_just,[status(thm)],[c_72574]) ).
tcf(c_106047,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK375),X0,the_carrier(sK375)) = X0 )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(prop_impl_just,[status(thm)],[c_71251]) ).
tcf(c_106049,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK375),the_carrier(sK375),X0) = subset_complement(the_carrier(sK375),X0) )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(prop_impl_just,[status(thm)],[c_72102]) ).
tcf(c_106051,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK375),the_carrier(sK375),subset_difference(the_carrier(sK375),the_carrier(sK375),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK375))) ),
inference(prop_impl_just,[status(thm)],[c_72567]) ).
tcf(c_106053,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK346),X0,the_carrier(sK346)) = X0 )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(prop_impl_just,[status(thm)],[c_71244]) ).
tcf(c_106055,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK346),the_carrier(sK346),X0) = subset_complement(the_carrier(sK346),X0) )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(prop_impl_just,[status(thm)],[c_72095]) ).
tcf(c_106057,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK346),the_carrier(sK346),subset_difference(the_carrier(sK346),the_carrier(sK346),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK346))) ),
inference(prop_impl_just,[status(thm)],[c_72560]) ).
tcf(c_106059,plain,
! [X0: $i] :
( sP38(sK137,X0,topstr_closure(sK137,X0))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(prop_impl_just,[status(thm)],[c_47747]) ).
tcf(c_106061,plain,
! [X0: $i] :
( element(topstr_closure(sK137,X0),powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(prop_impl_just,[status(thm)],[c_47831]) ).
tcf(c_106063,plain,
! [X0: $i] :
( subset(X0,topstr_closure(sK137,X0))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(prop_impl_just,[status(thm)],[c_48049]) ).
tcf(c_106065,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK137),X0,the_carrier(sK137)) = X0 )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(prop_impl_just,[status(thm)],[c_71237]) ).
tcf(c_106067,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK137),the_carrier(sK137),X0) = subset_complement(the_carrier(sK137),X0) )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(prop_impl_just,[status(thm)],[c_72004]) ).
tcf(c_106069,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK137),the_carrier(sK137),subset_difference(the_carrier(sK137),the_carrier(sK137),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(prop_impl_just,[status(thm)],[c_72509]) ).
tcf(c_106071,plain,
( sP42(sK137)
| ~ topological_space(sK137) ),
inference(prop_impl_just,[status(thm)],[c_47395]) ).
tcf(c_106073,plain,
( in(the_carrier(sK137),the_topology(sK137))
| ~ topological_space(sK137) ),
inference(prop_impl_just,[status(thm)],[c_47403]) ).
tcf(c_106075,plain,
( closed_subset(sK305(sK137),sK137)
| ~ topological_space(sK137) ),
inference(prop_impl_just,[status(thm)],[c_47478]) ).
tcf(c_106077,plain,
( element(sK305(sK137),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(prop_impl_just,[status(thm)],[c_47486]) ).
tcf(c_106079,plain,
( closed_subset(the_carrier(sK137),sK137)
| ~ topological_space(sK137) ),
inference(prop_impl_just,[status(thm)],[c_68983]) ).
tcf(c_106089,plain,
( sP42(sK291)
| ~ topological_space(sK291) ),
inference(prop_impl_just,[status(thm)],[c_47571]) ).
tcf(c_106091,plain,
( in(the_carrier(sK291),the_topology(sK291))
| ~ topological_space(sK291) ),
inference(prop_impl_just,[status(thm)],[c_47579]) ).
tcf(c_106093,plain,
( closed_subset(sK305(sK291),sK291)
| ~ topological_space(sK291) ),
inference(prop_impl_just,[status(thm)],[c_47654]) ).
tcf(c_106095,plain,
( element(sK305(sK291),powerset(the_carrier(sK291)))
| ~ topological_space(sK291) ),
inference(prop_impl_just,[status(thm)],[c_47662]) ).
tcf(c_106097,plain,
( closed_subset(the_carrier(sK291),sK291)
| ~ topological_space(sK291) ),
inference(prop_impl_just,[status(thm)],[c_68972]) ).
tcf(c_106103,plain,
! [X0: $i] :
( sP38(sK291,X0,topstr_closure(sK291,X0))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(prop_impl_just,[status(thm)],[c_48505]) ).
tcf(c_106105,plain,
! [X0: $i] :
( element(topstr_closure(sK291,X0),powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(prop_impl_just,[status(thm)],[c_48589]) ).
tcf(c_106107,plain,
! [X0: $i] :
( subset(X0,topstr_closure(sK291,X0))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(prop_impl_just,[status(thm)],[c_48807]) ).
tcf(c_106109,plain,
! [X0: $i] :
( ( subset_intersection2(the_carrier(sK291),X0,the_carrier(sK291)) = X0 )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(prop_impl_just,[status(thm)],[c_71230]) ).
tcf(c_106111,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK291),the_carrier(sK291),X0) = subset_complement(the_carrier(sK291),X0) )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(prop_impl_just,[status(thm)],[c_71997]) ).
tcf(c_106113,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK291),the_carrier(sK291),subset_difference(the_carrier(sK291),the_carrier(sK291),X0)) = X0 )
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(prop_impl_just,[status(thm)],[c_72502]) ).
tcf(c_151099,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_10
| ( join(sK346,meet(sK346,X0,X1),X1) = X1 )
| ~ element(X1,the_carrier(sK346))
| ~ element(X0,the_carrier(sK346)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_22215]) ).
tcf(c_151100,plain,
( iPr_def_10
| ~ meet_absorbing(sK346)
| ( sK320 != sK346 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_22215]) ).
tcf(c_151106,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_14
| ( sK268(X0) = X1 )
| ( X0 = empty_set )
| ~ in(X1,X0)
| ~ subset(sK268(X0),X1)
| ~ element(X0,powerset(powerset(sK267))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_830]) ).
tcf(c_151107,plain,
( iPr_def_14
| iPr_def_11
| ~ in(sK267,omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_830]) ).
tcf(c_151108,plain,
! [X0: $i] :
( ~ iPr_def_15
| ( X0 = empty_set )
| in(sK268(X0),X0)
| ~ element(X0,powerset(powerset(sK267))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_15])],[c_829]) ).
tcf(c_151109,plain,
( iPr_def_15
| iPr_def_11
| ~ in(sK267,omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_829]) ).
tcf(c_151110,plain,
! [X0: $i] :
( ~ iPr_def_16
| ~ ordinal(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_16])],[c_803]) ).
tcf(c_151111,plain,
! [X0: $i] :
( ~ iPr_def_17
| ~ ordinal(X0)
| ordinal_subset(X0,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_17])],[c_803]) ).
tcf(c_151112,plain,
( iPr_def_17
| iPr_def_16 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_803]) ).
tcf(c_151113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_18
| ( sK76(X0) = X2 )
| ( X0 = empty_set )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ in(X2,X0)
| ~ subset(sK76(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_18])],[c_154]) ).
tcf(c_151114,plain,
( iPr_def_18
| sP6
| sP7
| sP8 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_154]) ).
tcf(c_151115,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_19
| ( X0 = empty_set )
| ~ ordinal(X1)
| in(sK76(X0),X0)
| ~ in(X1,omega)
| ~ element(X0,powerset(powerset(X1))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_19])],[c_153]) ).
tcf(c_151116,plain,
( iPr_def_19
| sP6
| sP7
| sP8 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_153]) ).
tcf(c_151117,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_20
| ( sK67(X0) = X1 )
| ( X0 = empty_set )
| ~ in(X1,X0)
| ~ subset(sK67(X0),X1)
| ~ element(X0,powerset(powerset(sK66))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_20])],[c_128]) ).
tcf(c_151118,plain,
( iPr_def_20
| ~ sP8
| ~ in(sK66,omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_128]) ).
tcf(c_151119,plain,
! [X0: $i] :
( ~ iPr_def_21
| ( X0 = empty_set )
| in(sK67(X0),X0)
| ~ element(X0,powerset(powerset(sK66))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_21])],[c_127]) ).
tcf(c_151120,plain,
( iPr_def_21
| ~ sP8
| ~ in(sK66,omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_127]) ).
tcf(c_151317,plain,
( ~ iPr_def_16
| ~ ordinal(empty_set) ),
inference(instantiation,[status(thm)],[c_151110]) ).
tcf(c_174884,plain,
( in(sK138,the_topology(sK137))
| ~ open_subset(sK138,sK137) ),
inference(superposition,[status(thm)],[c_376,c_47840]) ).
tcf(c_174897,plain,
( open_subset(sK138,sK137)
| ~ in(sK138,the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_376,c_47852]) ).
tcf(c_174919,plain,
( ( topstr_closure(sK137,sK138) = sK138 )
| ~ closed_subset(sK138,sK137) ),
inference(superposition,[status(thm)],[c_376,c_48037]) ).
tcf(c_174960,plain,
! [X0: $i] :
( subset(sK138,X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_48431]) ).
tcf(c_174993,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK138)) = topstr_closure(sK137,sK138) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_376,c_48058]) ).
tcf(c_175008,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_48490]) ).
tcf(c_175029,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(sK138,X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_47876]) ).
tcf(c_175058,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),the_topology(sK137)),sK137)
| in(sK145(sK137,the_topology(sK137)),the_topology(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_47453,c_48237]) ).
tcf(c_175059,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,X0)),sK137)
| in(sK145(sK137,sK147(sK137,X0)),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48126,c_48237]) ).
tcf(c_175060,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK125(sK137,X0)),sK137)
| in(sK145(sK137,sK125(sK137,X0)),sK125(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48285,c_48237]) ).
tcf(c_175061,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,X0)),sK137)
| in(sK145(sK137,sK123(sK137,X0)),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48389,c_48237]) ).
tcf(c_175089,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_47453,c_48416]) ).
tcf(c_175090,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48126,c_48416]) ).
tcf(c_175091,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK93(sK137,sK125(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48285,c_48416]) ).
tcf(c_175092,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48389,c_48416]) ).
tcf(c_175154,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),the_topology(sK137)),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,the_topology(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_47453,c_48252]) ).
tcf(c_175155,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,X0)),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK145(sK137,sK147(sK137,X0)),sK137) ),
inference(superposition,[status(thm)],[c_48126,c_48252]) ).
tcf(c_175156,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK125(sK137,X0)),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ closed_subset(sK145(sK137,sK125(sK137,X0)),sK137) ),
inference(superposition,[status(thm)],[c_48285,c_48252]) ).
tcf(c_175157,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,X0)),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK145(sK137,sK123(sK137,X0)),sK137) ),
inference(superposition,[status(thm)],[c_48389,c_48252]) ).
tcf(c_175190,plain,
! [X0: $i] :
( ( sK92(sK137,sK138,X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_48460]) ).
tcf(c_175209,plain,
! [X0: $i] :
( ( topstr_closure(sK137,sK138) = X0 )
| ~ sP38(sK137,sK138,X0)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_376,c_47756]) ).
tcf(c_175220,plain,
( ( topstr_closure(sK137,sK138) = sK138 )
| ~ sP38(sK137,sK138,sK138) ),
inference(superposition,[status(thm)],[c_376,c_175209]) ).
tcf(c_175243,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ( topstr_closure(sK137,sK145(sK137,X0)) = X1 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ sP38(sK137,sK145(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_48222,c_47756]) ).
tcf(c_175244,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X1),sK137)
| ( sK92(sK137,sK145(sK137,X1),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK91(sK137,sK145(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48222,c_48460]) ).
tcf(c_175245,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,sK145(sK137,X1))
| subset(sK145(sK137,X1),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK302(sK137,sK145(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48222,c_47876]) ).
tcf(c_175246,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK137)))
| closed_subset(meet_of_subsets(the_carrier(sK137),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK91(sK137,sK145(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48222,c_48490]) ).
tcf(c_175247,plain,
! [X0: $i,X1: $i] :
( subset(sK145(sK137,X1),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK91(sK137,sK145(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48222,c_48431]) ).
tcf(c_175248,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ( sK145(sK137,X0) = topstr_closure(sK137,sK138) )
| ~ topological_space(sK137)
| ~ sP38(sK137,sK138,sK145(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_175209]) ).
tcf(c_175249,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK145(sK137,X0))) = topstr_closure(sK137,sK145(sK137,X0)) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_48058]) ).
tcf(c_175250,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ( topstr_closure(sK137,sK145(sK137,X0)) = sK145(sK137,X0) )
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,X0),sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_48037]) ).
tcf(c_175251,plain,
! [X0: $i] :
( open_subset(sK145(sK137,X0),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ in(sK145(sK137,X0),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_48222,c_47852]) ).
tcf(c_175252,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| in(sK145(sK137,X0),the_topology(sK137))
| ~ topological_space(sK137)
| ~ open_subset(sK145(sK137,X0),sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_47840]) ).
tcf(c_175321,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( topstr_closure(sK137,sK92(sK137,X0,X1)) = X2 )
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ sP38(sK137,sK92(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_48475,c_47756]) ).
tcf(c_175322,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK92(sK137,sK92(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ in(X0,sK91(sK137,sK92(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48475,c_48460]) ).
tcf(c_175323,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,sK92(sK137,X1,X2))
| subset(sK92(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ in(X0,sK302(sK137,sK92(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48475,c_47876]) ).
tcf(c_175324,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ in(X0,sK91(sK137,sK92(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48475,c_48490]) ).
tcf(c_175325,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK92(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ in(X0,sK91(sK137,sK92(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48475,c_48431]) ).
tcf(c_175326,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,X0,X1) = topstr_closure(sK137,sK138) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ sP38(sK137,sK138,sK92(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_175209]) ).
tcf(c_175327,plain,
! [X0: $i,X1: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK92(sK137,X1,X0))) = topstr_closure(sK137,sK92(sK137,X1,X0)) )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_48058]) ).
tcf(c_175328,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(sK137,sK92(sK137,X0,X1)) = sK92(sK137,X0,X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ closed_subset(sK92(sK137,X0,X1),sK137) ),
inference(superposition,[status(thm)],[c_48475,c_48037]) ).
tcf(c_175329,plain,
! [X0: $i,X1: $i] :
( open_subset(sK92(sK137,X0,X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ in(sK92(sK137,X0,X1),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_48475,c_47852]) ).
tcf(c_175330,plain,
! [X0: $i,X1: $i] :
( in(sK92(sK137,X0,X1),the_topology(sK137))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ open_subset(sK92(sK137,X0,X1),sK137) ),
inference(superposition,[status(thm)],[c_48475,c_47840]) ).
tcf(c_175418,plain,
! [X0: $i] :
( subset(sK138,X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_48070]) ).
tcf(c_175419,plain,
! [X0: $i,X1: $i] :
( subset(sK145(sK137,X1),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK147(sK137,sK145(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48222,c_48070]) ).
tcf(c_175420,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK92(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ in(X0,sK147(sK137,sK92(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48475,c_48070]) ).
tcf(c_175448,plain,
( subset(sK138,sK138)
| ~ topological_space(sK137)
| ~ in(sK138,sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_175418]) ).
tcf(c_175449,plain,
! [X0: $i] :
( subset(sK138,sK145(sK137,X0))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ in(sK145(sK137,X0),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48222,c_175418]) ).
tcf(c_175450,plain,
! [X0: $i,X1: $i] :
( subset(sK138,sK92(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ in(sK92(sK137,X0,X1),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48475,c_175418]) ).
tcf(c_175482,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_48087]) ).
tcf(c_175483,plain,
! [X0: $i,X1: $i] :
( closed_subset(X0,sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK147(sK137,sK145(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48222,c_48087]) ).
tcf(c_175484,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ in(X0,sK147(sK137,sK92(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48475,c_48087]) ).
tcf(c_175512,plain,
( closed_subset(sK138,sK137)
| ~ topological_space(sK137)
| ~ in(sK138,sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_175482]) ).
tcf(c_175513,plain,
! [X0: $i] :
( closed_subset(sK145(sK137,X0),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ in(sK145(sK137,X0),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48222,c_175482]) ).
tcf(c_175514,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK92(sK137,X0,X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ in(sK92(sK137,X0,X1),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48475,c_175482]) ).
tcf(c_175543,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(X0,sK137)
| in(X2,topstr_closure(sK137,X1))
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK146(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48162,c_48087]) ).
tcf(c_175544,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,X1))
| subset(sK146(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK146(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48162,c_48070]) ).
tcf(c_175545,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,topstr_closure(sK137,X0))
| ( topstr_closure(sK137,sK146(sK137,X0,X1)) = X2 )
| ~ in(X1,the_carrier(sK137))
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK146(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_48162,c_47756]) ).
tcf(c_175546,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,X1))
| ( sK92(sK137,sK146(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,sK146(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48162,c_48460]) ).
tcf(c_175547,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,X1))
| sP36(sK137,sK146(sK137,X1,X2))
| subset(sK146(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,sK146(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48162,c_47876]) ).
tcf(c_175548,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,powerset(the_carrier(sK137)))
| in(X2,topstr_closure(sK137,X1))
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,sK146(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48162,c_48490]) ).
tcf(c_175549,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,X1))
| subset(sK146(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,sK146(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48162,c_48431]) ).
tcf(c_175550,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| closed_subset(sK146(sK137,X0,X1),sK137)
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(sK146(sK137,X0,X1),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48162,c_175482]) ).
tcf(c_175551,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| subset(sK138,sK146(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(sK146(sK137,X0,X1),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48162,c_175418]) ).
tcf(c_175552,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| ( sK146(sK137,X0,X1) = topstr_closure(sK137,sK138) )
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK138,sK146(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_48162,c_175209]) ).
tcf(c_175553,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK146(sK137,X0,X1))) = topstr_closure(sK137,sK146(sK137,X0,X1)) )
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_48058]) ).
tcf(c_175554,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| ( topstr_closure(sK137,sK146(sK137,X0,X1)) = sK146(sK137,X0,X1) )
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK146(sK137,X0,X1),sK137) ),
inference(superposition,[status(thm)],[c_48162,c_48037]) ).
tcf(c_175555,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| open_subset(sK146(sK137,X0,X1),sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(sK146(sK137,X0,X1),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_48162,c_47852]) ).
tcf(c_175556,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| in(sK146(sK137,X0,X1),the_topology(sK137))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ open_subset(sK146(sK137,X0,X1),sK137) ),
inference(superposition,[status(thm)],[c_48162,c_47840]) ).
tcf(c_175660,plain,
iPr_def_17,
inference(global_subsumption_just,[status(thm)],[c_151112,c_1341,c_1414,c_151317,c_151112]) ).
tcf(c_175672,plain,
! [X0: $i] :
( subset(sK138,X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_48297]) ).
tcf(c_175673,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,X1))
| subset(sK146(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK146(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48162,c_48297]) ).
tcf(c_175674,plain,
! [X0: $i,X1: $i] :
( subset(sK145(sK137,X1),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK123(sK137,sK145(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48222,c_48297]) ).
tcf(c_175675,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK92(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ in(X0,sK123(sK137,sK92(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48475,c_48297]) ).
tcf(c_175711,plain,
( subset(sK138,sK138)
| ~ topological_space(sK137)
| ~ in(sK138,sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_175672]) ).
tcf(c_175712,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| subset(sK138,sK146(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(sK146(sK137,X0,X1),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48162,c_175672]) ).
tcf(c_175713,plain,
! [X0: $i] :
( subset(sK138,sK145(sK137,X0))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ in(sK145(sK137,X0),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48222,c_175672]) ).
tcf(c_175714,plain,
! [X0: $i,X1: $i] :
( subset(sK138,sK92(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ in(sK92(sK137,X0,X1),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48475,c_175672]) ).
tcf(c_175753,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_47911]) ).
tcf(c_175754,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,X1))
| sP36(sK137,sK146(sK137,X1,X2))
| ( sK304(sK137,sK146(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,sK146(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48162,c_47911]) ).
tcf(c_175755,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,sK145(sK137,X1))
| closed_subset(meet_of_subsets(the_carrier(sK137),X1),sK137)
| ( sK304(sK137,sK145(sK137,X1),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK302(sK137,sK145(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48222,c_47911]) ).
tcf(c_175756,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,sK92(sK137,X1,X2))
| ( sK304(sK137,sK92(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ in(X0,sK302(sK137,sK92(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48475,c_47911]) ).
tcf(c_175802,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_47947]) ).
tcf(c_175803,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,X1))
| sP36(sK137,sK146(sK137,X1,X2))
| ( sK303(sK137,sK146(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,sK146(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48162,c_47947]) ).
tcf(c_175804,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,sK145(sK137,X1))
| closed_subset(meet_of_subsets(the_carrier(sK137),X1),sK137)
| ( sK303(sK137,sK145(sK137,X1),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK302(sK137,sK145(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48222,c_47947]) ).
tcf(c_175805,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,sK92(sK137,X1,X2))
| ( sK303(sK137,sK92(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ in(X0,sK302(sK137,sK92(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48475,c_47947]) ).
tcf(c_175851,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| sP36(sK137,sK304(sK137,X1,X2))
| ( sK303(sK137,sK304(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ in(X0,sK302(sK137,sK304(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_47929,c_47947]) ).
tcf(c_175852,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| sP36(sK137,sK304(sK137,X1,X2))
| ( sK304(sK137,sK304(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ in(X0,sK302(sK137,sK304(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_47929,c_47911]) ).
tcf(c_175853,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| subset(sK304(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ in(X0,sK123(sK137,sK304(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_47929,c_48297]) ).
tcf(c_175854,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ in(X0,sK147(sK137,sK304(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_47929,c_48087]) ).
tcf(c_175855,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| subset(sK304(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ in(X0,sK147(sK137,sK304(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_47929,c_48070]) ).
tcf(c_175856,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X0)
| ( topstr_closure(sK137,sK304(sK137,X0,X1)) = X2 )
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ sP38(sK137,sK304(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_47929,c_47756]) ).
tcf(c_175857,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| ( sK92(sK137,sK304(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ in(X0,sK91(sK137,sK304(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_47929,c_48460]) ).
tcf(c_175858,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| sP36(sK137,sK304(sK137,X1,X2))
| subset(sK304(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ in(X0,sK302(sK137,sK304(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_47929,c_47876]) ).
tcf(c_175859,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ in(X0,sK91(sK137,sK304(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_47929,c_48490]) ).
tcf(c_175860,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| subset(sK304(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ in(X0,sK91(sK137,sK304(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_47929,c_48431]) ).
tcf(c_175861,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| subset(sK138,sK304(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ in(sK304(sK137,X0,X1),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_47929,c_175672]) ).
tcf(c_175862,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| closed_subset(sK304(sK137,X0,X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ in(sK304(sK137,X0,X1),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_47929,c_175482]) ).
tcf(c_175863,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| subset(sK138,sK304(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ in(sK304(sK137,X0,X1),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_47929,c_175418]) ).
tcf(c_175864,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| ( sK304(sK137,X0,X1) = topstr_closure(sK137,sK138) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ sP38(sK137,sK138,sK304(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_175209]) ).
tcf(c_175865,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK304(sK137,X1,X0))) = topstr_closure(sK137,sK304(sK137,X1,X0)) )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_48058]) ).
tcf(c_175866,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| ( topstr_closure(sK137,sK304(sK137,X0,X1)) = sK304(sK137,X0,X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ closed_subset(sK304(sK137,X0,X1),sK137) ),
inference(superposition,[status(thm)],[c_47929,c_48037]) ).
tcf(c_175867,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| open_subset(sK304(sK137,X0,X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ in(sK304(sK137,X0,X1),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_47929,c_47852]) ).
tcf(c_175868,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| in(sK304(sK137,X0,X1),the_topology(sK137))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ open_subset(sK304(sK137,X0,X1),sK137) ),
inference(superposition,[status(thm)],[c_47929,c_47840]) ).
tcf(c_176004,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,topstr_closure(sK137,X1))
| ( sK303(sK137,topstr_closure(sK137,X1),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,topstr_closure(sK137,X1))) ),
inference(superposition,[status(thm)],[c_106061,c_47947]) ).
tcf(c_176005,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,topstr_closure(sK137,X1))
| ( sK304(sK137,topstr_closure(sK137,X1),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,topstr_closure(sK137,X1))) ),
inference(superposition,[status(thm)],[c_106061,c_47911]) ).
tcf(c_176006,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK137,X1),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,topstr_closure(sK137,X1))) ),
inference(superposition,[status(thm)],[c_106061,c_48297]) ).
tcf(c_176007,plain,
! [X0: $i,X1: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,topstr_closure(sK137,X1))) ),
inference(superposition,[status(thm)],[c_106061,c_48087]) ).
tcf(c_176008,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK137,X1),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,topstr_closure(sK137,X1))) ),
inference(superposition,[status(thm)],[c_106061,c_48070]) ).
tcf(c_176009,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(sK137,topstr_closure(sK137,X0)) = X1 )
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,topstr_closure(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_106061,c_47756]) ).
tcf(c_176010,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,topstr_closure(sK137,X1),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,topstr_closure(sK137,X1))) ),
inference(superposition,[status(thm)],[c_106061,c_48460]) ).
tcf(c_176011,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,topstr_closure(sK137,X1))
| subset(topstr_closure(sK137,X1),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,topstr_closure(sK137,X1))) ),
inference(superposition,[status(thm)],[c_106061,c_47876]) ).
tcf(c_176012,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,topstr_closure(sK137,X1))) ),
inference(superposition,[status(thm)],[c_106061,c_48490]) ).
tcf(c_176013,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK137,X1),X0)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,topstr_closure(sK137,X1))) ),
inference(superposition,[status(thm)],[c_106061,c_48431]) ).
tcf(c_176014,plain,
! [X0: $i] :
( subset(sK138,topstr_closure(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(topstr_closure(sK137,X0),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_106061,c_175672]) ).
tcf(c_176015,plain,
! [X0: $i] :
( closed_subset(topstr_closure(sK137,X0),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(topstr_closure(sK137,X0),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_106061,c_175482]) ).
tcf(c_176016,plain,
! [X0: $i] :
( subset(sK138,topstr_closure(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(topstr_closure(sK137,X0),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_106061,c_175418]) ).
tcf(c_176017,plain,
! [X0: $i] :
( ( topstr_closure(sK137,X0) = topstr_closure(sK137,sK138) )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK138,topstr_closure(sK137,X0)) ),
inference(superposition,[status(thm)],[c_106061,c_175209]) ).
tcf(c_176018,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,X0))) = topstr_closure(sK137,topstr_closure(sK137,X0)) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_48058]) ).
tcf(c_176019,plain,
! [X0: $i] :
( ( topstr_closure(sK137,topstr_closure(sK137,X0)) = topstr_closure(sK137,X0) )
| ~ closed_subset(topstr_closure(sK137,X0),sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_48037]) ).
tcf(c_176020,plain,
! [X0: $i] :
( open_subset(topstr_closure(sK137,X0),sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(topstr_closure(sK137,X0),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_106061,c_47852]) ).
tcf(c_176021,plain,
! [X0: $i] :
( in(topstr_closure(sK137,X0),the_topology(sK137))
| ~ open_subset(topstr_closure(sK137,X0),sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_47840]) ).
tcf(c_176134,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_47453,c_48001]) ).
tcf(c_176135,plain,
! [X0: $i,X1: $i] :
( sP34(sK147(sK137,X1),sK137)
| ( sK296(sK137,sK147(sK137,X1),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK295(sK137,sK147(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48126,c_48001]) ).
tcf(c_176136,plain,
! [X0: $i,X1: $i] :
( sP34(sK125(sK137,X1),sK137)
| ( sK296(sK137,sK125(sK137,X1),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK295(sK137,sK125(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48285,c_48001]) ).
tcf(c_176137,plain,
! [X0: $i,X1: $i] :
( sP34(sK123(sK137,X1),sK137)
| ( sK296(sK137,sK123(sK137,X1),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK295(sK137,sK123(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48389,c_48001]) ).
tcf(c_176193,plain,
! [X0: $i] :
( in(X0,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_376,c_47795]) ).
tcf(c_176194,plain,
! [X0: $i,X1: $i] :
( in(X1,sK91(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(X1,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_106061,c_47795]) ).
tcf(c_176195,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X0)
| in(X2,sK91(sK137,sK304(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(X2,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ subset(sK304(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_47929,c_47795]) ).
tcf(c_176196,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,topstr_closure(sK137,X0))
| in(X2,sK91(sK137,sK146(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(X2,sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,powerset(the_carrier(sK137)))
| ~ subset(sK146(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_48162,c_47795]) ).
tcf(c_176197,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| in(X1,sK91(sK137,sK145(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(X1,sK137)
| ~ in(X1,powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,X0),X1)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_47795]) ).
tcf(c_176198,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK91(sK137,sK92(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(X2,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ subset(sK92(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_48475,c_47795]) ).
tcf(c_176256,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| in(sK303(sK137,X0,X1),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ closed_subset(sK303(sK137,X0,X1),sK137)
| ~ subset(sK138,sK303(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_47965,c_176193]) ).
tcf(c_176257,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK137)
| in(sK296(sK137,X0,X1),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ closed_subset(sK296(sK137,X0,X1),sK137)
| ~ subset(sK138,sK296(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_48019,c_176193]) ).
tcf(c_176286,plain,
! [X0: $i] :
( in(sK138,sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_376,c_48105]) ).
tcf(c_176287,plain,
! [X0: $i,X1: $i] :
( in(topstr_closure(sK137,X1),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(topstr_closure(sK137,X1),sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,topstr_closure(sK137,X1)) ),
inference(superposition,[status(thm)],[c_106061,c_48105]) ).
tcf(c_176288,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| in(sK304(sK137,X1,X2),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ closed_subset(sK304(sK137,X1,X2),sK137)
| ~ subset(X0,sK304(sK137,X1,X2)) ),
inference(superposition,[status(thm)],[c_47929,c_48105]) ).
tcf(c_176289,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,X1))
| in(sK146(sK137,X1,X2),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK146(sK137,X1,X2),sK137)
| ~ subset(X0,sK146(sK137,X1,X2)) ),
inference(superposition,[status(thm)],[c_48162,c_48105]) ).
tcf(c_176290,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| in(sK145(sK137,X0),sK147(sK137,X1))
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,X0),sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(X1,sK145(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_48105]) ).
tcf(c_176291,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK92(sK137,X1,X2),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ closed_subset(sK92(sK137,X1,X2),sK137)
| ~ subset(X0,sK92(sK137,X1,X2)) ),
inference(superposition,[status(thm)],[c_48475,c_48105]) ).
tcf(c_176348,plain,
( in(sK138,sK147(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK138,sK138) ),
inference(superposition,[status(thm)],[c_376,c_176286]) ).
tcf(c_176349,plain,
! [X0: $i] :
( in(sK138,sK147(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138) ),
inference(superposition,[status(thm)],[c_106061,c_176286]) ).
tcf(c_176350,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| in(sK138,sK147(sK137,sK304(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ subset(sK304(sK137,X0,X1),sK138) ),
inference(superposition,[status(thm)],[c_47929,c_176286]) ).
tcf(c_176351,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| in(sK138,sK147(sK137,sK146(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(sK146(sK137,X0,X1),sK138) ),
inference(superposition,[status(thm)],[c_48162,c_176286]) ).
tcf(c_176352,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| in(sK138,sK147(sK137,sK145(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK145(sK137,X0),sK138)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_176286]) ).
tcf(c_176353,plain,
! [X0: $i,X1: $i] :
( in(sK138,sK147(sK137,sK92(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ subset(sK92(sK137,X0,X1),sK138) ),
inference(superposition,[status(thm)],[c_48475,c_176286]) ).
tcf(c_176354,plain,
( in(sK138,sK147(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_176348,c_670]) ).
tcf(c_176408,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_48332]) ).
tcf(c_176409,plain,
! [X0: $i,X1: $i] :
( ( sK124(sK137,topstr_closure(sK137,X1),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,topstr_closure(sK137,X1))) ),
inference(superposition,[status(thm)],[c_106061,c_48332]) ).
tcf(c_176410,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| ( sK124(sK137,sK304(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ in(X0,sK123(sK137,sK304(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_47929,c_48332]) ).
tcf(c_176411,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,X1))
| ( sK124(sK137,sK146(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK146(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48162,c_48332]) ).
tcf(c_176412,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X1),sK137)
| ( sK124(sK137,sK145(sK137,X1),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK123(sK137,sK145(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48222,c_48332]) ).
tcf(c_176413,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK124(sK137,sK92(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ in(X0,sK123(sK137,sK92(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48475,c_48332]) ).
tcf(c_176463,plain,
( ( sK124(sK137,sK138,sK138) = sK138 )
| ~ topological_space(sK137)
| ~ in(sK138,sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_176408]) ).
tcf(c_176464,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,topstr_closure(sK137,X0)) = topstr_closure(sK137,X0) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(topstr_closure(sK137,X0),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_106061,c_176408]) ).
tcf(c_176465,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| ( sK124(sK137,sK138,sK304(sK137,X0,X1)) = sK304(sK137,X0,X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ in(sK304(sK137,X0,X1),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_47929,c_176408]) ).
tcf(c_176466,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| ( sK124(sK137,sK138,sK146(sK137,X0,X1)) = sK146(sK137,X0,X1) )
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(sK146(sK137,X0,X1),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48162,c_176408]) ).
tcf(c_176467,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ( sK124(sK137,sK138,sK145(sK137,X0)) = sK145(sK137,X0) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ in(sK145(sK137,X0),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48222,c_176408]) ).
tcf(c_176468,plain,
! [X0: $i,X1: $i] :
( ( sK124(sK137,sK138,sK92(sK137,X0,X1)) = sK92(sK137,X0,X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ in(sK92(sK137,X0,X1),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48475,c_176408]) ).
tcf(c_176521,plain,
! [X0: $i] :
( in(sK138,sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_376,c_48368]) ).
tcf(c_176522,plain,
! [X0: $i,X1: $i] :
( in(topstr_closure(sK137,X1),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(topstr_closure(sK137,X1),sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,topstr_closure(sK137,X1)) ),
inference(superposition,[status(thm)],[c_106061,c_48368]) ).
tcf(c_176523,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X1)
| in(sK304(sK137,X1,X2),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ closed_subset(sK304(sK137,X1,X2),sK137)
| ~ subset(X0,sK304(sK137,X1,X2)) ),
inference(superposition,[status(thm)],[c_47929,c_48368]) ).
tcf(c_176524,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,X1))
| in(sK146(sK137,X1,X2),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK146(sK137,X1,X2),sK137)
| ~ subset(X0,sK146(sK137,X1,X2)) ),
inference(superposition,[status(thm)],[c_48162,c_48368]) ).
tcf(c_176525,plain,
! [X0: $i,X1: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| in(sK145(sK137,X0),sK123(sK137,X1))
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,X0),sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(X1,sK145(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_48368]) ).
tcf(c_176526,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK92(sK137,X1,X2),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ closed_subset(sK92(sK137,X1,X2),sK137)
| ~ subset(X0,sK92(sK137,X1,X2)) ),
inference(superposition,[status(thm)],[c_48475,c_48368]) ).
tcf(c_176583,plain,
( in(sK138,sK123(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK138,sK138) ),
inference(superposition,[status(thm)],[c_376,c_176521]) ).
tcf(c_176584,plain,
! [X0: $i] :
( in(sK138,sK123(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138) ),
inference(superposition,[status(thm)],[c_106061,c_176521]) ).
tcf(c_176585,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| in(sK138,sK123(sK137,sK304(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ subset(sK304(sK137,X0,X1),sK138) ),
inference(superposition,[status(thm)],[c_47929,c_176521]) ).
tcf(c_176586,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| in(sK138,sK123(sK137,sK146(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(sK146(sK137,X0,X1),sK138) ),
inference(superposition,[status(thm)],[c_48162,c_176521]) ).
tcf(c_176587,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| in(sK138,sK123(sK137,sK145(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK145(sK137,X0),sK138)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_176521]) ).
tcf(c_176588,plain,
! [X0: $i,X1: $i] :
( in(sK138,sK123(sK137,sK92(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ subset(sK92(sK137,X0,X1),sK138) ),
inference(superposition,[status(thm)],[c_48475,c_176521]) ).
tcf(c_176589,plain,
( in(sK138,sK123(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_176583,c_670]) ).
tcf(c_176639,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK124(sK137,X1,X2),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ closed_subset(sK124(sK137,X1,X2),sK137)
| ~ subset(X0,sK124(sK137,X1,X2)) ),
inference(superposition,[status(thm)],[c_48350,c_48368]) ).
tcf(c_176640,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK124(sK137,sK124(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ in(X0,sK123(sK137,sK124(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48350,c_48332]) ).
tcf(c_176641,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK124(sK137,X1,X2),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ closed_subset(sK124(sK137,X1,X2),sK137)
| ~ subset(X0,sK124(sK137,X1,X2)) ),
inference(superposition,[status(thm)],[c_48350,c_48105]) ).
tcf(c_176642,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK91(sK137,sK124(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(X2,sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ subset(sK124(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_48350,c_47795]) ).
tcf(c_176643,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,sK124(sK137,X1,X2))
| ( sK303(sK137,sK124(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ in(X0,sK302(sK137,sK124(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48350,c_47947]) ).
tcf(c_176644,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,sK124(sK137,X1,X2))
| ( sK304(sK137,sK124(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ in(X0,sK302(sK137,sK124(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48350,c_47911]) ).
tcf(c_176645,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK124(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ in(X0,sK123(sK137,sK124(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48350,c_48297]) ).
tcf(c_176646,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ in(X0,sK147(sK137,sK124(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48350,c_48087]) ).
tcf(c_176647,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK124(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ in(X0,sK147(sK137,sK124(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48350,c_48070]) ).
tcf(c_176648,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( topstr_closure(sK137,sK124(sK137,X0,X1)) = X2 )
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ sP38(sK137,sK124(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_48350,c_47756]) ).
tcf(c_176649,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK92(sK137,sK124(sK137,X1,X2),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ in(X0,sK91(sK137,sK124(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48350,c_48460]) ).
tcf(c_176650,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,sK124(sK137,X1,X2))
| subset(sK124(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ in(X0,sK302(sK137,sK124(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48350,c_47876]) ).
tcf(c_176651,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ in(X0,sK91(sK137,sK124(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48350,c_48490]) ).
tcf(c_176652,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(sK124(sK137,X1,X2),X0)
| ~ topological_space(sK137)
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ in(X0,sK91(sK137,sK124(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48350,c_48431]) ).
tcf(c_176653,plain,
! [X0: $i,X1: $i] :
( in(sK138,sK123(sK137,sK124(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ subset(sK124(sK137,X0,X1),sK138) ),
inference(superposition,[status(thm)],[c_48350,c_176521]) ).
tcf(c_176654,plain,
! [X0: $i,X1: $i] :
( ( sK124(sK137,sK138,sK124(sK137,X0,X1)) = sK124(sK137,X0,X1) )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ in(sK124(sK137,X0,X1),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48350,c_176408]) ).
tcf(c_176655,plain,
! [X0: $i,X1: $i] :
( in(sK138,sK147(sK137,sK124(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ subset(sK124(sK137,X0,X1),sK138) ),
inference(superposition,[status(thm)],[c_48350,c_176286]) ).
tcf(c_176656,plain,
! [X0: $i,X1: $i] :
( subset(sK138,sK124(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ in(sK124(sK137,X0,X1),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48350,c_175672]) ).
tcf(c_176657,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK124(sK137,X0,X1),sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ in(sK124(sK137,X0,X1),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48350,c_175482]) ).
tcf(c_176658,plain,
! [X0: $i,X1: $i] :
( subset(sK138,sK124(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ in(sK124(sK137,X0,X1),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_48350,c_175418]) ).
tcf(c_176659,plain,
! [X0: $i,X1: $i] :
( ( sK124(sK137,X0,X1) = topstr_closure(sK137,sK138) )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ sP38(sK137,sK138,sK124(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_175209]) ).
tcf(c_176660,plain,
! [X0: $i,X1: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK124(sK137,X1,X0))) = topstr_closure(sK137,sK124(sK137,X1,X0)) )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_48058]) ).
tcf(c_176661,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(sK137,sK124(sK137,X0,X1)) = sK124(sK137,X0,X1) )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ closed_subset(sK124(sK137,X0,X1),sK137) ),
inference(superposition,[status(thm)],[c_48350,c_48037]) ).
tcf(c_176662,plain,
! [X0: $i,X1: $i] :
( open_subset(sK124(sK137,X0,X1),sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ in(sK124(sK137,X0,X1),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_48350,c_47852]) ).
tcf(c_176663,plain,
! [X0: $i,X1: $i] :
( in(sK124(sK137,X0,X1),the_topology(sK137))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ open_subset(sK124(sK137,X0,X1),sK137) ),
inference(superposition,[status(thm)],[c_48350,c_47840]) ).
tcf(c_176867,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(X0,sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_376,c_47771]) ).
tcf(c_176868,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,topstr_closure(sK137,X0))
| in(X1,sK302(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(X1,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_106061,c_47771]) ).
tcf(c_176869,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X0)
| sP36(sK137,sK304(sK137,X0,X1))
| in(X2,sK302(sK137,sK304(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(X2,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ subset(sK304(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_47929,c_47771]) ).
tcf(c_176870,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,topstr_closure(sK137,X0))
| sP36(sK137,sK146(sK137,X0,X1))
| in(X2,sK302(sK137,sK146(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(X2,sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,powerset(the_carrier(sK137)))
| ~ subset(sK146(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_48162,c_47771]) ).
tcf(c_176871,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,sK145(sK137,X0))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| in(X1,sK302(sK137,sK145(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(X1,sK137)
| ~ in(X1,powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,X0),X1)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_47771]) ).
tcf(c_176872,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,sK124(sK137,X0,X1))
| in(X2,sK302(sK137,sK124(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(X2,sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ subset(sK124(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_48350,c_47771]) ).
tcf(c_176873,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,sK92(sK137,X0,X1))
| in(X2,sK302(sK137,sK92(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(X2,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ subset(sK92(sK137,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_48475,c_47771]) ).
tcf(c_176949,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,sK138)
| sP36(sK137,X0)
| in(sK303(sK137,X0,X1),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ closed_subset(sK303(sK137,X0,X1),sK137)
| ~ subset(sK138,sK303(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_47965,c_176867]) ).
tcf(c_176950,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,sK138)
| sP34(X0,sK137)
| in(sK296(sK137,X0,X1),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ closed_subset(sK296(sK137,X0,X1),sK137)
| ~ subset(sK138,sK296(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_48019,c_176867]) ).
tcf(c_176969,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| in(X0,sK302(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(the_carrier(sK137),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_47771]) ).
tcf(c_176970,plain,
! [X0: $i] :
( in(the_carrier(sK137),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(the_carrier(sK137),sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_48368]) ).
tcf(c_176971,plain,
! [X0: $i] :
( ( sK124(sK137,the_carrier(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_48332]) ).
tcf(c_176972,plain,
! [X0: $i] :
( in(the_carrier(sK137),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(the_carrier(sK137),sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_48105]) ).
tcf(c_176973,plain,
! [X0: $i] :
( in(X0,sK91(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(the_carrier(sK137),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_47795]) ).
tcf(c_176974,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_47947]) ).
tcf(c_176975,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_47911]) ).
tcf(c_176976,plain,
! [X0: $i] :
( subset(the_carrier(sK137),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_48297]) ).
tcf(c_176977,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_48087]) ).
tcf(c_176978,plain,
! [X0: $i] :
( subset(the_carrier(sK137),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_48070]) ).
tcf(c_176979,plain,
! [X0: $i] :
( ( topstr_closure(sK137,the_carrier(sK137)) = X0 )
| ~ sP38(sK137,the_carrier(sK137),X0)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_47756]) ).
tcf(c_176980,plain,
! [X0: $i] :
( ( sK92(sK137,the_carrier(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_48460]) ).
tcf(c_176981,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_47876]) ).
tcf(c_176982,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_48490]) ).
tcf(c_176983,plain,
! [X0: $i] :
( subset(the_carrier(sK137),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_48431]) ).
tcf(c_176984,plain,
( in(sK138,sK123(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138) ),
inference(superposition,[status(thm)],[c_13308,c_176521]) ).
tcf(c_176985,plain,
( ( sK124(sK137,sK138,the_carrier(sK137)) = the_carrier(sK137) )
| ~ topological_space(sK137)
| ~ in(the_carrier(sK137),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_13308,c_176408]) ).
tcf(c_176986,plain,
( in(sK138,sK147(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138) ),
inference(superposition,[status(thm)],[c_13308,c_176286]) ).
tcf(c_176987,plain,
( subset(sK138,the_carrier(sK137))
| ~ topological_space(sK137)
| ~ in(the_carrier(sK137),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_13308,c_175672]) ).
tcf(c_176989,plain,
( subset(sK138,the_carrier(sK137))
| ~ topological_space(sK137)
| ~ in(the_carrier(sK137),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_13308,c_175418]) ).
tcf(c_176990,plain,
( ( topstr_closure(sK137,sK138) = the_carrier(sK137) )
| ~ sP38(sK137,sK138,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_13308,c_175209]) ).
tcf(c_176991,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,the_carrier(sK137))) = topstr_closure(sK137,the_carrier(sK137)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_13308,c_48058]) ).
tcf(c_176992,plain,
( ( topstr_closure(sK137,the_carrier(sK137)) = the_carrier(sK137) )
| ~ closed_subset(the_carrier(sK137),sK137) ),
inference(superposition,[status(thm)],[c_13308,c_48037]) ).
tcf(c_176993,plain,
( open_subset(the_carrier(sK137),sK137)
| ~ in(the_carrier(sK137),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_13308,c_47852]) ).
tcf(c_176994,plain,
( in(the_carrier(sK137),the_topology(sK137))
| ~ open_subset(the_carrier(sK137),sK137) ),
inference(superposition,[status(thm)],[c_13308,c_47840]) ).
tcf(c_176995,plain,
! [X0: $i] :
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_13308,c_48001]) ).
tcf(c_176996,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),powerset(the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_13308,c_48252]) ).
tcf(c_176997,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_13308,c_48416]) ).
tcf(c_176998,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),powerset(the_carrier(sK137))),sK137)
| in(sK145(sK137,powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_13308,c_48237]) ).
tcf(c_177131,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ subset(sK138,X1)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_48138]) ).
tcf(c_177132,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ subset(the_carrier(sK137),X1)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_13308,c_48138]) ).
tcf(c_177133,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ closed_subset(X2,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X1),X2)
| ~ in(X0,topstr_closure(sK137,topstr_closure(sK137,X1))) ),
inference(superposition,[status(thm)],[c_106061,c_48138]) ).
tcf(c_177134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP36(sK137,X1)
| in(X0,X3)
| ~ topological_space(sK137)
| ~ closed_subset(X3,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X3,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK302(sK137,X1))
| ~ subset(sK304(sK137,X1,X2),X3)
| ~ in(X0,topstr_closure(sK137,sK304(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_47929,c_48138]) ).
tcf(c_177135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| in(X2,topstr_closure(sK137,X1))
| ~ closed_subset(X3,sK137)
| ~ in(X2,the_carrier(sK137))
| ~ in(X0,the_carrier(sK137))
| ~ element(X3,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK146(sK137,X1,X2),X3)
| ~ in(X0,topstr_closure(sK137,sK146(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48162,c_48138]) ).
tcf(c_177136,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| closed_subset(meet_of_subsets(the_carrier(sK137),X1),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(X2,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,X1),X2)
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,topstr_closure(sK137,sK145(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48222,c_48138]) ).
tcf(c_177137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ topological_space(sK137)
| ~ closed_subset(X3,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X3,powerset(the_carrier(sK137)))
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK123(sK137,X1))
| ~ subset(sK124(sK137,X1,X2),X3)
| ~ in(X0,topstr_closure(sK137,sK124(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48350,c_48138]) ).
tcf(c_177138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X3)
| ~ topological_space(sK137)
| ~ closed_subset(X3,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X3,powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X2,sK91(sK137,X1))
| ~ subset(sK92(sK137,X1,X2),X3)
| ~ in(X0,topstr_closure(sK137,sK92(sK137,X1,X2))) ),
inference(superposition,[status(thm)],[c_48475,c_48138]) ).
tcf(c_177225,plain,
! [X0: $i] :
( in(X0,sK138)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK138,sK138)
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_376,c_177131]) ).
tcf(c_177227,plain,
! [X0: $i,X1: $i] :
( in(X0,topstr_closure(sK137,X1))
| ~ in(X0,the_carrier(sK137))
| ~ closed_subset(topstr_closure(sK137,X1),sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK138,topstr_closure(sK137,X1))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_106061,c_177131]) ).
tcf(c_177228,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP36(sK137,X0)
| in(X2,sK304(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,topstr_closure(sK137,sK138))
| ~ in(X1,sK302(sK137,X0))
| ~ closed_subset(sK304(sK137,X0,X1),sK137)
| ~ subset(sK138,sK304(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_177131]) ).
tcf(c_177229,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,topstr_closure(sK137,X0))
| in(X2,sK146(sK137,X0,X1))
| ~ in(X2,the_carrier(sK137))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,topstr_closure(sK137,sK138))
| ~ closed_subset(sK146(sK137,X0,X1),sK137)
| ~ subset(sK138,sK146(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_48162,c_177131]) ).
tcf(c_177230,plain,
! [X0: $i,X1: $i] :
( in(X1,sK145(sK137,X0))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ closed_subset(sK145(sK137,X0),sK137)
| ~ subset(sK138,sK145(sK137,X0))
| ~ in(X1,topstr_closure(sK137,sK138))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_177131]) ).
tcf(c_177231,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK124(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,topstr_closure(sK137,sK138))
| ~ in(X1,sK123(sK137,X0))
| ~ closed_subset(sK124(sK137,X0,X1),sK137)
| ~ subset(sK138,sK124(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_177131]) ).
tcf(c_177232,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK92(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ in(X2,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X2,topstr_closure(sK137,sK138))
| ~ in(X1,sK91(sK137,X0))
| ~ closed_subset(sK92(sK137,X0,X1),sK137)
| ~ subset(sK138,sK92(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_177131]) ).
tcf(c_177233,plain,
! [X0: $i] :
( in(X0,sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_177225,c_670]) ).
tcf(c_177301,plain,
( topological_space(sK137)
| subset(sK378(sK137),the_topology(sK137))
| ~ sP42(sK137)
| ~ open_subset(the_carrier(sK137),sK137) ),
inference(superposition,[status(thm)],[c_176994,c_47425]) ).
tcf(c_177319,plain,
( ( sK124(sK137,sK138,sK138) = sK138 )
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(superposition,[status(thm)],[c_176589,c_176463]) ).
tcf(c_177391,plain,
! [X0: $i] :
( in(X0,sK208(powerset(the_carrier(sK137))))
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138))
| ~ closed_subset(sK208(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK208(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_702,c_177131]) ).
tcf(c_177392,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK208(powerset(the_carrier(sK137))),X1)
| ~ in(X0,topstr_closure(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_702,c_48138]) ).
tcf(c_177393,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| in(X0,sK302(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK208(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_702,c_47771]) ).
tcf(c_177394,plain,
! [X0: $i] :
( in(sK208(powerset(the_carrier(sK137))),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK208(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK208(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_702,c_48368]) ).
tcf(c_177395,plain,
! [X0: $i] :
( ( sK124(sK137,sK208(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_702,c_48332]) ).
tcf(c_177396,plain,
! [X0: $i] :
( in(sK208(powerset(the_carrier(sK137))),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK208(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK208(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_702,c_48105]) ).
tcf(c_177397,plain,
! [X0: $i] :
( in(X0,sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK208(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_702,c_47795]) ).
tcf(c_177398,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| ( sK303(sK137,sK208(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_702,c_47947]) ).
tcf(c_177399,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| ( sK304(sK137,sK208(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_702,c_47911]) ).
tcf(c_177400,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_702,c_48297]) ).
tcf(c_177401,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_702,c_48087]) ).
tcf(c_177402,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_702,c_48070]) ).
tcf(c_177403,plain,
! [X0: $i] :
( ( topstr_closure(sK137,sK208(powerset(the_carrier(sK137)))) = X0 )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK208(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_702,c_47756]) ).
tcf(c_177404,plain,
! [X0: $i] :
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_702,c_48460]) ).
tcf(c_177405,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_702,c_47876]) ).
tcf(c_177406,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_702,c_48490]) ).
tcf(c_177407,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_702,c_48431]) ).
tcf(c_177408,plain,
( in(sK138,sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_702,c_176521]) ).
tcf(c_177409,plain,
( ( sK124(sK137,sK138,sK208(powerset(the_carrier(sK137)))) = sK208(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK208(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_702,c_176408]) ).
tcf(c_177410,plain,
( in(sK138,sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_702,c_176286]) ).
tcf(c_177411,plain,
( subset(sK138,sK208(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK208(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_702,c_175672]) ).
tcf(c_177412,plain,
( closed_subset(sK208(powerset(the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ in(sK208(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_702,c_175482]) ).
tcf(c_177413,plain,
( subset(sK138,sK208(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK208(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_702,c_175418]) ).
tcf(c_177414,plain,
( ( sK208(powerset(the_carrier(sK137))) = topstr_closure(sK137,sK138) )
| ~ sP38(sK137,sK138,sK208(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_702,c_175209]) ).
tcf(c_177415,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK208(powerset(the_carrier(sK137))))) = topstr_closure(sK137,sK208(powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_702,c_48058]) ).
tcf(c_177416,plain,
( ( topstr_closure(sK137,sK208(powerset(the_carrier(sK137)))) = sK208(powerset(the_carrier(sK137))) )
| ~ closed_subset(sK208(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_702,c_48037]) ).
tcf(c_177417,plain,
( open_subset(sK208(powerset(the_carrier(sK137))),sK137)
| ~ in(sK208(powerset(the_carrier(sK137))),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_702,c_47852]) ).
tcf(c_177418,plain,
( in(sK208(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK208(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_702,c_47840]) ).
tcf(c_177419,plain,
! [X0: $i] :
( sP34(sK208(powerset(powerset(the_carrier(sK137)))),sK137)
| ( sK296(sK137,sK208(powerset(powerset(the_carrier(sK137)))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_702,c_48001]) ).
tcf(c_177420,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK208(powerset(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK208(powerset(powerset(the_carrier(sK137))))),sK137) ),
inference(superposition,[status(thm)],[c_702,c_48252]) ).
tcf(c_177421,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_702,c_48416]) ).
tcf(c_177422,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK208(powerset(powerset(the_carrier(sK137))))),sK137)
| in(sK145(sK137,sK208(powerset(powerset(the_carrier(sK137))))),sK208(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_702,c_48237]) ).
tcf(c_177695,plain,
! [X0: $i] :
( in(X0,sK206(the_carrier(sK137)))
| ~ in(X0,the_carrier(sK137))
| ~ closed_subset(sK206(the_carrier(sK137)),sK137)
| ~ subset(sK138,sK206(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_696,c_177131]) ).
tcf(c_177696,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK206(the_carrier(sK137)),X1)
| ~ in(X0,topstr_closure(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_696,c_48138]) ).
tcf(c_177697,plain,
! [X0: $i] :
( sP36(sK137,sK206(the_carrier(sK137)))
| in(X0,sK302(sK137,sK206(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK206(the_carrier(sK137)),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_696,c_47771]) ).
tcf(c_177698,plain,
! [X0: $i] :
( in(sK206(the_carrier(sK137)),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK206(the_carrier(sK137)),sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,sK206(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_696,c_48368]) ).
tcf(c_177699,plain,
! [X0: $i] :
( ( sK124(sK137,sK206(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_696,c_48332]) ).
tcf(c_177700,plain,
! [X0: $i] :
( in(sK206(the_carrier(sK137)),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK206(the_carrier(sK137)),sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,sK206(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_696,c_48105]) ).
tcf(c_177701,plain,
! [X0: $i] :
( in(X0,sK91(sK137,sK206(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK206(the_carrier(sK137)),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_696,c_47795]) ).
tcf(c_177702,plain,
! [X0: $i] :
( sP36(sK137,sK206(the_carrier(sK137)))
| ( sK303(sK137,sK206(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_696,c_47947]) ).
tcf(c_177703,plain,
! [X0: $i] :
( sP36(sK137,sK206(the_carrier(sK137)))
| ( sK304(sK137,sK206(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_696,c_47911]) ).
tcf(c_177704,plain,
! [X0: $i] :
( subset(sK206(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_696,c_48297]) ).
tcf(c_177705,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_696,c_48087]) ).
tcf(c_177706,plain,
! [X0: $i] :
( subset(sK206(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_696,c_48070]) ).
tcf(c_177707,plain,
! [X0: $i] :
( ( topstr_closure(sK137,sK206(the_carrier(sK137))) = X0 )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK206(the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_696,c_47756]) ).
tcf(c_177708,plain,
! [X0: $i] :
( ( sK92(sK137,sK206(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_696,c_48460]) ).
tcf(c_177709,plain,
! [X0: $i] :
( sP36(sK137,sK206(the_carrier(sK137)))
| subset(sK206(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_696,c_47876]) ).
tcf(c_177710,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_696,c_48490]) ).
tcf(c_177711,plain,
! [X0: $i] :
( subset(sK206(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_696,c_48431]) ).
tcf(c_177712,plain,
( in(sK138,sK123(sK137,sK206(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK206(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_696,c_176521]) ).
tcf(c_177713,plain,
( ( sK124(sK137,sK138,sK206(the_carrier(sK137))) = sK206(the_carrier(sK137)) )
| ~ topological_space(sK137)
| ~ in(sK206(the_carrier(sK137)),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_696,c_176408]) ).
tcf(c_177714,plain,
( in(sK138,sK147(sK137,sK206(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK206(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_696,c_176286]) ).
tcf(c_177715,plain,
( subset(sK138,sK206(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(sK206(the_carrier(sK137)),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_696,c_175672]) ).
tcf(c_177716,plain,
( closed_subset(sK206(the_carrier(sK137)),sK137)
| ~ topological_space(sK137)
| ~ in(sK206(the_carrier(sK137)),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_696,c_175482]) ).
tcf(c_177717,plain,
( subset(sK138,sK206(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(sK206(the_carrier(sK137)),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_696,c_175418]) ).
tcf(c_177718,plain,
( ( topstr_closure(sK137,sK138) = sK206(the_carrier(sK137)) )
| ~ sP38(sK137,sK138,sK206(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_696,c_175209]) ).
tcf(c_177719,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK206(the_carrier(sK137)))) = topstr_closure(sK137,sK206(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_696,c_48058]) ).
tcf(c_177720,plain,
( ( topstr_closure(sK137,sK206(the_carrier(sK137))) = sK206(the_carrier(sK137)) )
| ~ closed_subset(sK206(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_696,c_48037]) ).
tcf(c_177721,plain,
( open_subset(sK206(the_carrier(sK137)),sK137)
| ~ in(sK206(the_carrier(sK137)),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_696,c_47852]) ).
tcf(c_177722,plain,
( in(sK206(the_carrier(sK137)),the_topology(sK137))
| ~ open_subset(sK206(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_696,c_47840]) ).
tcf(c_177723,plain,
! [X0: $i] :
( sP34(sK206(powerset(the_carrier(sK137))),sK137)
| ( sK296(sK137,sK206(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK206(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_696,c_48001]) ).
tcf(c_177724,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK206(powerset(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK206(powerset(the_carrier(sK137)))),sK137) ),
inference(superposition,[status(thm)],[c_696,c_48252]) ).
tcf(c_177725,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK206(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_696,c_48416]) ).
tcf(c_177726,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK206(powerset(the_carrier(sK137)))),sK137)
| in(sK145(sK137,sK206(powerset(the_carrier(sK137)))),sK206(powerset(the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_696,c_48237]) ).
tcf(c_177908,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_1341,c_779]) ).
tcf(c_177909,plain,
! [X0: $i] : function(sK206(X0)),
inference(superposition,[status(thm)],[c_697,c_779]) ).
tcf(c_177911,plain,
function(sK249),
inference(superposition,[status(thm)],[c_786,c_779]) ).
tcf(c_177912,plain,
function(sK250),
inference(superposition,[status(thm)],[c_787,c_779]) ).
tcf(c_177922,plain,
! [X0: $i] : relation(sK206(X0)),
inference(superposition,[status(thm)],[c_697,c_793]) ).
tcf(c_177924,plain,
relation(sK249),
inference(superposition,[status(thm)],[c_786,c_793]) ).
tcf(c_177985,plain,
finite(empty_set),
inference(superposition,[status(thm)],[c_1341,c_1015]) ).
tcf(c_177986,plain,
! [X0: $i] : finite(sK206(X0)),
inference(superposition,[status(thm)],[c_697,c_1015]) ).
tcf(c_177987,plain,
finite(sK245),
inference(superposition,[status(thm)],[c_775,c_1015]) ).
tcf(c_177988,plain,
finite(sK249),
inference(superposition,[status(thm)],[c_786,c_1015]) ).
tcf(c_177989,plain,
finite(sK250),
inference(superposition,[status(thm)],[c_787,c_1015]) ).
tcf(c_177990,plain,
finite(sK338),
inference(superposition,[status(thm)],[c_1070,c_1015]) ).
tcf(c_177991,plain,
finite(sK362),
inference(superposition,[status(thm)],[c_1203,c_1015]) ).
tcf(c_177998,plain,
epsilon_transitive(empty_set),
inference(superposition,[status(thm)],[c_1341,c_1083]) ).
tcf(c_177999,plain,
! [X0: $i] : epsilon_transitive(sK206(X0)),
inference(superposition,[status(thm)],[c_697,c_1083]) ).
tcf(c_178000,plain,
epsilon_transitive(sK245),
inference(superposition,[status(thm)],[c_775,c_1083]) ).
tcf(c_178001,plain,
epsilon_transitive(sK249),
inference(superposition,[status(thm)],[c_786,c_1083]) ).
tcf(c_178002,plain,
epsilon_transitive(sK250),
inference(superposition,[status(thm)],[c_787,c_1083]) ).
tcf(c_178004,plain,
epsilon_transitive(sK362),
inference(superposition,[status(thm)],[c_1203,c_1083]) ).
tcf(c_178053,plain,
( sP36(sK137,sK138)
| closed_subset(meet_of_subsets(the_carrier(sK137),powerset(the_carrier(sK137))),sK137)
| in(sK145(sK137,powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK145(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_176998,c_176867]) ).
tcf(c_178054,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),powerset(the_carrier(sK137))),sK137)
| in(sK145(sK137,powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK145(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_176998,c_176193]) ).
tcf(c_178074,plain,
epsilon_connected(empty_set),
inference(superposition,[status(thm)],[c_1341,c_1084]) ).
tcf(c_178075,plain,
! [X0: $i] : epsilon_connected(sK206(X0)),
inference(superposition,[status(thm)],[c_697,c_1084]) ).
tcf(c_178076,plain,
epsilon_connected(sK245),
inference(superposition,[status(thm)],[c_775,c_1084]) ).
tcf(c_178077,plain,
epsilon_connected(sK249),
inference(superposition,[status(thm)],[c_786,c_1084]) ).
tcf(c_178078,plain,
epsilon_connected(sK250),
inference(superposition,[status(thm)],[c_787,c_1084]) ).
tcf(c_178080,plain,
epsilon_connected(sK362),
inference(superposition,[status(thm)],[c_1203,c_1084]) ).
tcf(c_178087,plain,
ordinal(empty_set),
inference(superposition,[status(thm)],[c_1341,c_1085]) ).
tcf(c_178088,plain,
! [X0: $i] : ordinal(sK206(X0)),
inference(superposition,[status(thm)],[c_697,c_1085]) ).
tcf(c_178089,plain,
ordinal(sK245),
inference(superposition,[status(thm)],[c_775,c_1085]) ).
tcf(c_178090,plain,
ordinal(sK249),
inference(superposition,[status(thm)],[c_786,c_1085]) ).
tcf(c_178091,plain,
ordinal(sK250),
inference(superposition,[status(thm)],[c_787,c_1085]) ).
tcf(c_178093,plain,
ordinal(sK362),
inference(superposition,[status(thm)],[c_1203,c_1085]) ).
tcf(c_178100,plain,
( epsilon_transitive(sK66)
| ~ sP8 ),
inference(superposition,[status(thm)],[c_129,c_1087]) ).
tcf(c_178101,plain,
( epsilon_transitive(sK70)
| ~ sP6 ),
inference(superposition,[status(thm)],[c_142,c_1087]) ).
tcf(c_178102,plain,
( epsilon_transitive(sK117)
| ~ sP15 ),
inference(superposition,[status(thm)],[c_248,c_1087]) ).
tcf(c_178126,plain,
( epsilon_connected(sK66)
| ~ sP8 ),
inference(superposition,[status(thm)],[c_129,c_1088]) ).
tcf(c_178127,plain,
( epsilon_connected(sK70)
| ~ sP6 ),
inference(superposition,[status(thm)],[c_142,c_1088]) ).
tcf(c_178128,plain,
( epsilon_connected(sK117)
| ~ sP15 ),
inference(superposition,[status(thm)],[c_248,c_1088]) ).
tcf(c_178207,plain,
! [X0: $i] :
( in(X0,sK371(the_carrier(sK137)))
| ~ in(X0,the_carrier(sK137))
| ~ closed_subset(sK371(the_carrier(sK137)),sK137)
| ~ subset(sK138,sK371(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1259,c_177131]) ).
tcf(c_178208,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK371(the_carrier(sK137)),X1)
| ~ in(X0,topstr_closure(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1259,c_48138]) ).
tcf(c_178209,plain,
! [X0: $i] :
( sP36(sK137,sK371(the_carrier(sK137)))
| in(X0,sK302(sK137,sK371(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK371(the_carrier(sK137)),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1259,c_47771]) ).
tcf(c_178210,plain,
! [X0: $i] :
( in(sK371(the_carrier(sK137)),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK371(the_carrier(sK137)),sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,sK371(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1259,c_48368]) ).
tcf(c_178211,plain,
! [X0: $i] :
( ( sK124(sK137,sK371(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1259,c_48332]) ).
tcf(c_178212,plain,
! [X0: $i] :
( in(sK371(the_carrier(sK137)),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK371(the_carrier(sK137)),sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,sK371(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1259,c_48105]) ).
tcf(c_178213,plain,
! [X0: $i] :
( in(X0,sK91(sK137,sK371(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK371(the_carrier(sK137)),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1259,c_47795]) ).
tcf(c_178214,plain,
! [X0: $i] :
( sP36(sK137,sK371(the_carrier(sK137)))
| ( sK303(sK137,sK371(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1259,c_47947]) ).
tcf(c_178215,plain,
! [X0: $i] :
( sP36(sK137,sK371(the_carrier(sK137)))
| ( sK304(sK137,sK371(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1259,c_47911]) ).
tcf(c_178216,plain,
! [X0: $i] :
( subset(sK371(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1259,c_48297]) ).
tcf(c_178217,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1259,c_48087]) ).
tcf(c_178218,plain,
! [X0: $i] :
( subset(sK371(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1259,c_48070]) ).
tcf(c_178219,plain,
! [X0: $i] :
( ( topstr_closure(sK137,sK371(the_carrier(sK137))) = X0 )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK371(the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_1259,c_47756]) ).
tcf(c_178220,plain,
! [X0: $i] :
( ( sK92(sK137,sK371(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1259,c_48460]) ).
tcf(c_178221,plain,
! [X0: $i] :
( sP36(sK137,sK371(the_carrier(sK137)))
| subset(sK371(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1259,c_47876]) ).
tcf(c_178222,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1259,c_48490]) ).
tcf(c_178223,plain,
! [X0: $i] :
( subset(sK371(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1259,c_48431]) ).
tcf(c_178224,plain,
( in(sK138,sK123(sK137,sK371(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK371(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_1259,c_176521]) ).
tcf(c_178225,plain,
( ( sK124(sK137,sK138,sK371(the_carrier(sK137))) = sK371(the_carrier(sK137)) )
| ~ topological_space(sK137)
| ~ in(sK371(the_carrier(sK137)),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1259,c_176408]) ).
tcf(c_178226,plain,
( in(sK138,sK147(sK137,sK371(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK371(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_1259,c_176286]) ).
tcf(c_178227,plain,
( subset(sK138,sK371(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(sK371(the_carrier(sK137)),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1259,c_175672]) ).
tcf(c_178228,plain,
( closed_subset(sK371(the_carrier(sK137)),sK137)
| ~ topological_space(sK137)
| ~ in(sK371(the_carrier(sK137)),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1259,c_175482]) ).
tcf(c_178229,plain,
( subset(sK138,sK371(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(sK371(the_carrier(sK137)),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1259,c_175418]) ).
tcf(c_178230,plain,
( ( topstr_closure(sK137,sK138) = sK371(the_carrier(sK137)) )
| ~ sP38(sK137,sK138,sK371(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1259,c_175209]) ).
tcf(c_178231,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK371(the_carrier(sK137)))) = topstr_closure(sK137,sK371(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1259,c_48058]) ).
tcf(c_178232,plain,
( ( topstr_closure(sK137,sK371(the_carrier(sK137))) = sK371(the_carrier(sK137)) )
| ~ closed_subset(sK371(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_1259,c_48037]) ).
tcf(c_178233,plain,
( open_subset(sK371(the_carrier(sK137)),sK137)
| ~ in(sK371(the_carrier(sK137)),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_1259,c_47852]) ).
tcf(c_178234,plain,
( in(sK371(the_carrier(sK137)),the_topology(sK137))
| ~ open_subset(sK371(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_1259,c_47840]) ).
tcf(c_178235,plain,
! [X0: $i] :
( sP34(sK371(powerset(the_carrier(sK137))),sK137)
| ( sK296(sK137,sK371(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK371(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_1259,c_48001]) ).
tcf(c_178236,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK371(powerset(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK371(powerset(the_carrier(sK137)))),sK137) ),
inference(superposition,[status(thm)],[c_1259,c_48252]) ).
tcf(c_178237,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK371(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_1259,c_48416]) ).
tcf(c_178238,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK371(powerset(the_carrier(sK137)))),sK137)
| in(sK145(sK137,sK371(powerset(the_carrier(sK137)))),sK371(powerset(the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1259,c_48237]) ).
tcf(c_178377,plain,
one_to_one(empty_set),
inference(superposition,[status(thm)],[c_1341,c_104931]) ).
tcf(c_178378,plain,
! [X0: $i] : one_to_one(sK206(X0)),
inference(superposition,[status(thm)],[c_697,c_104931]) ).
tcf(c_178379,plain,
one_to_one(sK245),
inference(superposition,[status(thm)],[c_775,c_104931]) ).
tcf(c_178380,plain,
one_to_one(sK249),
inference(superposition,[status(thm)],[c_786,c_104931]) ).
tcf(c_178381,plain,
one_to_one(sK250),
inference(superposition,[status(thm)],[c_787,c_104931]) ).
tcf(c_178456,plain,
sP3(empty_set),
inference(superposition,[status(thm)],[c_120,c_599]) ).
tcf(c_178457,plain,
( sP36(sK137,sK138)
| sP3(powerset(the_carrier(sK137)))
| in(sK62(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK62(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK62(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_120,c_176867]) ).
tcf(c_178458,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK62(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK62(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK62(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_120,c_176193]) ).
tcf(c_178459,plain,
( sP3(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK62(sK91(sK137,sK138))) = sK62(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_175190]) ).
tcf(c_178460,plain,
( sP3(sK91(sK137,sK138))
| in(sK62(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_175008]) ).
tcf(c_178461,plain,
( sP3(sK91(sK137,sK138))
| subset(sK138,sK62(sK91(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_174960]) ).
tcf(c_178462,plain,
( sP36(sK137,sK138)
| sP3(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK62(sK302(sK137,sK138))) = sK62(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_175802]) ).
tcf(c_178463,plain,
( sP36(sK137,sK138)
| sP3(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK62(sK302(sK137,sK138))) = sK62(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_175753]) ).
tcf(c_178464,plain,
( sP36(sK137,sK138)
| sP3(sK302(sK137,sK138))
| subset(sK138,sK62(sK302(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_175029]) ).
tcf(c_178465,plain,
( sP3(sK93(sK137,the_topology(sK137)))
| in(sK62(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_175089]) ).
tcf(c_178466,plain,
( sP36(sK137,the_carrier(sK137))
| sP3(sK302(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK62(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_176981]) ).
tcf(c_178467,plain,
( sP3(sK123(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK62(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK62(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_176976]) ).
tcf(c_178468,plain,
( sP3(sK91(sK137,the_carrier(sK137)))
| ( sK92(sK137,the_carrier(sK137),sK62(sK91(sK137,the_carrier(sK137)))) = sK62(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_176980]) ).
tcf(c_178469,plain,
( sP3(sK91(sK137,the_carrier(sK137)))
| in(sK62(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_176982]) ).
tcf(c_178470,plain,
( sP3(sK91(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK62(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_176983]) ).
tcf(c_178471,plain,
( sP3(sK147(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK62(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_176978]) ).
tcf(c_178472,plain,
( sP3(sK147(sK137,the_carrier(sK137)))
| closed_subset(sK62(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_176977]) ).
tcf(c_178473,plain,
( sP3(sK93(sK137,powerset(the_carrier(sK137))))
| in(sK62(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_176997]) ).
tcf(c_178474,plain,
( sP3(topstr_closure(sK137,sK138))
| in(sK62(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(sK62(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_120,c_177233]) ).
tcf(c_178475,plain,
( sP3(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK62(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177407]) ).
tcf(c_178476,plain,
( sP3(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| in(sK62(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177406]) ).
tcf(c_178477,plain,
( sP3(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| closed_subset(sK62(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_177401]) ).
tcf(c_178478,plain,
( sP3(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))))
| in(sK62(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177421]) ).
tcf(c_178479,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| sP3(sK302(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK62(sK302(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177709]) ).
tcf(c_178480,plain,
( sP3(sK91(sK137,sK206(the_carrier(sK137))))
| ( sK92(sK137,sK206(the_carrier(sK137)),sK62(sK91(sK137,sK206(the_carrier(sK137))))) = sK62(sK91(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177708]) ).
tcf(c_178481,plain,
( sP3(sK91(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK62(sK91(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177711]) ).
tcf(c_178482,plain,
( sP3(sK91(sK137,sK206(the_carrier(sK137))))
| in(sK62(sK91(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177710]) ).
tcf(c_178483,plain,
( sP3(sK147(sK137,sK206(the_carrier(sK137))))
| closed_subset(sK62(sK147(sK137,sK206(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_177705]) ).
tcf(c_178484,plain,
( sP3(sK93(sK137,sK206(powerset(the_carrier(sK137)))))
| in(sK62(sK93(sK137,sK206(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177725]) ).
tcf(c_178485,plain,
( sP3(sK91(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK62(sK91(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_178223]) ).
tcf(c_178486,plain,
( sP3(sK91(sK137,sK371(the_carrier(sK137))))
| in(sK62(sK91(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_178222]) ).
tcf(c_178605,plain,
( sP36(sK137,sK138)
| sP3(sK91(sK137,sK138))
| in(sK62(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK62(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK62(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178460,c_176867]) ).
tcf(c_178606,plain,
( sP3(sK91(sK137,sK138))
| in(sK62(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK62(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK62(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178460,c_176193]) ).
tcf(c_178636,plain,
( sP3(sK93(sK137,sK371(powerset(the_carrier(sK137)))))
| in(sK62(sK93(sK137,sK371(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_178237]) ).
tcf(c_178652,plain,
( sP3(sK147(sK137,sK371(the_carrier(sK137))))
| closed_subset(sK62(sK147(sK137,sK371(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_178217]) ).
tcf(c_178663,plain,
( sP3(sK91(sK137,sK371(the_carrier(sK137))))
| ( sK92(sK137,sK371(the_carrier(sK137)),sK62(sK91(sK137,sK371(the_carrier(sK137))))) = sK62(sK91(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_178220]) ).
tcf(c_178667,plain,
powerset(empty_set) != empty_set,
inference(superposition,[status(thm)],[c_330,c_52]) ).
tcf(c_178668,plain,
finite(powerset(empty_set)),
inference(superposition,[status(thm)],[c_330,c_1010]) ).
tcf(c_178671,plain,
~ empty(powerset(empty_set)),
inference(superposition,[status(thm)],[c_330,c_960]) ).
tcf(c_178672,plain,
in(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_330,c_965]) ).
tcf(c_178673,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(X0,X1) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_330,c_273]) ).
tcf(c_178681,plain,
( sP36(sK137,sK138)
| ordinal(powerset(the_carrier(sK137)))
| in(sK139(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK139(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK139(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_383,c_176867]) ).
tcf(c_178682,plain,
( ordinal(powerset(the_carrier(sK137)))
| in(sK139(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK139(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK139(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_383,c_176193]) ).
tcf(c_178683,plain,
( ordinal(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK139(sK91(sK137,sK138))) = sK139(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_175190]) ).
tcf(c_178684,plain,
( ordinal(sK91(sK137,sK138))
| in(sK139(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_175008]) ).
tcf(c_178685,plain,
( ordinal(sK91(sK137,sK138))
| subset(sK138,sK139(sK91(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_174960]) ).
tcf(c_178686,plain,
( sP36(sK137,sK138)
| ordinal(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_175802]) ).
tcf(c_178687,plain,
( sP36(sK137,sK138)
| ordinal(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_175753]) ).
tcf(c_178688,plain,
( sP36(sK137,sK138)
| ordinal(sK302(sK137,sK138))
| subset(sK138,sK139(sK302(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_175029]) ).
tcf(c_178689,plain,
( ordinal(sK93(sK137,the_topology(sK137)))
| in(sK139(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_175089]) ).
tcf(c_178690,plain,
( sP36(sK137,the_carrier(sK137))
| ordinal(sK302(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK139(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_176981]) ).
tcf(c_178691,plain,
( ordinal(sK123(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK139(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK139(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_176976]) ).
tcf(c_178692,plain,
( ordinal(sK91(sK137,the_carrier(sK137)))
| ( sK92(sK137,the_carrier(sK137),sK139(sK91(sK137,the_carrier(sK137)))) = sK139(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_176980]) ).
tcf(c_178693,plain,
( ordinal(sK91(sK137,the_carrier(sK137)))
| in(sK139(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_176982]) ).
tcf(c_178694,plain,
( ordinal(sK91(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK139(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_176983]) ).
tcf(c_178695,plain,
( ordinal(sK147(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK139(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_176978]) ).
tcf(c_178696,plain,
( ordinal(sK147(sK137,the_carrier(sK137)))
| closed_subset(sK139(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_176977]) ).
tcf(c_178697,plain,
( ordinal(sK93(sK137,powerset(the_carrier(sK137))))
| in(sK139(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_176997]) ).
tcf(c_178698,plain,
( ordinal(topstr_closure(sK137,sK138))
| in(sK139(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(sK139(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_383,c_177233]) ).
tcf(c_178699,plain,
( ordinal(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK139(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177407]) ).
tcf(c_178700,plain,
( ordinal(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| in(sK139(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177406]) ).
tcf(c_178701,plain,
( ordinal(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| closed_subset(sK139(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_177401]) ).
tcf(c_178702,plain,
( ordinal(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))))
| in(sK139(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177421]) ).
tcf(c_178703,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| ordinal(sK302(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK139(sK302(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177709]) ).
tcf(c_178704,plain,
( ordinal(sK91(sK137,sK206(the_carrier(sK137))))
| ( sK92(sK137,sK206(the_carrier(sK137)),sK139(sK91(sK137,sK206(the_carrier(sK137))))) = sK139(sK91(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177708]) ).
tcf(c_178705,plain,
( ordinal(sK91(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK139(sK91(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177711]) ).
tcf(c_178706,plain,
( ordinal(sK91(sK137,sK206(the_carrier(sK137))))
| in(sK139(sK91(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177710]) ).
tcf(c_178707,plain,
( ordinal(sK147(sK137,sK206(the_carrier(sK137))))
| closed_subset(sK139(sK147(sK137,sK206(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_177705]) ).
tcf(c_178708,plain,
( ordinal(sK93(sK137,sK206(powerset(the_carrier(sK137)))))
| in(sK139(sK93(sK137,sK206(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177725]) ).
tcf(c_178709,plain,
( ordinal(sK91(sK137,sK371(the_carrier(sK137))))
| ( sK92(sK137,sK371(the_carrier(sK137)),sK139(sK91(sK137,sK371(the_carrier(sK137))))) = sK139(sK91(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_178220]) ).
tcf(c_178710,plain,
( ordinal(sK91(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK139(sK91(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_178223]) ).
tcf(c_178711,plain,
( ordinal(sK91(sK137,sK371(the_carrier(sK137))))
| in(sK139(sK91(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_178222]) ).
tcf(c_178712,plain,
( ordinal(sK147(sK137,sK371(the_carrier(sK137))))
| closed_subset(sK139(sK147(sK137,sK371(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_178217]) ).
tcf(c_178713,plain,
( ordinal(sK93(sK137,sK371(powerset(the_carrier(sK137)))))
| in(sK139(sK93(sK137,sK371(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_178237]) ).
tcf(c_178858,plain,
( sP36(sK137,sK138)
| ordinal(sK91(sK137,sK138))
| in(sK139(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK139(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK139(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178684,c_176867]) ).
tcf(c_178859,plain,
( ordinal(sK91(sK137,sK138))
| in(sK139(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK139(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK139(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178684,c_176193]) ).
tcf(c_178908,plain,
( epsilon_connected(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK139(sK91(sK137,sK138))) = sK139(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178683,c_1088]) ).
tcf(c_178909,plain,
( epsilon_transitive(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK139(sK91(sK137,sK138))) = sK139(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178683,c_1087]) ).
tcf(c_178928,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_392]) ).
tcf(c_178929,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(empty_set,X2),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_392]) ).
tcf(c_178944,plain,
( sP36(sK137,sK138)
| relation(powerset(the_carrier(sK137)))
| in(sK175(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK175(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK175(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_580,c_176867]) ).
tcf(c_178945,plain,
( relation(powerset(the_carrier(sK137)))
| in(sK175(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK175(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK175(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_580,c_176193]) ).
tcf(c_178946,plain,
( relation(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK175(sK91(sK137,sK138))) = sK175(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_175190]) ).
tcf(c_178947,plain,
( relation(sK91(sK137,sK138))
| in(sK175(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_175008]) ).
tcf(c_178948,plain,
( relation(sK91(sK137,sK138))
| subset(sK138,sK175(sK91(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_174960]) ).
tcf(c_178949,plain,
( sP36(sK137,sK138)
| relation(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_175802]) ).
tcf(c_178950,plain,
( sP36(sK137,sK138)
| relation(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_175753]) ).
tcf(c_178951,plain,
( sP36(sK137,sK138)
| relation(sK302(sK137,sK138))
| subset(sK138,sK175(sK302(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_175029]) ).
tcf(c_178952,plain,
( relation(sK93(sK137,the_topology(sK137)))
| in(sK175(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_175089]) ).
tcf(c_178953,plain,
( sP36(sK137,the_carrier(sK137))
| relation(sK302(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK175(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_176981]) ).
tcf(c_178954,plain,
( relation(sK123(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK175(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK175(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_176976]) ).
tcf(c_178955,plain,
( relation(sK91(sK137,the_carrier(sK137)))
| ( sK92(sK137,the_carrier(sK137),sK175(sK91(sK137,the_carrier(sK137)))) = sK175(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_176980]) ).
tcf(c_178956,plain,
( relation(sK91(sK137,the_carrier(sK137)))
| in(sK175(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_176982]) ).
tcf(c_178957,plain,
( relation(sK91(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK175(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_176983]) ).
tcf(c_178958,plain,
( relation(sK147(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK175(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_176978]) ).
tcf(c_178959,plain,
( relation(sK147(sK137,the_carrier(sK137)))
| closed_subset(sK175(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_176977]) ).
tcf(c_178960,plain,
( relation(sK93(sK137,powerset(the_carrier(sK137))))
| in(sK175(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_176997]) ).
tcf(c_178961,plain,
( relation(topstr_closure(sK137,sK138))
| in(sK175(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(sK175(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_580,c_177233]) ).
tcf(c_178962,plain,
( relation(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK175(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177407]) ).
tcf(c_178963,plain,
( relation(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| in(sK175(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177406]) ).
tcf(c_178964,plain,
( relation(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| closed_subset(sK175(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_177401]) ).
tcf(c_178965,plain,
( relation(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))))
| in(sK175(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177421]) ).
tcf(c_178966,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| relation(sK302(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK175(sK302(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177709]) ).
tcf(c_178967,plain,
( relation(sK91(sK137,sK206(the_carrier(sK137))))
| ( sK92(sK137,sK206(the_carrier(sK137)),sK175(sK91(sK137,sK206(the_carrier(sK137))))) = sK175(sK91(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177708]) ).
tcf(c_178968,plain,
( relation(sK91(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK175(sK91(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177711]) ).
tcf(c_178969,plain,
( relation(sK91(sK137,sK206(the_carrier(sK137))))
| in(sK175(sK91(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177710]) ).
tcf(c_178970,plain,
( relation(sK147(sK137,sK206(the_carrier(sK137))))
| closed_subset(sK175(sK147(sK137,sK206(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_177705]) ).
tcf(c_178971,plain,
( relation(sK93(sK137,sK206(powerset(the_carrier(sK137)))))
| in(sK175(sK93(sK137,sK206(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177725]) ).
tcf(c_178972,plain,
( relation(sK91(sK137,sK371(the_carrier(sK137))))
| ( sK92(sK137,sK371(the_carrier(sK137)),sK175(sK91(sK137,sK371(the_carrier(sK137))))) = sK175(sK91(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_178220]) ).
tcf(c_178973,plain,
( relation(sK91(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK175(sK91(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_178223]) ).
tcf(c_178974,plain,
( relation(sK91(sK137,sK371(the_carrier(sK137))))
| in(sK175(sK91(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_178222]) ).
tcf(c_178975,plain,
( relation(sK147(sK137,sK371(the_carrier(sK137))))
| closed_subset(sK175(sK147(sK137,sK371(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_178217]) ).
tcf(c_178976,plain,
( relation(sK93(sK137,sK371(powerset(the_carrier(sK137)))))
| in(sK175(sK93(sK137,sK371(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_178237]) ).
tcf(c_179107,plain,
( sP36(sK137,sK138)
| relation(sK91(sK137,sK138))
| in(sK175(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK175(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK175(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178947,c_176867]) ).
tcf(c_179108,plain,
( relation(sK91(sK137,sK138))
| in(sK175(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK175(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK175(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178947,c_176193]) ).
tcf(c_179148,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| sP3(sK302(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK62(sK302(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_178221]) ).
tcf(c_179149,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| ordinal(sK302(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK139(sK302(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_178221]) ).
tcf(c_179150,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| relation(sK302(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK175(sK302(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_178221]) ).
tcf(c_179177,plain,
! [X0: $i] :
( in(set_difference(the_carrier(sK137),X0),sK206(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK206(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_696,c_73134]) ).
tcf(c_179178,plain,
! [X0: $i] :
( in(set_difference(the_carrier(sK137),X0),sK208(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_702,c_73134]) ).
tcf(c_179179,plain,
! [X0: $i] :
( in(set_difference(the_carrier(sK137),X0),sK371(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK371(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_1259,c_73134]) ).
tcf(c_179180,plain,
! [X0: $i] :
( in(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_13308,c_73134]) ).
tcf(c_179182,plain,
! [X0: $i] :
( in(set_difference(the_carrier(sK137),X0),the_topology(sK137))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_47453,c_73134]) ).
tcf(c_179183,plain,
! [X0: $i,X1: $i] :
( in(set_difference(the_carrier(sK137),X0),sK147(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48126,c_73134]) ).
tcf(c_179184,plain,
! [X0: $i,X1: $i] :
( in(set_difference(the_carrier(sK137),X0),sK125(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK93(sK137,sK125(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48285,c_73134]) ).
tcf(c_179185,plain,
! [X0: $i,X1: $i] :
( in(set_difference(the_carrier(sK137),X0),sK123(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48389,c_73134]) ).
tcf(c_179227,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_393]) ).
tcf(c_179228,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(empty_set,X2),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_393]) ).
tcf(c_179240,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK122(X0)) ),
inference(superposition,[status(thm)],[c_258,c_646]) ).
tcf(c_179241,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_509,c_646]) ).
tcf(c_179243,plain,
! [X0: $i] :
( one_to_one(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_646,c_104931]) ).
tcf(c_179244,plain,
! [X0: $i] :
( ordinal(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_646,c_1085]) ).
tcf(c_179245,plain,
! [X0: $i] :
( epsilon_connected(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_646,c_1084]) ).
tcf(c_179246,plain,
! [X0: $i] :
( epsilon_transitive(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_646,c_1083]) ).
tcf(c_179247,plain,
! [X0: $i] :
( finite(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_646,c_1015]) ).
tcf(c_179249,plain,
! [X0: $i] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_646,c_779]) ).
tcf(c_179276,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(sK122(X0)) ),
inference(superposition,[status(thm)],[c_258,c_647]) ).
tcf(c_179277,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_509,c_647]) ).
tcf(c_179297,plain,
! [X0: $i] :
( sP3(sK93(sK137,sK147(sK137,X0)))
| in(sK62(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_175090]) ).
tcf(c_179298,plain,
! [X0: $i] :
( ordinal(sK93(sK137,sK147(sK137,X0)))
| in(sK139(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_175090]) ).
tcf(c_179299,plain,
! [X0: $i] :
( relation(sK93(sK137,sK147(sK137,X0)))
| in(sK175(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_175090]) ).
tcf(c_179323,plain,
! [X0: $i] :
( sP3(sK93(sK137,sK123(sK137,X0)))
| in(sK62(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_175092]) ).
tcf(c_179324,plain,
! [X0: $i] :
( ordinal(sK93(sK137,sK123(sK137,X0)))
| in(sK139(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_175092]) ).
tcf(c_179325,plain,
! [X0: $i] :
( relation(sK93(sK137,sK123(sK137,X0)))
| in(sK175(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_175092]) ).
tcf(c_179349,plain,
! [X0: $i] :
( sP3(sK91(sK137,topstr_closure(sK137,X0)))
| in(sK62(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_176012]) ).
tcf(c_179350,plain,
! [X0: $i] :
( ordinal(sK91(sK137,topstr_closure(sK137,X0)))
| in(sK139(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_176012]) ).
tcf(c_179351,plain,
! [X0: $i] :
( relation(sK91(sK137,topstr_closure(sK137,X0)))
| in(sK175(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_176012]) ).
tcf(c_179375,plain,
! [X0: $i] :
( sP3(sK91(sK137,topstr_closure(sK137,X0)))
| subset(topstr_closure(sK137,X0),sK62(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_176013]) ).
tcf(c_179376,plain,
! [X0: $i] :
( ordinal(sK91(sK137,topstr_closure(sK137,X0)))
| subset(topstr_closure(sK137,X0),sK139(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_176013]) ).
tcf(c_179377,plain,
! [X0: $i] :
( relation(sK91(sK137,topstr_closure(sK137,X0)))
| subset(topstr_closure(sK137,X0),sK175(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_176013]) ).
tcf(c_179418,plain,
subset(empty_set,empty_set),
inference(superposition,[status(thm)],[c_679,c_399]) ).
tcf(c_179429,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_536,c_704]) ).
tcf(c_179448,plain,
( sP34(the_topology(sK137),sK137)
| sP3(sK295(sK137,the_topology(sK137)))
| ( sK296(sK137,the_topology(sK137),sK62(sK295(sK137,the_topology(sK137)))) = sK62(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_176134]) ).
tcf(c_179449,plain,
( sP34(the_topology(sK137),sK137)
| ordinal(sK295(sK137,the_topology(sK137)))
| ( sK296(sK137,the_topology(sK137),sK139(sK295(sK137,the_topology(sK137)))) = sK139(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_176134]) ).
tcf(c_179450,plain,
( sP34(the_topology(sK137),sK137)
| relation(sK295(sK137,the_topology(sK137)))
| ( sK296(sK137,the_topology(sK137),sK175(sK295(sK137,the_topology(sK137)))) = sK175(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_176134]) ).
tcf(c_179471,plain,
( sP36(sK137,the_carrier(sK137))
| sP3(sK302(sK137,the_carrier(sK137)))
| ( sK303(sK137,the_carrier(sK137),sK62(sK302(sK137,the_carrier(sK137)))) = sK62(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_176974]) ).
tcf(c_179472,plain,
( sP36(sK137,the_carrier(sK137))
| ordinal(sK302(sK137,the_carrier(sK137)))
| ( sK303(sK137,the_carrier(sK137),sK139(sK302(sK137,the_carrier(sK137)))) = sK139(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_176974]) ).
tcf(c_179473,plain,
( sP36(sK137,the_carrier(sK137))
| relation(sK302(sK137,the_carrier(sK137)))
| ( sK303(sK137,the_carrier(sK137),sK175(sK302(sK137,the_carrier(sK137)))) = sK175(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_176974]) ).
tcf(c_179494,plain,
( sP36(sK137,the_carrier(sK137))
| sP3(sK302(sK137,the_carrier(sK137)))
| ( sK304(sK137,the_carrier(sK137),sK62(sK302(sK137,the_carrier(sK137)))) = sK62(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_176975]) ).
tcf(c_179495,plain,
( sP36(sK137,the_carrier(sK137))
| ordinal(sK302(sK137,the_carrier(sK137)))
| ( sK304(sK137,the_carrier(sK137),sK139(sK302(sK137,the_carrier(sK137)))) = sK139(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_176975]) ).
tcf(c_179496,plain,
( sP36(sK137,the_carrier(sK137))
| relation(sK302(sK137,the_carrier(sK137)))
| ( sK304(sK137,the_carrier(sK137),sK175(sK302(sK137,the_carrier(sK137)))) = sK175(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_176975]) ).
tcf(c_179515,plain,
( sP3(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK62(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK62(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177404]) ).
tcf(c_179516,plain,
( ordinal(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK139(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK139(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177404]) ).
tcf(c_179517,plain,
( relation(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK175(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK175(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177404]) ).
tcf(c_179552,plain,
( sP3(sK123(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK62(sK123(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK62(sK123(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_177704]) ).
tcf(c_179553,plain,
( ordinal(sK123(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK139(sK123(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK139(sK123(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_177704]) ).
tcf(c_179554,plain,
( relation(sK123(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK175(sK123(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK175(sK123(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_177704]) ).
tcf(c_179569,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X1,X0)) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_410,c_420]) ).
tcf(c_179570,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_420,c_399]) ).
tcf(c_179571,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X1,X0)) = set_union2(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_420,c_410]) ).
tcf(c_179572,plain,
! [X0: $i] : set_union2(X0,empty_set) = set_difference(X0,empty_set),
inference(superposition,[status(thm)],[c_420,c_680]) ).
tcf(c_179574,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X1,X0)) = set_union2(X0,X1),
inference(light_normalisation,[status(thm)],[c_179571,c_410]) ).
tcf(c_179582,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_536,c_705]) ).
tcf(c_179589,plain,
! [X0: $i] :
( ordinal(X0)
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_536,c_706]) ).
tcf(c_179618,plain,
( sP3(sK147(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK62(sK147(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_177706]) ).
tcf(c_179619,plain,
( ordinal(sK147(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK139(sK147(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_177706]) ).
tcf(c_179620,plain,
( relation(sK147(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK175(sK147(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_177706]) ).
tcf(c_179648,plain,
( sP3(sK123(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK62(sK123(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK62(sK123(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_178216]) ).
tcf(c_179649,plain,
( ordinal(sK123(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK139(sK123(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK139(sK123(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_178216]) ).
tcf(c_179650,plain,
( relation(sK123(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK175(sK123(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK175(sK123(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_178216]) ).
tcf(c_179672,plain,
( sP3(sK147(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK62(sK147(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_178218]) ).
tcf(c_179673,plain,
( ordinal(sK147(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK139(sK147(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_178218]) ).
tcf(c_179674,plain,
( relation(sK147(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK175(sK147(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_178218]) ).
tcf(c_179702,plain,
! [X0: $i] :
( sP3(sK93(sK137,sK125(sK137,X0)))
| in(sK62(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_120,c_175091]) ).
tcf(c_179703,plain,
! [X0: $i] :
( ordinal(sK93(sK137,sK125(sK137,X0)))
| in(sK139(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_383,c_175091]) ).
tcf(c_179704,plain,
! [X0: $i] :
( relation(sK93(sK137,sK125(sK137,X0)))
| in(sK175(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_580,c_175091]) ).
tcf(c_179732,plain,
pair_first(unordered_pair(powerset(empty_set),powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_330,c_515]) ).
tcf(c_179733,plain,
! [X0: $i] : pair_first(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_330,c_515]) ).
tcf(c_179747,plain,
epsilon_transitive(sK208(omega)),
inference(superposition,[status(thm)],[c_702,c_850]) ).
tcf(c_179752,plain,
epsilon_connected(sK208(omega)),
inference(superposition,[status(thm)],[c_702,c_851]) ).
tcf(c_179797,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178686,c_1088]) ).
tcf(c_179798,plain,
( sP36(sK137,sK138)
| epsilon_transitive(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178686,c_1087]) ).
tcf(c_179815,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178687,c_1088]) ).
tcf(c_179816,plain,
( sP36(sK137,sK138)
| epsilon_transitive(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178687,c_1087]) ).
tcf(c_179841,plain,
pair_second(unordered_pair(powerset(empty_set),powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_330,c_516]) ).
tcf(c_179842,plain,
! [X0: $i] : pair_second(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set))) = X0,
inference(superposition,[status(thm)],[c_330,c_516]) ).
tcf(c_179848,plain,
ordinal(sK208(omega)),
inference(superposition,[status(thm)],[c_702,c_852]) ).
tcf(c_179853,plain,
! [X0: $i] :
( epsilon_connected(sK274(X0))
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_856,c_1088]) ).
tcf(c_179854,plain,
! [X0: $i] :
( epsilon_transitive(sK274(X0))
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_856,c_1087]) ).
tcf(c_179867,plain,
! [X0: $i] :
( one_to_one(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_968,c_104931]) ).
tcf(c_179868,plain,
! [X0: $i] :
( ordinal(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_968,c_1085]) ).
tcf(c_179869,plain,
! [X0: $i] :
( epsilon_connected(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_968,c_1084]) ).
tcf(c_179870,plain,
! [X0: $i] :
( epsilon_transitive(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_968,c_1083]) ).
tcf(c_179871,plain,
! [X0: $i] :
( finite(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_968,c_1015]) ).
tcf(c_179873,plain,
! [X0: $i] :
( function(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_968,c_779]) ).
tcf(c_179918,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK138))) = topstr_closure(sK137,topstr_closure(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_376,c_176018]) ).
tcf(c_179919,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK206(the_carrier(sK137))))) = topstr_closure(sK137,topstr_closure(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_696,c_176018]) ).
tcf(c_179920,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK208(powerset(the_carrier(sK137)))))) = topstr_closure(sK137,topstr_closure(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_702,c_176018]) ).
tcf(c_179921,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK371(the_carrier(sK137))))) = topstr_closure(sK137,topstr_closure(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1259,c_176018]) ).
tcf(c_179922,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,the_carrier(sK137)))) = topstr_closure(sK137,topstr_closure(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_13308,c_176018]) ).
tcf(c_179923,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,topstr_closure(sK137,X0)))) = topstr_closure(sK137,topstr_closure(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_176018]) ).
tcf(c_179924,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK304(sK137,X1,X0)))) = topstr_closure(sK137,topstr_closure(sK137,sK304(sK137,X1,X0))) )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_176018]) ).
tcf(c_179925,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK146(sK137,X0,X1)))) = topstr_closure(sK137,topstr_closure(sK137,sK146(sK137,X0,X1))) )
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_176018]) ).
tcf(c_179926,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK145(sK137,X0)))) = topstr_closure(sK137,topstr_closure(sK137,sK145(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_176018]) ).
tcf(c_179927,plain,
! [X0: $i,X1: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK124(sK137,X1,X0)))) = topstr_closure(sK137,topstr_closure(sK137,sK124(sK137,X1,X0))) )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_176018]) ).
tcf(c_179928,plain,
! [X0: $i,X1: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK92(sK137,X1,X0)))) = topstr_closure(sK137,topstr_closure(sK137,sK92(sK137,X1,X0))) )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_176018]) ).
tcf(c_179983,plain,
( sP3(sK123(sK137,the_carrier(sK137)))
| ( sK124(sK137,the_carrier(sK137),sK62(sK123(sK137,the_carrier(sK137)))) = sK62(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(sK62(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_176971]) ).
tcf(c_179984,plain,
( ordinal(sK123(sK137,the_carrier(sK137)))
| ( sK124(sK137,the_carrier(sK137),sK139(sK123(sK137,the_carrier(sK137)))) = sK139(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(sK139(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_176971]) ).
tcf(c_179985,plain,
( relation(sK123(sK137,the_carrier(sK137)))
| ( sK124(sK137,the_carrier(sK137),sK175(sK123(sK137,the_carrier(sK137)))) = sK175(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(sK175(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_176971]) ).
tcf(c_179986,plain,
( ( sK124(sK137,the_carrier(sK137),sK138) = sK138 )
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138)
| ~ element(sK138,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176984,c_176971]) ).
tcf(c_179987,plain,
( ( sK124(sK137,the_carrier(sK137),sK138) = sK138 )
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138) ),
inference(forward_subsumption_resolution,[status(thm)],[c_179986,c_376]) ).
tcf(c_180022,plain,
! [X0: $i] :
( ( sK92(sK137,the_carrier(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(the_carrier(sK137),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176973,c_176980]) ).
tcf(c_180039,plain,
( sP3(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK62(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK62(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_177400]) ).
tcf(c_180040,plain,
( ordinal(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK139(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK139(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_177400]) ).
tcf(c_180041,plain,
( relation(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK175(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK175(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_177400]) ).
tcf(c_180063,plain,
( sP3(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK62(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_177402]) ).
tcf(c_180064,plain,
( ordinal(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK139(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_177402]) ).
tcf(c_180065,plain,
( relation(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK175(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_177402]) ).
tcf(c_180087,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| sP3(sK302(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK62(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177405]) ).
tcf(c_180088,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| ordinal(sK302(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK139(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177405]) ).
tcf(c_180089,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| relation(sK302(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK175(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177405]) ).
tcf(c_180107,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( unordered_pair(X0,X0) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_330,c_531]) ).
tcf(c_180137,plain,
! [X0: $i] :
( sP34(sK206(powerset(the_carrier(sK137))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK206(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK206(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_696,c_73951]) ).
tcf(c_180138,plain,
! [X0: $i] :
( sP34(sK208(powerset(powerset(the_carrier(sK137)))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK208(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_702,c_73951]) ).
tcf(c_180139,plain,
! [X0: $i] :
( sP34(sK371(powerset(the_carrier(sK137))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK371(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK371(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_1259,c_73951]) ).
tcf(c_180140,plain,
! [X0: $i] :
( sP34(powerset(the_carrier(sK137)),sK137)
| in(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_13308,c_73951]) ).
tcf(c_180142,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| in(set_difference(the_carrier(sK137),X0),the_topology(sK137))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_47453,c_73951]) ).
tcf(c_180143,plain,
! [X0: $i,X1: $i] :
( sP34(sK147(sK137,X1),sK137)
| in(set_difference(the_carrier(sK137),X0),sK147(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK295(sK137,sK147(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48126,c_73951]) ).
tcf(c_180144,plain,
! [X0: $i,X1: $i] :
( sP34(sK125(sK137,X1),sK137)
| in(set_difference(the_carrier(sK137),X0),sK125(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK295(sK137,sK125(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48285,c_73951]) ).
tcf(c_180145,plain,
! [X0: $i,X1: $i] :
( sP34(sK123(sK137,X1),sK137)
| in(set_difference(the_carrier(sK137),X0),sK123(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK295(sK137,sK123(sK137,X1))) ),
inference(superposition,[status(thm)],[c_48389,c_73951]) ).
tcf(c_180214,plain,
! [X0: $i] :
( in(the_carrier(sK137),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,the_carrier(sK137)) ),
inference(global_subsumption_just,[status(thm)],[c_176970,c_68983,c_176970]) ).
tcf(c_180215,plain,
! [X0: $i] :
( in(the_carrier(sK137),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(renaming,[status(thm)],[c_180214]) ).
tcf(c_180225,plain,
( ( sK124(sK137,the_carrier(sK137),the_carrier(sK137)) = the_carrier(sK137) )
| ~ topological_space(sK137)
| ~ subset(the_carrier(sK137),the_carrier(sK137))
| ~ element(the_carrier(sK137),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180215,c_176971]) ).
tcf(c_180227,plain,
( ( sK124(sK137,sK138,the_carrier(sK137)) = the_carrier(sK137) )
| ~ topological_space(sK137)
| ~ subset(sK138,the_carrier(sK137))
| ~ element(sK138,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180215,c_176985]) ).
tcf(c_180232,plain,
( ( sK124(sK137,sK138,the_carrier(sK137)) = the_carrier(sK137) )
| ~ topological_space(sK137)
| ~ subset(sK138,the_carrier(sK137)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_180227,c_376]) ).
tcf(c_180236,plain,
( ( sK124(sK137,the_carrier(sK137),the_carrier(sK137)) = the_carrier(sK137) )
| ~ topological_space(sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_180225,c_670,c_13308]) ).
tcf(c_180245,plain,
! [X0: $i] :
( in(the_carrier(sK137),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,the_carrier(sK137)) ),
inference(global_subsumption_just,[status(thm)],[c_176972,c_68983,c_176972]) ).
tcf(c_180246,plain,
! [X0: $i] :
( in(the_carrier(sK137),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(renaming,[status(thm)],[c_180245]) ).
tcf(c_180273,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| sP3(sK295(sK137,powerset(the_carrier(sK137))))
| ( sK296(sK137,powerset(the_carrier(sK137)),sK62(sK295(sK137,powerset(the_carrier(sK137))))) = sK62(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_176995]) ).
tcf(c_180274,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| ordinal(sK295(sK137,powerset(the_carrier(sK137))))
| ( sK296(sK137,powerset(the_carrier(sK137)),sK139(sK295(sK137,powerset(the_carrier(sK137))))) = sK139(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_176995]) ).
tcf(c_180275,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| relation(sK295(sK137,powerset(the_carrier(sK137))))
| ( sK296(sK137,powerset(the_carrier(sK137)),sK175(sK295(sK137,powerset(the_carrier(sK137))))) = sK175(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_176995]) ).
tcf(c_180292,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( unordered_pair(X0,X1) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_330,c_541]) ).
tcf(c_180302,plain,
( sP36(sK137,sK138)
| epsilon_transitive(powerset(the_carrier(sK137)))
| in(sK340(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK340(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK340(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1081,c_176867]) ).
tcf(c_180303,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(sK340(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK340(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK340(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1081,c_176193]) ).
tcf(c_180304,plain,
( epsilon_transitive(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK340(sK91(sK137,sK138))) = sK340(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_175190]) ).
tcf(c_180305,plain,
( epsilon_transitive(sK91(sK137,sK138))
| in(sK340(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_175008]) ).
tcf(c_180306,plain,
( epsilon_transitive(sK91(sK137,sK138))
| subset(sK138,sK340(sK91(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_174960]) ).
tcf(c_180307,plain,
( sP36(sK137,sK138)
| epsilon_transitive(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK340(sK302(sK137,sK138))) = sK340(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_175802]) ).
tcf(c_180308,plain,
( sP36(sK137,sK138)
| epsilon_transitive(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK340(sK302(sK137,sK138))) = sK340(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_175753]) ).
tcf(c_180309,plain,
( sP36(sK137,sK138)
| epsilon_transitive(sK302(sK137,sK138))
| subset(sK138,sK340(sK302(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_175029]) ).
tcf(c_180310,plain,
( epsilon_transitive(sK93(sK137,the_topology(sK137)))
| in(sK340(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_175089]) ).
tcf(c_180311,plain,
! [X0: $i] :
( epsilon_transitive(sK93(sK137,sK147(sK137,X0)))
| in(sK340(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_175090]) ).
tcf(c_180312,plain,
! [X0: $i] :
( epsilon_transitive(sK93(sK137,sK125(sK137,X0)))
| in(sK340(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1081,c_175091]) ).
tcf(c_180313,plain,
! [X0: $i] :
( epsilon_transitive(sK93(sK137,sK123(sK137,X0)))
| in(sK340(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_175092]) ).
tcf(c_180314,plain,
! [X0: $i] :
( epsilon_transitive(sK91(sK137,topstr_closure(sK137,X0)))
| subset(topstr_closure(sK137,X0),sK340(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_176013]) ).
tcf(c_180315,plain,
! [X0: $i] :
( epsilon_transitive(sK91(sK137,topstr_closure(sK137,X0)))
| in(sK340(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_176012]) ).
tcf(c_180316,plain,
( sP34(the_topology(sK137),sK137)
| epsilon_transitive(sK295(sK137,the_topology(sK137)))
| ( sK296(sK137,the_topology(sK137),sK340(sK295(sK137,the_topology(sK137)))) = sK340(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_176134]) ).
tcf(c_180317,plain,
( sP36(sK137,the_carrier(sK137))
| epsilon_transitive(sK302(sK137,the_carrier(sK137)))
| ( sK304(sK137,the_carrier(sK137),sK340(sK302(sK137,the_carrier(sK137)))) = sK340(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_176975]) ).
tcf(c_180318,plain,
( sP36(sK137,the_carrier(sK137))
| epsilon_transitive(sK302(sK137,the_carrier(sK137)))
| ( sK303(sK137,the_carrier(sK137),sK340(sK302(sK137,the_carrier(sK137)))) = sK340(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_176974]) ).
tcf(c_180319,plain,
( sP36(sK137,the_carrier(sK137))
| epsilon_transitive(sK302(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK340(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_176981]) ).
tcf(c_180320,plain,
( epsilon_transitive(sK123(sK137,the_carrier(sK137)))
| ( sK124(sK137,the_carrier(sK137),sK340(sK123(sK137,the_carrier(sK137)))) = sK340(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(sK340(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_176971]) ).
tcf(c_180321,plain,
( epsilon_transitive(sK123(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK340(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK340(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_176976]) ).
tcf(c_180322,plain,
( epsilon_transitive(sK91(sK137,the_carrier(sK137)))
| ( sK92(sK137,the_carrier(sK137),sK340(sK91(sK137,the_carrier(sK137)))) = sK340(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_176980]) ).
tcf(c_180323,plain,
( epsilon_transitive(sK91(sK137,the_carrier(sK137)))
| in(sK340(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_176982]) ).
tcf(c_180324,plain,
( epsilon_transitive(sK91(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK340(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_176983]) ).
tcf(c_180325,plain,
( epsilon_transitive(sK147(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK340(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_176978]) ).
tcf(c_180326,plain,
( epsilon_transitive(sK147(sK137,the_carrier(sK137)))
| closed_subset(sK340(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_176977]) ).
tcf(c_180327,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| epsilon_transitive(sK295(sK137,powerset(the_carrier(sK137))))
| ( sK296(sK137,powerset(the_carrier(sK137)),sK340(sK295(sK137,powerset(the_carrier(sK137))))) = sK340(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_176995]) ).
tcf(c_180328,plain,
( epsilon_transitive(sK93(sK137,powerset(the_carrier(sK137))))
| in(sK340(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_176997]) ).
tcf(c_180329,plain,
( epsilon_transitive(topstr_closure(sK137,sK138))
| in(sK340(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(sK340(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1081,c_177233]) ).
tcf(c_180330,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| epsilon_transitive(sK302(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK340(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177405]) ).
tcf(c_180331,plain,
( epsilon_transitive(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK340(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK340(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_177400]) ).
tcf(c_180332,plain,
( epsilon_transitive(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK340(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK340(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177404]) ).
tcf(c_180333,plain,
( epsilon_transitive(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK340(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177407]) ).
tcf(c_180334,plain,
( epsilon_transitive(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| in(sK340(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177406]) ).
tcf(c_180335,plain,
( epsilon_transitive(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK340(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_177402]) ).
tcf(c_180336,plain,
( epsilon_transitive(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| closed_subset(sK340(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_177401]) ).
tcf(c_180337,plain,
( epsilon_transitive(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))))
| in(sK340(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177421]) ).
tcf(c_180338,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| epsilon_transitive(sK302(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK340(sK302(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177709]) ).
tcf(c_180339,plain,
( epsilon_transitive(sK123(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK340(sK123(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK340(sK123(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_177704]) ).
tcf(c_180340,plain,
( epsilon_transitive(sK91(sK137,sK206(the_carrier(sK137))))
| ( sK92(sK137,sK206(the_carrier(sK137)),sK340(sK91(sK137,sK206(the_carrier(sK137))))) = sK340(sK91(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177708]) ).
tcf(c_180341,plain,
( epsilon_transitive(sK91(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK340(sK91(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177711]) ).
tcf(c_180342,plain,
( epsilon_transitive(sK91(sK137,sK206(the_carrier(sK137))))
| in(sK340(sK91(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177710]) ).
tcf(c_180343,plain,
( epsilon_transitive(sK147(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK340(sK147(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_177706]) ).
tcf(c_180344,plain,
( epsilon_transitive(sK147(sK137,sK206(the_carrier(sK137))))
| closed_subset(sK340(sK147(sK137,sK206(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_177705]) ).
tcf(c_180345,plain,
( epsilon_transitive(sK93(sK137,sK206(powerset(the_carrier(sK137)))))
| in(sK340(sK93(sK137,sK206(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177725]) ).
tcf(c_180346,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| epsilon_transitive(sK302(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK340(sK302(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_178221]) ).
tcf(c_180347,plain,
( epsilon_transitive(sK123(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK340(sK123(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK340(sK123(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_178216]) ).
tcf(c_180348,plain,
( epsilon_transitive(sK91(sK137,sK371(the_carrier(sK137))))
| ( sK92(sK137,sK371(the_carrier(sK137)),sK340(sK91(sK137,sK371(the_carrier(sK137))))) = sK340(sK91(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_178220]) ).
tcf(c_180349,plain,
( epsilon_transitive(sK91(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK340(sK91(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_178223]) ).
tcf(c_180350,plain,
( epsilon_transitive(sK91(sK137,sK371(the_carrier(sK137))))
| in(sK340(sK91(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_178222]) ).
tcf(c_180351,plain,
( epsilon_transitive(sK147(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK340(sK147(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_178218]) ).
tcf(c_180352,plain,
( epsilon_transitive(sK147(sK137,sK371(the_carrier(sK137))))
| closed_subset(sK340(sK147(sK137,sK371(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_178217]) ).
tcf(c_180353,plain,
( epsilon_transitive(sK93(sK137,sK371(powerset(the_carrier(sK137)))))
| in(sK340(sK93(sK137,sK371(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_178237]) ).
tcf(c_180554,plain,
! [X0: $i] :
( one_to_one(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1166,c_104931]) ).
tcf(c_180555,plain,
! [X0: $i] :
( ordinal(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1166,c_1085]) ).
tcf(c_180556,plain,
! [X0: $i] :
( epsilon_connected(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1166,c_1084]) ).
tcf(c_180557,plain,
! [X0: $i] :
( epsilon_transitive(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1166,c_1083]) ).
tcf(c_180558,plain,
! [X0: $i] :
( finite(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1166,c_1015]) ).
tcf(c_180560,plain,
! [X0: $i] :
( function(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1166,c_779]) ).
tcf(c_180587,plain,
~ iPr_def_16,
inference(global_subsumption_just,[status(thm)],[c_151110,c_1341,c_1414,c_151317]) ).
tcf(c_180594,plain,
( sP36(sK137,sK138)
| epsilon_connected(powerset(the_carrier(sK137)))
| in(sK369(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK369(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK369(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1253,c_176867]) ).
tcf(c_180595,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK369(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK369(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK369(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1253,c_176193]) ).
tcf(c_180596,plain,
( epsilon_connected(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK369(sK91(sK137,sK138))) = sK369(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_175190]) ).
tcf(c_180597,plain,
( epsilon_connected(sK91(sK137,sK138))
| in(sK369(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_175008]) ).
tcf(c_180598,plain,
( epsilon_connected(sK91(sK137,sK138))
| subset(sK138,sK369(sK91(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_174960]) ).
tcf(c_180599,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK369(sK302(sK137,sK138))) = sK369(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_175802]) ).
tcf(c_180600,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK369(sK302(sK137,sK138))) = sK369(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_175753]) ).
tcf(c_180601,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| subset(sK138,sK369(sK302(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_175029]) ).
tcf(c_180602,plain,
( epsilon_connected(sK93(sK137,the_topology(sK137)))
| in(sK369(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_175089]) ).
tcf(c_180603,plain,
! [X0: $i] :
( epsilon_connected(sK93(sK137,sK147(sK137,X0)))
| in(sK369(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_175090]) ).
tcf(c_180604,plain,
! [X0: $i] :
( epsilon_connected(sK93(sK137,sK125(sK137,X0)))
| in(sK369(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1253,c_175091]) ).
tcf(c_180605,plain,
! [X0: $i] :
( epsilon_connected(sK93(sK137,sK123(sK137,X0)))
| in(sK369(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_175092]) ).
tcf(c_180606,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,topstr_closure(sK137,X0)))
| subset(topstr_closure(sK137,X0),sK369(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_176013]) ).
tcf(c_180607,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,topstr_closure(sK137,X0)))
| in(sK369(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_176012]) ).
tcf(c_180608,plain,
( sP34(the_topology(sK137),sK137)
| epsilon_connected(sK295(sK137,the_topology(sK137)))
| ( sK296(sK137,the_topology(sK137),sK369(sK295(sK137,the_topology(sK137)))) = sK369(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_176134]) ).
tcf(c_180609,plain,
( sP36(sK137,the_carrier(sK137))
| epsilon_connected(sK302(sK137,the_carrier(sK137)))
| ( sK304(sK137,the_carrier(sK137),sK369(sK302(sK137,the_carrier(sK137)))) = sK369(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_176975]) ).
tcf(c_180610,plain,
( sP36(sK137,the_carrier(sK137))
| epsilon_connected(sK302(sK137,the_carrier(sK137)))
| ( sK303(sK137,the_carrier(sK137),sK369(sK302(sK137,the_carrier(sK137)))) = sK369(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_176974]) ).
tcf(c_180611,plain,
( sP36(sK137,the_carrier(sK137))
| epsilon_connected(sK302(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK369(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_176981]) ).
tcf(c_180612,plain,
( epsilon_connected(sK123(sK137,the_carrier(sK137)))
| ( sK124(sK137,the_carrier(sK137),sK369(sK123(sK137,the_carrier(sK137)))) = sK369(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(sK369(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_176971]) ).
tcf(c_180613,plain,
( epsilon_connected(sK123(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK369(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK369(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_176976]) ).
tcf(c_180614,plain,
( epsilon_connected(sK91(sK137,the_carrier(sK137)))
| ( sK92(sK137,the_carrier(sK137),sK369(sK91(sK137,the_carrier(sK137)))) = sK369(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_176980]) ).
tcf(c_180615,plain,
( epsilon_connected(sK91(sK137,the_carrier(sK137)))
| in(sK369(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_176982]) ).
tcf(c_180616,plain,
( epsilon_connected(sK91(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK369(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_176983]) ).
tcf(c_180617,plain,
( epsilon_connected(sK147(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK369(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_176978]) ).
tcf(c_180618,plain,
( epsilon_connected(sK147(sK137,the_carrier(sK137)))
| closed_subset(sK369(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_176977]) ).
tcf(c_180619,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| epsilon_connected(sK295(sK137,powerset(the_carrier(sK137))))
| ( sK296(sK137,powerset(the_carrier(sK137)),sK369(sK295(sK137,powerset(the_carrier(sK137))))) = sK369(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_176995]) ).
tcf(c_180620,plain,
( epsilon_connected(sK93(sK137,powerset(the_carrier(sK137))))
| in(sK369(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_176997]) ).
tcf(c_180621,plain,
( epsilon_connected(topstr_closure(sK137,sK138))
| in(sK369(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(sK369(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1253,c_177233]) ).
tcf(c_180622,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| epsilon_connected(sK302(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK369(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177405]) ).
tcf(c_180623,plain,
( epsilon_connected(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK369(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK369(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_177400]) ).
tcf(c_180624,plain,
( epsilon_connected(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK369(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK369(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177404]) ).
tcf(c_180625,plain,
( epsilon_connected(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK369(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177407]) ).
tcf(c_180626,plain,
( epsilon_connected(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| in(sK369(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177406]) ).
tcf(c_180627,plain,
( epsilon_connected(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK369(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_177402]) ).
tcf(c_180628,plain,
( epsilon_connected(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| closed_subset(sK369(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_177401]) ).
tcf(c_180629,plain,
( epsilon_connected(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))))
| in(sK369(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177421]) ).
tcf(c_180630,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK369(sK302(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177709]) ).
tcf(c_180631,plain,
( epsilon_connected(sK123(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK369(sK123(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK369(sK123(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_177704]) ).
tcf(c_180632,plain,
( epsilon_connected(sK91(sK137,sK206(the_carrier(sK137))))
| ( sK92(sK137,sK206(the_carrier(sK137)),sK369(sK91(sK137,sK206(the_carrier(sK137))))) = sK369(sK91(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177708]) ).
tcf(c_180633,plain,
( epsilon_connected(sK91(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK369(sK91(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177711]) ).
tcf(c_180634,plain,
( epsilon_connected(sK91(sK137,sK206(the_carrier(sK137))))
| in(sK369(sK91(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177710]) ).
tcf(c_180635,plain,
( epsilon_connected(sK147(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK369(sK147(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_177706]) ).
tcf(c_180636,plain,
( epsilon_connected(sK147(sK137,sK206(the_carrier(sK137))))
| closed_subset(sK369(sK147(sK137,sK206(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_177705]) ).
tcf(c_180637,plain,
( epsilon_connected(sK93(sK137,sK206(powerset(the_carrier(sK137)))))
| in(sK369(sK93(sK137,sK206(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177725]) ).
tcf(c_180638,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK369(sK302(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_178221]) ).
tcf(c_180639,plain,
( epsilon_connected(sK123(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK369(sK123(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK369(sK123(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_178216]) ).
tcf(c_180640,plain,
( epsilon_connected(sK91(sK137,sK371(the_carrier(sK137))))
| ( sK92(sK137,sK371(the_carrier(sK137)),sK369(sK91(sK137,sK371(the_carrier(sK137))))) = sK369(sK91(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_178220]) ).
tcf(c_180641,plain,
( epsilon_connected(sK91(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK369(sK91(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_178223]) ).
tcf(c_180642,plain,
( epsilon_connected(sK91(sK137,sK371(the_carrier(sK137))))
| in(sK369(sK91(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_178222]) ).
tcf(c_180643,plain,
( epsilon_connected(sK147(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK369(sK147(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_178218]) ).
tcf(c_180644,plain,
( epsilon_connected(sK147(sK137,sK371(the_carrier(sK137))))
| closed_subset(sK369(sK147(sK137,sK371(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_178217]) ).
tcf(c_180645,plain,
( epsilon_connected(sK93(sK137,sK371(powerset(the_carrier(sK137)))))
| in(sK369(sK93(sK137,sK371(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_178237]) ).
tcf(c_180847,plain,
( sP36(sK137,sK138)
| epsilon_connected(powerset(the_carrier(sK137)))
| in(sK370(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK370(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK370(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1254,c_176867]) ).
tcf(c_180848,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK370(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK370(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK370(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1254,c_176193]) ).
tcf(c_180849,plain,
( epsilon_connected(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK370(sK91(sK137,sK138))) = sK370(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_175190]) ).
tcf(c_180850,plain,
( epsilon_connected(sK91(sK137,sK138))
| in(sK370(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_175008]) ).
tcf(c_180851,plain,
( epsilon_connected(sK91(sK137,sK138))
| subset(sK138,sK370(sK91(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_174960]) ).
tcf(c_180852,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK370(sK302(sK137,sK138))) = sK370(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_175802]) ).
tcf(c_180853,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK370(sK302(sK137,sK138))) = sK370(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_175753]) ).
tcf(c_180854,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| subset(sK138,sK370(sK302(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_175029]) ).
tcf(c_180855,plain,
( epsilon_connected(sK93(sK137,the_topology(sK137)))
| in(sK370(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_175089]) ).
tcf(c_180856,plain,
! [X0: $i] :
( epsilon_connected(sK93(sK137,sK147(sK137,X0)))
| in(sK370(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_175090]) ).
tcf(c_180857,plain,
! [X0: $i] :
( epsilon_connected(sK93(sK137,sK125(sK137,X0)))
| in(sK370(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1254,c_175091]) ).
tcf(c_180858,plain,
! [X0: $i] :
( epsilon_connected(sK93(sK137,sK123(sK137,X0)))
| in(sK370(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_175092]) ).
tcf(c_180859,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,topstr_closure(sK137,X0)))
| subset(topstr_closure(sK137,X0),sK370(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_176013]) ).
tcf(c_180860,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,topstr_closure(sK137,X0)))
| in(sK370(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_176012]) ).
tcf(c_180861,plain,
( sP34(the_topology(sK137),sK137)
| epsilon_connected(sK295(sK137,the_topology(sK137)))
| ( sK296(sK137,the_topology(sK137),sK370(sK295(sK137,the_topology(sK137)))) = sK370(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_176134]) ).
tcf(c_180862,plain,
( sP36(sK137,the_carrier(sK137))
| epsilon_connected(sK302(sK137,the_carrier(sK137)))
| ( sK304(sK137,the_carrier(sK137),sK370(sK302(sK137,the_carrier(sK137)))) = sK370(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_176975]) ).
tcf(c_180863,plain,
( sP36(sK137,the_carrier(sK137))
| epsilon_connected(sK302(sK137,the_carrier(sK137)))
| ( sK303(sK137,the_carrier(sK137),sK370(sK302(sK137,the_carrier(sK137)))) = sK370(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_176974]) ).
tcf(c_180864,plain,
( sP36(sK137,the_carrier(sK137))
| epsilon_connected(sK302(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK370(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_176981]) ).
tcf(c_180865,plain,
( epsilon_connected(sK123(sK137,the_carrier(sK137)))
| ( sK124(sK137,the_carrier(sK137),sK370(sK123(sK137,the_carrier(sK137)))) = sK370(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(sK370(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_176971]) ).
tcf(c_180866,plain,
( epsilon_connected(sK123(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK370(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK370(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_176976]) ).
tcf(c_180867,plain,
( epsilon_connected(sK91(sK137,the_carrier(sK137)))
| ( sK92(sK137,the_carrier(sK137),sK370(sK91(sK137,the_carrier(sK137)))) = sK370(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_176980]) ).
tcf(c_180868,plain,
( epsilon_connected(sK91(sK137,the_carrier(sK137)))
| in(sK370(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_176982]) ).
tcf(c_180869,plain,
( epsilon_connected(sK91(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK370(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_176983]) ).
tcf(c_180870,plain,
( epsilon_connected(sK147(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK370(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_176978]) ).
tcf(c_180871,plain,
( epsilon_connected(sK147(sK137,the_carrier(sK137)))
| closed_subset(sK370(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_176977]) ).
tcf(c_180872,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| epsilon_connected(sK295(sK137,powerset(the_carrier(sK137))))
| ( sK296(sK137,powerset(the_carrier(sK137)),sK370(sK295(sK137,powerset(the_carrier(sK137))))) = sK370(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_176995]) ).
tcf(c_180873,plain,
( epsilon_connected(sK93(sK137,powerset(the_carrier(sK137))))
| in(sK370(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_176997]) ).
tcf(c_180874,plain,
( epsilon_connected(topstr_closure(sK137,sK138))
| in(sK370(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(sK370(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1254,c_177233]) ).
tcf(c_180875,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| epsilon_connected(sK302(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK370(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177405]) ).
tcf(c_180876,plain,
( epsilon_connected(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK370(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK370(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_177400]) ).
tcf(c_180877,plain,
( epsilon_connected(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK370(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK370(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177404]) ).
tcf(c_180878,plain,
( epsilon_connected(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK370(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177407]) ).
tcf(c_180879,plain,
( epsilon_connected(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| in(sK370(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177406]) ).
tcf(c_180880,plain,
( epsilon_connected(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK370(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_177402]) ).
tcf(c_180881,plain,
( epsilon_connected(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| closed_subset(sK370(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_177401]) ).
tcf(c_180882,plain,
( epsilon_connected(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))))
| in(sK370(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177421]) ).
tcf(c_180883,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK370(sK302(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177709]) ).
tcf(c_180884,plain,
( epsilon_connected(sK123(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK370(sK123(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK370(sK123(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_177704]) ).
tcf(c_180885,plain,
( epsilon_connected(sK91(sK137,sK206(the_carrier(sK137))))
| ( sK92(sK137,sK206(the_carrier(sK137)),sK370(sK91(sK137,sK206(the_carrier(sK137))))) = sK370(sK91(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177708]) ).
tcf(c_180886,plain,
( epsilon_connected(sK91(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK370(sK91(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177711]) ).
tcf(c_180887,plain,
( epsilon_connected(sK91(sK137,sK206(the_carrier(sK137))))
| in(sK370(sK91(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177710]) ).
tcf(c_180888,plain,
( epsilon_connected(sK147(sK137,sK206(the_carrier(sK137))))
| subset(sK206(the_carrier(sK137)),sK370(sK147(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_177706]) ).
tcf(c_180889,plain,
( epsilon_connected(sK147(sK137,sK206(the_carrier(sK137))))
| closed_subset(sK370(sK147(sK137,sK206(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_177705]) ).
tcf(c_180890,plain,
( epsilon_connected(sK93(sK137,sK206(powerset(the_carrier(sK137)))))
| in(sK370(sK93(sK137,sK206(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177725]) ).
tcf(c_180891,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK370(sK302(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_178221]) ).
tcf(c_180892,plain,
( epsilon_connected(sK123(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK370(sK123(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK370(sK123(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_178216]) ).
tcf(c_180893,plain,
( epsilon_connected(sK91(sK137,sK371(the_carrier(sK137))))
| ( sK92(sK137,sK371(the_carrier(sK137)),sK370(sK91(sK137,sK371(the_carrier(sK137))))) = sK370(sK91(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_178220]) ).
tcf(c_180894,plain,
( epsilon_connected(sK91(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK370(sK91(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_178223]) ).
tcf(c_180895,plain,
( epsilon_connected(sK91(sK137,sK371(the_carrier(sK137))))
| in(sK370(sK91(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_178222]) ).
tcf(c_180896,plain,
( epsilon_connected(sK147(sK137,sK371(the_carrier(sK137))))
| subset(sK371(the_carrier(sK137)),sK370(sK147(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_178218]) ).
tcf(c_180897,plain,
( epsilon_connected(sK147(sK137,sK371(the_carrier(sK137))))
| closed_subset(sK370(sK147(sK137,sK371(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_178217]) ).
tcf(c_180898,plain,
( epsilon_connected(sK93(sK137,sK371(powerset(the_carrier(sK137)))))
| in(sK370(sK93(sK137,sK371(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_178237]) ).
tcf(c_181119,plain,
( sP36(sK137,sK138)
| epsilon_transitive(sK91(sK137,sK138))
| in(sK340(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK340(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK340(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180305,c_176867]) ).
tcf(c_181120,plain,
( epsilon_transitive(sK91(sK137,sK138))
| in(sK340(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK340(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK340(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180305,c_176193]) ).
tcf(c_181138,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK91(sK137,sK138))
| in(sK369(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK369(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK369(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180597,c_176867]) ).
tcf(c_181139,plain,
( epsilon_connected(sK91(sK137,sK138))
| in(sK369(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK369(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK369(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180597,c_176193]) ).
tcf(c_181157,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK91(sK137,sK138))
| in(sK370(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK370(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK370(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180850,c_176867]) ).
tcf(c_181158,plain,
( epsilon_connected(sK91(sK137,sK138))
| in(sK370(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK370(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK370(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180850,c_176193]) ).
tcf(c_181191,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X0) = set_difference(X1,X0),
inference(superposition,[status(thm)],[c_642,c_420]) ).
tcf(c_181192,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_642,c_518]) ).
tcf(c_181193,plain,
! [X0: $i] : set_union2(empty_set,X0) = X0,
inference(superposition,[status(thm)],[c_642,c_630]) ).
tcf(c_181195,plain,
! [X0: $i] : set_union2(X0,X0) = set_union2(X0,empty_set),
inference(superposition,[status(thm)],[c_13761,c_410]) ).
tcf(c_181196,plain,
( sP34(the_topology(sK137),sK137)
| in(empty_set,the_topology(sK137))
| ~ topological_space(sK137)
| ~ in(the_carrier(sK137),sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_13761,c_180142]) ).
tcf(c_181197,plain,
( in(empty_set,the_topology(sK137))
| ~ topological_space(sK137)
| ~ in(the_carrier(sK137),sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_13761,c_179182]) ).
tcf(c_181211,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_410,c_181192]) ).
tcf(c_181304,plain,
! [X0: $i,X1: $i] : pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1))) = X0,
inference(superposition,[status(thm)],[c_967,c_516]) ).
tcf(c_181305,plain,
! [X0: $i,X1: $i] : pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1))) = X1,
inference(superposition,[status(thm)],[c_967,c_515]) ).
tcf(c_181308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( X1 = X2 )
| ( unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
inference(superposition,[status(thm)],[c_967,c_273]) ).
tcf(c_181311,plain,
! [X0: $i,X1: $i] : pair_second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1))) = X1,
inference(superposition,[status(thm)],[c_967,c_516]) ).
tcf(c_181312,plain,
! [X0: $i,X1: $i] : pair_first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1))) = X0,
inference(superposition,[status(thm)],[c_967,c_515]) ).
tcf(c_181316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_967,c_393]) ).
tcf(c_181317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_967,c_392]) ).
tcf(c_181319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(superposition,[status(thm)],[c_967,c_393]) ).
tcf(c_181320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(superposition,[status(thm)],[c_967,c_392]) ).
tcf(c_181322,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(superposition,[status(thm)],[c_967,c_531]) ).
tcf(c_181352,plain,
! [X0: $i] :
( sP3(sK99(X0))
| ordinal(sK62(sK99(X0))) ),
inference(superposition,[status(thm)],[c_120,c_206]) ).
tcf(c_181353,plain,
! [X0: $i] :
( ordinal(sK99(X0))
| ordinal(sK139(sK99(X0))) ),
inference(superposition,[status(thm)],[c_383,c_206]) ).
tcf(c_181354,plain,
! [X0: $i] :
( relation(sK99(X0))
| ordinal(sK175(sK99(X0))) ),
inference(superposition,[status(thm)],[c_580,c_206]) ).
tcf(c_181355,plain,
! [X0: $i] :
( epsilon_transitive(sK99(X0))
| ordinal(sK340(sK99(X0))) ),
inference(superposition,[status(thm)],[c_1081,c_206]) ).
tcf(c_181356,plain,
! [X0: $i] :
( epsilon_connected(sK99(X0))
| ordinal(sK369(sK99(X0))) ),
inference(superposition,[status(thm)],[c_1253,c_206]) ).
tcf(c_181357,plain,
! [X0: $i] :
( epsilon_connected(sK99(X0))
| ordinal(sK370(sK99(X0))) ),
inference(superposition,[status(thm)],[c_1254,c_206]) ).
tcf(c_181388,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(sK122(X0)) ),
inference(superposition,[status(thm)],[c_258,c_179243]) ).
tcf(c_181389,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_509,c_179243]) ).
tcf(c_181399,plain,
! [X0: $i] :
( ordinal(X0)
| ~ empty(sK122(X0)) ),
inference(superposition,[status(thm)],[c_258,c_179244]) ).
tcf(c_181400,plain,
! [X0: $i] :
( ordinal(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_509,c_179244]) ).
tcf(c_181438,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| sP3(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK303(sK137,sK206(the_carrier(sK137)),sK62(sK302(sK137,sK206(the_carrier(sK137))))) = sK62(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177702]) ).
tcf(c_181439,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| ordinal(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK303(sK137,sK206(the_carrier(sK137)),sK139(sK302(sK137,sK206(the_carrier(sK137))))) = sK139(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177702]) ).
tcf(c_181440,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| relation(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK303(sK137,sK206(the_carrier(sK137)),sK175(sK302(sK137,sK206(the_carrier(sK137))))) = sK175(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177702]) ).
tcf(c_181441,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| epsilon_transitive(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK303(sK137,sK206(the_carrier(sK137)),sK340(sK302(sK137,sK206(the_carrier(sK137))))) = sK340(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177702]) ).
tcf(c_181442,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK303(sK137,sK206(the_carrier(sK137)),sK369(sK302(sK137,sK206(the_carrier(sK137))))) = sK369(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177702]) ).
tcf(c_181443,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK303(sK137,sK206(the_carrier(sK137)),sK370(sK302(sK137,sK206(the_carrier(sK137))))) = sK370(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177702]) ).
tcf(c_181476,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| sP3(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK304(sK137,sK206(the_carrier(sK137)),sK62(sK302(sK137,sK206(the_carrier(sK137))))) = sK62(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_177703]) ).
tcf(c_181477,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| ordinal(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK304(sK137,sK206(the_carrier(sK137)),sK139(sK302(sK137,sK206(the_carrier(sK137))))) = sK139(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_177703]) ).
tcf(c_181478,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| relation(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK304(sK137,sK206(the_carrier(sK137)),sK175(sK302(sK137,sK206(the_carrier(sK137))))) = sK175(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_177703]) ).
tcf(c_181479,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| epsilon_transitive(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK304(sK137,sK206(the_carrier(sK137)),sK340(sK302(sK137,sK206(the_carrier(sK137))))) = sK340(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_177703]) ).
tcf(c_181480,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK304(sK137,sK206(the_carrier(sK137)),sK369(sK302(sK137,sK206(the_carrier(sK137))))) = sK369(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_177703]) ).
tcf(c_181481,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK206(the_carrier(sK137))))
| ( sK304(sK137,sK206(the_carrier(sK137)),sK370(sK302(sK137,sK206(the_carrier(sK137))))) = sK370(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_177703]) ).
tcf(c_181514,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| sP3(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK303(sK137,sK371(the_carrier(sK137)),sK62(sK302(sK137,sK371(the_carrier(sK137))))) = sK62(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_178214]) ).
tcf(c_181515,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| ordinal(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK303(sK137,sK371(the_carrier(sK137)),sK139(sK302(sK137,sK371(the_carrier(sK137))))) = sK139(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_178214]) ).
tcf(c_181516,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| relation(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK303(sK137,sK371(the_carrier(sK137)),sK175(sK302(sK137,sK371(the_carrier(sK137))))) = sK175(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_178214]) ).
tcf(c_181517,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| epsilon_transitive(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK303(sK137,sK371(the_carrier(sK137)),sK340(sK302(sK137,sK371(the_carrier(sK137))))) = sK340(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_178214]) ).
tcf(c_181518,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK303(sK137,sK371(the_carrier(sK137)),sK369(sK302(sK137,sK371(the_carrier(sK137))))) = sK369(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_178214]) ).
tcf(c_181519,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK303(sK137,sK371(the_carrier(sK137)),sK370(sK302(sK137,sK371(the_carrier(sK137))))) = sK370(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_178214]) ).
tcf(c_181552,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| sP3(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK304(sK137,sK371(the_carrier(sK137)),sK62(sK302(sK137,sK371(the_carrier(sK137))))) = sK62(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_178215]) ).
tcf(c_181553,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| ordinal(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK304(sK137,sK371(the_carrier(sK137)),sK139(sK302(sK137,sK371(the_carrier(sK137))))) = sK139(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_178215]) ).
tcf(c_181554,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| relation(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK304(sK137,sK371(the_carrier(sK137)),sK175(sK302(sK137,sK371(the_carrier(sK137))))) = sK175(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_178215]) ).
tcf(c_181555,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| epsilon_transitive(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK304(sK137,sK371(the_carrier(sK137)),sK340(sK302(sK137,sK371(the_carrier(sK137))))) = sK340(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_178215]) ).
tcf(c_181556,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK304(sK137,sK371(the_carrier(sK137)),sK369(sK302(sK137,sK371(the_carrier(sK137))))) = sK369(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_178215]) ).
tcf(c_181557,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK371(the_carrier(sK137))))
| ( sK304(sK137,sK371(the_carrier(sK137)),sK370(sK302(sK137,sK371(the_carrier(sK137))))) = sK370(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_178215]) ).
tcf(c_181590,plain,
! [X0: $i] :
( in(the_carrier(sK137),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(empty_set,sK93(sK137,sK147(sK137,X0))) ),
inference(superposition,[status(thm)],[c_680,c_179183]) ).
tcf(c_181591,plain,
! [X0: $i] :
( in(empty_set,sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(the_carrier(sK137),sK93(sK137,sK147(sK137,X0))) ),
inference(superposition,[status(thm)],[c_13761,c_179183]) ).
tcf(c_181592,plain,
! [X0: $i] :
( subset(the_carrier(sK137),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(the_carrier(sK137),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_179183,c_176978]) ).
tcf(c_181593,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(the_carrier(sK137),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_179183,c_176977]) ).
tcf(c_181594,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(sK208(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_179183,c_177402]) ).
tcf(c_181595,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK208(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_179183,c_177401]) ).
tcf(c_181596,plain,
! [X0: $i] :
( subset(sK206(the_carrier(sK137)),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(sK206(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK206(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_179183,c_177706]) ).
tcf(c_181597,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK206(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK206(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_179183,c_177705]) ).
tcf(c_181598,plain,
! [X0: $i] :
( subset(sK371(the_carrier(sK137)),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(sK371(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK371(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_179183,c_178218]) ).
tcf(c_181599,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK371(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK371(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_179183,c_178217]) ).
tcf(c_181608,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,the_carrier(sK137)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_181593,c_13308]) ).
tcf(c_181613,plain,
! [X0: $i] :
( subset(the_carrier(sK137),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,the_carrier(sK137)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_181592,c_13308]) ).
tcf(c_181618,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK371(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_181599,c_1259]) ).
tcf(c_181623,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK206(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_181597,c_696]) ).
tcf(c_181628,plain,
! [X0: $i] :
( subset(sK371(the_carrier(sK137)),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK371(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_181598,c_1259]) ).
tcf(c_181633,plain,
! [X0: $i] :
( subset(sK206(the_carrier(sK137)),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK206(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_181596,c_696]) ).
tcf(c_181638,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137)))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_181595,c_702]) ).
tcf(c_181643,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137)))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_181594,c_702]) ).
tcf(c_181663,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = set_difference(X1,set_difference(X1,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_420,c_986]) ).
tcf(c_181664,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = set_difference(empty_set,empty_set),
inference(superposition,[status(thm)],[c_679,c_986]) ).
tcf(c_181665,plain,
! [X0: $i] : set_difference(empty_set,set_difference(empty_set,X0)) = set_difference(X0,X0),
inference(superposition,[status(thm)],[c_680,c_986]) ).
tcf(c_181672,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X0,X1)),X1),
inference(superposition,[status(thm)],[c_986,c_399]) ).
tcf(c_181673,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))) = set_union2(set_difference(X0,X1),X0),
inference(superposition,[status(thm)],[c_986,c_410]) ).
tcf(c_181674,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_986,c_679]) ).
tcf(c_181675,plain,
! [X0: $i,X1: $i] :
( in(set_difference(X0,set_difference(X0,the_carrier(sK137))),sK147(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(set_difference(the_carrier(sK137),X0),sK93(sK137,sK147(sK137,X1))) ),
inference(superposition,[status(thm)],[c_986,c_179183]) ).
tcf(c_181676,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| in(set_difference(X0,set_difference(X0,the_carrier(sK137))),the_topology(sK137))
| ~ topological_space(sK137)
| ~ in(set_difference(the_carrier(sK137),X0),sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_986,c_180142]) ).
tcf(c_181677,plain,
! [X0: $i] :
( in(set_difference(X0,set_difference(X0,the_carrier(sK137))),the_topology(sK137))
| ~ topological_space(sK137)
| ~ in(set_difference(the_carrier(sK137),X0),sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_986,c_179182]) ).
tcf(c_181679,plain,
set_difference(empty_set,empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_181665,c_679,c_13761]) ).
tcf(c_181974,plain,
in(empty_set,set_union2(empty_set,powerset(empty_set))),
inference(superposition,[status(thm)],[c_330,c_272]) ).
tcf(c_181980,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_646,c_594]) ).
tcf(c_181981,plain,
! [X0: $i] : sK206(X0) = empty_set,
inference(superposition,[status(thm)],[c_697,c_594]) ).
tcf(c_181982,plain,
empty_set = sK245,
inference(superposition,[status(thm)],[c_775,c_594]) ).
tcf(c_181983,plain,
empty_set = sK249,
inference(superposition,[status(thm)],[c_786,c_594]) ).
tcf(c_181984,plain,
empty_set = sK250,
inference(superposition,[status(thm)],[c_787,c_594]) ).
tcf(c_181985,plain,
! [X0: $i] :
( ( relation_rng(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_968,c_594]) ).
tcf(c_181986,plain,
empty_set = sK338,
inference(superposition,[status(thm)],[c_1070,c_594]) ).
tcf(c_181987,plain,
! [X0: $i] :
( ( relation_inverse(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1166,c_594]) ).
tcf(c_181988,plain,
empty_set = sK362,
inference(superposition,[status(thm)],[c_1203,c_594]) ).
tcf(c_181989,plain,
! [X0: $i] : sK371(X0) = empty_set,
inference(superposition,[status(thm)],[c_1260,c_594]) ).
tcf(c_182003,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_696,c_181981]) ).
tcf(c_182005,plain,
! [X0: $i] :
( sP36(sK137,empty_set)
| ( sK304(sK137,empty_set,X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,empty_set)) ),
inference(demodulation,[status(thm)],[c_177703,c_181981]) ).
tcf(c_182006,plain,
! [X0: $i] :
( sP36(sK137,empty_set)
| ( sK303(sK137,empty_set,X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,empty_set)) ),
inference(demodulation,[status(thm)],[c_177702,c_181981]) ).
tcf(c_182007,plain,
( ( sK124(sK137,sK138,empty_set) = empty_set )
| ~ topological_space(sK137)
| ~ in(empty_set,sK123(sK137,sK138)) ),
inference(demodulation,[status(thm)],[c_177713,c_181981]) ).
tcf(c_182011,plain,
! [X0: $i] :
( ( topstr_closure(sK137,empty_set) = X0 )
| ~ sP38(sK137,empty_set,X0)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(demodulation,[status(thm)],[c_177707,c_181981]) ).
tcf(c_182012,plain,
( in(sK138,sK147(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(empty_set,sK138) ),
inference(demodulation,[status(thm)],[c_177714,c_181981]) ).
tcf(c_182013,plain,
( in(sK138,sK123(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(empty_set,sK138) ),
inference(demodulation,[status(thm)],[c_177712,c_181981]) ).
tcf(c_182014,plain,
! [X0: $i] :
( ( sK92(sK137,empty_set,X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,empty_set)) ),
inference(demodulation,[status(thm)],[c_177708,c_181981]) ).
tcf(c_182015,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,empty_set)) ),
inference(demodulation,[status(thm)],[c_177705,c_181981]) ).
tcf(c_182016,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,empty_set)) = topstr_closure(sK137,empty_set) )
| ~ topological_space(sK137) ),
inference(demodulation,[status(thm)],[c_177719,c_181981]) ).
tcf(c_182017,plain,
( ( topstr_closure(sK137,empty_set) = empty_set )
| ~ closed_subset(empty_set,sK137) ),
inference(demodulation,[status(thm)],[c_177720,c_181981]) ).
tcf(c_182018,plain,
( subset(sK138,empty_set)
| ~ topological_space(sK137)
| ~ in(empty_set,sK147(sK137,sK138)) ),
inference(demodulation,[status(thm)],[c_177717,c_181981]) ).
tcf(c_182019,plain,
( closed_subset(empty_set,sK137)
| ~ topological_space(sK137)
| ~ in(empty_set,sK147(sK137,sK138)) ),
inference(demodulation,[status(thm)],[c_177716,c_181981]) ).
tcf(c_182020,plain,
( subset(sK138,empty_set)
| ~ topological_space(sK137)
| ~ in(empty_set,sK123(sK137,sK138)) ),
inference(demodulation,[status(thm)],[c_177715,c_181981]) ).
tcf(c_182022,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,empty_set)) ),
inference(demodulation,[status(thm)],[c_177710,c_181981]) ).
tcf(c_182023,plain,
( ( topstr_closure(sK137,sK138) = empty_set )
| ~ sP38(sK137,sK138,empty_set) ),
inference(demodulation,[status(thm)],[c_177718,c_181981]) ).
tcf(c_182024,plain,
( in(empty_set,the_topology(sK137))
| ~ open_subset(empty_set,sK137) ),
inference(demodulation,[status(thm)],[c_177722,c_181981]) ).
tcf(c_182025,plain,
( open_subset(empty_set,sK137)
| ~ in(empty_set,the_topology(sK137)) ),
inference(demodulation,[status(thm)],[c_177721,c_181981]) ).
tcf(c_182026,plain,
( in(sK145(sK137,empty_set),empty_set)
| closed_subset(meet_of_subsets(the_carrier(sK137),empty_set),sK137)
| ~ topological_space(sK137) ),
inference(demodulation,[status(thm)],[c_177726,c_181981]) ).
tcf(c_182028,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,empty_set)) ),
inference(demodulation,[status(thm)],[c_177725,c_181981]) ).
tcf(c_182035,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),empty_set),sK137)
| ~ topological_space(sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182026,c_599]) ).
tcf(c_182067,plain,
( in(sK138,sK123(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182013,c_379]) ).
tcf(c_182071,plain,
( in(sK138,sK147(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182012,c_379]) ).
tcf(c_182174,plain,
! [X0: $i] :
( ordinal(sK185(sK99(X0)))
| ~ sP20(sK99(X0)) ),
inference(superposition,[status(thm)],[c_603,c_206]) ).
tcf(c_182175,plain,
~ sP20(empty_set),
inference(superposition,[status(thm)],[c_603,c_599]) ).
tcf(c_182176,plain,
( sP36(sK137,sK138)
| in(sK185(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP20(powerset(the_carrier(sK137)))
| ~ closed_subset(sK185(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK185(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_176867]) ).
tcf(c_182177,plain,
( in(sK185(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP20(powerset(the_carrier(sK137)))
| ~ closed_subset(sK185(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK185(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_176193]) ).
tcf(c_182178,plain,
( ( sK92(sK137,sK138,sK185(sK91(sK137,sK138))) = sK185(sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_603,c_175190]) ).
tcf(c_182179,plain,
( in(sK185(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_603,c_175008]) ).
tcf(c_182180,plain,
( subset(sK138,sK185(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_603,c_174960]) ).
tcf(c_182181,plain,
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,sK185(sK302(sK137,sK138))) = sK185(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_603,c_175802]) ).
tcf(c_182182,plain,
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,sK185(sK302(sK137,sK138))) = sK185(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_603,c_175753]) ).
tcf(c_182183,plain,
( sP36(sK137,sK138)
| subset(sK138,sK185(sK302(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_603,c_175029]) ).
tcf(c_182184,plain,
( in(sK185(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_175089]) ).
tcf(c_182185,plain,
! [X0: $i] :
( in(sK185(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK93(sK137,sK147(sK137,X0))) ),
inference(superposition,[status(thm)],[c_603,c_175090]) ).
tcf(c_182186,plain,
! [X0: $i] :
( in(sK185(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK125(sK137,X0)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_175091]) ).
tcf(c_182187,plain,
! [X0: $i] :
( in(sK185(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK93(sK137,sK123(sK137,X0))) ),
inference(superposition,[status(thm)],[c_603,c_175092]) ).
tcf(c_182188,plain,
! [X0: $i] :
( subset(topstr_closure(sK137,X0),sK185(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_603,c_176013]) ).
tcf(c_182189,plain,
! [X0: $i] :
( in(sK185(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_603,c_176012]) ).
tcf(c_182190,plain,
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),sK185(sK295(sK137,the_topology(sK137)))) = sK185(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176134]) ).
tcf(c_182191,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),sK185(sK302(sK137,the_carrier(sK137)))) = sK185(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176975]) ).
tcf(c_182192,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),sK185(sK302(sK137,the_carrier(sK137)))) = sK185(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176974]) ).
tcf(c_182193,plain,
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK185(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176981]) ).
tcf(c_182194,plain,
( ( sK124(sK137,the_carrier(sK137),sK185(sK123(sK137,the_carrier(sK137)))) = sK185(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,the_carrier(sK137)))
| ~ element(sK185(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176971]) ).
tcf(c_182195,plain,
( subset(the_carrier(sK137),sK185(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,the_carrier(sK137)))
| ~ element(sK185(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176976]) ).
tcf(c_182196,plain,
( ( sK92(sK137,the_carrier(sK137),sK185(sK91(sK137,the_carrier(sK137)))) = sK185(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176980]) ).
tcf(c_182197,plain,
( in(sK185(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176982]) ).
tcf(c_182198,plain,
( subset(the_carrier(sK137),sK185(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176983]) ).
tcf(c_182199,plain,
( subset(the_carrier(sK137),sK185(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,the_carrier(sK137)))
| ~ element(sK185(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176978]) ).
tcf(c_182200,plain,
( closed_subset(sK185(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,the_carrier(sK137)))
| ~ element(sK185(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176977]) ).
tcf(c_182201,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK185(sK295(sK137,powerset(the_carrier(sK137))))) = sK185(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP20(sK295(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_176995]) ).
tcf(c_182202,plain,
( in(sK185(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_176997]) ).
tcf(c_182203,plain,
( in(sK185(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ sP20(topstr_closure(sK137,sK138))
| ~ in(sK185(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_603,c_177233]) ).
tcf(c_182204,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK185(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_603,c_177405]) ).
tcf(c_182205,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK185(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK185(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_177400]) ).
tcf(c_182206,plain,
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK185(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK185(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_603,c_177404]) ).
tcf(c_182207,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK185(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_603,c_177407]) ).
tcf(c_182208,plain,
( in(sK185(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_603,c_177406]) ).
tcf(c_182209,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK185(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK185(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_177402]) ).
tcf(c_182210,plain,
( closed_subset(sK185(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK185(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_177401]) ).
tcf(c_182211,plain,
( in(sK185(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_603,c_177421]) ).
tcf(c_182392,plain,
( sP36(sK137,sK138)
| in(sK185(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138))
| ~ closed_subset(sK185(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK185(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_182179,c_176867]) ).
tcf(c_182393,plain,
( in(sK185(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138))
| ~ closed_subset(sK185(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK185(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_182179,c_176193]) ).
tcf(c_182433,plain,
! [X0: $i] :
( in(X0,empty_set)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_182003,c_177131]) ).
tcf(c_182434,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ subset(empty_set,X1)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_182003,c_48138]) ).
tcf(c_182435,plain,
! [X0: $i] :
( sP36(sK137,empty_set)
| in(X0,sK302(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(empty_set,X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_182003,c_47771]) ).
tcf(c_182436,plain,
! [X0: $i] :
( in(empty_set,sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(X0,empty_set)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_182003,c_48368]) ).
tcf(c_182437,plain,
! [X0: $i] :
( ( sK124(sK137,empty_set,X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_182003,c_48332]) ).
tcf(c_182438,plain,
! [X0: $i] :
( in(empty_set,sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(X0,empty_set)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_182003,c_48105]) ).
tcf(c_182439,plain,
! [X0: $i] :
( in(X0,sK91(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(empty_set,X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_182003,c_47795]) ).
tcf(c_182450,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,empty_set))) = topstr_closure(sK137,topstr_closure(sK137,empty_set)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_182003,c_176018]) ).
tcf(c_182462,plain,
! [X0: $i] :
( sP34(empty_set,sK137)
| in(set_difference(the_carrier(sK137),X0),empty_set)
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_182003,c_73951]) ).
tcf(c_182463,plain,
! [X0: $i] :
( in(set_difference(the_carrier(sK137),X0),empty_set)
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_182003,c_73134]) ).
tcf(c_182464,plain,
! [X0: $i] :
( sP34(empty_set,sK137)
| ( sK296(sK137,empty_set,X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_182003,c_48001]) ).
tcf(c_182468,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182463,c_599]) ).
tcf(c_182471,plain,
! [X0: $i] :
( sP34(empty_set,sK137)
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182462,c_599]) ).
tcf(c_182481,plain,
! [X0: $i] :
( in(X0,sK91(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182439,c_379]) ).
tcf(c_182500,plain,
! [X0: $i] :
( ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182433,c_599]) ).
tcf(c_182505,plain,
! [X0: $i] :
( sP36(sK137,empty_set)
| in(X0,sK302(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182435,c_379]) ).
tcf(c_182511,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182434,c_379]) ).
tcf(c_182713,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X1,X0))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_410,c_633]) ).
tcf(c_182784,plain,
( in(empty_set,sK123(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_376,c_182436]) ).
tcf(c_182785,plain,
( in(empty_set,sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_702,c_182436]) ).
tcf(c_182786,plain,
( in(empty_set,sK123(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(the_carrier(sK137),empty_set) ),
inference(superposition,[status(thm)],[c_13308,c_182436]) ).
tcf(c_182787,plain,
! [X0: $i] :
( in(empty_set,sK123(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),empty_set) ),
inference(superposition,[status(thm)],[c_106061,c_182436]) ).
tcf(c_182788,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| in(empty_set,sK123(sK137,sK304(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ subset(sK304(sK137,X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_47929,c_182436]) ).
tcf(c_182789,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| in(empty_set,sK123(sK137,sK146(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(sK146(sK137,X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_48162,c_182436]) ).
tcf(c_182790,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| in(empty_set,sK123(sK137,sK145(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK145(sK137,X0),empty_set)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_182436]) ).
tcf(c_182791,plain,
! [X0: $i,X1: $i] :
( in(empty_set,sK123(sK137,sK124(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ subset(sK124(sK137,X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_48350,c_182436]) ).
tcf(c_182792,plain,
! [X0: $i,X1: $i] :
( in(empty_set,sK123(sK137,sK92(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ subset(sK92(sK137,X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_48475,c_182436]) ).
tcf(c_182793,plain,
( in(empty_set,sK123(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(empty_set,empty_set) ),
inference(superposition,[status(thm)],[c_182003,c_182436]) ).
tcf(c_182794,plain,
( in(empty_set,sK123(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182793,c_379]) ).
tcf(c_182870,plain,
( ( sK124(sK137,empty_set,sK138) = sK138 )
| ~ topological_space(sK137)
| ~ in(sK138,sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_376,c_182437]) ).
tcf(c_182871,plain,
( ( sK124(sK137,empty_set,sK208(powerset(the_carrier(sK137)))) = sK208(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK208(powerset(the_carrier(sK137))),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_702,c_182437]) ).
tcf(c_182872,plain,
( ( sK124(sK137,empty_set,the_carrier(sK137)) = the_carrier(sK137) )
| ~ topological_space(sK137)
| ~ in(the_carrier(sK137),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_13308,c_182437]) ).
tcf(c_182873,plain,
! [X0: $i] :
( ( sK124(sK137,empty_set,topstr_closure(sK137,X0)) = topstr_closure(sK137,X0) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(topstr_closure(sK137,X0),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_106061,c_182437]) ).
tcf(c_182874,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| ( sK124(sK137,empty_set,sK304(sK137,X0,X1)) = sK304(sK137,X0,X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ in(sK304(sK137,X0,X1),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_47929,c_182437]) ).
tcf(c_182875,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| ( sK124(sK137,empty_set,sK146(sK137,X0,X1)) = sK146(sK137,X0,X1) )
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(sK146(sK137,X0,X1),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_48162,c_182437]) ).
tcf(c_182876,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ( sK124(sK137,empty_set,sK145(sK137,X0)) = sK145(sK137,X0) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ in(sK145(sK137,X0),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_48222,c_182437]) ).
tcf(c_182877,plain,
! [X0: $i,X1: $i] :
( ( sK124(sK137,empty_set,sK124(sK137,X0,X1)) = sK124(sK137,X0,X1) )
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ in(sK124(sK137,X0,X1),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_48350,c_182437]) ).
tcf(c_182878,plain,
! [X0: $i,X1: $i] :
( ( sK124(sK137,empty_set,sK92(sK137,X0,X1)) = sK92(sK137,X0,X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ in(sK92(sK137,X0,X1),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_48475,c_182437]) ).
tcf(c_182879,plain,
( ( sK124(sK137,empty_set,empty_set) = empty_set )
| ~ topological_space(sK137)
| ~ in(empty_set,sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_182003,c_182437]) ).
tcf(c_182934,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( sK365(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2) != X2 ) ),
inference(superposition,[status(thm)],[c_967,c_105505]) ).
tcf(c_182936,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2) != X2 ) ),
inference(superposition,[status(thm)],[c_967,c_105505]) ).
tcf(c_182938,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( sK365(unordered_pair(powerset(empty_set),powerset(empty_set)),X0) != X0 ) ),
inference(superposition,[status(thm)],[c_330,c_105505]) ).
tcf(c_182939,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( sK365(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),X1) != X1 ) ),
inference(superposition,[status(thm)],[c_330,c_105505]) ).
tcf(c_182956,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(X0,sK207(the_carrier(sK137)))
| ~ in(X0,the_carrier(sK137))
| ~ closed_subset(sK207(the_carrier(sK137)),sK137)
| ~ subset(sK138,sK207(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_698,c_177131]) ).
tcf(c_182957,plain,
! [X0: $i,X1: $i] :
( empty(the_carrier(sK137))
| in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK207(the_carrier(sK137)),X1)
| ~ in(X0,topstr_closure(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_48138]) ).
tcf(c_182958,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| in(X0,sK302(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK207(the_carrier(sK137)),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_698,c_47771]) ).
tcf(c_182959,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK207(the_carrier(sK137)),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK207(the_carrier(sK137)),sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,sK207(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_698,c_48368]) ).
tcf(c_182960,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK124(sK137,sK207(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_48332]) ).
tcf(c_182961,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK207(the_carrier(sK137)),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK207(the_carrier(sK137)),sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,sK207(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_698,c_48105]) ).
tcf(c_182962,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(X0,sK91(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK207(the_carrier(sK137)),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_698,c_47795]) ).
tcf(c_182963,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| ( sK303(sK137,sK207(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_47947]) ).
tcf(c_182964,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| ( sK304(sK137,sK207(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_47911]) ).
tcf(c_182965,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_48297]) ).
tcf(c_182966,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_48087]) ).
tcf(c_182967,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_48070]) ).
tcf(c_182968,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( topstr_closure(sK137,sK207(the_carrier(sK137))) = X0 )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK207(the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_698,c_47756]) ).
tcf(c_182969,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_48460]) ).
tcf(c_182970,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_47876]) ).
tcf(c_182971,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_48490]) ).
tcf(c_182972,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_48431]) ).
tcf(c_182973,plain,
( empty(the_carrier(sK137))
| ( sK124(sK137,empty_set,sK207(the_carrier(sK137))) = sK207(the_carrier(sK137)) )
| ~ topological_space(sK137)
| ~ in(sK207(the_carrier(sK137)),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_698,c_182437]) ).
tcf(c_182974,plain,
( empty(the_carrier(sK137))
| in(empty_set,sK123(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK207(the_carrier(sK137)),empty_set) ),
inference(superposition,[status(thm)],[c_698,c_182436]) ).
tcf(c_182975,plain,
( empty(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK207(the_carrier(sK137))))) = topstr_closure(sK137,topstr_closure(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_698,c_176018]) ).
tcf(c_182976,plain,
( empty(the_carrier(sK137))
| in(sK138,sK123(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_698,c_176521]) ).
tcf(c_182977,plain,
( empty(the_carrier(sK137))
| ( sK124(sK137,sK138,sK207(the_carrier(sK137))) = sK207(the_carrier(sK137)) )
| ~ topological_space(sK137)
| ~ in(sK207(the_carrier(sK137)),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_698,c_176408]) ).
tcf(c_182978,plain,
( empty(the_carrier(sK137))
| in(sK138,sK147(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_698,c_176286]) ).
tcf(c_182979,plain,
( empty(the_carrier(sK137))
| subset(sK138,sK207(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(sK207(the_carrier(sK137)),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_698,c_175672]) ).
tcf(c_182980,plain,
( empty(the_carrier(sK137))
| closed_subset(sK207(the_carrier(sK137)),sK137)
| ~ topological_space(sK137)
| ~ in(sK207(the_carrier(sK137)),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_698,c_175482]) ).
tcf(c_182981,plain,
( empty(the_carrier(sK137))
| subset(sK138,sK207(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(sK207(the_carrier(sK137)),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_698,c_175418]) ).
tcf(c_182982,plain,
( empty(the_carrier(sK137))
| ( topstr_closure(sK137,sK138) = sK207(the_carrier(sK137)) )
| ~ sP38(sK137,sK138,sK207(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_698,c_175209]) ).
tcf(c_182983,plain,
( empty(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_698,c_48058]) ).
tcf(c_182984,plain,
( empty(the_carrier(sK137))
| ( topstr_closure(sK137,sK207(the_carrier(sK137))) = sK207(the_carrier(sK137)) )
| ~ closed_subset(sK207(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_698,c_48037]) ).
tcf(c_182985,plain,
( empty(the_carrier(sK137))
| open_subset(sK207(the_carrier(sK137)),sK137)
| ~ in(sK207(the_carrier(sK137)),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_698,c_47852]) ).
tcf(c_182986,plain,
( empty(the_carrier(sK137))
| in(sK207(the_carrier(sK137)),the_topology(sK137))
| ~ open_subset(sK207(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_698,c_47840]) ).
tcf(c_182987,plain,
! [X0: $i] :
( empty(powerset(the_carrier(sK137)))
| sP34(sK207(powerset(the_carrier(sK137))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK207(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK207(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_698,c_73951]) ).
tcf(c_182988,plain,
! [X0: $i] :
( empty(powerset(the_carrier(sK137)))
| in(set_difference(the_carrier(sK137),X0),sK207(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK207(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_698,c_73134]) ).
tcf(c_182989,plain,
! [X0: $i] :
( empty(powerset(the_carrier(sK137)))
| sP34(sK207(powerset(the_carrier(sK137))),sK137)
| ( sK296(sK137,sK207(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK207(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_698,c_48001]) ).
tcf(c_182990,plain,
( empty(powerset(the_carrier(sK137)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK207(powerset(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK207(powerset(the_carrier(sK137)))),sK137) ),
inference(superposition,[status(thm)],[c_698,c_48252]) ).
tcf(c_182991,plain,
! [X0: $i] :
( empty(powerset(the_carrier(sK137)))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK207(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_698,c_48416]) ).
tcf(c_182992,plain,
( empty(powerset(the_carrier(sK137)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK207(powerset(the_carrier(sK137)))),sK137)
| in(sK145(sK137,sK207(powerset(the_carrier(sK137)))),sK207(powerset(the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_698,c_48237]) ).
tcf(c_183025,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK207(powerset(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182991,c_700]) ).
tcf(c_183065,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK207(powerset(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK207(powerset(the_carrier(sK137)))),sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182990,c_700]) ).
tcf(c_183069,plain,
! [X0: $i] :
( in(set_difference(the_carrier(sK137),X0),sK207(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK207(powerset(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182988,c_700]) ).
tcf(c_183094,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK207(powerset(the_carrier(sK137)))),sK137)
| in(sK145(sK137,sK207(powerset(the_carrier(sK137)))),sK207(powerset(the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182992,c_700]) ).
tcf(c_183119,plain,
! [X0: $i] :
( sP34(sK207(powerset(the_carrier(sK137))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK207(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK207(powerset(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182987,c_700]) ).
tcf(c_183142,plain,
! [X0: $i] :
( sP34(sK207(powerset(the_carrier(sK137))),sK137)
| ( sK296(sK137,sK207(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK207(powerset(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_182989,c_700]) ).
tcf(c_183186,plain,
! [X0: $i] :
( sP3(X0)
| element(sK62(X0),X0) ),
inference(superposition,[status(thm)],[c_120,c_701]) ).
tcf(c_183187,plain,
element(empty_set,omega),
inference(superposition,[status(thm)],[c_841,c_701]) ).
tcf(c_183188,plain,
( element(sK70,omega)
| ~ sP6 ),
inference(superposition,[status(thm)],[c_138,c_701]) ).
tcf(c_183190,plain,
( element(sK117,omega)
| ~ sP15 ),
inference(superposition,[status(thm)],[c_245,c_701]) ).
tcf(c_183191,plain,
! [X0: $i] : element(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(superposition,[status(thm)],[c_272,c_701]) ).
tcf(c_183192,plain,
! [X0: $i] : element(X0,sK126(X0)),
inference(superposition,[status(thm)],[c_288,c_701]) ).
tcf(c_183193,plain,
! [X0: $i] :
( ordinal(X0)
| element(sK139(X0),X0) ),
inference(superposition,[status(thm)],[c_383,c_701]) ).
tcf(c_183194,plain,
! [X0: $i] :
( relation(X0)
| element(sK175(X0),X0) ),
inference(superposition,[status(thm)],[c_580,c_701]) ).
tcf(c_183195,plain,
! [X0: $i] :
( element(sK185(X0),X0)
| ~ sP20(X0) ),
inference(superposition,[status(thm)],[c_603,c_701]) ).
tcf(c_183197,plain,
! [X0: $i,X1: $i] : element(X0,unordered_pair(X0,X1)),
inference(superposition,[status(thm)],[c_964,c_701]) ).
tcf(c_183198,plain,
! [X0: $i,X1: $i] : element(X0,unordered_pair(X1,X0)),
inference(superposition,[status(thm)],[c_965,c_701]) ).
tcf(c_183199,plain,
! [X0: $i] : element(X0,sK323(X0)),
inference(superposition,[status(thm)],[c_997,c_701]) ).
tcf(c_183200,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| element(sK340(X0),X0) ),
inference(superposition,[status(thm)],[c_1081,c_701]) ).
tcf(c_183201,plain,
! [X0: $i] :
( epsilon_connected(X0)
| element(sK369(X0),X0) ),
inference(superposition,[status(thm)],[c_1253,c_701]) ).
tcf(c_183202,plain,
! [X0: $i] :
( epsilon_connected(X0)
| element(sK370(X0),X0) ),
inference(superposition,[status(thm)],[c_1254,c_701]) ).
tcf(c_183203,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_178672,c_701]) ).
tcf(c_183204,plain,
( element(the_carrier(sK137),the_topology(sK137))
| ~ open_subset(the_carrier(sK137),sK137) ),
inference(superposition,[status(thm)],[c_176994,c_701]) ).
tcf(c_183205,plain,
! [X0: $i] :
( element(union_of_subsets(the_carrier(sK137),X0),the_topology(sK137))
| ~ topological_space(sK137)
| ~ subset(X0,the_topology(sK137))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_47816,c_701]) ).
tcf(c_183206,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| element(sK303(sK137,X1,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47965,c_701]) ).
tcf(c_183207,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK137)
| element(sK296(sK137,X0,X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48019,c_701]) ).
tcf(c_183208,plain,
( element(sK138,the_topology(sK137))
| ~ open_subset(sK138,sK137) ),
inference(superposition,[status(thm)],[c_174884,c_701]) ).
tcf(c_183209,plain,
( element(sK138,sK147(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(superposition,[status(thm)],[c_176354,c_701]) ).
tcf(c_183210,plain,
( element(empty_set,sK123(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_182784,c_701]) ).
tcf(c_183211,plain,
( element(sK138,sK123(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(superposition,[status(thm)],[c_176589,c_701]) ).
tcf(c_183212,plain,
! [X0: $i] :
( element(topstr_closure(sK137,X0),the_topology(sK137))
| ~ open_subset(topstr_closure(sK137,X0),sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176021,c_701]) ).
tcf(c_183213,plain,
! [X0: $i] :
( element(the_carrier(sK137),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180215,c_701]) ).
tcf(c_183214,plain,
! [X0: $i] :
( element(the_carrier(sK137),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180246,c_701]) ).
tcf(c_183215,plain,
! [X0: $i] :
( element(X0,sK91(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(the_carrier(sK137),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176973,c_701]) ).
tcf(c_183216,plain,
( element(sK138,sK123(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138) ),
inference(superposition,[status(thm)],[c_176984,c_701]) ).
tcf(c_183217,plain,
( element(sK138,sK147(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138) ),
inference(superposition,[status(thm)],[c_176986,c_701]) ).
tcf(c_183218,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),powerset(the_carrier(sK137))),sK137)
| element(sK145(sK137,powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_176998,c_701]) ).
tcf(c_183219,plain,
( element(sK138,sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_177408,c_701]) ).
tcf(c_183220,plain,
( element(sK138,sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_177410,c_701]) ).
tcf(c_183221,plain,
( element(sK208(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK208(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_177418,c_701]) ).
tcf(c_183222,plain,
( sP3(sK91(sK137,sK138))
| element(sK62(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178460,c_701]) ).
tcf(c_183223,plain,
( ordinal(sK91(sK137,sK138))
| element(sK139(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178684,c_701]) ).
tcf(c_183224,plain,
( relation(sK91(sK137,sK138))
| element(sK175(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178947,c_701]) ).
tcf(c_183225,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| element(set_difference(the_carrier(sK137),X0),the_topology(sK137))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_180142,c_701]) ).
tcf(c_183226,plain,
! [X0: $i] :
( element(set_difference(the_carrier(sK137),X0),the_topology(sK137))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_179182,c_701]) ).
tcf(c_183227,plain,
! [X0: $i,X1: $i] :
( element(set_difference(the_carrier(sK137),X0),sK147(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,X1))) ),
inference(superposition,[status(thm)],[c_179183,c_701]) ).
tcf(c_183228,plain,
( epsilon_transitive(sK91(sK137,sK138))
| element(sK340(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_180305,c_701]) ).
tcf(c_183229,plain,
( epsilon_connected(sK91(sK137,sK138))
| element(sK369(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_180597,c_701]) ).
tcf(c_183230,plain,
( epsilon_connected(sK91(sK137,sK138))
| element(sK370(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_180850,c_701]) ).
tcf(c_183232,plain,
( element(sK185(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_182179,c_701]) ).
tcf(c_183402,plain,
( empty(the_carrier(sK137))
| element(sK207(the_carrier(sK137)),the_topology(sK137))
| ~ open_subset(sK207(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_182986,c_701]) ).
tcf(c_183429,plain,
( empty(the_carrier(sK137))
| sP3(sK91(sK137,sK207(the_carrier(sK137))))
| in(sK62(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_182971]) ).
tcf(c_183431,plain,
( empty(the_carrier(sK137))
| ordinal(sK91(sK137,sK207(the_carrier(sK137))))
| in(sK139(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_182971]) ).
tcf(c_183432,plain,
( empty(the_carrier(sK137))
| relation(sK91(sK137,sK207(the_carrier(sK137))))
| in(sK175(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_182971]) ).
tcf(c_183433,plain,
( empty(the_carrier(sK137))
| in(sK185(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_182971]) ).
tcf(c_183435,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK91(sK137,sK207(the_carrier(sK137))))
| in(sK340(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_182971]) ).
tcf(c_183436,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK207(the_carrier(sK137))))
| in(sK369(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_182971]) ).
tcf(c_183437,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK207(the_carrier(sK137))))
| in(sK370(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_182971]) ).
tcf(c_183482,plain,
( empty(the_carrier(sK137))
| sP3(sK91(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK62(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_182972]) ).
tcf(c_183484,plain,
( empty(the_carrier(sK137))
| ordinal(sK91(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK139(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_182972]) ).
tcf(c_183485,plain,
( empty(the_carrier(sK137))
| relation(sK91(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK175(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_182972]) ).
tcf(c_183486,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK185(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_182972]) ).
tcf(c_183488,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK91(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK340(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_182972]) ).
tcf(c_183489,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK369(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_182972]) ).
tcf(c_183490,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK370(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_182972]) ).
tcf(c_183535,plain,
! [X0: $i] :
( sP3(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_120,c_781]) ).
tcf(c_183541,plain,
! [X0: $i] : ~ empty(sK126(X0)),
inference(superposition,[status(thm)],[c_288,c_781]) ).
tcf(c_183544,plain,
! [X0: $i] :
( ~ sP20(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_603,c_781]) ).
tcf(c_183548,plain,
! [X0: $i] : ~ empty(sK323(X0)),
inference(superposition,[status(thm)],[c_997,c_781]) ).
tcf(c_183553,plain,
( ~ empty(the_topology(sK137))
| ~ open_subset(the_carrier(sK137),sK137) ),
inference(superposition,[status(thm)],[c_176994,c_781]) ).
tcf(c_183554,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ empty(the_topology(sK137))
| ~ subset(X0,the_topology(sK137))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_47816,c_781]) ).
tcf(c_183555,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47965,c_781]) ).
tcf(c_183556,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK137)
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48019,c_781]) ).
tcf(c_183557,plain,
( ~ open_subset(sK138,sK137)
| ~ empty(the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_174884,c_781]) ).
tcf(c_183558,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ empty(sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_176354,c_781]) ).
tcf(c_183559,plain,
( ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ empty(sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_182784,c_781]) ).
tcf(c_183560,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ empty(sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_176589,c_781]) ).
tcf(c_183561,plain,
! [X0: $i] :
( ~ empty(the_topology(sK137))
| ~ open_subset(topstr_closure(sK137,X0),sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176021,c_781]) ).
tcf(c_183562,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ empty(sK123(sK137,X0))
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180215,c_781]) ).
tcf(c_183563,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ empty(sK147(sK137,X0))
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180246,c_781]) ).
tcf(c_183564,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(the_carrier(sK137),X0)
| ~ empty(sK91(sK137,the_carrier(sK137)))
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176973,c_781]) ).
tcf(c_183565,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138)
| ~ empty(sK123(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176984,c_781]) ).
tcf(c_183566,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138)
| ~ empty(sK147(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176986,c_781]) ).
tcf(c_183567,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),powerset(the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176998,c_781]) ).
tcf(c_183568,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138)
| ~ empty(sK123(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_177408,c_781]) ).
tcf(c_183569,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138)
| ~ empty(sK147(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_177410,c_781]) ).
tcf(c_183570,plain,
( ~ empty(the_topology(sK137))
| ~ open_subset(sK208(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_177418,c_781]) ).
tcf(c_183571,plain,
( sP3(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_178460,c_781]) ).
tcf(c_183572,plain,
( ordinal(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_178684,c_781]) ).
tcf(c_183573,plain,
( relation(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_178947,c_781]) ).
tcf(c_183574,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| ~ topological_space(sK137)
| ~ empty(the_topology(sK137))
| ~ in(X0,sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_180142,c_781]) ).
tcf(c_183575,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ empty(the_topology(sK137))
| ~ in(X0,sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_179182,c_781]) ).
tcf(c_183576,plain,
! [X0: $i,X1: $i] :
( ~ topological_space(sK137)
| ~ empty(sK147(sK137,X1))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,X1))) ),
inference(superposition,[status(thm)],[c_179183,c_781]) ).
tcf(c_183577,plain,
( epsilon_transitive(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180305,c_781]) ).
tcf(c_183578,plain,
( epsilon_connected(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180597,c_781]) ).
tcf(c_183581,plain,
( ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138))
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_182179,c_781]) ).
tcf(c_183583,plain,
( empty(the_carrier(sK137))
| ~ empty(the_topology(sK137))
| ~ open_subset(sK207(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_182986,c_781]) ).
tcf(c_183682,plain,
( sP30(sK66)
| ordinal(sK267)
| ~ sP8 ),
inference(superposition,[status(thm)],[c_129,c_827]) ).
tcf(c_183683,plain,
( sP30(sK70)
| ordinal(sK267)
| ~ sP6 ),
inference(superposition,[status(thm)],[c_142,c_827]) ).
tcf(c_183684,plain,
( sP30(sK117)
| ordinal(sK267)
| ~ sP15 ),
inference(superposition,[status(thm)],[c_248,c_827]) ).
tcf(c_183685,plain,
! [X0: $i] :
( ordinal(sK267)
| sP30(union(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_706,c_827]) ).
tcf(c_183688,plain,
( sP30(omega)
| ordinal(sK267) ),
inference(superposition,[status(thm)],[c_843,c_827]) ).
tcf(c_183689,plain,
! [X0: $i] :
( ordinal(sK267)
| sP30(sK274(X0))
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_856,c_827]) ).
tcf(c_183690,plain,
( sP30(sK287)
| ordinal(sK267) ),
inference(superposition,[status(thm)],[c_889,c_827]) ).
tcf(c_183691,plain,
( sP30(sK337)
| ordinal(sK267) ),
inference(superposition,[status(thm)],[c_1066,c_827]) ).
tcf(c_183692,plain,
( sP30(sK339)
| ordinal(sK267) ),
inference(superposition,[status(thm)],[c_1076,c_827]) ).
tcf(c_183693,plain,
( sP30(sK372)
| ordinal(sK267) ),
inference(superposition,[status(thm)],[c_1272,c_827]) ).
tcf(c_183694,plain,
( sP30(empty_set)
| ordinal(sK267) ),
inference(superposition,[status(thm)],[c_178087,c_827]) ).
tcf(c_183695,plain,
( ordinal(sK267)
| sP30(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK139(sK91(sK137,sK138))) = sK139(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178683,c_827]) ).
tcf(c_183696,plain,
( ordinal(sK267)
| sP36(sK137,sK138)
| sP30(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178687,c_827]) ).
tcf(c_183697,plain,
( ordinal(sK267)
| sP36(sK137,sK138)
| sP30(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178686,c_827]) ).
tcf(c_183698,plain,
! [X0: $i] :
( ordinal(sK267)
| sP30(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_179244,c_827]) ).
tcf(c_183699,plain,
( ordinal(sK267)
| sP30(sK208(omega)) ),
inference(superposition,[status(thm)],[c_179848,c_827]) ).
tcf(c_183825,plain,
( ~ topological_space(sK137)
| ~ empty(the_topology(sK137)) ),
inference(global_subsumption_just,[status(thm)],[c_183554,c_47403,c_176993,c_183553]) ).
tcf(c_183837,plain,
( ( the_carrier(sK137) = empty_set )
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_182983,c_594]) ).
tcf(c_183838,plain,
( one_to_one(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_182983,c_104931]) ).
tcf(c_183839,plain,
( ordinal(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_182983,c_1085]) ).
tcf(c_183840,plain,
( epsilon_connected(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_182983,c_1084]) ).
tcf(c_183841,plain,
( epsilon_transitive(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_182983,c_1083]) ).
tcf(c_183842,plain,
( finite(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_182983,c_1015]) ).
tcf(c_183843,plain,
( relation(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_182983,c_793]) ).
tcf(c_183844,plain,
( function(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_182983,c_779]) ).
tcf(c_183896,plain,
! [X0: $i] :
( ~ sP32(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_858,c_781]) ).
tcf(c_183897,plain,
! [X0: $i] :
( element(sK274(X0),X0)
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_858,c_701]) ).
tcf(c_183898,plain,
! [X0: $i] :
( ordinal(sK274(sK99(X0)))
| ~ sP32(sK99(X0)) ),
inference(superposition,[status(thm)],[c_858,c_206]) ).
tcf(c_183899,plain,
~ sP32(empty_set),
inference(superposition,[status(thm)],[c_858,c_599]) ).
tcf(c_183900,plain,
( sP36(sK137,sK138)
| in(sK274(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP32(powerset(the_carrier(sK137)))
| ~ closed_subset(sK274(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK274(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_176867]) ).
tcf(c_183901,plain,
( in(sK274(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP32(powerset(the_carrier(sK137)))
| ~ closed_subset(sK274(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK274(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_176193]) ).
tcf(c_183902,plain,
( ( sK92(sK137,sK138,sK274(sK91(sK137,sK138))) = sK274(sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_858,c_175190]) ).
tcf(c_183903,plain,
( in(sK274(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_858,c_175008]) ).
tcf(c_183904,plain,
( subset(sK138,sK274(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_858,c_174960]) ).
tcf(c_183905,plain,
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,sK274(sK302(sK137,sK138))) = sK274(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_858,c_175802]) ).
tcf(c_183906,plain,
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,sK274(sK302(sK137,sK138))) = sK274(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_858,c_175753]) ).
tcf(c_183907,plain,
( sP36(sK137,sK138)
| subset(sK138,sK274(sK302(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_858,c_175029]) ).
tcf(c_183908,plain,
( in(sK274(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_175089]) ).
tcf(c_183909,plain,
! [X0: $i] :
( in(sK274(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK93(sK137,sK147(sK137,X0))) ),
inference(superposition,[status(thm)],[c_858,c_175090]) ).
tcf(c_183910,plain,
! [X0: $i] :
( in(sK274(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK125(sK137,X0)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_175091]) ).
tcf(c_183911,plain,
! [X0: $i] :
( in(sK274(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK93(sK137,sK123(sK137,X0))) ),
inference(superposition,[status(thm)],[c_858,c_175092]) ).
tcf(c_183912,plain,
! [X0: $i] :
( subset(topstr_closure(sK137,X0),sK274(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_858,c_176013]) ).
tcf(c_183913,plain,
! [X0: $i] :
( in(sK274(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_858,c_176012]) ).
tcf(c_183914,plain,
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),sK274(sK295(sK137,the_topology(sK137)))) = sK274(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137)
| ~ sP32(sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176134]) ).
tcf(c_183915,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),sK274(sK302(sK137,the_carrier(sK137)))) = sK274(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176975]) ).
tcf(c_183916,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),sK274(sK302(sK137,the_carrier(sK137)))) = sK274(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176974]) ).
tcf(c_183917,plain,
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK274(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176981]) ).
tcf(c_183918,plain,
( ( sK124(sK137,the_carrier(sK137),sK274(sK123(sK137,the_carrier(sK137)))) = sK274(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,the_carrier(sK137)))
| ~ element(sK274(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176971]) ).
tcf(c_183919,plain,
( subset(the_carrier(sK137),sK274(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,the_carrier(sK137)))
| ~ element(sK274(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176976]) ).
tcf(c_183920,plain,
( ( sK92(sK137,the_carrier(sK137),sK274(sK91(sK137,the_carrier(sK137)))) = sK274(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176980]) ).
tcf(c_183921,plain,
( in(sK274(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176982]) ).
tcf(c_183922,plain,
( subset(the_carrier(sK137),sK274(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176983]) ).
tcf(c_183923,plain,
( subset(the_carrier(sK137),sK274(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,the_carrier(sK137)))
| ~ element(sK274(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176978]) ).
tcf(c_183924,plain,
( closed_subset(sK274(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,the_carrier(sK137)))
| ~ element(sK274(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176977]) ).
tcf(c_183925,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK274(sK295(sK137,powerset(the_carrier(sK137))))) = sK274(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP32(sK295(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_176995]) ).
tcf(c_183926,plain,
( in(sK274(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_176997]) ).
tcf(c_183927,plain,
( in(sK274(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ sP32(topstr_closure(sK137,sK138))
| ~ in(sK274(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_858,c_177233]) ).
tcf(c_183928,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK274(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_858,c_177405]) ).
tcf(c_183929,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK274(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK274(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_177400]) ).
tcf(c_183930,plain,
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK274(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK274(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_858,c_177404]) ).
tcf(c_183931,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK274(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_858,c_177407]) ).
tcf(c_183932,plain,
( in(sK274(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_858,c_177406]) ).
tcf(c_183933,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK274(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK274(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_177402]) ).
tcf(c_183934,plain,
( closed_subset(sK274(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK274(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_177401]) ).
tcf(c_183935,plain,
( in(sK274(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_858,c_177421]) ).
tcf(c_183936,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK274(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_182972]) ).
tcf(c_183937,plain,
( empty(the_carrier(sK137))
| in(sK274(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_182971]) ).
tcf(c_184146,plain,
~ empty(set_union2(empty_set,powerset(empty_set))),
inference(superposition,[status(thm)],[c_330,c_886]) ).
tcf(c_184155,plain,
! [X0: $i] : are_equipotent(X0,X0),
inference(superposition,[status(thm)],[c_672,c_1003]) ).
tcf(c_184177,plain,
( ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138))
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_183903,c_781]) ).
tcf(c_184178,plain,
( element(sK274(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183903,c_701]) ).
tcf(c_184179,plain,
( sP36(sK137,sK138)
| in(sK274(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138))
| ~ closed_subset(sK274(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK274(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_183903,c_176867]) ).
tcf(c_184180,plain,
( in(sK274(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138))
| ~ closed_subset(sK274(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK274(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_183903,c_176193]) ).
tcf(c_184219,plain,
( in(empty_set,sK147(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_376,c_182438]) ).
tcf(c_184220,plain,
( empty(the_carrier(sK137))
| in(empty_set,sK147(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK207(the_carrier(sK137)),empty_set) ),
inference(superposition,[status(thm)],[c_698,c_182438]) ).
tcf(c_184221,plain,
( in(empty_set,sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_702,c_182438]) ).
tcf(c_184222,plain,
( in(empty_set,sK147(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(the_carrier(sK137),empty_set) ),
inference(superposition,[status(thm)],[c_13308,c_182438]) ).
tcf(c_184223,plain,
! [X0: $i] :
( in(empty_set,sK147(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),empty_set) ),
inference(superposition,[status(thm)],[c_106061,c_182438]) ).
tcf(c_184224,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| in(empty_set,sK147(sK137,sK304(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ subset(sK304(sK137,X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_47929,c_182438]) ).
tcf(c_184225,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| in(empty_set,sK147(sK137,sK146(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(sK146(sK137,X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_48162,c_182438]) ).
tcf(c_184226,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| in(empty_set,sK147(sK137,sK145(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK145(sK137,X0),empty_set)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_182438]) ).
tcf(c_184227,plain,
! [X0: $i,X1: $i] :
( in(empty_set,sK147(sK137,sK124(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK123(sK137,X0))
| ~ subset(sK124(sK137,X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_48350,c_182438]) ).
tcf(c_184228,plain,
! [X0: $i,X1: $i] :
( in(empty_set,sK147(sK137,sK92(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK91(sK137,X0))
| ~ subset(sK92(sK137,X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_48475,c_182438]) ).
tcf(c_184229,plain,
( in(empty_set,sK147(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(empty_set,empty_set) ),
inference(superposition,[status(thm)],[c_182003,c_182438]) ).
tcf(c_184230,plain,
( in(empty_set,sK147(sK137,empty_set))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_184229,c_379]) ).
tcf(c_184327,plain,
( ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ empty(sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_184219,c_781]) ).
tcf(c_184328,plain,
( element(empty_set,sK147(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_184219,c_701]) ).
tcf(c_184361,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(X0,sK325(the_carrier(sK137)))
| ~ in(X0,the_carrier(sK137))
| ~ closed_subset(sK325(the_carrier(sK137)),sK137)
| ~ subset(sK138,sK325(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1004,c_177131]) ).
tcf(c_184362,plain,
! [X0: $i,X1: $i] :
( empty(the_carrier(sK137))
| in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK325(the_carrier(sK137)),X1)
| ~ in(X0,topstr_closure(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_48138]) ).
tcf(c_184363,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| in(X0,sK302(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK325(the_carrier(sK137)),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1004,c_47771]) ).
tcf(c_184364,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK325(the_carrier(sK137)),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK325(the_carrier(sK137)),sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,sK325(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1004,c_48368]) ).
tcf(c_184365,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK124(sK137,sK325(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_48332]) ).
tcf(c_184366,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK325(the_carrier(sK137)),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK325(the_carrier(sK137)),sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,sK325(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1004,c_48105]) ).
tcf(c_184367,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(X0,sK91(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK325(the_carrier(sK137)),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1004,c_47795]) ).
tcf(c_184368,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| ( sK303(sK137,sK325(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_47947]) ).
tcf(c_184369,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| ( sK304(sK137,sK325(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_47911]) ).
tcf(c_184370,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_48297]) ).
tcf(c_184371,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_48087]) ).
tcf(c_184372,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_48070]) ).
tcf(c_184373,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( topstr_closure(sK137,sK325(the_carrier(sK137))) = X0 )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK325(the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_1004,c_47756]) ).
tcf(c_184374,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_48460]) ).
tcf(c_184375,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_47876]) ).
tcf(c_184376,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_48490]) ).
tcf(c_184377,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_48431]) ).
tcf(c_184378,plain,
( empty(the_carrier(sK137))
| in(empty_set,sK147(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK325(the_carrier(sK137)),empty_set) ),
inference(superposition,[status(thm)],[c_1004,c_182438]) ).
tcf(c_184379,plain,
( empty(the_carrier(sK137))
| ( sK124(sK137,empty_set,sK325(the_carrier(sK137))) = sK325(the_carrier(sK137)) )
| ~ topological_space(sK137)
| ~ in(sK325(the_carrier(sK137)),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_1004,c_182437]) ).
tcf(c_184380,plain,
( empty(the_carrier(sK137))
| in(empty_set,sK123(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK325(the_carrier(sK137)),empty_set) ),
inference(superposition,[status(thm)],[c_1004,c_182436]) ).
tcf(c_184381,plain,
( empty(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK325(the_carrier(sK137))))) = topstr_closure(sK137,topstr_closure(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1004,c_176018]) ).
tcf(c_184382,plain,
( empty(the_carrier(sK137))
| in(sK138,sK123(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_1004,c_176521]) ).
tcf(c_184383,plain,
( empty(the_carrier(sK137))
| ( sK124(sK137,sK138,sK325(the_carrier(sK137))) = sK325(the_carrier(sK137)) )
| ~ topological_space(sK137)
| ~ in(sK325(the_carrier(sK137)),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1004,c_176408]) ).
tcf(c_184384,plain,
( empty(the_carrier(sK137))
| in(sK138,sK147(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_1004,c_176286]) ).
tcf(c_184385,plain,
( empty(the_carrier(sK137))
| subset(sK138,sK325(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(sK325(the_carrier(sK137)),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1004,c_175672]) ).
tcf(c_184386,plain,
( empty(the_carrier(sK137))
| closed_subset(sK325(the_carrier(sK137)),sK137)
| ~ topological_space(sK137)
| ~ in(sK325(the_carrier(sK137)),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1004,c_175482]) ).
tcf(c_184387,plain,
( empty(the_carrier(sK137))
| subset(sK138,sK325(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(sK325(the_carrier(sK137)),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1004,c_175418]) ).
tcf(c_184388,plain,
( empty(the_carrier(sK137))
| ( topstr_closure(sK137,sK138) = sK325(the_carrier(sK137)) )
| ~ sP38(sK137,sK138,sK325(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1004,c_175209]) ).
tcf(c_184389,plain,
( empty(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1004,c_48058]) ).
tcf(c_184390,plain,
( empty(the_carrier(sK137))
| ( topstr_closure(sK137,sK325(the_carrier(sK137))) = sK325(the_carrier(sK137)) )
| ~ closed_subset(sK325(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_1004,c_48037]) ).
tcf(c_184391,plain,
( empty(the_carrier(sK137))
| open_subset(sK325(the_carrier(sK137)),sK137)
| ~ in(sK325(the_carrier(sK137)),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_1004,c_47852]) ).
tcf(c_184392,plain,
( empty(the_carrier(sK137))
| in(sK325(the_carrier(sK137)),the_topology(sK137))
| ~ open_subset(sK325(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_1004,c_47840]) ).
tcf(c_184393,plain,
! [X0: $i] :
( empty(powerset(the_carrier(sK137)))
| sP34(sK325(powerset(the_carrier(sK137))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK325(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK325(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_1004,c_73951]) ).
tcf(c_184394,plain,
! [X0: $i] :
( empty(powerset(the_carrier(sK137)))
| in(set_difference(the_carrier(sK137),X0),sK325(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK325(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_1004,c_73134]) ).
tcf(c_184395,plain,
! [X0: $i] :
( empty(powerset(the_carrier(sK137)))
| sP34(sK325(powerset(the_carrier(sK137))),sK137)
| ( sK296(sK137,sK325(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK325(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_1004,c_48001]) ).
tcf(c_184396,plain,
( empty(powerset(the_carrier(sK137)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK325(powerset(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK325(powerset(the_carrier(sK137)))),sK137) ),
inference(superposition,[status(thm)],[c_1004,c_48252]) ).
tcf(c_184397,plain,
! [X0: $i] :
( empty(powerset(the_carrier(sK137)))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK325(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_1004,c_48416]) ).
tcf(c_184398,plain,
( empty(powerset(the_carrier(sK137)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK325(powerset(the_carrier(sK137)))),sK137)
| in(sK145(sK137,sK325(powerset(the_carrier(sK137)))),sK325(powerset(the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1004,c_48237]) ).
tcf(c_184431,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK325(powerset(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_184397,c_700]) ).
tcf(c_184476,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK325(powerset(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK325(powerset(the_carrier(sK137)))),sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_184396,c_700]) ).
tcf(c_184480,plain,
! [X0: $i] :
( in(set_difference(the_carrier(sK137),X0),sK325(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK325(powerset(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_184394,c_700]) ).
tcf(c_184505,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK325(powerset(the_carrier(sK137)))),sK137)
| in(sK145(sK137,sK325(powerset(the_carrier(sK137)))),sK325(powerset(the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_184398,c_700]) ).
tcf(c_184530,plain,
! [X0: $i] :
( sP34(sK325(powerset(the_carrier(sK137))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK325(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK325(powerset(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_184393,c_700]) ).
tcf(c_184553,plain,
! [X0: $i] :
( sP34(sK325(powerset(the_carrier(sK137))),sK137)
| ( sK296(sK137,sK325(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK325(powerset(the_carrier(sK137))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_184395,c_700]) ).
tcf(c_184761,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(X0,X1))
| ~ finite(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_420,c_1011]) ).
tcf(c_184804,plain,
( empty(the_carrier(sK137))
| ~ empty(the_topology(sK137))
| ~ open_subset(sK325(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_184392,c_781]) ).
tcf(c_184805,plain,
( empty(the_carrier(sK137))
| element(sK325(the_carrier(sK137)),the_topology(sK137))
| ~ open_subset(sK325(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_184392,c_701]) ).
tcf(c_184827,plain,
( empty(the_carrier(sK137))
| sP3(sK91(sK137,sK325(the_carrier(sK137))))
| in(sK62(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_184376]) ).
tcf(c_184829,plain,
( empty(the_carrier(sK137))
| ordinal(sK91(sK137,sK325(the_carrier(sK137))))
| in(sK139(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_184376]) ).
tcf(c_184830,plain,
( empty(the_carrier(sK137))
| relation(sK91(sK137,sK325(the_carrier(sK137))))
| in(sK175(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_184376]) ).
tcf(c_184831,plain,
( empty(the_carrier(sK137))
| in(sK185(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_184376]) ).
tcf(c_184833,plain,
( empty(the_carrier(sK137))
| in(sK274(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_184376]) ).
tcf(c_184834,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK91(sK137,sK325(the_carrier(sK137))))
| in(sK340(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_184376]) ).
tcf(c_184835,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK325(the_carrier(sK137))))
| in(sK369(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_184376]) ).
tcf(c_184836,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK325(the_carrier(sK137))))
| in(sK370(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_184376]) ).
tcf(c_184899,plain,
( empty(the_carrier(sK137))
| sP3(sK91(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK62(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_184377]) ).
tcf(c_184901,plain,
( empty(the_carrier(sK137))
| ordinal(sK91(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK139(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_184377]) ).
tcf(c_184902,plain,
( empty(the_carrier(sK137))
| relation(sK91(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK175(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_184377]) ).
tcf(c_184903,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK185(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_184377]) ).
tcf(c_184905,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK274(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_184377]) ).
tcf(c_184906,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK91(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK340(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_184377]) ).
tcf(c_184907,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK369(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_184377]) ).
tcf(c_184908,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK370(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_184377]) ).
tcf(c_184987,plain,
element(empty_set,set_union2(empty_set,powerset(empty_set))),
inference(superposition,[status(thm)],[c_330,c_183191]) ).
tcf(c_185040,plain,
! [X0: $i] :
( sP3(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_646,c_183535]) ).
tcf(c_185041,plain,
! [X0: $i] :
( sP3(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_968,c_183535]) ).
tcf(c_185042,plain,
! [X0: $i] :
( sP3(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1166,c_183535]) ).
tcf(c_185043,plain,
( sP3(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_182983,c_183535]) ).
tcf(c_185093,plain,
( sP3(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_184389,c_183535]) ).
tcf(c_185094,plain,
( ( the_carrier(sK137) = empty_set )
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_184389,c_594]) ).
tcf(c_185095,plain,
( one_to_one(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_184389,c_104931]) ).
tcf(c_185096,plain,
( ordinal(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_184389,c_1085]) ).
tcf(c_185097,plain,
( epsilon_connected(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_184389,c_1084]) ).
tcf(c_185098,plain,
( epsilon_transitive(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_184389,c_1083]) ).
tcf(c_185099,plain,
( finite(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_184389,c_1015]) ).
tcf(c_185100,plain,
( relation(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_184389,c_793]) ).
tcf(c_185101,plain,
( function(the_carrier(sK137))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_184389,c_779]) ).
tcf(c_185147,plain,
( empty(the_carrier(sK137))
| sP3(sK147(sK137,sK207(the_carrier(sK137))))
| closed_subset(sK62(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_182966]) ).
tcf(c_185149,plain,
( empty(the_carrier(sK137))
| ordinal(sK147(sK137,sK207(the_carrier(sK137))))
| closed_subset(sK139(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_182966]) ).
tcf(c_185150,plain,
( empty(the_carrier(sK137))
| relation(sK147(sK137,sK207(the_carrier(sK137))))
| closed_subset(sK175(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_182966]) ).
tcf(c_185151,plain,
( empty(the_carrier(sK137))
| closed_subset(sK185(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK185(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_182966]) ).
tcf(c_185153,plain,
( empty(the_carrier(sK137))
| closed_subset(sK274(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK274(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_182966]) ).
tcf(c_185154,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK147(sK137,sK207(the_carrier(sK137))))
| closed_subset(sK340(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_182966]) ).
tcf(c_185155,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK147(sK137,sK207(the_carrier(sK137))))
| closed_subset(sK369(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_182966]) ).
tcf(c_185156,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK147(sK137,sK207(the_carrier(sK137))))
| closed_subset(sK370(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_182966]) ).
tcf(c_185158,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK207(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK207(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_179183,c_182966]) ).
tcf(c_185227,plain,
( empty(the_carrier(sK137))
| sP3(sK91(sK137,sK207(the_carrier(sK137))))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK62(sK91(sK137,sK207(the_carrier(sK137))))) = sK62(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_182969]) ).
tcf(c_185229,plain,
( empty(the_carrier(sK137))
| ordinal(sK91(sK137,sK207(the_carrier(sK137))))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK139(sK91(sK137,sK207(the_carrier(sK137))))) = sK139(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_182969]) ).
tcf(c_185230,plain,
( empty(the_carrier(sK137))
| relation(sK91(sK137,sK207(the_carrier(sK137))))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK175(sK91(sK137,sK207(the_carrier(sK137))))) = sK175(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_182969]) ).
tcf(c_185231,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK185(sK91(sK137,sK207(the_carrier(sK137))))) = sK185(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_182969]) ).
tcf(c_185233,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK274(sK91(sK137,sK207(the_carrier(sK137))))) = sK274(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_182969]) ).
tcf(c_185234,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK91(sK137,sK207(the_carrier(sK137))))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK340(sK91(sK137,sK207(the_carrier(sK137))))) = sK340(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_182969]) ).
tcf(c_185235,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK207(the_carrier(sK137))))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK369(sK91(sK137,sK207(the_carrier(sK137))))) = sK369(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_182969]) ).
tcf(c_185236,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK207(the_carrier(sK137))))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK370(sK91(sK137,sK207(the_carrier(sK137))))) = sK370(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_182969]) ).
tcf(c_185315,plain,
( empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138)
| ~ empty(sK123(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_182976,c_781]) ).
tcf(c_185316,plain,
( empty(the_carrier(sK137))
| element(sK138,sK123(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_182976,c_701]) ).
tcf(c_185337,plain,
( empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138)
| ~ empty(sK147(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_182978,c_781]) ).
tcf(c_185338,plain,
( empty(the_carrier(sK137))
| element(sK138,sK147(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_182978,c_701]) ).
tcf(c_185374,plain,
( empty(the_carrier(sK137))
| sP3(sK147(sK137,sK325(the_carrier(sK137))))
| closed_subset(sK62(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_184371]) ).
tcf(c_185376,plain,
( empty(the_carrier(sK137))
| ordinal(sK147(sK137,sK325(the_carrier(sK137))))
| closed_subset(sK139(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_184371]) ).
tcf(c_185377,plain,
( empty(the_carrier(sK137))
| relation(sK147(sK137,sK325(the_carrier(sK137))))
| closed_subset(sK175(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_184371]) ).
tcf(c_185378,plain,
( empty(the_carrier(sK137))
| closed_subset(sK185(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK185(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_184371]) ).
tcf(c_185380,plain,
( empty(the_carrier(sK137))
| closed_subset(sK274(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK274(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_184371]) ).
tcf(c_185381,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK147(sK137,sK325(the_carrier(sK137))))
| closed_subset(sK340(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_184371]) ).
tcf(c_185382,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK147(sK137,sK325(the_carrier(sK137))))
| closed_subset(sK369(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_184371]) ).
tcf(c_185383,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK147(sK137,sK325(the_carrier(sK137))))
| closed_subset(sK370(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_184371]) ).
tcf(c_185385,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK325(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK325(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_179183,c_184371]) ).
tcf(c_185538,plain,
( ( topstr_closure(sK137,the_carrier(sK137)) = the_carrier(sK137) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_106079,c_176992]) ).
tcf(c_185557,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ empty(sK122(X0)) ),
inference(superposition,[status(thm)],[c_258,c_179245]) ).
tcf(c_185558,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_509,c_179245]) ).
tcf(c_185568,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ empty(sK122(X0)) ),
inference(superposition,[status(thm)],[c_258,c_179246]) ).
tcf(c_185569,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_509,c_179246]) ).
tcf(c_185579,plain,
! [X0: $i] :
( finite(X0)
| ~ empty(sK122(X0)) ),
inference(superposition,[status(thm)],[c_258,c_179247]) ).
tcf(c_185580,plain,
! [X0: $i] :
( finite(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_509,c_179247]) ).
tcf(c_185594,plain,
( empty(the_carrier(sK137))
| sP3(sK91(sK137,sK325(the_carrier(sK137))))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK62(sK91(sK137,sK325(the_carrier(sK137))))) = sK62(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_184374]) ).
tcf(c_185596,plain,
( empty(the_carrier(sK137))
| ordinal(sK91(sK137,sK325(the_carrier(sK137))))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK139(sK91(sK137,sK325(the_carrier(sK137))))) = sK139(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_184374]) ).
tcf(c_185597,plain,
( empty(the_carrier(sK137))
| relation(sK91(sK137,sK325(the_carrier(sK137))))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK175(sK91(sK137,sK325(the_carrier(sK137))))) = sK175(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_184374]) ).
tcf(c_185598,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK185(sK91(sK137,sK325(the_carrier(sK137))))) = sK185(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_184374]) ).
tcf(c_185600,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK274(sK91(sK137,sK325(the_carrier(sK137))))) = sK274(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_184374]) ).
tcf(c_185601,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK91(sK137,sK325(the_carrier(sK137))))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK340(sK91(sK137,sK325(the_carrier(sK137))))) = sK340(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_184374]) ).
tcf(c_185602,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK325(the_carrier(sK137))))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK369(sK91(sK137,sK325(the_carrier(sK137))))) = sK369(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_184374]) ).
tcf(c_185603,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK91(sK137,sK325(the_carrier(sK137))))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK370(sK91(sK137,sK325(the_carrier(sK137))))) = sK370(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_184374]) ).
tcf(c_185654,plain,
( empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138)
| ~ empty(sK123(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_184382,c_781]) ).
tcf(c_185655,plain,
( empty(the_carrier(sK137))
| element(sK138,sK123(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_184382,c_701]) ).
tcf(c_185676,plain,
( empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138)
| ~ empty(sK147(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_184384,c_781]) ).
tcf(c_185677,plain,
( empty(the_carrier(sK137))
| element(sK138,sK147(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_184384,c_701]) ).
tcf(c_185733,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sK368(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2) != X2 ) ),
inference(superposition,[status(thm)],[c_967,c_105507]) ).
tcf(c_185735,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2) != X2 ) ),
inference(superposition,[status(thm)],[c_967,c_105507]) ).
tcf(c_185737,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( sK368(unordered_pair(powerset(empty_set),powerset(empty_set)),X0) != X0 ) ),
inference(superposition,[status(thm)],[c_330,c_105507]) ).
tcf(c_185738,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( sK368(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),X1) != X1 ) ),
inference(superposition,[status(thm)],[c_330,c_105507]) ).
tcf(c_185751,plain,
! [X0: $i] :
( in(empty_set,X0)
| disjoint(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_330,c_55]) ).
tcf(c_185752,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| disjoint(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_55,c_643]) ).
tcf(c_185763,plain,
! [X0: $i] :
( sP3(sK99(X0))
| in(sK62(sK99(X0)),X0) ),
inference(superposition,[status(thm)],[c_120,c_205]) ).
tcf(c_185765,plain,
! [X0: $i] :
( ordinal(sK99(X0))
| in(sK139(sK99(X0)),X0) ),
inference(superposition,[status(thm)],[c_383,c_205]) ).
tcf(c_185766,plain,
! [X0: $i] :
( relation(sK99(X0))
| in(sK175(sK99(X0)),X0) ),
inference(superposition,[status(thm)],[c_580,c_205]) ).
tcf(c_185767,plain,
! [X0: $i] :
( in(sK185(sK99(X0)),X0)
| ~ sP20(sK99(X0)) ),
inference(superposition,[status(thm)],[c_603,c_205]) ).
tcf(c_185769,plain,
! [X0: $i] :
( in(sK274(sK99(X0)),X0)
| ~ sP32(sK99(X0)) ),
inference(superposition,[status(thm)],[c_858,c_205]) ).
tcf(c_185770,plain,
! [X0: $i] :
( epsilon_transitive(sK99(X0))
| in(sK340(sK99(X0)),X0) ),
inference(superposition,[status(thm)],[c_1081,c_205]) ).
tcf(c_185771,plain,
! [X0: $i] :
( epsilon_connected(sK99(X0))
| in(sK369(sK99(X0)),X0) ),
inference(superposition,[status(thm)],[c_1253,c_205]) ).
tcf(c_185772,plain,
! [X0: $i] :
( epsilon_connected(sK99(X0))
| in(sK370(sK99(X0)),X0) ),
inference(superposition,[status(thm)],[c_1254,c_205]) ).
tcf(c_185815,plain,
! [X0: $i] :
( function(X0)
| ~ empty(sK122(X0)) ),
inference(superposition,[status(thm)],[c_258,c_179249]) ).
tcf(c_185816,plain,
! [X0: $i] :
( function(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_509,c_179249]) ).
tcf(c_185860,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| sP3(sK302(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK62(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_182970]) ).
tcf(c_185862,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| ordinal(sK302(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK139(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_182970]) ).
tcf(c_185863,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| relation(sK302(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK175(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_182970]) ).
tcf(c_185864,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK185(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_182970]) ).
tcf(c_185866,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK274(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_182970]) ).
tcf(c_185867,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| epsilon_transitive(sK302(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK340(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_182970]) ).
tcf(c_185868,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK369(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_182970]) ).
tcf(c_185869,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK370(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_182970]) ).
tcf(c_185954,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| sP3(sK302(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK62(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_184375]) ).
tcf(c_185956,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| ordinal(sK302(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK139(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_184375]) ).
tcf(c_185957,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| relation(sK302(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK175(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_184375]) ).
tcf(c_185958,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK185(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_603,c_184375]) ).
tcf(c_185960,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK274(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_858,c_184375]) ).
tcf(c_185961,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| epsilon_transitive(sK302(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK340(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_184375]) ).
tcf(c_185962,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK369(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_184375]) ).
tcf(c_185963,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| epsilon_connected(sK302(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK370(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_184375]) ).
tcf(c_186039,plain,
! [X0: $i] :
( in(the_carrier(sK137),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(empty_set,sK93(sK137,sK123(sK137,X0))) ),
inference(superposition,[status(thm)],[c_680,c_179185]) ).
tcf(c_186040,plain,
! [X0: $i] :
( in(empty_set,sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(the_carrier(sK137),sK93(sK137,sK123(sK137,X0))) ),
inference(superposition,[status(thm)],[c_13761,c_179185]) ).
tcf(c_186041,plain,
! [X0: $i,X1: $i] :
( in(set_difference(X0,set_difference(X0,the_carrier(sK137))),sK123(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(set_difference(the_carrier(sK137),X0),sK93(sK137,sK123(sK137,X1))) ),
inference(superposition,[status(thm)],[c_986,c_179185]) ).
tcf(c_186042,plain,
! [X0: $i,X1: $i] :
( ~ topological_space(sK137)
| ~ empty(sK123(sK137,X1))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,X1))) ),
inference(superposition,[status(thm)],[c_179185,c_781]) ).
tcf(c_186043,plain,
! [X0: $i,X1: $i] :
( element(set_difference(the_carrier(sK137),X0),sK123(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,X1))) ),
inference(superposition,[status(thm)],[c_179185,c_701]) ).
tcf(c_186044,plain,
! [X0: $i] :
( ( sK124(sK137,the_carrier(sK137),set_difference(the_carrier(sK137),X0)) = set_difference(the_carrier(sK137),X0) )
| ~ topological_space(sK137)
| ~ element(the_carrier(sK137),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_179185,c_176971]) ).
tcf(c_186045,plain,
! [X0: $i] :
( subset(the_carrier(sK137),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(the_carrier(sK137),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_179185,c_176976]) ).
tcf(c_186046,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(sK208(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,sK208(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_179185,c_177400]) ).
tcf(c_186067,plain,
! [X0: $i] :
( subset(the_carrier(sK137),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,the_carrier(sK137)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_186045,c_13308]) ).
tcf(c_186072,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,sK208(powerset(the_carrier(sK137)))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_186046,c_702]) ).
tcf(c_186077,plain,
! [X0: $i] :
( ( sK124(sK137,the_carrier(sK137),set_difference(the_carrier(sK137),X0)) = set_difference(the_carrier(sK137),X0) )
| ~ topological_space(sK137)
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,the_carrier(sK137)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_186044,c_13308]) ).
tcf(c_186145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2),sK367(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2),sK368(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2))) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_967,c_105912]) ).
tcf(c_186147,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)) ) ),
inference(superposition,[status(thm)],[c_967,c_105912]) ).
tcf(c_186149,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(sK367(unordered_pair(powerset(empty_set),powerset(empty_set)),X0),sK367(unordered_pair(powerset(empty_set),powerset(empty_set)),X0)),unordered_pair(sK367(unordered_pair(powerset(empty_set),powerset(empty_set)),X0),sK368(unordered_pair(powerset(empty_set),powerset(empty_set)),X0))) = unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_105912]) ).
tcf(c_186151,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),X1),sK367(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),X1)),unordered_pair(sK367(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),X1),sK368(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),X1))) = unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_105912]) ).
tcf(c_186152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3),sK367(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3)),unordered_pair(sK367(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3),sK368(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3))) = unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) ) ),
inference(superposition,[status(thm)],[c_105912,c_105912]) ).
tcf(c_186153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( sK368(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3) != X3 ) ),
inference(superposition,[status(thm)],[c_105912,c_105507]) ).
tcf(c_186154,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(unordered_pair(sK367(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1),sK367(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1)),unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)))
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_105912,c_183197]) ).
tcf(c_186155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( sK365(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3) != X3 ) ),
inference(superposition,[status(thm)],[c_105912,c_105505]) ).
tcf(c_186156,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( pair_second(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))))) = unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105912,c_516]) ).
tcf(c_186157,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( pair_first(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))))) = unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105912,c_515]) ).
tcf(c_186160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X4 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X3 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X3) ) ),
inference(superposition,[status(thm)],[c_105912,c_273]) ).
tcf(c_186161,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK367(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1),sK367(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1)),unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)))
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_105912,c_964]) ).
tcf(c_186162,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ empty(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_105912,c_960]) ).
tcf(c_186163,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(unordered_pair(sK367(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1),sK368(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1)),unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)))
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_105912,c_183198]) ).
tcf(c_186164,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK367(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1),sK368(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X1)),unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)))
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_105912,c_965]) ).
tcf(c_186165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X4 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105912,c_393]) ).
tcf(c_186166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105912,c_392]) ).
tcf(c_186167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X4 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X3) ) ),
inference(superposition,[status(thm)],[c_105912,c_273]) ).
tcf(c_186168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)) = unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)) )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X2) ) ),
inference(superposition,[status(thm)],[c_105912,c_541]) ).
tcf(c_186169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)) = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X2) ) ),
inference(superposition,[status(thm)],[c_105912,c_531]) ).
tcf(c_186294,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_416,c_781]) ).
tcf(c_186295,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| element(sK142(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_416,c_701]) ).
tcf(c_186296,plain,
! [X0: $i,X1: $i] :
( disjoint(sK99(X0),X1)
| in(sK142(sK99(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_416,c_205]) ).
tcf(c_186297,plain,
! [X0: $i,X1: $i] :
( disjoint(sK99(X0),X1)
| ordinal(sK142(sK99(X0),X1)) ),
inference(superposition,[status(thm)],[c_416,c_206]) ).
tcf(c_186298,plain,
! [X0: $i] : disjoint(empty_set,X0),
inference(superposition,[status(thm)],[c_416,c_599]) ).
tcf(c_186299,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(powerset(the_carrier(sK137)),X0)
| in(sK142(powerset(the_carrier(sK137)),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK142(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK142(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_416,c_176867]) ).
tcf(c_186300,plain,
! [X0: $i] :
( disjoint(powerset(the_carrier(sK137)),X0)
| in(sK142(powerset(the_carrier(sK137)),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK142(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK142(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_416,c_176193]) ).
tcf(c_186301,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| ( sK92(sK137,sK138,sK142(sK91(sK137,sK138),X0)) = sK142(sK91(sK137,sK138),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_175190]) ).
tcf(c_186302,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| in(sK142(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_175008]) ).
tcf(c_186303,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| subset(sK138,sK142(sK91(sK137,sK138),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_174960]) ).
tcf(c_186304,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(sK302(sK137,sK138),X0)
| ( sK303(sK137,sK138,sK142(sK302(sK137,sK138),X0)) = sK142(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_175802]) ).
tcf(c_186305,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(sK302(sK137,sK138),X0)
| ( sK304(sK137,sK138,sK142(sK302(sK137,sK138),X0)) = sK142(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_175753]) ).
tcf(c_186306,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(sK302(sK137,sK138),X0)
| subset(sK138,sK142(sK302(sK137,sK138),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_175029]) ).
tcf(c_186307,plain,
! [X0: $i] :
( disjoint(sK93(sK137,the_topology(sK137)),X0)
| in(sK142(sK93(sK137,the_topology(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_175089]) ).
tcf(c_186308,plain,
! [X0: $i,X1: $i] :
( disjoint(sK93(sK137,sK147(sK137,X0)),X1)
| in(sK142(sK93(sK137,sK147(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_175090]) ).
tcf(c_186309,plain,
! [X0: $i,X1: $i] :
( disjoint(sK93(sK137,sK125(sK137,X0)),X1)
| in(sK142(sK93(sK137,sK125(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_416,c_175091]) ).
tcf(c_186310,plain,
! [X0: $i,X1: $i] :
( disjoint(sK93(sK137,sK123(sK137,X0)),X1)
| in(sK142(sK93(sK137,sK123(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_175092]) ).
tcf(c_186311,plain,
! [X0: $i,X1: $i] :
( disjoint(sK91(sK137,topstr_closure(sK137,X0)),X1)
| subset(topstr_closure(sK137,X0),sK142(sK91(sK137,topstr_closure(sK137,X0)),X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_176013]) ).
tcf(c_186312,plain,
! [X0: $i,X1: $i] :
( disjoint(sK91(sK137,topstr_closure(sK137,X0)),X1)
| in(sK142(sK91(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_176012]) ).
tcf(c_186313,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| disjoint(sK295(sK137,the_topology(sK137)),X0)
| ( sK296(sK137,the_topology(sK137),sK142(sK295(sK137,the_topology(sK137)),X0)) = sK142(sK295(sK137,the_topology(sK137)),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_176134]) ).
tcf(c_186314,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| disjoint(sK302(sK137,the_carrier(sK137)),X0)
| ( sK304(sK137,the_carrier(sK137),sK142(sK302(sK137,the_carrier(sK137)),X0)) = sK142(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_176975]) ).
tcf(c_186315,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| disjoint(sK302(sK137,the_carrier(sK137)),X0)
| ( sK303(sK137,the_carrier(sK137),sK142(sK302(sK137,the_carrier(sK137)),X0)) = sK142(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_176974]) ).
tcf(c_186316,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| disjoint(sK302(sK137,the_carrier(sK137)),X0)
| subset(the_carrier(sK137),sK142(sK302(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_176981]) ).
tcf(c_186317,plain,
! [X0: $i] :
( disjoint(sK123(sK137,the_carrier(sK137)),X0)
| ( sK124(sK137,the_carrier(sK137),sK142(sK123(sK137,the_carrier(sK137)),X0)) = sK142(sK123(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ element(sK142(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_176971]) ).
tcf(c_186318,plain,
! [X0: $i] :
( disjoint(sK123(sK137,the_carrier(sK137)),X0)
| subset(the_carrier(sK137),sK142(sK123(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ element(sK142(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_176976]) ).
tcf(c_186319,plain,
! [X0: $i] :
( disjoint(sK91(sK137,the_carrier(sK137)),X0)
| ( sK92(sK137,the_carrier(sK137),sK142(sK91(sK137,the_carrier(sK137)),X0)) = sK142(sK91(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_176980]) ).
tcf(c_186320,plain,
! [X0: $i] :
( disjoint(sK91(sK137,the_carrier(sK137)),X0)
| in(sK142(sK91(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_176982]) ).
tcf(c_186321,plain,
! [X0: $i] :
( disjoint(sK91(sK137,the_carrier(sK137)),X0)
| subset(the_carrier(sK137),sK142(sK91(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_176983]) ).
tcf(c_186322,plain,
! [X0: $i] :
( disjoint(sK147(sK137,the_carrier(sK137)),X0)
| subset(the_carrier(sK137),sK142(sK147(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ element(sK142(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_176978]) ).
tcf(c_186323,plain,
! [X0: $i] :
( disjoint(sK147(sK137,the_carrier(sK137)),X0)
| closed_subset(sK142(sK147(sK137,the_carrier(sK137)),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK142(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_176977]) ).
tcf(c_186324,plain,
! [X0: $i] :
( sP34(powerset(the_carrier(sK137)),sK137)
| disjoint(sK295(sK137,powerset(the_carrier(sK137))),X0)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK142(sK295(sK137,powerset(the_carrier(sK137))),X0)) = sK142(sK295(sK137,powerset(the_carrier(sK137))),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_176995]) ).
tcf(c_186325,plain,
! [X0: $i] :
( disjoint(sK93(sK137,powerset(the_carrier(sK137))),X0)
| in(sK142(sK93(sK137,powerset(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_176997]) ).
tcf(c_186326,plain,
! [X0: $i] :
( disjoint(topstr_closure(sK137,sK138),X0)
| in(sK142(topstr_closure(sK137,sK138),X0),sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(sK142(topstr_closure(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_416,c_177233]) ).
tcf(c_186327,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| disjoint(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| subset(sK208(powerset(the_carrier(sK137))),sK142(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_177405]) ).
tcf(c_186328,plain,
! [X0: $i] :
( disjoint(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| subset(sK208(powerset(the_carrier(sK137))),sK142(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ element(sK142(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_177400]) ).
tcf(c_186329,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK142(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)) = sK142(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_177404]) ).
tcf(c_186330,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| subset(sK208(powerset(the_carrier(sK137))),sK142(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_177407]) ).
tcf(c_186331,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| in(sK142(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_177406]) ).
tcf(c_186332,plain,
! [X0: $i] :
( disjoint(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| subset(sK208(powerset(the_carrier(sK137))),sK142(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ element(sK142(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_177402]) ).
tcf(c_186333,plain,
! [X0: $i] :
( disjoint(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| closed_subset(sK142(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK142(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_177401]) ).
tcf(c_186334,plain,
! [X0: $i] :
( disjoint(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0)
| in(sK142(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_177421]) ).
tcf(c_186335,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| disjoint(sK302(sK137,sK207(the_carrier(sK137))),X0)
| subset(sK207(the_carrier(sK137)),sK142(sK302(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_182970]) ).
tcf(c_186336,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK91(sK137,sK207(the_carrier(sK137))),X0)
| ( sK92(sK137,sK207(the_carrier(sK137)),sK142(sK91(sK137,sK207(the_carrier(sK137))),X0)) = sK142(sK91(sK137,sK207(the_carrier(sK137))),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_182969]) ).
tcf(c_186337,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK91(sK137,sK207(the_carrier(sK137))),X0)
| subset(sK207(the_carrier(sK137)),sK142(sK91(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_182972]) ).
tcf(c_186338,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK91(sK137,sK207(the_carrier(sK137))),X0)
| in(sK142(sK91(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_182971]) ).
tcf(c_186339,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK147(sK137,sK207(the_carrier(sK137))),X0)
| closed_subset(sK142(sK147(sK137,sK207(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK142(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_182966]) ).
tcf(c_186340,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| disjoint(sK302(sK137,sK325(the_carrier(sK137))),X0)
| subset(sK325(the_carrier(sK137)),sK142(sK302(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_184375]) ).
tcf(c_186341,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK91(sK137,sK325(the_carrier(sK137))),X0)
| ( sK92(sK137,sK325(the_carrier(sK137)),sK142(sK91(sK137,sK325(the_carrier(sK137))),X0)) = sK142(sK91(sK137,sK325(the_carrier(sK137))),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_184374]) ).
tcf(c_186342,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK91(sK137,sK325(the_carrier(sK137))),X0)
| subset(sK325(the_carrier(sK137)),sK142(sK91(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_184377]) ).
tcf(c_186343,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK91(sK137,sK325(the_carrier(sK137))),X0)
| in(sK142(sK91(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_184376]) ).
tcf(c_186344,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK147(sK137,sK325(the_carrier(sK137))),X0)
| closed_subset(sK142(sK147(sK137,sK325(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK142(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_184371]) ).
tcf(c_186673,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_417,c_781]) ).
tcf(c_186674,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| element(sK142(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_417,c_701]) ).
tcf(c_186675,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,sK99(X1))
| in(sK142(X0,sK99(X1)),X1) ),
inference(superposition,[status(thm)],[c_417,c_205]) ).
tcf(c_186676,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,sK99(X1))
| ordinal(sK142(X0,sK99(X1))) ),
inference(superposition,[status(thm)],[c_417,c_206]) ).
tcf(c_186677,plain,
! [X0: $i] : disjoint(X0,empty_set),
inference(superposition,[status(thm)],[c_417,c_599]) ).
tcf(c_186678,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(X0,powerset(the_carrier(sK137)))
| in(sK142(X0,powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK142(X0,powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK142(X0,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_417,c_176867]) ).
tcf(c_186679,plain,
! [X0: $i] :
( disjoint(X0,powerset(the_carrier(sK137)))
| in(sK142(X0,powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK142(X0,powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK142(X0,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_417,c_176193]) ).
tcf(c_186680,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK142(X0,sK91(sK137,sK138))) = sK142(X0,sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_175190]) ).
tcf(c_186681,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| in(sK142(X0,sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_175008]) ).
tcf(c_186682,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| subset(sK138,sK142(X0,sK91(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_174960]) ).
tcf(c_186683,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(X0,sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK142(X0,sK302(sK137,sK138))) = sK142(X0,sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_175802]) ).
tcf(c_186684,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(X0,sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK142(X0,sK302(sK137,sK138))) = sK142(X0,sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_175753]) ).
tcf(c_186685,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(X0,sK302(sK137,sK138))
| subset(sK138,sK142(X0,sK302(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_175029]) ).
tcf(c_186686,plain,
! [X0: $i] :
( disjoint(X0,sK93(sK137,the_topology(sK137)))
| in(sK142(X0,sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_175089]) ).
tcf(c_186687,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,sK93(sK137,sK147(sK137,X0)))
| in(sK142(X1,sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_175090]) ).
tcf(c_186688,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,sK93(sK137,sK125(sK137,X0)))
| in(sK142(X1,sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_417,c_175091]) ).
tcf(c_186689,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,sK93(sK137,sK123(sK137,X0)))
| in(sK142(X1,sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_175092]) ).
tcf(c_186690,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,sK91(sK137,topstr_closure(sK137,X0)))
| subset(topstr_closure(sK137,X0),sK142(X1,sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_176013]) ).
tcf(c_186691,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,sK91(sK137,topstr_closure(sK137,X0)))
| in(sK142(X1,sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_176012]) ).
tcf(c_186692,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| disjoint(X0,sK295(sK137,the_topology(sK137)))
| ( sK296(sK137,the_topology(sK137),sK142(X0,sK295(sK137,the_topology(sK137)))) = sK142(X0,sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_176134]) ).
tcf(c_186693,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| disjoint(X0,sK302(sK137,the_carrier(sK137)))
| ( sK304(sK137,the_carrier(sK137),sK142(X0,sK302(sK137,the_carrier(sK137)))) = sK142(X0,sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_176975]) ).
tcf(c_186694,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| disjoint(X0,sK302(sK137,the_carrier(sK137)))
| ( sK303(sK137,the_carrier(sK137),sK142(X0,sK302(sK137,the_carrier(sK137)))) = sK142(X0,sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_176974]) ).
tcf(c_186695,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| disjoint(X0,sK302(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK142(X0,sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_176981]) ).
tcf(c_186696,plain,
! [X0: $i] :
( disjoint(X0,sK123(sK137,the_carrier(sK137)))
| ( sK124(sK137,the_carrier(sK137),sK142(X0,sK123(sK137,the_carrier(sK137)))) = sK142(X0,sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_176971]) ).
tcf(c_186697,plain,
! [X0: $i] :
( disjoint(X0,sK123(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK142(X0,sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_176976]) ).
tcf(c_186698,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,the_carrier(sK137)))
| ( sK92(sK137,the_carrier(sK137),sK142(X0,sK91(sK137,the_carrier(sK137)))) = sK142(X0,sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_176980]) ).
tcf(c_186699,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,the_carrier(sK137)))
| in(sK142(X0,sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_176982]) ).
tcf(c_186700,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK142(X0,sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_176983]) ).
tcf(c_186701,plain,
! [X0: $i] :
( disjoint(X0,sK147(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK142(X0,sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_176978]) ).
tcf(c_186702,plain,
! [X0: $i] :
( disjoint(X0,sK147(sK137,the_carrier(sK137)))
| closed_subset(sK142(X0,sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_176977]) ).
tcf(c_186703,plain,
! [X0: $i] :
( sP34(powerset(the_carrier(sK137)),sK137)
| disjoint(X0,sK295(sK137,powerset(the_carrier(sK137))))
| ( sK296(sK137,powerset(the_carrier(sK137)),sK142(X0,sK295(sK137,powerset(the_carrier(sK137))))) = sK142(X0,sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_176995]) ).
tcf(c_186704,plain,
! [X0: $i] :
( disjoint(X0,sK93(sK137,powerset(the_carrier(sK137))))
| in(sK142(X0,sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_176997]) ).
tcf(c_186705,plain,
! [X0: $i] :
( disjoint(X0,topstr_closure(sK137,sK138))
| in(sK142(X0,topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(sK142(X0,topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_417,c_177233]) ).
tcf(c_186706,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| disjoint(X0,sK302(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK142(X0,sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_177405]) ).
tcf(c_186707,plain,
! [X0: $i] :
( disjoint(X0,sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK142(X0,sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_177400]) ).
tcf(c_186708,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK142(X0,sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK142(X0,sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_177404]) ).
tcf(c_186709,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK142(X0,sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_177407]) ).
tcf(c_186710,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| in(sK142(X0,sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_177406]) ).
tcf(c_186711,plain,
! [X0: $i] :
( disjoint(X0,sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK142(X0,sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_177402]) ).
tcf(c_186712,plain,
! [X0: $i] :
( disjoint(X0,sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| closed_subset(sK142(X0,sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_177401]) ).
tcf(c_186713,plain,
! [X0: $i] :
( disjoint(X0,sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))))
| in(sK142(X0,sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_177421]) ).
tcf(c_186714,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| disjoint(X0,sK302(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK142(X0,sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_182970]) ).
tcf(c_186715,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK91(sK137,sK207(the_carrier(sK137))))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK142(X0,sK91(sK137,sK207(the_carrier(sK137))))) = sK142(X0,sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_182969]) ).
tcf(c_186716,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK91(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK142(X0,sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_182972]) ).
tcf(c_186717,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK91(sK137,sK207(the_carrier(sK137))))
| in(sK142(X0,sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_182971]) ).
tcf(c_186718,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK147(sK137,sK207(the_carrier(sK137))))
| closed_subset(sK142(X0,sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_182966]) ).
tcf(c_186719,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| disjoint(X0,sK302(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK142(X0,sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_184375]) ).
tcf(c_186720,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK91(sK137,sK325(the_carrier(sK137))))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK142(X0,sK91(sK137,sK325(the_carrier(sK137))))) = sK142(X0,sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_184374]) ).
tcf(c_186721,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK91(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK142(X0,sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_184377]) ).
tcf(c_186722,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK91(sK137,sK325(the_carrier(sK137))))
| in(sK142(X0,sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_184376]) ).
tcf(c_186723,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK147(sK137,sK325(the_carrier(sK137))))
| closed_subset(sK142(X0,sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_184371]) ).
tcf(c_187075,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_186302,c_781]) ).
tcf(c_187076,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| element(sK142(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_186302,c_701]) ).
tcf(c_187077,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(sK91(sK137,sK138),X0)
| in(sK142(sK91(sK137,sK138),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK142(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK142(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_186302,c_176867]) ).
tcf(c_187078,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| in(sK142(sK91(sK137,sK138),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK142(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK142(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_186302,c_176193]) ).
tcf(c_187102,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_186681,c_781]) ).
tcf(c_187103,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| element(sK142(X0,sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_186681,c_701]) ).
tcf(c_187104,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(X0,sK91(sK137,sK138))
| in(sK142(X0,sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK142(X0,sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK142(X0,sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_186681,c_176867]) ).
tcf(c_187105,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| in(sK142(X0,sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK142(X0,sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK142(X0,sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_186681,c_176193]) ).
tcf(c_187145,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK142(sK91(sK137,sK138),X0)) = sK142(sK91(sK137,sK138),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_186301,c_643]) ).
tcf(c_187156,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| ( sK92(sK137,sK138,sK142(X0,sK91(sK137,sK138))) = sK142(X0,sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_186680,c_643]) ).
tcf(c_187189,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2),sK365(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2),sK366(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),X2))) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_967,c_105926]) ).
tcf(c_187191,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)) ) ),
inference(superposition,[status(thm)],[c_967,c_105926]) ).
tcf(c_187193,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(sK365(unordered_pair(powerset(empty_set),powerset(empty_set)),X0),sK365(unordered_pair(powerset(empty_set),powerset(empty_set)),X0)),unordered_pair(sK365(unordered_pair(powerset(empty_set),powerset(empty_set)),X0),sK366(unordered_pair(powerset(empty_set),powerset(empty_set)),X0))) = unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_105926]) ).
tcf(c_187194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3),sK365(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3)),unordered_pair(sK365(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3),sK366(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3))) = unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) ) ),
inference(superposition,[status(thm)],[c_105912,c_105926]) ).
tcf(c_187196,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),X1),sK365(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),X1)),unordered_pair(sK365(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),X1),sK366(unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)),X1))) = unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_105926]) ).
tcf(c_187197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3),sK365(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3)),unordered_pair(sK365(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3),sK366(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3))) = unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) ) ),
inference(superposition,[status(thm)],[c_105926,c_105926]) ).
tcf(c_187198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3),sK367(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3)),unordered_pair(sK367(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3),sK368(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3))) = unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) ) ),
inference(superposition,[status(thm)],[c_105926,c_105912]) ).
tcf(c_187199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( sK368(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3) != X3 ) ),
inference(superposition,[status(thm)],[c_105926,c_105507]) ).
tcf(c_187200,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1),sK365(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1)),unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)))
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_105926,c_183197]) ).
tcf(c_187201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( sK365(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))),X3) != X3 ) ),
inference(superposition,[status(thm)],[c_105926,c_105505]) ).
tcf(c_187202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( pair_second(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))))) = unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105926,c_516]) ).
tcf(c_187203,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( pair_first(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))))) = unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105926,c_515]) ).
tcf(c_187206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X4 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X3 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X3) ) ),
inference(superposition,[status(thm)],[c_105926,c_273]) ).
tcf(c_187207,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1),sK365(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1)),unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)))
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_105926,c_964]) ).
tcf(c_187208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ empty(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_105926,c_960]) ).
tcf(c_187209,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1),sK366(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1)),unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)))
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_105926,c_183198]) ).
tcf(c_187210,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1),sK366(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X1)),unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)))
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_105926,c_965]) ).
tcf(c_187211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X4 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105926,c_393]) ).
tcf(c_187212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105926,c_392]) ).
tcf(c_187213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X4 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X3) ) ),
inference(superposition,[status(thm)],[c_105926,c_273]) ).
tcf(c_187214,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)) = unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)) )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X2) ) ),
inference(superposition,[status(thm)],[c_105926,c_541]) ).
tcf(c_187215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)) = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X2) ) ),
inference(superposition,[status(thm)],[c_105926,c_531]) ).
tcf(c_187275,plain,
! [X0: $i] :
( ( relation_rng_restriction(X0,empty_set) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_278,c_419]) ).
tcf(c_187279,plain,
! [X0: $i] : relation_rng_restriction(X0,empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_187275,c_596]) ).
tcf(c_187287,plain,
! [X0: $i] :
( ordinal(sK267)
| being_limit_ordinal(X0)
| sP30(sK143(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_423,c_827]) ).
tcf(c_187288,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| epsilon_connected(sK143(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_423,c_1088]) ).
tcf(c_187289,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| epsilon_transitive(sK143(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_423,c_1087]) ).
tcf(c_187309,plain,
! [X0: $i] :
( ordinal(sK267)
| being_limit_ordinal(X0)
| sP30(sK144(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_426,c_827]) ).
tcf(c_187310,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| epsilon_connected(sK144(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_426,c_1088]) ).
tcf(c_187311,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| epsilon_transitive(sK144(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_426,c_1087]) ).
tcf(c_187329,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(X0,relation_rng_restriction(X1,X0)) ),
inference(superposition,[status(thm)],[c_278,c_492]) ).
tcf(c_187330,plain,
! [X0: $i] : ~ proper_subset(X0,empty_set),
inference(superposition,[status(thm)],[c_379,c_492]) ).
tcf(c_187331,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_399,c_492]) ).
tcf(c_187332,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),X0),
inference(superposition,[status(thm)],[c_518,c_492]) ).
tcf(c_187334,plain,
( topological_space(sK137)
| ~ sP42(sK137)
| ~ open_subset(the_carrier(sK137),sK137)
| ~ proper_subset(the_topology(sK137),sK378(sK137)) ),
inference(superposition,[status(thm)],[c_177301,c_492]) ).
tcf(c_187335,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ proper_subset(sK146(sK137,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_48177,c_492]) ).
tcf(c_187336,plain,
( sP3(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK62(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_178461,c_492]) ).
tcf(c_187337,plain,
( sP36(sK137,sK138)
| sP3(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK62(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_178464,c_492]) ).
tcf(c_187338,plain,
( ordinal(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK139(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_178685,c_492]) ).
tcf(c_187339,plain,
( sP36(sK137,sK138)
| ordinal(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK139(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_178688,c_492]) ).
tcf(c_187340,plain,
( relation(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK175(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_178948,c_492]) ).
tcf(c_187341,plain,
( sP36(sK137,sK138)
| relation(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK175(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_178951,c_492]) ).
tcf(c_187342,plain,
( epsilon_transitive(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK340(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_180306,c_492]) ).
tcf(c_187343,plain,
( sP36(sK137,sK138)
| epsilon_transitive(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK340(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_180309,c_492]) ).
tcf(c_187344,plain,
( epsilon_connected(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK369(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_180598,c_492]) ).
tcf(c_187345,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK369(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_180601,c_492]) ).
tcf(c_187346,plain,
( epsilon_connected(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK370(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_180851,c_492]) ).
tcf(c_187347,plain,
( sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK370(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_180854,c_492]) ).
tcf(c_187348,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),X1),
inference(superposition,[status(thm)],[c_181192,c_492]) ).
tcf(c_187351,plain,
( ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138))
| ~ proper_subset(sK185(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_182180,c_492]) ).
tcf(c_187352,plain,
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK138))
| ~ proper_subset(sK185(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_182183,c_492]) ).
tcf(c_187355,plain,
( ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138))
| ~ proper_subset(sK274(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_183904,c_492]) ).
tcf(c_187356,plain,
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK138))
| ~ proper_subset(sK274(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_183907,c_492]) ).
tcf(c_187357,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ proper_subset(sK142(sK91(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_186303,c_492]) ).
tcf(c_187358,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(sK302(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ proper_subset(sK142(sK302(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_186306,c_492]) ).
tcf(c_187359,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK142(X0,sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_186682,c_492]) ).
tcf(c_187360,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| disjoint(X0,sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ proper_subset(sK142(X0,sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_186685,c_492]) ).
tcf(c_187562,plain,
( empty(the_carrier(sK137))
| sP3(sK123(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK62(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK62(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_182965]) ).
tcf(c_187564,plain,
( empty(the_carrier(sK137))
| ordinal(sK123(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK139(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK139(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_182965]) ).
tcf(c_187565,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK123(sK137,sK207(the_carrier(sK137))),X0)
| subset(sK207(the_carrier(sK137)),sK142(sK123(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ element(sK142(sK123(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_182965]) ).
tcf(c_187566,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK123(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK142(X0,sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_182965]) ).
tcf(c_187567,plain,
( empty(the_carrier(sK137))
| relation(sK123(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK175(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK175(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_182965]) ).
tcf(c_187568,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK185(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,sK207(the_carrier(sK137))))
| ~ element(sK185(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_182965]) ).
tcf(c_187570,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK274(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,sK207(the_carrier(sK137))))
| ~ element(sK274(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_182965]) ).
tcf(c_187571,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK123(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK340(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK340(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_182965]) ).
tcf(c_187572,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK123(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK369(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK369(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_182965]) ).
tcf(c_187573,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK123(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK370(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK370(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_182965]) ).
tcf(c_187575,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(sK207(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,sK207(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_179185,c_182965]) ).
tcf(c_187731,plain,
( empty(the_carrier(sK137))
| sP3(sK147(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK62(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_182967]) ).
tcf(c_187733,plain,
( empty(the_carrier(sK137))
| ordinal(sK147(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK139(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_182967]) ).
tcf(c_187734,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK147(sK137,sK207(the_carrier(sK137))),X0)
| subset(sK207(the_carrier(sK137)),sK142(sK147(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ element(sK142(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_182967]) ).
tcf(c_187735,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK147(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK142(X0,sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_182967]) ).
tcf(c_187736,plain,
( empty(the_carrier(sK137))
| relation(sK147(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK175(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_182967]) ).
tcf(c_187737,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK185(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK185(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_182967]) ).
tcf(c_187739,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK274(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK274(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_182967]) ).
tcf(c_187740,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK147(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK340(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_182967]) ).
tcf(c_187741,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK147(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK369(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_182967]) ).
tcf(c_187742,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK147(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK370(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_182967]) ).
tcf(c_187744,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(sK207(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK207(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_179183,c_182967]) ).
tcf(c_187855,plain,
( empty(the_carrier(sK137))
| sP3(sK123(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK62(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK62(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_184370]) ).
tcf(c_187857,plain,
( empty(the_carrier(sK137))
| ordinal(sK123(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK139(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK139(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_184370]) ).
tcf(c_187858,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK123(sK137,sK325(the_carrier(sK137))),X0)
| subset(sK325(the_carrier(sK137)),sK142(sK123(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ element(sK142(sK123(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_184370]) ).
tcf(c_187859,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK123(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK142(X0,sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_184370]) ).
tcf(c_187860,plain,
( empty(the_carrier(sK137))
| relation(sK123(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK175(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK175(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_184370]) ).
tcf(c_187861,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK185(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,sK325(the_carrier(sK137))))
| ~ element(sK185(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_184370]) ).
tcf(c_187863,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK274(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,sK325(the_carrier(sK137))))
| ~ element(sK274(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_184370]) ).
tcf(c_187864,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK123(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK340(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK340(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_184370]) ).
tcf(c_187865,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK123(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK369(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK369(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_184370]) ).
tcf(c_187866,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK123(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK370(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK370(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_184370]) ).
tcf(c_187868,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(sK325(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,sK325(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_179185,c_184370]) ).
tcf(c_187987,plain,
( empty(the_carrier(sK137))
| sP3(sK147(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK62(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK62(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_184372]) ).
tcf(c_187989,plain,
( empty(the_carrier(sK137))
| ordinal(sK147(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK139(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK139(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_184372]) ).
tcf(c_187990,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(sK147(sK137,sK325(the_carrier(sK137))),X0)
| subset(sK325(the_carrier(sK137)),sK142(sK147(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ element(sK142(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_184372]) ).
tcf(c_187991,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| disjoint(X0,sK147(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK142(X0,sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK142(X0,sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_184372]) ).
tcf(c_187992,plain,
( empty(the_carrier(sK137))
| relation(sK147(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK175(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK175(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_184372]) ).
tcf(c_187993,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK185(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK185(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_184372]) ).
tcf(c_187995,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK274(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK274(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_184372]) ).
tcf(c_187996,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK147(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK340(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK340(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_184372]) ).
tcf(c_187997,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK147(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK369(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK369(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_184372]) ).
tcf(c_187998,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK147(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK370(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK370(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_184372]) ).
tcf(c_188000,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(sK325(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,sK325(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_179183,c_184372]) ).
tcf(c_188143,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,X0)),sK137)
| ~ topological_space(sK137)
| ~ empty(sK147(sK137,X0))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_781]) ).
tcf(c_188144,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,X0)),sK137)
| element(sK145(sK137,sK147(sK137,X0)),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_701]) ).
tcf(c_188145,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,the_carrier(sK137))),sK137)
| subset(the_carrier(sK137),sK145(sK137,sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(the_carrier(sK137),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_176978]) ).
tcf(c_188146,plain,
( closed_subset(sK145(sK137,sK147(sK137,the_carrier(sK137))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ element(the_carrier(sK137),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_176977]) ).
tcf(c_188147,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| subset(sK208(powerset(the_carrier(sK137))),sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK208(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_177402]) ).
tcf(c_188148,plain,
( closed_subset(sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ element(sK208(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_177401]) ).
tcf(c_188149,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| subset(sK207(the_carrier(sK137)),sK145(sK137,sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK207(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_182967]) ).
tcf(c_188150,plain,
( empty(the_carrier(sK137))
| closed_subset(sK145(sK137,sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK207(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_182966]) ).
tcf(c_188151,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| subset(sK325(the_carrier(sK137)),sK145(sK137,sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK325(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_184372]) ).
tcf(c_188152,plain,
( empty(the_carrier(sK137))
| closed_subset(sK145(sK137,sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK325(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_184371]) ).
tcf(c_188161,plain,
( closed_subset(sK145(sK137,sK147(sK137,the_carrier(sK137))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ element(sK145(sK137,sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_188146,c_13308]) ).
tcf(c_188166,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,the_carrier(sK137))),sK137)
| subset(the_carrier(sK137),sK145(sK137,sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK145(sK137,sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_188145,c_13308]) ).
tcf(c_188183,plain,
( closed_subset(sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ element(sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_188148,c_702]) ).
tcf(c_188200,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| subset(sK208(powerset(the_carrier(sK137))),sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_188147,c_702]) ).
tcf(c_188234,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( unordered_pair(X0,X1) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_967,c_178673]) ).
tcf(c_188237,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_105912,c_178673]) ).
tcf(c_188238,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_105926,c_178673]) ).
tcf(c_188241,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != powerset(empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_188238,c_52]) ).
tcf(c_188244,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != powerset(empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_188237,c_52]) ).
tcf(c_188251,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(X0,relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_524,c_492]) ).
tcf(c_188252,plain,
! [X0: $i] :
( ( relation_dom_restriction(empty_set,X0) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_524,c_419]) ).
tcf(c_188253,plain,
! [X0: $i] : relation_dom_restriction(empty_set,X0) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_188252,c_596]) ).
tcf(c_188287,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ proper_subset(union(X0),X1) ),
inference(superposition,[status(thm)],[c_533,c_492]) ).
tcf(c_188288,plain,
! [X0: $i] :
( epsilon_transitive(union(X0))
| ~ in(sK340(union(X0)),X0) ),
inference(superposition,[status(thm)],[c_533,c_1080]) ).
tcf(c_188320,plain,
! [X0: $i] :
( sP3(X0)
| in(sK154(X0),X0) ),
inference(superposition,[status(thm)],[c_120,c_542]) ).
tcf(c_188321,plain,
in(sK154(omega),omega),
inference(superposition,[status(thm)],[c_841,c_542]) ).
tcf(c_188325,plain,
! [X0: $i] : in(sK154(set_union2(X0,unordered_pair(X0,X0))),set_union2(X0,unordered_pair(X0,X0))),
inference(superposition,[status(thm)],[c_272,c_542]) ).
tcf(c_188326,plain,
! [X0: $i] : in(sK154(sK126(X0)),sK126(X0)),
inference(superposition,[status(thm)],[c_288,c_542]) ).
tcf(c_188327,plain,
! [X0: $i] :
( ordinal(X0)
| in(sK154(X0),X0) ),
inference(superposition,[status(thm)],[c_383,c_542]) ).
tcf(c_188328,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK154(X0),X0) ),
inference(superposition,[status(thm)],[c_416,c_542]) ).
tcf(c_188329,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| in(sK154(X0),X0) ),
inference(superposition,[status(thm)],[c_417,c_542]) ).
tcf(c_188330,plain,
! [X0: $i] :
( relation(X0)
| in(sK154(X0),X0) ),
inference(superposition,[status(thm)],[c_580,c_542]) ).
tcf(c_188331,plain,
! [X0: $i] :
( in(sK154(X0),X0)
| ~ sP20(X0) ),
inference(superposition,[status(thm)],[c_603,c_542]) ).
tcf(c_188333,plain,
! [X0: $i] :
( in(sK154(X0),X0)
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_858,c_542]) ).
tcf(c_188334,plain,
! [X0: $i,X1: $i] : in(sK154(unordered_pair(X0,X1)),unordered_pair(X0,X1)),
inference(superposition,[status(thm)],[c_964,c_542]) ).
tcf(c_188336,plain,
! [X0: $i] : in(sK154(sK323(X0)),sK323(X0)),
inference(superposition,[status(thm)],[c_997,c_542]) ).
tcf(c_188337,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK154(X0),X0) ),
inference(superposition,[status(thm)],[c_1081,c_542]) ).
tcf(c_188338,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK154(X0),X0) ),
inference(superposition,[status(thm)],[c_1253,c_542]) ).
tcf(c_188342,plain,
in(sK154(powerset(empty_set)),powerset(empty_set)),
inference(superposition,[status(thm)],[c_178672,c_542]) ).
tcf(c_188343,plain,
( in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(the_carrier(sK137),sK137) ),
inference(superposition,[status(thm)],[c_176994,c_542]) ).
tcf(c_188344,plain,
! [X0: $i] :
( in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ topological_space(sK137)
| ~ subset(X0,the_topology(sK137))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_47816,c_542]) ).
tcf(c_188345,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47965,c_542]) ).
tcf(c_188346,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK137)
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48019,c_542]) ).
tcf(c_188347,plain,
( in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(sK138,sK137) ),
inference(superposition,[status(thm)],[c_174884,c_542]) ).
tcf(c_188348,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,X0)),sK137)
| in(sK154(sK147(sK137,X0)),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_542]) ).
tcf(c_188349,plain,
( in(sK154(sK147(sK137,sK138)),sK147(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_184219,c_542]) ).
tcf(c_188350,plain,
( in(sK154(sK147(sK137,sK138)),sK147(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(superposition,[status(thm)],[c_176354,c_542]) ).
tcf(c_188351,plain,
( in(sK154(sK123(sK137,sK138)),sK123(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_182784,c_542]) ).
tcf(c_188352,plain,
( in(sK154(sK123(sK137,sK138)),sK123(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(superposition,[status(thm)],[c_176589,c_542]) ).
tcf(c_188353,plain,
! [X0: $i] :
( in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(topstr_closure(sK137,X0),sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176021,c_542]) ).
tcf(c_188354,plain,
! [X0: $i] :
( in(sK154(sK123(sK137,X0)),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180215,c_542]) ).
tcf(c_188355,plain,
! [X0: $i] :
( in(sK154(sK147(sK137,X0)),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180246,c_542]) ).
tcf(c_188356,plain,
! [X0: $i] :
( in(sK154(sK91(sK137,the_carrier(sK137))),sK91(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(the_carrier(sK137),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176973,c_542]) ).
tcf(c_188357,plain,
( in(sK154(sK123(sK137,the_carrier(sK137))),sK123(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138) ),
inference(superposition,[status(thm)],[c_176984,c_542]) ).
tcf(c_188358,plain,
( in(sK154(sK147(sK137,the_carrier(sK137))),sK147(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138) ),
inference(superposition,[status(thm)],[c_176986,c_542]) ).
tcf(c_188359,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),powerset(the_carrier(sK137))),sK137)
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_176998,c_542]) ).
tcf(c_188360,plain,
( in(sK154(sK123(sK137,sK208(powerset(the_carrier(sK137))))),sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_177408,c_542]) ).
tcf(c_188361,plain,
( in(sK154(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_177410,c_542]) ).
tcf(c_188362,plain,
( in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(sK208(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_177418,c_542]) ).
tcf(c_188363,plain,
( sP3(sK91(sK137,sK138))
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178460,c_542]) ).
tcf(c_188364,plain,
( ordinal(sK91(sK137,sK138))
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178684,c_542]) ).
tcf(c_188365,plain,
( relation(sK91(sK137,sK138))
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178947,c_542]) ).
tcf(c_188366,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_180142,c_542]) ).
tcf(c_188367,plain,
! [X0: $i] :
( in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_179182,c_542]) ).
tcf(c_188368,plain,
! [X0: $i,X1: $i] :
( in(sK154(sK147(sK137,X1)),sK147(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,X1))) ),
inference(superposition,[status(thm)],[c_179183,c_542]) ).
tcf(c_188369,plain,
! [X0: $i,X1: $i] :
( in(sK154(sK123(sK137,X1)),sK123(sK137,X1))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,X1))) ),
inference(superposition,[status(thm)],[c_179185,c_542]) ).
tcf(c_188370,plain,
( epsilon_transitive(sK91(sK137,sK138))
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_180305,c_542]) ).
tcf(c_188371,plain,
( epsilon_connected(sK91(sK137,sK138))
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_180597,c_542]) ).
tcf(c_188374,plain,
( in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_182179,c_542]) ).
tcf(c_188376,plain,
( empty(the_carrier(sK137))
| in(sK154(sK123(sK137,sK207(the_carrier(sK137)))),sK123(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_182976,c_542]) ).
tcf(c_188377,plain,
( empty(the_carrier(sK137))
| in(sK154(sK147(sK137,sK207(the_carrier(sK137)))),sK147(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_182978,c_542]) ).
tcf(c_188378,plain,
( empty(the_carrier(sK137))
| in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(sK207(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_182986,c_542]) ).
tcf(c_188379,plain,
( in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183903,c_542]) ).
tcf(c_188380,plain,
( empty(the_carrier(sK137))
| in(sK154(sK123(sK137,sK325(the_carrier(sK137)))),sK123(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_184382,c_542]) ).
tcf(c_188381,plain,
( empty(the_carrier(sK137))
| in(sK154(sK147(sK137,sK325(the_carrier(sK137)))),sK147(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_184384,c_542]) ).
tcf(c_188382,plain,
( empty(the_carrier(sK137))
| in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(sK325(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_184392,c_542]) ).
tcf(c_188383,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_186302,c_542]) ).
tcf(c_188384,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_186681,c_542]) ).
tcf(c_188644,plain,
! [X0: $i] :
( sP3(X0)
| ~ in(X0,sK62(X0)) ),
inference(superposition,[status(thm)],[c_120,c_546]) ).
tcf(c_188645,plain,
~ in(omega,empty_set),
inference(superposition,[status(thm)],[c_841,c_546]) ).
tcf(c_188646,plain,
( ~ sP6
| ~ in(omega,sK70) ),
inference(superposition,[status(thm)],[c_138,c_546]) ).
tcf(c_188648,plain,
( ~ sP15
| ~ in(omega,sK117) ),
inference(superposition,[status(thm)],[c_245,c_546]) ).
tcf(c_188649,plain,
! [X0: $i] : ~ in(set_union2(X0,unordered_pair(X0,X0)),X0),
inference(superposition,[status(thm)],[c_272,c_546]) ).
tcf(c_188650,plain,
! [X0: $i] : ~ in(sK126(X0),X0),
inference(superposition,[status(thm)],[c_288,c_546]) ).
tcf(c_188651,plain,
! [X0: $i] :
( ordinal(X0)
| ~ in(X0,sK139(X0)) ),
inference(superposition,[status(thm)],[c_383,c_546]) ).
tcf(c_188652,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ in(X0,sK142(X0,X1)) ),
inference(superposition,[status(thm)],[c_416,c_546]) ).
tcf(c_188653,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ in(X0,sK142(X1,X0)) ),
inference(superposition,[status(thm)],[c_417,c_546]) ).
tcf(c_188654,plain,
! [X0: $i] :
( relation(X0)
| ~ in(X0,sK175(X0)) ),
inference(superposition,[status(thm)],[c_580,c_546]) ).
tcf(c_188655,plain,
! [X0: $i] :
( ~ sP20(X0)
| ~ in(X0,sK185(X0)) ),
inference(superposition,[status(thm)],[c_603,c_546]) ).
tcf(c_188657,plain,
! [X0: $i] :
( ~ sP32(X0)
| ~ in(X0,sK274(X0)) ),
inference(superposition,[status(thm)],[c_858,c_546]) ).
tcf(c_188658,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,X1),X0),
inference(superposition,[status(thm)],[c_964,c_546]) ).
tcf(c_188659,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,X1),X1),
inference(superposition,[status(thm)],[c_965,c_546]) ).
tcf(c_188660,plain,
! [X0: $i] : ~ in(sK323(X0),X0),
inference(superposition,[status(thm)],[c_997,c_546]) ).
tcf(c_188661,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ in(X0,sK340(X0)) ),
inference(superposition,[status(thm)],[c_1081,c_546]) ).
tcf(c_188662,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(X0,sK369(X0)) ),
inference(superposition,[status(thm)],[c_1253,c_546]) ).
tcf(c_188663,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(X0,sK370(X0)) ),
inference(superposition,[status(thm)],[c_1254,c_546]) ).
tcf(c_188666,plain,
~ in(powerset(empty_set),empty_set),
inference(superposition,[status(thm)],[c_178672,c_546]) ).
tcf(c_188667,plain,
( ~ open_subset(the_carrier(sK137),sK137)
| ~ in(the_topology(sK137),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_176994,c_546]) ).
tcf(c_188668,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ subset(X0,the_topology(sK137))
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ in(the_topology(sK137),union_of_subsets(the_carrier(sK137),X0)) ),
inference(superposition,[status(thm)],[c_47816,c_546]) ).
tcf(c_188669,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK302(sK137,X0))
| ~ in(powerset(the_carrier(sK137)),sK303(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_47965,c_546]) ).
tcf(c_188670,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK137)
| ~ topological_space(sK137)
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ in(powerset(the_carrier(sK137)),sK296(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_48019,c_546]) ).
tcf(c_188671,plain,
( ~ open_subset(sK138,sK137)
| ~ in(the_topology(sK137),sK138) ),
inference(superposition,[status(thm)],[c_174884,c_546]) ).
tcf(c_188672,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,X0)),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(sK147(sK137,X0),sK145(sK137,sK147(sK137,X0))) ),
inference(superposition,[status(thm)],[c_175059,c_546]) ).
tcf(c_188673,plain,
( ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ in(sK147(sK137,sK138),empty_set) ),
inference(superposition,[status(thm)],[c_184219,c_546]) ).
tcf(c_188674,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ in(sK147(sK137,sK138),sK138) ),
inference(superposition,[status(thm)],[c_176354,c_546]) ).
tcf(c_188675,plain,
( ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ in(sK123(sK137,sK138),empty_set) ),
inference(superposition,[status(thm)],[c_182784,c_546]) ).
tcf(c_188676,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ in(sK123(sK137,sK138),sK138) ),
inference(superposition,[status(thm)],[c_176589,c_546]) ).
tcf(c_188677,plain,
! [X0: $i] :
( ~ open_subset(topstr_closure(sK137,X0),sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(the_topology(sK137),topstr_closure(sK137,X0)) ),
inference(superposition,[status(thm)],[c_176021,c_546]) ).
tcf(c_188678,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(sK123(sK137,X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_180215,c_546]) ).
tcf(c_188679,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(sK147(sK137,X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_180246,c_546]) ).
tcf(c_188680,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(the_carrier(sK137),X0)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ in(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_176973,c_546]) ).
tcf(c_188681,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138)
| ~ in(sK123(sK137,the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_176984,c_546]) ).
tcf(c_188682,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138)
| ~ in(sK147(sK137,the_carrier(sK137)),sK138) ),
inference(superposition,[status(thm)],[c_176986,c_546]) ).
tcf(c_188683,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),powerset(the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK145(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_176998,c_546]) ).
tcf(c_188684,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138)
| ~ in(sK123(sK137,sK208(powerset(the_carrier(sK137)))),sK138) ),
inference(superposition,[status(thm)],[c_177408,c_546]) ).
tcf(c_188685,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138)
| ~ in(sK147(sK137,sK208(powerset(the_carrier(sK137)))),sK138) ),
inference(superposition,[status(thm)],[c_177410,c_546]) ).
tcf(c_188686,plain,
( ~ open_subset(sK208(powerset(the_carrier(sK137))),sK137)
| ~ in(the_topology(sK137),sK208(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_177418,c_546]) ).
tcf(c_188687,plain,
( sP3(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK62(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178460,c_546]) ).
tcf(c_188688,plain,
( ordinal(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK139(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178684,c_546]) ).
tcf(c_188689,plain,
( relation(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK175(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178947,c_546]) ).
tcf(c_188690,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,the_topology(sK137)))
| ~ in(the_topology(sK137),set_difference(the_carrier(sK137),X0)) ),
inference(superposition,[status(thm)],[c_180142,c_546]) ).
tcf(c_188691,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,the_topology(sK137)))
| ~ in(the_topology(sK137),set_difference(the_carrier(sK137),X0)) ),
inference(superposition,[status(thm)],[c_179182,c_546]) ).
tcf(c_188692,plain,
! [X0: $i,X1: $i] :
( ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK93(sK137,sK147(sK137,X0)))
| ~ in(sK147(sK137,X0),set_difference(the_carrier(sK137),X1)) ),
inference(superposition,[status(thm)],[c_179183,c_546]) ).
tcf(c_188693,plain,
! [X0: $i,X1: $i] :
( ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X1,sK93(sK137,sK123(sK137,X0)))
| ~ in(sK123(sK137,X0),set_difference(the_carrier(sK137),X1)) ),
inference(superposition,[status(thm)],[c_179185,c_546]) ).
tcf(c_188694,plain,
( epsilon_transitive(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK340(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180305,c_546]) ).
tcf(c_188695,plain,
( epsilon_connected(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK369(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180597,c_546]) ).
tcf(c_188696,plain,
( epsilon_connected(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK370(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180850,c_546]) ).
tcf(c_188698,plain,
( ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138))
| ~ in(powerset(the_carrier(sK137)),sK185(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_182179,c_546]) ).
tcf(c_188700,plain,
( empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138)
| ~ in(sK123(sK137,sK207(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_182976,c_546]) ).
tcf(c_188701,plain,
( empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138)
| ~ in(sK147(sK137,sK207(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_182978,c_546]) ).
tcf(c_188702,plain,
( empty(the_carrier(sK137))
| ~ open_subset(sK207(the_carrier(sK137)),sK137)
| ~ in(the_topology(sK137),sK207(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_182986,c_546]) ).
tcf(c_188703,plain,
( ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138))
| ~ in(powerset(the_carrier(sK137)),sK274(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_183903,c_546]) ).
tcf(c_188704,plain,
( empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138)
| ~ in(sK123(sK137,sK325(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_184382,c_546]) ).
tcf(c_188705,plain,
( empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138)
| ~ in(sK147(sK137,sK325(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_184384,c_546]) ).
tcf(c_188706,plain,
( empty(the_carrier(sK137))
| ~ open_subset(sK325(the_carrier(sK137)),sK137)
| ~ in(the_topology(sK137),sK325(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_184392,c_546]) ).
tcf(c_188707,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK142(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_186302,c_546]) ).
tcf(c_188708,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK142(X0,sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_186681,c_546]) ).
tcf(c_188970,plain,
~ in(omega,sK154(omega)),
inference(superposition,[status(thm)],[c_188321,c_546]) ).
tcf(c_188973,plain,
element(sK154(omega),omega),
inference(superposition,[status(thm)],[c_188321,c_701]) ).
tcf(c_188974,plain,
ordinal(sK154(omega)),
inference(superposition,[status(thm)],[c_188973,c_852]) ).
tcf(c_188975,plain,
epsilon_connected(sK154(omega)),
inference(superposition,[status(thm)],[c_188973,c_851]) ).
tcf(c_188976,plain,
epsilon_transitive(sK154(omega)),
inference(superposition,[status(thm)],[c_188973,c_850]) ).
tcf(c_188986,plain,
( ordinal(sK267)
| sP30(sK154(omega)) ),
inference(superposition,[status(thm)],[c_188974,c_827]) ).
tcf(c_188999,plain,
( ~ open_subset(sK138,sK137)
| ~ in(the_topology(sK137),sK154(the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_188347,c_546]) ).
tcf(c_189002,plain,
( element(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(sK138,sK137) ),
inference(superposition,[status(thm)],[c_188347,c_701]) ).
tcf(c_189015,plain,
( ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ in(sK147(sK137,sK138),sK154(sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_188349,c_546]) ).
tcf(c_189018,plain,
( element(sK154(sK147(sK137,sK138)),sK147(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_188349,c_701]) ).
tcf(c_189035,plain,
( ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ in(sK123(sK137,sK138),sK154(sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_188351,c_546]) ).
tcf(c_189038,plain,
( element(sK154(sK123(sK137,sK138)),sK123(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_188351,c_701]) ).
tcf(c_189060,plain,
( in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ topological_space(sK137) ),
inference(global_subsumption_just,[status(thm)],[c_188344,c_47403,c_176993,c_188343]) ).
tcf(c_189066,plain,
( ~ topological_space(sK137)
| ~ in(the_topology(sK137),sK154(the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_189060,c_546]) ).
tcf(c_189069,plain,
( element(sK154(the_topology(sK137)),the_topology(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_189060,c_701]) ).
tcf(c_189090,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,X0)),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(sK123(sK137,X0),sK145(sK137,sK123(sK137,X0))) ),
inference(superposition,[status(thm)],[c_175061,c_546]) ).
tcf(c_189091,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,X0)),sK137)
| in(sK154(sK123(sK137,X0)),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175061,c_542]) ).
tcf(c_189092,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,X0)),sK137)
| ~ topological_space(sK137)
| ~ empty(sK123(sK137,X0))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175061,c_781]) ).
tcf(c_189093,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,X0)),sK137)
| element(sK145(sK137,sK123(sK137,X0)),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175061,c_701]) ).
tcf(c_189094,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,the_carrier(sK137))),sK137)
| ( sK124(sK137,the_carrier(sK137),sK145(sK137,sK123(sK137,the_carrier(sK137)))) = sK145(sK137,sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(the_carrier(sK137),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175061,c_176971]) ).
tcf(c_189095,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,the_carrier(sK137))),sK137)
| subset(the_carrier(sK137),sK145(sK137,sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(the_carrier(sK137),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175061,c_176976]) ).
tcf(c_189096,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| subset(sK208(powerset(the_carrier(sK137))),sK145(sK137,sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK208(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175061,c_177400]) ).
tcf(c_189097,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK207(the_carrier(sK137)))),sK137)
| subset(sK207(the_carrier(sK137)),sK145(sK137,sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK207(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175061,c_182965]) ).
tcf(c_189098,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK325(the_carrier(sK137)))),sK137)
| subset(sK325(the_carrier(sK137)),sK145(sK137,sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK325(the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175061,c_184370]) ).
tcf(c_189115,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,the_carrier(sK137))),sK137)
| subset(the_carrier(sK137),sK145(sK137,sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK145(sK137,sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_189095,c_13308]) ).
tcf(c_189132,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,the_carrier(sK137))),sK137)
| ( sK124(sK137,the_carrier(sK137),sK145(sK137,sK123(sK137,the_carrier(sK137)))) = sK145(sK137,sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(sK145(sK137,sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_189094,c_13308]) ).
tcf(c_189137,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| subset(sK208(powerset(the_carrier(sK137))),sK145(sK137,sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK145(sK137,sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_189096,c_702]) ).
tcf(c_189165,plain,
! [X0: $i,X1: $i] :
( reflexive(sK103(X0,X1))
| ~ sP12(X0,X1)
| ~ well_ordering(sK103(X0,X1)) ),
inference(superposition,[status(thm)],[c_215,c_589]) ).
tcf(c_189166,plain,
! [X0: $i] :
( sP13(X0)
| reflexive(sK115(X0))
| ~ well_ordering(sK115(X0)) ),
inference(superposition,[status(thm)],[c_237,c_589]) ).
tcf(c_189167,plain,
! [X0: $i] :
( reflexive(sK122(X0))
| ~ well_ordering(sK122(X0)) ),
inference(superposition,[status(thm)],[c_256,c_589]) ).
tcf(c_189168,plain,
! [X0: $i] :
( reflexive(sK134(X0))
| ~ well_ordering(sK134(X0)) ),
inference(superposition,[status(thm)],[c_362,c_589]) ).
tcf(c_189169,plain,
! [X0: $i] :
( reflexive(identity_relation(X0))
| ~ well_ordering(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1156,c_589]) ).
tcf(c_189170,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_767,c_589]) ).
tcf(c_189171,plain,
( reflexive(empty_set)
| ~ well_ordering(empty_set) ),
inference(superposition,[status(thm)],[c_596,c_589]) ).
tcf(c_189172,plain,
! [X0: $i] :
( reflexive(relation_dom(X0))
| ~ empty(X0)
| ~ well_ordering(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_647,c_589]) ).
tcf(c_189173,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ well_ordering(relation_rng_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_651,c_589]) ).
tcf(c_189174,plain,
( reflexive(sK246)
| ~ well_ordering(sK246) ),
inference(superposition,[status(thm)],[c_777,c_589]) ).
tcf(c_189175,plain,
( reflexive(sK248)
| ~ well_ordering(sK248) ),
inference(superposition,[status(thm)],[c_785,c_589]) ).
tcf(c_189176,plain,
! [X0: $i] :
( reflexive(sK270(X0))
| ~ finite(X0)
| ~ well_ordering(sK270(X0)) ),
inference(superposition,[status(thm)],[c_846,c_589]) ).
tcf(c_189177,plain,
! [X0: $i] :
( reflexive(relation_rng(X0))
| ~ empty(X0)
| ~ well_ordering(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_969,c_589]) ).
tcf(c_189178,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_1045,c_589]) ).
tcf(c_189179,plain,
! [X0: $i,X1: $i] :
( reflexive(sK336(X0,X1))
| ~ well_ordering(sK336(X0,X1)) ),
inference(superposition,[status(thm)],[c_1057,c_589]) ).
tcf(c_189181,plain,
! [X0: $i] :
( reflexive(relation_inverse(X0))
| ~ relation(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1168,c_589]) ).
tcf(c_189182,plain,
! [X0: $i] :
( reflexive(relation_inverse(X0))
| ~ empty(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1167,c_589]) ).
tcf(c_189183,plain,
( reflexive(sK361)
| ~ well_ordering(sK361) ),
inference(superposition,[status(thm)],[c_1197,c_589]) ).
tcf(c_189184,plain,
! [X0: $i,X1: $i] :
( reflexive(sK373(X0,X1))
| ~ well_ordering(sK373(X0,X1)) ),
inference(superposition,[status(thm)],[c_1283,c_589]) ).
tcf(c_189185,plain,
( reflexive(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK175(sK91(sK137,sK138))) = sK175(sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178946,c_589]) ).
tcf(c_189186,plain,
( sP36(sK137,sK138)
| reflexive(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178950,c_589]) ).
tcf(c_189187,plain,
( sP36(sK137,sK138)
| reflexive(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178949,c_589]) ).
tcf(c_189294,plain,
! [X0: $i,X1: $i] :
( transitive(sK103(X0,X1))
| ~ sP12(X0,X1)
| ~ well_ordering(sK103(X0,X1)) ),
inference(superposition,[status(thm)],[c_215,c_590]) ).
tcf(c_189295,plain,
! [X0: $i] :
( sP13(X0)
| transitive(sK115(X0))
| ~ well_ordering(sK115(X0)) ),
inference(superposition,[status(thm)],[c_237,c_590]) ).
tcf(c_189296,plain,
! [X0: $i] :
( transitive(sK122(X0))
| ~ well_ordering(sK122(X0)) ),
inference(superposition,[status(thm)],[c_256,c_590]) ).
tcf(c_189297,plain,
! [X0: $i] :
( transitive(sK134(X0))
| ~ well_ordering(sK134(X0)) ),
inference(superposition,[status(thm)],[c_362,c_590]) ).
tcf(c_189298,plain,
! [X0: $i] :
( transitive(identity_relation(X0))
| ~ well_ordering(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1156,c_590]) ).
tcf(c_189299,plain,
! [X0: $i,X1: $i] :
( transitive(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_767,c_590]) ).
tcf(c_189300,plain,
( transitive(empty_set)
| ~ well_ordering(empty_set) ),
inference(superposition,[status(thm)],[c_596,c_590]) ).
tcf(c_189301,plain,
! [X0: $i] :
( transitive(relation_dom(X0))
| ~ empty(X0)
| ~ well_ordering(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_647,c_590]) ).
tcf(c_189302,plain,
! [X0: $i,X1: $i] :
( transitive(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ well_ordering(relation_rng_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_651,c_590]) ).
tcf(c_189303,plain,
( transitive(sK246)
| ~ well_ordering(sK246) ),
inference(superposition,[status(thm)],[c_777,c_590]) ).
tcf(c_189304,plain,
( transitive(sK248)
| ~ well_ordering(sK248) ),
inference(superposition,[status(thm)],[c_785,c_590]) ).
tcf(c_189305,plain,
! [X0: $i] :
( transitive(sK270(X0))
| ~ finite(X0)
| ~ well_ordering(sK270(X0)) ),
inference(superposition,[status(thm)],[c_846,c_590]) ).
tcf(c_189306,plain,
! [X0: $i] :
( transitive(relation_rng(X0))
| ~ empty(X0)
| ~ well_ordering(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_969,c_590]) ).
tcf(c_189307,plain,
! [X0: $i,X1: $i] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_1045,c_590]) ).
tcf(c_189308,plain,
! [X0: $i,X1: $i] :
( transitive(sK336(X0,X1))
| ~ well_ordering(sK336(X0,X1)) ),
inference(superposition,[status(thm)],[c_1057,c_590]) ).
tcf(c_189310,plain,
! [X0: $i] :
( transitive(relation_inverse(X0))
| ~ relation(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1168,c_590]) ).
tcf(c_189311,plain,
! [X0: $i] :
( transitive(relation_inverse(X0))
| ~ empty(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1167,c_590]) ).
tcf(c_189312,plain,
( transitive(sK361)
| ~ well_ordering(sK361) ),
inference(superposition,[status(thm)],[c_1197,c_590]) ).
tcf(c_189313,plain,
! [X0: $i,X1: $i] :
( transitive(sK373(X0,X1))
| ~ well_ordering(sK373(X0,X1)) ),
inference(superposition,[status(thm)],[c_1283,c_590]) ).
tcf(c_189314,plain,
( transitive(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK175(sK91(sK137,sK138))) = sK175(sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178946,c_590]) ).
tcf(c_189315,plain,
( sP36(sK137,sK138)
| transitive(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178950,c_590]) ).
tcf(c_189316,plain,
( sP36(sK137,sK138)
| transitive(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178949,c_590]) ).
tcf(c_189431,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK103(X0,X1))
| ~ sP12(X0,X1)
| ~ well_ordering(sK103(X0,X1)) ),
inference(superposition,[status(thm)],[c_215,c_591]) ).
tcf(c_189432,plain,
! [X0: $i] :
( sP13(X0)
| antisymmetric(sK115(X0))
| ~ well_ordering(sK115(X0)) ),
inference(superposition,[status(thm)],[c_237,c_591]) ).
tcf(c_189433,plain,
! [X0: $i] :
( antisymmetric(sK122(X0))
| ~ well_ordering(sK122(X0)) ),
inference(superposition,[status(thm)],[c_256,c_591]) ).
tcf(c_189434,plain,
! [X0: $i] :
( antisymmetric(sK134(X0))
| ~ well_ordering(sK134(X0)) ),
inference(superposition,[status(thm)],[c_362,c_591]) ).
tcf(c_189435,plain,
! [X0: $i] :
( antisymmetric(identity_relation(X0))
| ~ well_ordering(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1156,c_591]) ).
tcf(c_189436,plain,
! [X0: $i,X1: $i] :
( antisymmetric(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_767,c_591]) ).
tcf(c_189437,plain,
( antisymmetric(empty_set)
| ~ well_ordering(empty_set) ),
inference(superposition,[status(thm)],[c_596,c_591]) ).
tcf(c_189438,plain,
! [X0: $i] :
( antisymmetric(relation_dom(X0))
| ~ empty(X0)
| ~ well_ordering(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_647,c_591]) ).
tcf(c_189439,plain,
! [X0: $i,X1: $i] :
( antisymmetric(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ well_ordering(relation_rng_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_651,c_591]) ).
tcf(c_189440,plain,
( antisymmetric(sK246)
| ~ well_ordering(sK246) ),
inference(superposition,[status(thm)],[c_777,c_591]) ).
tcf(c_189441,plain,
( antisymmetric(sK248)
| ~ well_ordering(sK248) ),
inference(superposition,[status(thm)],[c_785,c_591]) ).
tcf(c_189442,plain,
! [X0: $i] :
( antisymmetric(sK270(X0))
| ~ finite(X0)
| ~ well_ordering(sK270(X0)) ),
inference(superposition,[status(thm)],[c_846,c_591]) ).
tcf(c_189443,plain,
! [X0: $i] :
( antisymmetric(relation_rng(X0))
| ~ empty(X0)
| ~ well_ordering(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_969,c_591]) ).
tcf(c_189444,plain,
! [X0: $i,X1: $i] :
( antisymmetric(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_1045,c_591]) ).
tcf(c_189445,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK336(X0,X1))
| ~ well_ordering(sK336(X0,X1)) ),
inference(superposition,[status(thm)],[c_1057,c_591]) ).
tcf(c_189447,plain,
! [X0: $i] :
( antisymmetric(relation_inverse(X0))
| ~ relation(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1168,c_591]) ).
tcf(c_189448,plain,
! [X0: $i] :
( antisymmetric(relation_inverse(X0))
| ~ empty(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1167,c_591]) ).
tcf(c_189449,plain,
( antisymmetric(sK361)
| ~ well_ordering(sK361) ),
inference(superposition,[status(thm)],[c_1197,c_591]) ).
tcf(c_189450,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK373(X0,X1))
| ~ well_ordering(sK373(X0,X1)) ),
inference(superposition,[status(thm)],[c_1283,c_591]) ).
tcf(c_189451,plain,
( antisymmetric(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK175(sK91(sK137,sK138))) = sK175(sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178946,c_591]) ).
tcf(c_189452,plain,
( sP36(sK137,sK138)
| antisymmetric(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178950,c_591]) ).
tcf(c_189453,plain,
( sP36(sK137,sK138)
| antisymmetric(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178949,c_591]) ).
tcf(c_189558,plain,
! [X0: $i,X1: $i] :
( connected(sK103(X0,X1))
| ~ sP12(X0,X1)
| ~ well_ordering(sK103(X0,X1)) ),
inference(superposition,[status(thm)],[c_215,c_592]) ).
tcf(c_189559,plain,
! [X0: $i] :
( sP13(X0)
| connected(sK115(X0))
| ~ well_ordering(sK115(X0)) ),
inference(superposition,[status(thm)],[c_237,c_592]) ).
tcf(c_189560,plain,
! [X0: $i] :
( connected(sK122(X0))
| ~ well_ordering(sK122(X0)) ),
inference(superposition,[status(thm)],[c_256,c_592]) ).
tcf(c_189561,plain,
! [X0: $i] :
( connected(sK134(X0))
| ~ well_ordering(sK134(X0)) ),
inference(superposition,[status(thm)],[c_362,c_592]) ).
tcf(c_189562,plain,
! [X0: $i] :
( connected(identity_relation(X0))
| ~ well_ordering(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1156,c_592]) ).
tcf(c_189563,plain,
! [X0: $i,X1: $i] :
( connected(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_767,c_592]) ).
tcf(c_189564,plain,
( connected(empty_set)
| ~ well_ordering(empty_set) ),
inference(superposition,[status(thm)],[c_596,c_592]) ).
tcf(c_189565,plain,
! [X0: $i] :
( connected(relation_dom(X0))
| ~ empty(X0)
| ~ well_ordering(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_647,c_592]) ).
tcf(c_189566,plain,
! [X0: $i,X1: $i] :
( connected(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ well_ordering(relation_rng_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_651,c_592]) ).
tcf(c_189567,plain,
( connected(sK246)
| ~ well_ordering(sK246) ),
inference(superposition,[status(thm)],[c_777,c_592]) ).
tcf(c_189568,plain,
( connected(sK248)
| ~ well_ordering(sK248) ),
inference(superposition,[status(thm)],[c_785,c_592]) ).
tcf(c_189569,plain,
! [X0: $i] :
( connected(sK270(X0))
| ~ finite(X0)
| ~ well_ordering(sK270(X0)) ),
inference(superposition,[status(thm)],[c_846,c_592]) ).
tcf(c_189570,plain,
! [X0: $i] :
( connected(relation_rng(X0))
| ~ empty(X0)
| ~ well_ordering(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_969,c_592]) ).
tcf(c_189571,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_1045,c_592]) ).
tcf(c_189572,plain,
! [X0: $i,X1: $i] :
( connected(sK336(X0,X1))
| ~ well_ordering(sK336(X0,X1)) ),
inference(superposition,[status(thm)],[c_1057,c_592]) ).
tcf(c_189573,plain,
! [X0: $i] :
( connected(inclusion_relation(X0))
| ~ well_ordering(inclusion_relation(X0)) ),
inference(superposition,[status(thm)],[c_1146,c_592]) ).
tcf(c_189574,plain,
! [X0: $i] :
( connected(relation_inverse(X0))
| ~ relation(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1168,c_592]) ).
tcf(c_189575,plain,
! [X0: $i] :
( connected(relation_inverse(X0))
| ~ empty(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1167,c_592]) ).
tcf(c_189576,plain,
( connected(sK361)
| ~ well_ordering(sK361) ),
inference(superposition,[status(thm)],[c_1197,c_592]) ).
tcf(c_189577,plain,
! [X0: $i,X1: $i] :
( connected(sK373(X0,X1))
| ~ well_ordering(sK373(X0,X1)) ),
inference(superposition,[status(thm)],[c_1283,c_592]) ).
tcf(c_189578,plain,
( connected(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK175(sK91(sK137,sK138))) = sK175(sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178946,c_592]) ).
tcf(c_189579,plain,
( sP36(sK137,sK138)
| connected(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178950,c_592]) ).
tcf(c_189580,plain,
( sP36(sK137,sK138)
| connected(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178949,c_592]) ).
tcf(c_189709,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK126(sK91(sK137,the_carrier(sK137))),sK137)
| ~ subset(the_carrier(sK137),sK126(sK91(sK137,the_carrier(sK137))))
| ~ in(sK126(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176973,c_188650]) ).
tcf(c_189714,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK323(sK91(sK137,the_carrier(sK137))),sK137)
| ~ subset(the_carrier(sK137),sK323(sK91(sK137,the_carrier(sK137))))
| ~ in(sK323(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176973,c_188660]) ).
tcf(c_189729,plain,
! [X0: $i] :
( sP3(sK147(sK137,topstr_closure(sK137,X0)))
| closed_subset(sK62(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(sK62(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_176007]) ).
tcf(c_189731,plain,
! [X0: $i] :
( ordinal(sK147(sK137,topstr_closure(sK137,X0)))
| closed_subset(sK139(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(sK139(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_176007]) ).
tcf(c_189732,plain,
! [X0: $i,X1: $i] :
( disjoint(sK147(sK137,topstr_closure(sK137,X0)),X1)
| closed_subset(sK142(sK147(sK137,topstr_closure(sK137,X0)),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(sK142(sK147(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_176007]) ).
tcf(c_189733,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,sK147(sK137,topstr_closure(sK137,X1)))
| closed_subset(sK142(X0,sK147(sK137,topstr_closure(sK137,X1))),sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(sK142(X0,sK147(sK137,topstr_closure(sK137,X1))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_176007]) ).
tcf(c_189734,plain,
! [X0: $i] :
( relation(sK147(sK137,topstr_closure(sK137,X0)))
| closed_subset(sK175(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(sK175(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_176007]) ).
tcf(c_189735,plain,
! [X0: $i] :
( closed_subset(sK185(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK147(sK137,topstr_closure(sK137,X0)))
| ~ element(sK185(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_176007]) ).
tcf(c_189737,plain,
! [X0: $i] :
( closed_subset(sK274(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK147(sK137,topstr_closure(sK137,X0)))
| ~ element(sK274(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_176007]) ).
tcf(c_189738,plain,
! [X0: $i] :
( epsilon_transitive(sK147(sK137,topstr_closure(sK137,X0)))
| closed_subset(sK340(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(sK340(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_176007]) ).
tcf(c_189739,plain,
! [X0: $i] :
( epsilon_connected(sK147(sK137,topstr_closure(sK137,X0)))
| closed_subset(sK369(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(sK369(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_176007]) ).
tcf(c_189740,plain,
! [X0: $i] :
( epsilon_connected(sK147(sK137,topstr_closure(sK137,X0)))
| closed_subset(sK370(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(sK370(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_176007]) ).
tcf(c_189741,plain,
! [X0: $i] :
( closed_subset(sK145(sK137,sK147(sK137,topstr_closure(sK137,X0))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(topstr_closure(sK137,X0),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_176007]) ).
tcf(c_189743,plain,
! [X0: $i,X1: $i] :
( closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(topstr_closure(sK137,X1),powerset(the_carrier(sK137)))
| ~ element(set_difference(the_carrier(sK137),X0),powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,topstr_closure(sK137,X1)))) ),
inference(superposition,[status(thm)],[c_179183,c_176007]) ).
tcf(c_189851,plain,
! [X0: $i] :
( sP3(sK91(sK137,topstr_closure(sK137,X0)))
| ( sK92(sK137,topstr_closure(sK137,X0),sK62(sK91(sK137,topstr_closure(sK137,X0)))) = sK62(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_176010]) ).
tcf(c_189853,plain,
! [X0: $i] :
( ordinal(sK91(sK137,topstr_closure(sK137,X0)))
| ( sK92(sK137,topstr_closure(sK137,X0),sK139(sK91(sK137,topstr_closure(sK137,X0)))) = sK139(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_176010]) ).
tcf(c_189854,plain,
! [X0: $i,X1: $i] :
( disjoint(sK91(sK137,topstr_closure(sK137,X0)),X1)
| ( sK92(sK137,topstr_closure(sK137,X0),sK142(sK91(sK137,topstr_closure(sK137,X0)),X1)) = sK142(sK91(sK137,topstr_closure(sK137,X0)),X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_176010]) ).
tcf(c_189855,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,sK91(sK137,topstr_closure(sK137,X0)))
| ( sK92(sK137,topstr_closure(sK137,X0),sK142(X1,sK91(sK137,topstr_closure(sK137,X0)))) = sK142(X1,sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_176010]) ).
tcf(c_189856,plain,
! [X0: $i] :
( relation(sK91(sK137,topstr_closure(sK137,X0)))
| ( sK92(sK137,topstr_closure(sK137,X0),sK175(sK91(sK137,topstr_closure(sK137,X0)))) = sK175(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_176010]) ).
tcf(c_189857,plain,
! [X0: $i] :
( ( sK92(sK137,topstr_closure(sK137,X0),sK185(sK91(sK137,topstr_closure(sK137,X0)))) = sK185(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_603,c_176010]) ).
tcf(c_189859,plain,
! [X0: $i] :
( ( sK92(sK137,topstr_closure(sK137,X0),sK274(sK91(sK137,topstr_closure(sK137,X0)))) = sK274(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_858,c_176010]) ).
tcf(c_189860,plain,
! [X0: $i] :
( epsilon_transitive(sK91(sK137,topstr_closure(sK137,X0)))
| ( sK92(sK137,topstr_closure(sK137,X0),sK340(sK91(sK137,topstr_closure(sK137,X0)))) = sK340(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_176010]) ).
tcf(c_189861,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,topstr_closure(sK137,X0)))
| ( sK92(sK137,topstr_closure(sK137,X0),sK369(sK91(sK137,topstr_closure(sK137,X0)))) = sK369(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_176010]) ).
tcf(c_189862,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,topstr_closure(sK137,X0)))
| ( sK92(sK137,topstr_closure(sK137,X0),sK370(sK91(sK137,topstr_closure(sK137,X0)))) = sK370(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_176010]) ).
tcf(c_189933,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138)
| ~ in(sK147(sK137,topstr_closure(sK137,X0)),sK138) ),
inference(superposition,[status(thm)],[c_176349,c_546]) ).
tcf(c_189934,plain,
! [X0: $i] :
( in(sK154(sK147(sK137,topstr_closure(sK137,X0))),sK147(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138) ),
inference(superposition,[status(thm)],[c_176349,c_542]) ).
tcf(c_189935,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138)
| ~ empty(sK147(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_176349,c_781]) ).
tcf(c_189936,plain,
! [X0: $i] :
( element(sK138,sK147(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138) ),
inference(superposition,[status(thm)],[c_176349,c_701]) ).
tcf(c_189983,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138)
| ~ in(sK123(sK137,topstr_closure(sK137,X0)),sK138) ),
inference(superposition,[status(thm)],[c_176584,c_546]) ).
tcf(c_189984,plain,
! [X0: $i] :
( in(sK154(sK123(sK137,topstr_closure(sK137,X0))),sK123(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138) ),
inference(superposition,[status(thm)],[c_176584,c_542]) ).
tcf(c_189985,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138)
| ~ empty(sK123(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_176584,c_781]) ).
tcf(c_189986,plain,
! [X0: $i] :
( element(sK138,sK123(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138) ),
inference(superposition,[status(thm)],[c_176584,c_701]) ).
tcf(c_190017,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK208(powerset(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ in(sK208(powerset(powerset(the_carrier(sK137)))),sK145(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_177422,c_546]) ).
tcf(c_190018,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK208(powerset(powerset(the_carrier(sK137))))),sK137)
| in(sK154(sK208(powerset(powerset(the_carrier(sK137))))),sK208(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_177422,c_542]) ).
tcf(c_190019,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK208(powerset(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ empty(sK208(powerset(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_177422,c_781]) ).
tcf(c_190020,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK208(powerset(powerset(the_carrier(sK137))))),sK137)
| element(sK145(sK137,sK208(powerset(powerset(the_carrier(sK137))))),sK208(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_177422,c_701]) ).
tcf(c_190052,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_967,c_178928]) ).
tcf(c_190054,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_967,c_178928]) ).
tcf(c_190057,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = empty_set )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_105912,c_178928]) ).
tcf(c_190058,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = empty_set )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_105926,c_178928]) ).
tcf(c_190064,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_190058,c_52]) ).
tcf(c_190067,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_190057,c_52]) ).
tcf(c_190077,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(sK103(X0,X1))
| ~ sP12(X0,X1)
| ~ well_ordering(sK103(X0,X1)) ),
inference(superposition,[status(thm)],[c_215,c_593]) ).
tcf(c_190078,plain,
! [X0: $i] :
( sP13(X0)
| well_founded_relation(sK115(X0))
| ~ well_ordering(sK115(X0)) ),
inference(superposition,[status(thm)],[c_237,c_593]) ).
tcf(c_190079,plain,
! [X0: $i] :
( well_founded_relation(sK122(X0))
| ~ well_ordering(sK122(X0)) ),
inference(superposition,[status(thm)],[c_256,c_593]) ).
tcf(c_190080,plain,
! [X0: $i] :
( well_founded_relation(sK134(X0))
| ~ well_ordering(sK134(X0)) ),
inference(superposition,[status(thm)],[c_362,c_593]) ).
tcf(c_190081,plain,
! [X0: $i] :
( well_founded_relation(identity_relation(X0))
| ~ well_ordering(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1156,c_593]) ).
tcf(c_190082,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_767,c_593]) ).
tcf(c_190083,plain,
( well_founded_relation(empty_set)
| ~ well_ordering(empty_set) ),
inference(superposition,[status(thm)],[c_596,c_593]) ).
tcf(c_190084,plain,
! [X0: $i] :
( well_founded_relation(relation_dom(X0))
| ~ empty(X0)
| ~ well_ordering(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_647,c_593]) ).
tcf(c_190085,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ well_ordering(relation_rng_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_651,c_593]) ).
tcf(c_190086,plain,
( well_founded_relation(sK246)
| ~ well_ordering(sK246) ),
inference(superposition,[status(thm)],[c_777,c_593]) ).
tcf(c_190087,plain,
( well_founded_relation(sK248)
| ~ well_ordering(sK248) ),
inference(superposition,[status(thm)],[c_785,c_593]) ).
tcf(c_190088,plain,
! [X0: $i] :
( well_founded_relation(sK270(X0))
| ~ finite(X0)
| ~ well_ordering(sK270(X0)) ),
inference(superposition,[status(thm)],[c_846,c_593]) ).
tcf(c_190089,plain,
! [X0: $i] :
( well_founded_relation(relation_rng(X0))
| ~ empty(X0)
| ~ well_ordering(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_969,c_593]) ).
tcf(c_190090,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_1045,c_593]) ).
tcf(c_190091,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(sK336(X0,X1))
| ~ well_ordering(sK336(X0,X1)) ),
inference(superposition,[status(thm)],[c_1057,c_593]) ).
tcf(c_190092,plain,
! [X0: $i] :
( well_founded_relation(inclusion_relation(X0))
| ~ well_ordering(inclusion_relation(X0)) ),
inference(superposition,[status(thm)],[c_1146,c_593]) ).
tcf(c_190093,plain,
! [X0: $i] :
( well_founded_relation(relation_inverse(X0))
| ~ relation(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1168,c_593]) ).
tcf(c_190094,plain,
! [X0: $i] :
( well_founded_relation(relation_inverse(X0))
| ~ empty(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1167,c_593]) ).
tcf(c_190095,plain,
( well_founded_relation(sK361)
| ~ well_ordering(sK361) ),
inference(superposition,[status(thm)],[c_1197,c_593]) ).
tcf(c_190096,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(sK373(X0,X1))
| ~ well_ordering(sK373(X0,X1)) ),
inference(superposition,[status(thm)],[c_1283,c_593]) ).
tcf(c_190097,plain,
( well_founded_relation(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK175(sK91(sK137,sK138))) = sK175(sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178946,c_593]) ).
tcf(c_190098,plain,
( sP36(sK137,sK138)
| well_founded_relation(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178950,c_593]) ).
tcf(c_190099,plain,
( sP36(sK137,sK138)
| well_founded_relation(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ well_ordering(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_178949,c_593]) ).
tcf(c_190226,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK181(X0)) ),
inference(superposition,[status(thm)],[c_598,c_546]) ).
tcf(c_190227,plain,
! [X0: $i] :
( in(sK154(X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_598,c_542]) ).
tcf(c_190229,plain,
! [X0: $i] :
( element(sK181(X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_598,c_701]) ).
tcf(c_190230,plain,
! [X0: $i] :
( in(sK181(sK99(X0)),X0)
| ( sK99(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_598,c_205]) ).
tcf(c_190231,plain,
! [X0: $i] :
( ordinal(sK181(sK99(X0)))
| ( sK99(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_598,c_206]) ).
tcf(c_190233,plain,
( sP36(sK137,sK138)
| in(sK181(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ( powerset(the_carrier(sK137)) = empty_set )
| ~ topological_space(sK137)
| ~ closed_subset(sK181(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK181(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_598,c_176867]) ).
tcf(c_190234,plain,
( in(sK181(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ( powerset(the_carrier(sK137)) = empty_set )
| ~ topological_space(sK137)
| ~ closed_subset(sK181(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK181(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_598,c_176193]) ).
tcf(c_190235,plain,
( ( sK91(sK137,sK138) = empty_set )
| ( sK92(sK137,sK138,sK181(sK91(sK137,sK138))) = sK181(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_175190]) ).
tcf(c_190236,plain,
( in(sK181(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_175008]) ).
tcf(c_190237,plain,
( subset(sK138,sK181(sK91(sK137,sK138)))
| ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_174960]) ).
tcf(c_190238,plain,
( sP36(sK137,sK138)
| ( sK302(sK137,sK138) = empty_set )
| ( sK303(sK137,sK138,sK181(sK302(sK137,sK138))) = sK181(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_175802]) ).
tcf(c_190239,plain,
( sP36(sK137,sK138)
| ( sK302(sK137,sK138) = empty_set )
| ( sK304(sK137,sK138,sK181(sK302(sK137,sK138))) = sK181(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_175753]) ).
tcf(c_190240,plain,
( sP36(sK137,sK138)
| subset(sK138,sK181(sK302(sK137,sK138)))
| ( sK302(sK137,sK138) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_175029]) ).
tcf(c_190241,plain,
( in(sK181(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ( sK93(sK137,the_topology(sK137)) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_175089]) ).
tcf(c_190242,plain,
! [X0: $i] :
( in(sK181(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ( sK93(sK137,sK147(sK137,X0)) = empty_set )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_175090]) ).
tcf(c_190243,plain,
! [X0: $i] :
( in(sK181(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ( sK93(sK137,sK125(sK137,X0)) = empty_set )
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_598,c_175091]) ).
tcf(c_190244,plain,
! [X0: $i] :
( in(sK181(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ( sK93(sK137,sK123(sK137,X0)) = empty_set )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_175092]) ).
tcf(c_190245,plain,
! [X0: $i] :
( closed_subset(sK181(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ( sK147(sK137,topstr_closure(sK137,X0)) = empty_set )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(sK181(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_176007]) ).
tcf(c_190246,plain,
! [X0: $i] :
( ( sK91(sK137,topstr_closure(sK137,X0)) = empty_set )
| ( sK92(sK137,topstr_closure(sK137,X0),sK181(sK91(sK137,topstr_closure(sK137,X0)))) = sK181(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_176010]) ).
tcf(c_190247,plain,
! [X0: $i] :
( subset(topstr_closure(sK137,X0),sK181(sK91(sK137,topstr_closure(sK137,X0))))
| ( sK91(sK137,topstr_closure(sK137,X0)) = empty_set )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_176013]) ).
tcf(c_190248,plain,
! [X0: $i] :
( in(sK181(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ( sK91(sK137,topstr_closure(sK137,X0)) = empty_set )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_176012]) ).
tcf(c_190249,plain,
( sP34(the_topology(sK137),sK137)
| ( sK295(sK137,the_topology(sK137)) = empty_set )
| ( sK296(sK137,the_topology(sK137),sK181(sK295(sK137,the_topology(sK137)))) = sK181(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_176134]) ).
tcf(c_190250,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK302(sK137,the_carrier(sK137)) = empty_set )
| ( sK304(sK137,the_carrier(sK137),sK181(sK302(sK137,the_carrier(sK137)))) = sK181(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_176975]) ).
tcf(c_190251,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK302(sK137,the_carrier(sK137)) = empty_set )
| ( sK303(sK137,the_carrier(sK137),sK181(sK302(sK137,the_carrier(sK137)))) = sK181(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_176974]) ).
tcf(c_190252,plain,
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK181(sK302(sK137,the_carrier(sK137))))
| ( sK302(sK137,the_carrier(sK137)) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_176981]) ).
tcf(c_190253,plain,
( ( sK123(sK137,the_carrier(sK137)) = empty_set )
| ( sK124(sK137,the_carrier(sK137),sK181(sK123(sK137,the_carrier(sK137)))) = sK181(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(sK181(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_176971]) ).
tcf(c_190254,plain,
( subset(the_carrier(sK137),sK181(sK123(sK137,the_carrier(sK137))))
| ( sK123(sK137,the_carrier(sK137)) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_176976]) ).
tcf(c_190255,plain,
( ( sK91(sK137,the_carrier(sK137)) = empty_set )
| ( sK92(sK137,the_carrier(sK137),sK181(sK91(sK137,the_carrier(sK137)))) = sK181(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_176980]) ).
tcf(c_190256,plain,
( in(sK181(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ( sK91(sK137,the_carrier(sK137)) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_176982]) ).
tcf(c_190257,plain,
( subset(the_carrier(sK137),sK181(sK91(sK137,the_carrier(sK137))))
| ( sK91(sK137,the_carrier(sK137)) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_176983]) ).
tcf(c_190258,plain,
( subset(the_carrier(sK137),sK181(sK147(sK137,the_carrier(sK137))))
| ( sK147(sK137,the_carrier(sK137)) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_176978]) ).
tcf(c_190259,plain,
( closed_subset(sK181(sK147(sK137,the_carrier(sK137))),sK137)
| ( sK147(sK137,the_carrier(sK137)) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_176977]) ).
tcf(c_190260,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK295(sK137,powerset(the_carrier(sK137))) = empty_set )
| ( sK296(sK137,powerset(the_carrier(sK137)),sK181(sK295(sK137,powerset(the_carrier(sK137))))) = sK181(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_176995]) ).
tcf(c_190261,plain,
( in(sK181(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ( sK93(sK137,powerset(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_176997]) ).
tcf(c_190262,plain,
( in(sK181(topstr_closure(sK137,sK138)),sK138)
| ( topstr_closure(sK137,sK138) = empty_set )
| ~ closed_subset(sK138,sK137)
| ~ in(sK181(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_598,c_177233]) ).
tcf(c_190263,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK181(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ( sK302(sK137,sK208(powerset(the_carrier(sK137)))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_177405]) ).
tcf(c_190264,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK181(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ( sK123(sK137,sK208(powerset(the_carrier(sK137)))) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_177400]) ).
tcf(c_190265,plain,
( ( sK91(sK137,sK208(powerset(the_carrier(sK137)))) = empty_set )
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK181(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK181(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_177404]) ).
tcf(c_190266,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK181(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ( sK91(sK137,sK208(powerset(the_carrier(sK137)))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_177407]) ).
tcf(c_190267,plain,
( in(sK181(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ( sK91(sK137,sK208(powerset(the_carrier(sK137)))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_177406]) ).
tcf(c_190268,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK181(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ( sK147(sK137,sK208(powerset(the_carrier(sK137)))) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_177402]) ).
tcf(c_190269,plain,
( closed_subset(sK181(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ( sK147(sK137,sK208(powerset(the_carrier(sK137)))) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_177401]) ).
tcf(c_190270,plain,
( in(sK181(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ( sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_177421]) ).
tcf(c_190271,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK181(sK302(sK137,sK207(the_carrier(sK137)))))
| ( sK302(sK137,sK207(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_182970]) ).
tcf(c_190272,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK181(sK123(sK137,sK207(the_carrier(sK137)))))
| ( sK123(sK137,sK207(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_182965]) ).
tcf(c_190273,plain,
( empty(the_carrier(sK137))
| ( sK91(sK137,sK207(the_carrier(sK137))) = empty_set )
| ( sK92(sK137,sK207(the_carrier(sK137)),sK181(sK91(sK137,sK207(the_carrier(sK137))))) = sK181(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_182969]) ).
tcf(c_190274,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK181(sK91(sK137,sK207(the_carrier(sK137)))))
| ( sK91(sK137,sK207(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_182972]) ).
tcf(c_190275,plain,
( empty(the_carrier(sK137))
| in(sK181(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ( sK91(sK137,sK207(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_182971]) ).
tcf(c_190276,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK181(sK147(sK137,sK207(the_carrier(sK137)))))
| ( sK147(sK137,sK207(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_182967]) ).
tcf(c_190277,plain,
( empty(the_carrier(sK137))
| closed_subset(sK181(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ( sK147(sK137,sK207(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_182966]) ).
tcf(c_190278,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK181(sK302(sK137,sK325(the_carrier(sK137)))))
| ( sK302(sK137,sK325(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_184375]) ).
tcf(c_190279,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK181(sK123(sK137,sK325(the_carrier(sK137)))))
| ( sK123(sK137,sK325(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_184370]) ).
tcf(c_190280,plain,
( empty(the_carrier(sK137))
| ( sK91(sK137,sK325(the_carrier(sK137))) = empty_set )
| ( sK92(sK137,sK325(the_carrier(sK137)),sK181(sK91(sK137,sK325(the_carrier(sK137))))) = sK181(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_184374]) ).
tcf(c_190281,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK181(sK91(sK137,sK325(the_carrier(sK137)))))
| ( sK91(sK137,sK325(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_184377]) ).
tcf(c_190282,plain,
( empty(the_carrier(sK137))
| in(sK181(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ( sK91(sK137,sK325(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_184376]) ).
tcf(c_190283,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK181(sK147(sK137,sK325(the_carrier(sK137)))))
| ( sK147(sK137,sK325(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_184372]) ).
tcf(c_190284,plain,
( empty(the_carrier(sK137))
| closed_subset(sK181(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ( sK147(sK137,sK325(the_carrier(sK137))) = empty_set )
| ~ topological_space(sK137)
| ~ element(sK181(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_184371]) ).
tcf(c_190578,plain,
! [X0: $i] :
( in(the_carrier(sK137),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_180215,c_658]) ).
tcf(c_190579,plain,
! [X0: $i] :
( in(the_carrier(sK137),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_180246,c_658]) ).
tcf(c_190588,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ subset(sK138,X1)
| ~ subset(X1,the_carrier(sK137))
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_658,c_177131]) ).
tcf(c_190589,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ closed_subset(X2,sK137)
| ~ subset(X1,X2)
| ~ subset(X1,the_carrier(sK137))
| ~ in(X0,the_carrier(sK137))
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_48138]) ).
tcf(c_190590,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| in(X0,sK302(sK137,X1))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(X1,X0)
| ~ subset(X1,the_carrier(sK137))
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_658,c_47771]) ).
tcf(c_190591,plain,
! [X0: $i,X1: $i] :
( in(X1,sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(X1,sK137)
| ~ subset(X0,X1)
| ~ subset(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_658,c_48368]) ).
tcf(c_190592,plain,
! [X0: $i,X1: $i] :
( ( sK124(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ subset(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_48332]) ).
tcf(c_190593,plain,
! [X0: $i,X1: $i] :
( in(X1,sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(X1,sK137)
| ~ subset(X0,X1)
| ~ subset(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_658,c_48105]) ).
tcf(c_190594,plain,
! [X0: $i,X1: $i] :
( in(X0,sK91(sK137,X1))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(X1,X0)
| ~ subset(X1,the_carrier(sK137))
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_658,c_47795]) ).
tcf(c_190595,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ( sK303(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ subset(X1,the_carrier(sK137))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_47947]) ).
tcf(c_190596,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ( sK304(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ subset(X1,the_carrier(sK137))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_47911]) ).
tcf(c_190597,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK137)
| ~ subset(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_48297]) ).
tcf(c_190598,plain,
! [X0: $i,X1: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ subset(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_48087]) ).
tcf(c_190599,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK137)
| ~ subset(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_48070]) ).
tcf(c_190600,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(sK137,X1) = X0 )
| ~ subset(X1,the_carrier(sK137))
| ~ sP38(sK137,X1,X0)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_658,c_47756]) ).
tcf(c_190601,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ subset(X1,the_carrier(sK137))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_48460]) ).
tcf(c_190602,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| subset(X1,X0)
| ~ topological_space(sK137)
| ~ subset(X1,the_carrier(sK137))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_47876]) ).
tcf(c_190603,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X1,the_carrier(sK137))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_48490]) ).
tcf(c_190604,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK137)
| ~ subset(X1,the_carrier(sK137))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_48431]) ).
tcf(c_190605,plain,
! [X0: $i] :
( in(empty_set,sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(X0,empty_set)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_658,c_182438]) ).
tcf(c_190606,plain,
! [X0: $i] :
( ( sK124(sK137,empty_set,X0) = X0 )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ in(X0,sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_658,c_182437]) ).
tcf(c_190607,plain,
! [X0: $i] :
( in(empty_set,sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(X0,empty_set)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_658,c_182436]) ).
tcf(c_190608,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,X0))) = topstr_closure(sK137,topstr_closure(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_658,c_176018]) ).
tcf(c_190609,plain,
! [X0: $i] :
( in(sK138,sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_658,c_176521]) ).
tcf(c_190610,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,X0) = X0 )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ in(X0,sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_658,c_176408]) ).
tcf(c_190611,plain,
! [X0: $i] :
( in(sK138,sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_658,c_176286]) ).
tcf(c_190612,plain,
! [X0: $i] :
( subset(sK138,X0)
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ in(X0,sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_658,c_175672]) ).
tcf(c_190613,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ in(X0,sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_658,c_175482]) ).
tcf(c_190614,plain,
! [X0: $i] :
( subset(sK138,X0)
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ in(X0,sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_658,c_175418]) ).
tcf(c_190615,plain,
! [X0: $i] :
( ( topstr_closure(sK137,sK138) = X0 )
| ~ sP38(sK137,sK138,X0)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_658,c_175209]) ).
tcf(c_190616,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,X0)) = topstr_closure(sK137,X0) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_658,c_48058]) ).
tcf(c_190617,plain,
! [X0: $i] :
( ( topstr_closure(sK137,X0) = X0 )
| ~ closed_subset(X0,sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_658,c_48037]) ).
tcf(c_190618,plain,
! [X0: $i] :
( open_subset(X0,sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ in(X0,the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_658,c_47852]) ).
tcf(c_190619,plain,
! [X0: $i] :
( in(X0,the_topology(sK137))
| ~ open_subset(X0,sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_658,c_47840]) ).
tcf(c_190620,plain,
! [X0: $i,X1: $i] :
( sP34(X1,sK137)
| in(set_difference(the_carrier(sK137),X0),X1)
| ~ topological_space(sK137)
| ~ subset(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK295(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_73951]) ).
tcf(c_190621,plain,
! [X0: $i,X1: $i] :
( in(set_difference(the_carrier(sK137),X0),X1)
| ~ topological_space(sK137)
| ~ subset(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_73134]) ).
tcf(c_190622,plain,
! [X0: $i,X1: $i] :
( sP34(X1,sK137)
| ( sK296(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ subset(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK295(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_48001]) ).
tcf(c_190623,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,X0),sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_658,c_48252]) ).
tcf(c_190624,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,X1)) ),
inference(superposition,[status(thm)],[c_658,c_48416]) ).
tcf(c_190625,plain,
! [X0: $i] :
( in(sK145(sK137,X0),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_658,c_48237]) ).
tcf(c_190837,plain,
( subset(sK68,powerset(empty_set))
| ~ sP7 ),
inference(superposition,[status(thm)],[c_134,c_659]) ).
tcf(c_190838,plain,
subset(sK138,the_carrier(sK137)),
inference(superposition,[status(thm)],[c_376,c_659]) ).
tcf(c_190839,plain,
! [X0: $i] :
( empty(X0)
| subset(sK207(X0),X0) ),
inference(superposition,[status(thm)],[c_698,c_659]) ).
tcf(c_190840,plain,
! [X0: $i] : subset(sK208(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_702,c_659]) ).
tcf(c_190841,plain,
! [X0: $i] :
( empty(X0)
| subset(sK325(X0),X0) ),
inference(superposition,[status(thm)],[c_1004,c_659]) ).
tcf(c_190843,plain,
subset(sK319(sK320),the_carrier(sK320)),
inference(superposition,[status(thm)],[c_22154,c_659]) ).
tcf(c_190844,plain,
( topological_space(sK137)
| subset(sK378(sK137),powerset(the_carrier(sK137)))
| ~ sP42(sK137)
| ~ in(the_carrier(sK137),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_47411,c_659]) ).
tcf(c_190845,plain,
subset(the_topology(sK137),powerset(the_carrier(sK137))),
inference(superposition,[status(thm)],[c_47453,c_659]) ).
tcf(c_190846,plain,
subset(the_topology(sK291),powerset(the_carrier(sK291))),
inference(superposition,[status(thm)],[c_47629,c_659]) ).
tcf(c_190847,plain,
! [X0: $i] :
( subset(topstr_closure(sK137,X0),the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_659]) ).
tcf(c_190848,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| subset(sK304(sK137,X1,X0),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_659]) ).
tcf(c_190849,plain,
! [X0: $i] :
( subset(sK147(sK137,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48126,c_659]) ).
tcf(c_190850,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| subset(sK146(sK137,X0,X1),the_carrier(sK137))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_659]) ).
tcf(c_190851,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| subset(sK145(sK137,X0),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_659]) ).
tcf(c_190852,plain,
! [X0: $i] :
( subset(sK125(sK137,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48285,c_659]) ).
tcf(c_190853,plain,
! [X0: $i,X1: $i] :
( subset(sK124(sK137,X1,X0),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_659]) ).
tcf(c_190854,plain,
! [X0: $i] :
( subset(sK123(sK137,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48389,c_659]) ).
tcf(c_190855,plain,
! [X0: $i,X1: $i] :
( subset(sK92(sK137,X1,X0),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_659]) ).
tcf(c_190856,plain,
! [X0: $i] :
( subset(topstr_closure(sK291,X0),the_carrier(sK291))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(superposition,[status(thm)],[c_106105,c_659]) ).
tcf(c_190903,plain,
( ( sK124(sK137,sK138,the_carrier(sK137)) = the_carrier(sK137) )
| ~ topological_space(sK137) ),
inference(backward_subsumption_resolution,[status(thm)],[c_180232,c_190838]) ).
tcf(c_190942,plain,
~ proper_subset(the_carrier(sK137),sK138),
inference(superposition,[status(thm)],[c_190838,c_492]) ).
tcf(c_190955,plain,
~ proper_subset(powerset(the_carrier(sK137)),the_topology(sK137)),
inference(superposition,[status(thm)],[c_190845,c_492]) ).
tcf(c_190966,plain,
( sP3(the_topology(sK137))
| open_subset(sK62(the_topology(sK137)),sK137)
| ~ subset(sK62(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_120,c_190618]) ).
tcf(c_190968,plain,
( ordinal(the_topology(sK137))
| open_subset(sK139(the_topology(sK137)),sK137)
| ~ subset(sK139(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_383,c_190618]) ).
tcf(c_190969,plain,
! [X0: $i] :
( disjoint(the_topology(sK137),X0)
| open_subset(sK142(the_topology(sK137),X0),sK137)
| ~ subset(sK142(the_topology(sK137),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_416,c_190618]) ).
tcf(c_190970,plain,
! [X0: $i] :
( disjoint(X0,the_topology(sK137))
| open_subset(sK142(X0,the_topology(sK137)),sK137)
| ~ subset(sK142(X0,the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_417,c_190618]) ).
tcf(c_190971,plain,
( relation(the_topology(sK137))
| open_subset(sK175(the_topology(sK137)),sK137)
| ~ subset(sK175(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_580,c_190618]) ).
tcf(c_190972,plain,
( open_subset(sK181(the_topology(sK137)),sK137)
| ( the_topology(sK137) = empty_set )
| ~ subset(sK181(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_598,c_190618]) ).
tcf(c_190973,plain,
( open_subset(sK185(the_topology(sK137)),sK137)
| ~ sP20(the_topology(sK137))
| ~ subset(sK185(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_603,c_190618]) ).
tcf(c_190975,plain,
( open_subset(sK274(the_topology(sK137)),sK137)
| ~ sP32(the_topology(sK137))
| ~ subset(sK274(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_858,c_190618]) ).
tcf(c_190976,plain,
( epsilon_transitive(the_topology(sK137))
| open_subset(sK340(the_topology(sK137)),sK137)
| ~ subset(sK340(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1081,c_190618]) ).
tcf(c_190977,plain,
( epsilon_connected(the_topology(sK137))
| open_subset(sK369(the_topology(sK137)),sK137)
| ~ subset(sK369(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1253,c_190618]) ).
tcf(c_190978,plain,
( epsilon_connected(the_topology(sK137))
| open_subset(sK370(the_topology(sK137)),sK137)
| ~ subset(sK370(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1254,c_190618]) ).
tcf(c_190982,plain,
! [X0: $i] :
( open_subset(union_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ subset(X0,the_topology(sK137))
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ subset(union_of_subsets(the_carrier(sK137),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_47816,c_190618]) ).
tcf(c_190986,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| open_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,the_topology(sK137)))
| ~ subset(set_difference(the_carrier(sK137),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_180142,c_190618]) ).
tcf(c_190987,plain,
! [X0: $i] :
( open_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,the_topology(sK137)))
| ~ subset(set_difference(the_carrier(sK137),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_179182,c_190618]) ).
tcf(c_190990,plain,
( open_subset(sK154(the_topology(sK137)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK154(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_189060,c_190618]) ).
tcf(c_190991,plain,
( open_subset(sK154(the_topology(sK137)),sK137)
| ~ open_subset(sK138,sK137)
| ~ subset(sK154(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_188347,c_190618]) ).
tcf(c_191043,plain,
! [X0: $i] :
( open_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,the_topology(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_190987,c_399]) ).
tcf(c_191047,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| open_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,the_topology(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_190986,c_399]) ).
tcf(c_191082,plain,
! [X0: $i] :
( in(relation_rng_restriction(X0,the_carrier(sK137)),the_topology(sK137))
| ~ relation(the_carrier(sK137))
| ~ open_subset(relation_rng_restriction(X0,the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_278,c_190619]) ).
tcf(c_191084,plain,
! [X0: $i] :
( in(set_difference(the_carrier(sK137),X0),the_topology(sK137))
| ~ open_subset(set_difference(the_carrier(sK137),X0),sK137) ),
inference(superposition,[status(thm)],[c_399,c_190619]) ).
tcf(c_191085,plain,
! [X0: $i] :
( in(relation_dom_restriction(the_carrier(sK137),X0),the_topology(sK137))
| ~ relation(the_carrier(sK137))
| ~ open_subset(relation_dom_restriction(the_carrier(sK137),X0),sK137) ),
inference(superposition,[status(thm)],[c_524,c_190619]) ).
tcf(c_191105,plain,
( ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ proper_subset(sK181(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_190237,c_492]) ).
tcf(c_191115,plain,
! [X0: $i] :
( ( topstr_closure(sK137,relation_rng_restriction(X0,the_carrier(sK137))) = relation_rng_restriction(X0,the_carrier(sK137)) )
| ~ relation(the_carrier(sK137))
| ~ closed_subset(relation_rng_restriction(X0,the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_278,c_190617]) ).
tcf(c_191117,plain,
! [X0: $i] :
( ( topstr_closure(sK137,set_difference(the_carrier(sK137),X0)) = set_difference(the_carrier(sK137),X0) )
| ~ closed_subset(set_difference(the_carrier(sK137),X0),sK137) ),
inference(superposition,[status(thm)],[c_399,c_190617]) ).
tcf(c_191118,plain,
! [X0: $i] :
( ( topstr_closure(sK137,relation_dom_restriction(the_carrier(sK137),X0)) = relation_dom_restriction(the_carrier(sK137),X0) )
| ~ relation(the_carrier(sK137))
| ~ closed_subset(relation_dom_restriction(the_carrier(sK137),X0),sK137) ),
inference(superposition,[status(thm)],[c_524,c_190617]) ).
tcf(c_191138,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X2)) ) ),
inference(demodulation,[status(thm)],[c_178929,c_967]) ).
tcf(c_191145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X2)) ) ),
inference(superposition,[status(thm)],[c_967,c_191138]) ).
tcf(c_191147,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X2)) ) ),
inference(superposition,[status(thm)],[c_967,c_191138]) ).
tcf(c_191150,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = empty_set )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X3)) ) ),
inference(superposition,[status(thm)],[c_105912,c_191138]) ).
tcf(c_191151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = empty_set )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X3)) ) ),
inference(superposition,[status(thm)],[c_105926,c_191138]) ).
tcf(c_191153,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(powerset(empty_set),unordered_pair(X2,empty_set)) ) ),
inference(superposition,[status(thm)],[c_967,c_191138]) ).
tcf(c_191161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_191151,c_52]) ).
tcf(c_191164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_191150,c_52]) ).
tcf(c_191188,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,sK202(X0,X1)) ),
inference(superposition,[status(thm)],[c_662,c_546]) ).
tcf(c_191189,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK154(X0),X0) ),
inference(superposition,[status(thm)],[c_662,c_542]) ).
tcf(c_191190,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_662,c_781]) ).
tcf(c_191191,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| element(sK202(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_662,c_701]) ).
tcf(c_191192,plain,
! [X0: $i,X1: $i] :
( subset(sK99(X0),X1)
| in(sK202(sK99(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_662,c_205]) ).
tcf(c_191193,plain,
! [X0: $i,X1: $i] :
( subset(sK99(X0),X1)
| ordinal(sK202(sK99(X0),X1)) ),
inference(superposition,[status(thm)],[c_662,c_206]) ).
tcf(c_191195,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(powerset(the_carrier(sK137)),X0)
| in(sK202(powerset(the_carrier(sK137)),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK202(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK202(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_662,c_176867]) ).
tcf(c_191196,plain,
! [X0: $i] :
( subset(powerset(the_carrier(sK137)),X0)
| in(sK202(powerset(the_carrier(sK137)),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK202(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK202(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_662,c_176193]) ).
tcf(c_191197,plain,
! [X0: $i] :
( subset(the_topology(sK137),X0)
| open_subset(sK202(the_topology(sK137),X0),sK137)
| ~ subset(sK202(the_topology(sK137),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_662,c_190618]) ).
tcf(c_191198,plain,
! [X0: $i] :
( subset(sK91(sK137,sK138),X0)
| ( sK92(sK137,sK138,sK202(sK91(sK137,sK138),X0)) = sK202(sK91(sK137,sK138),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_175190]) ).
tcf(c_191199,plain,
! [X0: $i] :
( subset(sK91(sK137,sK138),X0)
| in(sK202(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_175008]) ).
tcf(c_191200,plain,
! [X0: $i] :
( subset(sK91(sK137,sK138),X0)
| subset(sK138,sK202(sK91(sK137,sK138),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_174960]) ).
tcf(c_191201,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(sK302(sK137,sK138),X0)
| ( sK303(sK137,sK138,sK202(sK302(sK137,sK138),X0)) = sK202(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_175802]) ).
tcf(c_191202,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(sK302(sK137,sK138),X0)
| ( sK304(sK137,sK138,sK202(sK302(sK137,sK138),X0)) = sK202(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_175753]) ).
tcf(c_191203,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(sK302(sK137,sK138),X0)
| subset(sK138,sK202(sK302(sK137,sK138),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_175029]) ).
tcf(c_191204,plain,
! [X0: $i] :
( subset(sK93(sK137,the_topology(sK137)),X0)
| in(sK202(sK93(sK137,the_topology(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_175089]) ).
tcf(c_191205,plain,
! [X0: $i,X1: $i] :
( subset(sK93(sK137,sK147(sK137,X0)),X1)
| in(sK202(sK93(sK137,sK147(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_175090]) ).
tcf(c_191206,plain,
! [X0: $i,X1: $i] :
( subset(sK93(sK137,sK125(sK137,X0)),X1)
| in(sK202(sK93(sK137,sK125(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_662,c_175091]) ).
tcf(c_191207,plain,
! [X0: $i,X1: $i] :
( subset(sK93(sK137,sK123(sK137,X0)),X1)
| in(sK202(sK93(sK137,sK123(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_175092]) ).
tcf(c_191208,plain,
! [X0: $i,X1: $i] :
( subset(sK147(sK137,topstr_closure(sK137,X0)),X1)
| closed_subset(sK202(sK147(sK137,topstr_closure(sK137,X0)),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(sK202(sK147(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_176007]) ).
tcf(c_191209,plain,
! [X0: $i,X1: $i] :
( subset(sK91(sK137,topstr_closure(sK137,X0)),X1)
| ( sK92(sK137,topstr_closure(sK137,X0),sK202(sK91(sK137,topstr_closure(sK137,X0)),X1)) = sK202(sK91(sK137,topstr_closure(sK137,X0)),X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_176010]) ).
tcf(c_191210,plain,
! [X0: $i,X1: $i] :
( subset(sK91(sK137,topstr_closure(sK137,X0)),X1)
| subset(topstr_closure(sK137,X0),sK202(sK91(sK137,topstr_closure(sK137,X0)),X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_176013]) ).
tcf(c_191211,plain,
! [X0: $i,X1: $i] :
( subset(sK91(sK137,topstr_closure(sK137,X0)),X1)
| in(sK202(sK91(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_176012]) ).
tcf(c_191212,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| subset(sK295(sK137,the_topology(sK137)),X0)
| ( sK296(sK137,the_topology(sK137),sK202(sK295(sK137,the_topology(sK137)),X0)) = sK202(sK295(sK137,the_topology(sK137)),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_176134]) ).
tcf(c_191213,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| subset(sK302(sK137,the_carrier(sK137)),X0)
| ( sK304(sK137,the_carrier(sK137),sK202(sK302(sK137,the_carrier(sK137)),X0)) = sK202(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_176975]) ).
tcf(c_191214,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| subset(sK302(sK137,the_carrier(sK137)),X0)
| ( sK303(sK137,the_carrier(sK137),sK202(sK302(sK137,the_carrier(sK137)),X0)) = sK202(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_176974]) ).
tcf(c_191215,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| subset(sK302(sK137,the_carrier(sK137)),X0)
| subset(the_carrier(sK137),sK202(sK302(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_176981]) ).
tcf(c_191216,plain,
! [X0: $i] :
( subset(sK123(sK137,the_carrier(sK137)),X0)
| ( sK124(sK137,the_carrier(sK137),sK202(sK123(sK137,the_carrier(sK137)),X0)) = sK202(sK123(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ element(sK202(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_176971]) ).
tcf(c_191217,plain,
! [X0: $i] :
( subset(sK123(sK137,the_carrier(sK137)),X0)
| subset(the_carrier(sK137),sK202(sK123(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ element(sK202(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_176976]) ).
tcf(c_191218,plain,
! [X0: $i] :
( subset(sK91(sK137,the_carrier(sK137)),X0)
| ( sK92(sK137,the_carrier(sK137),sK202(sK91(sK137,the_carrier(sK137)),X0)) = sK202(sK91(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_176980]) ).
tcf(c_191219,plain,
! [X0: $i] :
( subset(sK91(sK137,the_carrier(sK137)),X0)
| in(sK202(sK91(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_176982]) ).
tcf(c_191220,plain,
! [X0: $i] :
( subset(sK91(sK137,the_carrier(sK137)),X0)
| subset(the_carrier(sK137),sK202(sK91(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_176983]) ).
tcf(c_191221,plain,
! [X0: $i] :
( subset(sK147(sK137,the_carrier(sK137)),X0)
| subset(the_carrier(sK137),sK202(sK147(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ element(sK202(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_176978]) ).
tcf(c_191222,plain,
! [X0: $i] :
( subset(sK147(sK137,the_carrier(sK137)),X0)
| closed_subset(sK202(sK147(sK137,the_carrier(sK137)),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK202(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_176977]) ).
tcf(c_191223,plain,
! [X0: $i] :
( sP34(powerset(the_carrier(sK137)),sK137)
| subset(sK295(sK137,powerset(the_carrier(sK137))),X0)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK202(sK295(sK137,powerset(the_carrier(sK137))),X0)) = sK202(sK295(sK137,powerset(the_carrier(sK137))),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_176995]) ).
tcf(c_191224,plain,
! [X0: $i] :
( subset(sK93(sK137,powerset(the_carrier(sK137))),X0)
| in(sK202(sK93(sK137,powerset(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_176997]) ).
tcf(c_191225,plain,
! [X0: $i] :
( subset(topstr_closure(sK137,sK138),X0)
| in(sK202(topstr_closure(sK137,sK138),X0),sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(sK202(topstr_closure(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_662,c_177233]) ).
tcf(c_191226,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| subset(sK208(powerset(the_carrier(sK137))),sK202(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_177405]) ).
tcf(c_191227,plain,
! [X0: $i] :
( subset(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| subset(sK208(powerset(the_carrier(sK137))),sK202(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ element(sK202(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_177400]) ).
tcf(c_191228,plain,
! [X0: $i] :
( subset(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK202(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)) = sK202(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_177404]) ).
tcf(c_191229,plain,
! [X0: $i] :
( subset(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| subset(sK208(powerset(the_carrier(sK137))),sK202(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_177407]) ).
tcf(c_191230,plain,
! [X0: $i] :
( subset(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| in(sK202(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_177406]) ).
tcf(c_191231,plain,
! [X0: $i] :
( subset(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| subset(sK208(powerset(the_carrier(sK137))),sK202(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ element(sK202(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_177402]) ).
tcf(c_191232,plain,
! [X0: $i] :
( subset(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| closed_subset(sK202(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK202(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_177401]) ).
tcf(c_191233,plain,
! [X0: $i] :
( subset(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0)
| in(sK202(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_177421]) ).
tcf(c_191234,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK302(sK137,sK207(the_carrier(sK137))),X0)
| subset(sK207(the_carrier(sK137)),sK202(sK302(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_182970]) ).
tcf(c_191235,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK123(sK137,sK207(the_carrier(sK137))),X0)
| subset(sK207(the_carrier(sK137)),sK202(sK123(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ element(sK202(sK123(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_182965]) ).
tcf(c_191236,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK91(sK137,sK207(the_carrier(sK137))),X0)
| ( sK92(sK137,sK207(the_carrier(sK137)),sK202(sK91(sK137,sK207(the_carrier(sK137))),X0)) = sK202(sK91(sK137,sK207(the_carrier(sK137))),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_182969]) ).
tcf(c_191237,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK91(sK137,sK207(the_carrier(sK137))),X0)
| subset(sK207(the_carrier(sK137)),sK202(sK91(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_182972]) ).
tcf(c_191238,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK91(sK137,sK207(the_carrier(sK137))),X0)
| in(sK202(sK91(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_182971]) ).
tcf(c_191239,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK147(sK137,sK207(the_carrier(sK137))),X0)
| subset(sK207(the_carrier(sK137)),sK202(sK147(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ element(sK202(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_182967]) ).
tcf(c_191240,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK147(sK137,sK207(the_carrier(sK137))),X0)
| closed_subset(sK202(sK147(sK137,sK207(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK202(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_182966]) ).
tcf(c_191241,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK302(sK137,sK325(the_carrier(sK137))),X0)
| subset(sK325(the_carrier(sK137)),sK202(sK302(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_184375]) ).
tcf(c_191242,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK123(sK137,sK325(the_carrier(sK137))),X0)
| subset(sK325(the_carrier(sK137)),sK202(sK123(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ element(sK202(sK123(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_184370]) ).
tcf(c_191243,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK91(sK137,sK325(the_carrier(sK137))),X0)
| ( sK92(sK137,sK325(the_carrier(sK137)),sK202(sK91(sK137,sK325(the_carrier(sK137))),X0)) = sK202(sK91(sK137,sK325(the_carrier(sK137))),X0) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_184374]) ).
tcf(c_191244,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK91(sK137,sK325(the_carrier(sK137))),X0)
| subset(sK325(the_carrier(sK137)),sK202(sK91(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_184377]) ).
tcf(c_191245,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK91(sK137,sK325(the_carrier(sK137))),X0)
| in(sK202(sK91(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_184376]) ).
tcf(c_191246,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK147(sK137,sK325(the_carrier(sK137))),X0)
| subset(sK325(the_carrier(sK137)),sK202(sK147(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ element(sK202(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_184372]) ).
tcf(c_191247,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK147(sK137,sK325(the_carrier(sK137))),X0)
| closed_subset(sK202(sK147(sK137,sK325(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK202(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_184371]) ).
tcf(c_191562,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_666,c_546]) ).
tcf(c_191563,plain,
! [X0: $i,X1: $i] :
( in(sK154(powerset(X1)),powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_666,c_542]) ).
tcf(c_191564,plain,
! [X0: $i,X1: $i] :
( ~ empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_666,c_781]) ).
tcf(c_191566,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(X0,sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_666,c_176867]) ).
tcf(c_191567,plain,
! [X0: $i] :
( in(X0,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_666,c_176193]) ).
tcf(c_191568,plain,
! [X0: $i] : ~ subset(sK126(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_666,c_188650]) ).
tcf(c_191569,plain,
! [X0: $i] : ~ subset(sK323(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_666,c_188660]) ).
tcf(c_191606,plain,
! [X0: $i] :
( sP3(powerset(X0))
| subset(sK62(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_120,c_667]) ).
tcf(c_191608,plain,
! [X0: $i] :
( ordinal(powerset(X0))
| subset(sK139(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_383,c_667]) ).
tcf(c_191609,plain,
! [X0: $i,X1: $i] :
( disjoint(powerset(X0),X1)
| subset(sK142(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_416,c_667]) ).
tcf(c_191610,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,powerset(X1))
| subset(sK142(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_417,c_667]) ).
tcf(c_191611,plain,
! [X0: $i] :
( relation(powerset(X0))
| subset(sK175(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_580,c_667]) ).
tcf(c_191612,plain,
! [X0: $i] :
( subset(sK181(powerset(X0)),X0)
| ( powerset(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_598,c_667]) ).
tcf(c_191613,plain,
! [X0: $i] :
( subset(sK185(powerset(X0)),X0)
| ~ sP20(powerset(X0)) ),
inference(superposition,[status(thm)],[c_603,c_667]) ).
tcf(c_191615,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| subset(sK202(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_662,c_667]) ).
tcf(c_191617,plain,
! [X0: $i] :
( subset(sK274(powerset(X0)),X0)
| ~ sP32(powerset(X0)) ),
inference(superposition,[status(thm)],[c_858,c_667]) ).
tcf(c_191618,plain,
! [X0: $i] :
( epsilon_transitive(powerset(X0))
| subset(sK340(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_1081,c_667]) ).
tcf(c_191619,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| subset(sK369(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_1253,c_667]) ).
tcf(c_191620,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| subset(sK370(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_1254,c_667]) ).
tcf(c_191622,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| subset(sK303(sK137,X1,X0),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47965,c_667]) ).
tcf(c_191623,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK137)
| subset(sK296(sK137,X0,X1),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48019,c_667]) ).
tcf(c_191624,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),powerset(the_carrier(sK137))),sK137)
| subset(sK145(sK137,powerset(the_carrier(sK137))),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_176998,c_667]) ).
tcf(c_191625,plain,
( sP3(sK91(sK137,sK138))
| subset(sK62(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178460,c_667]) ).
tcf(c_191626,plain,
( ordinal(sK91(sK137,sK138))
| subset(sK139(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178684,c_667]) ).
tcf(c_191627,plain,
( relation(sK91(sK137,sK138))
| subset(sK175(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178947,c_667]) ).
tcf(c_191628,plain,
( epsilon_transitive(sK91(sK137,sK138))
| subset(sK340(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_180305,c_667]) ).
tcf(c_191629,plain,
( epsilon_connected(sK91(sK137,sK138))
| subset(sK369(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_180597,c_667]) ).
tcf(c_191630,plain,
( epsilon_connected(sK91(sK137,sK138))
| subset(sK370(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_180850,c_667]) ).
tcf(c_191632,plain,
( subset(sK185(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_182179,c_667]) ).
tcf(c_191634,plain,
( subset(sK274(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183903,c_667]) ).
tcf(c_191635,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| subset(sK142(sK91(sK137,sK138),X0),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_186302,c_667]) ).
tcf(c_191636,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| subset(sK142(X0,sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_186681,c_667]) ).
tcf(c_191785,plain,
! [X0: $i] :
( being_limit_ordinal(powerset(X0))
| ( powerset(X0) != X0 ) ),
inference(superposition,[status(thm)],[c_536,c_707]) ).
tcf(c_191810,plain,
! [X0: $i] :
( subset(sK91(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ proper_subset(sK202(sK91(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_191200,c_492]) ).
tcf(c_191821,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ proper_subset(powerset(the_carrier(sK137)),sK147(sK137,X0)) ),
inference(superposition,[status(thm)],[c_190849,c_492]) ).
tcf(c_191832,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ proper_subset(powerset(the_carrier(sK137)),sK123(sK137,X0)) ),
inference(superposition,[status(thm)],[c_190854,c_492]) ).
tcf(c_191843,plain,
( ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK181(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_190236,c_546]) ).
tcf(c_191844,plain,
( in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_190236,c_542]) ).
tcf(c_191845,plain,
( ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190236,c_781]) ).
tcf(c_191846,plain,
( element(sK181(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_190236,c_701]) ).
tcf(c_191847,plain,
( subset(sK181(sK91(sK137,sK138)),the_carrier(sK137))
| ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_190236,c_667]) ).
tcf(c_191848,plain,
( sP36(sK137,sK138)
| in(sK181(sK91(sK137,sK138)),sK302(sK137,sK138))
| ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ closed_subset(sK181(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK181(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_190236,c_176867]) ).
tcf(c_191849,plain,
( in(sK181(sK91(sK137,sK138)),sK91(sK137,sK138))
| ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ closed_subset(sK181(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK181(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_190236,c_176193]) ).
tcf(c_191881,plain,
! [X0: $i] :
( sP3(sK91(sK137,X0))
| subset(X0,sK62(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_120,c_190604]) ).
tcf(c_191883,plain,
! [X0: $i] :
( ordinal(sK91(sK137,X0))
| subset(X0,sK139(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_383,c_190604]) ).
tcf(c_191884,plain,
! [X0: $i,X1: $i] :
( disjoint(sK91(sK137,X0),X1)
| subset(X0,sK142(sK91(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_416,c_190604]) ).
tcf(c_191885,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,sK91(sK137,X0))
| subset(X0,sK142(X1,sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_417,c_190604]) ).
tcf(c_191886,plain,
! [X0: $i] :
( relation(sK91(sK137,X0))
| subset(X0,sK175(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_580,c_190604]) ).
tcf(c_191887,plain,
! [X0: $i] :
( subset(X0,sK181(sK91(sK137,X0)))
| ( sK91(sK137,X0) = empty_set )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_598,c_190604]) ).
tcf(c_191888,plain,
! [X0: $i] :
( subset(X0,sK185(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_603,c_190604]) ).
tcf(c_191890,plain,
! [X0: $i,X1: $i] :
( subset(sK91(sK137,X0),X1)
| subset(X0,sK202(sK91(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_662,c_190604]) ).
tcf(c_191891,plain,
! [X0: $i] :
( subset(X0,sK274(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_858,c_190604]) ).
tcf(c_191892,plain,
! [X0: $i] :
( epsilon_transitive(sK91(sK137,X0))
| subset(X0,sK340(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1081,c_190604]) ).
tcf(c_191893,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,X0))
| subset(X0,sK369(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1253,c_190604]) ).
tcf(c_191894,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,X0))
| subset(X0,sK370(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1254,c_190604]) ).
tcf(c_191995,plain,
( sP3(sK123(sK137,sK138))
| subset(sK138,sK62(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK62(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_120,c_190612]) ).
tcf(c_191997,plain,
( ordinal(sK123(sK137,sK138))
| subset(sK138,sK139(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK139(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_383,c_190612]) ).
tcf(c_191998,plain,
! [X0: $i] :
( disjoint(sK123(sK137,sK138),X0)
| subset(sK138,sK142(sK123(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ subset(sK142(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_416,c_190612]) ).
tcf(c_191999,plain,
! [X0: $i] :
( disjoint(X0,sK123(sK137,sK138))
| subset(sK138,sK142(X0,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK142(X0,sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_417,c_190612]) ).
tcf(c_192000,plain,
( relation(sK123(sK137,sK138))
| subset(sK138,sK175(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK175(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_580,c_190612]) ).
tcf(c_192001,plain,
( subset(sK138,sK181(sK123(sK137,sK138)))
| ( sK123(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ subset(sK181(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_598,c_190612]) ).
tcf(c_192002,plain,
( subset(sK138,sK185(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,sK138))
| ~ subset(sK185(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_603,c_190612]) ).
tcf(c_192004,plain,
! [X0: $i] :
( subset(sK123(sK137,sK138),X0)
| subset(sK138,sK202(sK123(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ subset(sK202(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_662,c_190612]) ).
tcf(c_192005,plain,
( subset(sK138,sK274(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,sK138))
| ~ subset(sK274(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_858,c_190612]) ).
tcf(c_192006,plain,
( epsilon_transitive(sK123(sK137,sK138))
| subset(sK138,sK340(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK340(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1081,c_190612]) ).
tcf(c_192007,plain,
( epsilon_connected(sK123(sK137,sK138))
| subset(sK138,sK369(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK369(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1253,c_190612]) ).
tcf(c_192008,plain,
( epsilon_connected(sK123(sK137,sK138))
| subset(sK138,sK370(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK370(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1254,c_190612]) ).
tcf(c_192009,plain,
( subset(sK138,sK145(sK137,sK123(sK137,sK138)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ element(sK138,powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_175061,c_190612]) ).
tcf(c_192011,plain,
( subset(sK138,sK138)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK138,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_176589,c_190612]) ).
tcf(c_192012,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(sK138,powerset(the_carrier(sK137)))
| ~ subset(set_difference(the_carrier(sK137),X0),the_carrier(sK137))
| ~ in(X0,sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_179185,c_190612]) ).
tcf(c_192013,plain,
( subset(sK138,sK154(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ subset(sK154(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_188351,c_190612]) ).
tcf(c_192075,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK123(sK137,sK138))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_192012,c_376,c_399]) ).
tcf(c_192079,plain,
( subset(sK138,sK145(sK137,sK123(sK137,sK138)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK145(sK137,sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_192009,c_376]) ).
tcf(c_192113,plain,
( sP3(sK93(sK137,sK123(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK62(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_192075]) ).
tcf(c_192115,plain,
( ordinal(sK93(sK137,sK123(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK139(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_192075]) ).
tcf(c_192116,plain,
! [X0: $i] :
( disjoint(sK93(sK137,sK123(sK137,sK138)),X0)
| subset(sK138,set_difference(the_carrier(sK137),sK142(sK93(sK137,sK123(sK137,sK138)),X0)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_192075]) ).
tcf(c_192117,plain,
! [X0: $i] :
( disjoint(X0,sK93(sK137,sK123(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK142(X0,sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_192075]) ).
tcf(c_192118,plain,
( relation(sK93(sK137,sK123(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK175(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_192075]) ).
tcf(c_192119,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK181(sK93(sK137,sK123(sK137,sK138)))))
| ( sK93(sK137,sK123(sK137,sK138)) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_192075]) ).
tcf(c_192120,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK185(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_603,c_192075]) ).
tcf(c_192122,plain,
! [X0: $i] :
( subset(sK93(sK137,sK123(sK137,sK138)),X0)
| subset(sK138,set_difference(the_carrier(sK137),sK202(sK93(sK137,sK123(sK137,sK138)),X0)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_192075]) ).
tcf(c_192123,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK274(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_858,c_192075]) ).
tcf(c_192124,plain,
( epsilon_transitive(sK93(sK137,sK123(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK340(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_192075]) ).
tcf(c_192125,plain,
( epsilon_connected(sK93(sK137,sK123(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK369(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_192075]) ).
tcf(c_192126,plain,
( epsilon_connected(sK93(sK137,sK123(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK370(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_192075]) ).
tcf(c_192202,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_967,c_179227]) ).
tcf(c_192204,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_967,c_179227]) ).
tcf(c_192207,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = empty_set )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_105912,c_179227]) ).
tcf(c_192208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = empty_set )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_105926,c_179227]) ).
tcf(c_192209,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_179227]) ).
tcf(c_192227,plain,
( ( union(sK70) = sK70 )
| ~ sP6 ),
inference(superposition,[status(thm)],[c_139,c_708]) ).
tcf(c_192228,plain,
union(omega) = omega,
inference(superposition,[status(thm)],[c_842,c_708]) ).
tcf(c_192229,plain,
union(sK287) = sK287,
inference(superposition,[status(thm)],[c_890,c_708]) ).
tcf(c_192253,plain,
! [X0: $i] :
( sP27
| sP3(sK254(X0))
| ordinal(sK62(sK254(X0))) ),
inference(superposition,[status(thm)],[c_120,c_802]) ).
tcf(c_192255,plain,
! [X0: $i] :
( sP27
| ordinal(sK254(X0))
| ordinal(sK139(sK254(X0))) ),
inference(superposition,[status(thm)],[c_383,c_802]) ).
tcf(c_192256,plain,
! [X0: $i,X1: $i] :
( sP27
| disjoint(sK254(X0),X1)
| ordinal(sK142(sK254(X0),X1)) ),
inference(superposition,[status(thm)],[c_416,c_802]) ).
tcf(c_192257,plain,
! [X0: $i,X1: $i] :
( sP27
| disjoint(X0,sK254(X1))
| ordinal(sK142(X0,sK254(X1))) ),
inference(superposition,[status(thm)],[c_417,c_802]) ).
tcf(c_192258,plain,
! [X0: $i] :
( sP27
| relation(sK254(X0))
| ordinal(sK175(sK254(X0))) ),
inference(superposition,[status(thm)],[c_580,c_802]) ).
tcf(c_192259,plain,
! [X0: $i] :
( sP27
| ordinal(sK181(sK254(X0)))
| ( sK254(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_598,c_802]) ).
tcf(c_192260,plain,
! [X0: $i] :
( sP27
| ordinal(sK185(sK254(X0)))
| ~ sP20(sK254(X0)) ),
inference(superposition,[status(thm)],[c_603,c_802]) ).
tcf(c_192262,plain,
! [X0: $i,X1: $i] :
( sP27
| subset(sK254(X0),X1)
| ordinal(sK202(sK254(X0),X1)) ),
inference(superposition,[status(thm)],[c_662,c_802]) ).
tcf(c_192263,plain,
! [X0: $i] :
( sP27
| ordinal(sK274(sK254(X0)))
| ~ sP32(sK254(X0)) ),
inference(superposition,[status(thm)],[c_858,c_802]) ).
tcf(c_192264,plain,
! [X0: $i] :
( sP27
| epsilon_transitive(sK254(X0))
| ordinal(sK340(sK254(X0))) ),
inference(superposition,[status(thm)],[c_1081,c_802]) ).
tcf(c_192265,plain,
! [X0: $i] :
( sP27
| epsilon_connected(sK254(X0))
| ordinal(sK369(sK254(X0))) ),
inference(superposition,[status(thm)],[c_1253,c_802]) ).
tcf(c_192266,plain,
! [X0: $i] :
( sP27
| epsilon_connected(sK254(X0))
| ordinal(sK370(sK254(X0))) ),
inference(superposition,[status(thm)],[c_1254,c_802]) ).
tcf(c_192327,plain,
! [X0: $i] :
( ~ finite(X0)
| ~ in(omega,relation_dom(sK270(X0))) ),
inference(superposition,[status(thm)],[c_849,c_546]) ).
tcf(c_192330,plain,
! [X0: $i] :
( element(relation_dom(sK270(X0)),omega)
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_849,c_701]) ).
tcf(c_192366,plain,
( sP3(sK147(sK137,sK138))
| closed_subset(sK62(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK62(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_120,c_190613]) ).
tcf(c_192368,plain,
( ordinal(sK147(sK137,sK138))
| closed_subset(sK139(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK139(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_383,c_190613]) ).
tcf(c_192369,plain,
! [X0: $i] :
( disjoint(sK147(sK137,sK138),X0)
| closed_subset(sK142(sK147(sK137,sK138),X0),sK137)
| ~ topological_space(sK137)
| ~ subset(sK142(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_416,c_190613]) ).
tcf(c_192370,plain,
! [X0: $i] :
( disjoint(X0,sK147(sK137,sK138))
| closed_subset(sK142(X0,sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK142(X0,sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_417,c_190613]) ).
tcf(c_192371,plain,
( relation(sK147(sK137,sK138))
| closed_subset(sK175(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK175(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_580,c_190613]) ).
tcf(c_192372,plain,
( closed_subset(sK181(sK147(sK137,sK138)),sK137)
| ( sK147(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ subset(sK181(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_598,c_190613]) ).
tcf(c_192373,plain,
( closed_subset(sK185(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK138))
| ~ subset(sK185(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_603,c_190613]) ).
tcf(c_192375,plain,
! [X0: $i] :
( subset(sK147(sK137,sK138),X0)
| closed_subset(sK202(sK147(sK137,sK138),X0),sK137)
| ~ topological_space(sK137)
| ~ subset(sK202(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_662,c_190613]) ).
tcf(c_192376,plain,
( closed_subset(sK274(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK138))
| ~ subset(sK274(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_858,c_190613]) ).
tcf(c_192377,plain,
( epsilon_transitive(sK147(sK137,sK138))
| closed_subset(sK340(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK340(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1081,c_190613]) ).
tcf(c_192378,plain,
( epsilon_connected(sK147(sK137,sK138))
| closed_subset(sK369(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK369(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1253,c_190613]) ).
tcf(c_192379,plain,
( epsilon_connected(sK147(sK137,sK138))
| closed_subset(sK370(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK370(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1254,c_190613]) ).
tcf(c_192380,plain,
( closed_subset(sK145(sK137,sK147(sK137,sK138)),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ element(sK138,powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_175059,c_190613]) ).
tcf(c_192383,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ element(sK138,powerset(the_carrier(sK137)))
| ~ subset(set_difference(the_carrier(sK137),X0),the_carrier(sK137))
| ~ in(X0,sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_179183,c_190613]) ).
tcf(c_192384,plain,
( closed_subset(sK154(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ subset(sK154(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_188349,c_190613]) ).
tcf(c_192446,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK147(sK137,sK138))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_192383,c_376,c_399]) ).
tcf(c_192450,plain,
( closed_subset(sK145(sK137,sK147(sK137,sK138)),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK145(sK137,sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_192380,c_376]) ).
tcf(c_192521,plain,
( sP3(sK93(sK137,sK147(sK137,sK138)))
| closed_subset(set_difference(the_carrier(sK137),sK62(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_192446]) ).
tcf(c_192523,plain,
( ordinal(sK93(sK137,sK147(sK137,sK138)))
| closed_subset(set_difference(the_carrier(sK137),sK139(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_192446]) ).
tcf(c_192524,plain,
! [X0: $i] :
( disjoint(sK93(sK137,sK147(sK137,sK138)),X0)
| closed_subset(set_difference(the_carrier(sK137),sK142(sK93(sK137,sK147(sK137,sK138)),X0)),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_192446]) ).
tcf(c_192525,plain,
! [X0: $i] :
( disjoint(X0,sK93(sK137,sK147(sK137,sK138)))
| closed_subset(set_difference(the_carrier(sK137),sK142(X0,sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_192446]) ).
tcf(c_192526,plain,
( relation(sK93(sK137,sK147(sK137,sK138)))
| closed_subset(set_difference(the_carrier(sK137),sK175(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_192446]) ).
tcf(c_192527,plain,
( closed_subset(set_difference(the_carrier(sK137),sK181(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ( sK93(sK137,sK147(sK137,sK138)) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_192446]) ).
tcf(c_192528,plain,
( closed_subset(set_difference(the_carrier(sK137),sK185(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_603,c_192446]) ).
tcf(c_192530,plain,
! [X0: $i] :
( subset(sK93(sK137,sK147(sK137,sK138)),X0)
| closed_subset(set_difference(the_carrier(sK137),sK202(sK93(sK137,sK147(sK137,sK138)),X0)),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_192446]) ).
tcf(c_192531,plain,
( closed_subset(set_difference(the_carrier(sK137),sK274(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_858,c_192446]) ).
tcf(c_192532,plain,
( epsilon_transitive(sK93(sK137,sK147(sK137,sK138)))
| closed_subset(set_difference(the_carrier(sK137),sK340(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_192446]) ).
tcf(c_192533,plain,
( epsilon_connected(sK93(sK137,sK147(sK137,sK138)))
| closed_subset(set_difference(the_carrier(sK137),sK369(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_192446]) ).
tcf(c_192534,plain,
( epsilon_connected(sK93(sK137,sK147(sK137,sK138)))
| closed_subset(set_difference(the_carrier(sK137),sK370(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_192446]) ).
tcf(c_192596,plain,
( sP3(sK147(sK137,sK138))
| subset(sK138,sK62(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK62(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_120,c_190614]) ).
tcf(c_192598,plain,
( ordinal(sK147(sK137,sK138))
| subset(sK138,sK139(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK139(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_383,c_190614]) ).
tcf(c_192599,plain,
! [X0: $i] :
( disjoint(sK147(sK137,sK138),X0)
| subset(sK138,sK142(sK147(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ subset(sK142(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_416,c_190614]) ).
tcf(c_192600,plain,
! [X0: $i] :
( disjoint(X0,sK147(sK137,sK138))
| subset(sK138,sK142(X0,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK142(X0,sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_417,c_190614]) ).
tcf(c_192601,plain,
( relation(sK147(sK137,sK138))
| subset(sK138,sK175(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK175(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_580,c_190614]) ).
tcf(c_192602,plain,
( subset(sK138,sK181(sK147(sK137,sK138)))
| ( sK147(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ subset(sK181(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_598,c_190614]) ).
tcf(c_192603,plain,
( subset(sK138,sK185(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK138))
| ~ subset(sK185(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_603,c_190614]) ).
tcf(c_192605,plain,
! [X0: $i] :
( subset(sK147(sK137,sK138),X0)
| subset(sK138,sK202(sK147(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ subset(sK202(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_662,c_190614]) ).
tcf(c_192606,plain,
( subset(sK138,sK274(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK138))
| ~ subset(sK274(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_858,c_190614]) ).
tcf(c_192607,plain,
( epsilon_transitive(sK147(sK137,sK138))
| subset(sK138,sK340(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK340(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1081,c_190614]) ).
tcf(c_192608,plain,
( epsilon_connected(sK147(sK137,sK138))
| subset(sK138,sK369(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK369(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1253,c_190614]) ).
tcf(c_192609,plain,
( epsilon_connected(sK147(sK137,sK138))
| subset(sK138,sK370(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK370(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1254,c_190614]) ).
tcf(c_192610,plain,
( subset(sK138,sK145(sK137,sK147(sK137,sK138)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ element(sK138,powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_175059,c_190614]) ).
tcf(c_192613,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ element(sK138,powerset(the_carrier(sK137)))
| ~ subset(set_difference(the_carrier(sK137),X0),the_carrier(sK137))
| ~ in(X0,sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_179183,c_190614]) ).
tcf(c_192614,plain,
( subset(sK138,sK154(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ subset(sK154(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_188349,c_190614]) ).
tcf(c_192676,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK147(sK137,sK138))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_192613,c_376,c_399]) ).
tcf(c_192680,plain,
( subset(sK138,sK145(sK137,sK147(sK137,sK138)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK145(sK137,sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_192610,c_376]) ).
tcf(c_192720,plain,
( sP3(sK93(sK137,sK147(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK62(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_192676]) ).
tcf(c_192722,plain,
( ordinal(sK93(sK137,sK147(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK139(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_192676]) ).
tcf(c_192723,plain,
! [X0: $i] :
( disjoint(sK93(sK137,sK147(sK137,sK138)),X0)
| subset(sK138,set_difference(the_carrier(sK137),sK142(sK93(sK137,sK147(sK137,sK138)),X0)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_192676]) ).
tcf(c_192724,plain,
! [X0: $i] :
( disjoint(X0,sK93(sK137,sK147(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK142(X0,sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_192676]) ).
tcf(c_192725,plain,
( relation(sK93(sK137,sK147(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK175(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_192676]) ).
tcf(c_192726,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK181(sK93(sK137,sK147(sK137,sK138)))))
| ( sK93(sK137,sK147(sK137,sK138)) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_192676]) ).
tcf(c_192727,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK185(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_603,c_192676]) ).
tcf(c_192729,plain,
! [X0: $i] :
( subset(sK93(sK137,sK147(sK137,sK138)),X0)
| subset(sK138,set_difference(the_carrier(sK137),sK202(sK93(sK137,sK147(sK137,sK138)),X0)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_192676]) ).
tcf(c_192730,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK274(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_858,c_192676]) ).
tcf(c_192731,plain,
( epsilon_transitive(sK93(sK137,sK147(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK340(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_192676]) ).
tcf(c_192732,plain,
( epsilon_connected(sK93(sK137,sK147(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK369(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_192676]) ).
tcf(c_192733,plain,
( epsilon_connected(sK93(sK137,sK147(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK370(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_192676]) ).
tcf(c_192815,plain,
( topological_space(sK137)
| ~ sP42(sK137)
| ~ in(the_carrier(sK137),the_topology(sK137))
| ~ proper_subset(powerset(the_carrier(sK137)),sK378(sK137)) ),
inference(superposition,[status(thm)],[c_190844,c_492]) ).
tcf(c_192826,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ proper_subset(powerset(the_carrier(sK137)),sK125(sK137,X0)) ),
inference(superposition,[status(thm)],[c_190852,c_492]) ).
tcf(c_192831,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X2)) ) ),
inference(demodulation,[status(thm)],[c_179228,c_967]) ).
tcf(c_192838,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X2)) ) ),
inference(superposition,[status(thm)],[c_967,c_192831]) ).
tcf(c_192840,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X2)) ) ),
inference(superposition,[status(thm)],[c_967,c_192831]) ).
tcf(c_192842,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( unordered_pair(powerset(empty_set),unordered_pair(empty_set,X0)) != unordered_pair(powerset(empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_192831]) ).
tcf(c_192843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X3)) ) ),
inference(superposition,[status(thm)],[c_105912,c_192831]) ).
tcf(c_192844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X3)) ) ),
inference(superposition,[status(thm)],[c_105926,c_192831]) ).
tcf(c_192845,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( unordered_pair(unordered_pair(empty_set,X0),powerset(empty_set)) != unordered_pair(powerset(empty_set),unordered_pair(empty_set,X1)) ) ),
inference(superposition,[status(thm)],[c_330,c_192831]) ).
tcf(c_192846,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(powerset(empty_set),unordered_pair(X2,empty_set)) ) ),
inference(superposition,[status(thm)],[c_967,c_192831]) ).
tcf(c_192900,plain,
( ordinal(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK340(sK91(sK137,sK138))) = sK340(sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ epsilon_connected(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_180304,c_1086]) ).
tcf(c_192903,plain,
( sP36(sK137,sK138)
| ordinal(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK340(sK302(sK137,sK138))) = sK340(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ epsilon_connected(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_180308,c_1086]) ).
tcf(c_192904,plain,
( sP36(sK137,sK138)
| ordinal(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK340(sK302(sK137,sK138))) = sK340(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ epsilon_connected(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_180307,c_1086]) ).
tcf(c_193207,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_difference(X1,X0),X0)) = set_difference(X0,set_difference(set_difference(X1,X0),X0)),
inference(superposition,[status(thm)],[c_410,c_179569]) ).
tcf(c_193208,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X0,X1)) = set_difference(X1,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_642,c_179569]) ).
tcf(c_193210,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,set_union2(X1,X0)),set_difference(X1,X0)) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_420,c_179569]) ).
tcf(c_193211,plain,
! [X0: $i] : set_difference(set_union2(X0,empty_set),empty_set) = set_difference(X0,empty_set),
inference(superposition,[status(thm)],[c_679,c_179569]) ).
tcf(c_193212,plain,
! [X0: $i] : set_difference(set_union2(empty_set,X0),X0) = set_difference(empty_set,X0),
inference(superposition,[status(thm)],[c_680,c_179569]) ).
tcf(c_193213,plain,
! [X0: $i] : set_difference(set_union2(X0,X0),empty_set) = set_difference(X0,empty_set),
inference(superposition,[status(thm)],[c_13761,c_179569]) ).
tcf(c_193214,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(set_difference(X0,X1),X0),set_difference(X1,set_difference(X1,X0))) = set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X1,X0))),
inference(superposition,[status(thm)],[c_986,c_179569]) ).
tcf(c_193216,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(X0,set_difference(X1,X0)))
| ~ finite(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_179569,c_1011]) ).
tcf(c_193218,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,set_difference(X1,X0)),set_union2(X0,X1)),
inference(superposition,[status(thm)],[c_179569,c_399]) ).
tcf(c_193219,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(set_difference(X0,X1),set_union2(X1,X0)),set_difference(X1,set_difference(X0,X1))) = set_difference(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_179569,c_179569]) ).
tcf(c_193220,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),set_difference(set_difference(X0,X1),set_union2(X1,X0))) = set_difference(set_union2(X1,X0),set_difference(X1,set_difference(X0,X1))),
inference(superposition,[status(thm)],[c_179569,c_986]) ).
tcf(c_193221,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_difference(X1,set_difference(X0,X1))) = set_union2(set_difference(X0,X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_179569,c_410]) ).
tcf(c_193550,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,X1),set_union2(X1,X0)) = set_union2(set_difference(X0,X1),X1),
inference(superposition,[status(thm)],[c_410,c_179574]) ).
tcf(c_193551,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X0,X1)) = set_union2(X0,X1),
inference(superposition,[status(thm)],[c_642,c_179574]) ).
tcf(c_193553,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(set_union2(X1,X0),X0)) = set_difference(X0,set_difference(set_union2(X1,X0),X0)),
inference(superposition,[status(thm)],[c_179574,c_179569]) ).
tcf(c_193555,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X1,X0))
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_179574,c_633]) ).
tcf(c_193556,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_union2(X1,X0)) = set_difference(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_179574,c_420]) ).
tcf(c_193558,plain,
! [X0: $i,X1: $i] : set_union2(set_union2(X0,X1),set_union2(X1,X0)) = set_union2(set_union2(X0,X1),X1),
inference(superposition,[status(thm)],[c_179574,c_179574]) ).
tcf(c_193559,plain,
! [X0: $i,X1: $i] : subset(set_union2(X0,X1),set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_179574,c_181192]) ).
tcf(c_193589,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(sK204(X0,X1))
| ~ are_equipotent(X0,X1)
| ~ well_ordering(sK204(X0,X1)) ),
inference(superposition,[status(thm)],[c_105457,c_593]) ).
tcf(c_193590,plain,
! [X0: $i,X1: $i] :
( connected(sK204(X0,X1))
| ~ are_equipotent(X0,X1)
| ~ well_ordering(sK204(X0,X1)) ),
inference(superposition,[status(thm)],[c_105457,c_592]) ).
tcf(c_193591,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK204(X0,X1))
| ~ are_equipotent(X0,X1)
| ~ well_ordering(sK204(X0,X1)) ),
inference(superposition,[status(thm)],[c_105457,c_591]) ).
tcf(c_193592,plain,
! [X0: $i,X1: $i] :
( transitive(sK204(X0,X1))
| ~ are_equipotent(X0,X1)
| ~ well_ordering(sK204(X0,X1)) ),
inference(superposition,[status(thm)],[c_105457,c_590]) ).
tcf(c_193593,plain,
! [X0: $i,X1: $i] :
( reflexive(sK204(X0,X1))
| ~ are_equipotent(X0,X1)
| ~ well_ordering(sK204(X0,X1)) ),
inference(superposition,[status(thm)],[c_105457,c_589]) ).
tcf(c_193694,plain,
( ~ topological_space(sK137)
| ~ in(the_topology(sK137),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_106073,c_546]) ).
tcf(c_193697,plain,
( element(the_carrier(sK137),the_topology(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_106073,c_701]) ).
tcf(c_193698,plain,
( open_subset(the_carrier(sK137),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_106073,c_176993]) ).
tcf(c_193715,plain,
! [X0: $i] : ~ proper_subset(X0,sK208(powerset(X0))),
inference(superposition,[status(thm)],[c_190840,c_492]) ).
tcf(c_193716,plain,
sK208(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_190840,c_419]) ).
tcf(c_193720,plain,
~ proper_subset(the_carrier(sK320),sK319(sK320)),
inference(superposition,[status(thm)],[c_190843,c_492]) ).
tcf(c_193727,plain,
! [X0: $i] :
( subset(sK91(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK202(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_191199,c_546]) ).
tcf(c_193728,plain,
! [X0: $i] :
( subset(sK91(sK137,sK138),X0)
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_191199,c_542]) ).
tcf(c_193729,plain,
! [X0: $i] :
( subset(sK91(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_191199,c_781]) ).
tcf(c_193730,plain,
! [X0: $i] :
( subset(sK91(sK137,sK138),X0)
| element(sK202(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_191199,c_701]) ).
tcf(c_193731,plain,
! [X0: $i] :
( subset(sK91(sK137,sK138),X0)
| subset(sK202(sK91(sK137,sK138),X0),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_191199,c_667]) ).
tcf(c_193732,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(sK91(sK137,sK138),X0)
| in(sK202(sK91(sK137,sK138),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK202(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK202(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_191199,c_176867]) ).
tcf(c_193733,plain,
! [X0: $i] :
( subset(sK91(sK137,sK138),X0)
| in(sK202(sK91(sK137,sK138),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK202(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK202(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_191199,c_176193]) ).
tcf(c_193775,plain,
( sP36(sK137,sK138)
| ( sK302(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ proper_subset(sK181(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_190240,c_492]) ).
tcf(c_193788,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(sK302(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ proper_subset(sK202(sK302(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_191203,c_492]) ).
tcf(c_193806,plain,
! [X0: $i] :
( sP3(sK91(sK137,X0))
| in(sK62(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_120,c_190603]) ).
tcf(c_193808,plain,
! [X0: $i] :
( ordinal(sK91(sK137,X0))
| in(sK139(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_383,c_190603]) ).
tcf(c_193809,plain,
! [X0: $i,X1: $i] :
( disjoint(sK91(sK137,X0),X1)
| in(sK142(sK91(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_416,c_190603]) ).
tcf(c_193810,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,sK91(sK137,X0))
| in(sK142(X1,sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_417,c_190603]) ).
tcf(c_193811,plain,
! [X0: $i] :
( relation(sK91(sK137,X0))
| in(sK175(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_580,c_190603]) ).
tcf(c_193812,plain,
! [X0: $i] :
( in(sK181(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ( sK91(sK137,X0) = empty_set )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_598,c_190603]) ).
tcf(c_193813,plain,
! [X0: $i] :
( in(sK185(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_603,c_190603]) ).
tcf(c_193815,plain,
! [X0: $i,X1: $i] :
( subset(sK91(sK137,X0),X1)
| in(sK202(sK91(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_662,c_190603]) ).
tcf(c_193816,plain,
! [X0: $i] :
( in(sK274(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_858,c_190603]) ).
tcf(c_193817,plain,
! [X0: $i] :
( epsilon_transitive(sK91(sK137,X0))
| in(sK340(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1081,c_190603]) ).
tcf(c_193818,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,X0))
| in(sK369(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1253,c_190603]) ).
tcf(c_193819,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,X0))
| in(sK370(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1254,c_190603]) ).
tcf(c_193899,plain,
( ~ topological_space(sK291)
| ~ in(the_topology(sK291),the_carrier(sK291)) ),
inference(superposition,[status(thm)],[c_106091,c_546]) ).
tcf(c_193900,plain,
( in(sK154(the_topology(sK291)),the_topology(sK291))
| ~ topological_space(sK291) ),
inference(superposition,[status(thm)],[c_106091,c_542]) ).
tcf(c_193901,plain,
( ~ topological_space(sK291)
| ~ empty(the_topology(sK291)) ),
inference(superposition,[status(thm)],[c_106091,c_781]) ).
tcf(c_193902,plain,
( element(the_carrier(sK291),the_topology(sK291))
| ~ topological_space(sK291) ),
inference(superposition,[status(thm)],[c_106091,c_701]) ).
tcf(c_193915,plain,
! [X0: $i,X1: $i] :
( ~ sP2(X0,X1)
| ~ in(X0,sK53(X0,X1)) ),
inference(superposition,[status(thm)],[c_96,c_546]) ).
tcf(c_193916,plain,
! [X0: $i,X1: $i] :
( in(sK154(X0),X0)
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_542]) ).
tcf(c_193917,plain,
! [X0: $i,X1: $i] :
( ~ empty(X0)
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_781]) ).
tcf(c_193918,plain,
! [X0: $i,X1: $i] :
( element(sK53(X0,X1),X0)
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_701]) ).
tcf(c_193919,plain,
! [X0: $i,X1: $i] :
( in(sK53(sK99(X0),X1),X0)
| ~ sP2(sK99(X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_205]) ).
tcf(c_193920,plain,
! [X0: $i,X1: $i] :
( ordinal(sK53(sK99(X0),X1))
| ~ sP2(sK99(X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_206]) ).
tcf(c_193921,plain,
! [X0: $i] : ~ sP2(empty_set,X0),
inference(superposition,[status(thm)],[c_96,c_599]) ).
tcf(c_193922,plain,
! [X0: $i,X1: $i] :
( subset(sK53(powerset(X0),X1),X0)
| ~ sP2(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_667]) ).
tcf(c_193923,plain,
! [X0: $i,X1: $i] :
( sP27
| ordinal(sK53(sK254(X0),X1))
| ~ sP2(sK254(X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_802]) ).
tcf(c_193924,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(sK53(powerset(the_carrier(sK137)),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP2(powerset(the_carrier(sK137)),X0)
| ~ closed_subset(sK53(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK53(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_96,c_176867]) ).
tcf(c_193925,plain,
! [X0: $i] :
( in(sK53(powerset(the_carrier(sK137)),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP2(powerset(the_carrier(sK137)),X0)
| ~ closed_subset(sK53(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK53(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_96,c_176193]) ).
tcf(c_193926,plain,
! [X0: $i,X1: $i] :
( in(sK53(sK91(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP2(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_190603]) ).
tcf(c_193927,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK53(sK91(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP2(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_190604]) ).
tcf(c_193928,plain,
! [X0: $i] :
( open_subset(sK53(the_topology(sK137),X0),sK137)
| ~ sP2(the_topology(sK137),X0)
| ~ subset(sK53(the_topology(sK137),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_96,c_190618]) ).
tcf(c_193929,plain,
! [X0: $i] :
( ( sK92(sK137,sK138,sK53(sK91(sK137,sK138),X0)) = sK53(sK91(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_96,c_175190]) ).
tcf(c_193930,plain,
! [X0: $i] :
( in(sK53(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_96,c_175008]) ).
tcf(c_193931,plain,
! [X0: $i] :
( subset(sK138,sK53(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_96,c_174960]) ).
tcf(c_193932,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,sK53(sK302(sK137,sK138),X0)) = sK53(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_96,c_175802]) ).
tcf(c_193933,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,sK53(sK302(sK137,sK138),X0)) = sK53(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_96,c_175753]) ).
tcf(c_193934,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(sK138,sK53(sK302(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP2(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_96,c_175029]) ).
tcf(c_193935,plain,
! [X0: $i] :
( in(sK53(sK93(sK137,the_topology(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP2(sK93(sK137,the_topology(sK137)),X0) ),
inference(superposition,[status(thm)],[c_96,c_175089]) ).
tcf(c_193936,plain,
! [X0: $i,X1: $i] :
( in(sK53(sK93(sK137,sK147(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP2(sK93(sK137,sK147(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_96,c_175090]) ).
tcf(c_193937,plain,
! [X0: $i,X1: $i] :
( in(sK53(sK93(sK137,sK125(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ sP2(sK93(sK137,sK125(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_96,c_175091]) ).
tcf(c_193938,plain,
! [X0: $i,X1: $i] :
( in(sK53(sK93(sK137,sK123(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP2(sK93(sK137,sK123(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_96,c_175092]) ).
tcf(c_193939,plain,
! [X0: $i] :
( subset(sK138,sK53(sK147(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP2(sK147(sK137,sK138),X0)
| ~ subset(sK53(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_96,c_190614]) ).
tcf(c_193940,plain,
! [X0: $i] :
( closed_subset(sK53(sK147(sK137,sK138),X0),sK137)
| ~ topological_space(sK137)
| ~ sP2(sK147(sK137,sK138),X0)
| ~ subset(sK53(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_96,c_190613]) ).
tcf(c_193941,plain,
! [X0: $i] :
( subset(sK138,sK53(sK123(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP2(sK123(sK137,sK138),X0)
| ~ subset(sK53(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_96,c_190612]) ).
tcf(c_193942,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK53(sK147(sK137,topstr_closure(sK137,X0)),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP2(sK147(sK137,topstr_closure(sK137,X0)),X1)
| ~ element(sK53(sK147(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_176007]) ).
tcf(c_193943,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,topstr_closure(sK137,X0),sK53(sK91(sK137,topstr_closure(sK137,X0)),X1)) = sK53(sK91(sK137,topstr_closure(sK137,X0)),X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP2(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_96,c_176010]) ).
tcf(c_193944,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK137,X0),sK53(sK91(sK137,topstr_closure(sK137,X0)),X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP2(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_96,c_176013]) ).
tcf(c_193945,plain,
! [X0: $i,X1: $i] :
( in(sK53(sK91(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP2(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_96,c_176012]) ).
tcf(c_193946,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),sK53(sK295(sK137,the_topology(sK137)),X0)) = sK53(sK295(sK137,the_topology(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK295(sK137,the_topology(sK137)),X0) ),
inference(superposition,[status(thm)],[c_96,c_176134]) ).
tcf(c_193947,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),sK53(sK302(sK137,the_carrier(sK137)),X0)) = sK53(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_96,c_176975]) ).
tcf(c_193948,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),sK53(sK302(sK137,the_carrier(sK137)),X0)) = sK53(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_96,c_176974]) ).
tcf(c_193949,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK53(sK302(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP2(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_96,c_176981]) ).
tcf(c_193950,plain,
! [X0: $i] :
( ( sK124(sK137,the_carrier(sK137),sK53(sK123(sK137,the_carrier(sK137)),X0)) = sK53(sK123(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK123(sK137,the_carrier(sK137)),X0)
| ~ element(sK53(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_176971]) ).
tcf(c_193951,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK53(sK123(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP2(sK123(sK137,the_carrier(sK137)),X0)
| ~ element(sK53(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_176976]) ).
tcf(c_193952,plain,
! [X0: $i] :
( ( sK92(sK137,the_carrier(sK137),sK53(sK91(sK137,the_carrier(sK137)),X0)) = sK53(sK91(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_96,c_176980]) ).
tcf(c_193953,plain,
! [X0: $i] :
( in(sK53(sK91(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_96,c_176982]) ).
tcf(c_193954,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK53(sK91(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_96,c_176983]) ).
tcf(c_193955,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK53(sK147(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP2(sK147(sK137,the_carrier(sK137)),X0)
| ~ element(sK53(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_176978]) ).
tcf(c_193956,plain,
! [X0: $i] :
( closed_subset(sK53(sK147(sK137,the_carrier(sK137)),X0),sK137)
| ~ topological_space(sK137)
| ~ sP2(sK147(sK137,the_carrier(sK137)),X0)
| ~ element(sK53(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_176977]) ).
tcf(c_193957,plain,
! [X0: $i] :
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK53(sK295(sK137,powerset(the_carrier(sK137))),X0)) = sK53(sK295(sK137,powerset(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK295(sK137,powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_96,c_176995]) ).
tcf(c_193958,plain,
! [X0: $i] :
( in(sK53(sK93(sK137,powerset(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP2(sK93(sK137,powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_96,c_176997]) ).
tcf(c_193959,plain,
! [X0: $i] :
( in(sK53(topstr_closure(sK137,sK138),X0),sK138)
| ~ closed_subset(sK138,sK137)
| ~ sP2(topstr_closure(sK137,sK138),X0)
| ~ in(sK53(topstr_closure(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_96,c_177233]) ).
tcf(c_193960,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK53(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_96,c_177405]) ).
tcf(c_193961,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK53(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK53(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_177400]) ).
tcf(c_193962,plain,
! [X0: $i] :
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK53(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)) = sK53(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_96,c_177404]) ).
tcf(c_193963,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK53(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_96,c_177407]) ).
tcf(c_193964,plain,
! [X0: $i] :
( in(sK53(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_96,c_177406]) ).
tcf(c_193965,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK53(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK53(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_177402]) ).
tcf(c_193966,plain,
! [X0: $i] :
( closed_subset(sK53(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP2(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK53(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_177401]) ).
tcf(c_193967,plain,
! [X0: $i] :
( in(sK53(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP2(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0) ),
inference(superposition,[status(thm)],[c_96,c_177421]) ).
tcf(c_193968,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK53(sK302(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK302(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_96,c_182970]) ).
tcf(c_193969,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK53(sK123(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK123(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK53(sK123(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_182965]) ).
tcf(c_193970,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK53(sK91(sK137,sK207(the_carrier(sK137))),X0)) = sK53(sK91(sK137,sK207(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_96,c_182969]) ).
tcf(c_193971,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK53(sK91(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_96,c_182972]) ).
tcf(c_193972,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK53(sK91(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_96,c_182971]) ).
tcf(c_193973,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK53(sK147(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK147(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK53(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_182967]) ).
tcf(c_193974,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(sK53(sK147(sK137,sK207(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP2(sK147(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK53(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_182966]) ).
tcf(c_193975,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK53(sK302(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK302(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_96,c_184375]) ).
tcf(c_193976,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK53(sK123(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK123(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK53(sK123(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_184370]) ).
tcf(c_193977,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK53(sK91(sK137,sK325(the_carrier(sK137))),X0)) = sK53(sK91(sK137,sK325(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_96,c_184374]) ).
tcf(c_193978,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK53(sK91(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_96,c_184377]) ).
tcf(c_193979,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK53(sK91(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_96,c_184376]) ).
tcf(c_193980,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK53(sK147(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP2(sK147(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK53(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_184372]) ).
tcf(c_193981,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(sK53(sK147(sK137,sK325(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP2(sK147(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK53(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_96,c_184371]) ).
tcf(c_193982,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),sK53(sK93(sK137,sK123(sK137,sK138)),X0)))
| ~ topological_space(sK137)
| ~ sP2(sK93(sK137,sK123(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_96,c_192075]) ).
tcf(c_193983,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),sK53(sK93(sK137,sK147(sK137,sK138)),X0)))
| ~ topological_space(sK137)
| ~ sP2(sK93(sK137,sK147(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_96,c_192676]) ).
tcf(c_193984,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),sK53(sK93(sK137,sK147(sK137,sK138)),X0)),sK137)
| ~ topological_space(sK137)
| ~ sP2(sK93(sK137,sK147(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_96,c_192446]) ).
tcf(c_194406,plain,
( ~ sP8
| ~ in(omega,set_union2(sK66,unordered_pair(sK66,sK66))) ),
inference(superposition,[status(thm)],[c_126,c_546]) ).
tcf(c_194409,plain,
( element(set_union2(sK66,unordered_pair(sK66,sK66)),omega)
| ~ sP8 ),
inference(superposition,[status(thm)],[c_126,c_701]) ).
tcf(c_194414,plain,
! [X0: $i] :
( subset(X0,omega)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_192228,c_533]) ).
tcf(c_194421,plain,
! [X0: $i] :
( subset(X0,sK287)
| ~ in(X0,sK287) ),
inference(superposition,[status(thm)],[c_192229,c_533]) ).
tcf(c_194434,plain,
! [X0: $i] :
( ordinal(sK267)
| sP30(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_179868,c_827]) ).
tcf(c_194504,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK138),X0)
| ~ proper_subset(sK53(sK91(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_193931,c_492]) ).
tcf(c_194515,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK138),X0)
| ~ in(powerset(the_carrier(sK137)),sK53(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_193930,c_546]) ).
tcf(c_194516,plain,
! [X0: $i] :
( in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_193930,c_542]) ).
tcf(c_194517,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137)))
| ~ sP2(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_193930,c_781]) ).
tcf(c_194518,plain,
! [X0: $i] :
( element(sK53(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_193930,c_701]) ).
tcf(c_194519,plain,
! [X0: $i] :
( subset(sK53(sK91(sK137,sK138),X0),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_193930,c_667]) ).
tcf(c_194520,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(sK53(sK91(sK137,sK138),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK138),X0)
| ~ closed_subset(sK53(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK53(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_193930,c_176867]) ).
tcf(c_194521,plain,
! [X0: $i] :
( in(sK53(sK91(sK137,sK138),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK138),X0)
| ~ closed_subset(sK53(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK53(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_193930,c_176193]) ).
tcf(c_194557,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,relation_rng_restriction(X0,the_carrier(sK137)))) = topstr_closure(sK137,relation_rng_restriction(X0,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ relation(the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_278,c_190616]) ).
tcf(c_194559,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,set_difference(the_carrier(sK137),X0))) = topstr_closure(sK137,set_difference(the_carrier(sK137),X0)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_399,c_190616]) ).
tcf(c_194560,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,relation_dom_restriction(the_carrier(sK137),X0))) = topstr_closure(sK137,relation_dom_restriction(the_carrier(sK137),X0)) )
| ~ topological_space(sK137)
| ~ relation(the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_524,c_190616]) ).
tcf(c_194583,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP2(sK302(sK137,sK138),X0)
| ~ proper_subset(sK53(sK302(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_193934,c_492]) ).
tcf(c_194599,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| subset(X0,sK53(sK302(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP2(sK302(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_190602]) ).
tcf(c_194600,plain,
! [X0: $i] :
( sP36(sK137,X0)
| sP3(sK302(sK137,X0))
| subset(X0,sK62(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_120,c_190602]) ).
tcf(c_194602,plain,
! [X0: $i] :
( sP36(sK137,X0)
| ordinal(sK302(sK137,X0))
| subset(X0,sK139(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_383,c_190602]) ).
tcf(c_194603,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| disjoint(sK302(sK137,X0),X1)
| subset(X0,sK142(sK302(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_416,c_190602]) ).
tcf(c_194604,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| disjoint(X1,sK302(sK137,X0))
| subset(X0,sK142(X1,sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_417,c_190602]) ).
tcf(c_194605,plain,
! [X0: $i] :
( sP36(sK137,X0)
| relation(sK302(sK137,X0))
| subset(X0,sK175(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_580,c_190602]) ).
tcf(c_194606,plain,
! [X0: $i] :
( sP36(sK137,X0)
| subset(X0,sK181(sK302(sK137,X0)))
| ( sK302(sK137,X0) = empty_set )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_598,c_190602]) ).
tcf(c_194607,plain,
! [X0: $i] :
( sP36(sK137,X0)
| subset(X0,sK185(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_603,c_190602]) ).
tcf(c_194609,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| subset(sK302(sK137,X0),X1)
| subset(X0,sK202(sK302(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_662,c_190602]) ).
tcf(c_194610,plain,
! [X0: $i] :
( sP36(sK137,X0)
| subset(X0,sK274(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_858,c_190602]) ).
tcf(c_194611,plain,
! [X0: $i] :
( sP36(sK137,X0)
| epsilon_transitive(sK302(sK137,X0))
| subset(X0,sK340(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1081,c_190602]) ).
tcf(c_194612,plain,
! [X0: $i] :
( sP36(sK137,X0)
| epsilon_connected(sK302(sK137,X0))
| subset(X0,sK369(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1253,c_190602]) ).
tcf(c_194613,plain,
! [X0: $i] :
( sP36(sK137,X0)
| epsilon_connected(sK302(sK137,X0))
| subset(X0,sK370(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1254,c_190602]) ).
tcf(c_194712,plain,
! [X0: $i,X1: $i] :
( in(sK53(sK93(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137)))
| ~ sP2(sK93(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_190624]) ).
tcf(c_194713,plain,
! [X0: $i] :
( sP3(sK93(sK137,X0))
| in(sK62(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_120,c_190624]) ).
tcf(c_194715,plain,
! [X0: $i] :
( ordinal(sK93(sK137,X0))
| in(sK139(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_383,c_190624]) ).
tcf(c_194716,plain,
! [X0: $i,X1: $i] :
( disjoint(sK93(sK137,X0),X1)
| in(sK142(sK93(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_416,c_190624]) ).
tcf(c_194717,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,sK93(sK137,X0))
| in(sK142(X1,sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_417,c_190624]) ).
tcf(c_194718,plain,
! [X0: $i] :
( relation(sK93(sK137,X0))
| in(sK175(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_580,c_190624]) ).
tcf(c_194719,plain,
! [X0: $i] :
( in(sK181(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ( sK93(sK137,X0) = empty_set )
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_598,c_190624]) ).
tcf(c_194720,plain,
! [X0: $i] :
( in(sK185(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,X0))
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_603,c_190624]) ).
tcf(c_194722,plain,
! [X0: $i,X1: $i] :
( subset(sK93(sK137,X0),X1)
| in(sK202(sK93(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_662,c_190624]) ).
tcf(c_194723,plain,
! [X0: $i] :
( in(sK274(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,X0))
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_858,c_190624]) ).
tcf(c_194724,plain,
! [X0: $i] :
( epsilon_transitive(sK93(sK137,X0))
| in(sK340(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1081,c_190624]) ).
tcf(c_194725,plain,
! [X0: $i] :
( epsilon_connected(sK93(sK137,X0))
| in(sK369(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1253,c_190624]) ).
tcf(c_194726,plain,
! [X0: $i] :
( epsilon_connected(sK93(sK137,X0))
| in(sK370(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1254,c_190624]) ).
tcf(c_194810,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK145(sK137,X0)) ),
inference(superposition,[status(thm)],[c_190625,c_546]) ).
tcf(c_194811,plain,
! [X0: $i] :
( in(sK154(X0),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_542]) ).
tcf(c_194812,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_781]) ).
tcf(c_194813,plain,
! [X0: $i] :
( element(sK145(sK137,X0),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_701]) ).
tcf(c_194814,plain,
! [X0: $i] :
( in(sK145(sK137,sK99(X0)),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK99(X0)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK99(X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_205]) ).
tcf(c_194815,plain,
! [X0: $i] :
( ordinal(sK145(sK137,sK99(X0)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK99(X0)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK99(X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_206]) ).
tcf(c_194817,plain,
! [X0: $i] :
( subset(sK145(sK137,powerset(X0)),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),powerset(X0)),sK137)
| ~ topological_space(sK137)
| ~ subset(powerset(X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_667]) ).
tcf(c_194818,plain,
! [X0: $i] :
( sP27
| ordinal(sK145(sK137,sK254(X0)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK254(X0)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK254(X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_802]) ).
tcf(c_194821,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK93(sK137,X0)),sK137)
| in(sK145(sK137,sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137)))
| ~ subset(sK93(sK137,X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_190624]) ).
tcf(c_194822,plain,
! [X0: $i] :
( sP36(sK137,X0)
| subset(X0,sK145(sK137,sK302(sK137,X0)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK302(sK137,X0)),sK137)
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ subset(sK302(sK137,X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_190602]) ).
tcf(c_194823,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,X0)),sK137)
| in(sK145(sK137,sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ subset(sK91(sK137,X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_190603]) ).
tcf(c_194824,plain,
! [X0: $i] :
( subset(X0,sK145(sK137,sK91(sK137,X0)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,X0)),sK137)
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ subset(sK91(sK137,X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_190604]) ).
tcf(c_194825,plain,
( open_subset(sK145(sK137,the_topology(sK137)),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),the_topology(sK137)),sK137)
| ~ topological_space(sK137)
| ~ subset(the_topology(sK137),powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190625,c_190618]) ).
tcf(c_194826,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK138)),sK137)
| ( sK92(sK137,sK138,sK145(sK137,sK91(sK137,sK138))) = sK145(sK137,sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK138),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_175190]) ).
tcf(c_194827,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK138)),sK137)
| in(sK145(sK137,sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK138),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_175008]) ).
tcf(c_194828,plain,
( subset(sK138,sK145(sK137,sK91(sK137,sK138)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK138),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_174960]) ).
tcf(c_194829,plain,
( sP36(sK137,sK138)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK302(sK137,sK138)),sK137)
| ( sK303(sK137,sK138,sK145(sK137,sK302(sK137,sK138))) = sK145(sK137,sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK302(sK137,sK138),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_175802]) ).
tcf(c_194830,plain,
( sP36(sK137,sK138)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK302(sK137,sK138)),sK137)
| ( sK304(sK137,sK138,sK145(sK137,sK302(sK137,sK138))) = sK145(sK137,sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK302(sK137,sK138),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_175753]) ).
tcf(c_194831,plain,
( sP36(sK137,sK138)
| subset(sK138,sK145(sK137,sK302(sK137,sK138)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK302(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK302(sK137,sK138),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_175029]) ).
tcf(c_194832,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK93(sK137,the_topology(sK137))),sK137)
| in(sK145(sK137,sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(sK93(sK137,the_topology(sK137)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_175089]) ).
tcf(c_194833,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK93(sK137,sK147(sK137,X0))),sK137)
| in(sK145(sK137,sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(sK93(sK137,sK147(sK137,X0)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_175090]) ).
tcf(c_194834,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK93(sK137,sK125(sK137,X0))),sK137)
| in(sK145(sK137,sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ subset(sK93(sK137,sK125(sK137,X0)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_175091]) ).
tcf(c_194835,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK93(sK137,sK123(sK137,X0))),sK137)
| in(sK145(sK137,sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(sK93(sK137,sK123(sK137,X0)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_175092]) ).
tcf(c_194836,plain,
( subset(sK138,sK145(sK137,sK147(sK137,sK138)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK147(sK137,sK138),powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190625,c_190614]) ).
tcf(c_194837,plain,
( closed_subset(sK145(sK137,sK147(sK137,sK138)),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK147(sK137,sK138),powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190625,c_190613]) ).
tcf(c_194838,plain,
( subset(sK138,sK145(sK137,sK123(sK137,sK138)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK123(sK137,sK138),powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190625,c_190612]) ).
tcf(c_194839,plain,
! [X0: $i] :
( closed_subset(sK145(sK137,sK147(sK137,topstr_closure(sK137,X0))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(sK147(sK137,topstr_closure(sK137,X0)),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176007]) ).
tcf(c_194840,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,topstr_closure(sK137,X0))),sK137)
| ( sK92(sK137,topstr_closure(sK137,X0),sK145(sK137,sK91(sK137,topstr_closure(sK137,X0)))) = sK145(sK137,sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(sK91(sK137,topstr_closure(sK137,X0)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176010]) ).
tcf(c_194841,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,topstr_closure(sK137,X0))),sK137)
| subset(topstr_closure(sK137,X0),sK145(sK137,sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(sK91(sK137,topstr_closure(sK137,X0)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176013]) ).
tcf(c_194842,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,topstr_closure(sK137,X0))),sK137)
| in(sK145(sK137,sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(sK91(sK137,topstr_closure(sK137,X0)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176012]) ).
tcf(c_194843,plain,
( sP34(the_topology(sK137),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK295(sK137,the_topology(sK137))),sK137)
| ( sK296(sK137,the_topology(sK137),sK145(sK137,sK295(sK137,the_topology(sK137)))) = sK145(sK137,sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137)
| ~ subset(sK295(sK137,the_topology(sK137)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176134]) ).
tcf(c_194844,plain,
( sP36(sK137,the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK302(sK137,the_carrier(sK137))),sK137)
| ( sK304(sK137,the_carrier(sK137),sK145(sK137,sK302(sK137,the_carrier(sK137)))) = sK145(sK137,sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ subset(sK302(sK137,the_carrier(sK137)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176975]) ).
tcf(c_194845,plain,
( sP36(sK137,the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK302(sK137,the_carrier(sK137))),sK137)
| ( sK303(sK137,the_carrier(sK137),sK145(sK137,sK302(sK137,the_carrier(sK137)))) = sK145(sK137,sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ subset(sK302(sK137,the_carrier(sK137)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176974]) ).
tcf(c_194846,plain,
( sP36(sK137,the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK302(sK137,the_carrier(sK137))),sK137)
| subset(the_carrier(sK137),sK145(sK137,sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ subset(sK302(sK137,the_carrier(sK137)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176981]) ).
tcf(c_194847,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,the_carrier(sK137))),sK137)
| ( sK124(sK137,the_carrier(sK137),sK145(sK137,sK123(sK137,the_carrier(sK137)))) = sK145(sK137,sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ subset(sK123(sK137,the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176971]) ).
tcf(c_194848,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,the_carrier(sK137))),sK137)
| subset(the_carrier(sK137),sK145(sK137,sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ subset(sK123(sK137,the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176976]) ).
tcf(c_194849,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,the_carrier(sK137))),sK137)
| ( sK92(sK137,the_carrier(sK137),sK145(sK137,sK91(sK137,the_carrier(sK137)))) = sK145(sK137,sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,the_carrier(sK137)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176980]) ).
tcf(c_194850,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,the_carrier(sK137))),sK137)
| in(sK145(sK137,sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,the_carrier(sK137)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176982]) ).
tcf(c_194851,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,the_carrier(sK137))),sK137)
| subset(the_carrier(sK137),sK145(sK137,sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,the_carrier(sK137)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176983]) ).
tcf(c_194852,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,the_carrier(sK137))),sK137)
| subset(the_carrier(sK137),sK145(sK137,sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ subset(sK147(sK137,the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176978]) ).
tcf(c_194853,plain,
( closed_subset(sK145(sK137,sK147(sK137,the_carrier(sK137))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ subset(sK147(sK137,the_carrier(sK137)),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176977]) ).
tcf(c_194854,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK295(sK137,powerset(the_carrier(sK137)))),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK145(sK137,sK295(sK137,powerset(the_carrier(sK137))))) = sK145(sK137,sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ subset(sK295(sK137,powerset(the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176995]) ).
tcf(c_194855,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK93(sK137,powerset(the_carrier(sK137)))),sK137)
| in(sK145(sK137,sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(sK93(sK137,powerset(the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_176997]) ).
tcf(c_194856,plain,
( in(sK145(sK137,topstr_closure(sK137,sK138)),sK138)
| closed_subset(meet_of_subsets(the_carrier(sK137),topstr_closure(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(topstr_closure(sK137,sK138),powerset(the_carrier(sK137)))
| ~ in(sK145(sK137,topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190625,c_177233]) ).
tcf(c_194857,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK302(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| subset(sK208(powerset(the_carrier(sK137))),sK145(sK137,sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ subset(sK302(sK137,sK208(powerset(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_177405]) ).
tcf(c_194858,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| subset(sK208(powerset(the_carrier(sK137))),sK145(sK137,sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ subset(sK123(sK137,sK208(powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_177400]) ).
tcf(c_194859,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK145(sK137,sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK145(sK137,sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK208(powerset(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_177404]) ).
tcf(c_194860,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| subset(sK208(powerset(the_carrier(sK137))),sK145(sK137,sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK208(powerset(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_177407]) ).
tcf(c_194861,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| in(sK145(sK137,sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK208(powerset(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_177406]) ).
tcf(c_194862,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| subset(sK208(powerset(the_carrier(sK137))),sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ subset(sK147(sK137,sK208(powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_177402]) ).
tcf(c_194863,plain,
( closed_subset(sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ subset(sK147(sK137,sK208(powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_177401]) ).
tcf(c_194864,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),sK137)
| in(sK145(sK137,sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_177421]) ).
tcf(c_194865,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK302(sK137,sK207(the_carrier(sK137)))),sK137)
| subset(sK207(the_carrier(sK137)),sK145(sK137,sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ subset(sK302(sK137,sK207(the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_182970]) ).
tcf(c_194866,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK207(the_carrier(sK137)))),sK137)
| subset(sK207(the_carrier(sK137)),sK145(sK137,sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ subset(sK123(sK137,sK207(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_182965]) ).
tcf(c_194867,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK207(the_carrier(sK137)))),sK137)
| ( sK92(sK137,sK207(the_carrier(sK137)),sK145(sK137,sK91(sK137,sK207(the_carrier(sK137))))) = sK145(sK137,sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK207(the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_182969]) ).
tcf(c_194868,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK207(the_carrier(sK137)))),sK137)
| subset(sK207(the_carrier(sK137)),sK145(sK137,sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK207(the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_182972]) ).
tcf(c_194869,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK207(the_carrier(sK137)))),sK137)
| in(sK145(sK137,sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK207(the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_182971]) ).
tcf(c_194870,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| subset(sK207(the_carrier(sK137)),sK145(sK137,sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ subset(sK147(sK137,sK207(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_182967]) ).
tcf(c_194871,plain,
( empty(the_carrier(sK137))
| closed_subset(sK145(sK137,sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ subset(sK147(sK137,sK207(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_182966]) ).
tcf(c_194872,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK302(sK137,sK325(the_carrier(sK137)))),sK137)
| subset(sK325(the_carrier(sK137)),sK145(sK137,sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ subset(sK302(sK137,sK325(the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_184375]) ).
tcf(c_194873,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK325(the_carrier(sK137)))),sK137)
| subset(sK325(the_carrier(sK137)),sK145(sK137,sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ subset(sK123(sK137,sK325(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_184370]) ).
tcf(c_194874,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK325(the_carrier(sK137)))),sK137)
| ( sK92(sK137,sK325(the_carrier(sK137)),sK145(sK137,sK91(sK137,sK325(the_carrier(sK137))))) = sK145(sK137,sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK325(the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_184374]) ).
tcf(c_194875,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK325(the_carrier(sK137)))),sK137)
| subset(sK325(the_carrier(sK137)),sK145(sK137,sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK325(the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_184377]) ).
tcf(c_194876,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK325(the_carrier(sK137)))),sK137)
| in(sK145(sK137,sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK325(the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_184376]) ).
tcf(c_194877,plain,
( empty(the_carrier(sK137))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| subset(sK325(the_carrier(sK137)),sK145(sK137,sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ subset(sK147(sK137,sK325(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_184372]) ).
tcf(c_194878,plain,
( empty(the_carrier(sK137))
| closed_subset(sK145(sK137,sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ subset(sK147(sK137,sK325(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ element(sK145(sK137,sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_184371]) ).
tcf(c_194879,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK93(sK137,sK123(sK137,sK138))),sK137)
| subset(sK138,set_difference(the_carrier(sK137),sK145(sK137,sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ subset(sK93(sK137,sK123(sK137,sK138)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_192075]) ).
tcf(c_194880,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK93(sK137,sK147(sK137,sK138))),sK137)
| subset(sK138,set_difference(the_carrier(sK137),sK145(sK137,sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ subset(sK93(sK137,sK147(sK137,sK138)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_192676]) ).
tcf(c_194881,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK93(sK137,sK147(sK137,sK138))),sK137)
| closed_subset(set_difference(the_carrier(sK137),sK145(sK137,sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137)
| ~ subset(sK93(sK137,sK147(sK137,sK138)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_192446]) ).
tcf(c_194940,plain,
( open_subset(sK145(sK137,the_topology(sK137)),sK137)
| closed_subset(meet_of_subsets(the_carrier(sK137),the_topology(sK137)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK145(sK137,the_topology(sK137)),the_carrier(sK137)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_194825,c_190845]) ).
tcf(c_195389,plain,
( sP3(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK62(sK93(sK137,sK123(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192113,c_492]) ).
tcf(c_195393,plain,
! [X0: $i] : pair_first(unordered_pair(powerset(empty_set),unordered_pair(empty_set,X0))) = empty_set,
inference(demodulation,[status(thm)],[c_179733,c_967]) ).
tcf(c_195394,plain,
! [X0: $i] : pair_first(unordered_pair(powerset(empty_set),unordered_pair(X0,empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_967,c_195393]) ).
tcf(c_195834,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ proper_subset(X0,relation_rng(relation_rng_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_277,c_492]) ).
tcf(c_195835,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(empty_set,X0)) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_277,c_419]) ).
tcf(c_195836,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,relation_rng(relation_rng_restriction(the_carrier(sK137),X0)))) = topstr_closure(sK137,relation_rng(relation_rng_restriction(the_carrier(sK137),X0))) )
| ~ topological_space(sK137)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_277,c_190616]) ).
tcf(c_195837,plain,
! [X0: $i] :
( ( topstr_closure(sK137,relation_rng(relation_rng_restriction(the_carrier(sK137),X0))) = relation_rng(relation_rng_restriction(the_carrier(sK137),X0)) )
| ~ relation(X0)
| ~ closed_subset(relation_rng(relation_rng_restriction(the_carrier(sK137),X0)),sK137) ),
inference(superposition,[status(thm)],[c_277,c_190617]) ).
tcf(c_195838,plain,
! [X0: $i] :
( in(relation_rng(relation_rng_restriction(the_carrier(sK137),X0)),the_topology(sK137))
| ~ relation(X0)
| ~ open_subset(relation_rng(relation_rng_restriction(the_carrier(sK137),X0)),sK137) ),
inference(superposition,[status(thm)],[c_277,c_190619]) ).
tcf(c_195863,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ finite(union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_292]) ).
tcf(c_195864,plain,
! [X0: $i,X1: $i] :
( finite(relation_rng(relation_rng_restriction(X1,X0)))
| ~ finite(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_277,c_292]) ).
tcf(c_195865,plain,
! [X0: $i,X1: $i] :
( finite(relation_rng_restriction(X1,X0))
| ~ finite(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_278,c_292]) ).
tcf(c_195868,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ finite(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_518,c_292]) ).
tcf(c_195869,plain,
! [X0: $i,X1: $i] :
( finite(relation_dom_restriction(X0,X1))
| ~ finite(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_524,c_292]) ).
tcf(c_195871,plain,
( finite(sK138)
| ~ finite(the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190838,c_292]) ).
tcf(c_195872,plain,
( topological_space(sK137)
| finite(sK378(sK137))
| ~ sP42(sK137)
| ~ finite(the_topology(sK137))
| ~ open_subset(the_carrier(sK137),sK137) ),
inference(superposition,[status(thm)],[c_177301,c_292]) ).
tcf(c_195873,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| in(X1,topstr_closure(sK137,X0))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ finite(sK146(sK137,X0,X1)) ),
inference(superposition,[status(thm)],[c_48177,c_292]) ).
tcf(c_195874,plain,
( finite(sK319(sK320))
| ~ finite(the_carrier(sK320)) ),
inference(superposition,[status(thm)],[c_190843,c_292]) ).
tcf(c_195875,plain,
( topological_space(sK137)
| finite(sK378(sK137))
| ~ sP42(sK137)
| ~ finite(powerset(the_carrier(sK137)))
| ~ in(the_carrier(sK137),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_190844,c_292]) ).
tcf(c_195876,plain,
( finite(the_topology(sK137))
| ~ finite(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190845,c_292]) ).
tcf(c_195877,plain,
! [X0: $i] :
( finite(sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ finite(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190849,c_292]) ).
tcf(c_195878,plain,
! [X0: $i] :
( finite(sK125(sK137,X0))
| ~ topological_space(sK137)
| ~ finite(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_190852,c_292]) ).
tcf(c_195879,plain,
! [X0: $i] :
( finite(sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ finite(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190854,c_292]) ).
tcf(c_195880,plain,
( finite(sK138)
| sP3(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK62(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178461,c_292]) ).
tcf(c_195881,plain,
( finite(sK138)
| sP36(sK137,sK138)
| sP3(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK62(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178464,c_292]) ).
tcf(c_195882,plain,
( finite(sK138)
| ordinal(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK139(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178685,c_292]) ).
tcf(c_195883,plain,
( finite(sK138)
| sP36(sK137,sK138)
| ordinal(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK139(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178688,c_292]) ).
tcf(c_195884,plain,
( finite(sK138)
| relation(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK175(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178948,c_292]) ).
tcf(c_195885,plain,
( finite(sK138)
| sP36(sK137,sK138)
| relation(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK175(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_178951,c_292]) ).
tcf(c_195886,plain,
( finite(sK138)
| epsilon_transitive(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK340(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180306,c_292]) ).
tcf(c_195887,plain,
( finite(sK138)
| sP36(sK137,sK138)
| epsilon_transitive(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK340(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180309,c_292]) ).
tcf(c_195888,plain,
( finite(sK138)
| epsilon_connected(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK369(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180598,c_292]) ).
tcf(c_195889,plain,
( finite(sK138)
| sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK369(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180601,c_292]) ).
tcf(c_195890,plain,
( finite(sK138)
| epsilon_connected(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK370(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180851,c_292]) ).
tcf(c_195891,plain,
( finite(sK138)
| sP36(sK137,sK138)
| epsilon_connected(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK370(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_180854,c_292]) ).
tcf(c_195892,plain,
! [X0: $i,X1: $i] :
( finite(X1)
| ~ finite(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_181192,c_292]) ).
tcf(c_195895,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138))
| ~ finite(sK185(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_182180,c_292]) ).
tcf(c_195896,plain,
( finite(sK138)
| sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK138))
| ~ finite(sK185(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_182183,c_292]) ).
tcf(c_195899,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138))
| ~ finite(sK274(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_183904,c_292]) ).
tcf(c_195900,plain,
( finite(sK138)
| sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK138))
| ~ finite(sK274(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_183907,c_292]) ).
tcf(c_195901,plain,
! [X0: $i] :
( finite(sK138)
| disjoint(sK91(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ finite(sK142(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_186303,c_292]) ).
tcf(c_195902,plain,
! [X0: $i] :
( finite(sK138)
| sP36(sK137,sK138)
| disjoint(sK302(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ finite(sK142(sK302(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_186306,c_292]) ).
tcf(c_195903,plain,
! [X0: $i] :
( finite(sK138)
| disjoint(X0,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK142(X0,sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_186682,c_292]) ).
tcf(c_195904,plain,
! [X0: $i] :
( finite(sK138)
| sP36(sK137,sK138)
| disjoint(X0,sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ finite(sK142(X0,sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_186685,c_292]) ).
tcf(c_195905,plain,
( finite(sK138)
| ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ finite(sK181(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_190237,c_292]) ).
tcf(c_195906,plain,
( finite(sK138)
| sP36(sK137,sK138)
| ( sK302(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ finite(sK181(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_190240,c_292]) ).
tcf(c_195907,plain,
! [X0: $i] :
( finite(sK208(powerset(X0)))
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_190840,c_292]) ).
tcf(c_195908,plain,
! [X0: $i] :
( finite(sK138)
| subset(sK91(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ finite(sK202(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_191200,c_292]) ).
tcf(c_195909,plain,
! [X0: $i] :
( finite(sK138)
| sP36(sK137,sK138)
| subset(sK302(sK137,sK138),X0)
| ~ topological_space(sK137)
| ~ finite(sK202(sK302(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_191203,c_292]) ).
tcf(c_195910,plain,
( finite(sK138)
| sP3(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK62(sK93(sK137,sK123(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192113,c_292]) ).
tcf(c_195911,plain,
! [X0: $i] :
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK138),X0)
| ~ finite(sK53(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_193931,c_292]) ).
tcf(c_195912,plain,
! [X0: $i] :
( finite(sK138)
| sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP2(sK302(sK137,sK138),X0)
| ~ finite(sK53(sK302(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_193934,c_292]) ).
tcf(c_196286,plain,
( finite(sK138)
| ordinal(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK139(sK93(sK137,sK123(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192115,c_292]) ).
tcf(c_196287,plain,
( ordinal(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK139(sK93(sK137,sK123(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192115,c_492]) ).
tcf(c_196301,plain,
( finite(sK138)
| relation(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK175(sK93(sK137,sK123(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192118,c_292]) ).
tcf(c_196302,plain,
( relation(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK175(sK93(sK137,sK123(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192118,c_492]) ).
tcf(c_196316,plain,
( finite(sK138)
| epsilon_transitive(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK340(sK93(sK137,sK123(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192124,c_292]) ).
tcf(c_196317,plain,
( epsilon_transitive(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK340(sK93(sK137,sK123(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192124,c_492]) ).
tcf(c_196331,plain,
( finite(sK138)
| epsilon_connected(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK369(sK93(sK137,sK123(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192125,c_292]) ).
tcf(c_196332,plain,
( epsilon_connected(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK369(sK93(sK137,sK123(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192125,c_492]) ).
tcf(c_196344,plain,
! [X0: $i] :
( subset(relation_image(empty_set,X0),empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_491,c_298]) ).
tcf(c_196345,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(identity_relation(X0),X1),X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_510,c_298]) ).
tcf(c_196346,plain,
! [X0: $i,X1: $i] :
( finite(relation_image(X0,X1))
| ~ relation(X0)
| ~ finite(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_298,c_292]) ).
tcf(c_196347,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(relation_rng(X0),relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_298,c_492]) ).
tcf(c_196348,plain,
! [X0: $i] : subset(relation_image(empty_set,X0),empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_196344,c_596]) ).
tcf(c_196351,plain,
! [X0: $i,X1: $i] : subset(relation_image(identity_relation(X0),X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_196345,c_1156]) ).
tcf(c_196414,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK122(X0),X1),X0)
| ~ relation(sK122(X0)) ),
inference(superposition,[status(thm)],[c_258,c_312]) ).
tcf(c_196415,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(identity_relation(X0),X1),X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_509,c_312]) ).
tcf(c_196416,plain,
! [X0: $i] :
( subset(relation_inverse_image(empty_set,X0),empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_490,c_312]) ).
tcf(c_196417,plain,
! [X0: $i,X1: $i] :
( finite(relation_inverse_image(X0,X1))
| ~ relation(X0)
| ~ finite(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_312,c_292]) ).
tcf(c_196418,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(relation_dom(X0),relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_312,c_492]) ).
tcf(c_196419,plain,
! [X0: $i] : subset(relation_inverse_image(empty_set,X0),empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_196416,c_596]) ).
tcf(c_196422,plain,
! [X0: $i,X1: $i] : subset(relation_inverse_image(identity_relation(X0),X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_196415,c_1156]) ).
tcf(c_196423,plain,
! [X0: $i,X1: $i] : subset(relation_inverse_image(sK122(X0),X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_196414,c_256]) ).
tcf(c_196436,plain,
! [X0: $i,X1: $i] :
( finite(relation_field(relation_restriction(X0,X1)))
| ~ finite(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_292]) ).
tcf(c_196437,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ proper_subset(X0,relation_field(relation_restriction(X1,X0))) ),
inference(superposition,[status(thm)],[c_334,c_492]) ).
tcf(c_196438,plain,
! [X0: $i] :
( ( relation_field(relation_restriction(X0,empty_set)) = empty_set )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_419]) ).
tcf(c_196439,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,relation_field(relation_restriction(X0,the_carrier(sK137))))) = topstr_closure(sK137,relation_field(relation_restriction(X0,the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_334,c_190616]) ).
tcf(c_196440,plain,
! [X0: $i] :
( ( topstr_closure(sK137,relation_field(relation_restriction(X0,the_carrier(sK137)))) = relation_field(relation_restriction(X0,the_carrier(sK137))) )
| ~ relation(X0)
| ~ closed_subset(relation_field(relation_restriction(X0,the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_334,c_190617]) ).
tcf(c_196441,plain,
! [X0: $i] :
( in(relation_field(relation_restriction(X0,the_carrier(sK137))),the_topology(sK137))
| ~ relation(X0)
| ~ open_subset(relation_field(relation_restriction(X0,the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_334,c_190619]) ).
tcf(c_196470,plain,
! [X0: $i,X1: $i] :
( ordinal(sK53(X0,X1))
| ~ ordinal(X0)
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_96,c_349]) ).
tcf(c_196471,plain,
! [X0: $i] :
( sP3(X0)
| ordinal(sK62(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_120,c_349]) ).
tcf(c_196472,plain,
( ordinal(set_union2(sK66,unordered_pair(sK66,sK66)))
| ~ sP8
| ~ ordinal(omega) ),
inference(superposition,[status(thm)],[c_126,c_349]) ).
tcf(c_196478,plain,
! [X0: $i] :
( ordinal(X0)
| ~ ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_272,c_349]) ).
tcf(c_196479,plain,
! [X0: $i] :
( ordinal(X0)
| ~ ordinal(sK126(X0)) ),
inference(superposition,[status(thm)],[c_288,c_349]) ).
tcf(c_196481,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ordinal(sK142(X0,X1))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_416,c_349]) ).
tcf(c_196482,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ordinal(sK142(X1,X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_417,c_349]) ).
tcf(c_196483,plain,
! [X0: $i] :
( relation(X0)
| ordinal(sK175(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_580,c_349]) ).
tcf(c_196484,plain,
! [X0: $i] :
( ordinal(sK181(X0))
| ( X0 = empty_set )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_598,c_349]) ).
tcf(c_196485,plain,
! [X0: $i] :
( ordinal(sK185(X0))
| ~ sP20(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_603,c_349]) ).
tcf(c_196487,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ordinal(sK202(X0,X1))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_662,c_349]) ).
tcf(c_196488,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_666,c_349]) ).
tcf(c_196489,plain,
! [X0: $i] :
( ordinal(relation_dom(sK270(X0)))
| ~ ordinal(omega)
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_849,c_349]) ).
tcf(c_196491,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_964,c_349]) ).
tcf(c_196492,plain,
! [X0: $i,X1: $i] :
( ordinal(X1)
| ~ ordinal(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_965,c_349]) ).
tcf(c_196493,plain,
! [X0: $i] :
( ordinal(X0)
| ~ ordinal(sK323(X0)) ),
inference(superposition,[status(thm)],[c_997,c_349]) ).
tcf(c_196494,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ordinal(sK340(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_1081,c_349]) ).
tcf(c_196495,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ordinal(sK369(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_1253,c_349]) ).
tcf(c_196496,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ordinal(sK370(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_1254,c_349]) ).
tcf(c_196500,plain,
( ordinal(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ ordinal(the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_106073,c_349]) ).
tcf(c_196501,plain,
( ordinal(the_carrier(sK137))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(the_carrier(sK137),sK137) ),
inference(superposition,[status(thm)],[c_176994,c_349]) ).
tcf(c_196502,plain,
( ordinal(the_carrier(sK291))
| ~ topological_space(sK291)
| ~ ordinal(the_topology(sK291)) ),
inference(superposition,[status(thm)],[c_106091,c_349]) ).
tcf(c_196503,plain,
! [X0: $i] :
( ordinal(union_of_subsets(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ ordinal(the_topology(sK137))
| ~ subset(X0,the_topology(sK137))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_47816,c_349]) ).
tcf(c_196504,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ordinal(sK303(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47965,c_349]) ).
tcf(c_196505,plain,
! [X0: $i,X1: $i] :
( sP34(X0,sK137)
| ordinal(sK296(sK137,X0,X1))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ in(X1,sK295(sK137,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48019,c_349]) ).
tcf(c_196506,plain,
! [X0: $i] :
( ordinal(sK145(sK137,X0))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ ordinal(X0)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_349]) ).
tcf(c_196507,plain,
( ordinal(sK138)
| ~ open_subset(sK138,sK137)
| ~ ordinal(the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_174884,c_349]) ).
tcf(c_196508,plain,
! [X0: $i] :
( ordinal(sK145(sK137,sK147(sK137,X0)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK147(sK137,X0)),sK137)
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,X0))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175059,c_349]) ).
tcf(c_196509,plain,
! [X0: $i] :
( ordinal(sK145(sK137,sK123(sK137,X0)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,X0)),sK137)
| ~ topological_space(sK137)
| ~ ordinal(sK123(sK137,X0))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_175061,c_349]) ).
tcf(c_196511,plain,
( ordinal(sK138)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ ordinal(sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_176354,c_349]) ).
tcf(c_196513,plain,
( ordinal(sK138)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ ordinal(sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_176589,c_349]) ).
tcf(c_196514,plain,
! [X0: $i] :
( ordinal(topstr_closure(sK137,X0))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(topstr_closure(sK137,X0),sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176021,c_349]) ).
tcf(c_196515,plain,
! [X0: $i] :
( ordinal(sK138)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138)
| ~ ordinal(sK147(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_176349,c_349]) ).
tcf(c_196516,plain,
! [X0: $i] :
( ordinal(sK138)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ subset(topstr_closure(sK137,X0),sK138)
| ~ ordinal(sK123(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_176584,c_349]) ).
tcf(c_196517,plain,
! [X0: $i] :
( ordinal(X0)
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(the_carrier(sK137),X0)
| ~ ordinal(sK91(sK137,the_carrier(sK137)))
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176973,c_349]) ).
tcf(c_196518,plain,
( ordinal(sK138)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138)
| ~ ordinal(sK123(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176984,c_349]) ).
tcf(c_196519,plain,
( ordinal(sK138)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(the_carrier(sK137),sK138)
| ~ ordinal(sK147(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176986,c_349]) ).
tcf(c_196520,plain,
( ordinal(sK145(sK137,powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),powerset(the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176998,c_349]) ).
tcf(c_196521,plain,
( ordinal(sK138)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138)
| ~ ordinal(sK123(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_177408,c_349]) ).
tcf(c_196522,plain,
( ordinal(sK138)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK208(powerset(the_carrier(sK137))),sK138)
| ~ ordinal(sK147(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_177410,c_349]) ).
tcf(c_196523,plain,
( ordinal(sK208(powerset(the_carrier(sK137))))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(sK208(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_177418,c_349]) ).
tcf(c_196524,plain,
( ordinal(sK145(sK137,sK208(powerset(powerset(the_carrier(sK137))))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK208(powerset(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ ordinal(sK208(powerset(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_177422,c_349]) ).
tcf(c_196525,plain,
( sP3(sK91(sK137,sK138))
| ordinal(sK62(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_178460,c_349]) ).
tcf(c_196526,plain,
( ordinal(sK91(sK137,sK138))
| ordinal(sK139(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_178684,c_349]) ).
tcf(c_196527,plain,
( relation(sK91(sK137,sK138))
| ordinal(sK175(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_178947,c_349]) ).
tcf(c_196528,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| ordinal(set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ ordinal(the_topology(sK137))
| ~ in(X0,sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_180142,c_349]) ).
tcf(c_196529,plain,
! [X0: $i] :
( ordinal(set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ ordinal(the_topology(sK137))
| ~ in(X0,sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_179182,c_349]) ).
tcf(c_196530,plain,
! [X0: $i,X1: $i] :
( ordinal(set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,X1))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK147(sK137,X1))) ),
inference(superposition,[status(thm)],[c_179183,c_349]) ).
tcf(c_196531,plain,
! [X0: $i,X1: $i] :
( ordinal(set_difference(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ ordinal(sK123(sK137,X1))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK93(sK137,sK123(sK137,X1))) ),
inference(superposition,[status(thm)],[c_179185,c_349]) ).
tcf(c_196532,plain,
( epsilon_transitive(sK91(sK137,sK138))
| ordinal(sK340(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180305,c_349]) ).
tcf(c_196533,plain,
( epsilon_connected(sK91(sK137,sK138))
| ordinal(sK369(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180597,c_349]) ).
tcf(c_196534,plain,
( epsilon_connected(sK91(sK137,sK138))
| ordinal(sK370(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_180850,c_349]) ).
tcf(c_196536,plain,
( ordinal(sK185(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138))
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_182179,c_349]) ).
tcf(c_196538,plain,
( ordinal(sK138)
| empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138)
| ~ ordinal(sK123(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_182976,c_349]) ).
tcf(c_196539,plain,
( ordinal(sK138)
| empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK207(the_carrier(sK137)),sK138)
| ~ ordinal(sK147(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_182978,c_349]) ).
tcf(c_196540,plain,
( empty(the_carrier(sK137))
| ordinal(sK207(the_carrier(sK137)))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(sK207(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_182986,c_349]) ).
tcf(c_196541,plain,
( ordinal(sK274(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138))
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_183903,c_349]) ).
tcf(c_196542,plain,
( ordinal(sK138)
| empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138)
| ~ ordinal(sK123(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_184382,c_349]) ).
tcf(c_196543,plain,
( ordinal(sK138)
| empty(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK325(the_carrier(sK137)),sK138)
| ~ ordinal(sK147(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_184384,c_349]) ).
tcf(c_196544,plain,
( empty(the_carrier(sK137))
| ordinal(sK325(the_carrier(sK137)))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(sK325(the_carrier(sK137)),sK137) ),
inference(superposition,[status(thm)],[c_184392,c_349]) ).
tcf(c_196545,plain,
! [X0: $i] :
( disjoint(sK91(sK137,sK138),X0)
| ordinal(sK142(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_186302,c_349]) ).
tcf(c_196546,plain,
! [X0: $i] :
( disjoint(X0,sK91(sK137,sK138))
| ordinal(sK142(X0,sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_186681,c_349]) ).
tcf(c_196548,plain,
( ordinal(sK154(the_topology(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_189060,c_349]) ).
tcf(c_196549,plain,
( ordinal(sK154(the_topology(sK137)))
| ~ open_subset(sK138,sK137)
| ~ ordinal(the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_188347,c_349]) ).
tcf(c_196550,plain,
( ordinal(sK154(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ ordinal(sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_188349,c_349]) ).
tcf(c_196551,plain,
( ordinal(sK154(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ ordinal(sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_188351,c_349]) ).
tcf(c_196552,plain,
( ordinal(sK181(sK91(sK137,sK138)))
| ( sK91(sK137,sK138) = empty_set )
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190236,c_349]) ).
tcf(c_196553,plain,
! [X0: $i] :
( subset(sK91(sK137,sK138),X0)
| ordinal(sK202(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_191199,c_349]) ).
tcf(c_196554,plain,
! [X0: $i] :
( ordinal(sK53(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ sP2(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_193930,c_349]) ).
tcf(c_196605,plain,
! [X0: $i] :
( ordinal(relation_dom(sK270(X0)))
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_196489,c_843]) ).
tcf(c_196629,plain,
( ordinal(set_union2(sK66,unordered_pair(sK66,sK66)))
| ~ sP8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_196472,c_843]) ).
tcf(c_196881,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,the_carrier(sK137)) ),
inference(instantiation,[status(thm)],[c_666]) ).
tcf(c_197040,plain,
! [X0: $i] :
( finite(relation_image(empty_set,X0))
| ~ finite(empty_set) ),
inference(superposition,[status(thm)],[c_196348,c_292]) ).
tcf(c_197041,plain,
! [X0: $i] : ~ proper_subset(empty_set,relation_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_196348,c_492]) ).
tcf(c_197042,plain,
! [X0: $i] : relation_image(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_196348,c_419]) ).
tcf(c_197043,plain,
! [X0: $i] : finite(relation_image(empty_set,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_197040,c_177985]) ).
tcf(c_197049,plain,
! [X0: $i] :
( finite(relation_inverse_image(empty_set,X0))
| ~ finite(empty_set) ),
inference(superposition,[status(thm)],[c_196419,c_292]) ).
tcf(c_197050,plain,
! [X0: $i] : ~ proper_subset(empty_set,relation_inverse_image(empty_set,X0)),
inference(superposition,[status(thm)],[c_196419,c_492]) ).
tcf(c_197051,plain,
! [X0: $i] : relation_inverse_image(empty_set,X0) = empty_set,
inference(superposition,[status(thm)],[c_196419,c_419]) ).
tcf(c_197052,plain,
! [X0: $i] : finite(relation_inverse_image(empty_set,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_197049,c_177985]) ).
tcf(c_197070,plain,
( finite(sK138)
| epsilon_connected(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK370(sK93(sK137,sK123(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192126,c_292]) ).
tcf(c_197071,plain,
( epsilon_connected(sK93(sK137,sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK370(sK93(sK137,sK123(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192126,c_492]) ).
tcf(c_197115,plain,
! [X0: $i] : pair_second(unordered_pair(powerset(empty_set),unordered_pair(empty_set,X0))) = X0,
inference(demodulation,[status(thm)],[c_179842,c_967]) ).
tcf(c_197116,plain,
! [X0: $i] : pair_second(unordered_pair(powerset(empty_set),unordered_pair(X0,empty_set))) = X0,
inference(superposition,[status(thm)],[c_967,c_197115]) ).
tcf(c_197126,plain,
! [X0: $i] :
( empty(X0)
| ordinal(sK135(X0))
| relation(sK136(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_367,c_349]) ).
tcf(c_197127,plain,
! [X0: $i] :
( empty(X0)
| relation(sK136(X0))
| ~ in(X0,sK135(X0)) ),
inference(superposition,[status(thm)],[c_367,c_546]) ).
tcf(c_197128,plain,
! [X0: $i] :
( empty(X0)
| relation(sK136(X0))
| in(sK154(X0),X0) ),
inference(superposition,[status(thm)],[c_367,c_542]) ).
tcf(c_197130,plain,
! [X0: $i] :
( empty(X0)
| relation(sK136(X0))
| element(sK135(X0),X0) ),
inference(superposition,[status(thm)],[c_367,c_701]) ).
tcf(c_197131,plain,
! [X0: $i] :
( empty(sK99(X0))
| relation(sK136(sK99(X0)))
| in(sK135(sK99(X0)),X0) ),
inference(superposition,[status(thm)],[c_367,c_205]) ).
tcf(c_197132,plain,
! [X0: $i] :
( empty(sK99(X0))
| ordinal(sK135(sK99(X0)))
| relation(sK136(sK99(X0))) ),
inference(superposition,[status(thm)],[c_367,c_206]) ).
tcf(c_197134,plain,
! [X0: $i] :
( empty(powerset(X0))
| relation(sK136(powerset(X0)))
| subset(sK135(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_367,c_667]) ).
tcf(c_197135,plain,
! [X0: $i] :
( sP27
| empty(sK254(X0))
| ordinal(sK135(sK254(X0)))
| relation(sK136(sK254(X0))) ),
inference(superposition,[status(thm)],[c_367,c_802]) ).
tcf(c_197136,plain,
( sP36(sK137,sK138)
| empty(powerset(the_carrier(sK137)))
| relation(sK136(powerset(the_carrier(sK137))))
| in(sK135(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK135(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_367,c_176867]) ).
tcf(c_197137,plain,
( empty(powerset(the_carrier(sK137)))
| relation(sK136(powerset(the_carrier(sK137))))
| in(sK135(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK135(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_367,c_176193]) ).
tcf(c_197138,plain,
! [X0: $i] :
( empty(sK93(sK137,X0))
| relation(sK136(sK93(sK137,X0)))
| in(sK135(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_190624]) ).
tcf(c_197139,plain,
! [X0: $i] :
( sP36(sK137,X0)
| empty(sK302(sK137,X0))
| relation(sK136(sK302(sK137,X0)))
| subset(X0,sK135(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_367,c_190602]) ).
tcf(c_197140,plain,
! [X0: $i] :
( empty(sK91(sK137,X0))
| relation(sK136(sK91(sK137,X0)))
| in(sK135(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_367,c_190603]) ).
tcf(c_197141,plain,
! [X0: $i] :
( empty(sK91(sK137,X0))
| relation(sK136(sK91(sK137,X0)))
| subset(X0,sK135(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_367,c_190604]) ).
tcf(c_197142,plain,
( empty(the_topology(sK137))
| relation(sK136(the_topology(sK137)))
| open_subset(sK135(the_topology(sK137)),sK137)
| ~ subset(sK135(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_367,c_190618]) ).
tcf(c_197143,plain,
( empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| ( sK92(sK137,sK138,sK135(sK91(sK137,sK138))) = sK135(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_175190]) ).
tcf(c_197144,plain,
( empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| in(sK135(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_175008]) ).
tcf(c_197145,plain,
( empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| subset(sK138,sK135(sK91(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_174960]) ).
tcf(c_197146,plain,
( sP36(sK137,sK138)
| empty(sK302(sK137,sK138))
| relation(sK136(sK302(sK137,sK138)))
| ( sK303(sK137,sK138,sK135(sK302(sK137,sK138))) = sK135(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_175802]) ).
tcf(c_197147,plain,
( sP36(sK137,sK138)
| empty(sK302(sK137,sK138))
| relation(sK136(sK302(sK137,sK138)))
| ( sK304(sK137,sK138,sK135(sK302(sK137,sK138))) = sK135(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_175753]) ).
tcf(c_197148,plain,
( sP36(sK137,sK138)
| empty(sK302(sK137,sK138))
| relation(sK136(sK302(sK137,sK138)))
| subset(sK138,sK135(sK302(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_175029]) ).
tcf(c_197149,plain,
( empty(sK93(sK137,the_topology(sK137)))
| relation(sK136(sK93(sK137,the_topology(sK137))))
| in(sK135(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_175089]) ).
tcf(c_197150,plain,
! [X0: $i] :
( empty(sK93(sK137,sK147(sK137,X0)))
| relation(sK136(sK93(sK137,sK147(sK137,X0))))
| in(sK135(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_175090]) ).
tcf(c_197151,plain,
! [X0: $i] :
( empty(sK93(sK137,sK125(sK137,X0)))
| relation(sK136(sK93(sK137,sK125(sK137,X0))))
| in(sK135(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_367,c_175091]) ).
tcf(c_197152,plain,
! [X0: $i] :
( empty(sK93(sK137,sK123(sK137,X0)))
| relation(sK136(sK93(sK137,sK123(sK137,X0))))
| in(sK135(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_175092]) ).
tcf(c_197153,plain,
( empty(sK147(sK137,sK138))
| relation(sK136(sK147(sK137,sK138)))
| subset(sK138,sK135(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK135(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_367,c_190614]) ).
tcf(c_197154,plain,
( empty(sK147(sK137,sK138))
| relation(sK136(sK147(sK137,sK138)))
| closed_subset(sK135(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK135(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_367,c_190613]) ).
tcf(c_197155,plain,
( empty(sK123(sK137,sK138))
| relation(sK136(sK123(sK137,sK138)))
| subset(sK138,sK135(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK135(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_367,c_190612]) ).
tcf(c_197156,plain,
! [X0: $i] :
( empty(sK147(sK137,topstr_closure(sK137,X0)))
| relation(sK136(sK147(sK137,topstr_closure(sK137,X0))))
| closed_subset(sK135(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(sK135(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_176007]) ).
tcf(c_197157,plain,
! [X0: $i] :
( empty(sK91(sK137,topstr_closure(sK137,X0)))
| relation(sK136(sK91(sK137,topstr_closure(sK137,X0))))
| ( sK92(sK137,topstr_closure(sK137,X0),sK135(sK91(sK137,topstr_closure(sK137,X0)))) = sK135(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_176010]) ).
tcf(c_197158,plain,
! [X0: $i] :
( empty(sK91(sK137,topstr_closure(sK137,X0)))
| relation(sK136(sK91(sK137,topstr_closure(sK137,X0))))
| subset(topstr_closure(sK137,X0),sK135(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_176013]) ).
tcf(c_197159,plain,
! [X0: $i] :
( empty(sK91(sK137,topstr_closure(sK137,X0)))
| relation(sK136(sK91(sK137,topstr_closure(sK137,X0))))
| in(sK135(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_176012]) ).
tcf(c_197160,plain,
( sP34(the_topology(sK137),sK137)
| empty(sK295(sK137,the_topology(sK137)))
| relation(sK136(sK295(sK137,the_topology(sK137))))
| ( sK296(sK137,the_topology(sK137),sK135(sK295(sK137,the_topology(sK137)))) = sK135(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_176134]) ).
tcf(c_197161,plain,
( sP36(sK137,the_carrier(sK137))
| empty(sK302(sK137,the_carrier(sK137)))
| relation(sK136(sK302(sK137,the_carrier(sK137))))
| ( sK304(sK137,the_carrier(sK137),sK135(sK302(sK137,the_carrier(sK137)))) = sK135(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_176975]) ).
tcf(c_197162,plain,
( sP36(sK137,the_carrier(sK137))
| empty(sK302(sK137,the_carrier(sK137)))
| relation(sK136(sK302(sK137,the_carrier(sK137))))
| ( sK303(sK137,the_carrier(sK137),sK135(sK302(sK137,the_carrier(sK137)))) = sK135(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_176974]) ).
tcf(c_197163,plain,
( sP36(sK137,the_carrier(sK137))
| empty(sK302(sK137,the_carrier(sK137)))
| relation(sK136(sK302(sK137,the_carrier(sK137))))
| subset(the_carrier(sK137),sK135(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_176981]) ).
tcf(c_197164,plain,
( empty(sK123(sK137,the_carrier(sK137)))
| relation(sK136(sK123(sK137,the_carrier(sK137))))
| ( sK124(sK137,the_carrier(sK137),sK135(sK123(sK137,the_carrier(sK137)))) = sK135(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(sK135(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_176971]) ).
tcf(c_197165,plain,
( empty(sK123(sK137,the_carrier(sK137)))
| relation(sK136(sK123(sK137,the_carrier(sK137))))
| subset(the_carrier(sK137),sK135(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK135(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_176976]) ).
tcf(c_197166,plain,
( empty(sK91(sK137,the_carrier(sK137)))
| relation(sK136(sK91(sK137,the_carrier(sK137))))
| ( sK92(sK137,the_carrier(sK137),sK135(sK91(sK137,the_carrier(sK137)))) = sK135(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_176980]) ).
tcf(c_197167,plain,
( empty(sK91(sK137,the_carrier(sK137)))
| relation(sK136(sK91(sK137,the_carrier(sK137))))
| in(sK135(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_176982]) ).
tcf(c_197168,plain,
( empty(sK91(sK137,the_carrier(sK137)))
| relation(sK136(sK91(sK137,the_carrier(sK137))))
| subset(the_carrier(sK137),sK135(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_176983]) ).
tcf(c_197169,plain,
( empty(sK147(sK137,the_carrier(sK137)))
| relation(sK136(sK147(sK137,the_carrier(sK137))))
| subset(the_carrier(sK137),sK135(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_176978]) ).
tcf(c_197170,plain,
( empty(sK147(sK137,the_carrier(sK137)))
| relation(sK136(sK147(sK137,the_carrier(sK137))))
| closed_subset(sK135(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_176977]) ).
tcf(c_197171,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| empty(sK295(sK137,powerset(the_carrier(sK137))))
| relation(sK136(sK295(sK137,powerset(the_carrier(sK137)))))
| ( sK296(sK137,powerset(the_carrier(sK137)),sK135(sK295(sK137,powerset(the_carrier(sK137))))) = sK135(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_176995]) ).
tcf(c_197172,plain,
( empty(sK93(sK137,powerset(the_carrier(sK137))))
| relation(sK136(sK93(sK137,powerset(the_carrier(sK137)))))
| in(sK135(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_176997]) ).
tcf(c_197173,plain,
( empty(topstr_closure(sK137,sK138))
| relation(sK136(topstr_closure(sK137,sK138)))
| in(sK135(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(sK135(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_367,c_177233]) ).
tcf(c_197174,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| empty(sK302(sK137,sK208(powerset(the_carrier(sK137)))))
| relation(sK136(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| subset(sK208(powerset(the_carrier(sK137))),sK135(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_177405]) ).
tcf(c_197175,plain,
( empty(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| relation(sK136(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| subset(sK208(powerset(the_carrier(sK137))),sK135(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK135(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_177400]) ).
tcf(c_197176,plain,
( empty(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| relation(sK136(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK135(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK135(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_177404]) ).
tcf(c_197177,plain,
( empty(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| relation(sK136(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| subset(sK208(powerset(the_carrier(sK137))),sK135(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_177407]) ).
tcf(c_197178,plain,
( empty(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| relation(sK136(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| in(sK135(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_177406]) ).
tcf(c_197179,plain,
( empty(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| relation(sK136(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| subset(sK208(powerset(the_carrier(sK137))),sK135(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_177402]) ).
tcf(c_197180,plain,
( empty(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| relation(sK136(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| closed_subset(sK135(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_177401]) ).
tcf(c_197181,plain,
( empty(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))))
| relation(sK136(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))))
| in(sK135(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_177421]) ).
tcf(c_197182,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| empty(sK302(sK137,sK207(the_carrier(sK137))))
| relation(sK136(sK302(sK137,sK207(the_carrier(sK137)))))
| subset(sK207(the_carrier(sK137)),sK135(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_182970]) ).
tcf(c_197183,plain,
( empty(the_carrier(sK137))
| empty(sK123(sK137,sK207(the_carrier(sK137))))
| relation(sK136(sK123(sK137,sK207(the_carrier(sK137)))))
| subset(sK207(the_carrier(sK137)),sK135(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK135(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_182965]) ).
tcf(c_197184,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK207(the_carrier(sK137))))
| relation(sK136(sK91(sK137,sK207(the_carrier(sK137)))))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK135(sK91(sK137,sK207(the_carrier(sK137))))) = sK135(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_182969]) ).
tcf(c_197185,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK207(the_carrier(sK137))))
| relation(sK136(sK91(sK137,sK207(the_carrier(sK137)))))
| subset(sK207(the_carrier(sK137)),sK135(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_182972]) ).
tcf(c_197186,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK207(the_carrier(sK137))))
| relation(sK136(sK91(sK137,sK207(the_carrier(sK137)))))
| in(sK135(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_182971]) ).
tcf(c_197187,plain,
( empty(the_carrier(sK137))
| empty(sK147(sK137,sK207(the_carrier(sK137))))
| relation(sK136(sK147(sK137,sK207(the_carrier(sK137)))))
| subset(sK207(the_carrier(sK137)),sK135(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_182967]) ).
tcf(c_197188,plain,
( empty(the_carrier(sK137))
| empty(sK147(sK137,sK207(the_carrier(sK137))))
| relation(sK136(sK147(sK137,sK207(the_carrier(sK137)))))
| closed_subset(sK135(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_182966]) ).
tcf(c_197189,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| empty(sK302(sK137,sK325(the_carrier(sK137))))
| relation(sK136(sK302(sK137,sK325(the_carrier(sK137)))))
| subset(sK325(the_carrier(sK137)),sK135(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_184375]) ).
tcf(c_197190,plain,
( empty(the_carrier(sK137))
| empty(sK123(sK137,sK325(the_carrier(sK137))))
| relation(sK136(sK123(sK137,sK325(the_carrier(sK137)))))
| subset(sK325(the_carrier(sK137)),sK135(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK135(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_184370]) ).
tcf(c_197191,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK325(the_carrier(sK137))))
| relation(sK136(sK91(sK137,sK325(the_carrier(sK137)))))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK135(sK91(sK137,sK325(the_carrier(sK137))))) = sK135(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_184374]) ).
tcf(c_197192,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK325(the_carrier(sK137))))
| relation(sK136(sK91(sK137,sK325(the_carrier(sK137)))))
| subset(sK325(the_carrier(sK137)),sK135(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_184377]) ).
tcf(c_197193,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK325(the_carrier(sK137))))
| relation(sK136(sK91(sK137,sK325(the_carrier(sK137)))))
| in(sK135(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_184376]) ).
tcf(c_197194,plain,
( empty(the_carrier(sK137))
| empty(sK147(sK137,sK325(the_carrier(sK137))))
| relation(sK136(sK147(sK137,sK325(the_carrier(sK137)))))
| subset(sK325(the_carrier(sK137)),sK135(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_184372]) ).
tcf(c_197195,plain,
( empty(the_carrier(sK137))
| empty(sK147(sK137,sK325(the_carrier(sK137))))
| relation(sK136(sK147(sK137,sK325(the_carrier(sK137)))))
| closed_subset(sK135(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_367,c_184371]) ).
tcf(c_197196,plain,
( empty(sK93(sK137,sK123(sK137,sK138)))
| relation(sK136(sK93(sK137,sK123(sK137,sK138))))
| subset(sK138,set_difference(the_carrier(sK137),sK135(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_192075]) ).
tcf(c_197197,plain,
( empty(sK93(sK137,sK147(sK137,sK138)))
| relation(sK136(sK93(sK137,sK147(sK137,sK138))))
| subset(sK138,set_difference(the_carrier(sK137),sK135(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_192676]) ).
tcf(c_197198,plain,
( empty(sK93(sK137,sK147(sK137,sK138)))
| relation(sK136(sK93(sK137,sK147(sK137,sK138))))
| closed_subset(set_difference(the_carrier(sK137),sK135(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_192446]) ).
tcf(c_197219,plain,
! [X0: $i] :
( relation(sK136(powerset(X0)))
| subset(sK135(powerset(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_197134,c_700]) ).
tcf(c_197433,plain,
( relation(sK136(powerset(the_carrier(sK137))))
| in(sK135(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK135(powerset(the_carrier(sK137)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_197137,c_700]) ).
tcf(c_197444,plain,
( sP36(sK137,sK138)
| relation(sK136(powerset(the_carrier(sK137))))
| in(sK135(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK135(powerset(the_carrier(sK137)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_197136,c_700]) ).
tcf(c_197837,plain,
! [X0: $i] :
( empty(X0)
| ordinal(sK135(X0))
| function(sK136(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_368,c_349]) ).
tcf(c_197838,plain,
! [X0: $i] :
( empty(X0)
| function(sK136(X0))
| ~ in(X0,sK135(X0)) ),
inference(superposition,[status(thm)],[c_368,c_546]) ).
tcf(c_197839,plain,
! [X0: $i] :
( empty(X0)
| function(sK136(X0))
| in(sK154(X0),X0) ),
inference(superposition,[status(thm)],[c_368,c_542]) ).
tcf(c_197841,plain,
! [X0: $i] :
( empty(X0)
| function(sK136(X0))
| element(sK135(X0),X0) ),
inference(superposition,[status(thm)],[c_368,c_701]) ).
tcf(c_197842,plain,
! [X0: $i] :
( empty(sK99(X0))
| function(sK136(sK99(X0)))
| in(sK135(sK99(X0)),X0) ),
inference(superposition,[status(thm)],[c_368,c_205]) ).
tcf(c_197843,plain,
! [X0: $i] :
( empty(sK99(X0))
| ordinal(sK135(sK99(X0)))
| function(sK136(sK99(X0))) ),
inference(superposition,[status(thm)],[c_368,c_206]) ).
tcf(c_197845,plain,
! [X0: $i] :
( empty(powerset(X0))
| function(sK136(powerset(X0)))
| subset(sK135(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_368,c_667]) ).
tcf(c_197846,plain,
! [X0: $i] :
( sP27
| empty(sK254(X0))
| ordinal(sK135(sK254(X0)))
| function(sK136(sK254(X0))) ),
inference(superposition,[status(thm)],[c_368,c_802]) ).
tcf(c_197847,plain,
( sP36(sK137,sK138)
| empty(powerset(the_carrier(sK137)))
| function(sK136(powerset(the_carrier(sK137))))
| in(sK135(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK135(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_368,c_176867]) ).
tcf(c_197848,plain,
( empty(powerset(the_carrier(sK137)))
| function(sK136(powerset(the_carrier(sK137))))
| in(sK135(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK135(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_368,c_176193]) ).
tcf(c_197849,plain,
! [X0: $i] :
( empty(sK93(sK137,X0))
| function(sK136(sK93(sK137,X0)))
| in(sK135(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_190624]) ).
tcf(c_197850,plain,
! [X0: $i] :
( sP36(sK137,X0)
| empty(sK302(sK137,X0))
| function(sK136(sK302(sK137,X0)))
| subset(X0,sK135(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_368,c_190602]) ).
tcf(c_197851,plain,
! [X0: $i] :
( empty(sK91(sK137,X0))
| function(sK136(sK91(sK137,X0)))
| in(sK135(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_368,c_190603]) ).
tcf(c_197852,plain,
! [X0: $i] :
( empty(sK91(sK137,X0))
| function(sK136(sK91(sK137,X0)))
| subset(X0,sK135(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_368,c_190604]) ).
tcf(c_197853,plain,
( empty(the_topology(sK137))
| function(sK136(the_topology(sK137)))
| open_subset(sK135(the_topology(sK137)),sK137)
| ~ subset(sK135(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_368,c_190618]) ).
tcf(c_197854,plain,
( empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| ( sK92(sK137,sK138,sK135(sK91(sK137,sK138))) = sK135(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_175190]) ).
tcf(c_197855,plain,
( empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| in(sK135(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_175008]) ).
tcf(c_197856,plain,
( empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| subset(sK138,sK135(sK91(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_174960]) ).
tcf(c_197857,plain,
( sP36(sK137,sK138)
| empty(sK302(sK137,sK138))
| function(sK136(sK302(sK137,sK138)))
| ( sK303(sK137,sK138,sK135(sK302(sK137,sK138))) = sK135(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_175802]) ).
tcf(c_197858,plain,
( sP36(sK137,sK138)
| empty(sK302(sK137,sK138))
| function(sK136(sK302(sK137,sK138)))
| ( sK304(sK137,sK138,sK135(sK302(sK137,sK138))) = sK135(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_175753]) ).
tcf(c_197859,plain,
( sP36(sK137,sK138)
| empty(sK302(sK137,sK138))
| function(sK136(sK302(sK137,sK138)))
| subset(sK138,sK135(sK302(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_175029]) ).
tcf(c_197860,plain,
( empty(sK93(sK137,the_topology(sK137)))
| function(sK136(sK93(sK137,the_topology(sK137))))
| in(sK135(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_175089]) ).
tcf(c_197861,plain,
! [X0: $i] :
( empty(sK93(sK137,sK147(sK137,X0)))
| function(sK136(sK93(sK137,sK147(sK137,X0))))
| in(sK135(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_175090]) ).
tcf(c_197862,plain,
! [X0: $i] :
( empty(sK93(sK137,sK125(sK137,X0)))
| function(sK136(sK93(sK137,sK125(sK137,X0))))
| in(sK135(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_368,c_175091]) ).
tcf(c_197863,plain,
! [X0: $i] :
( empty(sK93(sK137,sK123(sK137,X0)))
| function(sK136(sK93(sK137,sK123(sK137,X0))))
| in(sK135(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_175092]) ).
tcf(c_197864,plain,
( empty(sK147(sK137,sK138))
| function(sK136(sK147(sK137,sK138)))
| subset(sK138,sK135(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK135(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_368,c_190614]) ).
tcf(c_197865,plain,
( empty(sK147(sK137,sK138))
| function(sK136(sK147(sK137,sK138)))
| closed_subset(sK135(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ subset(sK135(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_368,c_190613]) ).
tcf(c_197866,plain,
( empty(sK123(sK137,sK138))
| function(sK136(sK123(sK137,sK138)))
| subset(sK138,sK135(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ subset(sK135(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_368,c_190612]) ).
tcf(c_197867,plain,
! [X0: $i] :
( empty(sK147(sK137,topstr_closure(sK137,X0)))
| function(sK136(sK147(sK137,topstr_closure(sK137,X0))))
| closed_subset(sK135(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ element(sK135(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_176007]) ).
tcf(c_197868,plain,
! [X0: $i] :
( empty(sK91(sK137,topstr_closure(sK137,X0)))
| function(sK136(sK91(sK137,topstr_closure(sK137,X0))))
| ( sK92(sK137,topstr_closure(sK137,X0),sK135(sK91(sK137,topstr_closure(sK137,X0)))) = sK135(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_176010]) ).
tcf(c_197869,plain,
! [X0: $i] :
( empty(sK91(sK137,topstr_closure(sK137,X0)))
| function(sK136(sK91(sK137,topstr_closure(sK137,X0))))
| subset(topstr_closure(sK137,X0),sK135(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_176013]) ).
tcf(c_197870,plain,
! [X0: $i] :
( empty(sK91(sK137,topstr_closure(sK137,X0)))
| function(sK136(sK91(sK137,topstr_closure(sK137,X0))))
| in(sK135(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_176012]) ).
tcf(c_197871,plain,
( sP34(the_topology(sK137),sK137)
| empty(sK295(sK137,the_topology(sK137)))
| function(sK136(sK295(sK137,the_topology(sK137))))
| ( sK296(sK137,the_topology(sK137),sK135(sK295(sK137,the_topology(sK137)))) = sK135(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_176134]) ).
tcf(c_197872,plain,
( sP36(sK137,the_carrier(sK137))
| empty(sK302(sK137,the_carrier(sK137)))
| function(sK136(sK302(sK137,the_carrier(sK137))))
| ( sK304(sK137,the_carrier(sK137),sK135(sK302(sK137,the_carrier(sK137)))) = sK135(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_176975]) ).
tcf(c_197873,plain,
( sP36(sK137,the_carrier(sK137))
| empty(sK302(sK137,the_carrier(sK137)))
| function(sK136(sK302(sK137,the_carrier(sK137))))
| ( sK303(sK137,the_carrier(sK137),sK135(sK302(sK137,the_carrier(sK137)))) = sK135(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_176974]) ).
tcf(c_197874,plain,
( sP36(sK137,the_carrier(sK137))
| empty(sK302(sK137,the_carrier(sK137)))
| function(sK136(sK302(sK137,the_carrier(sK137))))
| subset(the_carrier(sK137),sK135(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_176981]) ).
tcf(c_197875,plain,
( empty(sK123(sK137,the_carrier(sK137)))
| function(sK136(sK123(sK137,the_carrier(sK137))))
| ( sK124(sK137,the_carrier(sK137),sK135(sK123(sK137,the_carrier(sK137)))) = sK135(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ element(sK135(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_176971]) ).
tcf(c_197876,plain,
( empty(sK123(sK137,the_carrier(sK137)))
| function(sK136(sK123(sK137,the_carrier(sK137))))
| subset(the_carrier(sK137),sK135(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK135(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_176976]) ).
tcf(c_197877,plain,
( empty(sK91(sK137,the_carrier(sK137)))
| function(sK136(sK91(sK137,the_carrier(sK137))))
| ( sK92(sK137,the_carrier(sK137),sK135(sK91(sK137,the_carrier(sK137)))) = sK135(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_176980]) ).
tcf(c_197878,plain,
( empty(sK91(sK137,the_carrier(sK137)))
| function(sK136(sK91(sK137,the_carrier(sK137))))
| in(sK135(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_176982]) ).
tcf(c_197879,plain,
( empty(sK91(sK137,the_carrier(sK137)))
| function(sK136(sK91(sK137,the_carrier(sK137))))
| subset(the_carrier(sK137),sK135(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_176983]) ).
tcf(c_197880,plain,
( empty(sK147(sK137,the_carrier(sK137)))
| function(sK136(sK147(sK137,the_carrier(sK137))))
| subset(the_carrier(sK137),sK135(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_176978]) ).
tcf(c_197881,plain,
( empty(sK147(sK137,the_carrier(sK137)))
| function(sK136(sK147(sK137,the_carrier(sK137))))
| closed_subset(sK135(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_176977]) ).
tcf(c_197882,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| empty(sK295(sK137,powerset(the_carrier(sK137))))
| function(sK136(sK295(sK137,powerset(the_carrier(sK137)))))
| ( sK296(sK137,powerset(the_carrier(sK137)),sK135(sK295(sK137,powerset(the_carrier(sK137))))) = sK135(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_176995]) ).
tcf(c_197883,plain,
( empty(sK93(sK137,powerset(the_carrier(sK137))))
| function(sK136(sK93(sK137,powerset(the_carrier(sK137)))))
| in(sK135(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_176997]) ).
tcf(c_197884,plain,
( empty(topstr_closure(sK137,sK138))
| function(sK136(topstr_closure(sK137,sK138)))
| in(sK135(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ in(sK135(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_368,c_177233]) ).
tcf(c_197885,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| empty(sK302(sK137,sK208(powerset(the_carrier(sK137)))))
| function(sK136(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| subset(sK208(powerset(the_carrier(sK137))),sK135(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_177405]) ).
tcf(c_197886,plain,
( empty(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| function(sK136(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| subset(sK208(powerset(the_carrier(sK137))),sK135(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK135(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_177400]) ).
tcf(c_197887,plain,
( empty(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| function(sK136(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK135(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK135(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_177404]) ).
tcf(c_197888,plain,
( empty(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| function(sK136(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| subset(sK208(powerset(the_carrier(sK137))),sK135(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_177407]) ).
tcf(c_197889,plain,
( empty(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| function(sK136(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| in(sK135(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_177406]) ).
tcf(c_197890,plain,
( empty(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| function(sK136(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| subset(sK208(powerset(the_carrier(sK137))),sK135(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_177402]) ).
tcf(c_197891,plain,
( empty(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| function(sK136(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| closed_subset(sK135(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_177401]) ).
tcf(c_197892,plain,
( empty(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))))
| function(sK136(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))))
| in(sK135(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_177421]) ).
tcf(c_197893,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| empty(sK302(sK137,sK207(the_carrier(sK137))))
| function(sK136(sK302(sK137,sK207(the_carrier(sK137)))))
| subset(sK207(the_carrier(sK137)),sK135(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_182970]) ).
tcf(c_197894,plain,
( empty(the_carrier(sK137))
| empty(sK123(sK137,sK207(the_carrier(sK137))))
| function(sK136(sK123(sK137,sK207(the_carrier(sK137)))))
| subset(sK207(the_carrier(sK137)),sK135(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK135(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_182965]) ).
tcf(c_197895,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK207(the_carrier(sK137))))
| function(sK136(sK91(sK137,sK207(the_carrier(sK137)))))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK135(sK91(sK137,sK207(the_carrier(sK137))))) = sK135(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_182969]) ).
tcf(c_197896,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK207(the_carrier(sK137))))
| function(sK136(sK91(sK137,sK207(the_carrier(sK137)))))
| subset(sK207(the_carrier(sK137)),sK135(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_182972]) ).
tcf(c_197897,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK207(the_carrier(sK137))))
| function(sK136(sK91(sK137,sK207(the_carrier(sK137)))))
| in(sK135(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_182971]) ).
tcf(c_197898,plain,
( empty(the_carrier(sK137))
| empty(sK147(sK137,sK207(the_carrier(sK137))))
| function(sK136(sK147(sK137,sK207(the_carrier(sK137)))))
| subset(sK207(the_carrier(sK137)),sK135(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_182967]) ).
tcf(c_197899,plain,
( empty(the_carrier(sK137))
| empty(sK147(sK137,sK207(the_carrier(sK137))))
| function(sK136(sK147(sK137,sK207(the_carrier(sK137)))))
| closed_subset(sK135(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_182966]) ).
tcf(c_197900,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| empty(sK302(sK137,sK325(the_carrier(sK137))))
| function(sK136(sK302(sK137,sK325(the_carrier(sK137)))))
| subset(sK325(the_carrier(sK137)),sK135(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_184375]) ).
tcf(c_197901,plain,
( empty(the_carrier(sK137))
| empty(sK123(sK137,sK325(the_carrier(sK137))))
| function(sK136(sK123(sK137,sK325(the_carrier(sK137)))))
| subset(sK325(the_carrier(sK137)),sK135(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK135(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_184370]) ).
tcf(c_197902,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK325(the_carrier(sK137))))
| function(sK136(sK91(sK137,sK325(the_carrier(sK137)))))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK135(sK91(sK137,sK325(the_carrier(sK137))))) = sK135(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_184374]) ).
tcf(c_197903,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK325(the_carrier(sK137))))
| function(sK136(sK91(sK137,sK325(the_carrier(sK137)))))
| subset(sK325(the_carrier(sK137)),sK135(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_184377]) ).
tcf(c_197904,plain,
( empty(the_carrier(sK137))
| empty(sK91(sK137,sK325(the_carrier(sK137))))
| function(sK136(sK91(sK137,sK325(the_carrier(sK137)))))
| in(sK135(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_184376]) ).
tcf(c_197905,plain,
( empty(the_carrier(sK137))
| empty(sK147(sK137,sK325(the_carrier(sK137))))
| function(sK136(sK147(sK137,sK325(the_carrier(sK137)))))
| subset(sK325(the_carrier(sK137)),sK135(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_184372]) ).
tcf(c_197906,plain,
( empty(the_carrier(sK137))
| empty(sK147(sK137,sK325(the_carrier(sK137))))
| function(sK136(sK147(sK137,sK325(the_carrier(sK137)))))
| closed_subset(sK135(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ element(sK135(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_368,c_184371]) ).
tcf(c_197907,plain,
( empty(sK93(sK137,sK123(sK137,sK138)))
| function(sK136(sK93(sK137,sK123(sK137,sK138))))
| subset(sK138,set_difference(the_carrier(sK137),sK135(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_192075]) ).
tcf(c_197908,plain,
( empty(sK93(sK137,sK147(sK137,sK138)))
| function(sK136(sK93(sK137,sK147(sK137,sK138))))
| subset(sK138,set_difference(the_carrier(sK137),sK135(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_192676]) ).
tcf(c_197909,plain,
( empty(sK93(sK137,sK147(sK137,sK138)))
| function(sK136(sK93(sK137,sK147(sK137,sK138))))
| closed_subset(set_difference(the_carrier(sK137),sK135(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_192446]) ).
tcf(c_197930,plain,
! [X0: $i] :
( function(sK136(powerset(X0)))
| subset(sK135(powerset(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_197845,c_700]) ).
tcf(c_198144,plain,
( function(sK136(powerset(the_carrier(sK137))))
| in(sK135(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK135(powerset(the_carrier(sK137)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_197848,c_700]) ).
tcf(c_198155,plain,
( sP36(sK137,sK138)
| function(sK136(powerset(the_carrier(sK137))))
| in(sK135(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK135(powerset(the_carrier(sK137)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_197847,c_700]) ).
tcf(c_198347,plain,
! [X0: $i] :
( subset(powerset(empty_set),X0)
| ~ in(empty_set,X0) ),
inference(superposition,[status(thm)],[c_330,c_404]) ).
tcf(c_198349,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ proper_subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_404,c_492]) ).
tcf(c_198351,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,unordered_pair(X0,X0))) = topstr_closure(sK137,unordered_pair(X0,X0)) )
| ~ topological_space(sK137)
| ~ in(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_404,c_190616]) ).
tcf(c_198352,plain,
! [X0: $i] :
( ( topstr_closure(sK137,unordered_pair(X0,X0)) = unordered_pair(X0,X0) )
| ~ in(X0,the_carrier(sK137))
| ~ closed_subset(unordered_pair(X0,X0),sK137) ),
inference(superposition,[status(thm)],[c_404,c_190617]) ).
tcf(c_198353,plain,
! [X0: $i] :
( in(unordered_pair(X0,X0),the_topology(sK137))
| ~ in(X0,the_carrier(sK137))
| ~ open_subset(unordered_pair(X0,X0),sK137) ),
inference(superposition,[status(thm)],[c_404,c_190619]) ).
tcf(c_198375,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ in(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_533,c_407]) ).
tcf(c_198376,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(unordered_pair(X0,X1),X2)),
inference(superposition,[status(thm)],[c_518,c_407]) ).
tcf(c_198378,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,unordered_pair(X0,X1)))
| in(X0,sK146(sK137,unordered_pair(X0,X1),X2))
| ~ in(X2,the_carrier(sK137))
| ~ element(unordered_pair(X0,X1),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48177,c_407]) ).
tcf(c_198379,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(X1,unordered_pair(X0,X2))),
inference(superposition,[status(thm)],[c_181192,c_407]) ).
tcf(c_198382,plain,
! [X0: $i] :
( in(empty_set,X0)
| ~ subset(powerset(empty_set),X0) ),
inference(superposition,[status(thm)],[c_330,c_407]) ).
tcf(c_198383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)),X2)
| ( X1 = X3 )
| ~ subset(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(superposition,[status(thm)],[c_105912,c_407]) ).
tcf(c_198384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)),X2)
| ( X0 = X3 )
| ~ subset(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(superposition,[status(thm)],[c_105926,c_407]) ).
tcf(c_198425,plain,
! [X0: $i] :
( ordinal(sK267)
| sP30(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_180555,c_827]) ).
tcf(c_198444,plain,
( finite(sK138)
| empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(sK135(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_197145,c_292]) ).
tcf(c_198445,plain,
( empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(sK135(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_197145,c_492]) ).
tcf(c_198463,plain,
( finite(sK138)
| empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(sK135(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_197856,c_292]) ).
tcf(c_198464,plain,
( empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(sK135(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_197856,c_492]) ).
tcf(c_198480,plain,
( finite(sK138)
| sP3(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK62(sK93(sK137,sK147(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192720,c_292]) ).
tcf(c_198481,plain,
( sP3(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK62(sK93(sK137,sK147(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192720,c_492]) ).
tcf(c_198495,plain,
( finite(sK138)
| ordinal(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK139(sK93(sK137,sK147(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192722,c_292]) ).
tcf(c_198496,plain,
( ordinal(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK139(sK93(sK137,sK147(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192722,c_492]) ).
tcf(c_198519,plain,
( finite(sK138)
| relation(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK175(sK93(sK137,sK147(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192725,c_292]) ).
tcf(c_198520,plain,
( relation(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK175(sK93(sK137,sK147(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192725,c_492]) ).
tcf(c_198534,plain,
( finite(sK138)
| epsilon_transitive(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK340(sK93(sK137,sK147(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192731,c_292]) ).
tcf(c_198535,plain,
( epsilon_transitive(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK340(sK93(sK137,sK147(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192731,c_492]) ).
tcf(c_198549,plain,
( finite(sK138)
| epsilon_connected(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK369(sK93(sK137,sK147(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192732,c_292]) ).
tcf(c_198550,plain,
( epsilon_connected(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK369(sK93(sK137,sK147(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192732,c_492]) ).
tcf(c_198564,plain,
( finite(sK138)
| epsilon_connected(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(set_difference(the_carrier(sK137),sK370(sK93(sK137,sK147(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192733,c_292]) ).
tcf(c_198565,plain,
( epsilon_connected(sK93(sK137,sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(set_difference(the_carrier(sK137),sK370(sK93(sK137,sK147(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192733,c_492]) ).
tcf(c_198578,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,union(X2))
| ~ in(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_533,c_408]) ).
tcf(c_198579,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(unordered_pair(X1,X0),X2)),
inference(superposition,[status(thm)],[c_518,c_408]) ).
tcf(c_198581,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(sK137,unordered_pair(X0,X1)))
| in(X1,sK146(sK137,unordered_pair(X0,X1),X2))
| ~ in(X2,the_carrier(sK137))
| ~ element(unordered_pair(X0,X1),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48177,c_408]) ).
tcf(c_198582,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(X1,unordered_pair(X2,X0))),
inference(superposition,[status(thm)],[c_181192,c_408]) ).
tcf(c_198586,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)),X2)
| ( X1 = X3 )
| ~ subset(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(superposition,[status(thm)],[c_105912,c_408]) ).
tcf(c_198587,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)),X2)
| ( X0 = X3 )
| ~ subset(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(superposition,[status(thm)],[c_105926,c_408]) ).
tcf(c_198616,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(X0,sK143(X0)) ),
inference(superposition,[status(thm)],[c_422,c_546]) ).
tcf(c_198617,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| in(sK154(X0),X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_422,c_542]) ).
tcf(c_198618,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_422,c_781]) ).
tcf(c_198619,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| element(sK143(X0),X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_422,c_701]) ).
tcf(c_198620,plain,
! [X0: $i] :
( being_limit_ordinal(sK99(X0))
| in(sK143(sK99(X0)),X0)
| ~ ordinal(sK99(X0)) ),
inference(superposition,[status(thm)],[c_422,c_205]) ).
tcf(c_198621,plain,
! [X0: $i] :
( being_limit_ordinal(sK99(X0))
| ordinal(sK143(sK99(X0)))
| ~ ordinal(sK99(X0)) ),
inference(superposition,[status(thm)],[c_422,c_206]) ).
tcf(c_198622,plain,
( being_limit_ordinal(empty_set)
| ~ ordinal(empty_set) ),
inference(superposition,[status(thm)],[c_422,c_599]) ).
tcf(c_198623,plain,
! [X0: $i] :
( being_limit_ordinal(powerset(X0))
| subset(sK143(powerset(X0)),X0)
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_422,c_667]) ).
tcf(c_198624,plain,
! [X0: $i] :
( sP27
| being_limit_ordinal(sK254(X0))
| ordinal(sK143(sK254(X0)))
| ~ ordinal(sK254(X0)) ),
inference(superposition,[status(thm)],[c_422,c_802]) ).
tcf(c_198625,plain,
( sP36(sK137,sK138)
| being_limit_ordinal(powerset(the_carrier(sK137)))
| in(sK143(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ closed_subset(sK143(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK143(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_176867]) ).
tcf(c_198626,plain,
( being_limit_ordinal(powerset(the_carrier(sK137)))
| in(sK143(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ closed_subset(sK143(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK143(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_176193]) ).
tcf(c_198627,plain,
! [X0: $i] :
( being_limit_ordinal(sK93(sK137,X0))
| in(sK143(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK93(sK137,X0))
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_190624]) ).
tcf(c_198628,plain,
! [X0: $i] :
( sP36(sK137,X0)
| being_limit_ordinal(sK302(sK137,X0))
| subset(X0,sK143(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_422,c_190602]) ).
tcf(c_198629,plain,
! [X0: $i] :
( being_limit_ordinal(sK91(sK137,X0))
| in(sK143(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_422,c_190603]) ).
tcf(c_198630,plain,
! [X0: $i] :
( being_limit_ordinal(sK91(sK137,X0))
| subset(X0,sK143(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_422,c_190604]) ).
tcf(c_198631,plain,
( being_limit_ordinal(the_topology(sK137))
| open_subset(sK143(the_topology(sK137)),sK137)
| ~ ordinal(the_topology(sK137))
| ~ subset(sK143(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_422,c_190618]) ).
tcf(c_198632,plain,
( being_limit_ordinal(sK91(sK137,sK138))
| ( sK92(sK137,sK138,sK143(sK91(sK137,sK138))) = sK143(sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_422,c_175190]) ).
tcf(c_198633,plain,
( being_limit_ordinal(sK91(sK137,sK138))
| in(sK143(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_422,c_175008]) ).
tcf(c_198634,plain,
( being_limit_ordinal(sK91(sK137,sK138))
| subset(sK138,sK143(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_422,c_174960]) ).
tcf(c_198635,plain,
( sP36(sK137,sK138)
| being_limit_ordinal(sK302(sK137,sK138))
| ( sK303(sK137,sK138,sK143(sK302(sK137,sK138))) = sK143(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_422,c_175802]) ).
tcf(c_198636,plain,
( sP36(sK137,sK138)
| being_limit_ordinal(sK302(sK137,sK138))
| ( sK304(sK137,sK138,sK143(sK302(sK137,sK138))) = sK143(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_422,c_175753]) ).
tcf(c_198637,plain,
( sP36(sK137,sK138)
| being_limit_ordinal(sK302(sK137,sK138))
| subset(sK138,sK143(sK302(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_422,c_175029]) ).
tcf(c_198638,plain,
( being_limit_ordinal(sK93(sK137,the_topology(sK137)))
| in(sK143(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_175089]) ).
tcf(c_198639,plain,
! [X0: $i] :
( being_limit_ordinal(sK93(sK137,sK147(sK137,X0)))
| in(sK143(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ ordinal(sK93(sK137,sK147(sK137,X0))) ),
inference(superposition,[status(thm)],[c_422,c_175090]) ).
tcf(c_198640,plain,
! [X0: $i] :
( being_limit_ordinal(sK93(sK137,sK125(sK137,X0)))
| in(sK143(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK93(sK137,sK125(sK137,X0)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_175091]) ).
tcf(c_198641,plain,
! [X0: $i] :
( being_limit_ordinal(sK93(sK137,sK123(sK137,X0)))
| in(sK143(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ ordinal(sK93(sK137,sK123(sK137,X0))) ),
inference(superposition,[status(thm)],[c_422,c_175092]) ).
tcf(c_198642,plain,
( being_limit_ordinal(sK147(sK137,sK138))
| subset(sK138,sK143(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,sK138))
| ~ subset(sK143(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_422,c_190614]) ).
tcf(c_198643,plain,
( being_limit_ordinal(sK147(sK137,sK138))
| closed_subset(sK143(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,sK138))
| ~ subset(sK143(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_422,c_190613]) ).
tcf(c_198644,plain,
( being_limit_ordinal(sK123(sK137,sK138))
| subset(sK138,sK143(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(sK123(sK137,sK138))
| ~ subset(sK143(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_422,c_190612]) ).
tcf(c_198645,plain,
! [X0: $i] :
( being_limit_ordinal(sK147(sK137,topstr_closure(sK137,X0)))
| closed_subset(sK143(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ ordinal(sK147(sK137,topstr_closure(sK137,X0)))
| ~ element(sK143(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176007]) ).
tcf(c_198646,plain,
! [X0: $i] :
( being_limit_ordinal(sK91(sK137,topstr_closure(sK137,X0)))
| ( sK92(sK137,topstr_closure(sK137,X0),sK143(sK91(sK137,topstr_closure(sK137,X0)))) = sK143(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ ordinal(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_422,c_176010]) ).
tcf(c_198647,plain,
! [X0: $i] :
( being_limit_ordinal(sK91(sK137,topstr_closure(sK137,X0)))
| subset(topstr_closure(sK137,X0),sK143(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ ordinal(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_422,c_176013]) ).
tcf(c_198648,plain,
! [X0: $i] :
( being_limit_ordinal(sK91(sK137,topstr_closure(sK137,X0)))
| in(sK143(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ ordinal(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_422,c_176012]) ).
tcf(c_198649,plain,
( sP34(the_topology(sK137),sK137)
| being_limit_ordinal(sK295(sK137,the_topology(sK137)))
| ( sK296(sK137,the_topology(sK137),sK143(sK295(sK137,the_topology(sK137)))) = sK143(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137)
| ~ ordinal(sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176134]) ).
tcf(c_198650,plain,
( sP36(sK137,the_carrier(sK137))
| being_limit_ordinal(sK302(sK137,the_carrier(sK137)))
| ( sK304(sK137,the_carrier(sK137),sK143(sK302(sK137,the_carrier(sK137)))) = sK143(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176975]) ).
tcf(c_198651,plain,
( sP36(sK137,the_carrier(sK137))
| being_limit_ordinal(sK302(sK137,the_carrier(sK137)))
| ( sK303(sK137,the_carrier(sK137),sK143(sK302(sK137,the_carrier(sK137)))) = sK143(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176974]) ).
tcf(c_198652,plain,
( sP36(sK137,the_carrier(sK137))
| being_limit_ordinal(sK302(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK143(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176981]) ).
tcf(c_198653,plain,
( being_limit_ordinal(sK123(sK137,the_carrier(sK137)))
| ( sK124(sK137,the_carrier(sK137),sK143(sK123(sK137,the_carrier(sK137)))) = sK143(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ ordinal(sK123(sK137,the_carrier(sK137)))
| ~ element(sK143(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176971]) ).
tcf(c_198654,plain,
( being_limit_ordinal(sK123(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK143(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(sK123(sK137,the_carrier(sK137)))
| ~ element(sK143(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176976]) ).
tcf(c_198655,plain,
( being_limit_ordinal(sK91(sK137,the_carrier(sK137)))
| ( sK92(sK137,the_carrier(sK137),sK143(sK91(sK137,the_carrier(sK137)))) = sK143(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176980]) ).
tcf(c_198656,plain,
( being_limit_ordinal(sK91(sK137,the_carrier(sK137)))
| in(sK143(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176982]) ).
tcf(c_198657,plain,
( being_limit_ordinal(sK91(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK143(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176983]) ).
tcf(c_198658,plain,
( being_limit_ordinal(sK147(sK137,the_carrier(sK137)))
| subset(the_carrier(sK137),sK143(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,the_carrier(sK137)))
| ~ element(sK143(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176978]) ).
tcf(c_198659,plain,
( being_limit_ordinal(sK147(sK137,the_carrier(sK137)))
| closed_subset(sK143(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,the_carrier(sK137)))
| ~ element(sK143(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_176977]) ).
tcf(c_198660,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| being_limit_ordinal(sK295(sK137,powerset(the_carrier(sK137))))
| ( sK296(sK137,powerset(the_carrier(sK137)),sK143(sK295(sK137,powerset(the_carrier(sK137))))) = sK143(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ ordinal(sK295(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_176995]) ).
tcf(c_198661,plain,
( being_limit_ordinal(sK93(sK137,powerset(the_carrier(sK137))))
| in(sK143(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK93(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_176997]) ).
tcf(c_198662,plain,
( being_limit_ordinal(topstr_closure(sK137,sK138))
| in(sK143(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ ordinal(topstr_closure(sK137,sK138))
| ~ in(sK143(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_422,c_177233]) ).
tcf(c_198663,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| being_limit_ordinal(sK302(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK143(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_422,c_177405]) ).
tcf(c_198664,plain,
( being_limit_ordinal(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK143(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ ordinal(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK143(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_177400]) ).
tcf(c_198665,plain,
( being_limit_ordinal(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK143(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK143(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_422,c_177404]) ).
tcf(c_198666,plain,
( being_limit_ordinal(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK143(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_422,c_177407]) ).
tcf(c_198667,plain,
( being_limit_ordinal(sK91(sK137,sK208(powerset(the_carrier(sK137)))))
| in(sK143(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_422,c_177406]) ).
tcf(c_198668,plain,
( being_limit_ordinal(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| subset(sK208(powerset(the_carrier(sK137))),sK143(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK143(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_177402]) ).
tcf(c_198669,plain,
( being_limit_ordinal(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| closed_subset(sK143(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK143(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_177401]) ).
tcf(c_198670,plain,
( being_limit_ordinal(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))))
| in(sK143(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_422,c_177421]) ).
tcf(c_198671,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| being_limit_ordinal(sK302(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK143(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_182970]) ).
tcf(c_198672,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK123(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK143(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(sK123(sK137,sK207(the_carrier(sK137))))
| ~ element(sK143(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_182965]) ).
tcf(c_198673,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK91(sK137,sK207(the_carrier(sK137))))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK143(sK91(sK137,sK207(the_carrier(sK137))))) = sK143(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_182969]) ).
tcf(c_198674,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK91(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK143(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_182972]) ).
tcf(c_198675,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK91(sK137,sK207(the_carrier(sK137))))
| in(sK143(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_182971]) ).
tcf(c_198676,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK147(sK137,sK207(the_carrier(sK137))))
| subset(sK207(the_carrier(sK137)),sK143(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK143(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_182967]) ).
tcf(c_198677,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK147(sK137,sK207(the_carrier(sK137))))
| closed_subset(sK143(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK143(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_182966]) ).
tcf(c_198678,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| being_limit_ordinal(sK302(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK143(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_184375]) ).
tcf(c_198679,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK123(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK143(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(sK123(sK137,sK325(the_carrier(sK137))))
| ~ element(sK143(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_184370]) ).
tcf(c_198680,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK91(sK137,sK325(the_carrier(sK137))))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK143(sK91(sK137,sK325(the_carrier(sK137))))) = sK143(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_184374]) ).
tcf(c_198681,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK91(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK143(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_184377]) ).
tcf(c_198682,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK91(sK137,sK325(the_carrier(sK137))))
| in(sK143(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_422,c_184376]) ).
tcf(c_198683,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK147(sK137,sK325(the_carrier(sK137))))
| subset(sK325(the_carrier(sK137)),sK143(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK143(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_184372]) ).
tcf(c_198684,plain,
( empty(the_carrier(sK137))
| being_limit_ordinal(sK147(sK137,sK325(the_carrier(sK137))))
| closed_subset(sK143(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ ordinal(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK143(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_422,c_184371]) ).
tcf(c_198685,plain,
( being_limit_ordinal(sK93(sK137,sK123(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK143(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ ordinal(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_422,c_192075]) ).
tcf(c_198686,plain,
( being_limit_ordinal(sK93(sK137,sK147(sK137,sK138)))
| subset(sK138,set_difference(the_carrier(sK137),sK143(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ ordinal(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_422,c_192676]) ).
tcf(c_198687,plain,
( being_limit_ordinal(sK93(sK137,sK147(sK137,sK138)))
| closed_subset(set_difference(the_carrier(sK137),sK143(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137)
| ~ ordinal(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_422,c_192446]) ).
tcf(c_198688,plain,
being_limit_ordinal(empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_198622,c_178087]) ).
tcf(c_199134,plain,
! [X0: $i,X1: $i] :
( ordinal(sK156(X0,X1))
| ~ ordinal(X0)
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_552,c_349]) ).
tcf(c_199135,plain,
! [X0: $i,X1: $i] :
( ~ sP18(X0,X1)
| ~ in(X0,sK156(X0,X1)) ),
inference(superposition,[status(thm)],[c_552,c_546]) ).
tcf(c_199136,plain,
! [X0: $i,X1: $i] :
( in(sK154(X0),X0)
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_552,c_542]) ).
tcf(c_199137,plain,
! [X0: $i,X1: $i] :
( ~ empty(X0)
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_552,c_781]) ).
tcf(c_199138,plain,
! [X0: $i,X1: $i] :
( element(sK156(X0,X1),X0)
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_552,c_701]) ).
tcf(c_199139,plain,
! [X0: $i,X1: $i] :
( in(sK156(sK99(X0),X1),X0)
| ~ sP18(sK99(X0),X1) ),
inference(superposition,[status(thm)],[c_552,c_205]) ).
tcf(c_199140,plain,
! [X0: $i,X1: $i] :
( ordinal(sK156(sK99(X0),X1))
| ~ sP18(sK99(X0),X1) ),
inference(superposition,[status(thm)],[c_552,c_206]) ).
tcf(c_199141,plain,
! [X0: $i] : ~ sP18(empty_set,X0),
inference(superposition,[status(thm)],[c_552,c_599]) ).
tcf(c_199142,plain,
! [X0: $i,X1: $i] :
( subset(sK156(powerset(X0),X1),X0)
| ~ sP18(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_552,c_667]) ).
tcf(c_199143,plain,
! [X0: $i,X1: $i] :
( sP27
| ordinal(sK156(sK254(X0),X1))
| ~ sP18(sK254(X0),X1) ),
inference(superposition,[status(thm)],[c_552,c_802]) ).
tcf(c_199144,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(sK156(powerset(the_carrier(sK137)),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP18(powerset(the_carrier(sK137)),X0)
| ~ closed_subset(sK156(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK156(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_552,c_176867]) ).
tcf(c_199145,plain,
! [X0: $i] :
( in(sK156(powerset(the_carrier(sK137)),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP18(powerset(the_carrier(sK137)),X0)
| ~ closed_subset(sK156(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK156(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_552,c_176193]) ).
tcf(c_199146,plain,
! [X0: $i,X1: $i] :
( in(sK156(sK93(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137)))
| ~ sP18(sK93(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_552,c_190624]) ).
tcf(c_199147,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| subset(X0,sK156(sK302(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP18(sK302(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_552,c_190602]) ).
tcf(c_199148,plain,
! [X0: $i,X1: $i] :
( in(sK156(sK91(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP18(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_552,c_190603]) ).
tcf(c_199149,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK156(sK91(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP18(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_552,c_190604]) ).
tcf(c_199150,plain,
! [X0: $i] :
( open_subset(sK156(the_topology(sK137),X0),sK137)
| ~ sP18(the_topology(sK137),X0)
| ~ subset(sK156(the_topology(sK137),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_552,c_190618]) ).
tcf(c_199151,plain,
! [X0: $i] :
( ( sK92(sK137,sK138,sK156(sK91(sK137,sK138),X0)) = sK156(sK91(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_552,c_175190]) ).
tcf(c_199152,plain,
! [X0: $i] :
( in(sK156(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_552,c_175008]) ).
tcf(c_199153,plain,
! [X0: $i] :
( subset(sK138,sK156(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_552,c_174960]) ).
tcf(c_199154,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,sK156(sK302(sK137,sK138),X0)) = sK156(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_552,c_175802]) ).
tcf(c_199155,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,sK156(sK302(sK137,sK138),X0)) = sK156(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_552,c_175753]) ).
tcf(c_199156,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(sK138,sK156(sK302(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP18(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_552,c_175029]) ).
tcf(c_199157,plain,
! [X0: $i] :
( in(sK156(sK93(sK137,the_topology(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP18(sK93(sK137,the_topology(sK137)),X0) ),
inference(superposition,[status(thm)],[c_552,c_175089]) ).
tcf(c_199158,plain,
! [X0: $i,X1: $i] :
( in(sK156(sK93(sK137,sK147(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP18(sK93(sK137,sK147(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_552,c_175090]) ).
tcf(c_199159,plain,
! [X0: $i,X1: $i] :
( in(sK156(sK93(sK137,sK125(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ sP18(sK93(sK137,sK125(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_552,c_175091]) ).
tcf(c_199160,plain,
! [X0: $i,X1: $i] :
( in(sK156(sK93(sK137,sK123(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP18(sK93(sK137,sK123(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_552,c_175092]) ).
tcf(c_199161,plain,
! [X0: $i] :
( subset(sK138,sK156(sK147(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP18(sK147(sK137,sK138),X0)
| ~ subset(sK156(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_552,c_190614]) ).
tcf(c_199162,plain,
! [X0: $i] :
( closed_subset(sK156(sK147(sK137,sK138),X0),sK137)
| ~ topological_space(sK137)
| ~ sP18(sK147(sK137,sK138),X0)
| ~ subset(sK156(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_552,c_190613]) ).
tcf(c_199163,plain,
! [X0: $i] :
( subset(sK138,sK156(sK123(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP18(sK123(sK137,sK138),X0)
| ~ subset(sK156(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_552,c_190612]) ).
tcf(c_199164,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK156(sK147(sK137,topstr_closure(sK137,X0)),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP18(sK147(sK137,topstr_closure(sK137,X0)),X1)
| ~ element(sK156(sK147(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_176007]) ).
tcf(c_199165,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,topstr_closure(sK137,X0),sK156(sK91(sK137,topstr_closure(sK137,X0)),X1)) = sK156(sK91(sK137,topstr_closure(sK137,X0)),X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP18(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_552,c_176010]) ).
tcf(c_199166,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK137,X0),sK156(sK91(sK137,topstr_closure(sK137,X0)),X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP18(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_552,c_176013]) ).
tcf(c_199167,plain,
! [X0: $i,X1: $i] :
( in(sK156(sK91(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP18(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_552,c_176012]) ).
tcf(c_199168,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),sK156(sK295(sK137,the_topology(sK137)),X0)) = sK156(sK295(sK137,the_topology(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK295(sK137,the_topology(sK137)),X0) ),
inference(superposition,[status(thm)],[c_552,c_176134]) ).
tcf(c_199169,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),sK156(sK302(sK137,the_carrier(sK137)),X0)) = sK156(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_552,c_176975]) ).
tcf(c_199170,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),sK156(sK302(sK137,the_carrier(sK137)),X0)) = sK156(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_552,c_176974]) ).
tcf(c_199171,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK156(sK302(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP18(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_552,c_176981]) ).
tcf(c_199172,plain,
! [X0: $i] :
( ( sK124(sK137,the_carrier(sK137),sK156(sK123(sK137,the_carrier(sK137)),X0)) = sK156(sK123(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK123(sK137,the_carrier(sK137)),X0)
| ~ element(sK156(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_176971]) ).
tcf(c_199173,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK156(sK123(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP18(sK123(sK137,the_carrier(sK137)),X0)
| ~ element(sK156(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_176976]) ).
tcf(c_199174,plain,
! [X0: $i] :
( ( sK92(sK137,the_carrier(sK137),sK156(sK91(sK137,the_carrier(sK137)),X0)) = sK156(sK91(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_552,c_176980]) ).
tcf(c_199175,plain,
! [X0: $i] :
( in(sK156(sK91(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_552,c_176982]) ).
tcf(c_199176,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK156(sK91(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_552,c_176983]) ).
tcf(c_199177,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK156(sK147(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP18(sK147(sK137,the_carrier(sK137)),X0)
| ~ element(sK156(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_176978]) ).
tcf(c_199178,plain,
! [X0: $i] :
( closed_subset(sK156(sK147(sK137,the_carrier(sK137)),X0),sK137)
| ~ topological_space(sK137)
| ~ sP18(sK147(sK137,the_carrier(sK137)),X0)
| ~ element(sK156(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_176977]) ).
tcf(c_199179,plain,
! [X0: $i] :
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK156(sK295(sK137,powerset(the_carrier(sK137))),X0)) = sK156(sK295(sK137,powerset(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK295(sK137,powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_552,c_176995]) ).
tcf(c_199180,plain,
! [X0: $i] :
( in(sK156(sK93(sK137,powerset(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP18(sK93(sK137,powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_552,c_176997]) ).
tcf(c_199181,plain,
! [X0: $i] :
( in(sK156(topstr_closure(sK137,sK138),X0),sK138)
| ~ closed_subset(sK138,sK137)
| ~ sP18(topstr_closure(sK137,sK138),X0)
| ~ in(sK156(topstr_closure(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_552,c_177233]) ).
tcf(c_199182,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK156(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_552,c_177405]) ).
tcf(c_199183,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK156(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK156(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_177400]) ).
tcf(c_199184,plain,
! [X0: $i] :
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK156(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)) = sK156(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_552,c_177404]) ).
tcf(c_199185,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK156(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_552,c_177407]) ).
tcf(c_199186,plain,
! [X0: $i] :
( in(sK156(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_552,c_177406]) ).
tcf(c_199187,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK156(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK156(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_177402]) ).
tcf(c_199188,plain,
! [X0: $i] :
( closed_subset(sK156(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP18(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK156(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_177401]) ).
tcf(c_199189,plain,
! [X0: $i] :
( in(sK156(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP18(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0) ),
inference(superposition,[status(thm)],[c_552,c_177421]) ).
tcf(c_199190,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK156(sK302(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK302(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_552,c_182970]) ).
tcf(c_199191,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK156(sK123(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK123(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK156(sK123(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_182965]) ).
tcf(c_199192,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK156(sK91(sK137,sK207(the_carrier(sK137))),X0)) = sK156(sK91(sK137,sK207(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_552,c_182969]) ).
tcf(c_199193,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK156(sK91(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_552,c_182972]) ).
tcf(c_199194,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK156(sK91(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_552,c_182971]) ).
tcf(c_199195,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK156(sK147(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK147(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK156(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_182967]) ).
tcf(c_199196,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(sK156(sK147(sK137,sK207(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP18(sK147(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK156(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_182966]) ).
tcf(c_199197,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK156(sK302(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK302(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_552,c_184375]) ).
tcf(c_199198,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK156(sK123(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK123(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK156(sK123(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_184370]) ).
tcf(c_199199,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK156(sK91(sK137,sK325(the_carrier(sK137))),X0)) = sK156(sK91(sK137,sK325(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_552,c_184374]) ).
tcf(c_199200,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK156(sK91(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_552,c_184377]) ).
tcf(c_199201,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK156(sK91(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_552,c_184376]) ).
tcf(c_199202,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK156(sK147(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP18(sK147(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK156(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_184372]) ).
tcf(c_199203,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(sK156(sK147(sK137,sK325(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP18(sK147(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK156(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_552,c_184371]) ).
tcf(c_199204,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),sK156(sK93(sK137,sK123(sK137,sK138)),X0)))
| ~ topological_space(sK137)
| ~ sP18(sK93(sK137,sK123(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_552,c_192075]) ).
tcf(c_199205,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),sK156(sK93(sK137,sK147(sK137,sK138)),X0)))
| ~ topological_space(sK137)
| ~ sP18(sK93(sK137,sK147(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_552,c_192676]) ).
tcf(c_199206,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),sK156(sK93(sK137,sK147(sK137,sK138)),X0)),sK137)
| ~ topological_space(sK137)
| ~ sP18(sK93(sK137,sK147(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_552,c_192446]) ).
tcf(c_199580,plain,
union(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_198688,c_708]) ).
tcf(c_199614,plain,
! [X0: $i] :
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK138),X0)
| ~ finite(sK156(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_199153,c_292]) ).
tcf(c_199615,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK138),X0)
| ~ proper_subset(sK156(sK91(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_199153,c_492]) ).
tcf(c_199633,plain,
( finite(sK138)
| being_limit_ordinal(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138))
| ~ finite(sK143(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_198634,c_292]) ).
tcf(c_199634,plain,
( being_limit_ordinal(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138))
| ~ proper_subset(sK143(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_198634,c_492]) ).
tcf(c_199650,plain,
! [X0: $i] :
( ordinal(sK156(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ sP18(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_199152,c_349]) ).
tcf(c_199651,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK138),X0)
| ~ in(powerset(the_carrier(sK137)),sK156(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_199152,c_546]) ).
tcf(c_199652,plain,
! [X0: $i] :
( in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_199152,c_542]) ).
tcf(c_199653,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137)))
| ~ sP18(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_199152,c_781]) ).
tcf(c_199654,plain,
! [X0: $i] :
( element(sK156(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_199152,c_701]) ).
tcf(c_199655,plain,
! [X0: $i] :
( subset(sK156(sK91(sK137,sK138),X0),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_199152,c_667]) ).
tcf(c_199656,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(sK156(sK91(sK137,sK138),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK138),X0)
| ~ closed_subset(sK156(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK156(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_199152,c_176867]) ).
tcf(c_199657,plain,
! [X0: $i] :
( in(sK156(sK91(sK137,sK138),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK138),X0)
| ~ closed_subset(sK156(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK156(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_199152,c_176193]) ).
tcf(c_199729,plain,
! [X0: $i] :
( finite(sK138)
| sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP18(sK302(sK137,sK138),X0)
| ~ finite(sK156(sK302(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_199156,c_292]) ).
tcf(c_199730,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP18(sK302(sK137,sK138),X0)
| ~ proper_subset(sK156(sK302(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_199156,c_492]) ).
tcf(c_199757,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_105912,c_180292]) ).
tcf(c_199758,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != powerset(empty_set) ) ),
inference(superposition,[status(thm)],[c_105926,c_180292]) ).
tcf(c_199787,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(X2)
| ~ in(X2,X0)
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_639,c_349]) ).
tcf(c_199788,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_639,c_546]) ).
tcf(c_199789,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK154(set_union2(X1,X2)),set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_639,c_542]) ).
tcf(c_199790,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_639,c_781]) ).
tcf(c_199791,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_639,c_701]) ).
tcf(c_199792,plain,
! [X0: $i,X1: $i] : ~ in(sK126(set_union2(X0,X1)),X0),
inference(superposition,[status(thm)],[c_639,c_188650]) ).
tcf(c_199793,plain,
! [X0: $i,X1: $i] : ~ in(sK323(set_union2(X0,X1)),X0),
inference(superposition,[status(thm)],[c_639,c_188660]) ).
tcf(c_199819,plain,
element(empty_set,unordered_pair(empty_set,empty_set)),
inference(superposition,[status(thm)],[c_181193,c_183191]) ).
tcf(c_199820,plain,
~ empty(unordered_pair(empty_set,empty_set)),
inference(superposition,[status(thm)],[c_181193,c_886]) ).
tcf(c_199821,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = set_difference(empty_set,set_difference(X0,empty_set)),
inference(superposition,[status(thm)],[c_181193,c_179569]) ).
tcf(c_199825,plain,
! [X0: $i] : set_difference(X0,X0) = set_difference(empty_set,X0),
inference(superposition,[status(thm)],[c_181193,c_420]) ).
tcf(c_199827,plain,
! [X0: $i] : set_union2(empty_set,X0) = set_difference(X0,empty_set),
inference(superposition,[status(thm)],[c_181193,c_410]) ).
tcf(c_199832,plain,
! [X0: $i] : set_union2(X0,empty_set) = set_union2(empty_set,X0),
inference(superposition,[status(thm)],[c_181193,c_179574]) ).
tcf(c_199859,plain,
( empty(sK91(sK137,sK138))
| ordinal(sK135(sK91(sK137,sK138)))
| relation(sK136(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_197144,c_349]) ).
tcf(c_199860,plain,
( empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK135(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_197144,c_546]) ).
tcf(c_199861,plain,
( empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_197144,c_542]) ).
tcf(c_199862,plain,
( empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_197144,c_781]) ).
tcf(c_199863,plain,
( empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| element(sK135(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_197144,c_701]) ).
tcf(c_199864,plain,
( empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| subset(sK135(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_197144,c_667]) ).
tcf(c_199865,plain,
( sP36(sK137,sK138)
| empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| in(sK135(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK135(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_197144,c_176867]) ).
tcf(c_199866,plain,
( empty(sK91(sK137,sK138))
| relation(sK136(sK91(sK137,sK138)))
| in(sK135(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK135(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_197144,c_176193]) ).
tcf(c_199909,plain,
( empty(sK91(sK137,sK138))
| ordinal(sK135(sK91(sK137,sK138)))
| function(sK136(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_197855,c_349]) ).
tcf(c_199910,plain,
( empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ in(powerset(the_carrier(sK137)),sK135(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_197855,c_546]) ).
tcf(c_199911,plain,
( empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_197855,c_542]) ).
tcf(c_199912,plain,
( empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_197855,c_781]) ).
tcf(c_199913,plain,
( empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| element(sK135(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_197855,c_701]) ).
tcf(c_199914,plain,
( empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| subset(sK135(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_197855,c_667]) ).
tcf(c_199915,plain,
( sP36(sK137,sK138)
| empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| in(sK135(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK135(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_197855,c_176867]) ).
tcf(c_199916,plain,
( empty(sK91(sK137,sK138))
| function(sK136(sK91(sK137,sK138)))
| in(sK135(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK135(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK135(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_197855,c_176193]) ).
tcf(c_199972,plain,
( being_limit_ordinal(sK91(sK137,sK138))
| ordinal(sK143(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138))
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_198633,c_349]) ).
tcf(c_199973,plain,
( being_limit_ordinal(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138))
| ~ in(powerset(the_carrier(sK137)),sK143(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_198633,c_546]) ).
tcf(c_199974,plain,
( being_limit_ordinal(sK91(sK137,sK138))
| in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_198633,c_542]) ).
tcf(c_199975,plain,
( being_limit_ordinal(sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138))
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_198633,c_781]) ).
tcf(c_199976,plain,
( being_limit_ordinal(sK91(sK137,sK138))
| element(sK143(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_198633,c_701]) ).
tcf(c_199977,plain,
( being_limit_ordinal(sK91(sK137,sK138))
| subset(sK143(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_198633,c_667]) ).
tcf(c_199978,plain,
( sP36(sK137,sK138)
| being_limit_ordinal(sK91(sK137,sK138))
| in(sK143(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138))
| ~ closed_subset(sK143(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK143(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_198633,c_176867]) ).
tcf(c_199979,plain,
( being_limit_ordinal(sK91(sK137,sK138))
| in(sK143(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138))
| ~ closed_subset(sK143(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK143(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_198633,c_176193]) ).
tcf(c_200022,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,X0,sK53(sK91(sK137,X0),X1)) = sK53(sK91(sK137,X0),X1) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP2(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_96,c_190601]) ).
tcf(c_200023,plain,
! [X0: $i] :
( sP3(sK91(sK137,X0))
| ( sK92(sK137,X0,sK62(sK91(sK137,X0))) = sK62(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_120,c_190601]) ).
tcf(c_200026,plain,
! [X0: $i] :
( empty(sK91(sK137,X0))
| function(sK136(sK91(sK137,X0)))
| ( sK92(sK137,X0,sK135(sK91(sK137,X0))) = sK135(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_368,c_190601]) ).
tcf(c_200027,plain,
! [X0: $i] :
( empty(sK91(sK137,X0))
| relation(sK136(sK91(sK137,X0)))
| ( sK92(sK137,X0,sK135(sK91(sK137,X0))) = sK135(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_367,c_190601]) ).
tcf(c_200028,plain,
! [X0: $i] :
( ordinal(sK91(sK137,X0))
| ( sK92(sK137,X0,sK139(sK91(sK137,X0))) = sK139(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_383,c_190601]) ).
tcf(c_200029,plain,
! [X0: $i,X1: $i] :
( disjoint(sK91(sK137,X0),X1)
| ( sK92(sK137,X0,sK142(sK91(sK137,X0),X1)) = sK142(sK91(sK137,X0),X1) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_416,c_190601]) ).
tcf(c_200030,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,sK91(sK137,X0))
| ( sK92(sK137,X0,sK142(X1,sK91(sK137,X0))) = sK142(X1,sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_417,c_190601]) ).
tcf(c_200031,plain,
! [X0: $i] :
( being_limit_ordinal(sK91(sK137,X0))
| ( sK92(sK137,X0,sK143(sK91(sK137,X0))) = sK143(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_422,c_190601]) ).
tcf(c_200032,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,X0,sK156(sK91(sK137,X0),X1)) = sK156(sK91(sK137,X0),X1) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP18(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_552,c_190601]) ).
tcf(c_200033,plain,
! [X0: $i] :
( relation(sK91(sK137,X0))
| ( sK92(sK137,X0,sK175(sK91(sK137,X0))) = sK175(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_580,c_190601]) ).
tcf(c_200034,plain,
! [X0: $i] :
( ( sK91(sK137,X0) = empty_set )
| ( sK92(sK137,X0,sK181(sK91(sK137,X0))) = sK181(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_598,c_190601]) ).
tcf(c_200035,plain,
! [X0: $i] :
( ( sK92(sK137,X0,sK185(sK91(sK137,X0))) = sK185(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_603,c_190601]) ).
tcf(c_200037,plain,
! [X0: $i,X1: $i] :
( subset(sK91(sK137,X0),X1)
| ( sK92(sK137,X0,sK202(sK91(sK137,X0),X1)) = sK202(sK91(sK137,X0),X1) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_662,c_190601]) ).
tcf(c_200038,plain,
! [X0: $i] :
( ( sK92(sK137,X0,sK274(sK91(sK137,X0))) = sK274(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_858,c_190601]) ).
tcf(c_200039,plain,
! [X0: $i] :
( epsilon_transitive(sK91(sK137,X0))
| ( sK92(sK137,X0,sK340(sK91(sK137,X0))) = sK340(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1081,c_190601]) ).
tcf(c_200040,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,X0))
| ( sK92(sK137,X0,sK369(sK91(sK137,X0))) = sK369(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1253,c_190601]) ).
tcf(c_200041,plain,
! [X0: $i] :
( epsilon_connected(sK91(sK137,X0))
| ( sK92(sK137,X0,sK370(sK91(sK137,X0))) = sK370(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1254,c_190601]) ).
tcf(c_200042,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,X0)),sK137)
| ( sK92(sK137,X0,sK145(sK137,sK91(sK137,X0))) = sK145(sK137,sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ subset(sK91(sK137,X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_190601]) ).
tcf(c_200043,plain,
! [X0: $i] :
( ( sK92(sK137,the_carrier(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(the_carrier(sK137),X0)
| ~ subset(the_carrier(sK137),the_carrier(sK137))
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176973,c_190601]) ).
tcf(c_200189,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X0) = set_difference(set_difference(X1,X0),X0),
inference(superposition,[status(thm)],[c_410,c_181191]) ).
tcf(c_200192,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X0) = set_difference(set_union2(X1,X0),X0),
inference(superposition,[status(thm)],[c_179574,c_181191]) ).
tcf(c_200193,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(X1,X0))
| ~ finite(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_181191,c_1011]) ).
tcf(c_200196,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,set_union2(X0,X1)),set_difference(X1,X0)) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_181191,c_179569]) ).
tcf(c_200197,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),set_difference(X1,X0)) = set_difference(X0,set_difference(X0,set_union2(X0,X1))),
inference(superposition,[status(thm)],[c_181191,c_986]) ).
tcf(c_200198,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_union2(X0,X1)) = set_union2(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c_181191,c_410]) ).
tcf(c_200204,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),X1) = set_difference(X0,X1),
inference(light_normalisation,[status(thm)],[c_200189,c_181191]) ).
tcf(c_200205,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,set_union2(X0,X1))) = set_difference(X0,set_difference(X1,X0)),
inference(light_normalisation,[status(thm)],[c_200197,c_179569]) ).
tcf(c_200214,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_410,c_640]) ).
tcf(c_200219,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_179574,c_640]) ).
tcf(c_200220,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(X2)
| ~ in(X2,X1)
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_640,c_349]) ).
tcf(c_200221,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_640,c_546]) ).
tcf(c_200222,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK154(set_union2(X2,X1)),set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_640,c_542]) ).
tcf(c_200223,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_640,c_781]) ).
tcf(c_200224,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_640,c_701]) ).
tcf(c_200225,plain,
! [X0: $i,X1: $i] : ~ in(sK126(set_union2(X0,X1)),X1),
inference(superposition,[status(thm)],[c_640,c_188650]) ).
tcf(c_200226,plain,
! [X0: $i,X1: $i] : ~ in(sK323(set_union2(X0,X1)),X1),
inference(superposition,[status(thm)],[c_640,c_188660]) ).
tcf(c_200250,plain,
! [X0: $i] :
( empty(sK122(X0))
| ~ empty(X0)
| ~ relation(sK122(X0)) ),
inference(superposition,[status(thm)],[c_258,c_648]) ).
tcf(c_200251,plain,
! [X0: $i] :
( empty(identity_relation(X0))
| ~ empty(X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_509,c_648]) ).
tcf(c_200253,plain,
! [X0: $i] :
( empty(identity_relation(X0))
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_200251,c_1156]) ).
tcf(c_200256,plain,
! [X0: $i] :
( empty(sK122(X0))
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_200250,c_256]) ).
tcf(c_200265,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_union2(X1,X2))
| ~ in(sK202(X0,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_639,c_661]) ).
tcf(c_200266,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_union2(X1,X2))
| ~ in(sK202(X0,set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_640,c_661]) ).
tcf(c_200268,plain,
! [X0: $i,X1: $i] :
( subset(X0,powerset(X1))
| ~ subset(sK202(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_666,c_661]) ).
tcf(c_200269,plain,
! [X0: $i] :
( subset(X0,sK91(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(sK202(X0,sK91(sK137,the_carrier(sK137))),sK137)
| ~ subset(the_carrier(sK137),sK202(X0,sK91(sK137,the_carrier(sK137))))
| ~ in(sK202(X0,sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176973,c_661]) ).
tcf(c_200270,plain,
( subset(sK91(sK137,sK138),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_191199,c_661]) ).
tcf(c_200318,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK53(set_difference(X0,X1),X2),X0)
| ~ sP2(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_96,c_692]) ).
tcf(c_200319,plain,
! [X0: $i,X1: $i] :
( sP3(set_difference(X0,X1))
| in(sK62(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_120,c_692]) ).
tcf(c_200322,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X0,X1))
| function(sK136(set_difference(X0,X1)))
| in(sK135(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_368,c_692]) ).
tcf(c_200323,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X0,X1))
| relation(sK136(set_difference(X0,X1)))
| in(sK135(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_367,c_692]) ).
tcf(c_200324,plain,
! [X0: $i,X1: $i] :
( ordinal(set_difference(X0,X1))
| in(sK139(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_383,c_692]) ).
tcf(c_200325,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,X1),X2)
| in(sK142(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_416,c_692]) ).
tcf(c_200326,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X1,X2))
| in(sK142(X0,set_difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_417,c_692]) ).
tcf(c_200327,plain,
! [X0: $i,X1: $i] :
( being_limit_ordinal(set_difference(X0,X1))
| in(sK143(set_difference(X0,X1)),X0)
| ~ ordinal(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_422,c_692]) ).
tcf(c_200328,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK156(set_difference(X0,X1),X2),X0)
| ~ sP18(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_552,c_692]) ).
tcf(c_200329,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,X1))
| in(sK175(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_580,c_692]) ).
tcf(c_200330,plain,
! [X0: $i,X1: $i] :
( in(sK181(set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_598,c_692]) ).
tcf(c_200331,plain,
! [X0: $i,X1: $i] :
( in(sK185(set_difference(X0,X1)),X0)
| ~ sP20(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_603,c_692]) ).
tcf(c_200333,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| in(sK202(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_662,c_692]) ).
tcf(c_200334,plain,
! [X0: $i,X1: $i] :
( in(sK274(set_difference(X0,X1)),X0)
| ~ sP32(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_858,c_692]) ).
tcf(c_200335,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_difference(X0,X1))
| in(sK340(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_1081,c_692]) ).
tcf(c_200336,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_difference(X0,X1))
| in(sK369(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_1253,c_692]) ).
tcf(c_200337,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_difference(X0,X1))
| in(sK370(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_1254,c_692]) ).
tcf(c_200338,plain,
! [X0: $i,X1: $i] :
( in(sK145(sK137,set_difference(X0,X1)),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),set_difference(X0,X1)),sK137)
| ~ topological_space(sK137)
| ~ subset(set_difference(X0,X1),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_692]) ).
tcf(c_200340,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_420,c_692]) ).
tcf(c_200345,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,set_difference(X1,set_difference(X2,X1))) ),
inference(superposition,[status(thm)],[c_179569,c_692]) ).
tcf(c_200441,plain,
! [X0: $i] :
( ordinal(sK138)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ ordinal(sK123(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190609,c_349]) ).
tcf(c_200442,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ subset(X0,the_carrier(sK137))
| ~ in(sK123(sK137,X0),sK138) ),
inference(superposition,[status(thm)],[c_190609,c_546]) ).
tcf(c_200443,plain,
! [X0: $i] :
( in(sK154(sK123(sK137,X0)),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190609,c_542]) ).
tcf(c_200444,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ empty(sK123(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190609,c_781]) ).
tcf(c_200445,plain,
! [X0: $i] :
( element(sK138,sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190609,c_701]) ).
tcf(c_200448,plain,
( ( sK124(sK137,empty_set,sK138) = sK138 )
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(empty_set,sK138)
| ~ subset(empty_set,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190609,c_182870]) ).
tcf(c_200469,plain,
( ( sK124(sK137,empty_set,sK138) = sK138 )
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_200448,c_379,c_379]) ).
tcf(c_200503,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,sK53(sK123(sK137,sK138),X0)) = sK53(sK123(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP2(sK123(sK137,sK138),X0)
| ~ subset(sK53(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_96,c_190610]) ).
tcf(c_200504,plain,
( sP3(sK123(sK137,sK138))
| ( sK124(sK137,sK138,sK62(sK123(sK137,sK138))) = sK62(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK62(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_120,c_190610]) ).
tcf(c_200507,plain,
( empty(sK123(sK137,sK138))
| function(sK136(sK123(sK137,sK138)))
| ( sK124(sK137,sK138,sK135(sK123(sK137,sK138))) = sK135(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK135(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_368,c_190610]) ).
tcf(c_200508,plain,
( empty(sK123(sK137,sK138))
| relation(sK136(sK123(sK137,sK138)))
| ( sK124(sK137,sK138,sK135(sK123(sK137,sK138))) = sK135(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK135(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_367,c_190610]) ).
tcf(c_200509,plain,
( ordinal(sK123(sK137,sK138))
| ( sK124(sK137,sK138,sK139(sK123(sK137,sK138))) = sK139(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK139(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_383,c_190610]) ).
tcf(c_200510,plain,
! [X0: $i] :
( disjoint(sK123(sK137,sK138),X0)
| ( sK124(sK137,sK138,sK142(sK123(sK137,sK138),X0)) = sK142(sK123(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ subset(sK142(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_416,c_190610]) ).
tcf(c_200511,plain,
! [X0: $i] :
( disjoint(X0,sK123(sK137,sK138))
| ( sK124(sK137,sK138,sK142(X0,sK123(sK137,sK138))) = sK142(X0,sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK142(X0,sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_417,c_190610]) ).
tcf(c_200512,plain,
( being_limit_ordinal(sK123(sK137,sK138))
| ( sK124(sK137,sK138,sK143(sK123(sK137,sK138))) = sK143(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ ordinal(sK123(sK137,sK138))
| ~ subset(sK143(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_422,c_190610]) ).
tcf(c_200513,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,sK156(sK123(sK137,sK138),X0)) = sK156(sK123(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP18(sK123(sK137,sK138),X0)
| ~ subset(sK156(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_552,c_190610]) ).
tcf(c_200514,plain,
( relation(sK123(sK137,sK138))
| ( sK124(sK137,sK138,sK175(sK123(sK137,sK138))) = sK175(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK175(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_580,c_190610]) ).
tcf(c_200515,plain,
( ( sK123(sK137,sK138) = empty_set )
| ( sK124(sK137,sK138,sK181(sK123(sK137,sK138))) = sK181(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK181(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_598,c_190610]) ).
tcf(c_200516,plain,
( ( sK124(sK137,sK138,sK185(sK123(sK137,sK138))) = sK185(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,sK138))
| ~ subset(sK185(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_603,c_190610]) ).
tcf(c_200518,plain,
! [X0: $i] :
( subset(sK123(sK137,sK138),X0)
| ( sK124(sK137,sK138,sK202(sK123(sK137,sK138),X0)) = sK202(sK123(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ subset(sK202(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_662,c_190610]) ).
tcf(c_200519,plain,
( ( sK124(sK137,sK138,sK274(sK123(sK137,sK138))) = sK274(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,sK138))
| ~ subset(sK274(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_858,c_190610]) ).
tcf(c_200520,plain,
( epsilon_transitive(sK123(sK137,sK138))
| ( sK124(sK137,sK138,sK340(sK123(sK137,sK138))) = sK340(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK340(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1081,c_190610]) ).
tcf(c_200521,plain,
( epsilon_connected(sK123(sK137,sK138))
| ( sK124(sK137,sK138,sK369(sK123(sK137,sK138))) = sK369(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK369(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1253,c_190610]) ).
tcf(c_200522,plain,
( epsilon_connected(sK123(sK137,sK138))
| ( sK124(sK137,sK138,sK370(sK123(sK137,sK138))) = sK370(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK370(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1254,c_190610]) ).
tcf(c_200523,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK138)),sK137)
| ( sK124(sK137,sK138,sK145(sK137,sK123(sK137,sK138))) = sK145(sK137,sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK123(sK137,sK138),powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190625,c_190610]) ).
tcf(c_200524,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK138)),sK137)
| ( sK124(sK137,sK138,sK145(sK137,sK123(sK137,sK138))) = sK145(sK137,sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ element(sK138,powerset(the_carrier(sK137)))
| ~ subset(sK145(sK137,sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_175061,c_190610]) ).
tcf(c_200525,plain,
( ( sK124(sK137,sK138,empty_set) = empty_set )
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ subset(empty_set,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_182784,c_190610]) ).
tcf(c_200528,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),X0)) = set_difference(the_carrier(sK137),X0) )
| ~ topological_space(sK137)
| ~ element(sK138,powerset(the_carrier(sK137)))
| ~ subset(set_difference(the_carrier(sK137),X0),the_carrier(sK137))
| ~ in(X0,sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_179185,c_190610]) ).
tcf(c_200529,plain,
( ( sK124(sK137,sK138,sK154(sK123(sK137,sK138))) = sK154(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ subset(sK154(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_188351,c_190610]) ).
tcf(c_200530,plain,
( ( sK124(sK137,sK138,empty_set) = empty_set )
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[c_200525,c_379]) ).
tcf(c_200623,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),X0)) = set_difference(the_carrier(sK137),X0) )
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK123(sK137,sK138))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_200528,c_376,c_399]) ).
tcf(c_200627,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK123(sK137,sK138)),sK137)
| ( sK124(sK137,sK138,sK145(sK137,sK123(sK137,sK138))) = sK145(sK137,sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ subset(sK145(sK137,sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_200524,c_376]) ).
tcf(c_200689,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK53(sK93(sK137,sK123(sK137,sK138)),X0))) = set_difference(the_carrier(sK137),sK53(sK93(sK137,sK123(sK137,sK138)),X0)) )
| ~ topological_space(sK137)
| ~ sP2(sK93(sK137,sK123(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_96,c_200623]) ).
tcf(c_200690,plain,
( sP3(sK93(sK137,sK123(sK137,sK138)))
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK62(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK62(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_200623]) ).
tcf(c_200693,plain,
( empty(sK93(sK137,sK123(sK137,sK138)))
| function(sK136(sK93(sK137,sK123(sK137,sK138))))
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK135(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK135(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_200623]) ).
tcf(c_200694,plain,
( empty(sK93(sK137,sK123(sK137,sK138)))
| relation(sK136(sK93(sK137,sK123(sK137,sK138))))
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK135(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK135(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_200623]) ).
tcf(c_200695,plain,
( ordinal(sK93(sK137,sK123(sK137,sK138)))
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK139(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK139(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_200623]) ).
tcf(c_200696,plain,
! [X0: $i] :
( disjoint(sK93(sK137,sK123(sK137,sK138)),X0)
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK142(sK93(sK137,sK123(sK137,sK138)),X0))) = set_difference(the_carrier(sK137),sK142(sK93(sK137,sK123(sK137,sK138)),X0)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_200623]) ).
tcf(c_200697,plain,
! [X0: $i] :
( disjoint(X0,sK93(sK137,sK123(sK137,sK138)))
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK142(X0,sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK142(X0,sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_200623]) ).
tcf(c_200698,plain,
( being_limit_ordinal(sK93(sK137,sK123(sK137,sK138)))
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK143(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK143(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137)
| ~ ordinal(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_422,c_200623]) ).
tcf(c_200699,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK156(sK93(sK137,sK123(sK137,sK138)),X0))) = set_difference(the_carrier(sK137),sK156(sK93(sK137,sK123(sK137,sK138)),X0)) )
| ~ topological_space(sK137)
| ~ sP18(sK93(sK137,sK123(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_552,c_200623]) ).
tcf(c_200700,plain,
( relation(sK93(sK137,sK123(sK137,sK138)))
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK175(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK175(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_200623]) ).
tcf(c_200701,plain,
( ( sK93(sK137,sK123(sK137,sK138)) = empty_set )
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK181(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK181(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_200623]) ).
tcf(c_200702,plain,
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK185(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK185(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_603,c_200623]) ).
tcf(c_200704,plain,
! [X0: $i] :
( subset(sK93(sK137,sK123(sK137,sK138)),X0)
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK202(sK93(sK137,sK123(sK137,sK138)),X0))) = set_difference(the_carrier(sK137),sK202(sK93(sK137,sK123(sK137,sK138)),X0)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_200623]) ).
tcf(c_200705,plain,
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK274(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK274(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_858,c_200623]) ).
tcf(c_200706,plain,
( epsilon_transitive(sK93(sK137,sK123(sK137,sK138)))
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK340(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK340(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_200623]) ).
tcf(c_200707,plain,
( epsilon_connected(sK93(sK137,sK123(sK137,sK138)))
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK369(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK369(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_200623]) ).
tcf(c_200708,plain,
( epsilon_connected(sK93(sK137,sK123(sK137,sK138)))
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK370(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK370(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_200623]) ).
tcf(c_200709,plain,
( closed_subset(meet_of_subsets(the_carrier(sK137),sK93(sK137,sK123(sK137,sK138))),sK137)
| ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK145(sK137,sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK145(sK137,sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137)
| ~ subset(sK93(sK137,sK123(sK137,sK138)),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_200623]) ).
tcf(c_200842,plain,
! [X0: $i] :
( ordinal(sK138)
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ ordinal(sK147(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190611,c_349]) ).
tcf(c_200843,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ subset(X0,the_carrier(sK137))
| ~ in(sK147(sK137,X0),sK138) ),
inference(superposition,[status(thm)],[c_190611,c_546]) ).
tcf(c_200844,plain,
! [X0: $i] :
( in(sK154(sK147(sK137,X0)),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190611,c_542]) ).
tcf(c_200845,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ empty(sK147(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190611,c_781]) ).
tcf(c_200846,plain,
! [X0: $i] :
( element(sK138,sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_190611,c_701]) ).
tcf(c_200908,plain,
! [X0: $i] :
( ordinal(X0)
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ ordinal(sK91(sK137,sK138))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_349]) ).
tcf(c_200909,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ subset(X0,the_carrier(sK137))
| ~ in(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_191567,c_546]) ).
tcf(c_200910,plain,
! [X0: $i] :
( in(sK154(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_542]) ).
tcf(c_200911,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ empty(sK91(sK137,sK138))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_781]) ).
tcf(c_200912,plain,
! [X0: $i] :
( element(X0,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_701]) ).
tcf(c_200913,plain,
! [X0: $i] :
( subset(X0,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK202(X0,sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK202(X0,sK91(sK137,sK138)))
| ~ subset(sK202(X0,sK91(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_661]) ).
tcf(c_200914,plain,
! [X0: $i] :
( ( sK92(sK137,sK138,X0) = X0 )
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ subset(sK138,the_carrier(sK137))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_190601]) ).
tcf(c_200915,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ subset(sK138,the_carrier(sK137))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_190603]) ).
tcf(c_200917,plain,
! [X0: $i] :
( ( sK92(sK137,sK138,X0) = X0 )
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_175190]) ).
tcf(c_200918,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK138,X0)
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_175008]) ).
tcf(c_200920,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK126(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK126(sK91(sK137,sK138)))
| ~ subset(sK126(sK91(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_188650]) ).
tcf(c_200921,plain,
( ~ topological_space(sK137)
| ~ closed_subset(sK323(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK323(sK91(sK137,sK138)))
| ~ subset(sK323(sK91(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_188660]) ).
tcf(c_200995,plain,
! [X0: $i,X1: $i] : pair_second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X1,X0))) = X1,
inference(superposition,[status(thm)],[c_967,c_181304]) ).
tcf(c_201000,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( pair_second(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))))) = unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181304]) ).
tcf(c_201001,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( pair_second(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))))) = unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181304]) ).
tcf(c_201002,plain,
! [X0: $i] : pair_second(unordered_pair(unordered_pair(X0,empty_set),powerset(empty_set))) = X0,
inference(superposition,[status(thm)],[c_330,c_181304]) ).
tcf(c_201058,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[status(thm)],[c_658,c_764]) ).
tcf(c_201059,plain,
! [X0: $i,X1: $i] :
( empty(cartesian_product2(X0,X1))
| relation(sK207(cartesian_product2(X0,X1))) ),
inference(superposition,[status(thm)],[c_698,c_764]) ).
tcf(c_201060,plain,
! [X0: $i,X1: $i] : relation(sK208(powerset(cartesian_product2(X0,X1)))),
inference(superposition,[status(thm)],[c_702,c_764]) ).
tcf(c_201061,plain,
! [X0: $i,X1: $i] :
( empty(cartesian_product2(X0,X1))
| relation(sK325(cartesian_product2(X0,X1))) ),
inference(superposition,[status(thm)],[c_1004,c_764]) ).
tcf(c_201062,plain,
! [X0: $i,X1: $i] : relation(cartesian_product2(X0,X1)),
inference(superposition,[status(thm)],[c_13308,c_764]) ).
tcf(c_201081,plain,
( empty(powerset(powerset(empty_set)))
| in(sK68,powerset(powerset(empty_set)))
| ~ sP7 ),
inference(superposition,[status(thm)],[c_134,c_790]) ).
tcf(c_201082,plain,
( empty(powerset(the_carrier(sK137)))
| in(sK138,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_376,c_790]) ).
tcf(c_201083,plain,
! [X0: $i] :
( empty(X0)
| empty(powerset(X0))
| in(sK207(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_698,c_790]) ).
tcf(c_201084,plain,
! [X0: $i] :
( empty(X0)
| in(sK208(X0),X0) ),
inference(superposition,[status(thm)],[c_702,c_790]) ).
tcf(c_201085,plain,
! [X0: $i] :
( empty(X0)
| empty(powerset(X0))
| in(sK325(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_1004,c_790]) ).
tcf(c_201089,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(X0,powerset(X0)) ),
inference(superposition,[status(thm)],[c_13308,c_790]) ).
tcf(c_201092,plain,
( empty(powerset(the_carrier(sK320)))
| in(sK319(sK320),powerset(the_carrier(sK320))) ),
inference(superposition,[status(thm)],[c_22154,c_790]) ).
tcf(c_201093,plain,
( topological_space(sK137)
| empty(powerset(powerset(the_carrier(sK137))))
| in(sK378(sK137),powerset(powerset(the_carrier(sK137))))
| ~ sP42(sK137)
| ~ in(the_carrier(sK137),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_47411,c_790]) ).
tcf(c_201094,plain,
( empty(powerset(powerset(the_carrier(sK137))))
| in(the_topology(sK137),powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_47453,c_790]) ).
tcf(c_201095,plain,
( empty(powerset(powerset(the_carrier(sK291))))
| in(the_topology(sK291),powerset(powerset(the_carrier(sK291)))) ),
inference(superposition,[status(thm)],[c_47629,c_790]) ).
tcf(c_201096,plain,
! [X0: $i] :
( empty(powerset(the_carrier(sK137)))
| in(topstr_closure(sK137,X0),powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_790]) ).
tcf(c_201097,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| empty(powerset(the_carrier(sK137)))
| in(sK304(sK137,X1,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_790]) ).
tcf(c_201098,plain,
! [X0: $i] :
( empty(powerset(powerset(the_carrier(sK137))))
| in(sK147(sK137,X0),powerset(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48126,c_790]) ).
tcf(c_201099,plain,
! [X0: $i,X1: $i] :
( empty(powerset(the_carrier(sK137)))
| in(X1,topstr_closure(sK137,X0))
| in(sK146(sK137,X0,X1),powerset(the_carrier(sK137)))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_790]) ).
tcf(c_201100,plain,
! [X0: $i] :
( empty(powerset(the_carrier(sK137)))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| in(sK145(sK137,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_790]) ).
tcf(c_201101,plain,
! [X0: $i] :
( empty(powerset(powerset(the_carrier(sK137))))
| in(sK125(sK137,X0),powerset(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48285,c_790]) ).
tcf(c_201102,plain,
! [X0: $i,X1: $i] :
( empty(powerset(the_carrier(sK137)))
| in(sK124(sK137,X1,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_790]) ).
tcf(c_201103,plain,
! [X0: $i] :
( empty(powerset(powerset(the_carrier(sK137))))
| in(sK123(sK137,X0),powerset(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48389,c_790]) ).
tcf(c_201104,plain,
! [X0: $i,X1: $i] :
( empty(powerset(the_carrier(sK137)))
| in(sK92(sK137,X1,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_790]) ).
tcf(c_201105,plain,
! [X0: $i] :
( empty(powerset(the_carrier(sK291)))
| in(topstr_closure(sK291,X0),powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(superposition,[status(thm)],[c_106105,c_790]) ).
tcf(c_201106,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(empty_set,powerset(X0)) ),
inference(superposition,[status(thm)],[c_182003,c_790]) ).
tcf(c_201109,plain,
! [X0: $i] :
( empty(set_union2(X0,unordered_pair(X0,X0)))
| in(X0,set_union2(X0,unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_183191,c_790]) ).
tcf(c_201125,plain,
! [X0: $i] : in(empty_set,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_201106,c_700]) ).
tcf(c_201126,plain,
! [X0: $i] : in(X0,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_201089,c_700]) ).
tcf(c_201127,plain,
in(sK138,powerset(the_carrier(sK137))),
inference(forward_subsumption_resolution,[status(thm)],[c_201082,c_700]) ).
tcf(c_201128,plain,
in(sK319(sK320),powerset(the_carrier(sK320))),
inference(forward_subsumption_resolution,[status(thm)],[c_201092,c_700]) ).
tcf(c_201129,plain,
! [X0: $i] :
( empty(X0)
| in(sK325(X0),powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201085,c_700]) ).
tcf(c_201132,plain,
! [X0: $i] :
( empty(X0)
| in(sK207(X0),powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201083,c_700]) ).
tcf(c_201135,plain,
( in(sK68,powerset(powerset(empty_set)))
| ~ sP7 ),
inference(forward_subsumption_resolution,[status(thm)],[c_201081,c_700]) ).
tcf(c_201138,plain,
in(the_topology(sK291),powerset(powerset(the_carrier(sK291)))),
inference(forward_subsumption_resolution,[status(thm)],[c_201095,c_700]) ).
tcf(c_201139,plain,
in(the_topology(sK137),powerset(powerset(the_carrier(sK137)))),
inference(forward_subsumption_resolution,[status(thm)],[c_201094,c_700]) ).
tcf(c_201153,plain,
! [X0: $i] :
( in(topstr_closure(sK291,X0),powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201105,c_700]) ).
tcf(c_201156,plain,
! [X0: $i] :
( in(topstr_closure(sK137,X0),powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201096,c_700]) ).
tcf(c_201159,plain,
! [X0: $i] :
( in(sK123(sK137,X0),powerset(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201103,c_700]) ).
tcf(c_201163,plain,
! [X0: $i] :
( in(sK147(sK137,X0),powerset(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201098,c_700]) ).
tcf(c_201167,plain,
! [X0: $i] :
( in(sK125(sK137,X0),powerset(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201101,c_700]) ).
tcf(c_201171,plain,
( topological_space(sK137)
| in(sK378(sK137),powerset(powerset(the_carrier(sK137))))
| ~ sP42(sK137)
| ~ in(the_carrier(sK137),the_topology(sK137)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201093,c_700]) ).
tcf(c_201176,plain,
! [X0: $i,X1: $i] :
( in(sK92(sK137,X1,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201104,c_700]) ).
tcf(c_201181,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| in(sK145(sK137,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201100,c_700]) ).
tcf(c_201186,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| in(sK146(sK137,X0,X1),powerset(the_carrier(sK137)))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201099,c_700]) ).
tcf(c_201191,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| in(sK304(sK137,X1,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201097,c_700]) ).
tcf(c_201197,plain,
! [X0: $i,X1: $i] :
( in(sK124(sK137,X1,X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201102,c_700]) ).
tcf(c_201223,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X2)
| ~ empty(X2)
| ~ empty(powerset(cartesian_product2(X0,X1))) ),
inference(superposition,[status(thm)],[c_791,c_764]) ).
tcf(c_201227,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ empty(X1)
| ~ closed_subset(X1,sK137)
| ~ subset(sK138,X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_791,c_177131]) ).
tcf(c_201228,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ empty(X1)
| ~ closed_subset(X2,sK137)
| ~ subset(X1,X2)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,the_carrier(sK137))
| ~ element(X2,powerset(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_48138]) ).
tcf(c_201229,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| in(X0,sK302(sK137,X1))
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ closed_subset(X0,sK137)
| ~ subset(X1,X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_47771]) ).
tcf(c_201230,plain,
! [X0: $i,X1: $i] :
( in(X1,sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ closed_subset(X1,sK137)
| ~ subset(X0,X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_48368]) ).
tcf(c_201231,plain,
! [X0: $i,X1: $i] :
( ( sK124(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_48332]) ).
tcf(c_201232,plain,
! [X0: $i,X1: $i] :
( in(X1,sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ closed_subset(X1,sK137)
| ~ subset(X0,X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_48105]) ).
tcf(c_201233,plain,
! [X0: $i,X1: $i] :
( in(X0,sK91(sK137,X1))
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ closed_subset(X0,sK137)
| ~ subset(X1,X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_47795]) ).
tcf(c_201234,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ( sK303(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_47947]) ).
tcf(c_201235,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ( sK304(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_47911]) ).
tcf(c_201236,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_48297]) ).
tcf(c_201237,plain,
! [X0: $i,X1: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_48087]) ).
tcf(c_201238,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_48070]) ).
tcf(c_201239,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(sK137,X1) = X0 )
| ~ empty(X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ sP38(sK137,X1,X0)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_47756]) ).
tcf(c_201240,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_48460]) ).
tcf(c_201241,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| subset(X1,X0)
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_47876]) ).
tcf(c_201242,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_48490]) ).
tcf(c_201243,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_48431]) ).
tcf(c_201244,plain,
! [X0: $i] :
( in(empty_set,sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ closed_subset(empty_set,sK137)
| ~ subset(X0,empty_set)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_182438]) ).
tcf(c_201245,plain,
! [X0: $i] :
( ( sK124(sK137,empty_set,X0) = X0 )
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_791,c_182437]) ).
tcf(c_201246,plain,
! [X0: $i] :
( in(empty_set,sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ closed_subset(empty_set,sK137)
| ~ subset(X0,empty_set)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_182436]) ).
tcf(c_201247,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,X0))) = topstr_closure(sK137,topstr_closure(sK137,X0)) )
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_176018]) ).
tcf(c_201248,plain,
! [X0: $i] :
( in(sK138,sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_176521]) ).
tcf(c_201249,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,X0) = X0 )
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_791,c_176408]) ).
tcf(c_201250,plain,
! [X0: $i] :
( in(sK138,sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ closed_subset(sK138,sK137)
| ~ subset(X0,sK138)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_176286]) ).
tcf(c_201251,plain,
! [X0: $i] :
( subset(sK138,X0)
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_791,c_175672]) ).
tcf(c_201252,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_791,c_175482]) ).
tcf(c_201253,plain,
! [X0: $i] :
( subset(sK138,X0)
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_791,c_175418]) ).
tcf(c_201254,plain,
! [X0: $i] :
( ( topstr_closure(sK137,sK138) = X0 )
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK138,X0) ),
inference(superposition,[status(thm)],[c_791,c_175209]) ).
tcf(c_201255,plain,
! [X0: $i] :
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,X0)) = topstr_closure(sK137,X0) )
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_48058]) ).
tcf(c_201256,plain,
! [X0: $i] :
( ( topstr_closure(sK137,X0) = X0 )
| ~ empty(X0)
| ~ closed_subset(X0,sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_48037]) ).
tcf(c_201257,plain,
! [X0: $i] :
( open_subset(X0,sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X0,the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_791,c_47852]) ).
tcf(c_201258,plain,
! [X0: $i] :
( in(X0,the_topology(sK137))
| ~ empty(X0)
| ~ open_subset(X0,sK137)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_791,c_47840]) ).
tcf(c_201259,plain,
! [X0: $i,X1: $i] :
( sP34(X1,sK137)
| in(set_difference(the_carrier(sK137),X0),X1)
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK295(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_73951]) ).
tcf(c_201260,plain,
! [X0: $i,X1: $i] :
( in(set_difference(the_carrier(sK137),X0),X1)
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK93(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_73134]) ).
tcf(c_201261,plain,
! [X0: $i,X1: $i] :
( sP34(X1,sK137)
| ( sK296(sK137,X1,X0) = X0 )
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK295(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_48001]) ).
tcf(c_201262,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(powerset(the_carrier(sK137))))
| ~ closed_subset(sK145(sK137,X0),sK137) ),
inference(superposition,[status(thm)],[c_791,c_48252]) ).
tcf(c_201263,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ empty(X1)
| ~ empty(powerset(powerset(the_carrier(sK137))))
| ~ in(X0,sK93(sK137,X1)) ),
inference(superposition,[status(thm)],[c_791,c_48416]) ).
tcf(c_201264,plain,
! [X0: $i] :
( in(sK145(sK137,X0),X0)
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_791,c_48237]) ).
tcf(c_201265,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(cartesian_product2(X0,X1))
| ~ well_ordering(cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_201062,c_593]) ).
tcf(c_201266,plain,
! [X0: $i,X1: $i] :
( connected(cartesian_product2(X0,X1))
| ~ well_ordering(cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_201062,c_592]) ).
tcf(c_201267,plain,
! [X0: $i,X1: $i] :
( antisymmetric(cartesian_product2(X0,X1))
| ~ well_ordering(cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_201062,c_591]) ).
tcf(c_201268,plain,
! [X0: $i,X1: $i] :
( transitive(cartesian_product2(X0,X1))
| ~ well_ordering(cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_201062,c_590]) ).
tcf(c_201269,plain,
! [X0: $i,X1: $i] :
( reflexive(cartesian_product2(X0,X1))
| ~ well_ordering(cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_201062,c_589]) ).
tcf(c_201354,plain,
! [X0: $i] : ~ in(powerset(X0),empty_set),
inference(superposition,[status(thm)],[c_201125,c_546]) ).
tcf(c_201355,plain,
! [X0: $i] : in(sK154(powerset(X0)),powerset(X0)),
inference(superposition,[status(thm)],[c_201125,c_542]) ).
tcf(c_201359,plain,
( sP36(sK137,sK138)
| in(empty_set,sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_201125,c_176867]) ).
tcf(c_201360,plain,
( in(empty_set,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_201125,c_176193]) ).
tcf(c_201371,plain,
! [X0: $i] : ~ in(powerset(X0),X0),
inference(superposition,[status(thm)],[c_201126,c_546]) ).
tcf(c_201376,plain,
( sP36(sK137,sK138)
| in(the_carrier(sK137),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(the_carrier(sK137),sK137)
| ~ subset(sK138,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_201126,c_176867]) ).
tcf(c_201377,plain,
( in(the_carrier(sK137),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(the_carrier(sK137),sK137)
| ~ subset(sK138,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_201126,c_176193]) ).
tcf(c_201378,plain,
( in(the_carrier(sK137),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(the_carrier(sK137),sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201377,c_190838]) ).
tcf(c_201382,plain,
( sP36(sK137,sK138)
| in(the_carrier(sK137),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(the_carrier(sK137),sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201376,c_190838]) ).
tcf(c_201388,plain,
( ordinal(sK138)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_201127,c_349]) ).
tcf(c_201389,plain,
~ in(powerset(the_carrier(sK137)),sK138),
inference(superposition,[status(thm)],[c_201127,c_546]) ).
tcf(c_201390,plain,
in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137))),
inference(superposition,[status(thm)],[c_201127,c_542]) ).
tcf(c_201391,plain,
~ empty(powerset(the_carrier(sK137))),
inference(superposition,[status(thm)],[c_201127,c_781]) ).
tcf(c_201394,plain,
( sP36(sK137,sK138)
| in(sK138,sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK138,sK138) ),
inference(superposition,[status(thm)],[c_201127,c_176867]) ).
tcf(c_201395,plain,
( in(sK138,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK138,sK138) ),
inference(superposition,[status(thm)],[c_201127,c_176193]) ).
tcf(c_201398,plain,
( in(sK138,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201395,c_670]) ).
tcf(c_201402,plain,
( sP36(sK137,sK138)
| in(sK138,sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201394,c_670]) ).
tcf(c_201407,plain,
( in(the_carrier(sK137),sK91(sK137,sK138))
| ~ topological_space(sK137) ),
inference(global_subsumption_just,[status(thm)],[c_201378,c_68983,c_201378]) ).
tcf(c_201413,plain,
( ordinal(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_201407,c_349]) ).
tcf(c_201414,plain,
( ~ topological_space(sK137)
| ~ in(sK91(sK137,sK138),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_201407,c_546]) ).
tcf(c_201415,plain,
( in(sK154(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_201407,c_542]) ).
tcf(c_201416,plain,
( ~ topological_space(sK137)
| ~ empty(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_201407,c_781]) ).
tcf(c_201417,plain,
( element(the_carrier(sK137),sK91(sK137,sK138))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_201407,c_701]) ).
tcf(c_201419,plain,
( in(the_carrier(sK137),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(sK138,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_201407,c_190603]) ).
tcf(c_201421,plain,
( ( sK92(sK137,sK138,the_carrier(sK137)) = the_carrier(sK137) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_201407,c_175190]) ).
tcf(c_201422,plain,
( in(the_carrier(sK137),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_201407,c_175008]) ).
tcf(c_201450,plain,
( ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ in(sK91(sK137,sK138),empty_set) ),
inference(superposition,[status(thm)],[c_201360,c_546]) ).
tcf(c_201452,plain,
( ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ empty(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_201360,c_781]) ).
tcf(c_201453,plain,
( element(empty_set,sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_201360,c_701]) ).
tcf(c_201455,plain,
( in(empty_set,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ subset(sK138,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_201360,c_190603]) ).
tcf(c_201457,plain,
( ( sK92(sK137,sK138,empty_set) = empty_set )
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_201360,c_175190]) ).
tcf(c_201458,plain,
( in(empty_set,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_201360,c_175008]) ).
tcf(c_201472,plain,
( sP36(sK137,sK138)
| in(the_carrier(sK137),sK302(sK137,sK138))
| ~ topological_space(sK137) ),
inference(global_subsumption_just,[status(thm)],[c_201382,c_68983,c_201382]) ).
tcf(c_201480,plain,
( sP36(sK137,sK138)
| ordinal(the_carrier(sK137))
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_201472,c_349]) ).
tcf(c_201481,plain,
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ in(sK302(sK137,sK138),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_201472,c_546]) ).
tcf(c_201482,plain,
( sP36(sK137,sK138)
| in(sK154(sK302(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_201472,c_542]) ).
tcf(c_201483,plain,
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ empty(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_201472,c_781]) ).
tcf(c_201484,plain,
( sP36(sK137,sK138)
| element(the_carrier(sK137),sK302(sK137,sK138))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_201472,c_701]) ).
tcf(c_201486,plain,
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,the_carrier(sK137)) = the_carrier(sK137) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_201472,c_175802]) ).
tcf(c_201487,plain,
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,the_carrier(sK137)) = the_carrier(sK137) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_201472,c_175753]) ).
tcf(c_201542,plain,
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ in(sK302(sK137,sK138),empty_set) ),
inference(superposition,[status(thm)],[c_201359,c_546]) ).
tcf(c_201544,plain,
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set)
| ~ empty(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_201359,c_781]) ).
tcf(c_201545,plain,
( sP36(sK137,sK138)
| element(empty_set,sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_201359,c_701]) ).
tcf(c_201547,plain,
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,empty_set) = empty_set )
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_201359,c_175802]) ).
tcf(c_201548,plain,
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,empty_set) = empty_set )
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK138,empty_set) ),
inference(superposition,[status(thm)],[c_201359,c_175753]) ).
tcf(c_201570,plain,
! [X0: $i,X1: $i] : pair_first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X1,X0))) = X0,
inference(superposition,[status(thm)],[c_967,c_181305]) ).
tcf(c_201575,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( pair_first(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))))) = unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181305]) ).
tcf(c_201576,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( pair_first(unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))))) = unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181305]) ).
tcf(c_201577,plain,
! [X0: $i] : pair_first(unordered_pair(unordered_pair(X0,empty_set),powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_330,c_181305]) ).
tcf(c_201588,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_658,c_792]) ).
tcf(c_201589,plain,
( empty(sK68)
| ~ sP7
| ~ empty(powerset(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_134,c_792]) ).
tcf(c_201590,plain,
( empty(sK138)
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_376,c_792]) ).
tcf(c_201593,plain,
! [X0: $i] :
( empty(sK208(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_702,c_792]) ).
tcf(c_201601,plain,
( empty(sK319(sK320))
| ~ empty(powerset(the_carrier(sK320))) ),
inference(superposition,[status(thm)],[c_22154,c_792]) ).
tcf(c_201602,plain,
( topological_space(sK137)
| empty(sK378(sK137))
| ~ sP42(sK137)
| ~ empty(powerset(powerset(the_carrier(sK137))))
| ~ in(the_carrier(sK137),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_47411,c_792]) ).
tcf(c_201603,plain,
( empty(the_topology(sK137))
| ~ empty(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_47453,c_792]) ).
tcf(c_201604,plain,
( empty(the_topology(sK291))
| ~ empty(powerset(powerset(the_carrier(sK291)))) ),
inference(superposition,[status(thm)],[c_47629,c_792]) ).
tcf(c_201605,plain,
! [X0: $i] :
( empty(topstr_closure(sK137,X0))
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_792]) ).
tcf(c_201606,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| empty(sK304(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_792]) ).
tcf(c_201607,plain,
! [X0: $i] :
( empty(sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48126,c_792]) ).
tcf(c_201608,plain,
! [X0: $i,X1: $i] :
( empty(sK146(sK137,X0,X1))
| in(X1,topstr_closure(sK137,X0))
| ~ empty(powerset(the_carrier(sK137)))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_792]) ).
tcf(c_201609,plain,
! [X0: $i] :
( empty(sK145(sK137,X0))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_792]) ).
tcf(c_201610,plain,
! [X0: $i] :
( empty(sK125(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48285,c_792]) ).
tcf(c_201611,plain,
! [X0: $i,X1: $i] :
( empty(sK124(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_792]) ).
tcf(c_201612,plain,
! [X0: $i] :
( empty(sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48389,c_792]) ).
tcf(c_201613,plain,
! [X0: $i,X1: $i] :
( empty(sK92(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_792]) ).
tcf(c_201614,plain,
! [X0: $i] :
( empty(topstr_closure(sK291,X0))
| ~ empty(powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(superposition,[status(thm)],[c_106105,c_792]) ).
tcf(c_201645,plain,
( sP30(sK66)
| ( sK265 = sK264 )
| ~ sP8 ),
inference(superposition,[status(thm)],[c_129,c_826]) ).
tcf(c_201646,plain,
( sP30(sK70)
| ( sK265 = sK264 )
| ~ sP6 ),
inference(superposition,[status(thm)],[c_142,c_826]) ).
tcf(c_201647,plain,
( sP30(sK117)
| ( sK265 = sK264 )
| ~ sP15 ),
inference(superposition,[status(thm)],[c_248,c_826]) ).
tcf(c_201648,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| sP30(sK143(X0))
| ( sK265 = sK264 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_423,c_826]) ).
tcf(c_201649,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| sP30(sK144(X0))
| ( sK265 = sK264 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_426,c_826]) ).
tcf(c_201650,plain,
! [X0: $i] :
( sP30(union(X0))
| ( sK265 = sK264 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_706,c_826]) ).
tcf(c_201653,plain,
( sP30(omega)
| ( sK265 = sK264 ) ),
inference(superposition,[status(thm)],[c_843,c_826]) ).
tcf(c_201654,plain,
! [X0: $i] :
( sP30(sK274(X0))
| ( sK265 = sK264 )
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_856,c_826]) ).
tcf(c_201655,plain,
( sP30(sK287)
| ( sK265 = sK264 ) ),
inference(superposition,[status(thm)],[c_889,c_826]) ).
tcf(c_201656,plain,
( sP30(sK337)
| ( sK265 = sK264 ) ),
inference(superposition,[status(thm)],[c_1066,c_826]) ).
tcf(c_201657,plain,
( sP30(sK339)
| ( sK265 = sK264 ) ),
inference(superposition,[status(thm)],[c_1076,c_826]) ).
tcf(c_201658,plain,
( sP30(sK372)
| ( sK265 = sK264 ) ),
inference(superposition,[status(thm)],[c_1272,c_826]) ).
tcf(c_201659,plain,
( sP30(empty_set)
| ( sK265 = sK264 ) ),
inference(superposition,[status(thm)],[c_178087,c_826]) ).
tcf(c_201661,plain,
( sP30(sK91(sK137,sK138))
| ( sK265 = sK264 )
| ( sK92(sK137,sK138,sK139(sK91(sK137,sK138))) = sK139(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178683,c_826]) ).
tcf(c_201662,plain,
( sP36(sK137,sK138)
| sP30(sK302(sK137,sK138))
| ( sK265 = sK264 )
| ( sK304(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178687,c_826]) ).
tcf(c_201663,plain,
( sP36(sK137,sK138)
| sP30(sK302(sK137,sK138))
| ( sK265 = sK264 )
| ( sK303(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178686,c_826]) ).
tcf(c_201664,plain,
! [X0: $i] :
( sP30(relation_dom(X0))
| ( sK265 = sK264 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_179244,c_826]) ).
tcf(c_201665,plain,
( sP30(sK208(omega))
| ( sK265 = sK264 ) ),
inference(superposition,[status(thm)],[c_179848,c_826]) ).
tcf(c_201666,plain,
! [X0: $i] :
( sP30(relation_rng(X0))
| ( sK265 = sK264 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_179868,c_826]) ).
tcf(c_201667,plain,
! [X0: $i] :
( sP30(relation_inverse(X0))
| ( sK265 = sK264 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_180555,c_826]) ).
tcf(c_201668,plain,
( sP30(sK154(omega))
| ( sK265 = sK264 ) ),
inference(superposition,[status(thm)],[c_188974,c_826]) ).
tcf(c_201818,plain,
( sP30(sK66)
| ( sK265 = sK267 )
| ~ sP8 ),
inference(superposition,[status(thm)],[c_129,c_828]) ).
tcf(c_201819,plain,
( sP30(sK70)
| ( sK265 = sK267 )
| ~ sP6 ),
inference(superposition,[status(thm)],[c_142,c_828]) ).
tcf(c_201820,plain,
( sP30(sK117)
| ( sK265 = sK267 )
| ~ sP15 ),
inference(superposition,[status(thm)],[c_248,c_828]) ).
tcf(c_201821,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| sP30(sK143(X0))
| ( sK265 = sK267 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_423,c_828]) ).
tcf(c_201822,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| sP30(sK144(X0))
| ( sK265 = sK267 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_426,c_828]) ).
tcf(c_201823,plain,
! [X0: $i] :
( sP30(union(X0))
| ( sK265 = sK267 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_706,c_828]) ).
tcf(c_201826,plain,
( sP30(omega)
| ( sK265 = sK267 ) ),
inference(superposition,[status(thm)],[c_843,c_828]) ).
tcf(c_201827,plain,
! [X0: $i] :
( sP30(sK274(X0))
| ( sK265 = sK267 )
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_856,c_828]) ).
tcf(c_201828,plain,
( sP30(sK287)
| ( sK265 = sK267 ) ),
inference(superposition,[status(thm)],[c_889,c_828]) ).
tcf(c_201829,plain,
( sP30(sK337)
| ( sK265 = sK267 ) ),
inference(superposition,[status(thm)],[c_1066,c_828]) ).
tcf(c_201830,plain,
( sP30(sK339)
| ( sK265 = sK267 ) ),
inference(superposition,[status(thm)],[c_1076,c_828]) ).
tcf(c_201831,plain,
( sP30(sK372)
| ( sK265 = sK267 ) ),
inference(superposition,[status(thm)],[c_1272,c_828]) ).
tcf(c_201832,plain,
( sP30(empty_set)
| ( sK265 = sK267 ) ),
inference(superposition,[status(thm)],[c_178087,c_828]) ).
tcf(c_201834,plain,
( sP30(sK91(sK137,sK138))
| ( sK265 = sK267 )
| ( sK92(sK137,sK138,sK139(sK91(sK137,sK138))) = sK139(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178683,c_828]) ).
tcf(c_201835,plain,
( sP36(sK137,sK138)
| sP30(sK302(sK137,sK138))
| ( sK265 = sK267 )
| ( sK304(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178687,c_828]) ).
tcf(c_201836,plain,
( sP36(sK137,sK138)
| sP30(sK302(sK137,sK138))
| ( sK265 = sK267 )
| ( sK303(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178686,c_828]) ).
tcf(c_201837,plain,
! [X0: $i] :
( sP30(relation_dom(X0))
| ( sK265 = sK267 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_179244,c_828]) ).
tcf(c_201838,plain,
( sP30(sK208(omega))
| ( sK265 = sK267 ) ),
inference(superposition,[status(thm)],[c_179848,c_828]) ).
tcf(c_201839,plain,
! [X0: $i] :
( sP30(relation_rng(X0))
| ( sK265 = sK267 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_179868,c_828]) ).
tcf(c_201840,plain,
! [X0: $i] :
( sP30(relation_inverse(X0))
| ( sK265 = sK267 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_180555,c_828]) ).
tcf(c_201841,plain,
( sP30(sK154(omega))
| ( sK265 = sK267 ) ),
inference(superposition,[status(thm)],[c_188974,c_828]) ).
tcf(c_201917,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),X0),
inference(superposition,[status(thm)],[c_639,c_201371]) ).
tcf(c_201918,plain,
! [X0: $i,X1: $i] : ~ in(powerset(set_union2(X0,X1)),X1),
inference(superposition,[status(thm)],[c_640,c_201371]) ).
tcf(c_201919,plain,
! [X0: $i] : ~ subset(powerset(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_666,c_201371]) ).
tcf(c_201920,plain,
( ~ topological_space(sK137)
| ~ closed_subset(powerset(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,powerset(sK91(sK137,sK138)))
| ~ subset(powerset(sK91(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_191567,c_201371]) ).
tcf(c_201921,plain,
( ~ topological_space(sK137)
| ~ closed_subset(powerset(sK91(sK137,the_carrier(sK137))),sK137)
| ~ subset(the_carrier(sK137),powerset(sK91(sK137,the_carrier(sK137))))
| ~ in(powerset(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_176973,c_201371]) ).
tcf(c_201937,plain,
! [X0: $i] :
( sP3(X0)
| empty(sK62(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_183186,c_792]) ).
tcf(c_201938,plain,
! [X0: $i] :
( sP3(X0)
| empty(X0)
| in(sK62(X0),X0) ),
inference(superposition,[status(thm)],[c_183186,c_790]) ).
tcf(c_201939,plain,
! [X0: $i,X1: $i] :
( sP3(powerset(cartesian_product2(X0,X1)))
| relation(sK62(powerset(cartesian_product2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_183186,c_764]) ).
tcf(c_201940,plain,
( sP3(omega)
| ordinal(sK62(omega)) ),
inference(superposition,[status(thm)],[c_183186,c_852]) ).
tcf(c_201941,plain,
( sP3(omega)
| epsilon_connected(sK62(omega)) ),
inference(superposition,[status(thm)],[c_183186,c_851]) ).
tcf(c_201942,plain,
( sP3(omega)
| epsilon_transitive(sK62(omega)) ),
inference(superposition,[status(thm)],[c_183186,c_850]) ).
tcf(c_201943,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| in(X0,sK62(powerset(the_carrier(sK137))))
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138))
| ~ closed_subset(sK62(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK62(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183186,c_177131]) ).
tcf(c_201944,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| sP3(powerset(the_carrier(sK137)))
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK62(powerset(the_carrier(sK137))),X1)
| ~ in(X0,topstr_closure(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183186,c_48138]) ).
tcf(c_201945,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| sP36(sK137,sK62(powerset(the_carrier(sK137))))
| in(X0,sK302(sK137,sK62(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK62(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183186,c_47771]) ).
tcf(c_201946,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| in(sK62(powerset(the_carrier(sK137))),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK62(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK62(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183186,c_48368]) ).
tcf(c_201947,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK62(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183186,c_48332]) ).
tcf(c_201948,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| in(sK62(powerset(the_carrier(sK137))),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK62(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK62(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183186,c_48105]) ).
tcf(c_201949,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| in(X0,sK91(sK137,sK62(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK62(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183186,c_47795]) ).
tcf(c_201950,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| sP36(sK137,sK62(powerset(the_carrier(sK137))))
| ( sK303(sK137,sK62(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183186,c_47947]) ).
tcf(c_201951,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| sP36(sK137,sK62(powerset(the_carrier(sK137))))
| ( sK304(sK137,sK62(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183186,c_47911]) ).
tcf(c_201952,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| subset(sK62(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183186,c_48297]) ).
tcf(c_201953,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| sP3(powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183186,c_48087]) ).
tcf(c_201954,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| subset(sK62(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183186,c_48070]) ).
tcf(c_201955,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK62(powerset(the_carrier(sK137)))) = X0 )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK62(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183186,c_47756]) ).
tcf(c_201956,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| ( sK92(sK137,sK62(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183186,c_48460]) ).
tcf(c_201957,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| sP36(sK137,sK62(powerset(the_carrier(sK137))))
| subset(sK62(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183186,c_47876]) ).
tcf(c_201958,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183186,c_48490]) ).
tcf(c_201959,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| subset(sK62(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183186,c_48431]) ).
tcf(c_201960,plain,
( sP3(powerset(the_carrier(sK137)))
| in(empty_set,sK147(sK137,sK62(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK62(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183186,c_182438]) ).
tcf(c_201961,plain,
( sP3(powerset(the_carrier(sK137)))
| ( sK124(sK137,empty_set,sK62(powerset(the_carrier(sK137)))) = sK62(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK62(powerset(the_carrier(sK137))),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_183186,c_182437]) ).
tcf(c_201962,plain,
( sP3(powerset(the_carrier(sK137)))
| in(empty_set,sK123(sK137,sK62(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK62(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183186,c_182436]) ).
tcf(c_201963,plain,
( sP3(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK62(powerset(the_carrier(sK137)))))) = topstr_closure(sK137,topstr_closure(sK137,sK62(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183186,c_176018]) ).
tcf(c_201964,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK138,sK123(sK137,sK62(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK62(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183186,c_176521]) ).
tcf(c_201965,plain,
( sP3(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK138,sK62(powerset(the_carrier(sK137)))) = sK62(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK62(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183186,c_176408]) ).
tcf(c_201966,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK138,sK147(sK137,sK62(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK62(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183186,c_176286]) ).
tcf(c_201967,plain,
( sP3(powerset(the_carrier(sK137)))
| subset(sK138,sK62(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK62(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183186,c_175672]) ).
tcf(c_201968,plain,
( sP3(powerset(the_carrier(sK137)))
| closed_subset(sK62(powerset(the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ in(sK62(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183186,c_175482]) ).
tcf(c_201969,plain,
( sP3(powerset(the_carrier(sK137)))
| subset(sK138,sK62(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK62(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183186,c_175418]) ).
tcf(c_201970,plain,
( sP3(powerset(the_carrier(sK137)))
| ( sK62(powerset(the_carrier(sK137))) = topstr_closure(sK137,sK138) )
| ~ sP38(sK137,sK138,sK62(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183186,c_175209]) ).
tcf(c_201971,plain,
( sP3(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK62(powerset(the_carrier(sK137))))) = topstr_closure(sK137,sK62(powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183186,c_48058]) ).
tcf(c_201972,plain,
( sP3(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK62(powerset(the_carrier(sK137)))) = sK62(powerset(the_carrier(sK137))) )
| ~ closed_subset(sK62(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183186,c_48037]) ).
tcf(c_201973,plain,
( sP3(powerset(the_carrier(sK137)))
| open_subset(sK62(powerset(the_carrier(sK137))),sK137)
| ~ in(sK62(powerset(the_carrier(sK137))),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_183186,c_47852]) ).
tcf(c_201974,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK62(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK62(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183186,c_47840]) ).
tcf(c_201975,plain,
! [X0: $i] :
( sP3(powerset(powerset(the_carrier(sK137))))
| sP34(sK62(powerset(powerset(the_carrier(sK137)))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK62(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK62(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183186,c_73951]) ).
tcf(c_201976,plain,
! [X0: $i] :
( sP3(powerset(powerset(the_carrier(sK137))))
| in(set_difference(the_carrier(sK137),X0),sK62(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK62(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183186,c_73134]) ).
tcf(c_201977,plain,
! [X0: $i] :
( sP3(powerset(powerset(the_carrier(sK137))))
| sP34(sK62(powerset(powerset(the_carrier(sK137)))),sK137)
| ( sK296(sK137,sK62(powerset(powerset(the_carrier(sK137)))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK62(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183186,c_48001]) ).
tcf(c_201978,plain,
( sP3(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK62(powerset(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK62(powerset(powerset(the_carrier(sK137))))),sK137) ),
inference(superposition,[status(thm)],[c_183186,c_48252]) ).
tcf(c_201979,plain,
! [X0: $i] :
( sP3(powerset(powerset(the_carrier(sK137))))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK62(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183186,c_48416]) ).
tcf(c_201980,plain,
( sP3(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK62(powerset(powerset(the_carrier(sK137))))),sK137)
| in(sK145(sK137,sK62(powerset(powerset(the_carrier(sK137))))),sK62(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183186,c_48237]) ).
tcf(c_202262,plain,
( sP3(omega)
| sP30(sK62(omega))
| ( sK265 = sK267 ) ),
inference(superposition,[status(thm)],[c_201940,c_828]) ).
tcf(c_202263,plain,
( sP3(omega)
| sP30(sK62(omega))
| ( sK265 = sK264 ) ),
inference(superposition,[status(thm)],[c_201940,c_826]) ).
tcf(c_202264,plain,
( ordinal(sK267)
| sP3(omega)
| sP30(sK62(omega)) ),
inference(superposition,[status(thm)],[c_201940,c_827]) ).
tcf(c_202292,plain,
( sP3(powerset(the_carrier(sK137)))
| ordinal(sK62(powerset(the_carrier(sK137))))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(sK62(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_201974,c_349]) ).
tcf(c_202293,plain,
( sP3(powerset(the_carrier(sK137)))
| ~ open_subset(sK62(powerset(the_carrier(sK137))),sK137)
| ~ in(the_topology(sK137),sK62(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_201974,c_546]) ).
tcf(c_202294,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(sK62(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_201974,c_542]) ).
tcf(c_202295,plain,
( sP3(powerset(the_carrier(sK137)))
| ~ empty(the_topology(sK137))
| ~ open_subset(sK62(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_201974,c_781]) ).
tcf(c_202296,plain,
( sP3(powerset(the_carrier(sK137)))
| element(sK62(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK62(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_201974,c_701]) ).
tcf(c_202321,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK123(sK137,sK138)))
| ~ finite(set_difference(the_carrier(sK137),sK185(sK93(sK137,sK123(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192120,c_292]) ).
tcf(c_202322,plain,
( ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK123(sK137,sK138)))
| ~ proper_subset(set_difference(the_carrier(sK137),sK185(sK93(sK137,sK123(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192120,c_492]) ).
tcf(c_202351,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK123(sK137,sK138)))
| ~ finite(set_difference(the_carrier(sK137),sK274(sK93(sK137,sK123(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192123,c_292]) ).
tcf(c_202352,plain,
( ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK123(sK137,sK138)))
| ~ proper_subset(set_difference(the_carrier(sK137),sK274(sK93(sK137,sK123(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192123,c_492]) ).
tcf(c_202387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X4 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X3 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X3) ) ),
inference(superposition,[status(thm)],[c_105912,c_181308]) ).
tcf(c_202388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X4 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X3 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X3) ) ),
inference(superposition,[status(thm)],[c_105926,c_181308]) ).
tcf(c_202392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X4 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X3 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X3 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X3) ) ),
inference(superposition,[status(thm)],[c_105912,c_181308]) ).
tcf(c_202393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X4 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X3 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4)) = X3 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(X2,X3) ) ),
inference(superposition,[status(thm)],[c_105926,c_181308]) ).
tcf(c_202417,plain,
( sP30(sK66)
| ( sK266 = sK264 )
| ~ sP8 ),
inference(superposition,[status(thm)],[c_129,c_831]) ).
tcf(c_202418,plain,
( sP30(sK70)
| ( sK266 = sK264 )
| ~ sP6 ),
inference(superposition,[status(thm)],[c_142,c_831]) ).
tcf(c_202419,plain,
( sP30(sK117)
| ( sK266 = sK264 )
| ~ sP15 ),
inference(superposition,[status(thm)],[c_248,c_831]) ).
tcf(c_202420,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| sP30(sK143(X0))
| ( sK266 = sK264 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_423,c_831]) ).
tcf(c_202421,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| sP30(sK144(X0))
| ( sK266 = sK264 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_426,c_831]) ).
tcf(c_202422,plain,
! [X0: $i] :
( sP30(union(X0))
| ( sK266 = sK264 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_706,c_831]) ).
tcf(c_202425,plain,
( sP30(omega)
| ( sK266 = sK264 ) ),
inference(superposition,[status(thm)],[c_843,c_831]) ).
tcf(c_202426,plain,
! [X0: $i] :
( sP30(sK274(X0))
| ( sK266 = sK264 )
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_856,c_831]) ).
tcf(c_202427,plain,
( sP30(sK287)
| ( sK266 = sK264 ) ),
inference(superposition,[status(thm)],[c_889,c_831]) ).
tcf(c_202428,plain,
( sP30(sK337)
| ( sK266 = sK264 ) ),
inference(superposition,[status(thm)],[c_1066,c_831]) ).
tcf(c_202429,plain,
( sP30(sK339)
| ( sK266 = sK264 ) ),
inference(superposition,[status(thm)],[c_1076,c_831]) ).
tcf(c_202430,plain,
( sP30(sK372)
| ( sK266 = sK264 ) ),
inference(superposition,[status(thm)],[c_1272,c_831]) ).
tcf(c_202431,plain,
( sP30(empty_set)
| ( sK266 = sK264 ) ),
inference(superposition,[status(thm)],[c_178087,c_831]) ).
tcf(c_202433,plain,
( sP30(sK91(sK137,sK138))
| ( sK266 = sK264 )
| ( sK92(sK137,sK138,sK139(sK91(sK137,sK138))) = sK139(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178683,c_831]) ).
tcf(c_202434,plain,
( sP36(sK137,sK138)
| sP30(sK302(sK137,sK138))
| ( sK266 = sK264 )
| ( sK304(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178687,c_831]) ).
tcf(c_202435,plain,
( sP36(sK137,sK138)
| sP30(sK302(sK137,sK138))
| ( sK266 = sK264 )
| ( sK303(sK137,sK138,sK139(sK302(sK137,sK138))) = sK139(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178686,c_831]) ).
tcf(c_202436,plain,
! [X0: $i] :
( sP30(relation_dom(X0))
| ( sK266 = sK264 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_179244,c_831]) ).
tcf(c_202437,plain,
( sP30(sK208(omega))
| ( sK266 = sK264 ) ),
inference(superposition,[status(thm)],[c_179848,c_831]) ).
tcf(c_202438,plain,
! [X0: $i] :
( sP30(relation_rng(X0))
| ( sK266 = sK264 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_179868,c_831]) ).
tcf(c_202439,plain,
! [X0: $i] :
( sP30(relation_inverse(X0))
| ( sK266 = sK264 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_180555,c_831]) ).
tcf(c_202440,plain,
( sP30(sK154(omega))
| ( sK266 = sK264 ) ),
inference(superposition,[status(thm)],[c_188974,c_831]) ).
tcf(c_202441,plain,
( sP3(omega)
| sP30(sK62(omega))
| ( sK266 = sK264 ) ),
inference(superposition,[status(thm)],[c_201940,c_831]) ).
tcf(c_202592,plain,
! [X0: $i] :
( ( relation_rng(sK270(relation_rng(X0))) = relation_rng(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_179871,c_848]) ).
tcf(c_202593,plain,
! [X0: $i] :
( ( relation_rng(sK270(relation_dom(X0))) = relation_dom(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_179247,c_848]) ).
tcf(c_202594,plain,
! [X0: $i] :
( empty(X0)
| ( relation_rng(sK270(sK325(X0))) = sK325(X0) ) ),
inference(superposition,[status(thm)],[c_1006,c_848]) ).
tcf(c_202595,plain,
relation_rng(sK270(sK326)) = sK326,
inference(superposition,[status(thm)],[c_1008,c_848]) ).
tcf(c_202596,plain,
! [X0: $i] : relation_rng(sK270(unordered_pair(X0,X0))) = unordered_pair(X0,X0),
inference(superposition,[status(thm)],[c_1010,c_848]) ).
tcf(c_202597,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK270(set_difference(X0,X1))) = set_difference(X0,X1) )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_1011,c_848]) ).
tcf(c_202598,plain,
relation_rng(sK270(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_177985,c_848]) ).
tcf(c_202599,plain,
relation_rng(sK270(powerset(empty_set))) = powerset(empty_set),
inference(superposition,[status(thm)],[c_178668,c_848]) ).
tcf(c_202600,plain,
! [X0: $i] :
( ( relation_rng(sK270(relation_inverse(X0))) = relation_inverse(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_180558,c_848]) ).
tcf(c_202634,plain,
! [X0: $i] :
( ordinal(X0)
| empty(sK139(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_183193,c_792]) ).
tcf(c_202635,plain,
! [X0: $i] :
( ordinal(X0)
| empty(X0)
| in(sK139(X0),X0) ),
inference(superposition,[status(thm)],[c_183193,c_790]) ).
tcf(c_202636,plain,
! [X0: $i,X1: $i] :
( ordinal(powerset(cartesian_product2(X0,X1)))
| relation(sK139(powerset(cartesian_product2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_183193,c_764]) ).
tcf(c_202640,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| in(X0,sK139(powerset(the_carrier(sK137))))
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138))
| ~ closed_subset(sK139(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK139(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183193,c_177131]) ).
tcf(c_202641,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ordinal(powerset(the_carrier(sK137)))
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK139(powerset(the_carrier(sK137))),X1)
| ~ in(X0,topstr_closure(sK137,sK139(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183193,c_48138]) ).
tcf(c_202642,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| sP36(sK137,sK139(powerset(the_carrier(sK137))))
| in(X0,sK302(sK137,sK139(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK139(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183193,c_47771]) ).
tcf(c_202643,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| in(sK139(powerset(the_carrier(sK137))),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK139(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK139(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183193,c_48368]) ).
tcf(c_202644,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK139(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK139(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183193,c_48332]) ).
tcf(c_202645,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| in(sK139(powerset(the_carrier(sK137))),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK139(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK139(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183193,c_48105]) ).
tcf(c_202646,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| in(X0,sK91(sK137,sK139(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK139(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183193,c_47795]) ).
tcf(c_202647,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| sP36(sK137,sK139(powerset(the_carrier(sK137))))
| ( sK303(sK137,sK139(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK139(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183193,c_47947]) ).
tcf(c_202648,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| sP36(sK137,sK139(powerset(the_carrier(sK137))))
| ( sK304(sK137,sK139(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK139(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183193,c_47911]) ).
tcf(c_202649,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| subset(sK139(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK139(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183193,c_48297]) ).
tcf(c_202650,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| ordinal(powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK139(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183193,c_48087]) ).
tcf(c_202651,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| subset(sK139(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK139(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183193,c_48070]) ).
tcf(c_202652,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK139(powerset(the_carrier(sK137)))) = X0 )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK139(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183193,c_47756]) ).
tcf(c_202653,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| ( sK92(sK137,sK139(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK139(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183193,c_48460]) ).
tcf(c_202654,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| sP36(sK137,sK139(powerset(the_carrier(sK137))))
| subset(sK139(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK139(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183193,c_47876]) ).
tcf(c_202655,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK139(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183193,c_48490]) ).
tcf(c_202656,plain,
! [X0: $i] :
( ordinal(powerset(the_carrier(sK137)))
| subset(sK139(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK139(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183193,c_48431]) ).
tcf(c_202657,plain,
( ordinal(powerset(the_carrier(sK137)))
| in(empty_set,sK147(sK137,sK139(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK139(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183193,c_182438]) ).
tcf(c_202658,plain,
( ordinal(powerset(the_carrier(sK137)))
| ( sK124(sK137,empty_set,sK139(powerset(the_carrier(sK137)))) = sK139(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK139(powerset(the_carrier(sK137))),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_183193,c_182437]) ).
tcf(c_202659,plain,
( ordinal(powerset(the_carrier(sK137)))
| in(empty_set,sK123(sK137,sK139(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK139(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183193,c_182436]) ).
tcf(c_202660,plain,
( ordinal(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK139(powerset(the_carrier(sK137)))))) = topstr_closure(sK137,topstr_closure(sK137,sK139(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183193,c_176018]) ).
tcf(c_202661,plain,
( ordinal(powerset(the_carrier(sK137)))
| in(sK138,sK123(sK137,sK139(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK139(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183193,c_176521]) ).
tcf(c_202662,plain,
( ordinal(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK138,sK139(powerset(the_carrier(sK137)))) = sK139(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK139(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183193,c_176408]) ).
tcf(c_202663,plain,
( ordinal(powerset(the_carrier(sK137)))
| in(sK138,sK147(sK137,sK139(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK139(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183193,c_176286]) ).
tcf(c_202664,plain,
( ordinal(powerset(the_carrier(sK137)))
| subset(sK138,sK139(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK139(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183193,c_175672]) ).
tcf(c_202665,plain,
( ordinal(powerset(the_carrier(sK137)))
| closed_subset(sK139(powerset(the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ in(sK139(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183193,c_175482]) ).
tcf(c_202666,plain,
( ordinal(powerset(the_carrier(sK137)))
| subset(sK138,sK139(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK139(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183193,c_175418]) ).
tcf(c_202667,plain,
( ordinal(powerset(the_carrier(sK137)))
| ( sK139(powerset(the_carrier(sK137))) = topstr_closure(sK137,sK138) )
| ~ sP38(sK137,sK138,sK139(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183193,c_175209]) ).
tcf(c_202668,plain,
( ordinal(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK139(powerset(the_carrier(sK137))))) = topstr_closure(sK137,sK139(powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183193,c_48058]) ).
tcf(c_202669,plain,
( ordinal(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK139(powerset(the_carrier(sK137)))) = sK139(powerset(the_carrier(sK137))) )
| ~ closed_subset(sK139(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183193,c_48037]) ).
tcf(c_202670,plain,
( ordinal(powerset(the_carrier(sK137)))
| open_subset(sK139(powerset(the_carrier(sK137))),sK137)
| ~ in(sK139(powerset(the_carrier(sK137))),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_183193,c_47852]) ).
tcf(c_202671,plain,
( ordinal(powerset(the_carrier(sK137)))
| in(sK139(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK139(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183193,c_47840]) ).
tcf(c_202672,plain,
! [X0: $i] :
( ordinal(powerset(powerset(the_carrier(sK137))))
| sP34(sK139(powerset(powerset(the_carrier(sK137)))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK139(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK139(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183193,c_73951]) ).
tcf(c_202673,plain,
! [X0: $i] :
( ordinal(powerset(powerset(the_carrier(sK137))))
| in(set_difference(the_carrier(sK137),X0),sK139(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK139(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183193,c_73134]) ).
tcf(c_202674,plain,
! [X0: $i] :
( ordinal(powerset(powerset(the_carrier(sK137))))
| sP34(sK139(powerset(powerset(the_carrier(sK137)))),sK137)
| ( sK296(sK137,sK139(powerset(powerset(the_carrier(sK137)))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK139(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183193,c_48001]) ).
tcf(c_202675,plain,
( ordinal(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK139(powerset(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK139(powerset(powerset(the_carrier(sK137))))),sK137) ),
inference(superposition,[status(thm)],[c_183193,c_48252]) ).
tcf(c_202676,plain,
! [X0: $i] :
( ordinal(powerset(powerset(the_carrier(sK137))))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK139(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183193,c_48416]) ).
tcf(c_202677,plain,
( ordinal(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK139(powerset(powerset(the_carrier(sK137))))),sK137)
| in(sK145(sK137,sK139(powerset(powerset(the_carrier(sK137))))),sK139(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183193,c_48237]) ).
tcf(c_202886,plain,
! [X0: $i] :
( relation(X0)
| empty(sK175(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_183194,c_792]) ).
tcf(c_202888,plain,
! [X0: $i,X1: $i] :
( relation(powerset(cartesian_product2(X0,X1)))
| relation(sK175(powerset(cartesian_product2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_183194,c_764]) ).
tcf(c_202889,plain,
( relation(omega)
| ordinal(sK175(omega)) ),
inference(superposition,[status(thm)],[c_183194,c_852]) ).
tcf(c_202890,plain,
( relation(omega)
| epsilon_connected(sK175(omega)) ),
inference(superposition,[status(thm)],[c_183194,c_851]) ).
tcf(c_202891,plain,
( relation(omega)
| epsilon_transitive(sK175(omega)) ),
inference(superposition,[status(thm)],[c_183194,c_850]) ).
tcf(c_202892,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| in(X0,sK175(powerset(the_carrier(sK137))))
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138))
| ~ closed_subset(sK175(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK175(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183194,c_177131]) ).
tcf(c_202893,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| relation(powerset(the_carrier(sK137)))
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK175(powerset(the_carrier(sK137))),X1)
| ~ in(X0,topstr_closure(sK137,sK175(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183194,c_48138]) ).
tcf(c_202894,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| sP36(sK137,sK175(powerset(the_carrier(sK137))))
| in(X0,sK302(sK137,sK175(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK175(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183194,c_47771]) ).
tcf(c_202895,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| in(sK175(powerset(the_carrier(sK137))),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK175(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK175(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183194,c_48368]) ).
tcf(c_202896,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK175(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK175(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183194,c_48332]) ).
tcf(c_202897,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| in(sK175(powerset(the_carrier(sK137))),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK175(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK175(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183194,c_48105]) ).
tcf(c_202898,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| in(X0,sK91(sK137,sK175(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK175(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183194,c_47795]) ).
tcf(c_202899,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| sP36(sK137,sK175(powerset(the_carrier(sK137))))
| ( sK303(sK137,sK175(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK175(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183194,c_47947]) ).
tcf(c_202900,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| sP36(sK137,sK175(powerset(the_carrier(sK137))))
| ( sK304(sK137,sK175(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK175(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183194,c_47911]) ).
tcf(c_202901,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| subset(sK175(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK175(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183194,c_48297]) ).
tcf(c_202902,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| relation(powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK175(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183194,c_48087]) ).
tcf(c_202903,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| subset(sK175(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK175(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183194,c_48070]) ).
tcf(c_202904,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK175(powerset(the_carrier(sK137)))) = X0 )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK175(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183194,c_47756]) ).
tcf(c_202905,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| ( sK92(sK137,sK175(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK175(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183194,c_48460]) ).
tcf(c_202906,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| sP36(sK137,sK175(powerset(the_carrier(sK137))))
| subset(sK175(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK175(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183194,c_47876]) ).
tcf(c_202907,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK175(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183194,c_48490]) ).
tcf(c_202908,plain,
! [X0: $i] :
( relation(powerset(the_carrier(sK137)))
| subset(sK175(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK175(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183194,c_48431]) ).
tcf(c_202909,plain,
( relation(powerset(the_carrier(sK137)))
| in(empty_set,sK147(sK137,sK175(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK175(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183194,c_182438]) ).
tcf(c_202910,plain,
( relation(powerset(the_carrier(sK137)))
| ( sK124(sK137,empty_set,sK175(powerset(the_carrier(sK137)))) = sK175(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK175(powerset(the_carrier(sK137))),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_183194,c_182437]) ).
tcf(c_202911,plain,
( relation(powerset(the_carrier(sK137)))
| in(empty_set,sK123(sK137,sK175(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK175(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183194,c_182436]) ).
tcf(c_202912,plain,
( relation(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK175(powerset(the_carrier(sK137)))))) = topstr_closure(sK137,topstr_closure(sK137,sK175(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183194,c_176018]) ).
tcf(c_202913,plain,
( relation(powerset(the_carrier(sK137)))
| in(sK138,sK123(sK137,sK175(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK175(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183194,c_176521]) ).
tcf(c_202914,plain,
( relation(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK138,sK175(powerset(the_carrier(sK137)))) = sK175(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK175(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183194,c_176408]) ).
tcf(c_202915,plain,
( relation(powerset(the_carrier(sK137)))
| in(sK138,sK147(sK137,sK175(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK175(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183194,c_176286]) ).
tcf(c_202916,plain,
( relation(powerset(the_carrier(sK137)))
| subset(sK138,sK175(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK175(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183194,c_175672]) ).
tcf(c_202917,plain,
( relation(powerset(the_carrier(sK137)))
| closed_subset(sK175(powerset(the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ in(sK175(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183194,c_175482]) ).
tcf(c_202918,plain,
( relation(powerset(the_carrier(sK137)))
| subset(sK138,sK175(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK175(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183194,c_175418]) ).
tcf(c_202919,plain,
( relation(powerset(the_carrier(sK137)))
| ( sK175(powerset(the_carrier(sK137))) = topstr_closure(sK137,sK138) )
| ~ sP38(sK137,sK138,sK175(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183194,c_175209]) ).
tcf(c_202920,plain,
( relation(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK175(powerset(the_carrier(sK137))))) = topstr_closure(sK137,sK175(powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183194,c_48058]) ).
tcf(c_202921,plain,
( relation(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK175(powerset(the_carrier(sK137)))) = sK175(powerset(the_carrier(sK137))) )
| ~ closed_subset(sK175(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183194,c_48037]) ).
tcf(c_202922,plain,
( relation(powerset(the_carrier(sK137)))
| open_subset(sK175(powerset(the_carrier(sK137))),sK137)
| ~ in(sK175(powerset(the_carrier(sK137))),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_183194,c_47852]) ).
tcf(c_202923,plain,
( relation(powerset(the_carrier(sK137)))
| in(sK175(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK175(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183194,c_47840]) ).
tcf(c_202924,plain,
! [X0: $i] :
( relation(powerset(powerset(the_carrier(sK137))))
| sP34(sK175(powerset(powerset(the_carrier(sK137)))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK175(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK175(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183194,c_73951]) ).
tcf(c_202925,plain,
! [X0: $i] :
( relation(powerset(powerset(the_carrier(sK137))))
| in(set_difference(the_carrier(sK137),X0),sK175(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK175(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183194,c_73134]) ).
tcf(c_202926,plain,
! [X0: $i] :
( relation(powerset(powerset(the_carrier(sK137))))
| sP34(sK175(powerset(powerset(the_carrier(sK137)))),sK137)
| ( sK296(sK137,sK175(powerset(powerset(the_carrier(sK137)))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK175(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183194,c_48001]) ).
tcf(c_202927,plain,
( relation(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK175(powerset(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK175(powerset(powerset(the_carrier(sK137))))),sK137) ),
inference(superposition,[status(thm)],[c_183194,c_48252]) ).
tcf(c_202928,plain,
! [X0: $i] :
( relation(powerset(powerset(the_carrier(sK137))))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK175(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183194,c_48416]) ).
tcf(c_202929,plain,
( relation(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK175(powerset(powerset(the_carrier(sK137))))),sK137)
| in(sK145(sK137,sK175(powerset(powerset(the_carrier(sK137))))),sK175(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183194,c_48237]) ).
tcf(c_203208,plain,
( relation(omega)
| sP30(sK175(omega))
| ( sK266 = sK264 ) ),
inference(superposition,[status(thm)],[c_202889,c_831]) ).
tcf(c_203209,plain,
( relation(omega)
| sP30(sK175(omega))
| ( sK265 = sK267 ) ),
inference(superposition,[status(thm)],[c_202889,c_828]) ).
tcf(c_203210,plain,
( relation(omega)
| sP30(sK175(omega))
| ( sK265 = sK264 ) ),
inference(superposition,[status(thm)],[c_202889,c_826]) ).
tcf(c_203211,plain,
( ordinal(sK267)
| relation(omega)
| sP30(sK175(omega)) ),
inference(superposition,[status(thm)],[c_202889,c_827]) ).
tcf(c_203238,plain,
( ordinal(powerset(the_carrier(sK137)))
| ordinal(sK139(powerset(the_carrier(sK137))))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(sK139(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_202671,c_349]) ).
tcf(c_203239,plain,
( ordinal(powerset(the_carrier(sK137)))
| ~ open_subset(sK139(powerset(the_carrier(sK137))),sK137)
| ~ in(the_topology(sK137),sK139(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_202671,c_546]) ).
tcf(c_203240,plain,
( ordinal(powerset(the_carrier(sK137)))
| in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(sK139(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_202671,c_542]) ).
tcf(c_203241,plain,
( ordinal(powerset(the_carrier(sK137)))
| ~ empty(the_topology(sK137))
| ~ open_subset(sK139(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_202671,c_781]) ).
tcf(c_203242,plain,
( ordinal(powerset(the_carrier(sK137)))
| element(sK139(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK139(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_202671,c_701]) ).
tcf(c_203273,plain,
( relation(powerset(the_carrier(sK137)))
| ordinal(sK175(powerset(the_carrier(sK137))))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(sK175(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_202923,c_349]) ).
tcf(c_203274,plain,
( relation(powerset(the_carrier(sK137)))
| ~ open_subset(sK175(powerset(the_carrier(sK137))),sK137)
| ~ in(the_topology(sK137),sK175(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_202923,c_546]) ).
tcf(c_203275,plain,
( relation(powerset(the_carrier(sK137)))
| in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(sK175(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_202923,c_542]) ).
tcf(c_203276,plain,
( relation(powerset(the_carrier(sK137)))
| ~ empty(the_topology(sK137))
| ~ open_subset(sK175(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_202923,c_781]) ).
tcf(c_203277,plain,
( relation(powerset(the_carrier(sK137)))
| element(sK175(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK175(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_202923,c_701]) ).
tcf(c_203357,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK147(sK137,sK138)))
| ~ finite(set_difference(the_carrier(sK137),sK185(sK93(sK137,sK147(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192727,c_292]) ).
tcf(c_203358,plain,
( ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK147(sK137,sK138)))
| ~ proper_subset(set_difference(the_carrier(sK137),sK185(sK93(sK137,sK147(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192727,c_492]) ).
tcf(c_203442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) = pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) ) ),
inference(superposition,[status(thm)],[c_105912,c_181311]) ).
tcf(c_203443,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) = pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) ) ),
inference(superposition,[status(thm)],[c_105926,c_181311]) ).
tcf(c_203448,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( pair_second(unordered_pair(unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))),unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)))) = unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181311]) ).
tcf(c_203449,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( pair_second(unordered_pair(unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))),unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)))) = unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181311]) ).
tcf(c_203450,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_203443,c_516]) ).
tcf(c_203453,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) = X1 ) ),
inference(light_normalisation,[status(thm)],[c_203442,c_516]) ).
tcf(c_204961,plain,
( epsilon_transitive(unordered_pair(empty_set,empty_set))
| ~ ordinal(empty_set) ),
inference(superposition,[status(thm)],[c_181193,c_883]) ).
tcf(c_204962,plain,
( epsilon_transitive(set_union2(empty_set,powerset(empty_set)))
| ~ ordinal(empty_set) ),
inference(superposition,[status(thm)],[c_330,c_883]) ).
tcf(c_204964,plain,
( epsilon_transitive(powerset(empty_set))
| ~ ordinal(empty_set) ),
inference(light_normalisation,[status(thm)],[c_204961,c_330]) ).
tcf(c_204965,plain,
epsilon_transitive(powerset(empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_204964,c_178087]) ).
tcf(c_204966,plain,
epsilon_transitive(set_union2(empty_set,powerset(empty_set))),
inference(forward_subsumption_resolution,[status(thm)],[c_204962,c_178087]) ).
tcf(c_204974,plain,
( ordinal(powerset(empty_set))
| ~ epsilon_connected(powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_204965,c_1086]) ).
tcf(c_205252,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK147(sK137,sK138)))
| ~ finite(set_difference(the_carrier(sK137),sK274(sK93(sK137,sK147(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192730,c_292]) ).
tcf(c_205253,plain,
( ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK147(sK137,sK138)))
| ~ proper_subset(set_difference(the_carrier(sK137),sK274(sK93(sK137,sK147(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192730,c_492]) ).
tcf(c_205265,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) = pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) ) ),
inference(superposition,[status(thm)],[c_105912,c_181312]) ).
tcf(c_205266,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) = pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) ) ),
inference(superposition,[status(thm)],[c_105926,c_181312]) ).
tcf(c_205271,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( pair_first(unordered_pair(unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))),unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)))) = unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181312]) ).
tcf(c_205272,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( pair_first(unordered_pair(unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))),unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)))) = unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181312]) ).
tcf(c_205273,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_205266,c_515]) ).
tcf(c_205276,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_205265,c_515]) ).
tcf(c_205322,plain,
( epsilon_connected(unordered_pair(empty_set,empty_set))
| ~ ordinal(empty_set) ),
inference(superposition,[status(thm)],[c_181193,c_884]) ).
tcf(c_205323,plain,
( epsilon_connected(set_union2(empty_set,powerset(empty_set)))
| ~ ordinal(empty_set) ),
inference(superposition,[status(thm)],[c_330,c_884]) ).
tcf(c_205324,plain,
( epsilon_connected(powerset(empty_set))
| ~ ordinal(empty_set) ),
inference(light_normalisation,[status(thm)],[c_205322,c_330]) ).
tcf(c_205325,plain,
epsilon_connected(powerset(empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_205324,c_178087]) ).
tcf(c_205326,plain,
epsilon_connected(set_union2(empty_set,powerset(empty_set))),
inference(forward_subsumption_resolution,[status(thm)],[c_205323,c_178087]) ).
tcf(c_205331,plain,
( ordinal(unordered_pair(empty_set,empty_set))
| ~ ordinal(empty_set) ),
inference(superposition,[status(thm)],[c_181193,c_885]) ).
tcf(c_205332,plain,
( ordinal(set_union2(empty_set,powerset(empty_set)))
| ~ ordinal(empty_set) ),
inference(superposition,[status(thm)],[c_330,c_885]) ).
tcf(c_205333,plain,
! [X0: $i] :
( sP30(set_union2(X0,unordered_pair(X0,X0)))
| ( sK266 = sK264 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_885,c_831]) ).
tcf(c_205334,plain,
! [X0: $i] :
( sP30(set_union2(X0,unordered_pair(X0,X0)))
| ( sK265 = sK267 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_885,c_828]) ).
tcf(c_205335,plain,
! [X0: $i] :
( sP30(set_union2(X0,unordered_pair(X0,X0)))
| ( sK265 = sK264 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_885,c_826]) ).
tcf(c_205336,plain,
! [X0: $i] :
( ordinal(sK267)
| sP30(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_885,c_827]) ).
tcf(c_205339,plain,
( ordinal(powerset(empty_set))
| ~ ordinal(empty_set) ),
inference(light_normalisation,[status(thm)],[c_205331,c_330]) ).
tcf(c_205340,plain,
ordinal(powerset(empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_205339,c_178087]) ).
tcf(c_205341,plain,
ordinal(set_union2(empty_set,powerset(empty_set))),
inference(forward_subsumption_resolution,[status(thm)],[c_205332,c_178087]) ).
tcf(c_205397,plain,
! [X0: $i,X1: $i] :
( finite(X1)
| ~ sP36(X0,X1)
| ~ finite(sK298(X0,X1)) ),
inference(superposition,[status(thm)],[c_917,c_292]) ).
tcf(c_205398,plain,
! [X0: $i,X1: $i] :
( ~ sP36(X0,X1)
| ~ proper_subset(sK298(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_917,c_492]) ).
tcf(c_205399,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK298(X0,unordered_pair(X1,X2)))
| ~ sP36(X0,unordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c_917,c_408]) ).
tcf(c_205400,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK298(X0,unordered_pair(X1,X2)))
| ~ sP36(X0,unordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c_917,c_407]) ).
tcf(c_205412,plain,
( sP30(powerset(empty_set))
| ( sK266 = sK264 ) ),
inference(superposition,[status(thm)],[c_205340,c_831]) ).
tcf(c_205413,plain,
( sP30(powerset(empty_set))
| ( sK265 = sK267 ) ),
inference(superposition,[status(thm)],[c_205340,c_828]) ).
tcf(c_205414,plain,
( sP30(powerset(empty_set))
| ( sK265 = sK264 ) ),
inference(superposition,[status(thm)],[c_205340,c_826]) ).
tcf(c_205415,plain,
( ordinal(sK267)
| sP30(powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_205340,c_827]) ).
tcf(c_205472,plain,
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| subset(sK138,sK135(sK302(sK137,sK138)))
| relation(sK136(sK302(sK137,sK138))) ),
inference(global_subsumption_just,[status(thm)],[c_197148,c_197148,c_201483]) ).
tcf(c_205473,plain,
( sP36(sK137,sK138)
| relation(sK136(sK302(sK137,sK138)))
| subset(sK138,sK135(sK302(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(renaming,[status(thm)],[c_205472]) ).
tcf(c_205482,plain,
( finite(sK138)
| sP36(sK137,sK138)
| relation(sK136(sK302(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(sK135(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_205473,c_292]) ).
tcf(c_205483,plain,
( sP36(sK137,sK138)
| relation(sK136(sK302(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(sK135(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_205473,c_492]) ).
tcf(c_205493,plain,
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| subset(sK138,sK135(sK302(sK137,sK138)))
| function(sK136(sK302(sK137,sK138))) ),
inference(global_subsumption_just,[status(thm)],[c_197859,c_197859,c_201483]) ).
tcf(c_205494,plain,
( sP36(sK137,sK138)
| function(sK136(sK302(sK137,sK138)))
| subset(sK138,sK135(sK302(sK137,sK138)))
| ~ topological_space(sK137) ),
inference(renaming,[status(thm)],[c_205493]) ).
tcf(c_205503,plain,
( finite(sK138)
| sP36(sK137,sK138)
| function(sK136(sK302(sK137,sK138)))
| ~ topological_space(sK137)
| ~ finite(sK135(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_205494,c_292]) ).
tcf(c_205504,plain,
( sP36(sK137,sK138)
| function(sK136(sK302(sK137,sK138)))
| ~ topological_space(sK137)
| ~ proper_subset(sK135(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_205494,c_492]) ).
tcf(c_205530,plain,
( finite(sK138)
| sP36(sK137,sK138)
| being_limit_ordinal(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,sK138))
| ~ finite(sK143(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_198637,c_292]) ).
tcf(c_205531,plain,
( sP36(sK137,sK138)
| being_limit_ordinal(sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(sK302(sK137,sK138))
| ~ proper_subset(sK143(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_198637,c_492]) ).
tcf(c_205651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_967,c_181316]) ).
tcf(c_205653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_967,c_181316]) ).
tcf(c_205656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X4,X4)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181316]) ).
tcf(c_205657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X4,X4)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181316]) ).
tcf(c_205658,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)) != unordered_pair(unordered_pair(empty_set,X2),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_181316]) ).
tcf(c_205659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X1,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(superposition,[status(thm)],[c_967,c_181316]) ).
tcf(c_205664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X4 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181316]) ).
tcf(c_205665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X4 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181316]) ).
tcf(c_205666,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_181316]) ).
tcf(c_205724,plain,
! [X0: $i,X1: $i] : relation_of2_as_subset(sK336(X0,X1),X0,X1),
inference(superposition,[status(thm)],[c_1056,c_994]) ).
tcf(c_205725,plain,
! [X0: $i,X1: $i] : relation_of2_as_subset(sK373(X0,X1),X0,X1),
inference(superposition,[status(thm)],[c_1282,c_994]) ).
tcf(c_205726,plain,
! [X0: $i,X1: $i] : relation_of2_as_subset(sK374(X0,X1),X0,X1),
inference(superposition,[status(thm)],[c_1285,c_994]) ).
tcf(c_205731,plain,
! [X0: $i,X1: $i] : relation_of2(sK322(X0,X1),X0,X1),
inference(superposition,[status(thm)],[c_996,c_995]) ).
tcf(c_205750,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(X0,set_difference(X0,X1)))
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_986,c_1013]) ).
tcf(c_205752,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(set_union2(X1,X0),set_difference(X1,X0)))
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_420,c_1013]) ).
tcf(c_205753,plain,
! [X0: $i] :
( finite(set_difference(empty_set,empty_set))
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_679,c_1013]) ).
tcf(c_205754,plain,
! [X0: $i] :
( finite(set_difference(X0,X0))
| ~ finite(empty_set) ),
inference(superposition,[status(thm)],[c_680,c_1013]) ).
tcf(c_205755,plain,
! [X0: $i] :
( finite(set_difference(X0,empty_set))
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_13761,c_1013]) ).
tcf(c_205756,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(X0,set_difference(X1,set_difference(X1,X0))))
| ~ finite(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_986,c_1013]) ).
tcf(c_205757,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(set_union2(X1,X0),set_difference(X1,set_difference(X0,X1))))
| ~ finite(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_179569,c_1013]) ).
tcf(c_205758,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(set_union2(X0,X1),set_difference(X1,X0)))
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_181191,c_1013]) ).
tcf(c_205759,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK270(set_difference(X1,set_difference(X1,X0)))) = set_difference(X1,set_difference(X1,X0)) )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_1013,c_848]) ).
tcf(c_205766,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(X0,set_difference(X1,X0)))
| ~ finite(X0) ),
inference(light_normalisation,[status(thm)],[c_205758,c_179569]) ).
tcf(c_205823,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| empty(sK340(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_183200,c_792]) ).
tcf(c_205824,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| empty(X0)
| in(sK340(X0),X0) ),
inference(superposition,[status(thm)],[c_183200,c_790]) ).
tcf(c_205825,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(powerset(cartesian_product2(X0,X1)))
| relation(sK340(powerset(cartesian_product2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_183200,c_764]) ).
tcf(c_205829,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(X0,sK340(powerset(the_carrier(sK137))))
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138))
| ~ closed_subset(sK340(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK340(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183200,c_177131]) ).
tcf(c_205830,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| epsilon_transitive(powerset(the_carrier(sK137)))
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK340(powerset(the_carrier(sK137))),X1)
| ~ in(X0,topstr_closure(sK137,sK340(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183200,c_48138]) ).
tcf(c_205831,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| sP36(sK137,sK340(powerset(the_carrier(sK137))))
| in(X0,sK302(sK137,sK340(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK340(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183200,c_47771]) ).
tcf(c_205832,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(sK340(powerset(the_carrier(sK137))),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK340(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK340(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183200,c_48368]) ).
tcf(c_205833,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK340(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK340(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183200,c_48332]) ).
tcf(c_205834,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(sK340(powerset(the_carrier(sK137))),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK340(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK340(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183200,c_48105]) ).
tcf(c_205835,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(X0,sK91(sK137,sK340(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK340(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183200,c_47795]) ).
tcf(c_205836,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| sP36(sK137,sK340(powerset(the_carrier(sK137))))
| ( sK303(sK137,sK340(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK340(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183200,c_47947]) ).
tcf(c_205837,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| sP36(sK137,sK340(powerset(the_carrier(sK137))))
| ( sK304(sK137,sK340(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK340(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183200,c_47911]) ).
tcf(c_205838,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| subset(sK340(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK340(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183200,c_48297]) ).
tcf(c_205839,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| epsilon_transitive(powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK340(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183200,c_48087]) ).
tcf(c_205840,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| subset(sK340(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK340(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183200,c_48070]) ).
tcf(c_205841,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK340(powerset(the_carrier(sK137)))) = X0 )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK340(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183200,c_47756]) ).
tcf(c_205842,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| ( sK92(sK137,sK340(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK340(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183200,c_48460]) ).
tcf(c_205843,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| sP36(sK137,sK340(powerset(the_carrier(sK137))))
| subset(sK340(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK340(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183200,c_47876]) ).
tcf(c_205844,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK340(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183200,c_48490]) ).
tcf(c_205845,plain,
! [X0: $i] :
( epsilon_transitive(powerset(the_carrier(sK137)))
| subset(sK340(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK340(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183200,c_48431]) ).
tcf(c_205846,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(empty_set,sK147(sK137,sK340(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK340(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183200,c_182438]) ).
tcf(c_205847,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| ( sK124(sK137,empty_set,sK340(powerset(the_carrier(sK137)))) = sK340(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK340(powerset(the_carrier(sK137))),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_183200,c_182437]) ).
tcf(c_205848,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(empty_set,sK123(sK137,sK340(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK340(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183200,c_182436]) ).
tcf(c_205849,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK340(powerset(the_carrier(sK137)))))) = topstr_closure(sK137,topstr_closure(sK137,sK340(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183200,c_176018]) ).
tcf(c_205850,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(sK138,sK123(sK137,sK340(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK340(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183200,c_176521]) ).
tcf(c_205851,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK138,sK340(powerset(the_carrier(sK137)))) = sK340(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK340(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183200,c_176408]) ).
tcf(c_205852,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(sK138,sK147(sK137,sK340(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK340(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183200,c_176286]) ).
tcf(c_205853,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| subset(sK138,sK340(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK340(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183200,c_175672]) ).
tcf(c_205854,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| closed_subset(sK340(powerset(the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ in(sK340(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183200,c_175482]) ).
tcf(c_205855,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| subset(sK138,sK340(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK340(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183200,c_175418]) ).
tcf(c_205856,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| ( sK340(powerset(the_carrier(sK137))) = topstr_closure(sK137,sK138) )
| ~ sP38(sK137,sK138,sK340(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183200,c_175209]) ).
tcf(c_205857,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK340(powerset(the_carrier(sK137))))) = topstr_closure(sK137,sK340(powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183200,c_48058]) ).
tcf(c_205858,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK340(powerset(the_carrier(sK137)))) = sK340(powerset(the_carrier(sK137))) )
| ~ closed_subset(sK340(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183200,c_48037]) ).
tcf(c_205859,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| open_subset(sK340(powerset(the_carrier(sK137))),sK137)
| ~ in(sK340(powerset(the_carrier(sK137))),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_183200,c_47852]) ).
tcf(c_205860,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(sK340(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK340(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183200,c_47840]) ).
tcf(c_205861,plain,
! [X0: $i] :
( epsilon_transitive(powerset(powerset(the_carrier(sK137))))
| sP34(sK340(powerset(powerset(the_carrier(sK137)))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK340(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK340(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183200,c_73951]) ).
tcf(c_205862,plain,
! [X0: $i] :
( epsilon_transitive(powerset(powerset(the_carrier(sK137))))
| in(set_difference(the_carrier(sK137),X0),sK340(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK340(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183200,c_73134]) ).
tcf(c_205863,plain,
! [X0: $i] :
( epsilon_transitive(powerset(powerset(the_carrier(sK137))))
| sP34(sK340(powerset(powerset(the_carrier(sK137)))),sK137)
| ( sK296(sK137,sK340(powerset(powerset(the_carrier(sK137)))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK340(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183200,c_48001]) ).
tcf(c_205864,plain,
( epsilon_transitive(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK340(powerset(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK340(powerset(powerset(the_carrier(sK137))))),sK137) ),
inference(superposition,[status(thm)],[c_183200,c_48252]) ).
tcf(c_205865,plain,
! [X0: $i] :
( epsilon_transitive(powerset(powerset(the_carrier(sK137))))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK340(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183200,c_48416]) ).
tcf(c_205866,plain,
( epsilon_transitive(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK340(powerset(powerset(the_carrier(sK137))))),sK137)
| in(sK145(sK137,sK340(powerset(powerset(the_carrier(sK137))))),sK340(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183200,c_48237]) ).
tcf(c_206103,plain,
! [X0: $i] :
( epsilon_connected(X0)
| empty(sK369(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_183201,c_792]) ).
tcf(c_206104,plain,
! [X0: $i] :
( epsilon_connected(X0)
| empty(X0)
| in(sK369(X0),X0) ),
inference(superposition,[status(thm)],[c_183201,c_790]) ).
tcf(c_206105,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(cartesian_product2(X0,X1)))
| relation(sK369(powerset(cartesian_product2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_183201,c_764]) ).
tcf(c_206109,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| in(X0,sK369(powerset(the_carrier(sK137))))
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138))
| ~ closed_subset(sK369(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK369(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183201,c_177131]) ).
tcf(c_206110,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| epsilon_connected(powerset(the_carrier(sK137)))
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK369(powerset(the_carrier(sK137))),X1)
| ~ in(X0,topstr_closure(sK137,sK369(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183201,c_48138]) ).
tcf(c_206111,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| sP36(sK137,sK369(powerset(the_carrier(sK137))))
| in(X0,sK302(sK137,sK369(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK369(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183201,c_47771]) ).
tcf(c_206112,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK369(powerset(the_carrier(sK137))),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK369(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK369(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183201,c_48368]) ).
tcf(c_206113,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK369(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK369(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183201,c_48332]) ).
tcf(c_206114,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK369(powerset(the_carrier(sK137))),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK369(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK369(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183201,c_48105]) ).
tcf(c_206115,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| in(X0,sK91(sK137,sK369(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK369(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183201,c_47795]) ).
tcf(c_206116,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| sP36(sK137,sK369(powerset(the_carrier(sK137))))
| ( sK303(sK137,sK369(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK369(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183201,c_47947]) ).
tcf(c_206117,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| sP36(sK137,sK369(powerset(the_carrier(sK137))))
| ( sK304(sK137,sK369(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK369(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183201,c_47911]) ).
tcf(c_206118,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| subset(sK369(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK369(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183201,c_48297]) ).
tcf(c_206119,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| epsilon_connected(powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK369(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183201,c_48087]) ).
tcf(c_206120,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| subset(sK369(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK369(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183201,c_48070]) ).
tcf(c_206121,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK369(powerset(the_carrier(sK137)))) = X0 )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK369(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183201,c_47756]) ).
tcf(c_206122,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| ( sK92(sK137,sK369(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK369(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183201,c_48460]) ).
tcf(c_206123,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| sP36(sK137,sK369(powerset(the_carrier(sK137))))
| subset(sK369(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK369(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183201,c_47876]) ).
tcf(c_206124,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK369(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183201,c_48490]) ).
tcf(c_206125,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| subset(sK369(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK369(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183201,c_48431]) ).
tcf(c_206126,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(empty_set,sK147(sK137,sK369(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK369(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183201,c_182438]) ).
tcf(c_206127,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( sK124(sK137,empty_set,sK369(powerset(the_carrier(sK137)))) = sK369(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK369(powerset(the_carrier(sK137))),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_183201,c_182437]) ).
tcf(c_206128,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(empty_set,sK123(sK137,sK369(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK369(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183201,c_182436]) ).
tcf(c_206129,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK369(powerset(the_carrier(sK137)))))) = topstr_closure(sK137,topstr_closure(sK137,sK369(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183201,c_176018]) ).
tcf(c_206130,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK138,sK123(sK137,sK369(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK369(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183201,c_176521]) ).
tcf(c_206131,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK138,sK369(powerset(the_carrier(sK137)))) = sK369(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK369(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183201,c_176408]) ).
tcf(c_206132,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK138,sK147(sK137,sK369(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK369(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183201,c_176286]) ).
tcf(c_206133,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| subset(sK138,sK369(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK369(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183201,c_175672]) ).
tcf(c_206134,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| closed_subset(sK369(powerset(the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ in(sK369(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183201,c_175482]) ).
tcf(c_206135,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| subset(sK138,sK369(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK369(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183201,c_175418]) ).
tcf(c_206136,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( sK369(powerset(the_carrier(sK137))) = topstr_closure(sK137,sK138) )
| ~ sP38(sK137,sK138,sK369(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183201,c_175209]) ).
tcf(c_206137,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK369(powerset(the_carrier(sK137))))) = topstr_closure(sK137,sK369(powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183201,c_48058]) ).
tcf(c_206138,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK369(powerset(the_carrier(sK137)))) = sK369(powerset(the_carrier(sK137))) )
| ~ closed_subset(sK369(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183201,c_48037]) ).
tcf(c_206139,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| open_subset(sK369(powerset(the_carrier(sK137))),sK137)
| ~ in(sK369(powerset(the_carrier(sK137))),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_183201,c_47852]) ).
tcf(c_206140,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK369(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK369(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183201,c_47840]) ).
tcf(c_206141,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| sP34(sK369(powerset(powerset(the_carrier(sK137)))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK369(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK369(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183201,c_73951]) ).
tcf(c_206142,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| in(set_difference(the_carrier(sK137),X0),sK369(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK369(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183201,c_73134]) ).
tcf(c_206143,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| sP34(sK369(powerset(powerset(the_carrier(sK137)))),sK137)
| ( sK296(sK137,sK369(powerset(powerset(the_carrier(sK137)))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK369(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183201,c_48001]) ).
tcf(c_206144,plain,
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK369(powerset(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK369(powerset(powerset(the_carrier(sK137))))),sK137) ),
inference(superposition,[status(thm)],[c_183201,c_48252]) ).
tcf(c_206145,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK369(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183201,c_48416]) ).
tcf(c_206146,plain,
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK369(powerset(powerset(the_carrier(sK137))))),sK137)
| in(sK145(sK137,sK369(powerset(powerset(the_carrier(sK137))))),sK369(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183201,c_48237]) ).
tcf(c_206532,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| ordinal(sK340(powerset(the_carrier(sK137))))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(sK340(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_205860,c_349]) ).
tcf(c_206533,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| ~ open_subset(sK340(powerset(the_carrier(sK137))),sK137)
| ~ in(the_topology(sK137),sK340(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_205860,c_546]) ).
tcf(c_206534,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(sK340(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_205860,c_542]) ).
tcf(c_206535,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| ~ empty(the_topology(sK137))
| ~ open_subset(sK340(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_205860,c_781]) ).
tcf(c_206536,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| element(sK340(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK340(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_205860,c_701]) ).
tcf(c_206631,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ordinal(sK369(powerset(the_carrier(sK137))))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(sK369(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_206140,c_349]) ).
tcf(c_206632,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ~ open_subset(sK369(powerset(the_carrier(sK137))),sK137)
| ~ in(the_topology(sK137),sK369(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_206140,c_546]) ).
tcf(c_206633,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(sK369(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_206140,c_542]) ).
tcf(c_206634,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ~ empty(the_topology(sK137))
| ~ open_subset(sK369(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_206140,c_781]) ).
tcf(c_206635,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| element(sK369(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK369(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_206140,c_701]) ).
tcf(c_206654,plain,
! [X0: $i] :
( in(X0,powerset(the_carrier(sK137)))
| ~ subset(X0,the_carrier(sK137)) ),
inference(global_subsumption_just,[status(thm)],[c_200918,c_196881]) ).
tcf(c_206684,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| in(sK53(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP2(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_96,c_201958]) ).
tcf(c_206685,plain,
( sP3(powerset(the_carrier(sK137)))
| sP3(sK91(sK137,sK62(powerset(the_carrier(sK137)))))
| in(sK62(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_120,c_201958]) ).
tcf(c_206688,plain,
( sP3(powerset(the_carrier(sK137)))
| empty(sK91(sK137,sK62(powerset(the_carrier(sK137)))))
| function(sK136(sK91(sK137,sK62(powerset(the_carrier(sK137))))))
| in(sK135(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_368,c_201958]) ).
tcf(c_206689,plain,
( sP3(powerset(the_carrier(sK137)))
| empty(sK91(sK137,sK62(powerset(the_carrier(sK137)))))
| relation(sK136(sK91(sK137,sK62(powerset(the_carrier(sK137))))))
| in(sK135(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_367,c_201958]) ).
tcf(c_206690,plain,
( sP3(powerset(the_carrier(sK137)))
| ordinal(sK91(sK137,sK62(powerset(the_carrier(sK137)))))
| in(sK139(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_383,c_201958]) ).
tcf(c_206691,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| disjoint(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0)
| in(sK142(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_416,c_201958]) ).
tcf(c_206692,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| disjoint(X0,sK91(sK137,sK62(powerset(the_carrier(sK137)))))
| in(sK142(X0,sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_417,c_201958]) ).
tcf(c_206693,plain,
( sP3(powerset(the_carrier(sK137)))
| being_limit_ordinal(sK91(sK137,sK62(powerset(the_carrier(sK137)))))
| in(sK143(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(sK91(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_422,c_201958]) ).
tcf(c_206694,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| in(sK156(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP18(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_552,c_201958]) ).
tcf(c_206695,plain,
( sP3(powerset(the_carrier(sK137)))
| relation(sK91(sK137,sK62(powerset(the_carrier(sK137)))))
| in(sK175(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_580,c_201958]) ).
tcf(c_206696,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK181(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ( sK91(sK137,sK62(powerset(the_carrier(sK137)))) = empty_set )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_598,c_201958]) ).
tcf(c_206697,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK185(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_603,c_201958]) ).
tcf(c_206699,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| subset(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0)
| in(sK202(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_662,c_201958]) ).
tcf(c_206700,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK274(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_858,c_201958]) ).
tcf(c_206703,plain,
( sP3(powerset(the_carrier(sK137)))
| epsilon_transitive(sK91(sK137,sK62(powerset(the_carrier(sK137)))))
| in(sK340(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1081,c_201958]) ).
tcf(c_206704,plain,
( sP3(powerset(the_carrier(sK137)))
| epsilon_connected(sK91(sK137,sK62(powerset(the_carrier(sK137)))))
| in(sK369(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1253,c_201958]) ).
tcf(c_206705,plain,
( sP3(powerset(the_carrier(sK137)))
| epsilon_connected(sK91(sK137,sK62(powerset(the_carrier(sK137)))))
| in(sK370(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1254,c_201958]) ).
tcf(c_206706,plain,
( sP3(powerset(the_carrier(sK137)))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK91(sK137,sK62(powerset(the_carrier(sK137))))),sK137)
| in(sK145(sK137,sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(sK91(sK137,sK62(powerset(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_190625,c_201958]) ).
tcf(c_206884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_967,c_181317]) ).
tcf(c_206886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_967,c_181317]) ).
tcf(c_206889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X4 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X4,X4)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181317]) ).
tcf(c_206890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X4 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X4,X4)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181317]) ).
tcf(c_206891,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)) != unordered_pair(unordered_pair(empty_set,X2),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_181317]) ).
tcf(c_206892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X1,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(superposition,[status(thm)],[c_967,c_181317]) ).
tcf(c_206897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181317]) ).
tcf(c_206898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181317]) ).
tcf(c_206899,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,empty_set),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_181317]) ).
tcf(c_207071,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ~ ordinal(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_658,c_1089]) ).
tcf(c_207072,plain,
( epsilon_transitive(sK68)
| ~ sP7
| ~ ordinal(powerset(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_134,c_1089]) ).
tcf(c_207073,plain,
( epsilon_transitive(sK138)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_376,c_1089]) ).
tcf(c_207074,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X1)
| ~ ordinal(X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_791,c_1089]) ).
tcf(c_207075,plain,
! [X0: $i] :
( empty(X0)
| epsilon_transitive(sK207(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_698,c_1089]) ).
tcf(c_207076,plain,
! [X0: $i] :
( epsilon_transitive(sK208(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_702,c_1089]) ).
tcf(c_207077,plain,
! [X0: $i] :
( empty(X0)
| epsilon_transitive(sK325(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_1004,c_1089]) ).
tcf(c_207084,plain,
( epsilon_transitive(sK319(sK320))
| ~ ordinal(powerset(the_carrier(sK320))) ),
inference(superposition,[status(thm)],[c_22154,c_1089]) ).
tcf(c_207085,plain,
( topological_space(sK137)
| epsilon_transitive(sK378(sK137))
| ~ sP42(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ in(the_carrier(sK137),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_47411,c_1089]) ).
tcf(c_207086,plain,
( epsilon_transitive(the_topology(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_47453,c_1089]) ).
tcf(c_207087,plain,
( epsilon_transitive(the_topology(sK291))
| ~ ordinal(powerset(powerset(the_carrier(sK291)))) ),
inference(superposition,[status(thm)],[c_47629,c_1089]) ).
tcf(c_207088,plain,
! [X0: $i] :
( epsilon_transitive(topstr_closure(sK137,X0))
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_1089]) ).
tcf(c_207089,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| epsilon_transitive(sK304(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_1089]) ).
tcf(c_207090,plain,
! [X0: $i] :
( epsilon_transitive(sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48126,c_1089]) ).
tcf(c_207091,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK146(sK137,X0,X1))
| in(X1,topstr_closure(sK137,X0))
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_1089]) ).
tcf(c_207092,plain,
! [X0: $i] :
( epsilon_transitive(sK145(sK137,X0))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_1089]) ).
tcf(c_207093,plain,
! [X0: $i] :
( epsilon_transitive(sK125(sK137,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48285,c_1089]) ).
tcf(c_207094,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK124(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_1089]) ).
tcf(c_207095,plain,
! [X0: $i] :
( epsilon_transitive(sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48389,c_1089]) ).
tcf(c_207096,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK92(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_1089]) ).
tcf(c_207097,plain,
! [X0: $i] :
( epsilon_transitive(topstr_closure(sK291,X0))
| ~ ordinal(powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(superposition,[status(thm)],[c_106105,c_1089]) ).
tcf(c_207099,plain,
! [X0: $i] :
( sP3(X0)
| epsilon_transitive(sK62(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_183186,c_1089]) ).
tcf(c_207102,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_183191,c_1089]) ).
tcf(c_207103,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(sK126(X0)) ),
inference(superposition,[status(thm)],[c_183192,c_1089]) ).
tcf(c_207105,plain,
! [X0: $i] :
( relation(X0)
| epsilon_transitive(sK175(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_183194,c_1089]) ).
tcf(c_207106,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ~ ordinal(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_183197,c_1089]) ).
tcf(c_207107,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X1)
| ~ ordinal(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_183198,c_1089]) ).
tcf(c_207108,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(sK323(X0)) ),
inference(superposition,[status(thm)],[c_183199,c_1089]) ).
tcf(c_207109,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| epsilon_transitive(sK340(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_183200,c_1089]) ).
tcf(c_207110,plain,
! [X0: $i] :
( epsilon_connected(X0)
| epsilon_transitive(sK369(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_183201,c_1089]) ).
tcf(c_207111,plain,
( epsilon_transitive(the_carrier(sK137))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(the_carrier(sK137),sK137) ),
inference(superposition,[status(thm)],[c_183204,c_1089]) ).
tcf(c_207112,plain,
! [X0: $i] :
( epsilon_transitive(union_of_subsets(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ ordinal(the_topology(sK137))
| ~ subset(X0,the_topology(sK137))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183205,c_1089]) ).
tcf(c_207113,plain,
( epsilon_transitive(sK138)
| ~ open_subset(sK138,sK137)
| ~ ordinal(the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_183208,c_1089]) ).
tcf(c_207115,plain,
! [X0: $i] :
( epsilon_transitive(topstr_closure(sK137,X0))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(topstr_closure(sK137,X0),sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_183212,c_1089]) ).
tcf(c_207116,plain,
( epsilon_transitive(sK208(powerset(the_carrier(sK137))))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(sK208(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183221,c_1089]) ).
tcf(c_207119,plain,
( epsilon_transitive(sK154(the_topology(sK137)))
| ~ open_subset(sK138,sK137)
| ~ ordinal(the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_189002,c_1089]) ).
tcf(c_207313,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| ~ ordinal(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_658,c_1090]) ).
tcf(c_207314,plain,
( epsilon_connected(sK68)
| ~ sP7
| ~ ordinal(powerset(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_134,c_1090]) ).
tcf(c_207315,plain,
( epsilon_connected(sK138)
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_376,c_1090]) ).
tcf(c_207316,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X1)
| ~ ordinal(X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_791,c_1090]) ).
tcf(c_207317,plain,
! [X0: $i] :
( empty(X0)
| epsilon_connected(sK207(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_698,c_1090]) ).
tcf(c_207318,plain,
! [X0: $i] :
( epsilon_connected(sK208(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_702,c_1090]) ).
tcf(c_207319,plain,
! [X0: $i] :
( empty(X0)
| epsilon_connected(sK325(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_1004,c_1090]) ).
tcf(c_207326,plain,
( epsilon_connected(sK319(sK320))
| ~ ordinal(powerset(the_carrier(sK320))) ),
inference(superposition,[status(thm)],[c_22154,c_1090]) ).
tcf(c_207327,plain,
( topological_space(sK137)
| epsilon_connected(sK378(sK137))
| ~ sP42(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ in(the_carrier(sK137),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_47411,c_1090]) ).
tcf(c_207328,plain,
( epsilon_connected(the_topology(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_47453,c_1090]) ).
tcf(c_207329,plain,
( epsilon_connected(the_topology(sK291))
| ~ ordinal(powerset(powerset(the_carrier(sK291)))) ),
inference(superposition,[status(thm)],[c_47629,c_1090]) ).
tcf(c_207330,plain,
! [X0: $i] :
( epsilon_connected(topstr_closure(sK137,X0))
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_1090]) ).
tcf(c_207331,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| epsilon_connected(sK304(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_1090]) ).
tcf(c_207332,plain,
! [X0: $i] :
( epsilon_connected(sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48126,c_1090]) ).
tcf(c_207333,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK146(sK137,X0,X1))
| in(X1,topstr_closure(sK137,X0))
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_1090]) ).
tcf(c_207334,plain,
! [X0: $i] :
( epsilon_connected(sK145(sK137,X0))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_1090]) ).
tcf(c_207335,plain,
! [X0: $i] :
( epsilon_connected(sK125(sK137,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48285,c_1090]) ).
tcf(c_207336,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK124(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_1090]) ).
tcf(c_207337,plain,
! [X0: $i] :
( epsilon_connected(sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48389,c_1090]) ).
tcf(c_207338,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK92(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_1090]) ).
tcf(c_207339,plain,
! [X0: $i] :
( epsilon_connected(topstr_closure(sK291,X0))
| ~ ordinal(powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(superposition,[status(thm)],[c_106105,c_1090]) ).
tcf(c_207341,plain,
! [X0: $i] :
( sP3(X0)
| epsilon_connected(sK62(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_183186,c_1090]) ).
tcf(c_207344,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_183191,c_1090]) ).
tcf(c_207345,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(sK126(X0)) ),
inference(superposition,[status(thm)],[c_183192,c_1090]) ).
tcf(c_207347,plain,
! [X0: $i] :
( relation(X0)
| epsilon_connected(sK175(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_183194,c_1090]) ).
tcf(c_207348,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| ~ ordinal(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_183197,c_1090]) ).
tcf(c_207349,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X1)
| ~ ordinal(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_183198,c_1090]) ).
tcf(c_207350,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(sK323(X0)) ),
inference(superposition,[status(thm)],[c_183199,c_1090]) ).
tcf(c_207351,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| epsilon_connected(sK340(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_183200,c_1090]) ).
tcf(c_207352,plain,
! [X0: $i] :
( epsilon_connected(X0)
| epsilon_connected(sK369(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_183201,c_1090]) ).
tcf(c_207353,plain,
( epsilon_connected(the_carrier(sK137))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(the_carrier(sK137),sK137) ),
inference(superposition,[status(thm)],[c_183204,c_1090]) ).
tcf(c_207354,plain,
! [X0: $i] :
( epsilon_connected(union_of_subsets(the_carrier(sK137),X0))
| ~ topological_space(sK137)
| ~ ordinal(the_topology(sK137))
| ~ subset(X0,the_topology(sK137))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183205,c_1090]) ).
tcf(c_207355,plain,
( epsilon_connected(sK138)
| ~ open_subset(sK138,sK137)
| ~ ordinal(the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_183208,c_1090]) ).
tcf(c_207357,plain,
! [X0: $i] :
( epsilon_connected(topstr_closure(sK137,X0))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(topstr_closure(sK137,X0),sK137)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_183212,c_1090]) ).
tcf(c_207358,plain,
( epsilon_connected(sK208(powerset(the_carrier(sK137))))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(sK208(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183221,c_1090]) ).
tcf(c_207361,plain,
( epsilon_connected(sK154(the_topology(sK137)))
| ~ open_subset(sK138,sK137)
| ~ ordinal(the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_189002,c_1090]) ).
tcf(c_207680,plain,
( ordinal(sK68)
| ~ sP7
| ~ ordinal(powerset(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_134,c_1091]) ).
tcf(c_207682,plain,
! [X0: $i,X1: $i] :
( ordinal(X1)
| ~ ordinal(X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_791,c_1091]) ).
tcf(c_207683,plain,
! [X0: $i] :
( empty(X0)
| ordinal(sK207(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_698,c_1091]) ).
tcf(c_207684,plain,
! [X0: $i] :
( ordinal(sK208(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_702,c_1091]) ).
tcf(c_207685,plain,
! [X0: $i] :
( empty(X0)
| ordinal(sK325(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_1004,c_1091]) ).
tcf(c_207692,plain,
( ordinal(sK319(sK320))
| ~ ordinal(powerset(the_carrier(sK320))) ),
inference(superposition,[status(thm)],[c_22154,c_1091]) ).
tcf(c_207693,plain,
( topological_space(sK137)
| ordinal(sK378(sK137))
| ~ sP42(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ in(the_carrier(sK137),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_47411,c_1091]) ).
tcf(c_207694,plain,
( ordinal(the_topology(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_47453,c_1091]) ).
tcf(c_207695,plain,
( ordinal(the_topology(sK291))
| ~ ordinal(powerset(powerset(the_carrier(sK291)))) ),
inference(superposition,[status(thm)],[c_47629,c_1091]) ).
tcf(c_207696,plain,
! [X0: $i] :
( ordinal(topstr_closure(sK137,X0))
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_1091]) ).
tcf(c_207697,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ordinal(sK304(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_1091]) ).
tcf(c_207698,plain,
! [X0: $i] :
( ordinal(sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48126,c_1091]) ).
tcf(c_207699,plain,
! [X0: $i,X1: $i] :
( ordinal(sK146(sK137,X0,X1))
| in(X1,topstr_closure(sK137,X0))
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ in(X1,the_carrier(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_1091]) ).
tcf(c_207700,plain,
! [X0: $i] :
( ordinal(sK145(sK137,X0))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_1091]) ).
tcf(c_207701,plain,
! [X0: $i] :
( ordinal(sK125(sK137,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48285,c_1091]) ).
tcf(c_207702,plain,
! [X0: $i,X1: $i] :
( ordinal(sK124(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_1091]) ).
tcf(c_207703,plain,
! [X0: $i] :
( ordinal(sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48389,c_1091]) ).
tcf(c_207704,plain,
! [X0: $i,X1: $i] :
( ordinal(sK92(sK137,X1,X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_1091]) ).
tcf(c_207705,plain,
! [X0: $i] :
( ordinal(topstr_closure(sK291,X0))
| ~ ordinal(powerset(the_carrier(sK291)))
| ~ element(X0,powerset(the_carrier(sK291))) ),
inference(superposition,[status(thm)],[c_106105,c_1091]) ).
tcf(c_207834,plain,
! [X0: $i] :
( epsilon_connected(X0)
| epsilon_connected(sK370(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_183202,c_1090]) ).
tcf(c_207835,plain,
! [X0: $i] :
( epsilon_connected(X0)
| epsilon_transitive(sK370(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_183202,c_1089]) ).
tcf(c_207836,plain,
! [X0: $i] :
( epsilon_connected(X0)
| empty(sK370(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_183202,c_792]) ).
tcf(c_207837,plain,
! [X0: $i] :
( epsilon_connected(X0)
| empty(X0)
| in(sK370(X0),X0) ),
inference(superposition,[status(thm)],[c_183202,c_790]) ).
tcf(c_207838,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(powerset(cartesian_product2(X0,X1)))
| relation(sK370(powerset(cartesian_product2(X0,X1)))) ),
inference(superposition,[status(thm)],[c_183202,c_764]) ).
tcf(c_207842,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| in(X0,sK370(powerset(the_carrier(sK137))))
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138))
| ~ closed_subset(sK370(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK370(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183202,c_177131]) ).
tcf(c_207843,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| epsilon_connected(powerset(the_carrier(sK137)))
| ~ closed_subset(X1,sK137)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ subset(sK370(powerset(the_carrier(sK137))),X1)
| ~ in(X0,topstr_closure(sK137,sK370(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183202,c_48138]) ).
tcf(c_207844,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| sP36(sK137,sK370(powerset(the_carrier(sK137))))
| in(X0,sK302(sK137,sK370(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK370(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183202,c_47771]) ).
tcf(c_207845,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK370(powerset(the_carrier(sK137))),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK370(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK370(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183202,c_48368]) ).
tcf(c_207846,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK370(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK370(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183202,c_48332]) ).
tcf(c_207847,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK370(powerset(the_carrier(sK137))),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ closed_subset(sK370(powerset(the_carrier(sK137))),sK137)
| ~ subset(X0,sK370(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183202,c_48105]) ).
tcf(c_207848,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| in(X0,sK91(sK137,sK370(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ in(X0,powerset(the_carrier(sK137)))
| ~ subset(sK370(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183202,c_47795]) ).
tcf(c_207849,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| sP36(sK137,sK370(powerset(the_carrier(sK137))))
| ( sK303(sK137,sK370(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK370(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183202,c_47947]) ).
tcf(c_207850,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| sP36(sK137,sK370(powerset(the_carrier(sK137))))
| ( sK304(sK137,sK370(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK370(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183202,c_47911]) ).
tcf(c_207851,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| subset(sK370(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK370(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183202,c_48297]) ).
tcf(c_207852,plain,
! [X0: $i] :
( closed_subset(X0,sK137)
| epsilon_connected(powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK370(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183202,c_48087]) ).
tcf(c_207853,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| subset(sK370(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK370(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183202,c_48070]) ).
tcf(c_207854,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK370(powerset(the_carrier(sK137)))) = X0 )
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP38(sK137,sK370(powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_183202,c_47756]) ).
tcf(c_207855,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| ( sK92(sK137,sK370(powerset(the_carrier(sK137))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK370(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183202,c_48460]) ).
tcf(c_207856,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| sP36(sK137,sK370(powerset(the_carrier(sK137))))
| subset(sK370(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK370(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183202,c_47876]) ).
tcf(c_207857,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK370(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183202,c_48490]) ).
tcf(c_207858,plain,
! [X0: $i] :
( epsilon_connected(powerset(the_carrier(sK137)))
| subset(sK370(powerset(the_carrier(sK137))),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK370(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_183202,c_48431]) ).
tcf(c_207859,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(empty_set,sK147(sK137,sK370(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK370(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183202,c_182438]) ).
tcf(c_207860,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( sK124(sK137,empty_set,sK370(powerset(the_carrier(sK137)))) = sK370(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK370(powerset(the_carrier(sK137))),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_183202,c_182437]) ).
tcf(c_207861,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(empty_set,sK123(sK137,sK370(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK370(powerset(the_carrier(sK137))),empty_set) ),
inference(superposition,[status(thm)],[c_183202,c_182436]) ).
tcf(c_207862,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK370(powerset(the_carrier(sK137)))))) = topstr_closure(sK137,topstr_closure(sK137,sK370(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183202,c_176018]) ).
tcf(c_207863,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK138,sK123(sK137,sK370(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK370(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183202,c_176521]) ).
tcf(c_207864,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( sK124(sK137,sK138,sK370(powerset(the_carrier(sK137)))) = sK370(powerset(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ in(sK370(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183202,c_176408]) ).
tcf(c_207865,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK138,sK147(sK137,sK370(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK370(powerset(the_carrier(sK137))),sK138) ),
inference(superposition,[status(thm)],[c_183202,c_176286]) ).
tcf(c_207866,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| subset(sK138,sK370(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK370(powerset(the_carrier(sK137))),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183202,c_175672]) ).
tcf(c_207867,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| closed_subset(sK370(powerset(the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ in(sK370(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183202,c_175482]) ).
tcf(c_207868,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| subset(sK138,sK370(powerset(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ in(sK370(powerset(the_carrier(sK137))),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_183202,c_175418]) ).
tcf(c_207869,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( sK370(powerset(the_carrier(sK137))) = topstr_closure(sK137,sK138) )
| ~ sP38(sK137,sK138,sK370(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183202,c_175209]) ).
tcf(c_207870,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK370(powerset(the_carrier(sK137))))) = topstr_closure(sK137,sK370(powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183202,c_48058]) ).
tcf(c_207871,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ( topstr_closure(sK137,sK370(powerset(the_carrier(sK137)))) = sK370(powerset(the_carrier(sK137))) )
| ~ closed_subset(sK370(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183202,c_48037]) ).
tcf(c_207872,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| open_subset(sK370(powerset(the_carrier(sK137))),sK137)
| ~ in(sK370(powerset(the_carrier(sK137))),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_183202,c_47852]) ).
tcf(c_207873,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK370(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK370(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_183202,c_47840]) ).
tcf(c_207874,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| sP34(sK370(powerset(powerset(the_carrier(sK137)))),sK137)
| in(set_difference(the_carrier(sK137),X0),sK370(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK370(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183202,c_73951]) ).
tcf(c_207875,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| in(set_difference(the_carrier(sK137),X0),sK370(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK370(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183202,c_73134]) ).
tcf(c_207876,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| sP34(sK370(powerset(powerset(the_carrier(sK137)))),sK137)
| ( sK296(sK137,sK370(powerset(powerset(the_carrier(sK137)))),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK295(sK137,sK370(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183202,c_48001]) ).
tcf(c_207877,plain,
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK370(powerset(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ closed_subset(sK145(sK137,sK370(powerset(powerset(the_carrier(sK137))))),sK137) ),
inference(superposition,[status(thm)],[c_183202,c_48252]) ).
tcf(c_207878,plain,
! [X0: $i] :
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK93(sK137,sK370(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_183202,c_48416]) ).
tcf(c_207879,plain,
( epsilon_connected(powerset(powerset(the_carrier(sK137))))
| closed_subset(meet_of_subsets(the_carrier(sK137),sK370(powerset(powerset(the_carrier(sK137))))),sK137)
| in(sK145(sK137,sK370(powerset(powerset(the_carrier(sK137))))),sK370(powerset(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_183202,c_48237]) ).
tcf(c_208304,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ sP20(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_646,c_183544]) ).
tcf(c_208305,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ sP20(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_968,c_183544]) ).
tcf(c_208306,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ sP20(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1166,c_183544]) ).
tcf(c_208307,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_184389,c_183544]) ).
tcf(c_208308,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_182983,c_183544]) ).
tcf(c_208439,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ordinal(sK370(powerset(the_carrier(sK137))))
| ~ ordinal(the_topology(sK137))
| ~ open_subset(sK370(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_207873,c_349]) ).
tcf(c_208440,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ~ open_subset(sK370(powerset(the_carrier(sK137))),sK137)
| ~ in(the_topology(sK137),sK370(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_207873,c_546]) ).
tcf(c_208441,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| in(sK154(the_topology(sK137)),the_topology(sK137))
| ~ open_subset(sK370(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_207873,c_542]) ).
tcf(c_208442,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ~ empty(the_topology(sK137))
| ~ open_subset(sK370(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_207873,c_781]) ).
tcf(c_208443,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| element(sK370(powerset(the_carrier(sK137))),the_topology(sK137))
| ~ open_subset(sK370(powerset(the_carrier(sK137))),sK137) ),
inference(superposition,[status(thm)],[c_207873,c_701]) ).
tcf(c_208470,plain,
! [X0: $i] :
( epsilon_transitive(sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_658,c_207090]) ).
tcf(c_208471,plain,
( epsilon_transitive(sK147(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_376,c_207090]) ).
tcf(c_208472,plain,
! [X0: $i] :
( epsilon_transitive(sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_791,c_207090]) ).
tcf(c_208473,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK147(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_207090]) ).
tcf(c_208474,plain,
( epsilon_transitive(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_702,c_207090]) ).
tcf(c_208475,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK147(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_207090]) ).
tcf(c_208478,plain,
( epsilon_transitive(sK147(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_13308,c_207090]) ).
tcf(c_208479,plain,
! [X0: $i] :
( epsilon_transitive(sK147(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_207090]) ).
tcf(c_208480,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| epsilon_transitive(sK147(sK137,sK304(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_207090]) ).
tcf(c_208481,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| epsilon_transitive(sK147(sK137,sK146(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_207090]) ).
tcf(c_208482,plain,
! [X0: $i] :
( epsilon_transitive(sK147(sK137,sK145(sK137,X0)))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_207090]) ).
tcf(c_208483,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK147(sK137,sK124(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_207090]) ).
tcf(c_208484,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK147(sK137,sK92(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_207090]) ).
tcf(c_208485,plain,
( epsilon_transitive(sK147(sK137,empty_set))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_182003,c_207090]) ).
tcf(c_208486,plain,
( sP3(powerset(the_carrier(sK137)))
| epsilon_transitive(sK147(sK137,sK62(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183186,c_207090]) ).
tcf(c_208487,plain,
( ordinal(powerset(the_carrier(sK137)))
| epsilon_transitive(sK147(sK137,sK139(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183193,c_207090]) ).
tcf(c_208488,plain,
( relation(powerset(the_carrier(sK137)))
| epsilon_transitive(sK147(sK137,sK175(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183194,c_207090]) ).
tcf(c_208489,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| epsilon_transitive(sK147(sK137,sK340(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183200,c_207090]) ).
tcf(c_208490,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| epsilon_transitive(sK147(sK137,sK369(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183201,c_207090]) ).
tcf(c_208491,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| epsilon_transitive(sK147(sK137,sK370(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183202,c_207090]) ).
tcf(c_208652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X4 )
| ( sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4) = X3 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181319]) ).
tcf(c_208653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X4 )
| ( sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4) = X3 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181319]) ).
tcf(c_208658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X4 )
| ( unordered_pair(unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))),unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181319]) ).
tcf(c_208659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X4 )
| ( unordered_pair(unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))),unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181319]) ).
tcf(c_208660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_967,c_181319]) ).
tcf(c_208665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK368(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X4 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181319]) ).
tcf(c_208666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK366(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X4 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181319]) ).
tcf(c_208667,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(unordered_pair(empty_set,X2),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_181319]) ).
tcf(c_208819,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(sK103(X0,X1))) = sK103(X0,X1) )
| ~ sP12(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_1163]) ).
tcf(c_208820,plain,
! [X0: $i] :
( sP13(X0)
| ( relation_inverse(relation_inverse(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_237,c_1163]) ).
tcf(c_208821,plain,
! [X0: $i] : relation_inverse(relation_inverse(sK122(X0))) = sK122(X0),
inference(superposition,[status(thm)],[c_256,c_1163]) ).
tcf(c_208822,plain,
! [X0: $i] : relation_inverse(relation_inverse(sK134(X0))) = sK134(X0),
inference(superposition,[status(thm)],[c_362,c_1163]) ).
tcf(c_208823,plain,
! [X0: $i] : relation_inverse(relation_inverse(identity_relation(X0))) = identity_relation(X0),
inference(superposition,[status(thm)],[c_1156,c_1163]) ).
tcf(c_208824,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(relation_dom_restriction(X0,X1))) = relation_dom_restriction(X0,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_767,c_1163]) ).
tcf(c_208825,plain,
relation_inverse(relation_inverse(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_596,c_1163]) ).
tcf(c_208826,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(X0))) = relation_dom(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_647,c_1163]) ).
tcf(c_208827,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(relation_rng_restriction(X1,X0))) = relation_rng_restriction(X1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_651,c_1163]) ).
tcf(c_208828,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(sK204(X0,X1))) = sK204(X0,X1) )
| ~ are_equipotent(X0,X1) ),
inference(superposition,[status(thm)],[c_105457,c_1163]) ).
tcf(c_208829,plain,
relation_inverse(relation_inverse(sK246)) = sK246,
inference(superposition,[status(thm)],[c_777,c_1163]) ).
tcf(c_208830,plain,
relation_inverse(relation_inverse(sK248)) = sK248,
inference(superposition,[status(thm)],[c_785,c_1163]) ).
tcf(c_208831,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK270(X0))) = sK270(X0) )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_846,c_1163]) ).
tcf(c_208832,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(X0))) = relation_rng(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_969,c_1163]) ).
tcf(c_208833,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(relation_restriction(X0,X1))) = relation_restriction(X0,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1045,c_1163]) ).
tcf(c_208834,plain,
! [X0: $i,X1: $i] : relation_inverse(relation_inverse(sK336(X0,X1))) = sK336(X0,X1),
inference(superposition,[status(thm)],[c_1057,c_1163]) ).
tcf(c_208835,plain,
! [X0: $i] : relation_inverse(relation_inverse(inclusion_relation(X0))) = inclusion_relation(X0),
inference(superposition,[status(thm)],[c_1146,c_1163]) ).
tcf(c_208836,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(X0))) = relation_inverse(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1168,c_1163]) ).
tcf(c_208837,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(X0))) = relation_inverse(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1167,c_1163]) ).
tcf(c_208838,plain,
relation_inverse(relation_inverse(sK361)) = sK361,
inference(superposition,[status(thm)],[c_1197,c_1163]) ).
tcf(c_208839,plain,
! [X0: $i,X1: $i] : relation_inverse(relation_inverse(sK373(X0,X1))) = sK373(X0,X1),
inference(superposition,[status(thm)],[c_1283,c_1163]) ).
tcf(c_208840,plain,
( ( relation_inverse(relation_inverse(sK91(sK137,sK138))) = sK91(sK137,sK138) )
| ( sK92(sK137,sK138,sK175(sK91(sK137,sK138))) = sK175(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178946,c_1163]) ).
tcf(c_208841,plain,
( sP36(sK137,sK138)
| ( relation_inverse(relation_inverse(sK302(sK137,sK138))) = sK302(sK137,sK138) )
| ( sK304(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178950,c_1163]) ).
tcf(c_208842,plain,
( sP36(sK137,sK138)
| ( relation_inverse(relation_inverse(sK302(sK137,sK138))) = sK302(sK137,sK138) )
| ( sK303(sK137,sK138,sK175(sK302(sK137,sK138))) = sK175(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_178949,c_1163]) ).
tcf(c_208843,plain,
! [X0: $i,X1: $i] : relation_inverse(relation_inverse(cartesian_product2(X0,X1))) = cartesian_product2(X0,X1),
inference(superposition,[status(thm)],[c_201062,c_1163]) ).
tcf(c_208904,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(function_inverse(X0))) = function_inverse(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1181,c_1163]) ).
tcf(c_208905,plain,
! [X0: $i] :
( well_founded_relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ well_ordering(function_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1181,c_593]) ).
tcf(c_208906,plain,
! [X0: $i] :
( connected(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ well_ordering(function_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1181,c_592]) ).
tcf(c_208907,plain,
! [X0: $i] :
( antisymmetric(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ well_ordering(function_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1181,c_591]) ).
tcf(c_208908,plain,
! [X0: $i] :
( transitive(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ well_ordering(function_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1181,c_590]) ).
tcf(c_208909,plain,
! [X0: $i] :
( reflexive(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ well_ordering(function_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1181,c_589]) ).
tcf(c_208987,plain,
! [X0: $i] :
( epsilon_transitive(sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_658,c_207095]) ).
tcf(c_208988,plain,
( epsilon_transitive(sK123(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_376,c_207095]) ).
tcf(c_208989,plain,
! [X0: $i] :
( epsilon_transitive(sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_791,c_207095]) ).
tcf(c_208990,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK123(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_207095]) ).
tcf(c_208991,plain,
( epsilon_transitive(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_702,c_207095]) ).
tcf(c_208992,plain,
( empty(the_carrier(sK137))
| epsilon_transitive(sK123(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_207095]) ).
tcf(c_208995,plain,
( epsilon_transitive(sK123(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_13308,c_207095]) ).
tcf(c_208996,plain,
! [X0: $i] :
( epsilon_transitive(sK123(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_207095]) ).
tcf(c_208997,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| epsilon_transitive(sK123(sK137,sK304(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_207095]) ).
tcf(c_208998,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| epsilon_transitive(sK123(sK137,sK146(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_207095]) ).
tcf(c_208999,plain,
! [X0: $i] :
( epsilon_transitive(sK123(sK137,sK145(sK137,X0)))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_207095]) ).
tcf(c_209000,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK123(sK137,sK124(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_207095]) ).
tcf(c_209001,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK123(sK137,sK92(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_207095]) ).
tcf(c_209002,plain,
( epsilon_transitive(sK123(sK137,empty_set))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_182003,c_207095]) ).
tcf(c_209003,plain,
( sP3(powerset(the_carrier(sK137)))
| epsilon_transitive(sK123(sK137,sK62(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183186,c_207095]) ).
tcf(c_209004,plain,
( ordinal(powerset(the_carrier(sK137)))
| epsilon_transitive(sK123(sK137,sK139(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183193,c_207095]) ).
tcf(c_209005,plain,
( relation(powerset(the_carrier(sK137)))
| epsilon_transitive(sK123(sK137,sK175(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183194,c_207095]) ).
tcf(c_209006,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| epsilon_transitive(sK123(sK137,sK340(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183200,c_207095]) ).
tcf(c_209007,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| epsilon_transitive(sK123(sK137,sK369(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183201,c_207095]) ).
tcf(c_209008,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| epsilon_transitive(sK123(sK137,sK370(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183202,c_207095]) ).
tcf(c_209216,plain,
! [X0: $i] :
( epsilon_connected(sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_658,c_207332]) ).
tcf(c_209217,plain,
( epsilon_connected(sK147(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_376,c_207332]) ).
tcf(c_209218,plain,
! [X0: $i] :
( epsilon_connected(sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_791,c_207332]) ).
tcf(c_209219,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK147(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_207332]) ).
tcf(c_209220,plain,
( epsilon_connected(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_702,c_207332]) ).
tcf(c_209221,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK147(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_207332]) ).
tcf(c_209224,plain,
( epsilon_connected(sK147(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_13308,c_207332]) ).
tcf(c_209225,plain,
! [X0: $i] :
( epsilon_connected(sK147(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_207332]) ).
tcf(c_209226,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| epsilon_connected(sK147(sK137,sK304(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_207332]) ).
tcf(c_209227,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| epsilon_connected(sK147(sK137,sK146(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_207332]) ).
tcf(c_209228,plain,
! [X0: $i] :
( epsilon_connected(sK147(sK137,sK145(sK137,X0)))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_207332]) ).
tcf(c_209229,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK147(sK137,sK124(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_207332]) ).
tcf(c_209230,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK147(sK137,sK92(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_207332]) ).
tcf(c_209231,plain,
( epsilon_connected(sK147(sK137,empty_set))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_182003,c_207332]) ).
tcf(c_209232,plain,
( sP3(powerset(the_carrier(sK137)))
| epsilon_connected(sK147(sK137,sK62(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183186,c_207332]) ).
tcf(c_209233,plain,
( ordinal(powerset(the_carrier(sK137)))
| epsilon_connected(sK147(sK137,sK139(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183193,c_207332]) ).
tcf(c_209234,plain,
( relation(powerset(the_carrier(sK137)))
| epsilon_connected(sK147(sK137,sK175(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183194,c_207332]) ).
tcf(c_209235,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| epsilon_connected(sK147(sK137,sK340(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183200,c_207332]) ).
tcf(c_209236,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| epsilon_connected(sK147(sK137,sK369(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183201,c_207332]) ).
tcf(c_209237,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| epsilon_connected(sK147(sK137,sK370(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183202,c_207332]) ).
tcf(c_209426,plain,
! [X0: $i] :
( epsilon_connected(sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_658,c_207337]) ).
tcf(c_209427,plain,
( epsilon_connected(sK123(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_376,c_207337]) ).
tcf(c_209428,plain,
! [X0: $i] :
( epsilon_connected(sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_791,c_207337]) ).
tcf(c_209429,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK123(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_207337]) ).
tcf(c_209430,plain,
( epsilon_connected(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_702,c_207337]) ).
tcf(c_209431,plain,
( empty(the_carrier(sK137))
| epsilon_connected(sK123(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_207337]) ).
tcf(c_209434,plain,
( epsilon_connected(sK123(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_13308,c_207337]) ).
tcf(c_209435,plain,
! [X0: $i] :
( epsilon_connected(sK123(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_207337]) ).
tcf(c_209436,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| epsilon_connected(sK123(sK137,sK304(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_207337]) ).
tcf(c_209437,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| epsilon_connected(sK123(sK137,sK146(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_207337]) ).
tcf(c_209438,plain,
! [X0: $i] :
( epsilon_connected(sK123(sK137,sK145(sK137,X0)))
| closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_207337]) ).
tcf(c_209439,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK123(sK137,sK124(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_207337]) ).
tcf(c_209440,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK123(sK137,sK92(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_207337]) ).
tcf(c_209441,plain,
( epsilon_connected(sK123(sK137,empty_set))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_182003,c_207337]) ).
tcf(c_209442,plain,
( sP3(powerset(the_carrier(sK137)))
| epsilon_connected(sK123(sK137,sK62(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183186,c_207337]) ).
tcf(c_209443,plain,
( ordinal(powerset(the_carrier(sK137)))
| epsilon_connected(sK123(sK137,sK139(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183193,c_207337]) ).
tcf(c_209444,plain,
( relation(powerset(the_carrier(sK137)))
| epsilon_connected(sK123(sK137,sK175(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183194,c_207337]) ).
tcf(c_209445,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| epsilon_connected(sK123(sK137,sK340(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183200,c_207337]) ).
tcf(c_209446,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| epsilon_connected(sK123(sK137,sK369(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183201,c_207337]) ).
tcf(c_209447,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| epsilon_connected(sK123(sK137,sK370(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183202,c_207337]) ).
tcf(c_209630,plain,
! [X0: $i] :
( ordinal(sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_658,c_207698]) ).
tcf(c_209631,plain,
( ordinal(sK147(sK137,sK138))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_376,c_207698]) ).
tcf(c_209632,plain,
! [X0: $i] :
( ordinal(sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ empty(X0)
| ~ empty(powerset(the_carrier(sK137)))
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_791,c_207698]) ).
tcf(c_209633,plain,
( empty(the_carrier(sK137))
| ordinal(sK147(sK137,sK207(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_698,c_207698]) ).
tcf(c_209634,plain,
( ordinal(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_702,c_207698]) ).
tcf(c_209635,plain,
( empty(the_carrier(sK137))
| ordinal(sK147(sK137,sK325(the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1004,c_207698]) ).
tcf(c_209638,plain,
( ordinal(sK147(sK137,the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_13308,c_207698]) ).
tcf(c_209639,plain,
! [X0: $i] :
( ordinal(sK147(sK137,topstr_closure(sK137,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_106061,c_207698]) ).
tcf(c_209640,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X1)
| ordinal(sK147(sK137,sK304(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK302(sK137,X1)) ),
inference(superposition,[status(thm)],[c_47929,c_207698]) ).
tcf(c_209641,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK137,X0))
| ordinal(sK147(sK137,sK146(sK137,X0,X1)))
| ~ topological_space(sK137)
| ~ in(X1,the_carrier(sK137))
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_48162,c_207698]) ).
tcf(c_209642,plain,
! [X0: $i] :
( closed_subset(meet_of_subsets(the_carrier(sK137),X0),sK137)
| ordinal(sK147(sK137,sK145(sK137,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_48222,c_207698]) ).
tcf(c_209643,plain,
! [X0: $i,X1: $i] :
( ordinal(sK147(sK137,sK124(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48350,c_207698]) ).
tcf(c_209644,plain,
! [X0: $i,X1: $i] :
( ordinal(sK147(sK137,sK92(sK137,X1,X0)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137))))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,sK91(sK137,X1)) ),
inference(superposition,[status(thm)],[c_48475,c_207698]) ).
tcf(c_209645,plain,
( ordinal(sK147(sK137,empty_set))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_182003,c_207698]) ).
tcf(c_209646,plain,
( sP3(powerset(the_carrier(sK137)))
| ordinal(sK147(sK137,sK62(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183186,c_207698]) ).
tcf(c_209647,plain,
( ordinal(powerset(the_carrier(sK137)))
| ordinal(sK147(sK137,sK139(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183193,c_207698]) ).
tcf(c_209648,plain,
( relation(powerset(the_carrier(sK137)))
| ordinal(sK147(sK137,sK175(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183194,c_207698]) ).
tcf(c_209649,plain,
( epsilon_transitive(powerset(the_carrier(sK137)))
| ordinal(sK147(sK137,sK340(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183200,c_207698]) ).
tcf(c_209650,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ordinal(sK147(sK137,sK369(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183201,c_207698]) ).
tcf(c_209651,plain,
( epsilon_connected(powerset(the_carrier(sK137)))
| ordinal(sK147(sK137,sK370(powerset(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_183202,c_207698]) ).
tcf(c_210004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X4 )
| ( sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4) = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181320]) ).
tcf(c_210005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X4 )
| ( sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X4) = X2 )
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181320]) ).
tcf(c_210010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))),unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181320]) ).
tcf(c_210011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))),unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181320]) ).
tcf(c_210012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X3)) ) ),
inference(superposition,[status(thm)],[c_967,c_181320]) ).
tcf(c_210017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ( unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK367(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_105912,c_181320]) ).
tcf(c_210018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X0 = X2 )
| ( unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)) = X3 )
| ( unordered_pair(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),unordered_pair(unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK365(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)))) != unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X4)) ) ),
inference(superposition,[status(thm)],[c_105926,c_181320]) ).
tcf(c_210019,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)) != unordered_pair(unordered_pair(empty_set,X2),powerset(empty_set)) ) ),
inference(superposition,[status(thm)],[c_330,c_181320]) ).
fof(f1075,definition,
! [X2,X4,X1] :
( ~ sP0(X2,X4,X1)
| ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f1076,definition,
! [X0,X1,X9] :
( ~ sP1(X0,X1,X9)
| ! [X10,X11] :
( in(ordered_pair(X10,X11),X9)
<=> ( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& in(X10,X0) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f1077,definition,
! [X0,X1] :
( ~ sP2(X0,X1)
| ? [X2,X3,X4] :
( sP0(X2,X4,X1)
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f1078,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| ? [X9] :
( sP1(X0,X1,X9)
& function(X9)
& relation(X9) ) ),
inference(definition_folding,[],[f585,f1077,f1076,f1075]) ).
fof(f1079,definition,
! [X0] :
( ~ sP3(X0)
| ? [X4] :
( ! [X5,X6] :
( in(ordered_pair(X5,X6),X4)
<=> ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& function(X4)
& relation(X4) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f1080,plain,
! [X0] :
( ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 )
| sP3(X0) ),
inference(definition_folding,[],[f587,f1079]) ).
fof(f1081,definition,
! [X10] :
( ~ sP4(X10)
| ? [X15] :
( element(X15,powerset(powerset(X10)))
& ! [X16] :
( ? [X17] :
( subset(X16,X17)
& in(X17,X15)
& X16 != X17 )
| ~ in(X16,X15) )
& empty_set != X15 ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f1082,definition,
! [X3] :
( ~ sP5(X3)
| ? [X7] :
( element(X7,powerset(powerset(succ(X3))))
& ! [X8] :
( ? [X9] :
( subset(X8,X9)
& in(X9,X7)
& X8 != X9 )
| ~ in(X8,X7) )
& X7 != empty_set ) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f1083,definition,
( ~ sP6
| ? [X10] :
( ordinal(X10)
& ! [X11] :
( ~ ordinal(X11)
| ~ in(X11,X10)
| ~ in(X11,omega)
| ! [X12] :
( ~ element(X12,powerset(powerset(X11)))
| ? [X13] :
( ! [X14] :
( ~ subset(X13,X14)
| ~ in(X14,X12)
| X13 = X14 )
& in(X13,X12) )
| empty_set = X12 ) )
& being_limit_ordinal(X10)
& in(X10,omega)
& sP4(X10)
& empty_set != X10 ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f1084,definition,
( ~ sP7
| ( in(empty_set,omega)
& ? [X0] :
( element(X0,powerset(powerset(empty_set)))
& ! [X1] :
( ? [X2] :
( subset(X1,X2)
& in(X2,X0)
& X1 != X2 )
| ~ in(X1,X0) )
& X0 != empty_set ) ) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f1085,definition,
( ~ sP8
| ? [X3] :
( ordinal(X3)
& ( ~ in(X3,omega)
| ! [X4] :
( ~ element(X4,powerset(powerset(X3)))
| ? [X5] :
( ! [X6] :
( ~ subset(X5,X6)
| ~ in(X6,X4)
| X6 = X5 )
& in(X5,X4) )
| empty_set = X4 ) )
& in(succ(X3),omega)
& sP5(X3) ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f1086,plain,
( sP6
| sP8
| sP7
| ! [X18] :
( ~ ordinal(X18)
| ~ in(X18,omega)
| ! [X19] :
( ~ element(X19,powerset(powerset(X18)))
| ? [X20] :
( ! [X21] :
( ~ subset(X20,X21)
| ~ in(X21,X19)
| X20 = X21 )
& in(X20,X19) )
| empty_set = X19 ) ) ),
inference(definition_folding,[],[f591,f1085,f1084,f1083,f1082,f1081]) ).
fof(f1087,definition,
! [X0,X2] :
( sP9(X0,X2)
<=> ( ? [X3] :
( ( ~ in(X3,omega)
| ! [X4] :
( ~ element(X4,powerset(powerset(X3)))
| ? [X5] :
( ! [X6] :
( ~ subset(X5,X6)
| ~ in(X6,X4)
| X6 = X5 )
& in(X5,X4) )
| empty_set = X4 ) )
& X2 = X3
& ordinal(X3) )
& in(X2,succ(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f1088,definition,
! [X0] :
( ~ sP10(X0)
| ? [X1] :
! [X2] :
( in(X2,X1)
<=> sP9(X0,X2) ) ),
introduced(definition,[new_symbols(definition,[sP10])],[predicate_definition_introduction]) ).
fof(f1089,plain,
! [X0] :
( ~ ordinal(X0)
| sP10(X0) ),
inference(definition_folding,[],[f597,f1088,f1087]) ).
fof(f1090,definition,
! [X0,X1] :
( ~ sP11(X0,X1)
| ? [X2,X3,X4] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 ) ),
introduced(definition,[new_symbols(definition,[sP11])],[predicate_definition_introduction]) ).
fof(f1091,definition,
! [X0,X1] :
( ~ sP12(X0,X1)
| ? [X13] :
( ! [X14] :
( ~ in(X14,X0)
| ? [X15] :
( ! [X16] :
( ~ in(X16,X15)
| in(ordered_pair(apply(X13,X14),X16),X1) )
& in(apply(X13,X14),X15)
& X14 = X15 ) )
& relation_dom(X13) = X0
& function(X13)
& relation(X13) ) ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f1092,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ? [X9] :
( ! [X10,X11] :
( ? [X12] :
( in(X12,X11)
& ~ in(ordered_pair(X10,X12),X1) )
| ~ in(X10,X11)
| X9 != X11 )
& in(X9,X0) )
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(definition_folding,[],[f610,f1091,f1090]) ).
fof(f1093,definition,
! [X0] :
( ~ sP13(X0)
| ? [X1,X2,X3] :
( X3 = singleton(X1)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 ) ),
introduced(definition,[new_symbols(definition,[sP13])],[predicate_definition_introduction]) ).
fof(f1094,plain,
! [X0] :
( ? [X4] :
( ! [X5] : singleton(X4) != X5
& in(X4,X0) )
| sP13(X0)
| ? [X6] :
( ! [X7] :
( ~ in(X7,X0)
| singleton(X7) = apply(X6,X7) )
& relation_dom(X6) = X0
& function(X6)
& relation(X6) ) ),
inference(definition_folding,[],[f612,f1093]) ).
fof(f1095,definition,
! [X0] :
( ~ sP14(X0)
| ? [X5] :
( element(X5,powerset(powerset(X0)))
& ! [X6] :
( ? [X7] :
( subset(X6,X7)
& in(X7,X5)
& X6 != X7 )
| ~ in(X6,X5) )
& X5 != empty_set ) ),
introduced(definition,[new_symbols(definition,[sP14])],[predicate_definition_introduction]) ).
fof(f1096,definition,
( ~ sP15
| ? [X0] :
( ordinal(X0)
& ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| ~ in(X1,omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(X1)))
| ? [X3] :
( ! [X4] :
( ~ subset(X3,X4)
| ~ in(X4,X2)
| X4 = X3 )
& in(X3,X2) )
| empty_set = X2 ) )
& in(X0,omega)
& sP14(X0) ) ),
introduced(definition,[new_symbols(definition,[sP15])],[predicate_definition_introduction]) ).
fof(f1097,plain,
( sP15
| ! [X8] :
( ~ ordinal(X8)
| ~ in(X8,omega)
| ! [X9] :
( ~ element(X9,powerset(powerset(X8)))
| ? [X10] :
( ! [X11] :
( ~ subset(X10,X11)
| ~ in(X11,X9)
| X10 = X11 )
& in(X10,X9) )
| empty_set = X9 ) ) ),
inference(definition_folding,[],[f614,f1096,f1095]) ).
fof(f1098,definition,
! [X0,X2,X3,X1] :
( sP16(X0,X2,X3,X1)
<=> ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])],[predicate_definition_introduction]) ).
fof(f1099,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( sP16(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ),
inference(definition_folding,[],[f774,f1098]) ).
fof(f1100,definition,
! [X2,X4,X1] :
( ~ sP17(X2,X4,X1)
| ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 ) ),
introduced(definition,[new_symbols(definition,[sP17])],[predicate_definition_introduction]) ).
fof(f1101,definition,
! [X0,X1] :
( ~ sP18(X0,X1)
| ? [X2,X3,X4] :
( sP17(X2,X4,X1)
& in(X2,X0)
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 ) ),
introduced(definition,[new_symbols(definition,[sP18])],[predicate_definition_introduction]) ).
fof(f1102,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X10,X13),X1) )
& in(X10,X12)
& X11 = X12 )
& in(X11,X0)
& in(X11,X0) ) ) ),
inference(definition_folding,[],[f825,f1101,f1100]) ).
fof(f1103,definition,
! [X4,X0] :
( ~ sP19(X4,X0)
| ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 ) ),
introduced(definition,[new_symbols(definition,[sP19])],[predicate_definition_introduction]) ).
fof(f1104,definition,
! [X0] :
( ~ sP20(X0)
| ? [X2,X3,X4] :
( sP19(X4,X0)
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3
& X3 != X4 ) ),
introduced(definition,[new_symbols(definition,[sP20])],[predicate_definition_introduction]) ).
fof(f1105,plain,
! [X0,X1] :
( sP20(X0)
| ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) ) ),
inference(definition_folding,[],[f837,f1104,f1103]) ).
fof(f1106,definition,
! [X0] :
( ~ sP21(X0)
| ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 ) ),
introduced(definition,[new_symbols(definition,[sP21])],[predicate_definition_introduction]) ).
fof(f1107,plain,
! [X0] :
( sP21(X0)
| ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( singleton(X6) = X5
& in(X6,X0)
& in(X6,X0) ) ) ),
inference(definition_folding,[],[f839,f1106]) ).
fof(f1108,definition,
! [X1,X2] :
( ~ sP22(X1,X2)
| ? [X3,X4,X5] :
( ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& X5 = ordered_pair(X8,X9) )
& X3 = X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& X4 = ordered_pair(X6,X7) )
& X3 = X4
& X4 != X5 ) ),
introduced(definition,[new_symbols(definition,[sP22])],[predicate_definition_introduction]) ).
fof(f1109,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP22(X1,X2)
| ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) ) ),
inference(definition_folding,[],[f869,f1108]) ).
fof(f1110,definition,
! [X5,X0,X1] :
( ~ sP23(X5,X0,X1)
| ? [X10,X11] :
( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& ordered_pair(X10,X11) = X5 ) ),
introduced(definition,[new_symbols(definition,[sP23])],[predicate_definition_introduction]) ).
fof(f1111,definition,
! [X4,X0,X1] :
( ~ sP24(X4,X0,X1)
| ? [X6,X7] :
( ? [X8] :
( ! [X9] :
( ~ in(X9,X8)
| in(ordered_pair(X7,X9),X1) )
& in(X7,X8)
& X6 = X8 )
& in(X6,X0)
& ordered_pair(X6,X7) = X4 ) ),
introduced(definition,[new_symbols(definition,[sP24])],[predicate_definition_introduction]) ).
fof(f1112,definition,
! [X2,X0,X15,X1] :
( sP25(X2,X0,X15,X1)
<=> ? [X16] :
( ? [X17,X18] :
( ? [X19] :
( ! [X20] :
( ~ in(X20,X19)
| in(ordered_pair(X18,X20),X1) )
& in(X18,X19)
& X17 = X19 )
& in(X17,X0)
& ordered_pair(X17,X18) = X15 )
& X15 = X16
& in(X16,cartesian_product2(X0,X2)) ) ),
introduced(definition,[new_symbols(definition,[sP25])],[predicate_definition_introduction]) ).
fof(f1113,definition,
! [X1,X0,X2] :
( ~ sP26(X1,X0,X2)
| ? [X14] :
! [X15] :
( in(X15,X14)
<=> sP25(X2,X0,X15,X1) ) ),
introduced(definition,[new_symbols(definition,[sP26])],[predicate_definition_introduction]) ).
fof(f1114,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2] :
( ? [X3,X4,X5] :
( sP23(X5,X0,X1)
& X3 = X5
& sP24(X4,X0,X1)
& X3 = X4
& X4 != X5 )
| sP26(X1,X0,X2) ) ),
inference(definition_folding,[],[f871,f1113,f1112,f1111,f1110]) ).
fof(f1115,definition,
( ~ sP27
| ? [X1,X2,X3] :
( ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2
& X2 != X3 ) ),
introduced(definition,[new_symbols(definition,[sP27])],[predicate_definition_introduction]) ).
fof(f1116,plain,
! [X0] :
( sP27
| ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( ordinal(X5)
& X5 = X6
& in(X6,X0) ) ) ),
inference(definition_folding,[],[f889,f1115]) ).
fof(f1117,definition,
! [X3] :
( ~ sP28(X3)
| ? [X8] :
( ( ~ in(X8,omega)
| ! [X9] :
( ~ element(X9,powerset(powerset(X8)))
| ? [X10] :
( ! [X11] :
( ~ subset(X10,X11)
| ~ in(X11,X9)
| X11 = X10 )
& in(X10,X9) )
| empty_set = X9 ) )
& X3 = X8
& ordinal(X8) ) ),
introduced(definition,[new_symbols(definition,[sP28])],[predicate_definition_introduction]) ).
fof(f1118,definition,
! [X0,X13] :
( sP29(X0,X13)
<=> ? [X14] :
( ? [X15] :
( ( ~ in(X15,omega)
| ! [X16] :
( ~ element(X16,powerset(powerset(X15)))
| ? [X17] :
( ! [X18] :
( ~ subset(X17,X18)
| ~ in(X18,X16)
| X17 = X18 )
& in(X17,X16) )
| empty_set = X16 ) )
& X13 = X15
& ordinal(X15) )
& X13 = X14
& in(X14,succ(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP29])],[predicate_definition_introduction]) ).
fof(f1119,definition,
! [X0] :
( ~ sP30(X0)
| ? [X12] :
! [X13] :
( in(X13,X12)
<=> sP29(X0,X13) ) ),
introduced(definition,[new_symbols(definition,[sP30])],[predicate_definition_introduction]) ).
fof(f1120,plain,
! [X0] :
( ~ ordinal(X0)
| ? [X1,X2,X3] :
( sP28(X3)
& X1 = X3
& ? [X4] :
( ( ~ in(X4,omega)
| ! [X5] :
( ~ element(X5,powerset(powerset(X4)))
| ? [X6] :
( ! [X7] :
( ~ subset(X6,X7)
| ~ in(X7,X5)
| X7 = X6 )
& in(X6,X5) )
| empty_set = X5 ) )
& X2 = X4
& ordinal(X4) )
& X1 = X2
& X2 != X3 )
| sP30(X0) ),
inference(definition_folding,[],[f897,f1119,f1118,f1117]) ).
fof(f1121,definition,
! [X4,X0] :
( ~ sP31(X4,X0)
| ? [X6] :
( in(X6,X0)
& X4 = X6
& ordinal(X6) ) ),
introduced(definition,[new_symbols(definition,[sP31])],[predicate_definition_introduction]) ).
fof(f1122,definition,
! [X0] :
( ~ sP32(X0)
| ? [X2,X3,X4] :
( sP31(X4,X0)
& X2 = X4
& ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& X2 = X3
& X3 != X4 ) ),
introduced(definition,[new_symbols(definition,[sP32])],[predicate_definition_introduction]) ).
fof(f1123,plain,
! [X0,X1] :
( ~ ordinal(X1)
| sP32(X0)
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( in(X10,X0)
& X8 = X10
& ordinal(X10) )
& X8 = X9
& in(X9,succ(X1)) ) ) ),
inference(definition_folding,[],[f902,f1122,f1121]) ).
fof(f1124,definition,
! [X1,X0] :
( ~ sP33(X1,X0)
| ? [X2,X3,X4] :
( ? [X6] :
( X4 = set_difference(X6,singleton(X0))
& in(X6,X1) )
& X2 = X4
& ? [X5] :
( X3 = set_difference(X5,singleton(X0))
& in(X5,X1) )
& X2 = X3
& X3 != X4 ) ),
introduced(definition,[new_symbols(definition,[sP33])],[predicate_definition_introduction]) ).
fof(f1125,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP33(X1,X0)
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( set_difference(X10,singleton(X0)) = X8
& in(X10,X1) )
& X8 = X9
& in(X9,powerset(X0)) ) ) ),
inference(definition_folding,[],[f904,f1124]) ).
fof(f1126,definition,
! [X1,X0] :
( ~ sP34(X1,X0)
| ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3
& X3 != X4 ) ),
introduced(definition,[new_symbols(definition,[sP34])],[predicate_definition_introduction]) ).
fof(f1127,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP34(X1,X0)
| ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) ) ),
inference(definition_folding,[],[f912,f1126]) ).
fof(f1128,definition,
! [X0,X4,X1] :
( ~ sP35(X0,X4,X1)
| ? [X6] :
( subset(X1,X4)
& closed_subset(X6,X0)
& X6 = X4
& element(X6,powerset(the_carrier(X0))) ) ),
introduced(definition,[new_symbols(definition,[sP35])],[predicate_definition_introduction]) ).
fof(f1129,definition,
! [X0,X1] :
( ~ sP36(X0,X1)
| ? [X2,X3,X4] :
( sP35(X0,X4,X1)
& X2 = X4
& ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X5 = X3
& element(X5,powerset(the_carrier(X0))) )
& X2 = X3
& X3 != X4 ) ),
introduced(definition,[new_symbols(definition,[sP36])],[predicate_definition_introduction]) ).
fof(f1130,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP36(X0,X1)
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) ) ),
inference(definition_folding,[],[f914,f1129,f1128]) ).
fof(f1131,definition,
! [X1,X2] :
( ~ sP37(X1,X2)
| ? [X3,X4,X5] :
( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4
& X4 != X5 ) ),
introduced(definition,[new_symbols(definition,[sP37])],[predicate_definition_introduction]) ).
fof(f1132,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP37(X1,X2)
| ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(relation_image(X2,X7),X1)
& X7 = X8
& in(X8,powerset(relation_dom(X2))) ) ) ),
inference(definition_folding,[],[f922,f1131]) ).
fof(f1133,definition,
! [X0,X1,X2] :
( sP38(X0,X1,X2)
<=> ! [X3] :
( ~ in(X3,the_carrier(X0))
| ( in(X3,X2)
<=> ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])],[predicate_definition_introduction]) ).
fof(f1134,definition,
! [X2,X1,X0] :
( ~ sP39(X2,X1,X0)
| ( X2 = topstr_closure(X0,X1)
<=> sP38(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sP39])],[predicate_definition_introduction]) ).
fof(f1135,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| sP39(X2,X1,X0) ) ) ),
inference(definition_folding,[],[f1005,f1134,f1133]) ).
fof(f1136,definition,
! [X2,X0,X1] :
( sP40(X2,X0,X1)
<=> ( ! [X3,X4] :
( in(ordered_pair(X3,X4),X0)
<=> ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_dom(X2) = relation_field(X0) ) ),
introduced(definition,[new_symbols(definition,[sP40])],[predicate_definition_introduction]) ).
fof(f1137,definition,
! [X1,X0,X2] :
( ~ sP41(X1,X0,X2)
| ( relation_isomorphism(X0,X1,X2)
<=> sP40(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP41])],[predicate_definition_introduction]) ).
fof(f1138,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| sP41(X1,X0,X2) ) ) ),
inference(definition_folding,[],[f1026,f1137,f1136]) ).
fof(f1139,definition,
! [X0] :
( sP42(X0)
<=> ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,the_topology(X0))
| ~ in(X2,the_topology(X0))
| in(subset_intersection2(the_carrier(X0),X2,X3),the_topology(X0)) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])],[predicate_definition_introduction]) ).
fof(f1140,plain,
! [X0] :
( ~ top_str(X0)
| ( topological_space(X0)
<=> ( sP42(X0)
& ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ subset(X1,the_topology(X0))
| in(union_of_subsets(the_carrier(X0),X1),the_topology(X0)) )
& in(the_carrier(X0),the_topology(X0)) ) ) ),
inference(definition_folding,[],[f1058,f1139]) ).
fof(f1169,plain,
! [X2,X4,X1] :
( ~ sP0(X2,X4,X1)
| ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 ) ),
inference(nnf_transformation,[],[f1075]) ).
fof(f1170,plain,
! [X0,X1,X2] :
( ~ sP0(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ in(X4,X3)
| in(ordered_pair(X1,X4),X2) )
& in(X1,X3)
& X0 = X3 ) ),
inference(rectify,[],[f1169]) ).
fof(f1171,plain,
! [X0,X1,X2] :
( ~ sP0(X0,X1,X2)
| ( ! [X4] :
( ~ in(X4,sK59(X0,X1,X2))
| in(ordered_pair(X1,X4),X2) )
& in(X1,sK59(X0,X1,X2))
& sK59(X0,X1,X2) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(X3,sK59(X0,X1,X2))],[f1170]) ).
fof(f1174,plain,
! [X0] :
( ~ sP3(X0)
| ? [X4] :
( ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X4)
| ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& ( singleton(X5) != X6
| ~ in(X5,X0)
| ~ in(X5,X0)
| in(ordered_pair(X5,X6),X4) ) )
& function(X4)
& relation(X4) ) ),
inference(nnf_transformation,[],[f1079]) ).
fof(f1175,plain,
! [X0] :
( ~ sP3(X0)
| ? [X4] :
( ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X4)
| ( singleton(X5) = X6
& in(X5,X0)
& in(X5,X0) ) )
& ( singleton(X5) != X6
| ~ in(X5,X0)
| ~ in(X5,X0)
| in(ordered_pair(X5,X6),X4) ) )
& function(X4)
& relation(X4) ) ),
inference(flattening,[],[f1174]) ).
fof(f1176,plain,
! [X0] :
( ~ sP3(X0)
| ? [X1] :
( ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ( singleton(X2) = X3
& in(X2,X0)
& in(X2,X0) ) )
& ( singleton(X2) != X3
| ~ in(X2,X0)
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),X1) ) )
& function(X1)
& relation(X1) ) ),
inference(rectify,[],[f1175]) ).
fof(f1177,plain,
! [X0] :
( ~ sP3(X0)
| ( ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),sK61(X0))
| ( singleton(X2) = X3
& in(X2,X0)
& in(X2,X0) ) )
& ( singleton(X2) != X3
| ~ in(X2,X0)
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),sK61(X0)) ) )
& function(sK61(X0))
& relation(sK61(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(X1,sK61(X0))],[f1176]) ).
fof(f1192,plain,
! [X10] :
( ~ sP4(X10)
| ? [X15] :
( element(X15,powerset(powerset(X10)))
& ! [X16] :
( ? [X17] :
( subset(X16,X17)
& in(X17,X15)
& X16 != X17 )
| ~ in(X16,X15) )
& empty_set != X15 ) ),
inference(nnf_transformation,[],[f1081]) ).
fof(f1193,plain,
! [X0] :
( ~ sP4(X0)
| ? [X1] :
( element(X1,powerset(powerset(X0)))
& ! [X2] :
( ? [X3] :
( subset(X2,X3)
& in(X3,X1)
& X2 != X3 )
| ~ in(X2,X1) )
& empty_set != X1 ) ),
inference(rectify,[],[f1192]) ).
fof(f1194,plain,
! [X0] :
( ~ sP4(X0)
| ( element(sK74(X0),powerset(powerset(X0)))
& ! [X2] :
( ( subset(X2,sK75(X0,X2))
& in(sK75(X0,X2),sK74(X0))
& sK75(X0,X2) != X2 )
| ~ in(X2,sK74(X0)) )
& empty_set != sK74(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74,sK75]),skolemize(X1,sK74(X0)),skolemize(X3,sK75(X0,X2))],[f1193]) ).
fof(f1210,plain,
! [X0,X2] :
( ( ~ sP9(X0,X2)
| ( ? [X3] :
( ( ~ in(X3,omega)
| ! [X4] :
( ~ element(X4,powerset(powerset(X3)))
| ? [X5] :
( ! [X6] :
( ~ subset(X5,X6)
| ~ in(X6,X4)
| X6 = X5 )
& in(X5,X4) )
| empty_set = X4 ) )
& X2 = X3
& ordinal(X3) )
& in(X2,succ(X0)) ) )
& ( ! [X3] :
( ( in(X3,omega)
& ? [X4] :
( element(X4,powerset(powerset(X3)))
& ! [X5] :
( ? [X6] :
( subset(X5,X6)
& in(X6,X4)
& X5 != X6 )
| ~ in(X5,X4) )
& empty_set != X4 ) )
| X2 != X3
| ~ ordinal(X3) )
| ~ in(X2,succ(X0))
| sP9(X0,X2) ) ),
inference(nnf_transformation,[],[f1087]) ).
fof(f1211,plain,
! [X0,X2] :
( ( ~ sP9(X0,X2)
| ( ? [X3] :
( ( ~ in(X3,omega)
| ! [X4] :
( ~ element(X4,powerset(powerset(X3)))
| ? [X5] :
( ! [X6] :
( ~ subset(X5,X6)
| ~ in(X6,X4)
| X6 = X5 )
& in(X5,X4) )
| empty_set = X4 ) )
& X2 = X3
& ordinal(X3) )
& in(X2,succ(X0)) ) )
& ( ! [X3] :
( ( in(X3,omega)
& ? [X4] :
( element(X4,powerset(powerset(X3)))
& ! [X5] :
( ? [X6] :
( subset(X5,X6)
& in(X6,X4)
& X5 != X6 )
| ~ in(X5,X4) )
& empty_set != X4 ) )
| X2 != X3
| ~ ordinal(X3) )
| ~ in(X2,succ(X0))
| sP9(X0,X2) ) ),
inference(flattening,[],[f1210]) ).
fof(f1212,plain,
! [X0,X1] :
( ( ~ sP9(X0,X1)
| ( ? [X6] :
( ( ~ in(X6,omega)
| ! [X7] :
( ~ element(X7,powerset(powerset(X6)))
| ? [X8] :
( ! [X9] :
( ~ subset(X8,X9)
| ~ in(X9,X7)
| X8 = X9 )
& in(X8,X7) )
| empty_set = X7 ) )
& X1 = X6
& ordinal(X6) )
& in(X1,succ(X0)) ) )
& ( ! [X2] :
( ( in(X2,omega)
& ? [X3] :
( element(X3,powerset(powerset(X2)))
& ! [X4] :
( ? [X5] :
( subset(X4,X5)
& in(X5,X3)
& X4 != X5 )
| ~ in(X4,X3) )
& empty_set != X3 ) )
| X1 != X2
| ~ ordinal(X2) )
| ~ in(X1,succ(X0))
| sP9(X0,X1) ) ),
inference(rectify,[],[f1211]) ).
fof(f1213,plain,
! [X0,X1] :
( ( ~ sP9(X0,X1)
| ( ( ~ in(sK89(X1),omega)
| ! [X7] :
( ~ element(X7,powerset(powerset(sK89(X1))))
| ( ! [X9] :
( ~ subset(sK90(X7),X9)
| ~ in(X9,X7)
| sK90(X7) = X9 )
& in(sK90(X7),X7) )
| empty_set = X7 ) )
& sK89(X1) = X1
& ordinal(sK89(X1))
& in(X1,succ(X0)) ) )
& ( ! [X2] :
( ( in(X2,omega)
& element(sK87(X2),powerset(powerset(X2)))
& ! [X4] :
( ( subset(X4,sK88(X2,X4))
& in(sK88(X2,X4),sK87(X2))
& sK88(X2,X4) != X4 )
| ~ in(X4,sK87(X2)) )
& empty_set != sK87(X2) )
| X1 != X2
| ~ ordinal(X2) )
| ~ in(X1,succ(X0))
| sP9(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87,sK88,sK89,sK90]),skolemize(X3,sK87(X2)),skolemize(X5,sK88(X2,X4)),skolemize(X6,sK89(X1)),skolemize(X8,sK90(X7))],[f1212]) ).
fof(f1242,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| ? [X2,X3,X4] :
( ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 )
& ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X3,X6),X1) )
& in(X3,X5)
& X2 = X5 )
& in(X2,X0)
& X3 != X4 ) ),
inference(nnf_transformation,[],[f1090]) ).
fof(f1243,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| ( ! [X8] :
( ~ in(X8,sK109(X0,X1))
| in(ordered_pair(sK107(X0,X1),X8),X1) )
& in(sK107(X0,X1),sK109(X0,X1))
& sK105(X0,X1) = sK109(X0,X1)
& ! [X6] :
( ~ in(X6,sK108(X0,X1))
| in(ordered_pair(sK106(X0,X1),X6),X1) )
& in(sK106(X0,X1),sK108(X0,X1))
& sK105(X0,X1) = sK108(X0,X1)
& in(sK105(X0,X1),X0)
& sK106(X0,X1) != sK107(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105,sK106,sK107,sK108,sK109]),skolemize(X2,sK105(X0,X1)),skolemize(X3,sK106(X0,X1)),skolemize(X4,sK107(X0,X1)),skolemize(X5,sK108(X0,X1)),skolemize(X7,sK109(X0,X1))],[f1242]) ).
fof(f1246,plain,
! [X0] :
( ~ sP13(X0)
| ? [X1,X2,X3] :
( X3 = singleton(X1)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 ) ),
inference(nnf_transformation,[],[f1093]) ).
fof(f1247,plain,
! [X0] :
( ~ sP13(X0)
| ( sK114(X0) = singleton(sK112(X0))
& sK113(X0) = singleton(sK112(X0))
& in(sK112(X0),X0)
& sK113(X0) != sK114(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112,sK113,sK114]),skolemize(X1,sK112(X0)),skolemize(X2,sK113(X0)),skolemize(X3,sK114(X0))],[f1246]) ).
fof(f1252,plain,
! [X0] :
( ~ sP14(X0)
| ? [X5] :
( element(X5,powerset(powerset(X0)))
& ! [X6] :
( ? [X7] :
( subset(X6,X7)
& in(X7,X5)
& X6 != X7 )
| ~ in(X6,X5) )
& X5 != empty_set ) ),
inference(nnf_transformation,[],[f1095]) ).
fof(f1253,plain,
! [X0] :
( ~ sP14(X0)
| ? [X1] :
( element(X1,powerset(powerset(X0)))
& ! [X2] :
( ? [X3] :
( subset(X2,X3)
& in(X3,X1)
& X2 != X3 )
| ~ in(X2,X1) )
& empty_set != X1 ) ),
inference(rectify,[],[f1252]) ).
fof(f1254,plain,
! [X0] :
( ~ sP14(X0)
| ( element(sK119(X0),powerset(powerset(X0)))
& ! [X2] :
( ( subset(X2,sK120(X0,X2))
& in(sK120(X0,X2),sK119(X0))
& sK120(X0,X2) != X2 )
| ~ in(X2,sK119(X0)) )
& empty_set != sK119(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119,sK120]),skolemize(X1,sK119(X0)),skolemize(X3,sK120(X0,X2))],[f1253]) ).
fof(f1319,plain,
! [X0,X2,X3,X1] :
( ( ~ sP16(X0,X2,X3,X1)
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0))
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
| sP16(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f1098]) ).
fof(f1320,plain,
! [X0,X2,X3,X1] :
( ( ~ sP16(X0,X2,X3,X1)
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0))
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
| sP16(X0,X2,X3,X1) ) ),
inference(flattening,[],[f1319]) ).
fof(f1321,plain,
! [X0,X1,X2,X3] :
( ( ~ sP16(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| ( apply(X3,X1) = X2
& in(X1,relation_rng(X0)) ) )
& ( ( apply(X0,X2) = X1
& in(X2,relation_dom(X0))
& ( apply(X3,X1) != X2
| ~ in(X1,relation_rng(X0)) ) )
| sP16(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1320]) ).
fof(f1347,plain,
! [X2,X4,X1] :
( ~ sP17(X2,X4,X1)
| ? [X7] :
( ! [X8] :
( ~ in(X8,X7)
| in(ordered_pair(X4,X8),X1) )
& in(X4,X7)
& X2 = X7 ) ),
inference(nnf_transformation,[],[f1100]) ).
fof(f1348,plain,
! [X0,X1,X2] :
( ~ sP17(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ in(X4,X3)
| in(ordered_pair(X1,X4),X2) )
& in(X1,X3)
& X0 = X3 ) ),
inference(rectify,[],[f1347]) ).
fof(f1349,plain,
! [X0,X1,X2] :
( ~ sP17(X0,X1,X2)
| ( ! [X4] :
( ~ in(X4,sK160(X0,X1,X2))
| in(ordered_pair(X1,X4),X2) )
& in(X1,sK160(X0,X1,X2))
& sK160(X0,X1,X2) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(X3,sK160(X0,X1,X2))],[f1348]) ).
fof(f1379,plain,
! [X4,X0] :
( ~ sP19(X4,X0)
| ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 ) ),
inference(nnf_transformation,[],[f1103]) ).
fof(f1380,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| ? [X2,X3] :
( singleton(X2) = X3
& in(X2,X1)
& ordered_pair(X2,X3) = X0 ) ),
inference(rectify,[],[f1379]) ).
fof(f1381,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| ( sK188(X0,X1) = singleton(sK187(X0,X1))
& in(sK187(X0,X1),X1)
& ordered_pair(sK187(X0,X1),sK188(X0,X1)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK187,sK188]),skolemize(X2,sK187(X0,X1)),skolemize(X3,sK188(X0,X1))],[f1380]) ).
fof(f1385,plain,
! [X0] :
( ~ sP21(X0)
| ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 ) ),
inference(nnf_transformation,[],[f1106]) ).
fof(f1386,plain,
! [X0] :
( ~ sP21(X0)
| ( sK195(X0) = singleton(sK193(X0))
& in(sK193(X0),X0)
& sK194(X0) = singleton(sK193(X0))
& in(sK193(X0),X0)
& sK194(X0) != sK195(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK193,sK194,sK195]),skolemize(X1,sK193(X0)),skolemize(X2,sK194(X0)),skolemize(X3,sK195(X0))],[f1385]) ).
fof(f1425,plain,
! [X1,X2] :
( ~ sP22(X1,X2)
| ? [X3,X4,X5] :
( ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& X5 = ordered_pair(X8,X9) )
& X3 = X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& X4 = ordered_pair(X6,X7) )
& X3 = X4
& X4 != X5 ) ),
inference(nnf_transformation,[],[f1108]) ).
fof(f1426,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| ? [X2,X3,X4] :
( ? [X7,X8] :
( in(ordered_pair(apply(X1,X7),apply(X1,X8)),X0)
& ordered_pair(X7,X8) = X4 )
& X2 = X4
& ? [X5,X6] :
( in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3
& X3 != X4 ) ),
inference(rectify,[],[f1425]) ).
fof(f1427,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| ( in(ordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK218(X0,X1))),X0)
& sK214(X0,X1) = ordered_pair(sK217(X0,X1),sK218(X0,X1))
& sK212(X0,X1) = sK214(X0,X1)
& in(ordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK216(X0,X1))),X0)
& sK213(X0,X1) = ordered_pair(sK215(X0,X1),sK216(X0,X1))
& sK212(X0,X1) = sK213(X0,X1)
& sK213(X0,X1) != sK214(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK212,sK213,sK214,sK215,sK216,sK217,sK218]),skolemize(X2,sK212(X0,X1)),skolemize(X3,sK213(X0,X1)),skolemize(X4,sK214(X0,X1)),skolemize(X5,sK215(X0,X1)),skolemize(X6,sK216(X0,X1)),skolemize(X7,sK217(X0,X1)),skolemize(X8,sK218(X0,X1))],[f1426]) ).
fof(f1440,plain,
! [X5,X0,X1] :
( ~ sP23(X5,X0,X1)
| ? [X10,X11] :
( ? [X12] :
( ! [X13] :
( ~ in(X13,X12)
| in(ordered_pair(X11,X13),X1) )
& in(X11,X12)
& X10 = X12 )
& in(X10,X0)
& ordered_pair(X10,X11) = X5 ) ),
inference(nnf_transformation,[],[f1110]) ).
fof(f1441,plain,
! [X0,X1,X2] :
( ~ sP23(X0,X1,X2)
| ? [X3,X4] :
( ? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X4,X6),X2) )
& in(X4,X5)
& X3 = X5 )
& in(X3,X1)
& ordered_pair(X3,X4) = X0 ) ),
inference(rectify,[],[f1440]) ).
fof(f1442,plain,
! [X0,X1,X2] :
( ~ sP23(X0,X1,X2)
| ( ! [X6] :
( ~ in(X6,sK234(X0,X1,X2))
| in(ordered_pair(sK233(X0,X1,X2),X6),X2) )
& in(sK233(X0,X1,X2),sK234(X0,X1,X2))
& sK232(X0,X1,X2) = sK234(X0,X1,X2)
& in(sK232(X0,X1,X2),X1)
& ordered_pair(sK232(X0,X1,X2),sK233(X0,X1,X2)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK232,sK233,sK234]),skolemize(X3,sK232(X0,X1,X2)),skolemize(X4,sK233(X0,X1,X2)),skolemize(X5,sK234(X0,X1,X2))],[f1441]) ).
fof(f1458,plain,
( ~ sP27
| ? [X1,X2,X3] :
( ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2
& X2 != X3 ) ),
inference(nnf_transformation,[],[f1115]) ).
fof(f1459,plain,
( ~ sP27
| ? [X0,X1,X2] :
( ordinal(X2)
& X0 = X2
& ordinal(X1)
& X0 = X1
& X1 != X2 ) ),
inference(rectify,[],[f1458]) ).
fof(f1460,plain,
( ~ sP27
| ( ordinal(sK253)
& sK251 = sK253
& ordinal(sK252)
& sK251 = sK252
& sK252 != sK253 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK251,sK252,sK253]),skolemize(X0,sK251),skolemize(X1,sK252),skolemize(X2,sK253)],[f1459]) ).
fof(f1471,plain,
! [X3] :
( ~ sP28(X3)
| ? [X8] :
( ( ~ in(X8,omega)
| ! [X9] :
( ~ element(X9,powerset(powerset(X8)))
| ? [X10] :
( ! [X11] :
( ~ subset(X10,X11)
| ~ in(X11,X9)
| X11 = X10 )
& in(X10,X9) )
| empty_set = X9 ) )
& X3 = X8
& ordinal(X8) ) ),
inference(nnf_transformation,[],[f1117]) ).
fof(f1472,plain,
! [X0] :
( ~ sP28(X0)
| ? [X1] :
( ( ~ in(X1,omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(X1)))
| ? [X3] :
( ! [X4] :
( ~ subset(X3,X4)
| ~ in(X4,X2)
| X3 = X4 )
& in(X3,X2) )
| empty_set = X2 ) )
& X0 = X1
& ordinal(X1) ) ),
inference(rectify,[],[f1471]) ).
fof(f1473,plain,
! [X0] :
( ~ sP28(X0)
| ( ( ~ in(sK262(X0),omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(sK262(X0))))
| ( ! [X4] :
( ~ subset(sK263(X2),X4)
| ~ in(X4,X2)
| sK263(X2) = X4 )
& in(sK263(X2),X2) )
| empty_set = X2 ) )
& sK262(X0) = X0
& ordinal(sK262(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK262,sK263]),skolemize(X1,sK262(X0)),skolemize(X3,sK263(X2))],[f1472]) ).
fof(f1485,plain,
! [X4,X0] :
( ~ sP31(X4,X0)
| ? [X6] :
( in(X6,X0)
& X4 = X6
& ordinal(X6) ) ),
inference(nnf_transformation,[],[f1121]) ).
fof(f1486,plain,
! [X0,X1] :
( ~ sP31(X0,X1)
| ? [X2] :
( in(X2,X1)
& X0 = X2
& ordinal(X2) ) ),
inference(rectify,[],[f1485]) ).
fof(f1487,plain,
! [X0,X1] :
( ~ sP31(X0,X1)
| ( in(sK275(X0,X1),X1)
& sK275(X0,X1) = X0
& ordinal(sK275(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(X2,sK275(X0,X1))],[f1486]) ).
fof(f1491,plain,
! [X1,X0] :
( ~ sP33(X1,X0)
| ? [X2,X3,X4] :
( ? [X6] :
( X4 = set_difference(X6,singleton(X0))
& in(X6,X1) )
& X2 = X4
& ? [X5] :
( X3 = set_difference(X5,singleton(X0))
& in(X5,X1) )
& X2 = X3
& X3 != X4 ) ),
inference(nnf_transformation,[],[f1124]) ).
fof(f1492,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| ? [X2,X3,X4] :
( ? [X6] :
( set_difference(X6,singleton(X1)) = X4
& in(X6,X0) )
& X2 = X4
& ? [X5] :
( set_difference(X5,singleton(X1)) = X3
& in(X5,X0) )
& X2 = X3
& X3 != X4 ) ),
inference(rectify,[],[f1491]) ).
fof(f1493,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| ( sK281(X0,X1) = set_difference(sK283(X0,X1),singleton(X1))
& in(sK283(X0,X1),X0)
& sK279(X0,X1) = sK281(X0,X1)
& sK280(X0,X1) = set_difference(sK282(X0,X1),singleton(X1))
& in(sK282(X0,X1),X0)
& sK279(X0,X1) = sK280(X0,X1)
& sK280(X0,X1) != sK281(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK279,sK280,sK281,sK282,sK283]),skolemize(X2,sK279(X0,X1)),skolemize(X3,sK280(X0,X1)),skolemize(X4,sK281(X0,X1)),skolemize(X5,sK282(X0,X1)),skolemize(X6,sK283(X0,X1))],[f1492]) ).
fof(f1503,plain,
! [X1,X0] :
( ~ sP34(X1,X0)
| ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3
& X3 != X4 ) ),
inference(nnf_transformation,[],[f1126]) ).
fof(f1504,plain,
! [X0,X1] :
( ~ sP34(X0,X1)
| ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X1),X4),X0)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X1),X3),X0)
& X2 = X3
& X3 != X4 ) ),
inference(rectify,[],[f1503]) ).
fof(f1505,plain,
! [X0,X1] :
( ~ sP34(X0,X1)
| ( in(set_difference(cast_as_carrier_subset(X1),sK294(X0,X1)),X0)
& sK292(X0,X1) = sK294(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK293(X0,X1)),X0)
& sK292(X0,X1) = sK293(X0,X1)
& sK293(X0,X1) != sK294(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK292,sK293,sK294]),skolemize(X2,sK292(X0,X1)),skolemize(X3,sK293(X0,X1)),skolemize(X4,sK294(X0,X1))],[f1504]) ).
fof(f1511,plain,
! [X0,X4,X1] :
( ~ sP35(X0,X4,X1)
| ? [X6] :
( subset(X1,X4)
& closed_subset(X6,X0)
& X6 = X4
& element(X6,powerset(the_carrier(X0))) ) ),
inference(nnf_transformation,[],[f1128]) ).
fof(f1512,plain,
! [X0,X1,X2] :
( ~ sP35(X0,X1,X2)
| ? [X3] :
( subset(X2,X1)
& closed_subset(X3,X0)
& X1 = X3
& element(X3,powerset(the_carrier(X0))) ) ),
inference(rectify,[],[f1511]) ).
fof(f1513,plain,
! [X0,X1,X2] :
( ~ sP35(X0,X1,X2)
| ( subset(X2,X1)
& closed_subset(sK301(X0,X1,X2),X0)
& sK301(X0,X1,X2) = X1
& element(sK301(X0,X1,X2),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(X3,sK301(X0,X1,X2))],[f1512]) ).
fof(f1518,plain,
! [X1,X2] :
( ~ sP37(X1,X2)
| ? [X3,X4,X5] :
( in(relation_image(X2,X5),X1)
& X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4
& X4 != X5 ) ),
inference(nnf_transformation,[],[f1131]) ).
fof(f1519,plain,
! [X0,X1] :
( ~ sP37(X0,X1)
| ? [X2,X3,X4] :
( in(relation_image(X1,X4),X0)
& X2 = X4
& in(relation_image(X1,X3),X0)
& X2 = X3
& X3 != X4 ) ),
inference(rectify,[],[f1518]) ).
fof(f1520,plain,
! [X0,X1] :
( ~ sP37(X0,X1)
| ( in(relation_image(X1,sK308(X0,X1)),X0)
& sK306(X0,X1) = sK308(X0,X1)
& in(relation_image(X1,sK307(X0,X1)),X0)
& sK306(X0,X1) = sK307(X0,X1)
& sK307(X0,X1) != sK308(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK306,sK307,sK308]),skolemize(X2,sK306(X0,X1)),skolemize(X3,sK307(X0,X1)),skolemize(X4,sK308(X0,X1))],[f1519]) ).
fof(f1591,plain,
! [X0,X1,X2] :
( ( ~ sP38(X0,X1,X2)
| ! [X3] :
( ~ in(X3,the_carrier(X0))
| ( ( ~ in(X3,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) )
& ( ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) )
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( in(X3,the_carrier(X0))
& ( in(X3,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) )
& ( ~ in(X3,X2)
| ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) ) ) )
| sP38(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f1133]) ).
fof(f1592,plain,
! [X0,X1,X2] :
( ( ~ sP38(X0,X1,X2)
| ! [X3] :
( ~ in(X3,the_carrier(X0))
| ( ( ~ in(X3,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) )
& ( ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) )
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( in(X3,the_carrier(X0))
& ( in(X3,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0) ) )
& ( ~ in(X3,X2)
| ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) ) ) )
| sP38(X0,X1,X2) ) ),
inference(flattening,[],[f1591]) ).
fof(f1593,plain,
! [X0,X1,X2] :
( ( ~ sP38(X0,X1,X2)
| ! [X6] :
( ~ in(X6,the_carrier(X0))
| ( ( ~ in(X6,X2)
| ! [X8] :
( ~ element(X8,powerset(the_carrier(X0)))
| ~ disjoint(X1,X8)
| ~ in(X6,X8)
| ~ open_subset(X8,X0) ) )
& ( ? [X7] :
( element(X7,powerset(the_carrier(X0)))
& disjoint(X1,X7)
& in(X6,X7)
& open_subset(X7,X0) )
| in(X6,X2) ) ) ) )
& ( ? [X3] :
( in(X3,the_carrier(X0))
& ( in(X3,X2)
| ! [X5] :
( ~ element(X5,powerset(the_carrier(X0)))
| ~ disjoint(X1,X5)
| ~ in(X3,X5)
| ~ open_subset(X5,X0) ) )
& ( ~ in(X3,X2)
| ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) ) ) )
| sP38(X0,X1,X2) ) ),
inference(rectify,[],[f1592]) ).
fof(f1594,plain,
! [X0,X1,X2] :
( ( ~ sP38(X0,X1,X2)
| ! [X6] :
( ~ in(X6,the_carrier(X0))
| ( ( ~ in(X6,X2)
| ! [X8] :
( ~ element(X8,powerset(the_carrier(X0)))
| ~ disjoint(X1,X8)
| ~ in(X6,X8)
| ~ open_subset(X8,X0) ) )
& ( ( element(sK352(X0,X1,X6),powerset(the_carrier(X0)))
& disjoint(X1,sK352(X0,X1,X6))
& in(X6,sK352(X0,X1,X6))
& open_subset(sK352(X0,X1,X6),X0) )
| in(X6,X2) ) ) ) )
& ( ( in(sK350(X0,X1,X2),the_carrier(X0))
& ( in(sK350(X0,X1,X2),X2)
| ! [X5] :
( ~ element(X5,powerset(the_carrier(X0)))
| ~ disjoint(X1,X5)
| ~ in(sK350(X0,X1,X2),X5)
| ~ open_subset(X5,X0) ) )
& ( ~ in(sK350(X0,X1,X2),X2)
| ( element(sK351(X0,X1,X2),powerset(the_carrier(X0)))
& disjoint(X1,sK351(X0,X1,X2))
& in(sK350(X0,X1,X2),sK351(X0,X1,X2))
& open_subset(sK351(X0,X1,X2),X0) ) ) )
| sP38(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK350,sK351,sK352]),skolemize(X3,sK350(X0,X1,X2)),skolemize(X4,sK351(X0,X1,X2)),skolemize(X7,sK352(X0,X1,X6))],[f1593]) ).
fof(f1608,plain,
! [X2,X0,X1] :
( ( ~ sP40(X2,X0,X1)
| ( ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& ( ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| in(ordered_pair(X3,X4),X0) ) )
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_dom(X2) = relation_field(X0) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
| ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) ) )
| ~ one_to_one(X2)
| relation_field(X1) != relation_rng(X2)
| relation_field(X0) != relation_dom(X2)
| sP40(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1136]) ).
fof(f1609,plain,
! [X2,X0,X1] :
( ( ~ sP40(X2,X0,X1)
| ( ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& ( ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| in(ordered_pair(X3,X4),X0) ) )
& one_to_one(X2)
& relation_rng(X2) = relation_field(X1)
& relation_dom(X2) = relation_field(X0) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
| ( in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
& in(X4,relation_field(X0))
& in(X3,relation_field(X0)) ) )
& ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(apply(X2,X3),apply(X2,X4)),X1)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0)) ) )
| ~ one_to_one(X2)
| relation_field(X1) != relation_rng(X2)
| relation_field(X0) != relation_dom(X2)
| sP40(X2,X0,X1) ) ),
inference(flattening,[],[f1608]) ).
fof(f1610,plain,
! [X0,X1,X2] :
( ( ~ sP40(X0,X1,X2)
| ( ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X1)
| ( in(ordered_pair(apply(X0,X5),apply(X0,X6)),X2)
& in(X6,relation_field(X1))
& in(X5,relation_field(X1)) ) )
& ( ~ in(ordered_pair(apply(X0,X5),apply(X0,X6)),X2)
| ~ in(X6,relation_field(X1))
| ~ in(X5,relation_field(X1))
| in(ordered_pair(X5,X6),X1) ) )
& one_to_one(X0)
& relation_rng(X0) = relation_field(X2)
& relation_dom(X0) = relation_field(X1) ) )
& ( ? [X3,X4] :
( ( in(ordered_pair(X3,X4),X1)
| ( in(ordered_pair(apply(X0,X3),apply(X0,X4)),X2)
& in(X4,relation_field(X1))
& in(X3,relation_field(X1)) ) )
& ( ~ in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(apply(X0,X3),apply(X0,X4)),X2)
| ~ in(X4,relation_field(X1))
| ~ in(X3,relation_field(X1)) ) )
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP40(X0,X1,X2) ) ),
inference(rectify,[],[f1609]) ).
fof(f1611,plain,
! [X0,X1,X2] :
( ( ~ sP40(X0,X1,X2)
| ( ! [X5,X6] :
( ( ~ in(ordered_pair(X5,X6),X1)
| ( in(ordered_pair(apply(X0,X5),apply(X0,X6)),X2)
& in(X6,relation_field(X1))
& in(X5,relation_field(X1)) ) )
& ( ~ in(ordered_pair(apply(X0,X5),apply(X0,X6)),X2)
| ~ in(X6,relation_field(X1))
| ~ in(X5,relation_field(X1))
| in(ordered_pair(X5,X6),X1) ) )
& one_to_one(X0)
& relation_rng(X0) = relation_field(X2)
& relation_dom(X0) = relation_field(X1) ) )
& ( ( ( in(ordered_pair(sK359(X0,X1,X2),sK360(X0,X1,X2)),X1)
| ( in(ordered_pair(apply(X0,sK359(X0,X1,X2)),apply(X0,sK360(X0,X1,X2))),X2)
& in(sK360(X0,X1,X2),relation_field(X1))
& in(sK359(X0,X1,X2),relation_field(X1)) ) )
& ( ~ in(ordered_pair(sK359(X0,X1,X2),sK360(X0,X1,X2)),X1)
| ~ in(ordered_pair(apply(X0,sK359(X0,X1,X2)),apply(X0,sK360(X0,X1,X2))),X2)
| ~ in(sK360(X0,X1,X2),relation_field(X1))
| ~ in(sK359(X0,X1,X2),relation_field(X1)) ) )
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP40(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK359,sK360]),skolemize(X3,sK359(X0,X1,X2)),skolemize(X4,sK360(X0,X1,X2))],[f1610]) ).
fof(f1634,plain,
! [X0] :
( ( ~ sP42(X0)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,the_topology(X0))
| ~ in(X2,the_topology(X0))
| in(subset_intersection2(the_carrier(X0),X2,X3),the_topology(X0)) ) ) )
& ( ? [X2] :
( element(X2,powerset(the_carrier(X0)))
& ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& in(X3,the_topology(X0))
& in(X2,the_topology(X0))
& ~ in(subset_intersection2(the_carrier(X0),X2,X3),the_topology(X0)) ) )
| sP42(X0) ) ),
inference(nnf_transformation,[],[f1139]) ).
fof(f1635,plain,
! [X0] :
( ( ~ sP42(X0)
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,the_topology(X0))
| ~ in(X3,the_topology(X0))
| in(subset_intersection2(the_carrier(X0),X3,X4),the_topology(X0)) ) ) )
& ( ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,powerset(the_carrier(X0)))
& in(X2,the_topology(X0))
& in(X1,the_topology(X0))
& ~ in(subset_intersection2(the_carrier(X0),X1,X2),the_topology(X0)) ) )
| sP42(X0) ) ),
inference(rectify,[],[f1634]) ).
fof(f1636,plain,
! [X0] :
( ( ~ sP42(X0)
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,the_topology(X0))
| ~ in(X3,the_topology(X0))
| in(subset_intersection2(the_carrier(X0),X3,X4),the_topology(X0)) ) ) )
& ( ( element(sK376(X0),powerset(the_carrier(X0)))
& element(sK377(X0),powerset(the_carrier(X0)))
& in(sK377(X0),the_topology(X0))
& in(sK376(X0),the_topology(X0))
& ~ in(subset_intersection2(the_carrier(X0),sK376(X0),sK377(X0)),the_topology(X0)) )
| sP42(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK376,sK377]),skolemize(X1,sK376(X0)),skolemize(X2,sK377(X0))],[f1635]) ).
fof(f1714,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,sK59(X0,X1,X2))
| in(ordered_pair(X1,X4),X2) ),
inference(cnf_transformation,[],[f1171]) ).
fof(f1715,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| in(X1,sK59(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1171]) ).
fof(f1716,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| sK59(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f1171]) ).
fof(f1720,plain,
! [X2,X3,X0] :
( ~ sP3(X0)
| ~ in(ordered_pair(X2,X3),sK61(X0))
| singleton(X2) = X3 ),
inference(cnf_transformation,[],[f1177]) ).
fof(f1721,plain,
! [X2,X3,X0] :
( ~ sP3(X0)
| ~ in(ordered_pair(X2,X3),sK61(X0))
| in(X2,X0) ),
inference(cnf_transformation,[],[f1177]) ).
fof(f1724,plain,
! [X0] :
( ~ sP3(X0)
| function(sK61(X0)) ),
inference(cnf_transformation,[],[f1177]) ).
fof(f1725,plain,
! [X0] :
( ~ sP3(X0)
| relation(sK61(X0)) ),
inference(cnf_transformation,[],[f1177]) ).
fof(f1757,plain,
! [X0] :
( ~ sP4(X0)
| element(sK74(X0),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1194]) ).
fof(f1758,plain,
! [X2,X0] :
( ~ sP4(X0)
| subset(X2,sK75(X0,X2))
| ~ in(X2,sK74(X0)) ),
inference(cnf_transformation,[],[f1194]) ).
fof(f1759,plain,
! [X2,X0] :
( ~ sP4(X0)
| in(sK75(X0,X2),sK74(X0))
| ~ in(X2,sK74(X0)) ),
inference(cnf_transformation,[],[f1194]) ).
fof(f1760,plain,
! [X2,X0] :
( ~ sP4(X0)
| sK75(X0,X2) != X2
| ~ in(X2,sK74(X0)) ),
inference(cnf_transformation,[],[f1194]) ).
fof(f1761,plain,
! [X0] :
( ~ sP4(X0)
| empty_set != sK74(X0) ),
inference(cnf_transformation,[],[f1194]) ).
fof(f1784,plain,
! [X0,X1,X9,X7] :
( ~ sP9(X0,X1)
| ~ in(sK89(X1),omega)
| ~ element(X7,powerset(powerset(sK89(X1))))
| ~ subset(sK90(X7),X9)
| ~ in(X9,X7)
| sK90(X7) = X9
| empty_set = X7 ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1785,plain,
! [X0,X1,X7] :
( ~ sP9(X0,X1)
| ~ in(sK89(X1),omega)
| ~ element(X7,powerset(powerset(sK89(X1))))
| in(sK90(X7),X7)
| empty_set = X7 ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1786,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| sK89(X1) = X1 ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1787,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| ordinal(sK89(X1)) ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1788,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| in(X1,succ(X0)) ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1789,plain,
! [X2,X0,X1] :
( in(X2,omega)
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1790,plain,
! [X2,X0,X1] :
( element(sK87(X2),powerset(powerset(X2)))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1791,plain,
! [X2,X0,X1,X4] :
( subset(X4,sK88(X2,X4))
| ~ in(X4,sK87(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1792,plain,
! [X2,X0,X1,X4] :
( in(sK88(X2,X4),sK87(X2))
| ~ in(X4,sK87(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1793,plain,
! [X2,X0,X1,X4] :
( sK88(X2,X4) != X4
| ~ in(X4,sK87(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1794,plain,
! [X2,X0,X1] :
( empty_set != sK87(X2)
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1830,plain,
! [X0,X1,X8] :
( ~ sP11(X0,X1)
| ~ in(X8,sK109(X0,X1))
| in(ordered_pair(sK107(X0,X1),X8),X1) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f1831,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| in(sK107(X0,X1),sK109(X0,X1)) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f1832,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| sK105(X0,X1) = sK109(X0,X1) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f1833,plain,
! [X0,X1,X6] :
( ~ sP11(X0,X1)
| ~ in(X6,sK108(X0,X1))
| in(ordered_pair(sK106(X0,X1),X6),X1) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f1834,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| in(sK106(X0,X1),sK108(X0,X1)) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f1835,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| sK105(X0,X1) = sK108(X0,X1) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f1836,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| in(sK105(X0,X1),X0) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f1837,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| sK106(X0,X1) != sK107(X0,X1) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f1841,plain,
! [X0] :
( ~ sP13(X0)
| sK114(X0) = singleton(sK112(X0)) ),
inference(cnf_transformation,[],[f1247]) ).
fof(f1842,plain,
! [X0] :
( ~ sP13(X0)
| sK113(X0) = singleton(sK112(X0)) ),
inference(cnf_transformation,[],[f1247]) ).
fof(f1843,plain,
! [X0] :
( ~ sP13(X0)
| in(sK112(X0),X0) ),
inference(cnf_transformation,[],[f1247]) ).
fof(f1844,plain,
! [X0] :
( ~ sP13(X0)
| sK113(X0) != sK114(X0) ),
inference(cnf_transformation,[],[f1247]) ).
fof(f1858,plain,
! [X0] :
( ~ sP14(X0)
| element(sK119(X0),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1859,plain,
! [X2,X0] :
( ~ sP14(X0)
| subset(X2,sK120(X0,X2))
| ~ in(X2,sK119(X0)) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1860,plain,
! [X2,X0] :
( ~ sP14(X0)
| in(sK120(X0,X2),sK119(X0))
| ~ in(X2,sK119(X0)) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1861,plain,
! [X2,X0] :
( ~ sP14(X0)
| sK120(X0,X2) != X2
| ~ in(X2,sK119(X0)) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1862,plain,
! [X0] :
( ~ sP14(X0)
| empty_set != sK119(X0) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f2078,plain,
! [X2,X3,X0,X1] :
( ~ sP16(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| apply(X3,X1) = X2 ),
inference(cnf_transformation,[],[f1321]) ).
fof(f2079,plain,
! [X2,X3,X0,X1] :
( ~ sP16(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| in(X1,relation_rng(X0)) ),
inference(cnf_transformation,[],[f1321]) ).
fof(f2080,plain,
! [X2,X3,X0,X1] :
( apply(X0,X2) = X1
| sP16(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1321]) ).
fof(f2081,plain,
! [X2,X3,X0,X1] :
( in(X2,relation_dom(X0))
| sP16(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1321]) ).
fof(f2082,plain,
! [X2,X3,X0,X1] :
( apply(X3,X1) != X2
| ~ in(X1,relation_rng(X0))
| sP16(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1321]) ).
fof(f2167,plain,
! [X2,X0,X1,X4] :
( ~ sP17(X0,X1,X2)
| ~ in(X4,sK160(X0,X1,X2))
| in(ordered_pair(X1,X4),X2) ),
inference(cnf_transformation,[],[f1349]) ).
fof(f2168,plain,
! [X2,X0,X1] :
( ~ sP17(X0,X1,X2)
| in(X1,sK160(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1349]) ).
fof(f2169,plain,
! [X2,X0,X1] :
( ~ sP17(X0,X1,X2)
| sK160(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f1349]) ).
fof(f2220,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| sK188(X0,X1) = singleton(sK187(X0,X1)) ),
inference(cnf_transformation,[],[f1381]) ).
fof(f2221,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| in(sK187(X0,X1),X1) ),
inference(cnf_transformation,[],[f1381]) ).
fof(f2222,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| ordered_pair(sK187(X0,X1),sK188(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f1381]) ).
fof(f2229,plain,
! [X0] :
( ~ sP21(X0)
| sK195(X0) = singleton(sK193(X0)) ),
inference(cnf_transformation,[],[f1386]) ).
fof(f2230,plain,
! [X0] :
( ~ sP21(X0)
| in(sK193(X0),X0) ),
inference(cnf_transformation,[],[f1386]) ).
fof(f2231,plain,
! [X0] :
( ~ sP21(X0)
| sK194(X0) = singleton(sK193(X0)) ),
inference(cnf_transformation,[],[f1386]) ).
fof(f2233,plain,
! [X0] :
( ~ sP21(X0)
| sK194(X0) != sK195(X0) ),
inference(cnf_transformation,[],[f1386]) ).
fof(f2329,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| in(ordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK218(X0,X1))),X0) ),
inference(cnf_transformation,[],[f1427]) ).
fof(f2330,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| sK214(X0,X1) = ordered_pair(sK217(X0,X1),sK218(X0,X1)) ),
inference(cnf_transformation,[],[f1427]) ).
fof(f2331,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| sK212(X0,X1) = sK214(X0,X1) ),
inference(cnf_transformation,[],[f1427]) ).
fof(f2332,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| in(ordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK216(X0,X1))),X0) ),
inference(cnf_transformation,[],[f1427]) ).
fof(f2333,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| sK213(X0,X1) = ordered_pair(sK215(X0,X1),sK216(X0,X1)) ),
inference(cnf_transformation,[],[f1427]) ).
fof(f2334,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| sK212(X0,X1) = sK213(X0,X1) ),
inference(cnf_transformation,[],[f1427]) ).
fof(f2335,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| sK213(X0,X1) != sK214(X0,X1) ),
inference(cnf_transformation,[],[f1427]) ).
fof(f2357,plain,
! [X2,X0,X1,X6] :
( ~ sP23(X0,X1,X2)
| ~ in(X6,sK234(X0,X1,X2))
| in(ordered_pair(sK233(X0,X1,X2),X6),X2) ),
inference(cnf_transformation,[],[f1442]) ).
fof(f2358,plain,
! [X2,X0,X1] :
( ~ sP23(X0,X1,X2)
| in(sK233(X0,X1,X2),sK234(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1442]) ).
fof(f2359,plain,
! [X2,X0,X1] :
( ~ sP23(X0,X1,X2)
| sK232(X0,X1,X2) = sK234(X0,X1,X2) ),
inference(cnf_transformation,[],[f1442]) ).
fof(f2360,plain,
! [X2,X0,X1] :
( ~ sP23(X0,X1,X2)
| in(sK232(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1442]) ).
fof(f2361,plain,
! [X2,X0,X1] :
( ~ sP23(X0,X1,X2)
| ordered_pair(sK232(X0,X1,X2),sK233(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f1442]) ).
fof(f2408,plain,
( ~ sP27
| ordinal(sK253) ),
inference(cnf_transformation,[],[f1460]) ).
fof(f2409,plain,
( ~ sP27
| sK251 = sK253 ),
inference(cnf_transformation,[],[f1460]) ).
fof(f2410,plain,
( ~ sP27
| ordinal(sK252) ),
inference(cnf_transformation,[],[f1460]) ).
fof(f2411,plain,
( ~ sP27
| sK251 = sK252 ),
inference(cnf_transformation,[],[f1460]) ).
fof(f2412,plain,
( ~ sP27
| sK252 != sK253 ),
inference(cnf_transformation,[],[f1460]) ).
fof(f2435,plain,
! [X2,X0,X4] :
( ~ sP28(X0)
| ~ in(sK262(X0),omega)
| ~ element(X2,powerset(powerset(sK262(X0))))
| ~ subset(sK263(X2),X4)
| ~ in(X4,X2)
| sK263(X2) = X4
| empty_set = X2 ),
inference(cnf_transformation,[],[f1473]) ).
fof(f2436,plain,
! [X2,X0] :
( ~ sP28(X0)
| ~ in(sK262(X0),omega)
| ~ element(X2,powerset(powerset(sK262(X0))))
| in(sK263(X2),X2)
| empty_set = X2 ),
inference(cnf_transformation,[],[f1473]) ).
fof(f2437,plain,
! [X0] :
( ~ sP28(X0)
| sK262(X0) = X0 ),
inference(cnf_transformation,[],[f1473]) ).
fof(f2438,plain,
! [X0] :
( ~ sP28(X0)
| ordinal(sK262(X0)) ),
inference(cnf_transformation,[],[f1473]) ).
fof(f2475,plain,
! [X0,X1] :
( ~ sP31(X0,X1)
| in(sK275(X0,X1),X1) ),
inference(cnf_transformation,[],[f1487]) ).
fof(f2476,plain,
! [X0,X1] :
( ~ sP31(X0,X1)
| sK275(X0,X1) = X0 ),
inference(cnf_transformation,[],[f1487]) ).
fof(f2477,plain,
! [X0,X1] :
( ~ sP31(X0,X1)
| ordinal(sK275(X0,X1)) ),
inference(cnf_transformation,[],[f1487]) ).
fof(f2484,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| sK281(X0,X1) = set_difference(sK283(X0,X1),singleton(X1)) ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2485,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| in(sK283(X0,X1),X0) ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2486,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| sK279(X0,X1) = sK281(X0,X1) ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2487,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| sK280(X0,X1) = set_difference(sK282(X0,X1),singleton(X1)) ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2488,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| in(sK282(X0,X1),X0) ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2489,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| sK279(X0,X1) = sK280(X0,X1) ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2490,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| sK280(X0,X1) != sK281(X0,X1) ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2517,plain,
! [X0,X1] :
( ~ sP34(X0,X1)
| in(set_difference(cast_as_carrier_subset(X1),sK294(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2518,plain,
! [X0,X1] :
( ~ sP34(X0,X1)
| sK292(X0,X1) = sK294(X0,X1) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2519,plain,
! [X0,X1] :
( ~ sP34(X0,X1)
| in(set_difference(cast_as_carrier_subset(X1),sK293(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2520,plain,
! [X0,X1] :
( ~ sP34(X0,X1)
| sK292(X0,X1) = sK293(X0,X1) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2521,plain,
! [X0,X1] :
( ~ sP34(X0,X1)
| sK293(X0,X1) != sK294(X0,X1) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2534,plain,
! [X2,X0,X1] :
( ~ sP35(X0,X1,X2)
| subset(X2,X1) ),
inference(cnf_transformation,[],[f1513]) ).
fof(f2535,plain,
! [X2,X0,X1] :
( ~ sP35(X0,X1,X2)
| closed_subset(sK301(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f1513]) ).
fof(f2536,plain,
! [X2,X0,X1] :
( ~ sP35(X0,X1,X2)
| sK301(X0,X1,X2) = X1 ),
inference(cnf_transformation,[],[f1513]) ).
fof(f2537,plain,
! [X2,X0,X1] :
( ~ sP35(X0,X1,X2)
| element(sK301(X0,X1,X2),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1513]) ).
fof(f2550,plain,
! [X0,X1] :
( ~ sP37(X0,X1)
| in(relation_image(X1,sK308(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1520]) ).
fof(f2551,plain,
! [X0,X1] :
( ~ sP37(X0,X1)
| sK306(X0,X1) = sK308(X0,X1) ),
inference(cnf_transformation,[],[f1520]) ).
fof(f2552,plain,
! [X0,X1] :
( ~ sP37(X0,X1)
| in(relation_image(X1,sK307(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1520]) ).
fof(f2553,plain,
! [X0,X1] :
( ~ sP37(X0,X1)
| sK306(X0,X1) = sK307(X0,X1) ),
inference(cnf_transformation,[],[f1520]) ).
fof(f2554,plain,
! [X0,X1] :
( ~ sP37(X0,X1)
| sK307(X0,X1) != sK308(X0,X1) ),
inference(cnf_transformation,[],[f1520]) ).
fof(f2749,plain,
! [X2,X0,X1,X8,X6] :
( ~ sP38(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| ~ in(X6,X2)
| ~ element(X8,powerset(the_carrier(X0)))
| ~ disjoint(X1,X8)
| ~ in(X6,X8)
| ~ open_subset(X8,X0) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2750,plain,
! [X2,X0,X1,X6] :
( ~ sP38(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| element(sK352(X0,X1,X6),powerset(the_carrier(X0)))
| in(X6,X2) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2751,plain,
! [X2,X0,X1,X6] :
( ~ sP38(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| disjoint(X1,sK352(X0,X1,X6))
| in(X6,X2) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2752,plain,
! [X2,X0,X1,X6] :
( ~ sP38(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| in(X6,sK352(X0,X1,X6))
| in(X6,X2) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2753,plain,
! [X2,X0,X1,X6] :
( ~ sP38(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| open_subset(sK352(X0,X1,X6),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2754,plain,
! [X2,X0,X1] :
( in(sK350(X0,X1,X2),the_carrier(X0))
| sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2755,plain,
! [X2,X0,X1,X5] :
( in(sK350(X0,X1,X2),X2)
| ~ element(X5,powerset(the_carrier(X0)))
| ~ disjoint(X1,X5)
| ~ in(sK350(X0,X1,X2),X5)
| ~ open_subset(X5,X0)
| sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2756,plain,
! [X2,X0,X1] :
( ~ in(sK350(X0,X1,X2),X2)
| element(sK351(X0,X1,X2),powerset(the_carrier(X0)))
| sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2757,plain,
! [X2,X0,X1] :
( ~ in(sK350(X0,X1,X2),X2)
| disjoint(X1,sK351(X0,X1,X2))
| sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2758,plain,
! [X2,X0,X1] :
( ~ in(sK350(X0,X1,X2),X2)
| in(sK350(X0,X1,X2),sK351(X0,X1,X2))
| sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2759,plain,
! [X2,X0,X1] :
( ~ in(sK350(X0,X1,X2),X2)
| open_subset(sK351(X0,X1,X2),X0)
| sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2800,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP40(X0,X1,X2)
| ~ in(ordered_pair(X5,X6),X1)
| in(ordered_pair(apply(X0,X5),apply(X0,X6)),X2) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f2801,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP40(X0,X1,X2)
| ~ in(ordered_pair(X5,X6),X1)
| in(X6,relation_field(X1)) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f2802,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP40(X0,X1,X2)
| ~ in(ordered_pair(X5,X6),X1)
| in(X5,relation_field(X1)) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f2803,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP40(X0,X1,X2)
| ~ in(ordered_pair(apply(X0,X5),apply(X0,X6)),X2)
| ~ in(X6,relation_field(X1))
| ~ in(X5,relation_field(X1))
| in(ordered_pair(X5,X6),X1) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f2804,plain,
! [X2,X0,X1] :
( ~ sP40(X0,X1,X2)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f2805,plain,
! [X2,X0,X1] :
( ~ sP40(X0,X1,X2)
| relation_rng(X0) = relation_field(X2) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f2806,plain,
! [X2,X0,X1] :
( ~ sP40(X0,X1,X2)
| relation_dom(X0) = relation_field(X1) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f2807,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK359(X0,X1,X2),sK360(X0,X1,X2)),X1)
| in(ordered_pair(apply(X0,sK359(X0,X1,X2)),apply(X0,sK360(X0,X1,X2))),X2)
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f2808,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK359(X0,X1,X2),sK360(X0,X1,X2)),X1)
| in(sK360(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f2809,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK359(X0,X1,X2),sK360(X0,X1,X2)),X1)
| in(sK359(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f2810,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(sK359(X0,X1,X2),sK360(X0,X1,X2)),X1)
| ~ in(ordered_pair(apply(X0,sK359(X0,X1,X2)),apply(X0,sK360(X0,X1,X2))),X2)
| ~ in(sK360(X0,X1,X2),relation_field(X1))
| ~ in(sK359(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f2911,plain,
! [X3,X0,X4] :
( ~ sP42(X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,the_topology(X0))
| ~ in(X3,the_topology(X0))
| in(subset_intersection2(the_carrier(X0),X3,X4),the_topology(X0)) ),
inference(cnf_transformation,[],[f1636]) ).
fof(f2912,plain,
! [X0] :
( element(sK376(X0),powerset(the_carrier(X0)))
| sP42(X0) ),
inference(cnf_transformation,[],[f1636]) ).
fof(f2913,plain,
! [X0] :
( element(sK377(X0),powerset(the_carrier(X0)))
| sP42(X0) ),
inference(cnf_transformation,[],[f1636]) ).
fof(f2914,plain,
! [X0] :
( in(sK377(X0),the_topology(X0))
| sP42(X0) ),
inference(cnf_transformation,[],[f1636]) ).
fof(f2915,plain,
! [X0] :
( in(sK376(X0),the_topology(X0))
| sP42(X0) ),
inference(cnf_transformation,[],[f1636]) ).
fof(f2916,plain,
! [X0] :
( ~ in(subset_intersection2(the_carrier(X0),sK376(X0),sK377(X0)),the_topology(X0))
| sP42(X0) ),
inference(cnf_transformation,[],[f1636]) ).
fof(f3026,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,sK59(X0,X1,X2))
| in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),X2) ),
inference(definition_unfolding,[],[f1714,f2992]) ).
fof(f3029,plain,
! [X2,X3,X0] :
( ~ sP3(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),sK61(X0))
| in(X2,X0) ),
inference(definition_unfolding,[],[f1721,f2992]) ).
fof(f3030,plain,
! [X2,X3,X0] :
( ~ sP3(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),sK61(X0))
| unordered_pair(X2,X2) = X3 ),
inference(definition_unfolding,[],[f1720,f2115,f2992]) ).
fof(f3046,plain,
! [X2,X0,X1] :
( empty_set != sK87(X2)
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X1) ),
inference(definition_unfolding,[],[f1794,f2991]) ).
fof(f3047,plain,
! [X2,X0,X1,X4] :
( sK88(X2,X4) != X4
| ~ in(X4,sK87(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X1) ),
inference(definition_unfolding,[],[f1793,f2991]) ).
fof(f3048,plain,
! [X2,X0,X1,X4] :
( in(sK88(X2,X4),sK87(X2))
| ~ in(X4,sK87(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X1) ),
inference(definition_unfolding,[],[f1792,f2991]) ).
fof(f3049,plain,
! [X2,X0,X1,X4] :
( subset(X4,sK88(X2,X4))
| ~ in(X4,sK87(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X1) ),
inference(definition_unfolding,[],[f1791,f2991]) ).
fof(f3050,plain,
! [X2,X0,X1] :
( element(sK87(X2),powerset(powerset(X2)))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X1) ),
inference(definition_unfolding,[],[f1790,f2991]) ).
fof(f3051,plain,
! [X2,X0,X1] :
( in(X2,omega)
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X1) ),
inference(definition_unfolding,[],[f1789,f2991]) ).
fof(f3052,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| in(X1,set_union2(X0,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f1788,f2991]) ).
fof(f3063,plain,
! [X0,X1,X6] :
( ~ sP11(X0,X1)
| ~ in(X6,sK108(X0,X1))
| in(unordered_pair(unordered_pair(sK106(X0,X1),X6),unordered_pair(sK106(X0,X1),sK106(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1833,f2992]) ).
fof(f3064,plain,
! [X0,X1,X8] :
( ~ sP11(X0,X1)
| ~ in(X8,sK109(X0,X1))
| in(unordered_pair(unordered_pair(sK107(X0,X1),X8),unordered_pair(sK107(X0,X1),sK107(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1830,f2992]) ).
fof(f3066,plain,
! [X0] :
( ~ sP13(X0)
| sK113(X0) = unordered_pair(sK112(X0),sK112(X0)) ),
inference(definition_unfolding,[],[f1842,f2115]) ).
fof(f3067,plain,
! [X0] :
( ~ sP13(X0)
| sK114(X0) = unordered_pair(sK112(X0),sK112(X0)) ),
inference(definition_unfolding,[],[f1841,f2115]) ).
fof(f3133,plain,
! [X2,X0,X1,X4] :
( ~ sP17(X0,X1,X2)
| ~ in(X4,sK160(X0,X1,X2))
| in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),X2) ),
inference(definition_unfolding,[],[f2167,f2992]) ).
fof(f3159,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| unordered_pair(unordered_pair(sK187(X0,X1),sK188(X0,X1)),unordered_pair(sK187(X0,X1),sK187(X0,X1))) = X0 ),
inference(definition_unfolding,[],[f2222,f2992]) ).
fof(f3160,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| sK188(X0,X1) = unordered_pair(sK187(X0,X1),sK187(X0,X1)) ),
inference(definition_unfolding,[],[f2220,f2115]) ).
fof(f3164,plain,
! [X0] :
( ~ sP21(X0)
| sK194(X0) = unordered_pair(sK193(X0),sK193(X0)) ),
inference(definition_unfolding,[],[f2231,f2115]) ).
fof(f3165,plain,
! [X0] :
( ~ sP21(X0)
| sK195(X0) = unordered_pair(sK193(X0),sK193(X0)) ),
inference(definition_unfolding,[],[f2229,f2115]) ).
fof(f3181,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| sK213(X0,X1) = unordered_pair(unordered_pair(sK215(X0,X1),sK216(X0,X1)),unordered_pair(sK215(X0,X1),sK215(X0,X1))) ),
inference(definition_unfolding,[],[f2333,f2992]) ).
fof(f3182,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| in(unordered_pair(unordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK216(X0,X1))),unordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK215(X0,X1)))),X0) ),
inference(definition_unfolding,[],[f2332,f2992]) ).
fof(f3183,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| sK214(X0,X1) = unordered_pair(unordered_pair(sK217(X0,X1),sK218(X0,X1)),unordered_pair(sK217(X0,X1),sK217(X0,X1))) ),
inference(definition_unfolding,[],[f2330,f2992]) ).
fof(f3184,plain,
! [X0,X1] :
( ~ sP22(X0,X1)
| in(unordered_pair(unordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK218(X0,X1))),unordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK217(X0,X1)))),X0) ),
inference(definition_unfolding,[],[f2329,f2992]) ).
fof(f3194,plain,
! [X2,X0,X1] :
( ~ sP23(X0,X1,X2)
| unordered_pair(unordered_pair(sK232(X0,X1,X2),sK233(X0,X1,X2)),unordered_pair(sK232(X0,X1,X2),sK232(X0,X1,X2))) = X0 ),
inference(definition_unfolding,[],[f2361,f2992]) ).
fof(f3195,plain,
! [X2,X0,X1,X6] :
( ~ sP23(X0,X1,X2)
| ~ in(X6,sK234(X0,X1,X2))
| in(unordered_pair(unordered_pair(sK233(X0,X1,X2),X6),unordered_pair(sK233(X0,X1,X2),sK233(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f2357,f2992]) ).
fof(f3216,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| sK280(X0,X1) = set_difference(sK282(X0,X1),unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f2487,f2115]) ).
fof(f3217,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| sK281(X0,X1) = set_difference(sK283(X0,X1),unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f2484,f2115]) ).
fof(f3283,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK359(X0,X1,X2),sK360(X0,X1,X2)),unordered_pair(sK359(X0,X1,X2),sK359(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(apply(X0,sK359(X0,X1,X2)),apply(X0,sK360(X0,X1,X2))),unordered_pair(apply(X0,sK359(X0,X1,X2)),apply(X0,sK359(X0,X1,X2)))),X2)
| ~ in(sK360(X0,X1,X2),relation_field(X1))
| ~ in(sK359(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP40(X0,X1,X2) ),
inference(definition_unfolding,[],[f2810,f2992,f2992]) ).
fof(f3284,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK359(X0,X1,X2),sK360(X0,X1,X2)),unordered_pair(sK359(X0,X1,X2),sK359(X0,X1,X2))),X1)
| in(sK359(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP40(X0,X1,X2) ),
inference(definition_unfolding,[],[f2809,f2992]) ).
fof(f3285,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK359(X0,X1,X2),sK360(X0,X1,X2)),unordered_pair(sK359(X0,X1,X2),sK359(X0,X1,X2))),X1)
| in(sK360(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP40(X0,X1,X2) ),
inference(definition_unfolding,[],[f2808,f2992]) ).
fof(f3286,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK359(X0,X1,X2),sK360(X0,X1,X2)),unordered_pair(sK359(X0,X1,X2),sK359(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(apply(X0,sK359(X0,X1,X2)),apply(X0,sK360(X0,X1,X2))),unordered_pair(apply(X0,sK359(X0,X1,X2)),apply(X0,sK359(X0,X1,X2)))),X2)
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP40(X0,X1,X2) ),
inference(definition_unfolding,[],[f2807,f2992,f2992]) ).
fof(f3287,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP40(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(apply(X0,X5),apply(X0,X6)),unordered_pair(apply(X0,X5),apply(X0,X5))),X2)
| ~ in(X6,relation_field(X1))
| ~ in(X5,relation_field(X1))
| in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1) ),
inference(definition_unfolding,[],[f2803,f2992,f2992]) ).
fof(f3288,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP40(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| in(X5,relation_field(X1)) ),
inference(definition_unfolding,[],[f2802,f2992]) ).
fof(f3289,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP40(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| in(X6,relation_field(X1)) ),
inference(definition_unfolding,[],[f2801,f2992]) ).
fof(f3290,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP40(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| in(unordered_pair(unordered_pair(apply(X0,X5),apply(X0,X6)),unordered_pair(apply(X0,X5),apply(X0,X5))),X2) ),
inference(definition_unfolding,[],[f2800,f2992,f2992]) ).
fof(f3349,plain,
! [X2,X0] :
( empty_set != sK87(X2)
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f3046]) ).
fof(f3350,plain,
! [X2,X0,X4] :
( sK88(X2,X4) != X4
| ~ in(X4,sK87(X2))
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f3047]) ).
fof(f3351,plain,
! [X2,X0,X4] :
( in(sK88(X2,X4),sK87(X2))
| ~ in(X4,sK87(X2))
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f3048]) ).
fof(f3352,plain,
! [X2,X0,X4] :
( subset(X4,sK88(X2,X4))
| ~ in(X4,sK87(X2))
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f3049]) ).
fof(f3353,plain,
! [X2,X0] :
( element(sK87(X2),powerset(powerset(X2)))
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f3050]) ).
fof(f3354,plain,
! [X2,X0] :
( in(X2,omega)
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f3051]) ).
fof(f3373,plain,
! [X3,X0,X1] :
( ~ in(X1,relation_rng(X0))
| sP16(X0,X1,apply(X3,X1),X3) ),
inference(equality_resolution,[],[f2082]) ).
fof(f3374,plain,
! [X2,X3,X0] :
( ~ sP16(X0,apply(X0,X2),X2,X3)
| ~ in(X2,relation_dom(X0))
| in(apply(X0,X2),relation_rng(X0)) ),
inference(equality_resolution,[],[f2079]) ).
fof(f3375,plain,
! [X2,X3,X0] :
( ~ sP16(X0,apply(X0,X2),X2,X3)
| ~ in(X2,relation_dom(X0))
| apply(X3,apply(X0,X2)) = X2 ),
inference(equality_resolution,[],[f2078]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK59(X0,X1,X2) = X0 )
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f1716]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK59(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f1715]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X3)
| ~ sP0(X1,X2,X3)
| ~ in(X0,sK59(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3026]) ).
tcf(c_111,plain,
! [X0: $i] :
( relation(sK61(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f1725]) ).
tcf(c_112,plain,
! [X0: $i] :
( function(sK61(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f1724]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ sP3(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK61(X2)) ),
inference(cnf_transformation,[],[f3029]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X0) = X1 )
| ~ sP3(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK61(X2)) ),
inference(cnf_transformation,[],[f3030]) ).
tcf(c_148,plain,
! [X0: $i] :
( ~ sP4(X0)
| ( sK74(X0) != empty_set ) ),
inference(cnf_transformation,[],[f1761]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] :
( ~ sP4(X0)
| ~ in(X1,sK74(X0))
| ( sK75(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f1760]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( in(sK75(X1,X0),sK74(X1))
| ~ sP4(X1)
| ~ in(X0,sK74(X1)) ),
inference(cnf_transformation,[],[f1759]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK75(X1,X0))
| ~ sP4(X1)
| ~ in(X0,sK74(X1)) ),
inference(cnf_transformation,[],[f1758]) ).
tcf(c_152,plain,
! [X0: $i] :
( element(sK74(X0),powerset(powerset(X0)))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f1757]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( sP9(X1,X0)
| ~ ordinal(X0)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1)))
| ( sK87(X0) != empty_set ) ),
inference(cnf_transformation,[],[f3349]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP9(X2,X0)
| ~ ordinal(X0)
| ~ in(X1,sK87(X0))
| ~ in(X0,set_union2(X2,unordered_pair(X2,X2)))
| ( sK88(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f3350]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP9(X1,X0)
| in(sK88(X0,X2),sK87(X0))
| ~ ordinal(X0)
| ~ in(X2,sK87(X0))
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3351]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP9(X1,X0)
| subset(X2,sK88(X0,X2))
| ~ ordinal(X0)
| ~ in(X2,sK87(X0))
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3352]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] :
( sP9(X1,X0)
| element(sK87(X0),powerset(powerset(X0)))
| ~ ordinal(X0)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3353]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] :
( in(X0,omega)
| sP9(X1,X0)
| ~ ordinal(X0)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3354]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i] :
( in(X1,set_union2(X0,unordered_pair(X0,X0)))
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f3052]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] :
( ordinal(sK89(X1))
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f1787]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ( sK89(X1) = X1 )
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f1786]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK90(X0),X0)
| ( X0 = empty_set )
| ~ sP9(X2,X1)
| ~ in(sK89(X1),omega)
| ~ element(X0,powerset(powerset(sK89(X1)))) ),
inference(cnf_transformation,[],[f1785]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = empty_set )
| ( sK90(X0) = X2 )
| ~ sP9(X3,X1)
| ~ in(X2,X0)
| ~ in(sK89(X1),omega)
| ~ subset(sK90(X0),X2)
| ~ element(X0,powerset(powerset(sK89(X1)))) ),
inference(cnf_transformation,[],[f1784]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i] :
( ~ sP11(X0,X1)
| ( sK106(X0,X1) != sK107(X0,X1) ) ),
inference(cnf_transformation,[],[f1837]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i] :
( in(sK105(X0,X1),X0)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1836]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i] :
( ( sK105(X0,X1) = sK108(X0,X1) )
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1835]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i] :
( in(sK106(X0,X1),sK108(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1834]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK106(X1,X2),X0),unordered_pair(sK106(X1,X2),sK106(X1,X2))),X2)
| ~ sP11(X1,X2)
| ~ in(X0,sK108(X1,X2)) ),
inference(cnf_transformation,[],[f3063]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i] :
( ( sK105(X0,X1) = sK109(X0,X1) )
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1832]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( in(sK107(X0,X1),sK109(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1831]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK107(X1,X2),X0),unordered_pair(sK107(X1,X2),sK107(X1,X2))),X2)
| ~ sP11(X1,X2)
| ~ in(X0,sK109(X1,X2)) ),
inference(cnf_transformation,[],[f3064]) ).
tcf(c_232,plain,
! [X0: $i] :
( ~ sP13(X0)
| ( sK113(X0) != sK114(X0) ) ),
inference(cnf_transformation,[],[f1844]) ).
tcf(c_233,plain,
! [X0: $i] :
( in(sK112(X0),X0)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f1843]) ).
tcf(c_234,plain,
! [X0: $i] :
( ( unordered_pair(sK112(X0),sK112(X0)) = sK113(X0) )
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f3066]) ).
tcf(c_235,plain,
! [X0: $i] :
( ( unordered_pair(sK112(X0),sK112(X0)) = sK114(X0) )
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f3067]) ).
tcf(c_249,plain,
! [X0: $i] :
( ~ sP14(X0)
| ( sK119(X0) != empty_set ) ),
inference(cnf_transformation,[],[f1862]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] :
( ~ sP14(X0)
| ~ in(X1,sK119(X0))
| ( sK120(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f1861]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] :
( in(sK120(X1,X0),sK119(X1))
| ~ sP14(X1)
| ~ in(X0,sK119(X1)) ),
inference(cnf_transformation,[],[f1860]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK120(X1,X0))
| ~ sP14(X1)
| ~ in(X0,sK119(X1)) ),
inference(cnf_transformation,[],[f1859]) ).
tcf(c_253,plain,
! [X0: $i] :
( element(sK119(X0),powerset(powerset(X0)))
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f1858]) ).
tcf(c_468,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP16(X1,X0,apply(X2,X0),X2)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f3373]) ).
tcf(c_469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,relation_dom(X0))
| sP16(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2081]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP16(X0,X2,X1,X3)
| ( apply(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f2080]) ).
tcf(c_471,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,X1),relation_rng(X0))
| ~ in(X1,relation_dom(X0))
| ~ sP16(X0,apply(X0,X1),X1,X2) ),
inference(cnf_transformation,[],[f3374]) ).
tcf(c_472,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,apply(X0,X1)) = X1 )
| ~ in(X1,relation_dom(X0))
| ~ sP16(X0,apply(X0,X1),X1,X2) ),
inference(cnf_transformation,[],[f3375]) ).
tcf(c_554,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK160(X0,X1,X2) = X0 )
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f2169]) ).
tcf(c_555,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK160(X0,X1,X2))
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f2168]) ).
tcf(c_556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),X3)
| ~ sP17(X1,X2,X3)
| ~ in(X0,sK160(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3133]) ).
tcf(c_607,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK187(X0,X1),sK188(X0,X1)),unordered_pair(sK187(X0,X1),sK187(X0,X1))) = X0 )
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f3159]) ).
tcf(c_608,plain,
! [X0: $i,X1: $i] :
( in(sK187(X0,X1),X1)
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f2221]) ).
tcf(c_609,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(sK187(X0,X1),sK187(X0,X1)) = sK188(X0,X1) )
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f3160]) ).
tcf(c_616,plain,
! [X0: $i] :
( ~ sP21(X0)
| ( sK194(X0) != sK195(X0) ) ),
inference(cnf_transformation,[],[f2233]) ).
tcf(c_618,plain,
! [X0: $i] :
( ( unordered_pair(sK193(X0),sK193(X0)) = sK194(X0) )
| ~ sP21(X0) ),
inference(cnf_transformation,[],[f3164]) ).
tcf(c_619,plain,
! [X0: $i] :
( in(sK193(X0),X0)
| ~ sP21(X0) ),
inference(cnf_transformation,[],[f2230]) ).
tcf(c_620,plain,
! [X0: $i] :
( ( unordered_pair(sK193(X0),sK193(X0)) = sK195(X0) )
| ~ sP21(X0) ),
inference(cnf_transformation,[],[f3165]) ).
tcf(c_715,plain,
! [X0: $i,X1: $i] :
( ~ sP22(X0,X1)
| ( sK213(X0,X1) != sK214(X0,X1) ) ),
inference(cnf_transformation,[],[f2335]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i] :
( ( sK213(X0,X1) = sK212(X0,X1) )
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f2334]) ).
tcf(c_717,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK215(X0,X1),sK216(X0,X1)),unordered_pair(sK215(X0,X1),sK215(X0,X1))) = sK213(X0,X1) )
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f3181]) ).
tcf(c_718,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK216(X0,X1))),unordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK215(X0,X1)))),X0)
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f3182]) ).
tcf(c_719,plain,
! [X0: $i,X1: $i] :
( ( sK214(X0,X1) = sK212(X0,X1) )
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f2331]) ).
tcf(c_720,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK217(X0,X1),sK218(X0,X1)),unordered_pair(sK217(X0,X1),sK217(X0,X1))) = sK214(X0,X1) )
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f3183]) ).
tcf(c_721,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK218(X0,X1))),unordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK217(X0,X1)))),X0)
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f3184]) ).
tcf(c_743,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK232(X0,X1,X2),sK233(X0,X1,X2)),unordered_pair(sK232(X0,X1,X2),sK232(X0,X1,X2))) = X0 )
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f3194]) ).
tcf(c_744,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK232(X0,X1,X2),X1)
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f2360]) ).
tcf(c_745,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK232(X0,X1,X2) = sK234(X0,X1,X2) )
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f2359]) ).
tcf(c_746,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK233(X0,X1,X2),sK234(X0,X1,X2))
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f2358]) ).
tcf(c_747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK233(X1,X2,X3),X0),unordered_pair(sK233(X1,X2,X3),sK233(X1,X2,X3))),X3)
| ~ sP23(X1,X2,X3)
| ~ in(X0,sK234(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3195]) ).
tcf(c_794,plain,
( ~ sP27
| ( sK252 != sK253 ) ),
inference(cnf_transformation,[],[f2412]) ).
tcf(c_795,plain,
( ( sK252 = sK251 )
| ~ sP27 ),
inference(cnf_transformation,[],[f2411]) ).
tcf(c_796,plain,
( ordinal(sK252)
| ~ sP27 ),
inference(cnf_transformation,[],[f2410]) ).
tcf(c_797,plain,
( ( sK253 = sK251 )
| ~ sP27 ),
inference(cnf_transformation,[],[f2409]) ).
tcf(c_798,plain,
( ordinal(sK253)
| ~ sP27 ),
inference(cnf_transformation,[],[f2408]) ).
tcf(c_821,plain,
! [X0: $i] :
( ordinal(sK262(X0))
| ~ sP28(X0) ),
inference(cnf_transformation,[],[f2438]) ).
tcf(c_822,plain,
! [X0: $i] :
( ( sK262(X0) = X0 )
| ~ sP28(X0) ),
inference(cnf_transformation,[],[f2437]) ).
tcf(c_823,plain,
! [X0: $i,X1: $i] :
( in(sK263(X0),X0)
| ( X0 = empty_set )
| ~ sP28(X1)
| ~ in(sK262(X1),omega)
| ~ element(X0,powerset(powerset(sK262(X1)))) ),
inference(cnf_transformation,[],[f2436]) ).
tcf(c_824,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = empty_set )
| ( sK263(X0) = X2 )
| ~ sP28(X1)
| ~ in(X2,X0)
| ~ in(sK262(X1),omega)
| ~ subset(sK263(X0),X2)
| ~ element(X0,powerset(powerset(sK262(X1)))) ),
inference(cnf_transformation,[],[f2435]) ).
tcf(c_861,plain,
! [X0: $i,X1: $i] :
( ordinal(sK275(X0,X1))
| ~ sP31(X0,X1) ),
inference(cnf_transformation,[],[f2477]) ).
tcf(c_862,plain,
! [X0: $i,X1: $i] :
( ( sK275(X0,X1) = X0 )
| ~ sP31(X0,X1) ),
inference(cnf_transformation,[],[f2476]) ).
tcf(c_863,plain,
! [X0: $i,X1: $i] :
( in(sK275(X0,X1),X1)
| ~ sP31(X0,X1) ),
inference(cnf_transformation,[],[f2475]) ).
tcf(c_870,plain,
! [X0: $i,X1: $i] :
( ~ sP33(X0,X1)
| ( sK280(X0,X1) != sK281(X0,X1) ) ),
inference(cnf_transformation,[],[f2490]) ).
tcf(c_871,plain,
! [X0: $i,X1: $i] :
( ( sK280(X0,X1) = sK279(X0,X1) )
| ~ sP33(X0,X1) ),
inference(cnf_transformation,[],[f2489]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i] :
( in(sK282(X0,X1),X0)
| ~ sP33(X0,X1) ),
inference(cnf_transformation,[],[f2488]) ).
tcf(c_873,plain,
! [X0: $i,X1: $i] :
( ( set_difference(sK282(X0,X1),unordered_pair(X1,X1)) = sK280(X0,X1) )
| ~ sP33(X0,X1) ),
inference(cnf_transformation,[],[f3216]) ).
tcf(c_874,plain,
! [X0: $i,X1: $i] :
( ( sK281(X0,X1) = sK279(X0,X1) )
| ~ sP33(X0,X1) ),
inference(cnf_transformation,[],[f2486]) ).
tcf(c_875,plain,
! [X0: $i,X1: $i] :
( in(sK283(X0,X1),X0)
| ~ sP33(X0,X1) ),
inference(cnf_transformation,[],[f2485]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i] :
( ( set_difference(sK283(X0,X1),unordered_pair(X1,X1)) = sK281(X0,X1) )
| ~ sP33(X0,X1) ),
inference(cnf_transformation,[],[f3217]) ).
tcf(c_903,plain,
! [X0: $i,X1: $i] :
( ~ sP34(X0,X1)
| ( sK293(X0,X1) != sK294(X0,X1) ) ),
inference(cnf_transformation,[],[f2521]) ).
tcf(c_904,plain,
! [X0: $i,X1: $i] :
( ( sK293(X0,X1) = sK292(X0,X1) )
| ~ sP34(X0,X1) ),
inference(cnf_transformation,[],[f2520]) ).
tcf(c_905,plain,
! [X0: $i,X1: $i] :
( in(set_difference(cast_as_carrier_subset(X1),sK293(X0,X1)),X0)
| ~ sP34(X0,X1) ),
inference(cnf_transformation,[],[f2519]) ).
tcf(c_906,plain,
! [X0: $i,X1: $i] :
( ( sK294(X0,X1) = sK292(X0,X1) )
| ~ sP34(X0,X1) ),
inference(cnf_transformation,[],[f2518]) ).
tcf(c_907,plain,
! [X0: $i,X1: $i] :
( in(set_difference(cast_as_carrier_subset(X1),sK294(X0,X1)),X0)
| ~ sP34(X0,X1) ),
inference(cnf_transformation,[],[f2517]) ).
tcf(c_920,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK301(X0,X1,X2),powerset(the_carrier(X0)))
| ~ sP35(X0,X1,X2) ),
inference(cnf_transformation,[],[f2537]) ).
tcf(c_921,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK301(X0,X1,X2) = X1 )
| ~ sP35(X0,X1,X2) ),
inference(cnf_transformation,[],[f2536]) ).
tcf(c_922,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(sK301(X0,X1,X2),X0)
| ~ sP35(X0,X1,X2) ),
inference(cnf_transformation,[],[f2535]) ).
tcf(c_923,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ sP35(X0,X1,X2) ),
inference(cnf_transformation,[],[f2534]) ).
tcf(c_936,plain,
! [X0: $i,X1: $i] :
( ~ sP37(X0,X1)
| ( sK307(X0,X1) != sK308(X0,X1) ) ),
inference(cnf_transformation,[],[f2554]) ).
tcf(c_937,plain,
! [X0: $i,X1: $i] :
( ( sK307(X0,X1) = sK306(X0,X1) )
| ~ sP37(X0,X1) ),
inference(cnf_transformation,[],[f2553]) ).
tcf(c_938,plain,
! [X0: $i,X1: $i] :
( in(relation_image(X1,sK307(X0,X1)),X0)
| ~ sP37(X0,X1) ),
inference(cnf_transformation,[],[f2552]) ).
tcf(c_939,plain,
! [X0: $i,X1: $i] :
( ( sK308(X0,X1) = sK306(X0,X1) )
| ~ sP37(X0,X1) ),
inference(cnf_transformation,[],[f2551]) ).
tcf(c_940,plain,
! [X0: $i,X1: $i] :
( in(relation_image(X1,sK308(X0,X1)),X0)
| ~ sP37(X0,X1) ),
inference(cnf_transformation,[],[f2550]) ).
tcf(c_1134,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP38(X0,X1,X2)
| open_subset(sK351(X0,X1,X2),X0)
| ~ in(sK350(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2759]) ).
tcf(c_1135,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP38(X0,X1,X2)
| in(sK350(X0,X1,X2),sK351(X0,X1,X2))
| ~ in(sK350(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2758]) ).
tcf(c_1136,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP38(X0,X1,X2)
| disjoint(X1,sK351(X0,X1,X2))
| ~ in(sK350(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2757]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP38(X0,X1,X2)
| element(sK351(X0,X1,X2),powerset(the_carrier(X0)))
| ~ in(sK350(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2756]) ).
tcf(c_1138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP38(X0,X1,X2)
| in(sK350(X0,X1,X2),X2)
| ~ open_subset(X3,X0)
| ~ disjoint(X1,X3)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(sK350(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f2755]) ).
tcf(c_1139,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP38(X0,X1,X2)
| in(sK350(X0,X1,X2),the_carrier(X0)) ),
inference(cnf_transformation,[],[f2754]) ).
tcf(c_1140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| open_subset(sK352(X0,X1,X3),X0)
| ~ in(X3,the_carrier(X0))
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f2753]) ).
tcf(c_1141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| in(X3,sK352(X0,X1,X3))
| ~ in(X3,the_carrier(X0))
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f2752]) ).
tcf(c_1142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| disjoint(X1,sK352(X0,X1,X3))
| ~ in(X3,the_carrier(X0))
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f2751]) ).
tcf(c_1143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| element(sK352(X0,X1,X3),powerset(the_carrier(X0)))
| ~ in(X3,the_carrier(X0))
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f2750]) ).
tcf(c_1144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ open_subset(X0,X1)
| ~ disjoint(X2,X0)
| ~ in(X4,X3)
| ~ in(X4,X0)
| ~ in(X4,the_carrier(X1))
| ~ sP38(X1,X2,X3)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2749]) ).
tcf(c_1185,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP40(X1,X0,X2)
| ~ one_to_one(X1)
| ~ in(sK360(X1,X0,X2),relation_field(X0))
| ~ in(sK359(X1,X0,X2),relation_field(X0))
| ~ in(unordered_pair(unordered_pair(sK359(X1,X0,X2),sK360(X1,X0,X2)),unordered_pair(sK359(X1,X0,X2),sK359(X1,X0,X2))),X0)
| ~ in(unordered_pair(unordered_pair(apply(X1,sK359(X1,X0,X2)),apply(X1,sK360(X1,X0,X2))),unordered_pair(apply(X1,sK359(X1,X0,X2)),apply(X1,sK359(X1,X0,X2)))),X2)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(cnf_transformation,[],[f3283]) ).
tcf(c_1186,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP40(X1,X0,X2)
| in(sK359(X1,X0,X2),relation_field(X0))
| in(unordered_pair(unordered_pair(sK359(X1,X0,X2),sK360(X1,X0,X2)),unordered_pair(sK359(X1,X0,X2),sK359(X1,X0,X2))),X0)
| ~ one_to_one(X1)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(cnf_transformation,[],[f3284]) ).
tcf(c_1187,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP40(X1,X0,X2)
| in(sK360(X1,X0,X2),relation_field(X0))
| in(unordered_pair(unordered_pair(sK359(X1,X0,X2),sK360(X1,X0,X2)),unordered_pair(sK359(X1,X0,X2),sK359(X1,X0,X2))),X0)
| ~ one_to_one(X1)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(cnf_transformation,[],[f3285]) ).
tcf(c_1188,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP40(X1,X0,X2)
| in(unordered_pair(unordered_pair(sK359(X1,X0,X2),sK360(X1,X0,X2)),unordered_pair(sK359(X1,X0,X2),sK359(X1,X0,X2))),X0)
| in(unordered_pair(unordered_pair(apply(X1,sK359(X1,X0,X2)),apply(X1,sK360(X1,X0,X2))),unordered_pair(apply(X1,sK359(X1,X0,X2)),apply(X1,sK359(X1,X0,X2)))),X2)
| ~ one_to_one(X1)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(cnf_transformation,[],[f3286]) ).
tcf(c_1189,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_field(X1) = relation_dom(X0) )
| ~ sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f2806]) ).
tcf(c_1190,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_field(X2) = relation_rng(X0) )
| ~ sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f2805]) ).
tcf(c_1191,plain,
! [X0: $i,X1: $i,X2: $i] :
( one_to_one(X0)
| ~ sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f2804]) ).
tcf(c_1192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4)
| ~ in(X2,relation_field(X4))
| ~ in(X1,relation_field(X4))
| ~ sP40(X0,X4,X3)
| ~ in(unordered_pair(unordered_pair(apply(X0,X1),apply(X0,X2)),unordered_pair(apply(X0,X1),apply(X0,X1))),X3) ),
inference(cnf_transformation,[],[f3287]) ).
tcf(c_1193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,relation_field(X2))
| ~ sP40(X3,X2,X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3288]) ).
tcf(c_1194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X1,relation_field(X2))
| ~ sP40(X3,X2,X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3289]) ).
tcf(c_1195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(apply(X3,X0),apply(X3,X1)),unordered_pair(apply(X3,X0),apply(X3,X0))),X4)
| ~ sP40(X3,X2,X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3290]) ).
tcf(c_1293,plain,
! [X0: $i] :
( sP42(X0)
| ~ in(subset_intersection2(the_carrier(X0),sK376(X0),sK377(X0)),the_topology(X0)) ),
inference(cnf_transformation,[],[f2916]) ).
tcf(c_1294,plain,
! [X0: $i] :
( sP42(X0)
| in(sK376(X0),the_topology(X0)) ),
inference(cnf_transformation,[],[f2915]) ).
tcf(c_1295,plain,
! [X0: $i] :
( sP42(X0)
| in(sK377(X0),the_topology(X0)) ),
inference(cnf_transformation,[],[f2914]) ).
tcf(c_1296,plain,
! [X0: $i] :
( sP42(X0)
| element(sK377(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f2913]) ).
tcf(c_1297,plain,
! [X0: $i] :
( sP42(X0)
| element(sK376(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f2912]) ).
tcf(c_1298,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_intersection2(the_carrier(X1),X2,X0),the_topology(X1))
| ~ sP42(X1)
| ~ in(X2,the_topology(X1))
| ~ in(X0,the_topology(X1))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2911]) ).
tcf(c_2679,plain,
! [X0: $i] :
( ( sK74(X0) != empty_set )
| ~ sP4(X0) ),
inference(prop_impl_just,[status(thm)],[c_148]) ).
tcf(c_2680,plain,
! [X0: $i] :
( ~ sP4(X0)
| ( sK74(X0) != empty_set ) ),
inference(renaming,[status(thm)],[c_2679]) ).
tcf(c_2681,plain,
! [X0: $i] :
( element(sK74(X0),powerset(powerset(X0)))
| ~ sP4(X0) ),
inference(prop_impl_just,[status(thm)],[c_152]) ).
tcf(c_2767,plain,
! [X0: $i] :
( ( sK119(X0) != empty_set )
| ~ sP14(X0) ),
inference(prop_impl_just,[status(thm)],[c_249]) ).
tcf(c_2768,plain,
! [X0: $i] :
( ~ sP14(X0)
| ( sK119(X0) != empty_set ) ),
inference(renaming,[status(thm)],[c_2767]) ).
tcf(c_2769,plain,
! [X0: $i] :
( element(sK119(X0),powerset(powerset(X0)))
| ~ sP14(X0) ),
inference(prop_impl_just,[status(thm)],[c_253]) ).
tcf(c_2805,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ sP35(X0,X1,X2)
| subset(X2,X1) ),
inference(prop_impl_just,[status(thm)],[c_923]) ).
tcf(c_2806,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ sP35(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_2805]) ).
tcf(c_2913,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK187(X0,X1),sK188(X0,X1)),unordered_pair(sK187(X0,X1),sK187(X0,X1))) = X0 )
| ~ sP19(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_607]) ).
tcf(c_2915,plain,
! [X0: $i,X1: $i] :
( in(sK187(X0,X1),X1)
| ~ sP19(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_608]) ).
tcf(c_2917,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(sK187(X0,X1),sK187(X0,X1)) = sK188(X0,X1) )
| ~ sP19(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_609]) ).
tcf(c_3011,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK215(X0,X1),sK216(X0,X1)),unordered_pair(sK215(X0,X1),sK215(X0,X1))) = sK213(X0,X1) )
| ~ sP22(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_717]) ).
tcf(c_3013,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK216(X0,X1))),unordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK215(X0,X1)))),X0)
| ~ sP22(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_718]) ).
tcf(c_3017,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK217(X0,X1),sK218(X0,X1)),unordered_pair(sK217(X0,X1),sK217(X0,X1))) = sK214(X0,X1) )
| ~ sP22(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_720]) ).
tcf(c_3019,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK218(X0,X1))),unordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK217(X0,X1)))),X0)
| ~ sP22(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_721]) ).
tcf(c_3041,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK232(X0,X1,X2),sK233(X0,X1,X2)),unordered_pair(sK232(X0,X1,X2),sK232(X0,X1,X2))) = X0 )
| ~ sP23(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_743]) ).
tcf(c_3077,plain,
! [X0: $i] :
( ordinal(sK262(X0))
| ~ sP28(X0) ),
inference(prop_impl_just,[status(thm)],[c_821]) ).
tcf(c_3079,plain,
! [X0: $i] :
( ( sK262(X0) = X0 )
| ~ sP28(X0) ),
inference(prop_impl_just,[status(thm)],[c_822]) ).
tcf(c_3105,plain,
! [X0: $i,X1: $i] :
( ordinal(sK275(X0,X1))
| ~ sP31(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_861]) ).
tcf(c_3107,plain,
! [X0: $i,X1: $i] :
( ( sK275(X0,X1) = X0 )
| ~ sP31(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_862]) ).
tcf(c_3109,plain,
! [X0: $i,X1: $i] :
( in(sK275(X0,X1),X1)
| ~ sP31(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_863]) ).
tcf(c_3161,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK301(X0,X1,X2),powerset(the_carrier(X0)))
| ~ sP35(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_920]) ).
tcf(c_3163,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK301(X0,X1,X2) = X1 )
| ~ sP35(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_921]) ).
tcf(c_3165,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(sK301(X0,X1,X2),X0)
| ~ sP35(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_922]) ).
tcf(c_17737,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK187(X0,X1),sK187(X0,X1)),unordered_pair(sK187(X0,X1),sK188(X0,X1))) = X0 )
| ~ sP19(X0,X1) ),
inference(demodulation,[status(thm)],[c_2913,c_967]) ).
tcf(c_18217,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK217(X0,X1),sK217(X0,X1)),unordered_pair(sK217(X0,X1),sK218(X0,X1))) = sK214(X0,X1) )
| ~ sP22(X0,X1) ),
inference(demodulation,[status(thm)],[c_3017,c_967]) ).
tcf(c_18224,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK215(X0,X1),sK215(X0,X1)),unordered_pair(sK215(X0,X1),sK216(X0,X1))) = sK213(X0,X1) )
| ~ sP22(X0,X1) ),
inference(demodulation,[status(thm)],[c_3011,c_967]) ).
tcf(c_18790,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK232(X0,X1,X2),sK232(X0,X1,X2)),unordered_pair(sK232(X0,X1,X2),sK233(X0,X1,X2))) = X0 )
| ~ sP23(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_3041,c_967]) ).
tcf(c_19184,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK217(X0,X1))),unordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK218(X0,X1)))),X0)
| ~ sP22(X0,X1) ),
inference(demodulation,[status(thm)],[c_3019,c_967]) ).
tcf(c_19191,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK215(X0,X1))),unordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK216(X0,X1)))),X0)
| ~ sP22(X0,X1) ),
inference(demodulation,[status(thm)],[c_3013,c_967]) ).
tcf(c_20542,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP40(X1,X0,X2)
| in(sK360(X1,X0,X2),relation_field(X0))
| in(unordered_pair(unordered_pair(sK359(X1,X0,X2),sK359(X1,X0,X2)),unordered_pair(sK359(X1,X0,X2),sK360(X1,X0,X2))),X0)
| ~ one_to_one(X1)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(demodulation,[status(thm)],[c_1187,c_967]) ).
tcf(c_20561,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP40(X1,X0,X2)
| in(sK359(X1,X0,X2),relation_field(X0))
| in(unordered_pair(unordered_pair(sK359(X1,X0,X2),sK359(X1,X0,X2)),unordered_pair(sK359(X1,X0,X2),sK360(X1,X0,X2))),X0)
| ~ one_to_one(X1)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(demodulation,[status(thm)],[c_1186,c_967]) ).
tcf(c_20772,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP40(X1,X0,X2)
| in(unordered_pair(unordered_pair(sK359(X1,X0,X2),sK359(X1,X0,X2)),unordered_pair(sK359(X1,X0,X2),sK360(X1,X0,X2))),X0)
| in(unordered_pair(unordered_pair(apply(X1,sK359(X1,X0,X2)),apply(X1,sK359(X1,X0,X2))),unordered_pair(apply(X1,sK359(X1,X0,X2)),apply(X1,sK360(X1,X0,X2)))),X2)
| ~ one_to_one(X1)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(demodulation,[status(thm)],[c_1188,c_967]) ).
tcf(c_20791,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP40(X1,X0,X2)
| ~ one_to_one(X1)
| ~ in(sK360(X1,X0,X2),relation_field(X0))
| ~ in(sK359(X1,X0,X2),relation_field(X0))
| ~ in(unordered_pair(unordered_pair(sK359(X1,X0,X2),sK359(X1,X0,X2)),unordered_pair(sK359(X1,X0,X2),sK360(X1,X0,X2))),X0)
| ~ in(unordered_pair(unordered_pair(apply(X1,sK359(X1,X0,X2)),apply(X1,sK359(X1,X0,X2))),unordered_pair(apply(X1,sK359(X1,X0,X2)),apply(X1,sK360(X1,X0,X2)))),X2)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(demodulation,[status(thm)],[c_1185,c_967]) ).
tcf(c_21028,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK187(X1,X2),sK187(X1,X2)),unordered_pair(sK187(X1,X2),sK188(X1,X2))) = X1 )
| ~ sP20(X0)
| ( X0 != X2 )
| ( sK184(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2911,c_17737]) ).
tcf(c_21029,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK187(sK184(X0),X0),sK187(sK184(X0),X0)),unordered_pair(sK187(sK184(X0),X0),sK188(sK184(X0),X0))) = sK184(X0) )
| ~ sP20(X0) ),
inference(unflattening,[status(thm)],[c_21028]) ).
tcf(c_21037,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(sK187(X1,X2),sK187(X1,X2)) = sK188(X1,X2) )
| ~ sP20(X0)
| ( X0 != X2 )
| ( sK184(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2911,c_2917]) ).
tcf(c_21038,plain,
! [X0: $i] :
( ( unordered_pair(sK187(sK184(X0),X0),sK187(sK184(X0),X0)) = sK188(sK184(X0),X0) )
| ~ sP20(X0) ),
inference(unflattening,[status(thm)],[c_21037]) ).
tcf(c_21046,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK187(X1,X2),X2)
| ~ sP20(X0)
| ( X0 != X2 )
| ( sK184(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2911,c_2915]) ).
tcf(c_21047,plain,
! [X0: $i] :
( in(sK187(sK184(X0),X0),X0)
| ~ sP20(X0) ),
inference(unflattening,[status(thm)],[c_21046]) ).
tcf(c_21061,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK275(X1,X2),X2)
| ~ sP32(X0)
| ( X0 != X2 )
| ( sK273(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_3103,c_3109]) ).
tcf(c_21062,plain,
! [X0: $i] :
( in(sK275(sK273(X0),X0),X0)
| ~ sP32(X0) ),
inference(unflattening,[status(thm)],[c_21061]) ).
tcf(c_21070,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK275(X1,X2) = X1 )
| ~ sP32(X0)
| ( X0 != X2 )
| ( sK273(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_3103,c_3107]) ).
tcf(c_21071,plain,
! [X0: $i] :
( ( sK275(sK273(X0),X0) = sK273(X0) )
| ~ sP32(X0) ),
inference(unflattening,[status(thm)],[c_21070]) ).
tcf(c_21079,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK275(X1,X2))
| ~ sP32(X0)
| ( X0 != X2 )
| ( sK273(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_3103,c_3105]) ).
tcf(c_21080,plain,
! [X0: $i] :
( ordinal(sK275(sK273(X0),X0))
| ~ sP32(X0) ),
inference(unflattening,[status(thm)],[c_21079]) ).
tcf(c_21168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(X4,X2)
| ~ sP36(X0,X1)
| ( X1 != X4 )
| ( X0 != X3 )
| ( sK299(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_3157,c_2806]) ).
tcf(c_21169,plain,
! [X0: $i,X1: $i] :
( subset(X1,sK299(X0,X1))
| ~ sP36(X0,X1) ),
inference(unflattening,[status(thm)],[c_21168]) ).
tcf(c_21177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( closed_subset(sK301(X3,X2,X4),X3)
| ~ sP36(X0,X1)
| ( X1 != X4 )
| ( X0 != X3 )
| ( sK299(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_3157,c_3165]) ).
tcf(c_21178,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK301(X0,sK299(X0,X1),X1),X0)
| ~ sP36(X0,X1) ),
inference(unflattening,[status(thm)],[c_21177]) ).
tcf(c_21186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK301(X3,X2,X4) = X2 )
| ~ sP36(X0,X1)
| ( X1 != X4 )
| ( X0 != X3 )
| ( sK299(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_3157,c_3163]) ).
tcf(c_21187,plain,
! [X0: $i,X1: $i] :
( ( sK301(X0,sK299(X0,X1),X1) = sK299(X0,X1) )
| ~ sP36(X0,X1) ),
inference(unflattening,[status(thm)],[c_21186]) ).
tcf(c_21195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK301(X3,X2,X4),powerset(the_carrier(X3)))
| ~ sP36(X0,X1)
| ( X1 != X4 )
| ( X0 != X3 )
| ( sK299(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_3157,c_3161]) ).
tcf(c_21196,plain,
! [X0: $i,X1: $i] :
( element(sK301(X0,sK299(X0,X1),X1),powerset(the_carrier(X0)))
| ~ sP36(X0,X1) ),
inference(unflattening,[status(thm)],[c_21195]) ).
tcf(c_21492,plain,
! [X0: $i] :
( element(sK74(X0),powerset(powerset(X0)))
| ~ sP6
| ( X0 != sK70 ) ),
inference(resolution_lifted,[status(thm)],[c_2655,c_2681]) ).
tcf(c_21493,plain,
( element(sK74(sK70),powerset(powerset(sK70)))
| ~ sP6 ),
inference(unflattening,[status(thm)],[c_21492]) ).
tcf(c_21500,plain,
! [X0: $i,X1: $i] :
( ~ sP6
| ~ in(X1,sK74(X0))
| ( X0 != sK70 )
| ( sK75(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2655,c_149]) ).
tcf(c_21501,plain,
! [X0: $i] :
( ~ sP6
| ~ in(X0,sK74(sK70))
| ( sK75(sK70,X0) != X0 ) ),
inference(unflattening,[status(thm)],[c_21500]) ).
tcf(c_21512,plain,
! [X0: $i] :
( ~ sP6
| ( X0 != sK70 )
| ( sK74(X0) != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_2655,c_2680]) ).
tcf(c_21513,plain,
( ~ sP6
| ( sK74(sK70) != empty_set ) ),
inference(unflattening,[status(thm)],[c_21512]) ).
tcf(c_21520,plain,
! [X0: $i,X1: $i] :
( subset(X1,sK75(X0,X1))
| ~ sP6
| ~ in(X1,sK74(X0))
| ( X0 != sK70 ) ),
inference(resolution_lifted,[status(thm)],[c_2655,c_151]) ).
tcf(c_21521,plain,
! [X0: $i] :
( subset(X0,sK75(sK70,X0))
| ~ sP6
| ~ in(X0,sK74(sK70)) ),
inference(unflattening,[status(thm)],[c_21520]) ).
tcf(c_21532,plain,
! [X0: $i,X1: $i] :
( in(sK75(X0,X1),sK74(X0))
| ~ sP6
| ~ in(X1,sK74(X0))
| ( X0 != sK70 ) ),
inference(resolution_lifted,[status(thm)],[c_2655,c_150]) ).
tcf(c_21533,plain,
! [X0: $i] :
( in(sK75(sK70,X0),sK74(sK70))
| ~ sP6
| ~ in(X0,sK74(sK70)) ),
inference(unflattening,[status(thm)],[c_21532]) ).
tcf(c_21557,plain,
! [X0: $i] :
( element(sK119(X0),powerset(powerset(X0)))
| ~ sP15
| ( X0 != sK117 ) ),
inference(resolution_lifted,[status(thm)],[c_2761,c_2769]) ).
tcf(c_21558,plain,
( element(sK119(sK117),powerset(powerset(sK117)))
| ~ sP15 ),
inference(unflattening,[status(thm)],[c_21557]) ).
tcf(c_21565,plain,
! [X0: $i,X1: $i] :
( ~ sP15
| ~ in(X1,sK119(X0))
| ( X0 != sK117 )
| ( sK120(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2761,c_250]) ).
tcf(c_21566,plain,
! [X0: $i] :
( ~ sP15
| ~ in(X0,sK119(sK117))
| ( sK120(sK117,X0) != X0 ) ),
inference(unflattening,[status(thm)],[c_21565]) ).
tcf(c_21577,plain,
! [X0: $i] :
( ~ sP15
| ( X0 != sK117 )
| ( sK119(X0) != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_2761,c_2768]) ).
tcf(c_21578,plain,
( ~ sP15
| ( sK119(sK117) != empty_set ) ),
inference(unflattening,[status(thm)],[c_21577]) ).
tcf(c_21585,plain,
! [X0: $i,X1: $i] :
( subset(X1,sK120(X0,X1))
| ~ sP15
| ~ in(X1,sK119(X0))
| ( X0 != sK117 ) ),
inference(resolution_lifted,[status(thm)],[c_2761,c_252]) ).
tcf(c_21586,plain,
! [X0: $i] :
( subset(X0,sK120(sK117,X0))
| ~ sP15
| ~ in(X0,sK119(sK117)) ),
inference(unflattening,[status(thm)],[c_21585]) ).
tcf(c_21597,plain,
! [X0: $i,X1: $i] :
( in(sK120(X0,X1),sK119(X0))
| ~ sP15
| ~ in(X1,sK119(X0))
| ( X0 != sK117 ) ),
inference(resolution_lifted,[status(thm)],[c_2761,c_251]) ).
tcf(c_21598,plain,
! [X0: $i] :
( in(sK120(sK117,X0),sK119(sK117))
| ~ sP15
| ~ in(X0,sK119(sK117)) ),
inference(unflattening,[status(thm)],[c_21597]) ).
tcf(c_21859,plain,
! [X0: $i,X1: $i] :
( sP30(X1)
| ( sK262(X0) = X0 )
| ~ ordinal(X1)
| ( X0 != sK266 ) ),
inference(resolution_lifted,[status(thm)],[c_3079,c_832]) ).
tcf(c_21860,plain,
! [X0: $i] :
( sP30(X0)
| ( sK262(sK266) = sK266 )
| ~ ordinal(X0) ),
inference(unflattening,[status(thm)],[c_21859]) ).
tcf(c_21871,plain,
! [X0: $i,X1: $i] :
( sP30(X1)
| ordinal(sK262(X0))
| ~ ordinal(X1)
| ( X0 != sK266 ) ),
inference(resolution_lifted,[status(thm)],[c_3077,c_832]) ).
tcf(c_21872,plain,
! [X0: $i] :
( sP30(X0)
| ordinal(sK262(sK266))
| ~ ordinal(X0) ),
inference(unflattening,[status(thm)],[c_21871]) ).
tcf(c_21883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP30(X3)
| ( X1 = empty_set )
| ( sK263(X1) = X2 )
| ~ ordinal(X3)
| ~ in(X2,X1)
| ~ in(sK262(X0),omega)
| ~ subset(sK263(X1),X2)
| ~ element(X1,powerset(powerset(sK262(X0))))
| ( X0 != sK266 ) ),
inference(resolution_lifted,[status(thm)],[c_824,c_832]) ).
tcf(c_21884,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP30(X2)
| ( X0 = empty_set )
| ( sK263(X0) = X1 )
| ~ ordinal(X2)
| ~ in(X1,X0)
| ~ in(sK262(sK266),omega)
| ~ subset(sK263(X0),X1)
| ~ element(X0,powerset(powerset(sK262(sK266)))) ),
inference(unflattening,[status(thm)],[c_21883]) ).
tcf(c_21909,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP30(X2)
| in(sK263(X1),X1)
| ( X1 = empty_set )
| ~ ordinal(X2)
| ~ in(sK262(X0),omega)
| ~ element(X1,powerset(powerset(sK262(X0))))
| ( X0 != sK266 ) ),
inference(resolution_lifted,[status(thm)],[c_823,c_832]) ).
tcf(c_21910,plain,
! [X0: $i,X1: $i] :
( sP30(X1)
| in(sK263(X0),X0)
| ( X0 = empty_set )
| ~ ordinal(X1)
| ~ in(sK262(sK266),omega)
| ~ element(X0,powerset(powerset(sK262(sK266)))) ),
inference(unflattening,[status(thm)],[c_21909]) ).
tcf(c_105019,plain,
( element(sK74(sK70),powerset(powerset(sK70)))
| ~ sP6 ),
inference(prop_impl_just,[status(thm)],[c_21493]) ).
tcf(c_105021,plain,
( ( sK74(sK70) != empty_set )
| ~ sP6 ),
inference(prop_impl_just,[status(thm)],[c_21513]) ).
tcf(c_105022,plain,
( ~ sP6
| ( sK74(sK70) != empty_set ) ),
inference(renaming,[status(thm)],[c_105021]) ).
tcf(c_105107,plain,
( element(sK119(sK117),powerset(powerset(sK117)))
| ~ sP15 ),
inference(prop_impl_just,[status(thm)],[c_21558]) ).
tcf(c_105109,plain,
( ( sK119(sK117) != empty_set )
| ~ sP15 ),
inference(prop_impl_just,[status(thm)],[c_21578]) ).
tcf(c_105110,plain,
( ~ sP15
| ( sK119(sK117) != empty_set ) ),
inference(renaming,[status(thm)],[c_105109]) ).
tcf(c_105233,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK187(sK184(X0),X0),sK187(sK184(X0),X0)),unordered_pair(sK187(sK184(X0),X0),sK188(sK184(X0),X0))) = sK184(X0) )
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_21029]) ).
tcf(c_105235,plain,
! [X0: $i] :
( ( unordered_pair(sK187(sK184(X0),X0),sK187(sK184(X0),X0)) = sK188(sK184(X0),X0) )
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_21038]) ).
tcf(c_105237,plain,
! [X0: $i] :
( in(sK187(sK184(X0),X0),X0)
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_21047]) ).
tcf(c_105281,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK217(X0,X1),sK217(X0,X1)),unordered_pair(sK217(X0,X1),sK218(X0,X1))) = sK214(X0,X1) )
| ~ sP22(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_18217]) ).
tcf(c_105283,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK215(X0,X1),sK215(X0,X1)),unordered_pair(sK215(X0,X1),sK216(X0,X1))) = sK213(X0,X1) )
| ~ sP22(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_18224]) ).
tcf(c_105285,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK217(X0,X1))),unordered_pair(apply(X1,sK217(X0,X1)),apply(X1,sK218(X0,X1)))),X0)
| ~ sP22(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_19184]) ).
tcf(c_105287,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK215(X0,X1))),unordered_pair(apply(X1,sK215(X0,X1)),apply(X1,sK216(X0,X1)))),X0)
| ~ sP22(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_19191]) ).
tcf(c_105315,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK232(X0,X1,X2),sK232(X0,X1,X2)),unordered_pair(sK232(X0,X1,X2),sK233(X0,X1,X2))) = X0 )
| ~ sP23(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_18790]) ).
tcf(c_105365,plain,
! [X0: $i] :
( in(sK275(sK273(X0),X0),X0)
| ~ sP32(X0) ),
inference(prop_impl_just,[status(thm)],[c_21062]) ).
tcf(c_105367,plain,
! [X0: $i] :
( ( sK275(sK273(X0),X0) = sK273(X0) )
| ~ sP32(X0) ),
inference(prop_impl_just,[status(thm)],[c_21071]) ).
tcf(c_105369,plain,
! [X0: $i] :
( ordinal(sK275(sK273(X0),X0))
| ~ sP32(X0) ),
inference(prop_impl_just,[status(thm)],[c_21080]) ).
tcf(c_105417,plain,
! [X0: $i,X1: $i] :
( subset(X1,sK299(X0,X1))
| ~ sP36(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_21169]) ).
tcf(c_105419,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK301(X0,sK299(X0,X1),X1),X0)
| ~ sP36(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_21178]) ).
tcf(c_105421,plain,
! [X0: $i,X1: $i] :
( ( sK301(X0,sK299(X0,X1),X1) = sK299(X0,X1) )
| ~ sP36(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_21187]) ).
tcf(c_105423,plain,
! [X0: $i,X1: $i] :
( element(sK301(X0,sK299(X0,X1),X1),powerset(the_carrier(X0)))
| ~ sP36(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_21196]) ).
tcf(c_151101,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ordinal(X0)
| sP30(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_21910]) ).
tcf(c_151102,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( X0 = empty_set )
| in(sK263(X0),X0)
| ~ element(X0,powerset(powerset(sK262(sK266)))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_21910]) ).
tcf(c_151103,plain,
( iPr_def_12
| iPr_def_11
| ~ in(sK262(sK266),omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_21910]) ).
tcf(c_151104,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_13
| ( sK263(X0) = X1 )
| ( X0 = empty_set )
| ~ in(X1,X0)
| ~ subset(sK263(X0),X1)
| ~ element(X0,powerset(powerset(sK262(sK266)))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_21884]) ).
tcf(c_151105,plain,
( iPr_def_13
| iPr_def_11
| ~ in(sK262(sK266),omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_21884]) ).
tcf(c_178103,plain,
( epsilon_transitive(sK252)
| ~ sP27 ),
inference(superposition,[status(thm)],[c_796,c_1087]) ).
tcf(c_178104,plain,
( epsilon_transitive(sK253)
| ~ sP27 ),
inference(superposition,[status(thm)],[c_798,c_1087]) ).
tcf(c_178129,plain,
( epsilon_connected(sK252)
| ~ sP27 ),
inference(superposition,[status(thm)],[c_796,c_1088]) ).
tcf(c_178130,plain,
( epsilon_connected(sK253)
| ~ sP27 ),
inference(superposition,[status(thm)],[c_798,c_1088]) ).
tcf(c_181701,plain,
! [X0: $i] :
( ordinal(sK112(sK99(X0)))
| ~ sP13(sK99(X0)) ),
inference(superposition,[status(thm)],[c_233,c_206]) ).
tcf(c_181702,plain,
~ sP13(empty_set),
inference(superposition,[status(thm)],[c_233,c_599]) ).
tcf(c_181703,plain,
( sP36(sK137,sK138)
| in(sK112(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP13(powerset(the_carrier(sK137)))
| ~ closed_subset(sK112(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK112(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_176867]) ).
tcf(c_181704,plain,
( in(sK112(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP13(powerset(the_carrier(sK137)))
| ~ closed_subset(sK112(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK112(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_176193]) ).
tcf(c_181705,plain,
( ( sK92(sK137,sK138,sK112(sK91(sK137,sK138))) = sK112(sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_233,c_175190]) ).
tcf(c_181706,plain,
( in(sK112(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_233,c_175008]) ).
tcf(c_181707,plain,
( subset(sK138,sK112(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_233,c_174960]) ).
tcf(c_181708,plain,
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,sK112(sK302(sK137,sK138))) = sK112(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_233,c_175802]) ).
tcf(c_181709,plain,
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,sK112(sK302(sK137,sK138))) = sK112(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_233,c_175753]) ).
tcf(c_181710,plain,
( sP36(sK137,sK138)
| subset(sK138,sK112(sK302(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_233,c_175029]) ).
tcf(c_181711,plain,
( in(sK112(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_175089]) ).
tcf(c_181712,plain,
! [X0: $i] :
( in(sK112(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP13(sK93(sK137,sK147(sK137,X0))) ),
inference(superposition,[status(thm)],[c_233,c_175090]) ).
tcf(c_181713,plain,
! [X0: $i] :
( in(sK112(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK125(sK137,X0)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_175091]) ).
tcf(c_181714,plain,
! [X0: $i] :
( in(sK112(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP13(sK93(sK137,sK123(sK137,X0))) ),
inference(superposition,[status(thm)],[c_233,c_175092]) ).
tcf(c_181715,plain,
! [X0: $i] :
( subset(topstr_closure(sK137,X0),sK112(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP13(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_233,c_176013]) ).
tcf(c_181716,plain,
! [X0: $i] :
( in(sK112(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP13(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_233,c_176012]) ).
tcf(c_181717,plain,
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),sK112(sK295(sK137,the_topology(sK137)))) = sK112(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137)
| ~ sP13(sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176134]) ).
tcf(c_181718,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),sK112(sK302(sK137,the_carrier(sK137)))) = sK112(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176975]) ).
tcf(c_181719,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),sK112(sK302(sK137,the_carrier(sK137)))) = sK112(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176974]) ).
tcf(c_181720,plain,
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK112(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176981]) ).
tcf(c_181721,plain,
( ( sK124(sK137,the_carrier(sK137),sK112(sK123(sK137,the_carrier(sK137)))) = sK112(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP13(sK123(sK137,the_carrier(sK137)))
| ~ element(sK112(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176971]) ).
tcf(c_181722,plain,
( subset(the_carrier(sK137),sK112(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP13(sK123(sK137,the_carrier(sK137)))
| ~ element(sK112(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176976]) ).
tcf(c_181723,plain,
( ( sK92(sK137,the_carrier(sK137),sK112(sK91(sK137,the_carrier(sK137)))) = sK112(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176980]) ).
tcf(c_181724,plain,
( in(sK112(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176982]) ).
tcf(c_181725,plain,
( subset(the_carrier(sK137),sK112(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176983]) ).
tcf(c_181726,plain,
( subset(the_carrier(sK137),sK112(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,the_carrier(sK137)))
| ~ element(sK112(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176978]) ).
tcf(c_181727,plain,
( closed_subset(sK112(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,the_carrier(sK137)))
| ~ element(sK112(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176977]) ).
tcf(c_181728,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK112(sK295(sK137,powerset(the_carrier(sK137))))) = sK112(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP13(sK295(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_176995]) ).
tcf(c_181729,plain,
( in(sK112(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_176997]) ).
tcf(c_181730,plain,
( in(sK112(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ sP13(topstr_closure(sK137,sK138))
| ~ in(sK112(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_233,c_177233]) ).
tcf(c_181731,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK112(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_233,c_177405]) ).
tcf(c_181732,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK112(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP13(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK112(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_177400]) ).
tcf(c_181733,plain,
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK112(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK112(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_233,c_177404]) ).
tcf(c_181734,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK112(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_233,c_177407]) ).
tcf(c_181735,plain,
( in(sK112(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_233,c_177406]) ).
tcf(c_181736,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK112(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK112(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_177402]) ).
tcf(c_181737,plain,
( closed_subset(sK112(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK112(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_177401]) ).
tcf(c_181738,plain,
( in(sK112(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_233,c_177421]) ).
tcf(c_181739,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| ( sK304(sK137,sK206(the_carrier(sK137)),sK112(sK302(sK137,sK206(the_carrier(sK137))))) = sK112(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_177703]) ).
tcf(c_181740,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| ( sK303(sK137,sK206(the_carrier(sK137)),sK112(sK302(sK137,sK206(the_carrier(sK137))))) = sK112(sK302(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_177702]) ).
tcf(c_181741,plain,
( sP36(sK137,sK206(the_carrier(sK137)))
| subset(sK206(the_carrier(sK137)),sK112(sK302(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_177709]) ).
tcf(c_181742,plain,
( subset(sK206(the_carrier(sK137)),sK112(sK123(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK123(sK137,sK206(the_carrier(sK137))))
| ~ element(sK112(sK123(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_177704]) ).
tcf(c_181743,plain,
( ( sK92(sK137,sK206(the_carrier(sK137)),sK112(sK91(sK137,sK206(the_carrier(sK137))))) = sK112(sK91(sK137,sK206(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_177708]) ).
tcf(c_181744,plain,
( subset(sK206(the_carrier(sK137)),sK112(sK91(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_177711]) ).
tcf(c_181745,plain,
( in(sK112(sK91(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK206(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_177710]) ).
tcf(c_181746,plain,
( subset(sK206(the_carrier(sK137)),sK112(sK147(sK137,sK206(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK206(the_carrier(sK137))))
| ~ element(sK112(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_177706]) ).
tcf(c_181747,plain,
( closed_subset(sK112(sK147(sK137,sK206(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK206(the_carrier(sK137))))
| ~ element(sK112(sK147(sK137,sK206(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_177705]) ).
tcf(c_181748,plain,
( in(sK112(sK93(sK137,sK206(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK206(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_233,c_177725]) ).
tcf(c_181749,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| ( sK304(sK137,sK371(the_carrier(sK137)),sK112(sK302(sK137,sK371(the_carrier(sK137))))) = sK112(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_178215]) ).
tcf(c_181750,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| ( sK303(sK137,sK371(the_carrier(sK137)),sK112(sK302(sK137,sK371(the_carrier(sK137))))) = sK112(sK302(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_178214]) ).
tcf(c_181751,plain,
( sP36(sK137,sK371(the_carrier(sK137)))
| subset(sK371(the_carrier(sK137)),sK112(sK302(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_178221]) ).
tcf(c_181752,plain,
( subset(sK371(the_carrier(sK137)),sK112(sK123(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK123(sK137,sK371(the_carrier(sK137))))
| ~ element(sK112(sK123(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_178216]) ).
tcf(c_181753,plain,
( ( sK92(sK137,sK371(the_carrier(sK137)),sK112(sK91(sK137,sK371(the_carrier(sK137))))) = sK112(sK91(sK137,sK371(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_178220]) ).
tcf(c_181754,plain,
( subset(sK371(the_carrier(sK137)),sK112(sK91(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_178223]) ).
tcf(c_181755,plain,
( in(sK112(sK91(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK371(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_178222]) ).
tcf(c_181756,plain,
( subset(sK371(the_carrier(sK137)),sK112(sK147(sK137,sK371(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK371(the_carrier(sK137))))
| ~ element(sK112(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_178218]) ).
tcf(c_181757,plain,
( closed_subset(sK112(sK147(sK137,sK371(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK371(the_carrier(sK137))))
| ~ element(sK112(sK147(sK137,sK371(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_178217]) ).
tcf(c_181758,plain,
( in(sK112(sK93(sK137,sK371(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK371(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_233,c_178237]) ).
tcf(c_182373,plain,
( sP36(sK137,sK138)
| in(sK112(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138))
| ~ closed_subset(sK112(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK112(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_181706,c_176867]) ).
tcf(c_182374,plain,
( in(sK112(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138))
| ~ closed_subset(sK112(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK112(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_181706,c_176193]) ).
tcf(c_182527,plain,
! [X0: $i] :
( ordinal(sK193(sK99(X0)))
| ~ sP21(sK99(X0)) ),
inference(superposition,[status(thm)],[c_619,c_206]) ).
tcf(c_182528,plain,
~ sP21(empty_set),
inference(superposition,[status(thm)],[c_619,c_599]) ).
tcf(c_182529,plain,
( sP36(sK137,sK138)
| in(sK193(powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP21(powerset(the_carrier(sK137)))
| ~ closed_subset(sK193(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK193(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_176867]) ).
tcf(c_182530,plain,
( in(sK193(powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP21(powerset(the_carrier(sK137)))
| ~ closed_subset(sK193(powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK193(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_176193]) ).
tcf(c_182531,plain,
( ( sK92(sK137,sK138,sK193(sK91(sK137,sK138))) = sK193(sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_619,c_175190]) ).
tcf(c_182532,plain,
( in(sK193(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_619,c_175008]) ).
tcf(c_182533,plain,
( subset(sK138,sK193(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_619,c_174960]) ).
tcf(c_182534,plain,
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,sK193(sK302(sK137,sK138))) = sK193(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_619,c_175802]) ).
tcf(c_182535,plain,
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,sK193(sK302(sK137,sK138))) = sK193(sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_619,c_175753]) ).
tcf(c_182536,plain,
( sP36(sK137,sK138)
| subset(sK138,sK193(sK302(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_619,c_175029]) ).
tcf(c_182537,plain,
( in(sK193(sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_175089]) ).
tcf(c_182538,plain,
! [X0: $i] :
( in(sK193(sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP21(sK93(sK137,sK147(sK137,X0))) ),
inference(superposition,[status(thm)],[c_619,c_175090]) ).
tcf(c_182539,plain,
! [X0: $i] :
( in(sK193(sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK93(sK137,sK125(sK137,X0)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_175091]) ).
tcf(c_182540,plain,
! [X0: $i] :
( in(sK193(sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP21(sK93(sK137,sK123(sK137,X0))) ),
inference(superposition,[status(thm)],[c_619,c_175092]) ).
tcf(c_182541,plain,
! [X0: $i] :
( subset(topstr_closure(sK137,X0),sK193(sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP21(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_619,c_176013]) ).
tcf(c_182542,plain,
! [X0: $i] :
( in(sK193(sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP21(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_619,c_176012]) ).
tcf(c_182543,plain,
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),sK193(sK295(sK137,the_topology(sK137)))) = sK193(sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137)
| ~ sP21(sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176134]) ).
tcf(c_182544,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),sK193(sK302(sK137,the_carrier(sK137)))) = sK193(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176975]) ).
tcf(c_182545,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),sK193(sK302(sK137,the_carrier(sK137)))) = sK193(sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176974]) ).
tcf(c_182546,plain,
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK193(sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176981]) ).
tcf(c_182547,plain,
( ( sK124(sK137,the_carrier(sK137),sK193(sK123(sK137,the_carrier(sK137)))) = sK193(sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP21(sK123(sK137,the_carrier(sK137)))
| ~ element(sK193(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176971]) ).
tcf(c_182548,plain,
( subset(the_carrier(sK137),sK193(sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP21(sK123(sK137,the_carrier(sK137)))
| ~ element(sK193(sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176976]) ).
tcf(c_182549,plain,
( ( sK92(sK137,the_carrier(sK137),sK193(sK91(sK137,the_carrier(sK137)))) = sK193(sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176980]) ).
tcf(c_182550,plain,
( in(sK193(sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176982]) ).
tcf(c_182551,plain,
( subset(the_carrier(sK137),sK193(sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176983]) ).
tcf(c_182552,plain,
( subset(the_carrier(sK137),sK193(sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP21(sK147(sK137,the_carrier(sK137)))
| ~ element(sK193(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176978]) ).
tcf(c_182553,plain,
( closed_subset(sK193(sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ sP21(sK147(sK137,the_carrier(sK137)))
| ~ element(sK193(sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176977]) ).
tcf(c_182554,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK193(sK295(sK137,powerset(the_carrier(sK137))))) = sK193(sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP21(sK295(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_176995]) ).
tcf(c_182555,plain,
( in(sK193(sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK93(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_176997]) ).
tcf(c_182556,plain,
( in(sK193(topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ sP21(topstr_closure(sK137,sK138))
| ~ in(sK193(topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_619,c_177233]) ).
tcf(c_182557,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK193(sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_619,c_177405]) ).
tcf(c_182558,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK193(sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP21(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK193(sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_177400]) ).
tcf(c_182559,plain,
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK193(sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK193(sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_619,c_177404]) ).
tcf(c_182560,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK193(sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_619,c_177407]) ).
tcf(c_182561,plain,
( in(sK193(sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_619,c_177406]) ).
tcf(c_182562,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK193(sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP21(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK193(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_177402]) ).
tcf(c_182563,plain,
( closed_subset(sK193(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ sP21(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK193(sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_177401]) ).
tcf(c_182564,plain,
( in(sK193(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_619,c_177421]) ).
tcf(c_182745,plain,
( sP36(sK137,sK138)
| in(sK193(sK91(sK137,sK138)),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138))
| ~ closed_subset(sK193(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK193(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_182532,c_176867]) ).
tcf(c_182746,plain,
( in(sK193(sK91(sK137,sK138)),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138))
| ~ closed_subset(sK193(sK91(sK137,sK138)),sK137)
| ~ subset(sK138,sK193(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_182532,c_176193]) ).
tcf(c_183189,plain,
! [X0: $i] :
( element(sK112(X0),X0)
| ~ sP13(X0) ),
inference(superposition,[status(thm)],[c_233,c_701]) ).
tcf(c_183196,plain,
! [X0: $i] :
( element(sK193(X0),X0)
| ~ sP21(X0) ),
inference(superposition,[status(thm)],[c_619,c_701]) ).
tcf(c_183231,plain,
( element(sK112(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_181706,c_701]) ).
tcf(c_183233,plain,
( element(sK193(sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_182532,c_701]) ).
tcf(c_183430,plain,
( empty(the_carrier(sK137))
| in(sK112(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_182971]) ).
tcf(c_183434,plain,
( empty(the_carrier(sK137))
| in(sK193(sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_182971]) ).
tcf(c_183483,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK112(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_182972]) ).
tcf(c_183487,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK193(sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_182972]) ).
tcf(c_183538,plain,
! [X0: $i] :
( ~ sP13(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_233,c_781]) ).
tcf(c_183545,plain,
! [X0: $i] :
( ~ sP21(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_619,c_781]) ).
tcf(c_183580,plain,
( ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138))
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_181706,c_781]) ).
tcf(c_183582,plain,
( ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138))
| ~ empty(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_182532,c_781]) ).
tcf(c_183686,plain,
( sP30(sK252)
| ordinal(sK267)
| ~ sP27 ),
inference(superposition,[status(thm)],[c_796,c_827]) ).
tcf(c_183687,plain,
( sP30(sK253)
| ordinal(sK267)
| ~ sP27 ),
inference(superposition,[status(thm)],[c_798,c_827]) ).
tcf(c_184828,plain,
( empty(the_carrier(sK137))
| in(sK112(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_184376]) ).
tcf(c_184832,plain,
( empty(the_carrier(sK137))
| in(sK193(sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_184376]) ).
tcf(c_184900,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK112(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_184377]) ).
tcf(c_184904,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK193(sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_184377]) ).
tcf(c_184996,plain,
! [X0: $i] :
( sP42(X0)
| ~ empty(the_topology(X0)) ),
inference(superposition,[status(thm)],[c_1294,c_781]) ).
tcf(c_184997,plain,
! [X0: $i] :
( sP42(X0)
| element(sK376(X0),the_topology(X0)) ),
inference(superposition,[status(thm)],[c_1294,c_701]) ).
tcf(c_185009,plain,
! [X0: $i] :
( sP42(X0)
| element(sK377(X0),the_topology(X0)) ),
inference(superposition,[status(thm)],[c_1295,c_701]) ).
tcf(c_185148,plain,
( empty(the_carrier(sK137))
| closed_subset(sK112(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK112(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_182966]) ).
tcf(c_185152,plain,
( empty(the_carrier(sK137))
| closed_subset(sK193(sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP21(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK193(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_182966]) ).
tcf(c_185228,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK112(sK91(sK137,sK207(the_carrier(sK137))))) = sK112(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_182969]) ).
tcf(c_185232,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK193(sK91(sK137,sK207(the_carrier(sK137))))) = sK193(sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_182969]) ).
tcf(c_185375,plain,
( empty(the_carrier(sK137))
| closed_subset(sK112(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK112(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_184371]) ).
tcf(c_185379,plain,
( empty(the_carrier(sK137))
| closed_subset(sK193(sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP21(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK193(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_184371]) ).
tcf(c_185595,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK112(sK91(sK137,sK325(the_carrier(sK137))))) = sK112(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_184374]) ).
tcf(c_185599,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK193(sK91(sK137,sK325(the_carrier(sK137))))) = sK193(sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_184374]) ).
tcf(c_185764,plain,
! [X0: $i] :
( in(sK112(sK99(X0)),X0)
| ~ sP13(sK99(X0)) ),
inference(superposition,[status(thm)],[c_233,c_205]) ).
tcf(c_185768,plain,
! [X0: $i] :
( in(sK193(sK99(X0)),X0)
| ~ sP21(sK99(X0)) ),
inference(superposition,[status(thm)],[c_619,c_205]) ).
tcf(c_185861,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK112(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_182970]) ).
tcf(c_185865,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK193(sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_182970]) ).
tcf(c_185955,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK112(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_233,c_184375]) ).
tcf(c_185959,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK193(sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_619,c_184375]) ).
tcf(c_186247,plain,
relation_dom(sK115(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_241,c_181702]) ).
tcf(c_186248,plain,
( ( relation_dom(sK115(sK91(sK137,sK138))) = sK91(sK137,sK138) )
| ( sK92(sK137,sK138,sK112(sK91(sK137,sK138))) = sK112(sK91(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_241,c_181705]) ).
tcf(c_186249,plain,
( sP36(sK137,sK138)
| ( relation_dom(sK115(sK302(sK137,sK138))) = sK302(sK137,sK138) )
| ( sK304(sK137,sK138,sK112(sK302(sK137,sK138))) = sK112(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_241,c_181709]) ).
tcf(c_186250,plain,
( sP36(sK137,sK138)
| ( relation_dom(sK115(sK302(sK137,sK138))) = sK302(sK137,sK138) )
| ( sK303(sK137,sK138,sK112(sK302(sK137,sK138))) = sK112(sK302(sK137,sK138)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_241,c_181708]) ).
tcf(c_187349,plain,
( ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138))
| ~ proper_subset(sK112(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_181707,c_492]) ).
tcf(c_187350,plain,
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK138))
| ~ proper_subset(sK112(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_181710,c_492]) ).
tcf(c_187353,plain,
( ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138))
| ~ proper_subset(sK193(sK91(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_182533,c_492]) ).
tcf(c_187354,plain,
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,sK138))
| ~ proper_subset(sK193(sK302(sK137,sK138)),sK138) ),
inference(superposition,[status(thm)],[c_182536,c_492]) ).
tcf(c_187563,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK112(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK123(sK137,sK207(the_carrier(sK137))))
| ~ element(sK112(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_182965]) ).
tcf(c_187569,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK193(sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP21(sK123(sK137,sK207(the_carrier(sK137))))
| ~ element(sK193(sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_182965]) ).
tcf(c_187732,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK112(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK112(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_182967]) ).
tcf(c_187738,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK193(sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP21(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK193(sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_182967]) ).
tcf(c_187856,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK112(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK123(sK137,sK325(the_carrier(sK137))))
| ~ element(sK112(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_184370]) ).
tcf(c_187862,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK193(sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP21(sK123(sK137,sK325(the_carrier(sK137))))
| ~ element(sK193(sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_184370]) ).
tcf(c_187988,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK112(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK112(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_184372]) ).
tcf(c_187994,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK193(sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP21(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK193(sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_184372]) ).
tcf(c_188323,plain,
! [X0: $i] :
( in(sK154(X0),X0)
| ~ sP13(X0) ),
inference(superposition,[status(thm)],[c_233,c_542]) ).
tcf(c_188332,plain,
! [X0: $i] :
( in(sK154(X0),X0)
| ~ sP21(X0) ),
inference(superposition,[status(thm)],[c_619,c_542]) ).
tcf(c_188340,plain,
! [X0: $i] :
( sP42(X0)
| in(sK154(the_topology(X0)),the_topology(X0)) ),
inference(superposition,[status(thm)],[c_1294,c_542]) ).
tcf(c_188373,plain,
( in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_181706,c_542]) ).
tcf(c_188375,plain,
( in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_182532,c_542]) ).
tcf(c_188647,plain,
! [X0: $i] :
( ~ sP13(X0)
| ~ in(X0,sK112(X0)) ),
inference(superposition,[status(thm)],[c_233,c_546]) ).
tcf(c_188656,plain,
! [X0: $i] :
( ~ sP21(X0)
| ~ in(X0,sK193(X0)) ),
inference(superposition,[status(thm)],[c_619,c_546]) ).
tcf(c_188664,plain,
! [X0: $i] :
( sP42(X0)
| ~ in(the_topology(X0),sK376(X0)) ),
inference(superposition,[status(thm)],[c_1294,c_546]) ).
tcf(c_188665,plain,
! [X0: $i] :
( sP42(X0)
| ~ in(the_topology(X0),sK377(X0)) ),
inference(superposition,[status(thm)],[c_1295,c_546]) ).
tcf(c_188697,plain,
( ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138))
| ~ in(powerset(the_carrier(sK137)),sK112(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_181706,c_546]) ).
tcf(c_188699,plain,
( ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138))
| ~ in(powerset(the_carrier(sK137)),sK193(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_182532,c_546]) ).
tcf(c_189164,plain,
! [X0: $i] :
( reflexive(sK61(X0))
| ~ sP3(X0)
| ~ well_ordering(sK61(X0)) ),
inference(superposition,[status(thm)],[c_111,c_589]) ).
tcf(c_189293,plain,
! [X0: $i] :
( transitive(sK61(X0))
| ~ sP3(X0)
| ~ well_ordering(sK61(X0)) ),
inference(superposition,[status(thm)],[c_111,c_590]) ).
tcf(c_189430,plain,
! [X0: $i] :
( antisymmetric(sK61(X0))
| ~ sP3(X0)
| ~ well_ordering(sK61(X0)) ),
inference(superposition,[status(thm)],[c_111,c_591]) ).
tcf(c_189557,plain,
! [X0: $i] :
( connected(sK61(X0))
| ~ sP3(X0)
| ~ well_ordering(sK61(X0)) ),
inference(superposition,[status(thm)],[c_111,c_592]) ).
tcf(c_189730,plain,
! [X0: $i] :
( closed_subset(sK112(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP13(sK147(sK137,topstr_closure(sK137,X0)))
| ~ element(sK112(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_176007]) ).
tcf(c_189736,plain,
! [X0: $i] :
( closed_subset(sK193(sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP21(sK147(sK137,topstr_closure(sK137,X0)))
| ~ element(sK193(sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_176007]) ).
tcf(c_189852,plain,
! [X0: $i] :
( ( sK92(sK137,topstr_closure(sK137,X0),sK112(sK91(sK137,topstr_closure(sK137,X0)))) = sK112(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP13(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_233,c_176010]) ).
tcf(c_189858,plain,
! [X0: $i] :
( ( sK92(sK137,topstr_closure(sK137,X0),sK193(sK91(sK137,topstr_closure(sK137,X0)))) = sK193(sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP21(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_619,c_176010]) ).
tcf(c_190076,plain,
! [X0: $i] :
( well_founded_relation(sK61(X0))
| ~ sP3(X0)
| ~ well_ordering(sK61(X0)) ),
inference(superposition,[status(thm)],[c_111,c_593]) ).
tcf(c_190967,plain,
( open_subset(sK112(the_topology(sK137)),sK137)
| ~ sP13(the_topology(sK137))
| ~ subset(sK112(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_233,c_190618]) ).
tcf(c_190974,plain,
( open_subset(sK193(the_topology(sK137)),sK137)
| ~ sP21(the_topology(sK137))
| ~ subset(sK193(the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_619,c_190618]) ).
tcf(c_190979,plain,
( sP42(sK137)
| open_subset(sK376(sK137),sK137)
| ~ subset(sK376(sK137),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1294,c_190618]) ).
tcf(c_190980,plain,
( sP42(sK137)
| open_subset(sK377(sK137),sK137)
| ~ subset(sK377(sK137),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_1295,c_190618]) ).
tcf(c_191607,plain,
! [X0: $i] :
( subset(sK112(powerset(X0)),X0)
| ~ sP13(powerset(X0)) ),
inference(superposition,[status(thm)],[c_233,c_667]) ).
tcf(c_191614,plain,
! [X0: $i] :
( subset(sK193(powerset(X0)),X0)
| ~ sP21(powerset(X0)) ),
inference(superposition,[status(thm)],[c_619,c_667]) ).
tcf(c_191631,plain,
( subset(sK112(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_181706,c_667]) ).
tcf(c_191633,plain,
( subset(sK193(sK91(sK137,sK138)),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_182532,c_667]) ).
tcf(c_191882,plain,
! [X0: $i] :
( subset(X0,sK112(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_233,c_190604]) ).
tcf(c_191889,plain,
! [X0: $i] :
( subset(X0,sK193(sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_619,c_190604]) ).
tcf(c_191996,plain,
( subset(sK138,sK112(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP13(sK123(sK137,sK138))
| ~ subset(sK112(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_233,c_190612]) ).
tcf(c_192003,plain,
( subset(sK138,sK193(sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP21(sK123(sK137,sK138))
| ~ subset(sK193(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_619,c_190612]) ).
tcf(c_192114,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK112(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_233,c_192075]) ).
tcf(c_192121,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK193(sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP21(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_619,c_192075]) ).
tcf(c_192254,plain,
! [X0: $i] :
( sP27
| ordinal(sK112(sK254(X0)))
| ~ sP13(sK254(X0)) ),
inference(superposition,[status(thm)],[c_233,c_802]) ).
tcf(c_192261,plain,
! [X0: $i] :
( sP27
| ordinal(sK193(sK254(X0)))
| ~ sP21(sK254(X0)) ),
inference(superposition,[status(thm)],[c_619,c_802]) ).
tcf(c_192367,plain,
( closed_subset(sK112(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK138))
| ~ subset(sK112(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_233,c_190613]) ).
tcf(c_192374,plain,
( closed_subset(sK193(sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ sP21(sK147(sK137,sK138))
| ~ subset(sK193(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_619,c_190613]) ).
tcf(c_192522,plain,
( closed_subset(set_difference(the_carrier(sK137),sK112(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_233,c_192446]) ).
tcf(c_192529,plain,
( closed_subset(set_difference(the_carrier(sK137),sK193(sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137)
| ~ sP21(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_619,c_192446]) ).
tcf(c_192597,plain,
( subset(sK138,sK112(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP13(sK147(sK137,sK138))
| ~ subset(sK112(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_233,c_190614]) ).
tcf(c_192604,plain,
( subset(sK138,sK193(sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP21(sK147(sK137,sK138))
| ~ subset(sK193(sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_619,c_190614]) ).
tcf(c_192721,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK112(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_233,c_192676]) ).
tcf(c_192728,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK193(sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP21(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_619,c_192676]) ).
tcf(c_192933,plain,
! [X0: $i] :
( sP42(X0)
| subset(sK377(X0),the_carrier(X0)) ),
inference(superposition,[status(thm)],[c_1296,c_659]) ).
tcf(c_192934,plain,
! [X0: $i] :
( sP42(sK137)
| in(X0,sK377(sK137))
| ~ closed_subset(sK377(sK137),sK137)
| ~ subset(sK138,sK377(sK137))
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1296,c_177131]) ).
tcf(c_192935,plain,
! [X0: $i,X1: $i] :
( sP42(sK137)
| in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ subset(sK377(sK137),X1)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,sK377(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_48138]) ).
tcf(c_192936,plain,
! [X0: $i] :
( sP42(sK137)
| sP36(sK137,sK377(sK137))
| in(X0,sK302(sK137,sK377(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK377(sK137),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_47771]) ).
tcf(c_192937,plain,
! [X0: $i] :
( sP42(sK137)
| in(sK377(sK137),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK377(sK137),sK137)
| ~ subset(X0,sK377(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_48368]) ).
tcf(c_192938,plain,
! [X0: $i] :
( sP42(sK137)
| ( sK124(sK137,sK377(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK377(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_48332]) ).
tcf(c_192939,plain,
! [X0: $i] :
( sP42(sK137)
| in(sK377(sK137),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK377(sK137),sK137)
| ~ subset(X0,sK377(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_48105]) ).
tcf(c_192940,plain,
! [X0: $i] :
( sP42(sK137)
| in(X0,sK91(sK137,sK377(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK377(sK137),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_47795]) ).
tcf(c_192941,plain,
! [X0: $i] :
( sP42(sK137)
| sP36(sK137,sK377(sK137))
| ( sK303(sK137,sK377(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK377(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_47947]) ).
tcf(c_192942,plain,
! [X0: $i] :
( sP42(sK137)
| sP36(sK137,sK377(sK137))
| ( sK304(sK137,sK377(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK377(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_47911]) ).
tcf(c_192943,plain,
! [X0: $i] :
( sP42(sK137)
| subset(sK377(sK137),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK377(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_48297]) ).
tcf(c_192944,plain,
! [X0: $i] :
( sP42(sK137)
| closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK377(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_48087]) ).
tcf(c_192945,plain,
! [X0: $i] :
( sP42(sK137)
| subset(sK377(sK137),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK377(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_48070]) ).
tcf(c_192946,plain,
! [X0: $i] :
( sP42(sK137)
| ( topstr_closure(sK137,sK377(sK137)) = X0 )
| ~ sP38(sK137,sK377(sK137),X0)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_47756]) ).
tcf(c_192947,plain,
! [X0: $i] :
( sP42(sK137)
| ( sK92(sK137,sK377(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK377(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_48460]) ).
tcf(c_192948,plain,
! [X0: $i] :
( sP42(sK137)
| sP36(sK137,sK377(sK137))
| subset(sK377(sK137),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK377(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_47876]) ).
tcf(c_192949,plain,
! [X0: $i] :
( sP42(sK137)
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK377(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_48490]) ).
tcf(c_192950,plain,
! [X0: $i] :
( sP42(sK137)
| subset(sK377(sK137),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK377(sK137))) ),
inference(superposition,[status(thm)],[c_1296,c_48431]) ).
tcf(c_192951,plain,
( sP42(sK137)
| in(empty_set,sK147(sK137,sK377(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK377(sK137),empty_set) ),
inference(superposition,[status(thm)],[c_1296,c_182438]) ).
tcf(c_192952,plain,
( sP42(sK137)
| ( sK124(sK137,empty_set,sK377(sK137)) = sK377(sK137) )
| ~ topological_space(sK137)
| ~ in(sK377(sK137),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_1296,c_182437]) ).
tcf(c_192953,plain,
( sP42(sK137)
| in(empty_set,sK123(sK137,sK377(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK377(sK137),empty_set) ),
inference(superposition,[status(thm)],[c_1296,c_182436]) ).
tcf(c_192954,plain,
( sP42(sK137)
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK377(sK137)))) = topstr_closure(sK137,topstr_closure(sK137,sK377(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1296,c_176018]) ).
tcf(c_192955,plain,
( sP42(sK137)
| in(sK138,sK123(sK137,sK377(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK377(sK137),sK138) ),
inference(superposition,[status(thm)],[c_1296,c_176521]) ).
tcf(c_192956,plain,
( sP42(sK137)
| ( sK124(sK137,sK138,sK377(sK137)) = sK377(sK137) )
| ~ topological_space(sK137)
| ~ in(sK377(sK137),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1296,c_176408]) ).
tcf(c_192957,plain,
( sP42(sK137)
| in(sK138,sK147(sK137,sK377(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK377(sK137),sK138) ),
inference(superposition,[status(thm)],[c_1296,c_176286]) ).
tcf(c_192958,plain,
( sP42(sK137)
| subset(sK138,sK377(sK137))
| ~ topological_space(sK137)
| ~ in(sK377(sK137),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1296,c_175672]) ).
tcf(c_192959,plain,
( sP42(sK137)
| closed_subset(sK377(sK137),sK137)
| ~ topological_space(sK137)
| ~ in(sK377(sK137),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1296,c_175482]) ).
tcf(c_192960,plain,
( sP42(sK137)
| subset(sK138,sK377(sK137))
| ~ topological_space(sK137)
| ~ in(sK377(sK137),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1296,c_175418]) ).
tcf(c_192961,plain,
( sP42(sK137)
| ( topstr_closure(sK137,sK138) = sK377(sK137) )
| ~ sP38(sK137,sK138,sK377(sK137)) ),
inference(superposition,[status(thm)],[c_1296,c_175209]) ).
tcf(c_192962,plain,
( sP42(sK137)
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK377(sK137))) = topstr_closure(sK137,sK377(sK137)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1296,c_48058]) ).
tcf(c_192963,plain,
( sP42(sK137)
| ( topstr_closure(sK137,sK377(sK137)) = sK377(sK137) )
| ~ closed_subset(sK377(sK137),sK137) ),
inference(superposition,[status(thm)],[c_1296,c_48037]) ).
tcf(c_192964,plain,
( sP42(sK137)
| open_subset(sK377(sK137),sK137)
| ~ in(sK377(sK137),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_1296,c_47852]) ).
tcf(c_192965,plain,
( sP42(sK137)
| in(sK377(sK137),the_topology(sK137))
| ~ open_subset(sK377(sK137),sK137) ),
inference(superposition,[status(thm)],[c_1296,c_47840]) ).
tcf(c_193179,plain,
( sP42(sK137)
| open_subset(sK377(sK137),sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_192964,c_1295]) ).
tcf(c_193239,plain,
! [X0: $i] :
( sP42(X0)
| subset(sK376(X0),the_carrier(X0)) ),
inference(superposition,[status(thm)],[c_1297,c_659]) ).
tcf(c_193240,plain,
! [X0: $i] :
( sP42(sK137)
| in(X0,sK376(sK137))
| ~ closed_subset(sK376(sK137),sK137)
| ~ subset(sK138,sK376(sK137))
| ~ in(X0,the_carrier(sK137))
| ~ in(X0,topstr_closure(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1297,c_177131]) ).
tcf(c_193241,plain,
! [X0: $i,X1: $i] :
( sP42(sK137)
| in(X0,X1)
| ~ closed_subset(X1,sK137)
| ~ subset(sK376(sK137),X1)
| ~ in(X0,the_carrier(sK137))
| ~ element(X1,powerset(the_carrier(sK137)))
| ~ in(X0,topstr_closure(sK137,sK376(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_48138]) ).
tcf(c_193242,plain,
! [X0: $i] :
( sP42(sK137)
| sP36(sK137,sK376(sK137))
| in(X0,sK302(sK137,sK376(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK376(sK137),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_47771]) ).
tcf(c_193243,plain,
! [X0: $i] :
( sP42(sK137)
| in(sK376(sK137),sK123(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK376(sK137),sK137)
| ~ subset(X0,sK376(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_48368]) ).
tcf(c_193244,plain,
! [X0: $i] :
( sP42(sK137)
| ( sK124(sK137,sK376(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK376(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_48332]) ).
tcf(c_193245,plain,
! [X0: $i] :
( sP42(sK137)
| in(sK376(sK137),sK147(sK137,X0))
| ~ topological_space(sK137)
| ~ closed_subset(sK376(sK137),sK137)
| ~ subset(X0,sK376(sK137))
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_48105]) ).
tcf(c_193246,plain,
! [X0: $i] :
( sP42(sK137)
| in(X0,sK91(sK137,sK376(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(X0,sK137)
| ~ subset(sK376(sK137),X0)
| ~ in(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_47795]) ).
tcf(c_193247,plain,
! [X0: $i] :
( sP42(sK137)
| sP36(sK137,sK376(sK137))
| ( sK303(sK137,sK376(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK376(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_47947]) ).
tcf(c_193248,plain,
! [X0: $i] :
( sP42(sK137)
| sP36(sK137,sK376(sK137))
| ( sK304(sK137,sK376(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK376(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_47911]) ).
tcf(c_193249,plain,
! [X0: $i] :
( sP42(sK137)
| subset(sK376(sK137),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK123(sK137,sK376(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_48297]) ).
tcf(c_193250,plain,
! [X0: $i] :
( sP42(sK137)
| closed_subset(X0,sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK376(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_48087]) ).
tcf(c_193251,plain,
! [X0: $i] :
( sP42(sK137)
| subset(sK376(sK137),X0)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ in(X0,sK147(sK137,sK376(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_48070]) ).
tcf(c_193252,plain,
! [X0: $i] :
( sP42(sK137)
| ( topstr_closure(sK137,sK376(sK137)) = X0 )
| ~ sP38(sK137,sK376(sK137),X0)
| ~ element(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_47756]) ).
tcf(c_193253,plain,
! [X0: $i] :
( sP42(sK137)
| ( sK92(sK137,sK376(sK137),X0) = X0 )
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK376(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_48460]) ).
tcf(c_193254,plain,
! [X0: $i] :
( sP42(sK137)
| sP36(sK137,sK376(sK137))
| subset(sK376(sK137),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK302(sK137,sK376(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_47876]) ).
tcf(c_193255,plain,
! [X0: $i] :
( sP42(sK137)
| in(X0,powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK376(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_48490]) ).
tcf(c_193256,plain,
! [X0: $i] :
( sP42(sK137)
| subset(sK376(sK137),X0)
| ~ topological_space(sK137)
| ~ in(X0,sK91(sK137,sK376(sK137))) ),
inference(superposition,[status(thm)],[c_1297,c_48431]) ).
tcf(c_193257,plain,
( sP42(sK137)
| in(empty_set,sK147(sK137,sK376(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK376(sK137),empty_set) ),
inference(superposition,[status(thm)],[c_1297,c_182438]) ).
tcf(c_193258,plain,
( sP42(sK137)
| ( sK124(sK137,empty_set,sK376(sK137)) = sK376(sK137) )
| ~ topological_space(sK137)
| ~ in(sK376(sK137),sK123(sK137,empty_set)) ),
inference(superposition,[status(thm)],[c_1297,c_182437]) ).
tcf(c_193259,plain,
( sP42(sK137)
| in(empty_set,sK123(sK137,sK376(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(empty_set,sK137)
| ~ subset(sK376(sK137),empty_set) ),
inference(superposition,[status(thm)],[c_1297,c_182436]) ).
tcf(c_193260,plain,
( sP42(sK137)
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,topstr_closure(sK137,sK376(sK137)))) = topstr_closure(sK137,topstr_closure(sK137,sK376(sK137))) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1297,c_176018]) ).
tcf(c_193261,plain,
( sP42(sK137)
| in(sK138,sK123(sK137,sK376(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK376(sK137),sK138) ),
inference(superposition,[status(thm)],[c_1297,c_176521]) ).
tcf(c_193262,plain,
( sP42(sK137)
| ( sK124(sK137,sK138,sK376(sK137)) = sK376(sK137) )
| ~ topological_space(sK137)
| ~ in(sK376(sK137),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1297,c_176408]) ).
tcf(c_193263,plain,
( sP42(sK137)
| in(sK138,sK147(sK137,sK376(sK137)))
| ~ topological_space(sK137)
| ~ closed_subset(sK138,sK137)
| ~ subset(sK376(sK137),sK138) ),
inference(superposition,[status(thm)],[c_1297,c_176286]) ).
tcf(c_193264,plain,
( sP42(sK137)
| subset(sK138,sK376(sK137))
| ~ topological_space(sK137)
| ~ in(sK376(sK137),sK123(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1297,c_175672]) ).
tcf(c_193265,plain,
( sP42(sK137)
| closed_subset(sK376(sK137),sK137)
| ~ topological_space(sK137)
| ~ in(sK376(sK137),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1297,c_175482]) ).
tcf(c_193266,plain,
( sP42(sK137)
| subset(sK138,sK376(sK137))
| ~ topological_space(sK137)
| ~ in(sK376(sK137),sK147(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_1297,c_175418]) ).
tcf(c_193267,plain,
( sP42(sK137)
| ( topstr_closure(sK137,sK138) = sK376(sK137) )
| ~ sP38(sK137,sK138,sK376(sK137)) ),
inference(superposition,[status(thm)],[c_1297,c_175209]) ).
tcf(c_193268,plain,
( sP42(sK137)
| ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK376(sK137))) = topstr_closure(sK137,sK376(sK137)) )
| ~ topological_space(sK137) ),
inference(superposition,[status(thm)],[c_1297,c_48058]) ).
tcf(c_193269,plain,
( sP42(sK137)
| ( topstr_closure(sK137,sK376(sK137)) = sK376(sK137) )
| ~ closed_subset(sK376(sK137),sK137) ),
inference(superposition,[status(thm)],[c_1297,c_48037]) ).
tcf(c_193270,plain,
( sP42(sK137)
| open_subset(sK376(sK137),sK137)
| ~ in(sK376(sK137),the_topology(sK137)) ),
inference(superposition,[status(thm)],[c_1297,c_47852]) ).
tcf(c_193271,plain,
( sP42(sK137)
| in(sK376(sK137),the_topology(sK137))
| ~ open_subset(sK376(sK137),sK137) ),
inference(superposition,[status(thm)],[c_1297,c_47840]) ).
tcf(c_193479,plain,
( subset(sK74(sK70),powerset(sK70))
| ~ sP6 ),
inference(superposition,[status(thm)],[c_105019,c_659]) ).
tcf(c_193486,plain,
( subset(sK119(sK117),powerset(sK117))
| ~ sP15 ),
inference(superposition,[status(thm)],[c_105107,c_659]) ).
tcf(c_193493,plain,
! [X0: $i] :
( ordinal(sK267)
| sP30(sK275(sK273(X0),X0))
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_105369,c_827]) ).
tcf(c_193494,plain,
! [X0: $i] :
( epsilon_connected(sK275(sK273(X0),X0))
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_105369,c_1088]) ).
tcf(c_193495,plain,
! [X0: $i] :
( epsilon_transitive(sK275(sK273(X0),X0))
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_105369,c_1087]) ).
tcf(c_193522,plain,
( sP42(sK137)
| open_subset(sK376(sK137),sK137) ),
inference(forward_subsumption_resolution,[status(thm)],[c_193270,c_1294]) ).
tcf(c_193807,plain,
! [X0: $i] :
( in(sK112(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_233,c_190603]) ).
tcf(c_193814,plain,
! [X0: $i] :
( in(sK193(sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_619,c_190603]) ).
tcf(c_194601,plain,
! [X0: $i] :
( sP36(sK137,X0)
| subset(X0,sK112(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_233,c_190602]) ).
tcf(c_194608,plain,
! [X0: $i] :
( sP36(sK137,X0)
| subset(X0,sK193(sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_619,c_190602]) ).
tcf(c_194714,plain,
! [X0: $i] :
( in(sK112(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,X0))
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_233,c_190624]) ).
tcf(c_194721,plain,
! [X0: $i] :
( in(sK193(sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK93(sK137,X0))
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_619,c_190624]) ).
tcf(c_195406,plain,
! [X0: $i,X1: $i] :
( ~ sP11(X0,X1)
| ~ in(X0,sK105(X0,X1)) ),
inference(superposition,[status(thm)],[c_222,c_546]) ).
tcf(c_195407,plain,
! [X0: $i,X1: $i] :
( in(sK154(X0),X0)
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_542]) ).
tcf(c_195408,plain,
! [X0: $i,X1: $i] :
( ~ empty(X0)
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_781]) ).
tcf(c_195409,plain,
! [X0: $i,X1: $i] :
( element(sK105(X0,X1),X0)
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_701]) ).
tcf(c_195410,plain,
! [X0: $i,X1: $i] :
( in(sK105(sK99(X0),X1),X0)
| ~ sP11(sK99(X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_205]) ).
tcf(c_195411,plain,
! [X0: $i,X1: $i] :
( ordinal(sK105(sK99(X0),X1))
| ~ sP11(sK99(X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_206]) ).
tcf(c_195412,plain,
! [X0: $i] : ~ sP11(empty_set,X0),
inference(superposition,[status(thm)],[c_222,c_599]) ).
tcf(c_195413,plain,
! [X0: $i,X1: $i] :
( subset(sK105(powerset(X0),X1),X0)
| ~ sP11(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_667]) ).
tcf(c_195414,plain,
! [X0: $i,X1: $i] :
( sP27
| ordinal(sK105(sK254(X0),X1))
| ~ sP11(sK254(X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_802]) ).
tcf(c_195415,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(sK105(powerset(the_carrier(sK137)),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP11(powerset(the_carrier(sK137)),X0)
| ~ closed_subset(sK105(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK105(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_222,c_176867]) ).
tcf(c_195416,plain,
! [X0: $i] :
( in(sK105(powerset(the_carrier(sK137)),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP11(powerset(the_carrier(sK137)),X0)
| ~ closed_subset(sK105(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK105(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_222,c_176193]) ).
tcf(c_195417,plain,
! [X0: $i,X1: $i] :
( in(sK105(sK93(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137)))
| ~ sP11(sK93(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_190624]) ).
tcf(c_195418,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| subset(X0,sK105(sK302(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP11(sK302(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_190602]) ).
tcf(c_195419,plain,
! [X0: $i,X1: $i] :
( in(sK105(sK91(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP11(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_190603]) ).
tcf(c_195420,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK105(sK91(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP11(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_190604]) ).
tcf(c_195421,plain,
! [X0: $i] :
( open_subset(sK105(the_topology(sK137),X0),sK137)
| ~ sP11(the_topology(sK137),X0)
| ~ subset(sK105(the_topology(sK137),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_222,c_190618]) ).
tcf(c_195422,plain,
! [X0: $i] :
( ( sK92(sK137,sK138,sK105(sK91(sK137,sK138),X0)) = sK105(sK91(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_222,c_175190]) ).
tcf(c_195423,plain,
! [X0: $i] :
( in(sK105(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_222,c_175008]) ).
tcf(c_195424,plain,
! [X0: $i] :
( subset(sK138,sK105(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_222,c_174960]) ).
tcf(c_195425,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,sK105(sK302(sK137,sK138),X0)) = sK105(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_222,c_175802]) ).
tcf(c_195426,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,sK105(sK302(sK137,sK138),X0)) = sK105(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_222,c_175753]) ).
tcf(c_195427,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(sK138,sK105(sK302(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP11(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_222,c_175029]) ).
tcf(c_195428,plain,
! [X0: $i] :
( in(sK105(sK93(sK137,the_topology(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP11(sK93(sK137,the_topology(sK137)),X0) ),
inference(superposition,[status(thm)],[c_222,c_175089]) ).
tcf(c_195429,plain,
! [X0: $i,X1: $i] :
( in(sK105(sK93(sK137,sK147(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP11(sK93(sK137,sK147(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_222,c_175090]) ).
tcf(c_195430,plain,
! [X0: $i,X1: $i] :
( in(sK105(sK93(sK137,sK125(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ sP11(sK93(sK137,sK125(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_222,c_175091]) ).
tcf(c_195431,plain,
! [X0: $i,X1: $i] :
( in(sK105(sK93(sK137,sK123(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP11(sK93(sK137,sK123(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_222,c_175092]) ).
tcf(c_195432,plain,
! [X0: $i] :
( subset(sK138,sK105(sK147(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP11(sK147(sK137,sK138),X0)
| ~ subset(sK105(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_222,c_190614]) ).
tcf(c_195433,plain,
! [X0: $i] :
( closed_subset(sK105(sK147(sK137,sK138),X0),sK137)
| ~ topological_space(sK137)
| ~ sP11(sK147(sK137,sK138),X0)
| ~ subset(sK105(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_222,c_190613]) ).
tcf(c_195434,plain,
! [X0: $i] :
( subset(sK138,sK105(sK123(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP11(sK123(sK137,sK138),X0)
| ~ subset(sK105(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_222,c_190612]) ).
tcf(c_195435,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK105(sK147(sK137,topstr_closure(sK137,X0)),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP11(sK147(sK137,topstr_closure(sK137,X0)),X1)
| ~ element(sK105(sK147(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_176007]) ).
tcf(c_195436,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,topstr_closure(sK137,X0),sK105(sK91(sK137,topstr_closure(sK137,X0)),X1)) = sK105(sK91(sK137,topstr_closure(sK137,X0)),X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP11(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_222,c_176010]) ).
tcf(c_195437,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK137,X0),sK105(sK91(sK137,topstr_closure(sK137,X0)),X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP11(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_222,c_176013]) ).
tcf(c_195438,plain,
! [X0: $i,X1: $i] :
( in(sK105(sK91(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP11(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_222,c_176012]) ).
tcf(c_195439,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),sK105(sK295(sK137,the_topology(sK137)),X0)) = sK105(sK295(sK137,the_topology(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK295(sK137,the_topology(sK137)),X0) ),
inference(superposition,[status(thm)],[c_222,c_176134]) ).
tcf(c_195440,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),sK105(sK302(sK137,the_carrier(sK137)),X0)) = sK105(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_222,c_176975]) ).
tcf(c_195441,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),sK105(sK302(sK137,the_carrier(sK137)),X0)) = sK105(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_222,c_176974]) ).
tcf(c_195442,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK105(sK302(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP11(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_222,c_176981]) ).
tcf(c_195443,plain,
! [X0: $i] :
( ( sK124(sK137,the_carrier(sK137),sK105(sK123(sK137,the_carrier(sK137)),X0)) = sK105(sK123(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK123(sK137,the_carrier(sK137)),X0)
| ~ element(sK105(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_176971]) ).
tcf(c_195444,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK105(sK123(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP11(sK123(sK137,the_carrier(sK137)),X0)
| ~ element(sK105(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_176976]) ).
tcf(c_195445,plain,
! [X0: $i] :
( ( sK92(sK137,the_carrier(sK137),sK105(sK91(sK137,the_carrier(sK137)),X0)) = sK105(sK91(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_222,c_176980]) ).
tcf(c_195446,plain,
! [X0: $i] :
( in(sK105(sK91(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_222,c_176982]) ).
tcf(c_195447,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK105(sK91(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_222,c_176983]) ).
tcf(c_195448,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK105(sK147(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP11(sK147(sK137,the_carrier(sK137)),X0)
| ~ element(sK105(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_176978]) ).
tcf(c_195449,plain,
! [X0: $i] :
( closed_subset(sK105(sK147(sK137,the_carrier(sK137)),X0),sK137)
| ~ topological_space(sK137)
| ~ sP11(sK147(sK137,the_carrier(sK137)),X0)
| ~ element(sK105(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_176977]) ).
tcf(c_195450,plain,
! [X0: $i] :
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK105(sK295(sK137,powerset(the_carrier(sK137))),X0)) = sK105(sK295(sK137,powerset(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK295(sK137,powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_222,c_176995]) ).
tcf(c_195451,plain,
! [X0: $i] :
( in(sK105(sK93(sK137,powerset(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP11(sK93(sK137,powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_222,c_176997]) ).
tcf(c_195452,plain,
! [X0: $i] :
( in(sK105(topstr_closure(sK137,sK138),X0),sK138)
| ~ closed_subset(sK138,sK137)
| ~ sP11(topstr_closure(sK137,sK138),X0)
| ~ in(sK105(topstr_closure(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_222,c_177233]) ).
tcf(c_195453,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK105(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_222,c_177405]) ).
tcf(c_195454,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK105(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK105(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_177400]) ).
tcf(c_195455,plain,
! [X0: $i] :
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK105(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)) = sK105(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_222,c_177404]) ).
tcf(c_195456,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK105(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_222,c_177407]) ).
tcf(c_195457,plain,
! [X0: $i] :
( in(sK105(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_222,c_177406]) ).
tcf(c_195458,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK105(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK105(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_177402]) ).
tcf(c_195459,plain,
! [X0: $i] :
( closed_subset(sK105(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP11(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK105(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_177401]) ).
tcf(c_195460,plain,
! [X0: $i] :
( in(sK105(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP11(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0) ),
inference(superposition,[status(thm)],[c_222,c_177421]) ).
tcf(c_195461,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK105(sK302(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK302(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_222,c_182970]) ).
tcf(c_195462,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK105(sK123(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK123(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK105(sK123(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_182965]) ).
tcf(c_195463,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK105(sK91(sK137,sK207(the_carrier(sK137))),X0)) = sK105(sK91(sK137,sK207(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_222,c_182969]) ).
tcf(c_195464,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK105(sK91(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_222,c_182972]) ).
tcf(c_195465,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK105(sK91(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_222,c_182971]) ).
tcf(c_195466,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK105(sK147(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK147(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK105(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_182967]) ).
tcf(c_195467,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(sK105(sK147(sK137,sK207(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP11(sK147(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK105(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_182966]) ).
tcf(c_195468,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK105(sK302(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK302(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_222,c_184375]) ).
tcf(c_195469,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK105(sK123(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK123(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK105(sK123(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_184370]) ).
tcf(c_195470,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK105(sK91(sK137,sK325(the_carrier(sK137))),X0)) = sK105(sK91(sK137,sK325(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_222,c_184374]) ).
tcf(c_195471,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK105(sK91(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_222,c_184377]) ).
tcf(c_195472,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK105(sK91(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_222,c_184376]) ).
tcf(c_195473,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK105(sK147(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP11(sK147(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK105(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_184372]) ).
tcf(c_195474,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(sK105(sK147(sK137,sK325(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP11(sK147(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK105(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_222,c_184371]) ).
tcf(c_195475,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),sK105(sK93(sK137,sK123(sK137,sK138)),X0)))
| ~ topological_space(sK137)
| ~ sP11(sK93(sK137,sK123(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_222,c_192075]) ).
tcf(c_195476,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),sK105(sK93(sK137,sK147(sK137,sK138)),X0)))
| ~ topological_space(sK137)
| ~ sP11(sK93(sK137,sK147(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_222,c_192676]) ).
tcf(c_195477,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),sK105(sK93(sK137,sK147(sK137,sK138)),X0)),sK137)
| ~ topological_space(sK137)
| ~ sP11(sK93(sK137,sK147(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_222,c_192446]) ).
tcf(c_195893,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138))
| ~ finite(sK112(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_181707,c_292]) ).
tcf(c_195894,plain,
( finite(sK138)
| sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP13(sK302(sK137,sK138))
| ~ finite(sK112(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_181710,c_292]) ).
tcf(c_195897,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138))
| ~ finite(sK193(sK91(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_182533,c_292]) ).
tcf(c_195898,plain,
( finite(sK138)
| sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP21(sK302(sK137,sK138))
| ~ finite(sK193(sK302(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_182536,c_292]) ).
tcf(c_196197,plain,
! [X0: $i] :
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK138),X0)
| ~ finite(sK105(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_195424,c_292]) ).
tcf(c_196198,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK138),X0)
| ~ proper_subset(sK105(sK91(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_195424,c_492]) ).
tcf(c_196214,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK138),X0)
| ~ in(powerset(the_carrier(sK137)),sK105(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_195423,c_546]) ).
tcf(c_196215,plain,
! [X0: $i] :
( in(sK154(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_195423,c_542]) ).
tcf(c_196216,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137)))
| ~ sP11(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_195423,c_781]) ).
tcf(c_196217,plain,
! [X0: $i] :
( element(sK105(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_195423,c_701]) ).
tcf(c_196218,plain,
! [X0: $i] :
( subset(sK105(sK91(sK137,sK138),X0),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_195423,c_667]) ).
tcf(c_196219,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(sK105(sK91(sK137,sK138),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK138),X0)
| ~ closed_subset(sK105(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK105(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_195423,c_176867]) ).
tcf(c_196220,plain,
! [X0: $i] :
( in(sK105(sK91(sK137,sK138),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK138),X0)
| ~ closed_subset(sK105(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK105(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_195423,c_176193]) ).
tcf(c_196258,plain,
! [X0: $i] :
( finite(sK138)
| sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP11(sK302(sK137,sK138),X0)
| ~ finite(sK105(sK302(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_195427,c_292]) ).
tcf(c_196259,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP11(sK302(sK137,sK138),X0)
| ~ proper_subset(sK105(sK302(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_195427,c_492]) ).
tcf(c_196475,plain,
! [X0: $i,X1: $i] :
( ordinal(sK105(X0,X1))
| ~ ordinal(X0)
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_222,c_349]) ).
tcf(c_196476,plain,
! [X0: $i] :
( ordinal(sK112(X0))
| ~ sP13(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_233,c_349]) ).
tcf(c_196486,plain,
! [X0: $i] :
( ordinal(sK193(X0))
| ~ sP21(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_619,c_349]) ).
tcf(c_196497,plain,
! [X0: $i] :
( sP42(X0)
| ordinal(sK376(X0))
| ~ ordinal(the_topology(X0)) ),
inference(superposition,[status(thm)],[c_1294,c_349]) ).
tcf(c_196498,plain,
! [X0: $i] :
( sP42(X0)
| ordinal(sK377(X0))
| ~ ordinal(the_topology(X0)) ),
inference(superposition,[status(thm)],[c_1295,c_349]) ).
tcf(c_196535,plain,
( ordinal(sK112(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK138))
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_181706,c_349]) ).
tcf(c_196537,plain,
( ordinal(sK193(sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK138))
| ~ ordinal(powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_182532,c_349]) ).
tcf(c_196555,plain,
! [X0: $i] :
( ordinal(sK105(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ sP11(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_195423,c_349]) ).
tcf(c_200024,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,X0,sK105(sK91(sK137,X0),X1)) = sK105(sK91(sK137,X0),X1) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP11(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_222,c_190601]) ).
tcf(c_200025,plain,
! [X0: $i] :
( ( sK92(sK137,X0,sK112(sK91(sK137,X0))) = sK112(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_233,c_190601]) ).
tcf(c_200036,plain,
! [X0: $i] :
( ( sK92(sK137,X0,sK193(sK91(sK137,X0))) = sK193(sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_619,c_190601]) ).
tcf(c_200320,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK105(set_difference(X0,X1),X2),X0)
| ~ sP11(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_222,c_692]) ).
tcf(c_200321,plain,
! [X0: $i,X1: $i] :
( in(sK112(set_difference(X0,X1)),X0)
| ~ sP13(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_233,c_692]) ).
tcf(c_200332,plain,
! [X0: $i,X1: $i] :
( in(sK193(set_difference(X0,X1)),X0)
| ~ sP21(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_619,c_692]) ).
tcf(c_200505,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,sK105(sK123(sK137,sK138),X0)) = sK105(sK123(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP11(sK123(sK137,sK138),X0)
| ~ subset(sK105(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_222,c_190610]) ).
tcf(c_200506,plain,
( ( sK124(sK137,sK138,sK112(sK123(sK137,sK138))) = sK112(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP13(sK123(sK137,sK138))
| ~ subset(sK112(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_233,c_190610]) ).
tcf(c_200517,plain,
( ( sK124(sK137,sK138,sK193(sK123(sK137,sK138))) = sK193(sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP21(sK123(sK137,sK138))
| ~ subset(sK193(sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_619,c_190610]) ).
tcf(c_200691,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK105(sK93(sK137,sK123(sK137,sK138)),X0))) = set_difference(the_carrier(sK137),sK105(sK93(sK137,sK123(sK137,sK138)),X0)) )
| ~ topological_space(sK137)
| ~ sP11(sK93(sK137,sK123(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_222,c_200623]) ).
tcf(c_200692,plain,
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK112(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK112(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_233,c_200623]) ).
tcf(c_200703,plain,
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK193(sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK193(sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137)
| ~ sP21(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_619,c_200623]) ).
tcf(c_200986,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK123(sK137,sK138)))
| ~ finite(set_difference(the_carrier(sK137),sK112(sK93(sK137,sK123(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192114,c_292]) ).
tcf(c_200987,plain,
( ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK123(sK137,sK138)))
| ~ proper_subset(set_difference(the_carrier(sK137),sK112(sK93(sK137,sK123(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192114,c_492]) ).
tcf(c_201086,plain,
! [X0: $i] :
( sP42(X0)
| empty(powerset(the_carrier(X0)))
| in(sK377(X0),powerset(the_carrier(X0))) ),
inference(superposition,[status(thm)],[c_1296,c_790]) ).
tcf(c_201087,plain,
! [X0: $i] :
( sP42(X0)
| empty(powerset(the_carrier(X0)))
| in(sK376(X0),powerset(the_carrier(X0))) ),
inference(superposition,[status(thm)],[c_1297,c_790]) ).
tcf(c_201090,plain,
( empty(powerset(powerset(sK70)))
| in(sK74(sK70),powerset(powerset(sK70)))
| ~ sP6 ),
inference(superposition,[status(thm)],[c_105019,c_790]) ).
tcf(c_201091,plain,
( empty(powerset(powerset(sK117)))
| in(sK119(sK117),powerset(powerset(sK117)))
| ~ sP15 ),
inference(superposition,[status(thm)],[c_105107,c_790]) ).
tcf(c_201140,plain,
( in(sK119(sK117),powerset(powerset(sK117)))
| ~ sP15 ),
inference(forward_subsumption_resolution,[status(thm)],[c_201091,c_700]) ).
tcf(c_201143,plain,
( in(sK74(sK70),powerset(powerset(sK70)))
| ~ sP6 ),
inference(forward_subsumption_resolution,[status(thm)],[c_201090,c_700]) ).
tcf(c_201146,plain,
! [X0: $i] :
( sP42(X0)
| in(sK376(X0),powerset(the_carrier(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201087,c_700]) ).
tcf(c_201149,plain,
! [X0: $i] :
( sP42(X0)
| in(sK377(X0),powerset(the_carrier(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_201086,c_700]) ).
tcf(c_201595,plain,
! [X0: $i] :
( sP42(X0)
| empty(sK377(X0))
| ~ empty(powerset(the_carrier(X0))) ),
inference(superposition,[status(thm)],[c_1296,c_792]) ).
tcf(c_201596,plain,
! [X0: $i] :
( sP42(X0)
| empty(sK376(X0))
| ~ empty(powerset(the_carrier(X0))) ),
inference(superposition,[status(thm)],[c_1297,c_792]) ).
tcf(c_201599,plain,
( empty(sK74(sK70))
| ~ sP6
| ~ empty(powerset(powerset(sK70))) ),
inference(superposition,[status(thm)],[c_105019,c_792]) ).
tcf(c_201600,plain,
( empty(sK119(sK117))
| ~ sP15
| ~ empty(powerset(powerset(sK117))) ),
inference(superposition,[status(thm)],[c_105107,c_792]) ).
tcf(c_201651,plain,
( sP30(sK252)
| ( sK265 = sK264 )
| ~ sP27 ),
inference(superposition,[status(thm)],[c_796,c_826]) ).
tcf(c_201652,plain,
( sP30(sK253)
| ( sK265 = sK264 )
| ~ sP27 ),
inference(superposition,[status(thm)],[c_798,c_826]) ).
tcf(c_201660,plain,
! [X0: $i] :
( sP30(sK275(sK273(X0),X0))
| ( sK265 = sK264 )
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_105369,c_826]) ).
tcf(c_201824,plain,
( sP30(sK252)
| ( sK265 = sK267 )
| ~ sP27 ),
inference(superposition,[status(thm)],[c_796,c_828]) ).
tcf(c_201825,plain,
( sP30(sK253)
| ( sK265 = sK267 )
| ~ sP27 ),
inference(superposition,[status(thm)],[c_798,c_828]) ).
tcf(c_201833,plain,
! [X0: $i] :
( sP30(sK275(sK273(X0),X0))
| ( sK265 = sK267 )
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_105369,c_828]) ).
tcf(c_202336,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP21(sK93(sK137,sK123(sK137,sK138)))
| ~ finite(set_difference(the_carrier(sK137),sK193(sK93(sK137,sK123(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192121,c_292]) ).
tcf(c_202337,plain,
( ~ topological_space(sK137)
| ~ sP21(sK93(sK137,sK123(sK137,sK138)))
| ~ proper_subset(set_difference(the_carrier(sK137),sK193(sK93(sK137,sK123(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192121,c_492]) ).
tcf(c_202423,plain,
( sP30(sK252)
| ( sK266 = sK264 )
| ~ sP27 ),
inference(superposition,[status(thm)],[c_796,c_831]) ).
tcf(c_202424,plain,
( sP30(sK253)
| ( sK266 = sK264 )
| ~ sP27 ),
inference(superposition,[status(thm)],[c_798,c_831]) ).
tcf(c_202432,plain,
! [X0: $i] :
( sP30(sK275(sK273(X0),X0))
| ( sK266 = sK264 )
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_105369,c_831]) ).
tcf(c_203337,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK147(sK137,sK138)))
| ~ finite(set_difference(the_carrier(sK137),sK112(sK93(sK137,sK147(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192721,c_292]) ).
tcf(c_203338,plain,
( ~ topological_space(sK137)
| ~ sP13(sK93(sK137,sK147(sK137,sK138)))
| ~ proper_subset(set_difference(the_carrier(sK137),sK112(sK93(sK137,sK147(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192721,c_492]) ).
tcf(c_203393,plain,
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP21(sK93(sK137,sK147(sK137,sK138)))
| ~ finite(set_difference(the_carrier(sK137),sK193(sK93(sK137,sK147(sK137,sK138))))) ),
inference(superposition,[status(thm)],[c_192728,c_292]) ).
tcf(c_203394,plain,
( ~ topological_space(sK137)
| ~ sP21(sK93(sK137,sK147(sK137,sK138)))
| ~ proper_subset(set_difference(the_carrier(sK137),sK193(sK93(sK137,sK147(sK137,sK138)))),sK138) ),
inference(superposition,[status(thm)],[c_192728,c_492]) ).
tcf(c_203536,plain,
! [X0: $i,X1: $i] :
( ordinal(sK282(X0,X1))
| ~ ordinal(X0)
| ~ sP33(X0,X1) ),
inference(superposition,[status(thm)],[c_872,c_349]) ).
tcf(c_203537,plain,
! [X0: $i,X1: $i] :
( ~ sP33(X0,X1)
| ~ in(X0,sK282(X0,X1)) ),
inference(superposition,[status(thm)],[c_872,c_546]) ).
tcf(c_203538,plain,
! [X0: $i,X1: $i] :
( in(sK154(X0),X0)
| ~ sP33(X0,X1) ),
inference(superposition,[status(thm)],[c_872,c_542]) ).
tcf(c_203539,plain,
! [X0: $i,X1: $i] :
( ~ empty(X0)
| ~ sP33(X0,X1) ),
inference(superposition,[status(thm)],[c_872,c_781]) ).
tcf(c_203540,plain,
! [X0: $i,X1: $i] :
( element(sK282(X0,X1),X0)
| ~ sP33(X0,X1) ),
inference(superposition,[status(thm)],[c_872,c_701]) ).
tcf(c_203541,plain,
! [X0: $i,X1: $i] :
( in(sK282(sK99(X0),X1),X0)
| ~ sP33(sK99(X0),X1) ),
inference(superposition,[status(thm)],[c_872,c_205]) ).
tcf(c_203542,plain,
! [X0: $i,X1: $i] :
( ordinal(sK282(sK99(X0),X1))
| ~ sP33(sK99(X0),X1) ),
inference(superposition,[status(thm)],[c_872,c_206]) ).
tcf(c_203543,plain,
! [X0: $i] : ~ sP33(empty_set,X0),
inference(superposition,[status(thm)],[c_872,c_599]) ).
tcf(c_203544,plain,
! [X0: $i,X1: $i] :
( subset(sK282(powerset(X0),X1),X0)
| ~ sP33(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_872,c_667]) ).
tcf(c_203545,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK282(set_difference(X0,X1),X2),X0)
| ~ sP33(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_872,c_692]) ).
tcf(c_203546,plain,
! [X0: $i,X1: $i] :
( sP27
| ordinal(sK282(sK254(X0),X1))
| ~ sP33(sK254(X0),X1) ),
inference(superposition,[status(thm)],[c_872,c_802]) ).
tcf(c_203547,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(sK282(powerset(the_carrier(sK137)),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP33(powerset(the_carrier(sK137)),X0)
| ~ closed_subset(sK282(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK282(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_872,c_176867]) ).
tcf(c_203548,plain,
! [X0: $i] :
( in(sK282(powerset(the_carrier(sK137)),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP33(powerset(the_carrier(sK137)),X0)
| ~ closed_subset(sK282(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK282(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_872,c_176193]) ).
tcf(c_203549,plain,
! [X0: $i,X1: $i] :
( in(sK282(sK93(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK93(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_872,c_190624]) ).
tcf(c_203550,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| subset(X0,sK282(sK302(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP33(sK302(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_872,c_190602]) ).
tcf(c_203551,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,X0,sK282(sK91(sK137,X0),X1)) = sK282(sK91(sK137,X0),X1) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP33(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_872,c_190601]) ).
tcf(c_203552,plain,
! [X0: $i,X1: $i] :
( in(sK282(sK91(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP33(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_872,c_190603]) ).
tcf(c_203553,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK282(sK91(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP33(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_872,c_190604]) ).
tcf(c_203554,plain,
! [X0: $i] :
( open_subset(sK282(the_topology(sK137),X0),sK137)
| ~ sP33(the_topology(sK137),X0)
| ~ subset(sK282(the_topology(sK137),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_872,c_190618]) ).
tcf(c_203555,plain,
! [X0: $i] :
( ( sK92(sK137,sK138,sK282(sK91(sK137,sK138),X0)) = sK282(sK91(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_872,c_175190]) ).
tcf(c_203556,plain,
! [X0: $i] :
( in(sK282(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_872,c_175008]) ).
tcf(c_203557,plain,
! [X0: $i] :
( subset(sK138,sK282(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_872,c_174960]) ).
tcf(c_203558,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,sK282(sK302(sK137,sK138),X0)) = sK282(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_872,c_175802]) ).
tcf(c_203559,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,sK282(sK302(sK137,sK138),X0)) = sK282(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_872,c_175753]) ).
tcf(c_203560,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(sK138,sK282(sK302(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_872,c_175029]) ).
tcf(c_203561,plain,
! [X0: $i] :
( in(sK282(sK93(sK137,the_topology(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,the_topology(sK137)),X0) ),
inference(superposition,[status(thm)],[c_872,c_175089]) ).
tcf(c_203562,plain,
! [X0: $i,X1: $i] :
( in(sK282(sK93(sK137,sK147(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK93(sK137,sK147(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_872,c_175090]) ).
tcf(c_203563,plain,
! [X0: $i,X1: $i] :
( in(sK282(sK93(sK137,sK125(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ sP33(sK93(sK137,sK125(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_872,c_175091]) ).
tcf(c_203564,plain,
! [X0: $i,X1: $i] :
( in(sK282(sK93(sK137,sK123(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK93(sK137,sK123(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_872,c_175092]) ).
tcf(c_203565,plain,
! [X0: $i] :
( subset(sK138,sK282(sK147(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK138),X0)
| ~ subset(sK282(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_872,c_190614]) ).
tcf(c_203566,plain,
! [X0: $i] :
( closed_subset(sK282(sK147(sK137,sK138),X0),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK138),X0)
| ~ subset(sK282(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_872,c_190613]) ).
tcf(c_203567,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,sK282(sK123(sK137,sK138),X0)) = sK282(sK123(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,sK138),X0)
| ~ subset(sK282(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_872,c_190610]) ).
tcf(c_203568,plain,
! [X0: $i] :
( subset(sK138,sK282(sK123(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,sK138),X0)
| ~ subset(sK282(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_872,c_190612]) ).
tcf(c_203569,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK282(sK147(sK137,topstr_closure(sK137,X0)),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK147(sK137,topstr_closure(sK137,X0)),X1)
| ~ element(sK282(sK147(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_176007]) ).
tcf(c_203570,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,topstr_closure(sK137,X0),sK282(sK91(sK137,topstr_closure(sK137,X0)),X1)) = sK282(sK91(sK137,topstr_closure(sK137,X0)),X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_872,c_176010]) ).
tcf(c_203571,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK137,X0),sK282(sK91(sK137,topstr_closure(sK137,X0)),X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_872,c_176013]) ).
tcf(c_203572,plain,
! [X0: $i,X1: $i] :
( in(sK282(sK91(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_872,c_176012]) ).
tcf(c_203573,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),sK282(sK295(sK137,the_topology(sK137)),X0)) = sK282(sK295(sK137,the_topology(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK295(sK137,the_topology(sK137)),X0) ),
inference(superposition,[status(thm)],[c_872,c_176134]) ).
tcf(c_203574,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),sK282(sK302(sK137,the_carrier(sK137)),X0)) = sK282(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_872,c_176975]) ).
tcf(c_203575,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),sK282(sK302(sK137,the_carrier(sK137)),X0)) = sK282(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_872,c_176974]) ).
tcf(c_203576,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK282(sK302(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_872,c_176981]) ).
tcf(c_203577,plain,
! [X0: $i] :
( ( sK124(sK137,the_carrier(sK137),sK282(sK123(sK137,the_carrier(sK137)),X0)) = sK282(sK123(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,the_carrier(sK137)),X0)
| ~ element(sK282(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_176971]) ).
tcf(c_203578,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK282(sK123(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,the_carrier(sK137)),X0)
| ~ element(sK282(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_176976]) ).
tcf(c_203579,plain,
! [X0: $i] :
( ( sK92(sK137,the_carrier(sK137),sK282(sK91(sK137,the_carrier(sK137)),X0)) = sK282(sK91(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_872,c_176980]) ).
tcf(c_203580,plain,
! [X0: $i] :
( in(sK282(sK91(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_872,c_176982]) ).
tcf(c_203581,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK282(sK91(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_872,c_176983]) ).
tcf(c_203582,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK282(sK147(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,the_carrier(sK137)),X0)
| ~ element(sK282(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_176978]) ).
tcf(c_203583,plain,
! [X0: $i] :
( closed_subset(sK282(sK147(sK137,the_carrier(sK137)),X0),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,the_carrier(sK137)),X0)
| ~ element(sK282(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_176977]) ).
tcf(c_203584,plain,
! [X0: $i] :
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK282(sK295(sK137,powerset(the_carrier(sK137))),X0)) = sK282(sK295(sK137,powerset(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK295(sK137,powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_872,c_176995]) ).
tcf(c_203585,plain,
! [X0: $i] :
( in(sK282(sK93(sK137,powerset(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_872,c_176997]) ).
tcf(c_203586,plain,
! [X0: $i] :
( in(sK282(topstr_closure(sK137,sK138),X0),sK138)
| ~ closed_subset(sK138,sK137)
| ~ sP33(topstr_closure(sK137,sK138),X0)
| ~ in(sK282(topstr_closure(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_872,c_177233]) ).
tcf(c_203587,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK282(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_872,c_177405]) ).
tcf(c_203588,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK282(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK282(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_177400]) ).
tcf(c_203589,plain,
! [X0: $i] :
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK282(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)) = sK282(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_872,c_177404]) ).
tcf(c_203590,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK282(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_872,c_177407]) ).
tcf(c_203591,plain,
! [X0: $i] :
( in(sK282(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_872,c_177406]) ).
tcf(c_203592,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK282(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK282(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_177402]) ).
tcf(c_203593,plain,
! [X0: $i] :
( closed_subset(sK282(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK282(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_177401]) ).
tcf(c_203594,plain,
! [X0: $i] :
( in(sK282(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0) ),
inference(superposition,[status(thm)],[c_872,c_177421]) ).
tcf(c_203595,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK282(sK302(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_872,c_182970]) ).
tcf(c_203596,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK282(sK123(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK282(sK123(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_182965]) ).
tcf(c_203597,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK282(sK91(sK137,sK207(the_carrier(sK137))),X0)) = sK282(sK91(sK137,sK207(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_872,c_182969]) ).
tcf(c_203598,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK282(sK91(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_872,c_182972]) ).
tcf(c_203599,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK282(sK91(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_872,c_182971]) ).
tcf(c_203600,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK282(sK147(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK282(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_182967]) ).
tcf(c_203601,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(sK282(sK147(sK137,sK207(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK282(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_182966]) ).
tcf(c_203602,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK282(sK302(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_872,c_184375]) ).
tcf(c_203603,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK282(sK123(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK282(sK123(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_184370]) ).
tcf(c_203604,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK282(sK91(sK137,sK325(the_carrier(sK137))),X0)) = sK282(sK91(sK137,sK325(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_872,c_184374]) ).
tcf(c_203605,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK282(sK91(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_872,c_184377]) ).
tcf(c_203606,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK282(sK91(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_872,c_184376]) ).
tcf(c_203607,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK282(sK147(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK282(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_184372]) ).
tcf(c_203608,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(sK282(sK147(sK137,sK325(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK282(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_872,c_184371]) ).
tcf(c_203609,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK282(sK93(sK137,sK123(sK137,sK138)),X0))) = set_difference(the_carrier(sK137),sK282(sK93(sK137,sK123(sK137,sK138)),X0)) )
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,sK123(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_872,c_200623]) ).
tcf(c_203610,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),sK282(sK93(sK137,sK123(sK137,sK138)),X0)))
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,sK123(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_872,c_192075]) ).
tcf(c_203611,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),sK282(sK93(sK137,sK147(sK137,sK138)),X0)))
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,sK147(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_872,c_192676]) ).
tcf(c_203612,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),sK282(sK93(sK137,sK147(sK137,sK138)),X0)),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,sK147(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_872,c_192446]) ).
tcf(c_204319,plain,
! [X0: $i,X1: $i] :
( ordinal(sK283(X0,X1))
| ~ ordinal(X0)
| ~ sP33(X0,X1) ),
inference(superposition,[status(thm)],[c_875,c_349]) ).
tcf(c_204320,plain,
! [X0: $i,X1: $i] :
( ~ sP33(X0,X1)
| ~ in(X0,sK283(X0,X1)) ),
inference(superposition,[status(thm)],[c_875,c_546]) ).
tcf(c_204323,plain,
! [X0: $i,X1: $i] :
( element(sK283(X0,X1),X0)
| ~ sP33(X0,X1) ),
inference(superposition,[status(thm)],[c_875,c_701]) ).
tcf(c_204324,plain,
! [X0: $i,X1: $i] :
( in(sK283(sK99(X0),X1),X0)
| ~ sP33(sK99(X0),X1) ),
inference(superposition,[status(thm)],[c_875,c_205]) ).
tcf(c_204325,plain,
! [X0: $i,X1: $i] :
( ordinal(sK283(sK99(X0),X1))
| ~ sP33(sK99(X0),X1) ),
inference(superposition,[status(thm)],[c_875,c_206]) ).
tcf(c_204327,plain,
! [X0: $i,X1: $i] :
( subset(sK283(powerset(X0),X1),X0)
| ~ sP33(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_875,c_667]) ).
tcf(c_204328,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK283(set_difference(X0,X1),X2),X0)
| ~ sP33(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_875,c_692]) ).
tcf(c_204329,plain,
! [X0: $i,X1: $i] :
( sP27
| ordinal(sK283(sK254(X0),X1))
| ~ sP33(sK254(X0),X1) ),
inference(superposition,[status(thm)],[c_875,c_802]) ).
tcf(c_204330,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(sK283(powerset(the_carrier(sK137)),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP33(powerset(the_carrier(sK137)),X0)
| ~ closed_subset(sK283(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK283(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_875,c_176867]) ).
tcf(c_204331,plain,
! [X0: $i] :
( in(sK283(powerset(the_carrier(sK137)),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP33(powerset(the_carrier(sK137)),X0)
| ~ closed_subset(sK283(powerset(the_carrier(sK137)),X0),sK137)
| ~ subset(sK138,sK283(powerset(the_carrier(sK137)),X0)) ),
inference(superposition,[status(thm)],[c_875,c_176193]) ).
tcf(c_204332,plain,
! [X0: $i,X1: $i] :
( in(sK283(sK93(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK93(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_875,c_190624]) ).
tcf(c_204333,plain,
! [X0: $i,X1: $i] :
( sP36(sK137,X0)
| subset(X0,sK283(sK302(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP33(sK302(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_875,c_190602]) ).
tcf(c_204334,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,X0,sK283(sK91(sK137,X0),X1)) = sK283(sK91(sK137,X0),X1) )
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP33(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_875,c_190601]) ).
tcf(c_204335,plain,
! [X0: $i,X1: $i] :
( in(sK283(sK91(sK137,X0),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP33(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_875,c_190603]) ).
tcf(c_204336,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK283(sK91(sK137,X0),X1))
| ~ topological_space(sK137)
| ~ subset(X0,the_carrier(sK137))
| ~ sP33(sK91(sK137,X0),X1) ),
inference(superposition,[status(thm)],[c_875,c_190604]) ).
tcf(c_204337,plain,
! [X0: $i] :
( open_subset(sK283(the_topology(sK137),X0),sK137)
| ~ sP33(the_topology(sK137),X0)
| ~ subset(sK283(the_topology(sK137),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_875,c_190618]) ).
tcf(c_204338,plain,
! [X0: $i] :
( ( sK92(sK137,sK138,sK283(sK91(sK137,sK138),X0)) = sK283(sK91(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_875,c_175190]) ).
tcf(c_204339,plain,
! [X0: $i] :
( in(sK283(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_875,c_175008]) ).
tcf(c_204340,plain,
! [X0: $i] :
( subset(sK138,sK283(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_875,c_174960]) ).
tcf(c_204341,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,sK283(sK302(sK137,sK138),X0)) = sK283(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_875,c_175802]) ).
tcf(c_204342,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,sK283(sK302(sK137,sK138),X0)) = sK283(sK302(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_875,c_175753]) ).
tcf(c_204343,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| subset(sK138,sK283(sK302(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_875,c_175029]) ).
tcf(c_204344,plain,
! [X0: $i] :
( in(sK283(sK93(sK137,the_topology(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,the_topology(sK137)),X0) ),
inference(superposition,[status(thm)],[c_875,c_175089]) ).
tcf(c_204345,plain,
! [X0: $i,X1: $i] :
( in(sK283(sK93(sK137,sK147(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK93(sK137,sK147(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_875,c_175090]) ).
tcf(c_204346,plain,
! [X0: $i,X1: $i] :
( in(sK283(sK93(sK137,sK125(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(powerset(the_carrier(sK137))))
| ~ sP33(sK93(sK137,sK125(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_875,c_175091]) ).
tcf(c_204347,plain,
! [X0: $i,X1: $i] :
( in(sK283(sK93(sK137,sK123(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK93(sK137,sK123(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_875,c_175092]) ).
tcf(c_204348,plain,
! [X0: $i] :
( subset(sK138,sK283(sK147(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK138),X0)
| ~ subset(sK283(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_875,c_190614]) ).
tcf(c_204349,plain,
! [X0: $i] :
( closed_subset(sK283(sK147(sK137,sK138),X0),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK138),X0)
| ~ subset(sK283(sK147(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_875,c_190613]) ).
tcf(c_204350,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,sK283(sK123(sK137,sK138),X0)) = sK283(sK123(sK137,sK138),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,sK138),X0)
| ~ subset(sK283(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_875,c_190610]) ).
tcf(c_204351,plain,
! [X0: $i] :
( subset(sK138,sK283(sK123(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,sK138),X0)
| ~ subset(sK283(sK123(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_875,c_190612]) ).
tcf(c_204352,plain,
! [X0: $i,X1: $i] :
( closed_subset(sK283(sK147(sK137,topstr_closure(sK137,X0)),X1),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK147(sK137,topstr_closure(sK137,X0)),X1)
| ~ element(sK283(sK147(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_176007]) ).
tcf(c_204353,plain,
! [X0: $i,X1: $i] :
( ( sK92(sK137,topstr_closure(sK137,X0),sK283(sK91(sK137,topstr_closure(sK137,X0)),X1)) = sK283(sK91(sK137,topstr_closure(sK137,X0)),X1) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_875,c_176010]) ).
tcf(c_204354,plain,
! [X0: $i,X1: $i] :
( subset(topstr_closure(sK137,X0),sK283(sK91(sK137,topstr_closure(sK137,X0)),X1))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_875,c_176013]) ).
tcf(c_204355,plain,
! [X0: $i,X1: $i] :
( in(sK283(sK91(sK137,topstr_closure(sK137,X0)),X1),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP33(sK91(sK137,topstr_closure(sK137,X0)),X1) ),
inference(superposition,[status(thm)],[c_875,c_176012]) ).
tcf(c_204356,plain,
! [X0: $i] :
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),sK283(sK295(sK137,the_topology(sK137)),X0)) = sK283(sK295(sK137,the_topology(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK295(sK137,the_topology(sK137)),X0) ),
inference(superposition,[status(thm)],[c_875,c_176134]) ).
tcf(c_204357,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),sK283(sK302(sK137,the_carrier(sK137)),X0)) = sK283(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_875,c_176975]) ).
tcf(c_204358,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),sK283(sK302(sK137,the_carrier(sK137)),X0)) = sK283(sK302(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_875,c_176974]) ).
tcf(c_204359,plain,
! [X0: $i] :
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK283(sK302(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_875,c_176981]) ).
tcf(c_204360,plain,
! [X0: $i] :
( ( sK124(sK137,the_carrier(sK137),sK283(sK123(sK137,the_carrier(sK137)),X0)) = sK283(sK123(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,the_carrier(sK137)),X0)
| ~ element(sK283(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_176971]) ).
tcf(c_204361,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK283(sK123(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,the_carrier(sK137)),X0)
| ~ element(sK283(sK123(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_176976]) ).
tcf(c_204362,plain,
! [X0: $i] :
( ( sK92(sK137,the_carrier(sK137),sK283(sK91(sK137,the_carrier(sK137)),X0)) = sK283(sK91(sK137,the_carrier(sK137)),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_875,c_176980]) ).
tcf(c_204363,plain,
! [X0: $i] :
( in(sK283(sK91(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_875,c_176982]) ).
tcf(c_204364,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK283(sK91(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,the_carrier(sK137)),X0) ),
inference(superposition,[status(thm)],[c_875,c_176983]) ).
tcf(c_204365,plain,
! [X0: $i] :
( subset(the_carrier(sK137),sK283(sK147(sK137,the_carrier(sK137)),X0))
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,the_carrier(sK137)),X0)
| ~ element(sK283(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_176978]) ).
tcf(c_204366,plain,
! [X0: $i] :
( closed_subset(sK283(sK147(sK137,the_carrier(sK137)),X0),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,the_carrier(sK137)),X0)
| ~ element(sK283(sK147(sK137,the_carrier(sK137)),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_176977]) ).
tcf(c_204367,plain,
! [X0: $i] :
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK283(sK295(sK137,powerset(the_carrier(sK137))),X0)) = sK283(sK295(sK137,powerset(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK295(sK137,powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_875,c_176995]) ).
tcf(c_204368,plain,
! [X0: $i] :
( in(sK283(sK93(sK137,powerset(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,powerset(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_875,c_176997]) ).
tcf(c_204369,plain,
! [X0: $i] :
( in(sK283(topstr_closure(sK137,sK138),X0),sK138)
| ~ closed_subset(sK138,sK137)
| ~ sP33(topstr_closure(sK137,sK138),X0)
| ~ in(sK283(topstr_closure(sK137,sK138),X0),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_875,c_177233]) ).
tcf(c_204370,plain,
! [X0: $i] :
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK283(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_875,c_177405]) ).
tcf(c_204371,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK283(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK283(sK123(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_177400]) ).
tcf(c_204372,plain,
! [X0: $i] :
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK283(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0)) = sK283(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_875,c_177404]) ).
tcf(c_204373,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK283(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_875,c_177407]) ).
tcf(c_204374,plain,
! [X0: $i] :
( in(sK283(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK208(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_875,c_177406]) ).
tcf(c_204375,plain,
! [X0: $i] :
( subset(sK208(powerset(the_carrier(sK137))),sK283(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK283(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_177402]) ).
tcf(c_204376,plain,
! [X0: $i] :
( closed_subset(sK283(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0)
| ~ element(sK283(sK147(sK137,sK208(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_177401]) ).
tcf(c_204377,plain,
! [X0: $i] :
( in(sK283(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137))))),X0) ),
inference(superposition,[status(thm)],[c_875,c_177421]) ).
tcf(c_204378,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK283(sK302(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_875,c_182970]) ).
tcf(c_204379,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK283(sK123(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK283(sK123(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_182965]) ).
tcf(c_204380,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK283(sK91(sK137,sK207(the_carrier(sK137))),X0)) = sK283(sK91(sK137,sK207(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_875,c_182969]) ).
tcf(c_204381,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK283(sK91(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_875,c_182972]) ).
tcf(c_204382,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK283(sK91(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK207(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_875,c_182971]) ).
tcf(c_204383,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK283(sK147(sK137,sK207(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK283(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_182967]) ).
tcf(c_204384,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(sK283(sK147(sK137,sK207(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK207(the_carrier(sK137))),X0)
| ~ element(sK283(sK147(sK137,sK207(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_182966]) ).
tcf(c_204385,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK283(sK302(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_875,c_184375]) ).
tcf(c_204386,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK283(sK123(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK123(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK283(sK123(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_184370]) ).
tcf(c_204387,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK283(sK91(sK137,sK325(the_carrier(sK137))),X0)) = sK283(sK91(sK137,sK325(the_carrier(sK137))),X0) )
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_875,c_184374]) ).
tcf(c_204388,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK283(sK91(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_875,c_184377]) ).
tcf(c_204389,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| in(sK283(sK91(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK325(the_carrier(sK137))),X0) ),
inference(superposition,[status(thm)],[c_875,c_184376]) ).
tcf(c_204390,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK283(sK147(sK137,sK325(the_carrier(sK137))),X0))
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK283(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_184372]) ).
tcf(c_204391,plain,
! [X0: $i] :
( empty(the_carrier(sK137))
| closed_subset(sK283(sK147(sK137,sK325(the_carrier(sK137))),X0),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK147(sK137,sK325(the_carrier(sK137))),X0)
| ~ element(sK283(sK147(sK137,sK325(the_carrier(sK137))),X0),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_875,c_184371]) ).
tcf(c_204392,plain,
! [X0: $i] :
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK283(sK93(sK137,sK123(sK137,sK138)),X0))) = set_difference(the_carrier(sK137),sK283(sK93(sK137,sK123(sK137,sK138)),X0)) )
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,sK123(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_875,c_200623]) ).
tcf(c_204393,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),sK283(sK93(sK137,sK123(sK137,sK138)),X0)))
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,sK123(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_875,c_192075]) ).
tcf(c_204394,plain,
! [X0: $i] :
( subset(sK138,set_difference(the_carrier(sK137),sK283(sK93(sK137,sK147(sK137,sK138)),X0)))
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,sK147(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_875,c_192676]) ).
tcf(c_204395,plain,
! [X0: $i] :
( closed_subset(set_difference(the_carrier(sK137),sK283(sK93(sK137,sK147(sK137,sK138)),X0)),sK137)
| ~ topological_space(sK137)
| ~ sP33(sK93(sK137,sK147(sK137,sK138)),X0) ),
inference(superposition,[status(thm)],[c_875,c_192446]) ).
tcf(c_205031,plain,
! [X0: $i] :
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0)
| ~ finite(sK282(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_203557,c_292]) ).
tcf(c_205032,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0)
| ~ proper_subset(sK282(sK91(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_203557,c_492]) ).
tcf(c_205048,plain,
! [X0: $i] :
( finite(sK138)
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0)
| ~ finite(sK283(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_204340,c_292]) ).
tcf(c_205049,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0)
| ~ proper_subset(sK283(sK91(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_204340,c_492]) ).
tcf(c_205065,plain,
! [X0: $i] :
( ordinal(sK282(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_203556,c_349]) ).
tcf(c_205066,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0)
| ~ in(powerset(the_carrier(sK137)),sK282(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_203556,c_546]) ).
tcf(c_205068,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ empty(powerset(the_carrier(sK137)))
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_203556,c_781]) ).
tcf(c_205069,plain,
! [X0: $i] :
( element(sK282(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_203556,c_701]) ).
tcf(c_205070,plain,
! [X0: $i] :
( subset(sK282(sK91(sK137,sK138),X0),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_203556,c_667]) ).
tcf(c_205071,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(sK282(sK91(sK137,sK138),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0)
| ~ closed_subset(sK282(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK282(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_203556,c_176867]) ).
tcf(c_205072,plain,
! [X0: $i] :
( in(sK282(sK91(sK137,sK138),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0)
| ~ closed_subset(sK282(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK282(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_203556,c_176193]) ).
tcf(c_205142,plain,
! [X0: $i] :
( ordinal(sK283(sK91(sK137,sK138),X0))
| ~ topological_space(sK137)
| ~ ordinal(powerset(the_carrier(sK137)))
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_204339,c_349]) ).
tcf(c_205143,plain,
! [X0: $i] :
( ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0)
| ~ in(powerset(the_carrier(sK137)),sK283(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_204339,c_546]) ).
tcf(c_205146,plain,
! [X0: $i] :
( element(sK283(sK91(sK137,sK138),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_204339,c_701]) ).
tcf(c_205147,plain,
! [X0: $i] :
( subset(sK283(sK91(sK137,sK138),X0),the_carrier(sK137))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0) ),
inference(superposition,[status(thm)],[c_204339,c_667]) ).
tcf(c_205148,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| in(sK283(sK91(sK137,sK138),X0),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0)
| ~ closed_subset(sK283(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK283(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_204339,c_176867]) ).
tcf(c_205149,plain,
! [X0: $i] :
( in(sK283(sK91(sK137,sK138),X0),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK138),X0)
| ~ closed_subset(sK283(sK91(sK137,sK138),X0),sK137)
| ~ subset(sK138,sK283(sK91(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_204339,c_176193]) ).
tcf(c_205188,plain,
! [X0: $i] :
( finite(sK138)
| sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK138),X0)
| ~ finite(sK282(sK302(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_203560,c_292]) ).
tcf(c_205189,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK138),X0)
| ~ proper_subset(sK282(sK302(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_203560,c_492]) ).
tcf(c_205233,plain,
! [X0: $i] :
( finite(sK138)
| sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK138),X0)
| ~ finite(sK283(sK302(sK137,sK138),X0)) ),
inference(superposition,[status(thm)],[c_204343,c_292]) ).
tcf(c_205234,plain,
! [X0: $i] :
( sP36(sK137,sK138)
| ~ topological_space(sK137)
| ~ sP33(sK302(sK137,sK138),X0)
| ~ proper_subset(sK283(sK302(sK137,sK138),X0),sK138) ),
inference(superposition,[status(thm)],[c_204343,c_492]) ).
tcf(c_206686,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| in(sK105(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP11(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_222,c_201958]) ).
tcf(c_206687,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK112(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP13(sK91(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_233,c_201958]) ).
tcf(c_206698,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK193(sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP21(sK91(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_619,c_201958]) ).
tcf(c_206701,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| in(sK282(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_872,c_201958]) ).
tcf(c_206702,plain,
! [X0: $i] :
( sP3(powerset(the_carrier(sK137)))
| in(sK283(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP33(sK91(sK137,sK62(powerset(the_carrier(sK137)))),X0) ),
inference(superposition,[status(thm)],[c_875,c_201958]) ).
tcf(c_207078,plain,
! [X0: $i] :
( sP42(X0)
| epsilon_transitive(sK377(X0))
| ~ ordinal(powerset(the_carrier(X0))) ),
inference(superposition,[status(thm)],[c_1296,c_1089]) ).
tcf(c_207079,plain,
! [X0: $i] :
( sP42(X0)
| epsilon_transitive(sK376(X0))
| ~ ordinal(powerset(the_carrier(X0))) ),
inference(superposition,[status(thm)],[c_1297,c_1089]) ).
tcf(c_207082,plain,
( epsilon_transitive(sK74(sK70))
| ~ sP6
| ~ ordinal(powerset(powerset(sK70))) ),
inference(superposition,[status(thm)],[c_105019,c_1089]) ).
tcf(c_207083,plain,
( epsilon_transitive(sK119(sK117))
| ~ sP15
| ~ ordinal(powerset(powerset(sK117))) ),
inference(superposition,[status(thm)],[c_105107,c_1089]) ).
tcf(c_207320,plain,
! [X0: $i] :
( sP42(X0)
| epsilon_connected(sK377(X0))
| ~ ordinal(powerset(the_carrier(X0))) ),
inference(superposition,[status(thm)],[c_1296,c_1090]) ).
tcf(c_207321,plain,
! [X0: $i] :
( sP42(X0)
| epsilon_connected(sK376(X0))
| ~ ordinal(powerset(the_carrier(X0))) ),
inference(superposition,[status(thm)],[c_1297,c_1090]) ).
tcf(c_207324,plain,
( epsilon_connected(sK74(sK70))
| ~ sP6
| ~ ordinal(powerset(powerset(sK70))) ),
inference(superposition,[status(thm)],[c_105019,c_1090]) ).
tcf(c_207325,plain,
( epsilon_connected(sK119(sK117))
| ~ sP15
| ~ ordinal(powerset(powerset(sK117))) ),
inference(superposition,[status(thm)],[c_105107,c_1090]) ).
tcf(c_207686,plain,
! [X0: $i] :
( sP42(X0)
| ordinal(sK377(X0))
| ~ ordinal(powerset(the_carrier(X0))) ),
inference(superposition,[status(thm)],[c_1296,c_1091]) ).
tcf(c_207687,plain,
! [X0: $i] :
( sP42(X0)
| ordinal(sK376(X0))
| ~ ordinal(powerset(the_carrier(X0))) ),
inference(superposition,[status(thm)],[c_1297,c_1091]) ).
tcf(c_207690,plain,
( ordinal(sK74(sK70))
| ~ sP6
| ~ ordinal(powerset(powerset(sK70))) ),
inference(superposition,[status(thm)],[c_105019,c_1091]) ).
tcf(c_207691,plain,
( ordinal(sK119(sK117))
| ~ sP15
| ~ ordinal(powerset(powerset(sK117))) ),
inference(superposition,[status(thm)],[c_105107,c_1091]) ).
tcf(c_208290,plain,
! [X0: $i] :
( ( relation_dom(sK115(X0)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_241,c_183538]) ).
tcf(c_208355,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ sP21(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_646,c_183545]) ).
tcf(c_208356,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ sP21(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_968,c_183545]) ).
tcf(c_208357,plain,
! [X0: $i] :
( ~ empty(X0)
| ~ sP21(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1166,c_183545]) ).
tcf(c_208358,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK325(the_carrier(sK137)))) = topstr_closure(sK137,sK325(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP21(the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_184389,c_183545]) ).
tcf(c_208359,plain,
( ( meet_of_subsets(the_carrier(sK137),sK147(sK137,sK207(the_carrier(sK137)))) = topstr_closure(sK137,sK207(the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP21(the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_182983,c_183545]) ).
tcf(c_208476,plain,
( sP42(sK137)
| epsilon_transitive(sK147(sK137,sK377(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1296,c_207090]) ).
tcf(c_208477,plain,
( sP42(sK137)
| epsilon_transitive(sK147(sK137,sK376(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1297,c_207090]) ).
tcf(c_208818,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK61(X0))) = sK61(X0) )
| ~ sP3(X0) ),
inference(superposition,[status(thm)],[c_111,c_1163]) ).
tcf(c_208993,plain,
( sP42(sK137)
| epsilon_transitive(sK123(sK137,sK377(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1296,c_207095]) ).
tcf(c_208994,plain,
( sP42(sK137)
| epsilon_transitive(sK123(sK137,sK376(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1297,c_207095]) ).
tcf(c_209222,plain,
( sP42(sK137)
| epsilon_connected(sK147(sK137,sK377(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1296,c_207332]) ).
tcf(c_209223,plain,
( sP42(sK137)
| epsilon_connected(sK147(sK137,sK376(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1297,c_207332]) ).
tcf(c_209432,plain,
( sP42(sK137)
| epsilon_connected(sK123(sK137,sK377(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1296,c_207337]) ).
tcf(c_209433,plain,
( sP42(sK137)
| epsilon_connected(sK123(sK137,sK376(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1297,c_207337]) ).
tcf(c_209636,plain,
( sP42(sK137)
| ordinal(sK147(sK137,sK377(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1296,c_207698]) ).
tcf(c_209637,plain,
( sP42(sK137)
| ordinal(sK147(sK137,sK376(sK137)))
| ~ topological_space(sK137)
| ~ ordinal(powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_1297,c_207698]) ).
tcf(c_210047,plain,
! [X0: $i] :
( ordinal(sK187(sK184(X0),X0))
| ~ sP20(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_105237,c_349]) ).
tcf(c_210048,plain,
! [X0: $i] :
( ~ sP20(X0)
| ~ in(X0,sK187(sK184(X0),X0)) ),
inference(superposition,[status(thm)],[c_105237,c_546]) ).
tcf(c_210051,plain,
! [X0: $i] :
( element(sK187(sK184(X0),X0),X0)
| ~ sP20(X0) ),
inference(superposition,[status(thm)],[c_105237,c_701]) ).
tcf(c_210052,plain,
! [X0: $i] :
( in(sK187(sK184(sK99(X0)),sK99(X0)),X0)
| ~ sP20(sK99(X0)) ),
inference(superposition,[status(thm)],[c_105237,c_205]) ).
tcf(c_210053,plain,
! [X0: $i] :
( ordinal(sK187(sK184(sK99(X0)),sK99(X0)))
| ~ sP20(sK99(X0)) ),
inference(superposition,[status(thm)],[c_105237,c_206]) ).
tcf(c_210055,plain,
! [X0: $i] :
( subset(sK187(sK184(powerset(X0)),powerset(X0)),X0)
| ~ sP20(powerset(X0)) ),
inference(superposition,[status(thm)],[c_105237,c_667]) ).
tcf(c_210056,plain,
! [X0: $i,X1: $i] :
( in(sK187(sK184(set_difference(X0,X1)),set_difference(X0,X1)),X0)
| ~ sP20(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_105237,c_692]) ).
tcf(c_210057,plain,
! [X0: $i] :
( sP27
| ordinal(sK187(sK184(sK254(X0)),sK254(X0)))
| ~ sP20(sK254(X0)) ),
inference(superposition,[status(thm)],[c_105237,c_802]) ).
tcf(c_210058,plain,
( sP36(sK137,sK138)
| in(sK187(sK184(powerset(the_carrier(sK137))),powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP20(powerset(the_carrier(sK137)))
| ~ closed_subset(sK187(sK184(powerset(the_carrier(sK137))),powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK187(sK184(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_176867]) ).
tcf(c_210059,plain,
( in(sK187(sK184(powerset(the_carrier(sK137))),powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP20(powerset(the_carrier(sK137)))
| ~ closed_subset(sK187(sK184(powerset(the_carrier(sK137))),powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK187(sK184(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_176193]) ).
tcf(c_210060,plain,
! [X0: $i] :
( in(sK187(sK184(sK93(sK137,X0)),sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,X0))
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_190624]) ).
tcf(c_210061,plain,
! [X0: $i] :
( sP36(sK137,X0)
| subset(X0,sK187(sK184(sK302(sK137,X0)),sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105237,c_190602]) ).
tcf(c_210062,plain,
! [X0: $i] :
( ( sK92(sK137,X0,sK187(sK184(sK91(sK137,X0)),sK91(sK137,X0))) = sK187(sK184(sK91(sK137,X0)),sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105237,c_190601]) ).
tcf(c_210063,plain,
! [X0: $i] :
( in(sK187(sK184(sK91(sK137,X0)),sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105237,c_190603]) ).
tcf(c_210064,plain,
! [X0: $i] :
( subset(X0,sK187(sK184(sK91(sK137,X0)),sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105237,c_190604]) ).
tcf(c_210065,plain,
( open_subset(sK187(sK184(the_topology(sK137)),the_topology(sK137)),sK137)
| ~ sP20(the_topology(sK137))
| ~ subset(sK187(sK184(the_topology(sK137)),the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105237,c_190618]) ).
tcf(c_210066,plain,
( ( sK92(sK137,sK138,sK187(sK184(sK91(sK137,sK138)),sK91(sK137,sK138))) = sK187(sK184(sK91(sK137,sK138)),sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105237,c_175190]) ).
tcf(c_210067,plain,
( in(sK187(sK184(sK91(sK137,sK138)),sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105237,c_175008]) ).
tcf(c_210068,plain,
( subset(sK138,sK187(sK184(sK91(sK137,sK138)),sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105237,c_174960]) ).
tcf(c_210069,plain,
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,sK187(sK184(sK302(sK137,sK138)),sK302(sK137,sK138))) = sK187(sK184(sK302(sK137,sK138)),sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105237,c_175802]) ).
tcf(c_210070,plain,
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,sK187(sK184(sK302(sK137,sK138)),sK302(sK137,sK138))) = sK187(sK184(sK302(sK137,sK138)),sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105237,c_175753]) ).
tcf(c_210071,plain,
( sP36(sK137,sK138)
| subset(sK138,sK187(sK184(sK302(sK137,sK138)),sK302(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105237,c_175029]) ).
tcf(c_210072,plain,
( in(sK187(sK184(sK93(sK137,the_topology(sK137))),sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_175089]) ).
tcf(c_210073,plain,
! [X0: $i] :
( in(sK187(sK184(sK93(sK137,sK147(sK137,X0))),sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK93(sK137,sK147(sK137,X0))) ),
inference(superposition,[status(thm)],[c_105237,c_175090]) ).
tcf(c_210074,plain,
! [X0: $i] :
( in(sK187(sK184(sK93(sK137,sK125(sK137,X0))),sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK125(sK137,X0)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_175091]) ).
tcf(c_210075,plain,
! [X0: $i] :
( in(sK187(sK184(sK93(sK137,sK123(sK137,X0))),sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK93(sK137,sK123(sK137,X0))) ),
inference(superposition,[status(thm)],[c_105237,c_175092]) ).
tcf(c_210076,plain,
( subset(sK138,sK187(sK184(sK147(sK137,sK138)),sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK138))
| ~ subset(sK187(sK184(sK147(sK137,sK138)),sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105237,c_190614]) ).
tcf(c_210077,plain,
( closed_subset(sK187(sK184(sK147(sK137,sK138)),sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK138))
| ~ subset(sK187(sK184(sK147(sK137,sK138)),sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105237,c_190613]) ).
tcf(c_210078,plain,
( ( sK124(sK137,sK138,sK187(sK184(sK123(sK137,sK138)),sK123(sK137,sK138))) = sK187(sK184(sK123(sK137,sK138)),sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,sK138))
| ~ subset(sK187(sK184(sK123(sK137,sK138)),sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105237,c_190610]) ).
tcf(c_210079,plain,
( subset(sK138,sK187(sK184(sK123(sK137,sK138)),sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,sK138))
| ~ subset(sK187(sK184(sK123(sK137,sK138)),sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105237,c_190612]) ).
tcf(c_210080,plain,
! [X0: $i] :
( closed_subset(sK187(sK184(sK147(sK137,topstr_closure(sK137,X0))),sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK147(sK137,topstr_closure(sK137,X0)))
| ~ element(sK187(sK184(sK147(sK137,topstr_closure(sK137,X0))),sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176007]) ).
tcf(c_210081,plain,
! [X0: $i] :
( ( sK92(sK137,topstr_closure(sK137,X0),sK187(sK184(sK91(sK137,topstr_closure(sK137,X0))),sK91(sK137,topstr_closure(sK137,X0)))) = sK187(sK184(sK91(sK137,topstr_closure(sK137,X0))),sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_105237,c_176010]) ).
tcf(c_210082,plain,
! [X0: $i] :
( subset(topstr_closure(sK137,X0),sK187(sK184(sK91(sK137,topstr_closure(sK137,X0))),sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_105237,c_176013]) ).
tcf(c_210083,plain,
! [X0: $i] :
( in(sK187(sK184(sK91(sK137,topstr_closure(sK137,X0))),sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP20(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_105237,c_176012]) ).
tcf(c_210084,plain,
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),sK187(sK184(sK295(sK137,the_topology(sK137))),sK295(sK137,the_topology(sK137)))) = sK187(sK184(sK295(sK137,the_topology(sK137))),sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176134]) ).
tcf(c_210085,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),sK187(sK184(sK302(sK137,the_carrier(sK137))),sK302(sK137,the_carrier(sK137)))) = sK187(sK184(sK302(sK137,the_carrier(sK137))),sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176975]) ).
tcf(c_210086,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),sK187(sK184(sK302(sK137,the_carrier(sK137))),sK302(sK137,the_carrier(sK137)))) = sK187(sK184(sK302(sK137,the_carrier(sK137))),sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176974]) ).
tcf(c_210087,plain,
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK187(sK184(sK302(sK137,the_carrier(sK137))),sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176981]) ).
tcf(c_210088,plain,
( ( sK124(sK137,the_carrier(sK137),sK187(sK184(sK123(sK137,the_carrier(sK137))),sK123(sK137,the_carrier(sK137)))) = sK187(sK184(sK123(sK137,the_carrier(sK137))),sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,the_carrier(sK137)))
| ~ element(sK187(sK184(sK123(sK137,the_carrier(sK137))),sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176971]) ).
tcf(c_210089,plain,
( subset(the_carrier(sK137),sK187(sK184(sK123(sK137,the_carrier(sK137))),sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,the_carrier(sK137)))
| ~ element(sK187(sK184(sK123(sK137,the_carrier(sK137))),sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176976]) ).
tcf(c_210090,plain,
( ( sK92(sK137,the_carrier(sK137),sK187(sK184(sK91(sK137,the_carrier(sK137))),sK91(sK137,the_carrier(sK137)))) = sK187(sK184(sK91(sK137,the_carrier(sK137))),sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176980]) ).
tcf(c_210091,plain,
( in(sK187(sK184(sK91(sK137,the_carrier(sK137))),sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176982]) ).
tcf(c_210092,plain,
( subset(the_carrier(sK137),sK187(sK184(sK91(sK137,the_carrier(sK137))),sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176983]) ).
tcf(c_210093,plain,
( subset(the_carrier(sK137),sK187(sK184(sK147(sK137,the_carrier(sK137))),sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,the_carrier(sK137)))
| ~ element(sK187(sK184(sK147(sK137,the_carrier(sK137))),sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176978]) ).
tcf(c_210094,plain,
( closed_subset(sK187(sK184(sK147(sK137,the_carrier(sK137))),sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,the_carrier(sK137)))
| ~ element(sK187(sK184(sK147(sK137,the_carrier(sK137))),sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_176977]) ).
tcf(c_210095,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK187(sK184(sK295(sK137,powerset(the_carrier(sK137)))),sK295(sK137,powerset(the_carrier(sK137))))) = sK187(sK184(sK295(sK137,powerset(the_carrier(sK137)))),sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP20(sK295(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_176995]) ).
tcf(c_210096,plain,
( in(sK187(sK184(sK93(sK137,powerset(the_carrier(sK137)))),sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_176997]) ).
tcf(c_210097,plain,
( in(sK187(sK184(topstr_closure(sK137,sK138)),topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ sP20(topstr_closure(sK137,sK138))
| ~ in(sK187(sK184(topstr_closure(sK137,sK138)),topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105237,c_177233]) ).
tcf(c_210098,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK187(sK184(sK302(sK137,sK208(powerset(the_carrier(sK137))))),sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_105237,c_177405]) ).
tcf(c_210099,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK187(sK184(sK123(sK137,sK208(powerset(the_carrier(sK137))))),sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK187(sK184(sK123(sK137,sK208(powerset(the_carrier(sK137))))),sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_177400]) ).
tcf(c_210100,plain,
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK187(sK184(sK91(sK137,sK208(powerset(the_carrier(sK137))))),sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK187(sK184(sK91(sK137,sK208(powerset(the_carrier(sK137))))),sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_105237,c_177404]) ).
tcf(c_210101,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK187(sK184(sK91(sK137,sK208(powerset(the_carrier(sK137))))),sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_105237,c_177407]) ).
tcf(c_210102,plain,
( in(sK187(sK184(sK91(sK137,sK208(powerset(the_carrier(sK137))))),sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_105237,c_177406]) ).
tcf(c_210103,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK187(sK184(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK187(sK184(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_177402]) ).
tcf(c_210104,plain,
( closed_subset(sK187(sK184(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK187(sK184(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_177401]) ).
tcf(c_210105,plain,
( in(sK187(sK184(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_105237,c_177421]) ).
tcf(c_210106,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK187(sK184(sK302(sK137,sK207(the_carrier(sK137)))),sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_182970]) ).
tcf(c_210107,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK187(sK184(sK123(sK137,sK207(the_carrier(sK137)))),sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,sK207(the_carrier(sK137))))
| ~ element(sK187(sK184(sK123(sK137,sK207(the_carrier(sK137)))),sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_182965]) ).
tcf(c_210108,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK187(sK184(sK91(sK137,sK207(the_carrier(sK137)))),sK91(sK137,sK207(the_carrier(sK137))))) = sK187(sK184(sK91(sK137,sK207(the_carrier(sK137)))),sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_182969]) ).
tcf(c_210109,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK187(sK184(sK91(sK137,sK207(the_carrier(sK137)))),sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_182972]) ).
tcf(c_210110,plain,
( empty(the_carrier(sK137))
| in(sK187(sK184(sK91(sK137,sK207(the_carrier(sK137)))),sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_182971]) ).
tcf(c_210111,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK187(sK184(sK147(sK137,sK207(the_carrier(sK137)))),sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK187(sK184(sK147(sK137,sK207(the_carrier(sK137)))),sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_182967]) ).
tcf(c_210112,plain,
( empty(the_carrier(sK137))
| closed_subset(sK187(sK184(sK147(sK137,sK207(the_carrier(sK137)))),sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK187(sK184(sK147(sK137,sK207(the_carrier(sK137)))),sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_182966]) ).
tcf(c_210113,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK187(sK184(sK302(sK137,sK325(the_carrier(sK137)))),sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK302(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_184375]) ).
tcf(c_210114,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK187(sK184(sK123(sK137,sK325(the_carrier(sK137)))),sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK123(sK137,sK325(the_carrier(sK137))))
| ~ element(sK187(sK184(sK123(sK137,sK325(the_carrier(sK137)))),sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_184370]) ).
tcf(c_210115,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK187(sK184(sK91(sK137,sK325(the_carrier(sK137)))),sK91(sK137,sK325(the_carrier(sK137))))) = sK187(sK184(sK91(sK137,sK325(the_carrier(sK137)))),sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_184374]) ).
tcf(c_210116,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK187(sK184(sK91(sK137,sK325(the_carrier(sK137)))),sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_184377]) ).
tcf(c_210117,plain,
( empty(the_carrier(sK137))
| in(sK187(sK184(sK91(sK137,sK325(the_carrier(sK137)))),sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105237,c_184376]) ).
tcf(c_210118,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK187(sK184(sK147(sK137,sK325(the_carrier(sK137)))),sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK187(sK184(sK147(sK137,sK325(the_carrier(sK137)))),sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_184372]) ).
tcf(c_210119,plain,
( empty(the_carrier(sK137))
| closed_subset(sK187(sK184(sK147(sK137,sK325(the_carrier(sK137)))),sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK187(sK184(sK147(sK137,sK325(the_carrier(sK137)))),sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105237,c_184371]) ).
tcf(c_210120,plain,
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK187(sK184(sK93(sK137,sK123(sK137,sK138))),sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK187(sK184(sK93(sK137,sK123(sK137,sK138))),sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_105237,c_200623]) ).
tcf(c_210121,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK187(sK184(sK93(sK137,sK123(sK137,sK138))),sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_105237,c_192075]) ).
tcf(c_210122,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK187(sK184(sK93(sK137,sK147(sK137,sK138))),sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_105237,c_192676]) ).
tcf(c_210123,plain,
( closed_subset(set_difference(the_carrier(sK137),sK187(sK184(sK93(sK137,sK147(sK137,sK138))),sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137)
| ~ sP20(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_105237,c_192446]) ).
tcf(c_210124,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK187(sK184(sK91(sK137,sK62(powerset(the_carrier(sK137))))),sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP20(sK91(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_105237,c_201958]) ).
tcf(c_210579,plain,
! [X0: $i] :
( ~ sP32(X0)
| ~ in(X0,sK275(sK273(X0),X0)) ),
inference(superposition,[status(thm)],[c_105365,c_546]) ).
tcf(c_210582,plain,
! [X0: $i] :
( element(sK275(sK273(X0),X0),X0)
| ~ sP32(X0) ),
inference(superposition,[status(thm)],[c_105365,c_701]) ).
tcf(c_210583,plain,
! [X0: $i] :
( in(sK275(sK273(sK99(X0)),sK99(X0)),X0)
| ~ sP32(sK99(X0)) ),
inference(superposition,[status(thm)],[c_105365,c_205]) ).
tcf(c_210584,plain,
! [X0: $i] :
( ordinal(sK275(sK273(sK99(X0)),sK99(X0)))
| ~ sP32(sK99(X0)) ),
inference(superposition,[status(thm)],[c_105365,c_206]) ).
tcf(c_210586,plain,
! [X0: $i] :
( subset(sK275(sK273(powerset(X0)),powerset(X0)),X0)
| ~ sP32(powerset(X0)) ),
inference(superposition,[status(thm)],[c_105365,c_667]) ).
tcf(c_210587,plain,
! [X0: $i,X1: $i] :
( in(sK275(sK273(set_difference(X0,X1)),set_difference(X0,X1)),X0)
| ~ sP32(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_105365,c_692]) ).
tcf(c_210588,plain,
! [X0: $i] :
( sP27
| ordinal(sK275(sK273(sK254(X0)),sK254(X0)))
| ~ sP32(sK254(X0)) ),
inference(superposition,[status(thm)],[c_105365,c_802]) ).
tcf(c_210589,plain,
( sP36(sK137,sK138)
| in(sK275(sK273(powerset(the_carrier(sK137))),powerset(the_carrier(sK137))),sK302(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP32(powerset(the_carrier(sK137)))
| ~ closed_subset(sK275(sK273(powerset(the_carrier(sK137))),powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK275(sK273(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_176867]) ).
tcf(c_210590,plain,
( in(sK275(sK273(powerset(the_carrier(sK137))),powerset(the_carrier(sK137))),sK91(sK137,sK138))
| ~ topological_space(sK137)
| ~ sP32(powerset(the_carrier(sK137)))
| ~ closed_subset(sK275(sK273(powerset(the_carrier(sK137))),powerset(the_carrier(sK137))),sK137)
| ~ subset(sK138,sK275(sK273(powerset(the_carrier(sK137))),powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_176193]) ).
tcf(c_210591,plain,
! [X0: $i] :
( in(sK275(sK273(sK93(sK137,X0)),sK93(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,X0))
| ~ subset(X0,powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_190624]) ).
tcf(c_210592,plain,
! [X0: $i] :
( sP36(sK137,X0)
| subset(X0,sK275(sK273(sK302(sK137,X0)),sK302(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105365,c_190602]) ).
tcf(c_210593,plain,
! [X0: $i] :
( ( sK92(sK137,X0,sK275(sK273(sK91(sK137,X0)),sK91(sK137,X0))) = sK275(sK273(sK91(sK137,X0)),sK91(sK137,X0)) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105365,c_190601]) ).
tcf(c_210594,plain,
! [X0: $i] :
( in(sK275(sK273(sK91(sK137,X0)),sK91(sK137,X0)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105365,c_190603]) ).
tcf(c_210595,plain,
! [X0: $i] :
( subset(X0,sK275(sK273(sK91(sK137,X0)),sK91(sK137,X0)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,X0))
| ~ subset(X0,the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105365,c_190604]) ).
tcf(c_210596,plain,
( open_subset(sK275(sK273(the_topology(sK137)),the_topology(sK137)),sK137)
| ~ sP32(the_topology(sK137))
| ~ subset(sK275(sK273(the_topology(sK137)),the_topology(sK137)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105365,c_190618]) ).
tcf(c_210597,plain,
( ( sK92(sK137,sK138,sK275(sK273(sK91(sK137,sK138)),sK91(sK137,sK138))) = sK275(sK273(sK91(sK137,sK138)),sK91(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105365,c_175190]) ).
tcf(c_210598,plain,
( in(sK275(sK273(sK91(sK137,sK138)),sK91(sK137,sK138)),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105365,c_175008]) ).
tcf(c_210599,plain,
( subset(sK138,sK275(sK273(sK91(sK137,sK138)),sK91(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105365,c_174960]) ).
tcf(c_210600,plain,
( sP36(sK137,sK138)
| ( sK303(sK137,sK138,sK275(sK273(sK302(sK137,sK138)),sK302(sK137,sK138))) = sK275(sK273(sK302(sK137,sK138)),sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105365,c_175802]) ).
tcf(c_210601,plain,
( sP36(sK137,sK138)
| ( sK304(sK137,sK138,sK275(sK273(sK302(sK137,sK138)),sK302(sK137,sK138))) = sK275(sK273(sK302(sK137,sK138)),sK302(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105365,c_175753]) ).
tcf(c_210602,plain,
( sP36(sK137,sK138)
| subset(sK138,sK275(sK273(sK302(sK137,sK138)),sK302(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK138)) ),
inference(superposition,[status(thm)],[c_105365,c_175029]) ).
tcf(c_210603,plain,
( in(sK275(sK273(sK93(sK137,the_topology(sK137))),sK93(sK137,the_topology(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_175089]) ).
tcf(c_210604,plain,
! [X0: $i] :
( in(sK275(sK273(sK93(sK137,sK147(sK137,X0))),sK93(sK137,sK147(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK93(sK137,sK147(sK137,X0))) ),
inference(superposition,[status(thm)],[c_105365,c_175090]) ).
tcf(c_210605,plain,
! [X0: $i] :
( in(sK275(sK273(sK93(sK137,sK125(sK137,X0))),sK93(sK137,sK125(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK125(sK137,X0)))
| ~ element(X0,powerset(powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_175091]) ).
tcf(c_210606,plain,
! [X0: $i] :
( in(sK275(sK273(sK93(sK137,sK123(sK137,X0))),sK93(sK137,sK123(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK93(sK137,sK123(sK137,X0))) ),
inference(superposition,[status(thm)],[c_105365,c_175092]) ).
tcf(c_210607,plain,
( subset(sK138,sK275(sK273(sK147(sK137,sK138)),sK147(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK138))
| ~ subset(sK275(sK273(sK147(sK137,sK138)),sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105365,c_190614]) ).
tcf(c_210608,plain,
( closed_subset(sK275(sK273(sK147(sK137,sK138)),sK147(sK137,sK138)),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK138))
| ~ subset(sK275(sK273(sK147(sK137,sK138)),sK147(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105365,c_190613]) ).
tcf(c_210609,plain,
( ( sK124(sK137,sK138,sK275(sK273(sK123(sK137,sK138)),sK123(sK137,sK138))) = sK275(sK273(sK123(sK137,sK138)),sK123(sK137,sK138)) )
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,sK138))
| ~ subset(sK275(sK273(sK123(sK137,sK138)),sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105365,c_190610]) ).
tcf(c_210610,plain,
( subset(sK138,sK275(sK273(sK123(sK137,sK138)),sK123(sK137,sK138)))
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,sK138))
| ~ subset(sK275(sK273(sK123(sK137,sK138)),sK123(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105365,c_190612]) ).
tcf(c_210611,plain,
! [X0: $i] :
( closed_subset(sK275(sK273(sK147(sK137,topstr_closure(sK137,X0))),sK147(sK137,topstr_closure(sK137,X0))),sK137)
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK147(sK137,topstr_closure(sK137,X0)))
| ~ element(sK275(sK273(sK147(sK137,topstr_closure(sK137,X0))),sK147(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176007]) ).
tcf(c_210612,plain,
! [X0: $i] :
( ( sK92(sK137,topstr_closure(sK137,X0),sK275(sK273(sK91(sK137,topstr_closure(sK137,X0))),sK91(sK137,topstr_closure(sK137,X0)))) = sK275(sK273(sK91(sK137,topstr_closure(sK137,X0))),sK91(sK137,topstr_closure(sK137,X0))) )
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_105365,c_176010]) ).
tcf(c_210613,plain,
! [X0: $i] :
( subset(topstr_closure(sK137,X0),sK275(sK273(sK91(sK137,topstr_closure(sK137,X0))),sK91(sK137,topstr_closure(sK137,X0))))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_105365,c_176013]) ).
tcf(c_210614,plain,
! [X0: $i] :
( in(sK275(sK273(sK91(sK137,topstr_closure(sK137,X0))),sK91(sK137,topstr_closure(sK137,X0))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ element(X0,powerset(the_carrier(sK137)))
| ~ sP32(sK91(sK137,topstr_closure(sK137,X0))) ),
inference(superposition,[status(thm)],[c_105365,c_176012]) ).
tcf(c_210615,plain,
( sP34(the_topology(sK137),sK137)
| ( sK296(sK137,the_topology(sK137),sK275(sK273(sK295(sK137,the_topology(sK137))),sK295(sK137,the_topology(sK137)))) = sK275(sK273(sK295(sK137,the_topology(sK137))),sK295(sK137,the_topology(sK137))) )
| ~ topological_space(sK137)
| ~ sP32(sK295(sK137,the_topology(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176134]) ).
tcf(c_210616,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK304(sK137,the_carrier(sK137),sK275(sK273(sK302(sK137,the_carrier(sK137))),sK302(sK137,the_carrier(sK137)))) = sK275(sK273(sK302(sK137,the_carrier(sK137))),sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176975]) ).
tcf(c_210617,plain,
( sP36(sK137,the_carrier(sK137))
| ( sK303(sK137,the_carrier(sK137),sK275(sK273(sK302(sK137,the_carrier(sK137))),sK302(sK137,the_carrier(sK137)))) = sK275(sK273(sK302(sK137,the_carrier(sK137))),sK302(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176974]) ).
tcf(c_210618,plain,
( sP36(sK137,the_carrier(sK137))
| subset(the_carrier(sK137),sK275(sK273(sK302(sK137,the_carrier(sK137))),sK302(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176981]) ).
tcf(c_210619,plain,
( ( sK124(sK137,the_carrier(sK137),sK275(sK273(sK123(sK137,the_carrier(sK137))),sK123(sK137,the_carrier(sK137)))) = sK275(sK273(sK123(sK137,the_carrier(sK137))),sK123(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,the_carrier(sK137)))
| ~ element(sK275(sK273(sK123(sK137,the_carrier(sK137))),sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176971]) ).
tcf(c_210620,plain,
( subset(the_carrier(sK137),sK275(sK273(sK123(sK137,the_carrier(sK137))),sK123(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,the_carrier(sK137)))
| ~ element(sK275(sK273(sK123(sK137,the_carrier(sK137))),sK123(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176976]) ).
tcf(c_210621,plain,
( ( sK92(sK137,the_carrier(sK137),sK275(sK273(sK91(sK137,the_carrier(sK137))),sK91(sK137,the_carrier(sK137)))) = sK275(sK273(sK91(sK137,the_carrier(sK137))),sK91(sK137,the_carrier(sK137))) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176980]) ).
tcf(c_210622,plain,
( in(sK275(sK273(sK91(sK137,the_carrier(sK137))),sK91(sK137,the_carrier(sK137))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176982]) ).
tcf(c_210623,plain,
( subset(the_carrier(sK137),sK275(sK273(sK91(sK137,the_carrier(sK137))),sK91(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176983]) ).
tcf(c_210624,plain,
( subset(the_carrier(sK137),sK275(sK273(sK147(sK137,the_carrier(sK137))),sK147(sK137,the_carrier(sK137))))
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,the_carrier(sK137)))
| ~ element(sK275(sK273(sK147(sK137,the_carrier(sK137))),sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176978]) ).
tcf(c_210625,plain,
( closed_subset(sK275(sK273(sK147(sK137,the_carrier(sK137))),sK147(sK137,the_carrier(sK137))),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,the_carrier(sK137)))
| ~ element(sK275(sK273(sK147(sK137,the_carrier(sK137))),sK147(sK137,the_carrier(sK137))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_176977]) ).
tcf(c_210626,plain,
( sP34(powerset(the_carrier(sK137)),sK137)
| ( sK296(sK137,powerset(the_carrier(sK137)),sK275(sK273(sK295(sK137,powerset(the_carrier(sK137)))),sK295(sK137,powerset(the_carrier(sK137))))) = sK275(sK273(sK295(sK137,powerset(the_carrier(sK137)))),sK295(sK137,powerset(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP32(sK295(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_176995]) ).
tcf(c_210627,plain,
( in(sK275(sK273(sK93(sK137,powerset(the_carrier(sK137)))),sK93(sK137,powerset(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,powerset(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_176997]) ).
tcf(c_210628,plain,
( in(sK275(sK273(topstr_closure(sK137,sK138)),topstr_closure(sK137,sK138)),sK138)
| ~ closed_subset(sK138,sK137)
| ~ sP32(topstr_closure(sK137,sK138))
| ~ in(sK275(sK273(topstr_closure(sK137,sK138)),topstr_closure(sK137,sK138)),the_carrier(sK137)) ),
inference(superposition,[status(thm)],[c_105365,c_177233]) ).
tcf(c_210629,plain,
( sP36(sK137,sK208(powerset(the_carrier(sK137))))
| subset(sK208(powerset(the_carrier(sK137))),sK275(sK273(sK302(sK137,sK208(powerset(the_carrier(sK137))))),sK302(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_105365,c_177405]) ).
tcf(c_210630,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK275(sK273(sK123(sK137,sK208(powerset(the_carrier(sK137))))),sK123(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK275(sK273(sK123(sK137,sK208(powerset(the_carrier(sK137))))),sK123(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_177400]) ).
tcf(c_210631,plain,
( ( sK92(sK137,sK208(powerset(the_carrier(sK137))),sK275(sK273(sK91(sK137,sK208(powerset(the_carrier(sK137))))),sK91(sK137,sK208(powerset(the_carrier(sK137)))))) = sK275(sK273(sK91(sK137,sK208(powerset(the_carrier(sK137))))),sK91(sK137,sK208(powerset(the_carrier(sK137))))) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_105365,c_177404]) ).
tcf(c_210632,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK275(sK273(sK91(sK137,sK208(powerset(the_carrier(sK137))))),sK91(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_105365,c_177407]) ).
tcf(c_210633,plain,
( in(sK275(sK273(sK91(sK137,sK208(powerset(the_carrier(sK137))))),sK91(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK208(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_105365,c_177406]) ).
tcf(c_210634,plain,
( subset(sK208(powerset(the_carrier(sK137))),sK275(sK273(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK147(sK137,sK208(powerset(the_carrier(sK137))))))
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK275(sK273(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_177402]) ).
tcf(c_210635,plain,
( closed_subset(sK275(sK273(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK208(powerset(the_carrier(sK137)))))
| ~ element(sK275(sK273(sK147(sK137,sK208(powerset(the_carrier(sK137))))),sK147(sK137,sK208(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_177401]) ).
tcf(c_210636,plain,
( in(sK275(sK273(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK208(powerset(powerset(the_carrier(sK137)))))) ),
inference(superposition,[status(thm)],[c_105365,c_177421]) ).
tcf(c_210637,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK207(the_carrier(sK137)))
| subset(sK207(the_carrier(sK137)),sK275(sK273(sK302(sK137,sK207(the_carrier(sK137)))),sK302(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_182970]) ).
tcf(c_210638,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK275(sK273(sK123(sK137,sK207(the_carrier(sK137)))),sK123(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,sK207(the_carrier(sK137))))
| ~ element(sK275(sK273(sK123(sK137,sK207(the_carrier(sK137)))),sK123(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_182965]) ).
tcf(c_210639,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK207(the_carrier(sK137)),sK275(sK273(sK91(sK137,sK207(the_carrier(sK137)))),sK91(sK137,sK207(the_carrier(sK137))))) = sK275(sK273(sK91(sK137,sK207(the_carrier(sK137)))),sK91(sK137,sK207(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_182969]) ).
tcf(c_210640,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK275(sK273(sK91(sK137,sK207(the_carrier(sK137)))),sK91(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_182972]) ).
tcf(c_210641,plain,
( empty(the_carrier(sK137))
| in(sK275(sK273(sK91(sK137,sK207(the_carrier(sK137)))),sK91(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK207(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_182971]) ).
tcf(c_210642,plain,
( empty(the_carrier(sK137))
| subset(sK207(the_carrier(sK137)),sK275(sK273(sK147(sK137,sK207(the_carrier(sK137)))),sK147(sK137,sK207(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK275(sK273(sK147(sK137,sK207(the_carrier(sK137)))),sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_182967]) ).
tcf(c_210643,plain,
( empty(the_carrier(sK137))
| closed_subset(sK275(sK273(sK147(sK137,sK207(the_carrier(sK137)))),sK147(sK137,sK207(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK207(the_carrier(sK137))))
| ~ element(sK275(sK273(sK147(sK137,sK207(the_carrier(sK137)))),sK147(sK137,sK207(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_182966]) ).
tcf(c_210644,plain,
( empty(the_carrier(sK137))
| sP36(sK137,sK325(the_carrier(sK137)))
| subset(sK325(the_carrier(sK137)),sK275(sK273(sK302(sK137,sK325(the_carrier(sK137)))),sK302(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK302(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_184375]) ).
tcf(c_210645,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK275(sK273(sK123(sK137,sK325(the_carrier(sK137)))),sK123(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK123(sK137,sK325(the_carrier(sK137))))
| ~ element(sK275(sK273(sK123(sK137,sK325(the_carrier(sK137)))),sK123(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_184370]) ).
tcf(c_210646,plain,
( empty(the_carrier(sK137))
| ( sK92(sK137,sK325(the_carrier(sK137)),sK275(sK273(sK91(sK137,sK325(the_carrier(sK137)))),sK91(sK137,sK325(the_carrier(sK137))))) = sK275(sK273(sK91(sK137,sK325(the_carrier(sK137)))),sK91(sK137,sK325(the_carrier(sK137)))) )
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_184374]) ).
tcf(c_210647,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK275(sK273(sK91(sK137,sK325(the_carrier(sK137)))),sK91(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_184377]) ).
tcf(c_210648,plain,
( empty(the_carrier(sK137))
| in(sK275(sK273(sK91(sK137,sK325(the_carrier(sK137)))),sK91(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK325(the_carrier(sK137)))) ),
inference(superposition,[status(thm)],[c_105365,c_184376]) ).
tcf(c_210649,plain,
( empty(the_carrier(sK137))
| subset(sK325(the_carrier(sK137)),sK275(sK273(sK147(sK137,sK325(the_carrier(sK137)))),sK147(sK137,sK325(the_carrier(sK137)))))
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK275(sK273(sK147(sK137,sK325(the_carrier(sK137)))),sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_184372]) ).
tcf(c_210650,plain,
( empty(the_carrier(sK137))
| closed_subset(sK275(sK273(sK147(sK137,sK325(the_carrier(sK137)))),sK147(sK137,sK325(the_carrier(sK137)))),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK147(sK137,sK325(the_carrier(sK137))))
| ~ element(sK275(sK273(sK147(sK137,sK325(the_carrier(sK137)))),sK147(sK137,sK325(the_carrier(sK137)))),powerset(the_carrier(sK137))) ),
inference(superposition,[status(thm)],[c_105365,c_184371]) ).
tcf(c_210651,plain,
( ( sK124(sK137,sK138,set_difference(the_carrier(sK137),sK275(sK273(sK93(sK137,sK123(sK137,sK138))),sK93(sK137,sK123(sK137,sK138))))) = set_difference(the_carrier(sK137),sK275(sK273(sK93(sK137,sK123(sK137,sK138))),sK93(sK137,sK123(sK137,sK138)))) )
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_105365,c_200623]) ).
tcf(c_210652,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK275(sK273(sK93(sK137,sK123(sK137,sK138))),sK93(sK137,sK123(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK123(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_105365,c_192075]) ).
tcf(c_210653,plain,
( subset(sK138,set_difference(the_carrier(sK137),sK275(sK273(sK93(sK137,sK147(sK137,sK138))),sK93(sK137,sK147(sK137,sK138)))))
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_105365,c_192676]) ).
tcf(c_210654,plain,
( closed_subset(set_difference(the_carrier(sK137),sK275(sK273(sK93(sK137,sK147(sK137,sK138))),sK93(sK137,sK147(sK137,sK138)))),sK137)
| ~ topological_space(sK137)
| ~ sP32(sK93(sK137,sK147(sK137,sK138))) ),
inference(superposition,[status(thm)],[c_105365,c_192446]) ).
tcf(c_210655,plain,
( sP3(powerset(the_carrier(sK137)))
| in(sK275(sK273(sK91(sK137,sK62(powerset(the_carrier(sK137))))),sK91(sK137,sK62(powerset(the_carrier(sK137))))),powerset(the_carrier(sK137)))
| ~ topological_space(sK137)
| ~ sP32(sK91(sK137,sK62(powerset(the_carrier(sK137))))) ),
inference(superposition,[status(thm)],[c_105365,c_201958]) ).
tcf(c_211353,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_210655,c_210654,c_210653,c_210652,c_210651,c_210650,c_210649,c_210648,c_210647,c_210646,c_210645,c_210644,c_210643,c_210642,c_210641,c_210640,c_210639,c_210638,c_210637,c_210636,c_210635,c_210634,c_210633,c_210632,c_210631,c_210630,c_210629,c_210628,c_210627,c_210626,c_210625,c_210624,c_210623,c_210622,c_210621,c_210620,c_210619,c_210618,c_210617,c_210616,c_210615,c_210614,c_210613,c_210612,c_210611,c_210610,c_210609,c_210608,c_210607,c_210606,c_210605,c_210604,c_210603,c_210602,c_210601,c_210600,c_210599,c_210598,c_210597,c_210596,c_210595,c_210594,c_210593,c_210592,c_210591,c_210590,c_210589,c_210588,c_210587,c_210586,c_210584,c_210583,c_210582,c_210579,c_210124,c_210123,c_210122,c_210121,c_210120,c_210119,c_210118,c_210117,c_210116,c_210115,c_210114,c_210113,c_210112,c_210111,c_210110,c_210109,c_210108,c_210107,c_210106,c_210105,c_210104,c_210103,c_210102,c_210101,c_210100,c_210099,c_210098,c_210097,c_210096,c_210095,c_210094,c_210093,c_210092,c_210091,c_210090,c_210089,c_210088,c_210087,c_210086,c_210085,c_210084,c_210083,c_210082,c_210081,c_210080,c_210079,c_210078,c_210077,c_210076,c_210075,c_210074,c_210073,c_210072,c_210071,c_210070,c_210069,c_210068,c_210067,c_210066,c_210065,c_210064,c_210063,c_210062,c_210061,c_210060,c_210059,c_210058,c_210057,c_210056,c_210055,c_210053,c_210052,c_210051,c_210048,c_210047,c_210019,c_210018,c_210017,c_210012,c_210011,c_210010,c_210005,c_210004,c_209651,c_209650,c_209649,c_209648,c_209647,c_209646,c_209645,c_209644,c_209643,c_209642,c_209641,c_209640,c_209639,c_209638,c_209637,c_209636,c_209635,c_209634,c_209633,c_209632,c_209631,c_209630,c_209447,c_209446,c_209445,c_209444,c_209443,c_209442,c_209441,c_209440,c_209439,c_209438,c_209437,c_209436,c_209435,c_209434,c_209433,c_209432,c_209431,c_209430,c_209429,c_209428,c_209427,c_209426,c_209237,c_209236,c_209235,c_209234,c_209233,c_209232,c_209231,c_209230,c_209229,c_209228,c_209227,c_209226,c_209225,c_209224,c_209223,c_209222,c_209221,c_209220,c_209219,c_209218,c_209217,c_209216,c_209008,c_209007,c_209006,c_209005,c_209004,c_209003,c_209002,c_209001,c_209000,c_208999,c_208998,c_208997,c_208996,c_208995,c_208994,c_208993,c_208992,c_208991,c_208990,c_208989,c_208988,c_208987,c_208909,c_208908,c_208907,c_208906,c_208905,c_208904,c_208843,c_208842,c_208841,c_208840,c_208839,c_208838,c_208837,c_208836,c_208835,c_208834,c_208833,c_208832,c_208831,c_208830,c_208829,c_208828,c_208827,c_208826,c_208825,c_208824,c_208823,c_208822,c_208821,c_208820,c_208819,c_208818,c_208667,c_208666,c_208665,c_208660,c_208659,c_208658,c_208653,c_208652,c_208491,c_208490,c_208489,c_208488,c_208487,c_208486,c_208485,c_208484,c_208483,c_208482,c_208481,c_208480,c_208479,c_208478,c_208477,c_208476,c_208475,c_208474,c_208473,c_208472,c_208471,c_208470,c_208443,c_208442,c_208441,c_208440,c_208439,c_208359,c_208358,c_208357,c_208356,c_208355,c_208308,c_208307,c_208306,c_208305,c_208304,c_208290,c_207879,c_207878,c_207877,c_207876,c_207875,c_207874,c_207873,c_207872,c_207871,c_207870,c_207869,c_207868,c_207867,c_207866,c_207865,c_207864,c_207863,c_207862,c_207861,c_207860,c_207859,c_207858,c_207857,c_207856,c_207855,c_207854,c_207853,c_207852,c_207851,c_207850,c_207849,c_207848,c_207847,c_207846,c_207845,c_207844,c_207843,c_207842,c_207838,c_207837,c_207836,c_207835,c_207834,c_207705,c_207704,c_207703,c_207702,c_207701,c_207700,c_207699,c_207698,c_207697,c_207696,c_207695,c_207694,c_207693,c_207692,c_207691,c_207690,c_207687,c_207686,c_207685,c_207684,c_207683,c_207682,c_207680,c_207361,c_207358,c_207357,c_207355,c_207354,c_207353,c_207352,c_207351,c_207350,c_207349,c_207348,c_207347,c_207345,c_207344,c_207341,c_207339,c_207338,c_207337,c_207336,c_207335,c_207334,c_207333,c_207332,c_207331,c_207330,c_207329,c_207328,c_207327,c_207326,c_207325,c_207324,c_207321,c_207320,c_207319,c_207318,c_207317,c_207316,c_207315,c_207314,c_207313,c_207119,c_207116,c_207115,c_207113,c_207112,c_207111,c_207110,c_207109,c_207108,c_207107,c_207106,c_207105,c_207103,c_207102,c_207099,c_207097,c_207096,c_207095,c_207094,c_207093,c_207092,c_207091,c_207090,c_207089,c_207088,c_207087,c_207086,c_207085,c_207084,c_207083,c_207082,c_207079,c_207078,c_207077,c_207076,c_207075,c_207074,c_207073,c_207072,c_207071,c_206899,c_206898,c_206897,c_206892,c_206891,c_206890,c_206889,c_206886,c_206884,c_206706,c_206705,c_206704,c_206703,c_206702,c_206701,c_206700,c_206699,c_206698,c_206697,c_206696,c_206695,c_206694,c_206693,c_206692,c_206691,c_206690,c_206689,c_206688,c_206687,c_206686,c_206685,c_206684,c_206635,c_206634,c_206633,c_206632,c_206631,c_206536,c_206535,c_206534,c_206533,c_206532,c_206146,c_206145,c_206144,c_206143,c_206142,c_206141,c_206140,c_206139,c_206138,c_206137,c_206136,c_206135,c_206134,c_206133,c_206132,c_206131,c_206130,c_206129,c_206128,c_206127,c_206126,c_206125,c_206124,c_206123,c_206122,c_206121,c_206120,c_206119,c_206118,c_206117,c_206116,c_206115,c_206114,c_206113,c_206112,c_206111,c_206110,c_206109,c_206105,c_206104,c_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4,c_48553,c_48529,c_48514,c_106103,c_48490,c_48475,c_48460,c_48445,c_48431,c_48416,c_48389,c_48368,c_48350,c_48332,c_48314,c_48297,c_48285,c_48252,c_48237,c_48222,c_48207,c_48192,c_48177,c_48162,c_48138,c_48126,c_48105,c_48087,c_48070,c_48058,c_106063,c_48037,c_48019,c_48001,c_47965,c_47947,c_47929,c_47911,c_47893,c_47876,c_47852,c_47840,c_106061,c_47816,c_47795,c_47771,c_47756,c_106059,c_47696,c_106095,c_106093,c_47629,c_47615,c_47601,c_47587,c_106091,c_106089,c_47520,c_106077,c_106075,c_47453,c_47439,c_47425,c_47411,c_106073,c_106071,c_205726,c_205725,c_205724,c_194421,c_194414,c_49814,c_49804,c_49794,c_49784,c_49774,c_184155,c_22252,c_22242,c_22232,c_22201,c_22187,c_22173,c_22159,c_22154,c_22147,c_22140,c_21872,c_21860,c_21598,c_21586,c_105110,c_21566,c_105107,c_21533,c_21521,c_105022,c_21501,c_105019,c_21468,c_21456,c_105002,c_21436,c_104999,c_21395,c_21374,c_105423,c_105421,c_105419,c_105417,c_105369,c_105367,c_105365,c_105237,c_105235,c_105233,c_21011,c_20999,c_183203,c_20791,c_20772,c_20750,c_20731,c_20712,c_105926,c_105912,c_20677,c_20658,c_20622,c_20592,c_20561,c_20542,c_20523,c_20459,c_20443,c_20427,c_20411,c_20395,c_20379,c_20331,c_20302,c_20289,c_20273,c_20260,c_20234,c_20218,c_20195,c_20140,c_20110,c_20012,c_19953,c_19940,c_19902,c_19849,c_19718,c_19705,c_19666,c_19625,c_19534,c_19381,c_19298,c_19277,c_19230,c_105287,c_105285,c_19098,c_19075,c_105299,c_105053,c_18883,c_18824,c_105307,c_105315,c_18768,c_105977,c_18652,c_18642,c_105047,c_18259,c_18249,c_105283,c_105281,c_105505,c_105507,c_18151,c_18141,c_18131,c_18001,c_17951,c_17941,c_17931,c_17921,c_17752,c_17545,c_17489,c_17427,c_17273,c_17111,c_17101,c_17091,c_17075,c_17021,c_16907,c_16897,c_16887,c_16877,c_105231,c_105040,c_105038,c_13761,c_13308,c_8250,c_7868,c_7415,c_6347,c_6346,c_6345,c_6338,c_6337,c_6336,c_6193,c_6192,c_104855,c_104832,c_105493,c_5896,c_5895,c_5708,c_5700,c_5699,c_5698,c_5697,c_5696,c_5694,c_5693,c_5692,c_5691,c_5690,c_5689,c_105465,c_105463,c_105461,c_105459,c_105457,c_105455,c_105441,c_105439,c_105322,c_104888,c_104886,c_104883,c_104881,c_104879,c_2337,c_2335,c_2320,c_2310,c_2306,c_2297,c_2294,c_104968,c_2288,c_104931,c_2259,c_181679,c_199820,c_178671,c_179418,c_1335,c_1334,c_1333,c_1332,c_1331,c_1330,c_1329,c_1328,c_1327,c_1324,c_1323,c_1322,c_1320,c_1319,c_1318,c_1315,c_1314,c_1313,c_1312,c_1311,c_1310,c_1307,c_1306,c_1305,c_1298,c_1297,c_1296,c_1295,c_1294,c_1293,c_1287,c_1286,c_1285,c_1284,c_1283,c_1282,c_1272,c_1271,c_1270,c_1269,c_1268,c_1266,c_1265,c_1264,c_1263,c_1262,c_1261,c_1260,c_1259,c_1258,c_1257,c_1256,c_1255,c_1254,c_1253,c_1215,c_1214,c_1213,c_1212,c_1211,c_1210,c_1208,c_1207,c_1206,c_1205,c_1204,c_1203,c_1202,c_1201,c_1200,c_1199,c_1198,c_1197,c_1195,c_1194,c_1193,c_1192,c_1191,c_1190,c_1189,c_1182,c_1181,c_1180,c_1178,c_1177,c_1176,c_1174,c_1169,c_1168,c_1167,c_1166,c_1165,c_1163,c_1155,c_1156,c_1150,c_1149,c_1146,c_1144,c_1143,c_1142,c_1141,c_1140,c_1139,c_1138,c_1137,c_1136,c_1135,c_1134,c_1126,c_1125,c_1115,c_1114,c_1112,c_1111,c_1110,c_1109,c_1108,c_1107,c_1106,c_1105,c_1103,c_1101,c_1100,c_1099,c_1098,c_1097,c_1096,c_1095,c_1094,c_1093,c_1092,c_1091,c_1090,c_1089,c_1085,c_1084,c_1083,c_1082,c_1081,c_1080,c_1088,c_1087,c_1086,c_1076,c_1075,c_1074,c_1073,c_1072,c_1071,c_1070,c_1069,c_1068,c_1067,c_1066,c_1065,c_1064,c_1063,c_1062,c_1061,c_1060,c_1059,c_1058,c_1057,c_1056,c_1050,c_1049,c_1048,c_1045,c_1038,c_1037,c_1036,c_1035,c_1033,c_1032,c_1027,c_1026,c_1025,c_1024,c_1023,c_1022,c_1021,c_1019,c_1018,c_1016,c_1015,c_1013,c_1011,c_1010,c_1008,c_1007,c_1006,c_1005,c_1004,c_1003,c_1002,c_1001,c_1000,c_999,c_998,c_997,c_996,c_995,c_994,c_986,c_985,c_983,c_982,c_981,c_980,c_979,c_181674,c_970,c_969,c_968,c_967,c_966,c_965,c_964,c_963,c_962,c_961,c_960,c_959,c_958,c_957,c_956,c_955,c_954,c_953,c_952,c_951,c_949,c_948,c_946,c_944,c_943,c_942,c_941,c_940,c_939,c_938,c_937,c_936,c_918,c_917,c_916,c_915,c_914,c_913,c_912,c_907,c_906,c_905,c_904,c_903,c_900,c_896,c_895,c_894,c_893,c_892,c_891,c_890,c_889,c_888,c_887,c_886,c_885,c_884,c_883,c_881,c_880,c_879,c_878,c_877,c_876,c_875,c_874,c_873,c_872,c_871,c_870,c_869,c_868,c_867,c_866,c_865,c_864,c_859,c_858,c_857,c_856,c_855,c_854,c_852,c_851,c_850,c_849,c_848,c_847,c_846,c_845,c_844,c_842,c_841,c_840,c_839,c_838,c_837,c_836,c_843,c_834,c_833,c_831,c_828,c_827,c_826,c_825,c_820,c_819,c_818,c_817,c_816,c_815,c_814,c_813,c_812,c_811,c_810,c_809,c_808,c_807,c_806,c_805,c_804,c_802,c_801,c_800,c_799,c_798,c_797,c_796,c_795,c_794,c_793,c_792,c_791,c_788,c_787,c_786,c_785,c_784,c_783,c_790,c_781,c_780,c_779,c_778,c_777,c_776,c_775,c_774,c_767,c_766,c_764,c_762,c_761,c_758,c_757,c_756,c_755,c_753,c_752,c_751,c_750,c_749,c_748,c_747,c_746,c_745,c_744,c_742,c_741,c_740,c_739,c_737,c_736,c_735,c_734,c_732,c_731,c_728,c_727,c_724,c_723,c_722,c_719,c_716,c_715,c_714,c_713,c_712,c_711,c_710,c_709,c_708,c_707,c_706,c_705,c_704,c_703,c_702,c_701,c_700,c_699,c_698,c_697,c_696,c_693,c_692,c_691,c_690,c_689,c_688,c_681,c_680,c_679,c_673,c_672,c_668,c_667,c_666,c_665,c_664,c_663,c_662,c_661,c_670,c_659,c_658,c_651,c_650,c_648,c_647,c_646,c_645,c_644,c_643,c_642,c_641,c_640,c_639,c_638,c_637,c_636,c_635,c_634,c_633,c_632,c_631,c_630,c_629,c_627,c_626,c_624,c_623,c_621,c_620,c_618,c_619,c_616,c_615,c_614,c_612,c_611,c_605,c_604,c_603,c_601,c_600,c_599,c_598,c_596,c_1341,c_594,c_593,c_592,c_591,c_590,c_589,c_588,c_587,c_586,c_583,c_581,c_580,c_569,c_565,c_563,c_562,c_561,c_560,c_556,c_555,c_554,c_553,c_551,c_550,c_549,c_552,c_547,c_546,c_545,c_544,c_543,c_542,c_541,c_539,c_536,c_535,c_534,c_532,c_531,c_530,c_529,c_528,c_527,c_524,c_523,c_522,c_521,c_520,c_519,c_518,c_517,c_516,c_515,c_514,c_513,c_512,c_511,c_510,c_509,c_508,c_507,c_506,c_502,c_501,c_500,c_499,c_498,c_497,c_496,c_495,c_494,c_493,c_492,c_491,c_490,c_489,c_488,c_487,c_486,c_485,c_483,c_482,c_481,c_480,c_475,c_474,c_473,c_472,c_471,c_470,c_469,c_468,c_467,c_466,c_465,c_464,c_463,c_459,c_458,c_457,c_456,c_452,c_450,c_449,c_443,c_442,c_441,c_439,c_433,c_426,c_425,c_423,c_422,c_421,c_420,c_419,c_418,c_417,c_416,c_415,c_414,c_410,c_409,c_408,c_407,c_406,c_401,c_400,c_399,c_398,c_395,c_394,c_393,c_392,c_391,c_389,c_388,c_387,c_386,c_385,c_384,c_383,c_382,c_381,c_380,c_379,c_378,c_376,c_375,c_374,c_373,c_372,c_371,c_369,c_368,c_367,c_365,c_364,c_363,c_362,c_361,c_360,c_359,c_358,c_357,c_356,c_355,c_354,c_353,c_352,c_349,c_348,c_347,c_346,c_342,c_341,c_340,c_339,c_337,c_336,c_335,c_334,c_333,c_567,c_571,c_330,c_329,c_328,c_327,c_326,c_325,c_324,c_323,c_321,c_945,c_318,c_317,c_316,c_315,c_314,c_312,c_311,c_309,c_307,c_205750,c_303,c_302,c_301,c_300,c_299,c_298,c_297,c_295,c_293,c_292,c_291,c_290,c_289,c_288,c_287,c_283,c_282,c_281,c_280,c_279,c_278,c_277,c_276,c_275,c_274,c_273,c_272,c_259,c_258,c_257,c_256,c_255,c_254,c_248,c_247,c_246,c_245,c_243,c_241,c_239,c_237,c_235,c_234,c_233,c_232,c_231,c_229,c_228,c_227,c_226,c_225,c_224,c_223,c_222,c_221,c_220,c_219,c_218,c_217,c_216,c_215,c_214,c_213,c_212,c_211,c_210,c_209,c_208,c_207,c_206,c_205,c_204,c_201,c_200,c_199,c_198,c_197,c_196,c_185,c_184,c_183,c_182,c_181,c_180,c_179,c_178,c_177,c_176,c_175,c_172,c_171,c_169,c_167,c_166,c_165,c_164,c_162,c_159,c_158,c_157,c_156,c_155,c_142,c_141,c_140,c_139,c_138,c_136,c_134,c_133,c_132,c_131,c_130,c_129,c_126,c_124,c_123,c_122,c_121,c_119,c_120,c_117,c_116,c_115,c_112,c_111,c_110,c_109,c_108,c_107,c_106,c_105,c_104,c_103,c_102,c_101,c_99,c_97,c_95,c_94,c_93,c_96,c_91,c_271,c_270,c_760,c_533,c_413,c_78,c_75,c_74,c_73,c_72,c_71,c_68,c_403,c_402,c_64,c_63,c_404,c_60,c_56,c_55,c_54,c_451,c_52,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU319+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 13:42:37 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 105.44/17.50 % SZS status Started for theBenchmark.p
% 105.44/17.50 % SZS status Theorem for theBenchmark.p
% 105.44/17.50
% 105.44/17.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 105.44/17.50
% 105.44/17.50 % ------ iProver source info
% 105.44/17.50
% 105.44/17.50 % git: date: 2026-07-19 20:42:38 +0200
% 105.44/17.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 105.44/17.50 % git: non_committed_changes: false
% 105.44/17.50
% 105.44/17.50 % ------ Parsing...
% 105.44/17.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 105.44/17.50
% 105.44/17.50 % ------ Preprocessing... sup_sim: 96 sf_s rm: 76 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 46 sf_s rm: 21 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 21 0s sf_e pe_s pe_e %
% 105.44/17.50
% 105.44/17.50 % ------ Preprocessing... gs_s sp: 15 0s gs_e snvd_s sp: 0 0s snvd_e %
% 105.44/17.50
% 105.44/17.50 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 105.44/17.50 % ------ Proving...
% 105.44/17.50 % ------ Problem Properties
% 105.44/17.50
% 105.44/17.50 %
% 105.44/17.50 % clauses 1225
% 105.44/17.50 % conjectures 3
% 105.44/17.50 % EPR 165
% 105.44/17.50 % Horn 909
% 105.44/17.50 % unary 134
% 105.44/17.50 % binary 381
% 105.44/17.50 % lits 3771
% 105.44/17.50 % lits eq 507
% 105.44/17.50 % fd_pure 0
% 105.44/17.50 % fd_pseudo 0
% 105.44/17.50 % fd_cond 41
% 105.44/17.50 % fd_pseudo_cond 110
% 105.44/17.50 % AC symbols 0
% 105.44/17.50
% 105.44/17.50 % ------ Schedule dynamic 5 is on
% 105.44/17.50
% 105.44/17.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 105.44/17.50
% 105.44/17.50
% 105.44/17.50 % ------
% 105.44/17.50 % Current options:
% 105.44/17.50 % ------
% 105.44/17.50
% 105.44/17.50
% 105.44/17.50 %
% 105.44/17.50
% 105.44/17.50 % ------ Proving...
% 105.44/17.50 %
% 105.44/17.50
% 105.44/17.50 % SZS status Theorem for theBenchmark.p
% 105.44/17.50
% 105.44/17.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 121.72/17.75
% 121.72/17.75
%------------------------------------------------------------------------------