%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU325+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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:56:52 PM UTC 2026
% Result : Theorem 88.78s 18.45s
% Output : CNFRefutation 89.23s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f3544ERROR: Could not build tree for root c_170863ERROR: 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(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] :
( one_sorted_str(X0)
=> ( empty_carrier(X0)
<=> empty(the_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).
fof(f64,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f65,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
fof(f66,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(f67,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(f68,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f69,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f71,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(f72,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f74,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(f75,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(f76,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(f77,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(f78,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(f79,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(f81,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(f82,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(f83,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(f84,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f85,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(f86,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(f87,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(f89,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(f90,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(f91,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f92,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(f93,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(f94,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(f95,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(f96,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(f97,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(f99,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(f100,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(f101,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(f102,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(f103,axiom,
! [X0] :
( being_limit_ordinal(X0)
<=> X0 = union(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_ordinal1) ).
fof(f104,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(f105,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(f106,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(f107,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(f108,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(f109,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(f110,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f111,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(f112,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(f113,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( is_a_cover_of_carrier(X0,X1)
<=> cast_as_carrier_subset(X0) = union_of_subsets(the_carrier(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pre_topc) ).
fof(f114,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(f115,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(f116,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(f117,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f118,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(f119,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f124,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(f131,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f133,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f137,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(f138,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(f140,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(f142,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f144,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f149,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(f153,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f154,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(f158,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f159,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(f160,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(f161,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(f162,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(f163,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f164,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(f165,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(f166,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f167,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(f168,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f170,axiom,
! [X0] :
( meet_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f171,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f173,axiom,
! [X0] :
( join_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f174,axiom,
! [X0] :
( latt_str(X0)
=> ( join_semilatt_str(X0)
& meet_semilatt_str(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f177,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(f182,axiom,
? [X0] : meet_semilatt_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
fof(f183,axiom,
? [X0] : top_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
fof(f184,axiom,
? [X0] : one_sorted_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f185,axiom,
? [X0] : join_semilatt_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
fof(f186,axiom,
? [X0] : latt_str(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
fof(f187,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f188,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f189,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f190,axiom,
! [X0,X1] :
( finite(X1)
=> finite(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
fof(f191,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(f193,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
fof(f194,axiom,
! [X0,X1] :
( finite(X0)
=> finite(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
fof(f196,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(f198,axiom,
! [X0] :
( finite(singleton(X0))
& ~ empty(singleton(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
fof(f200,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(f201,axiom,
! [X0] : ~ empty(succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(f202,axiom,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal2) ).
fof(f204,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f206,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f213,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f215,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(cast_as_carrier_subset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(f216,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f219,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f230,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(f231,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(f232,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
fof(f233,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f235,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f238,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(f239,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(f240,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f241,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f243,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(f245,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f246,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(f247,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f249,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f250,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f251,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
fof(f252,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(f253,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f255,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(f256,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(f257,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f258,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(f259,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f260,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(f261,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f263,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f264,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f265,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(f266,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(f268,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(f271,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(f272,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(f273,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l40_tops_1) ).
fof(f274,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(f278,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(f280,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(f281,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f282,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f283,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(f284,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(f285,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f286,axiom,
? [X0] :
( being_limit_ordinal(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal2) ).
fof(f287,axiom,
? [X0] :
( empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
fof(f288,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f289,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f291,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f292,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(f293,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f294,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(f295,axiom,
! [X0,X1] :
? [X2] :
( function(X2)
& relation(X2)
& relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
fof(f296,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f297,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f299,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f300,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f301,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f302,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f304,axiom,
? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f306,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(f311,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(f312,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(f313,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(f314,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(f316,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(f317,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(f318,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(f319,axiom,
! [X0,X1] :
( equipotent(X0,X1)
<=> are_equipotent(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r2_wellord2) ).
fof(f320,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ordinal_subset(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(f322,axiom,
! [X0,X1] : equipotent(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_wellord2) ).
fof(f323,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(f324,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(f325,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(f326,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(f327,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(f328,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(f329,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(f330,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(f331,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(f332,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(f335,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(f336,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(f337,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(f338,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(f339,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(f340,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(f341,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(f342,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(f345,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(f346,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(f347,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(f348,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(f349,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(f350,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(f351,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(f352,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(f353,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(f356,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f357,axiom,
! [X0,X1] :
( equipotent(X0,X1)
=> equipotent(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r2_wellord2) ).
fof(f358,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(f359,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f360,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(f361,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(f362,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(f363,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng_restriction(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
fof(f364,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(f365,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(f366,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(f367,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(f369,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(f370,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f371,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(f372,axiom,
! [X0,X1] :
( ( finite(X1)
& subset(X0,X1) )
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f373,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(f374,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(f375,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f376,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(f377,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(f378,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(f379,axiom,
! [X0] :
( relation(X0)
=> relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f380,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(f381,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(f383,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(f384,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(f385,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(f386,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(f387,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(f388,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(f389,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(f390,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(f392,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(f393,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(f395,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(f396,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(f397,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(f398,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(f399,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f400,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f401,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f402,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f404,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(f405,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(f406,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(f407,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(f408,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(f409,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(f410,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(f411,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(f412,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(f413,axiom,
! [X0,X1] :
( relation(X1)
=> ( reflexive(X1)
=> reflexive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_wellord1) ).
fof(f414,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(f416,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f417,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(f418,axiom,
! [X0,X1] :
( relation(X1)
=> ( connected(X1)
=> connected(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_wellord1) ).
fof(f419,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(f420,axiom,
! [X0,X1] :
( relation(X1)
=> ( transitive(X1)
=> transitive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
fof(f421,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(f422,axiom,
! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord1) ).
fof(f423,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(f424,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(f426,axiom,
! [X0] :
? [X1] :
( well_orders(X1,X0)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_wellord2) ).
fof(f427,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(f428,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(f429,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f430,axiom,
! [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(f431,axiom,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f433,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f434,axiom,
! [X0] : reflexive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
fof(f435,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f436,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(f437,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
fof(f438,axiom,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( subset(X1,X0)
& ordinal(X1) ) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f439,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(f440,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(f441,axiom,
! [X0,X1] :
( relation(X1)
=> ( well_ordering(X1)
=> well_ordering(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_wellord1) ).
fof(f442,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(f443,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(f444,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(f445,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(f446,axiom,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f447,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f448,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(f449,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f450,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f451,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(f452,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(f453,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(f454,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f455,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(f456,axiom,
! [X0,X1,X2] :
~ ( in(X2,X0)
& in(X1,X2)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(f457,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f458,axiom,
! [X0] : transitive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_wellord2) ).
fof(f459,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(f460,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f461,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(f462,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(f463,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(f464,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(f466,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(f467,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(interior(X0,X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_1) ).
fof(f468,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(f469,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(f471,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(f473,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(f474,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(f475,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f476,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(f477,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(f478,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(f479,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(f480,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(f481,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(f482,axiom,
! [X0] : set_difference(empty_set,X0) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(f483,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f484,axiom,
! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_wellord2) ).
fof(f485,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(f486,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(f488,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(f489,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(f490,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(f491,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(f492,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(f493,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(f495,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(f496,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(f497,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f498,conjecture,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ~ ( X1 = empty_set
& is_a_cover_of_carrier(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tops_2) ).
fof(f499,negated_conjecture,
~ ! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ~ ( X1 = empty_set
& is_a_cover_of_carrier(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f498]) ).
fof(f500,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(f501,axiom,
! [X0] : antisymmetric(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord2) ).
fof(f502,axiom,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f503,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f504,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(f505,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f506,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(f507,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(f508,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f509,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(f510,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f511,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f512,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(f513,axiom,
! [X0] :
( ordinal(X0)
=> well_founded_relation(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_wellord2) ).
fof(f514,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f515,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(f516,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(f517,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(f518,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(f519,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f520,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(f521,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(f522,axiom,
! [X0] :
( ordinal(X0)
=> well_ordering(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_wellord2) ).
fof(f523,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f524,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f525,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(f526,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
fof(f527,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f528,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(f529,axiom,
! [X0] :
( relation(X0)
=> ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
fof(f530,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(f531,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f532,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(f533,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f534,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(f535,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(f536,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f537,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(f538,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(f539,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f540,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,[],[f323]) ).
fof(f541,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,[],[f324]) ).
fof(f542,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,[],[f325]) ).
fof(f543,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,[],[f326]) ).
fof(f544,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,[],[f350]) ).
fof(f545,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,[],[f351]) ).
fof(f546,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,[],[f352]) ).
fof(f547,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,[],[f371]) ).
fof(f548,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,[],[f428]) ).
fof(f549,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,[],[f459]) ).
fof(f550,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,[],[f463]) ).
fof(f551,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,[],[f485]) ).
fof(f552,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,[],[f328]) ).
fof(f553,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,[],[f331]) ).
fof(f554,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,[],[f330]) ).
fof(f555,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f253]) ).
fof(f557,plain,
! [X0] : equipotent(X0,X0),
inference(rectify,[],[f322]) ).
fof(f558,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,[],[f336]) ).
fof(f559,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,[],[f329]) ).
fof(f560,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,[],[f337]) ).
fof(f561,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,[],[f332]) ).
fof(f562,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,[],[f339]) ).
fof(f563,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,[],[f335]) ).
fof(f566,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,[],[f338]) ).
fof(f568,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,[],[f538]) ).
fof(f569,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f259]) ).
fof(f570,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(f571,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,[],[f71]) ).
fof(f572,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f117]) ).
fof(f587,plain,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
=> topstr_closure(X0,X1) = X1 ) ) ),
inference(pure_predicate_removal,[],[f488]) ).
fof(f600,plain,
! [X0] :
( ~ relation(X0)
| ( reflexive(X0)
<=> ! [X1] :
( ~ in(X1,relation_field(X0))
| in(ordered_pair(X1,X1),X0) ) ) ),
inference(ennf_transformation,[],[f260]) ).
fof(f602,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f263]) ).
fof(f603,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f264]) ).
fof(f604,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ),
inference(ennf_transformation,[],[f265]) ).
fof(f605,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,[],[f266]) ).
fof(f606,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,[],[f605]) ).
fof(f607,plain,
! [X0,X1] :
( ~ relation(X1)
| ? [X2] :
( relation(X2)
& well_orders(X2,X0) )
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1) ),
inference(ennf_transformation,[],[f268]) ).
fof(f608,plain,
! [X0,X1] :
( ~ relation(X1)
| ? [X2] :
( relation(X2)
& well_orders(X2,X0) )
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1) ),
inference(flattening,[],[f607]) ).
fof(f610,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,[],[f271]) ).
fof(f611,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> ! [X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X1 = X2 ) ) ),
inference(flattening,[],[f610]) ).
fof(f612,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(ennf_transformation,[],[f272]) ).
fof(f613,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(flattening,[],[f612]) ).
fof(f614,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
inference(ennf_transformation,[],[f273]) ).
fof(f615,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
inference(flattening,[],[f614]) ).
fof(f616,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,[],[f274]) ).
fof(f618,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f278]) ).
fof(f621,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,[],[f540]) ).
fof(f622,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,[],[f621]) ).
fof(f623,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,[],[f541]) ).
fof(f624,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,[],[f623]) ).
fof(f625,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,[],[f542]) ).
fof(f626,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,[],[f625]) ).
fof(f627,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,[],[f543]) ).
fof(f628,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,[],[f627]) ).
fof(f629,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,[],[f327]) ).
fof(f630,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,[],[f629]) ).
fof(f631,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,[],[f340]) ).
fof(f632,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,[],[f631]) ).
fof(f633,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,[],[f342]) ).
fof(f634,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,[],[f633]) ).
fof(f635,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,[],[f345]) ).
fof(f636,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,[],[f635]) ).
fof(f637,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,[],[f346]) ).
fof(f638,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,[],[f637]) ).
fof(f639,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,[],[f348]) ).
fof(f640,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,[],[f639]) ).
fof(f641,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,[],[f349]) ).
fof(f642,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,[],[f544]) ).
fof(f643,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,[],[f642]) ).
fof(f644,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,[],[f545]) ).
fof(f645,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,[],[f644]) ).
fof(f646,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,[],[f546]) ).
fof(f647,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,[],[f646]) ).
fof(f648,plain,
! [X0] :
? [X1] :
( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = singleton(X2) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f353]) ).
fof(f649,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f360]) ).
fof(f650,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,[],[f361]) ).
fof(f651,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
inference(ennf_transformation,[],[f362]) ).
fof(f652,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng_restriction(X0,X1),X1) ),
inference(ennf_transformation,[],[f363]) ).
fof(f653,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
inference(ennf_transformation,[],[f364]) ).
fof(f654,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,[],[f365]) ).
fof(f655,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
inference(ennf_transformation,[],[f366]) ).
fof(f656,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(ennf_transformation,[],[f367]) ).
fof(f657,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(flattening,[],[f656]) ).
fof(f659,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
inference(ennf_transformation,[],[f369]) ).
fof(f660,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f370]) ).
fof(f661,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,[],[f547]) ).
fof(f662,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,[],[f661]) ).
fof(f663,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(ennf_transformation,[],[f372]) ).
fof(f664,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(flattening,[],[f663]) ).
fof(f665,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,[],[f373]) ).
fof(f666,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,[],[f374]) ).
fof(f667,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(ennf_transformation,[],[f375]) ).
fof(f668,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(ennf_transformation,[],[f376]) ).
fof(f669,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(flattening,[],[f668]) ).
fof(f670,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(ennf_transformation,[],[f377]) ).
fof(f671,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_dom(X1))
| subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ),
inference(ennf_transformation,[],[f378]) ).
fof(f672,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_dom(X1))
| subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ),
inference(flattening,[],[f671]) ).
fof(f673,plain,
! [X0] :
( ~ relation(X0)
| relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
inference(ennf_transformation,[],[f379]) ).
fof(f674,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_rng(X1))
| relation_image(X1,relation_inverse_image(X1,X0)) = X0 ),
inference(ennf_transformation,[],[f380]) ).
fof(f675,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_rng(X1))
| relation_image(X1,relation_inverse_image(X1,X0)) = X0 ),
inference(flattening,[],[f674]) ).
fof(f676,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,[],[f381]) ).
fof(f677,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,[],[f676]) ).
fof(f679,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,[],[f383]) ).
fof(f680,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f384]) ).
fof(f681,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,[],[f385]) ).
fof(f682,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(ennf_transformation,[],[f386]) ).
fof(f683,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,[],[f387]) ).
fof(f684,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X0)
| ~ subset(X0,X1)
| relation_of2_as_subset(X3,X2,X1) ),
inference(flattening,[],[f683]) ).
fof(f685,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
inference(ennf_transformation,[],[f388]) ).
fof(f686,plain,
! [X0,X1] :
( ~ relation(X1)
| empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0 ),
inference(ennf_transformation,[],[f389]) ).
fof(f687,plain,
! [X0,X1] :
( ~ relation(X1)
| empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0 ),
inference(flattening,[],[f686]) ).
fof(f688,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ subset(X0,X1)
| subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(ennf_transformation,[],[f390]) ).
fof(f689,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ subset(X0,X1)
| subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(flattening,[],[f688]) ).
fof(f692,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,[],[f392]) ).
fof(f693,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
inference(ennf_transformation,[],[f393]) ).
fof(f694,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,[],[f395]) ).
fof(f695,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,[],[f694]) ).
fof(f696,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f396]) ).
fof(f697,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,[],[f397]) ).
fof(f698,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ( in(X0,X1)
& in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f697]) ).
fof(f699,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f398]) ).
fof(f700,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(flattening,[],[f699]) ).
fof(f701,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f401]) ).
fof(f702,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f701]) ).
fof(f705,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,[],[f404]) ).
fof(f706,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,[],[f405]) ).
fof(f707,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,[],[f706]) ).
fof(f708,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,[],[f406]) ).
fof(f709,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,[],[f708]) ).
fof(f710,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f407]) ).
fof(f711,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ) ),
inference(flattening,[],[f710]) ).
fof(f712,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(ennf_transformation,[],[f408]) ).
fof(f713,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
inference(ennf_transformation,[],[f409]) ).
fof(f714,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,[],[f410]) ).
fof(f715,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,[],[f714]) ).
fof(f716,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,[],[f411]) ).
fof(f717,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,[],[f412]) ).
fof(f718,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ reflexive(X1)
| reflexive(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f413]) ).
fof(f719,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ reflexive(X1)
| reflexive(relation_restriction(X1,X0)) ),
inference(flattening,[],[f718]) ).
fof(f720,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,[],[f414]) ).
fof(f721,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,[],[f720]) ).
fof(f722,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(ennf_transformation,[],[f416]) ).
fof(f723,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(flattening,[],[f722]) ).
fof(f724,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,[],[f417]) ).
fof(f725,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ connected(X1)
| connected(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f418]) ).
fof(f726,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ connected(X1)
| connected(relation_restriction(X1,X0)) ),
inference(flattening,[],[f725]) ).
fof(f727,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f419]) ).
fof(f728,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(flattening,[],[f727]) ).
fof(f729,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ transitive(X1)
| transitive(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f420]) ).
fof(f730,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ transitive(X1)
| transitive(relation_restriction(X1,X0)) ),
inference(flattening,[],[f729]) ).
fof(f731,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,[],[f421]) ).
fof(f732,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,[],[f731]) ).
fof(f733,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ antisymmetric(X1)
| antisymmetric(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f422]) ).
fof(f734,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ antisymmetric(X1)
| antisymmetric(relation_restriction(X1,X0)) ),
inference(flattening,[],[f733]) ).
fof(f735,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,[],[f423]) ).
fof(f736,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_orders(X1,X0)
| ( well_ordering(relation_restriction(X1,X0))
& relation_field(relation_restriction(X1,X0)) = X0 ) ),
inference(flattening,[],[f735]) ).
fof(f737,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ finite(relation_dom(X0))
| finite(relation_rng(X0)) ),
inference(ennf_transformation,[],[f424]) ).
fof(f738,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ finite(relation_dom(X0))
| finite(relation_rng(X0)) ),
inference(flattening,[],[f737]) ).
fof(f739,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f427]) ).
fof(f740,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,[],[f548]) ).
fof(f741,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,[],[f740]) ).
fof(f742,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(ennf_transformation,[],[f429]) ).
fof(f743,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,[],[f430]) ).
fof(f744,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,[],[f436]) ).
fof(f745,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f744]) ).
fof(f746,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f437]) ).
fof(f747,plain,
! [X0] :
( ? [X1] :
( in(X1,X0)
& ( ~ subset(X1,X0)
| ~ ordinal(X1) ) )
| ordinal(X0) ),
inference(ennf_transformation,[],[f438]) ).
fof(f748,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_founded_relation(X1)
| well_founded_relation(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f439]) ).
fof(f749,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_founded_relation(X1)
| well_founded_relation(relation_restriction(X1,X0)) ),
inference(flattening,[],[f748]) ).
fof(f750,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,[],[f440]) ).
fof(f751,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,[],[f750]) ).
fof(f752,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_ordering(X1)
| well_ordering(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f441]) ).
fof(f753,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_ordering(X1)
| well_ordering(relation_restriction(X1,X0)) ),
inference(flattening,[],[f752]) ).
fof(f754,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
inference(ennf_transformation,[],[f442]) ).
fof(f755,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(ennf_transformation,[],[f443]) ).
fof(f756,plain,
! [X0,X1,X2,X3] :
( ordered_pair(X2,X3) != ordered_pair(X0,X1)
| ( X1 = X3
& X0 = X2 ) ),
inference(ennf_transformation,[],[f444]) ).
fof(f757,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,[],[f445]) ).
fof(f758,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,[],[f757]) ).
fof(f759,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(ennf_transformation,[],[f446]) ).
fof(f760,plain,
! [X0] :
( ~ relation(X0)
| ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f448]) ).
fof(f761,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| relation_field(relation_restriction(X1,X0)) = X0 ),
inference(ennf_transformation,[],[f452]) ).
fof(f762,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| relation_field(relation_restriction(X1,X0)) = X0 ),
inference(flattening,[],[f761]) ).
fof(f763,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f456]) ).
fof(f764,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,[],[f549]) ).
fof(f765,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(ennf_transformation,[],[f460]) ).
fof(f766,plain,
! [X0] :
( ~ ordinal(X0)
| ( being_limit_ordinal(X0)
<=> ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0) ) ) ),
inference(ennf_transformation,[],[f462]) ).
fof(f767,plain,
! [X0] :
( ~ ordinal(X0)
| ( being_limit_ordinal(X0)
<=> ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,X0)
| in(succ(X1),X0) ) ) ),
inference(flattening,[],[f766]) ).
fof(f768,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,[],[f550]) ).
fof(f769,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,powerset(X0))
| ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
inference(ennf_transformation,[],[f464]) ).
fof(f770,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f466]) ).
fof(f771,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset(interior(X0,X1),X1) ) ),
inference(ennf_transformation,[],[f467]) ).
fof(f772,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,[],[f468]) ).
fof(f773,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,[],[f772]) ).
fof(f774,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
inference(ennf_transformation,[],[f469]) ).
fof(f776,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,[],[f471]) ).
fof(f777,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,[],[f776]) ).
fof(f778,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,[],[f473]) ).
fof(f779,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,[],[f778]) ).
fof(f780,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set != complements_of_subsets(X0,X1)
| empty_set = X1 ),
inference(ennf_transformation,[],[f474]) ).
fof(f781,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set != complements_of_subsets(X0,X1)
| empty_set = X1 ),
inference(flattening,[],[f780]) ).
fof(f782,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(ennf_transformation,[],[f475]) ).
fof(f783,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,[],[f476]) ).
fof(f784,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,[],[f783]) ).
fof(f785,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,[],[f477]) ).
fof(f786,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,[],[f785]) ).
fof(f787,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset(X1,topstr_closure(X0,X1)) ) ),
inference(ennf_transformation,[],[f478]) ).
fof(f788,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,[],[f479]) ).
fof(f789,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,[],[f788]) ).
fof(f790,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,[],[f481]) ).
fof(f791,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,[],[f790]) ).
fof(f792,plain,
! [X0] :
( ~ ordinal(X0)
| connected(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f484]) ).
fof(f793,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,[],[f551]) ).
fof(f794,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,[],[f486]) ).
fof(f795,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,[],[f794]) ).
fof(f796,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| topstr_closure(X0,X1) = X1 ) ),
inference(ennf_transformation,[],[f587]) ).
fof(f797,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| topstr_closure(X0,X1) = X1 ) ),
inference(flattening,[],[f796]) ).
fof(f798,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,[],[f489]) ).
fof(f799,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,[],[f798]) ).
fof(f800,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,[],[f490]) ).
fof(f801,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,[],[f800]) ).
fof(f802,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(ennf_transformation,[],[f491]) ).
fof(f803,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(flattening,[],[f802]) ).
fof(f804,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,[],[f492]) ).
fof(f805,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,[],[f804]) ).
fof(f806,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,[],[f493]) ).
fof(f807,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,[],[f806]) ).
fof(f808,plain,
! [X0] :
( ~ relation(X0)
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f495]) ).
fof(f809,plain,
! [X0] :
( ~ relation(X0)
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| X0 = empty_set ),
inference(flattening,[],[f808]) ).
fof(f810,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,[],[f496]) ).
fof(f811,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,[],[f810]) ).
fof(f812,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& X1 = empty_set
& is_a_cover_of_carrier(X0,X1) ) ),
inference(ennf_transformation,[],[f499]) ).
fof(f813,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& X1 = empty_set
& is_a_cover_of_carrier(X0,X1) ) ),
inference(flattening,[],[f812]) ).
fof(f814,plain,
! [X0] :
( ~ relation(X0)
| ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f500]) ).
fof(f815,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f503]) ).
fof(f816,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| one_to_one(function_inverse(X0)) ),
inference(ennf_transformation,[],[f504]) ).
fof(f817,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| one_to_one(function_inverse(X0)) ),
inference(flattening,[],[f816]) ).
fof(f818,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(ennf_transformation,[],[f505]) ).
fof(f819,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(flattening,[],[f818]) ).
fof(f820,plain,
! [X0] :
( ~ relation(X0)
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| X0 = empty_set ),
inference(ennf_transformation,[],[f506]) ).
fof(f821,plain,
! [X0] :
( ~ relation(X0)
| ( empty_set != relation_rng(X0)
& relation_dom(X0) != empty_set )
| X0 = empty_set ),
inference(flattening,[],[f820]) ).
fof(f822,plain,
! [X0] :
( ~ relation(X0)
| ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
inference(ennf_transformation,[],[f507]) ).
fof(f823,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,[],[f509]) ).
fof(f824,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,[],[f823]) ).
fof(f825,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,[],[f512]) ).
fof(f826,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,[],[f825]) ).
fof(f827,plain,
! [X0] :
( ~ ordinal(X0)
| well_founded_relation(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f513]) ).
fof(f828,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(ennf_transformation,[],[f514]) ).
fof(f829,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,[],[f515]) ).
fof(f830,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,[],[f829]) ).
fof(f831,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(ennf_transformation,[],[f517]) ).
fof(f832,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(flattening,[],[f831]) ).
fof(f833,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,[],[f518]) ).
fof(f834,plain,
! [X0] :
( ~ ordinal(X0)
| well_ordering(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f522]) ).
fof(f835,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,[],[f525]) ).
fof(f836,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom_restriction(X1,X0),X1) ),
inference(ennf_transformation,[],[f526]) ).
fof(f837,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,[],[f528]) ).
fof(f838,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,[],[f837]) ).
fof(f839,plain,
! [X0] :
( ~ relation(X0)
| ( well_orders(X0,relation_field(X0))
<=> well_ordering(X0) ) ),
inference(ennf_transformation,[],[f529]) ).
fof(f840,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(ennf_transformation,[],[f530]) ).
fof(f841,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(flattening,[],[f840]) ).
fof(f842,plain,
! [X0,X1,X2] :
( singleton(X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(ennf_transformation,[],[f531]) ).
fof(f843,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
inference(ennf_transformation,[],[f532]) ).
fof(f844,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(ennf_transformation,[],[f533]) ).
fof(f845,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
inference(ennf_transformation,[],[f534]) ).
fof(f846,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
inference(ennf_transformation,[],[f535]) ).
fof(f847,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,[],[f537]) ).
fof(f848,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,[],[f847]) ).
fof(f849,plain,
! [X0,X1,X2] :
( singleton(X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(ennf_transformation,[],[f539]) ).
fof(f850,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ in(X3,X2)
| ~ in(X3,X1) )
& in(X2,X1) )
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f521]) ).
fof(f851,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f433]) ).
fof(f852,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f400]) ).
fof(f853,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f854,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,[],[f552]) ).
fof(f855,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,[],[f854]) ).
fof(f856,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f99]) ).
fof(f857,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f89]) ).
fof(f858,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,[],[f83]) ).
fof(f859,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,[],[f74]) ).
fof(f860,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f59]) ).
fof(f861,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(f862,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| X2 = X3 ) ),
inference(flattening,[],[f861]) ).
fof(f863,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(ennf_transformation,[],[f105]) ).
fof(f864,plain,
! [X0] :
( ~ relation(X0)
| ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f865,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f511]) ).
fof(f866,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,[],[f553]) ).
fof(f867,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,[],[f866]) ).
fof(f868,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,[],[f554]) ).
fof(f869,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,[],[f868]) ).
fof(f870,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(set_union2(X0,X1)) ),
inference(ennf_transformation,[],[f251]) ).
fof(f871,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(set_union2(X0,X1)) ),
inference(flattening,[],[f870]) ).
fof(f872,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(ennf_transformation,[],[f235]) ).
fof(f873,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(ennf_transformation,[],[f219]) ).
fof(f874,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_union2(X0,X1)) ),
inference(ennf_transformation,[],[f216]) ).
fof(f875,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_union2(X0,X1)) ),
inference(flattening,[],[f874]) ).
fof(f876,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(ennf_transformation,[],[f356]) ).
fof(f877,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(f878,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,[],[f877]) ).
fof(f879,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f249]) ).
fof(f880,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f245]) ).
fof(f881,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f880]) ).
fof(f882,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f243]) ).
fof(f883,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
inference(flattening,[],[f882]) ).
fof(f884,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f168]) ).
fof(f885,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(f886,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f84]) ).
fof(f887,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| equipotent(X1,X0) ),
inference(ennf_transformation,[],[f357]) ).
fof(f888,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_difference(X0,X1)) ),
inference(ennf_transformation,[],[f232]) ).
fof(f889,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_difference(X0,X1)) ),
inference(flattening,[],[f888]) ).
fof(f893,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f497]) ).
fof(f894,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f483]) ).
fof(f895,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f894]) ).
fof(f896,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f289]) ).
fof(f897,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f306]) ).
fof(f898,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f897]) ).
fof(f901,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ( empty_carrier(X0)
<=> empty(the_carrier(X0)) ) ),
inference(ennf_transformation,[],[f63]) ).
fof(f902,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f256]) ).
fof(f903,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f149]) ).
fof(f904,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,X1) = set_difference(X0,X1) ),
inference(ennf_transformation,[],[f100]) ).
fof(f905,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f171]) ).
fof(f906,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,X1) = union(X1) ),
inference(ennf_transformation,[],[f313]) ).
fof(f907,plain,
! [X0] :
( ~ ordinal(X0)
| ( ordinal(union(X0))
& epsilon_connected(union(X0))
& epsilon_transitive(union(X0)) ) ),
inference(ennf_transformation,[],[f239]) ).
fof(f908,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,[],[f558]) ).
fof(f909,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,[],[f908]) ).
fof(f910,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,[],[f559]) ).
fof(f911,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,[],[f910]) ).
fof(f912,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(ennf_transformation,[],[f241]) ).
fof(f913,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(flattening,[],[f912]) ).
fof(f914,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f177]) ).
fof(f915,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] : relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
inference(ennf_transformation,[],[f107]) ).
fof(f916,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f917,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f238]) ).
fof(f918,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f917]) ).
fof(f919,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f166]) ).
fof(f920,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(f921,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f922,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f527]) ).
fof(f923,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f519]) ).
fof(f926,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( element(X1,X0)
<=> empty(X1) ) )
& ( empty(X0)
| ( element(X1,X0)
<=> in(X1,X0) ) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f927,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f928,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,[],[f560]) ).
fof(f929,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,[],[f928]) ).
fof(f930,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X0,X0) ),
inference(ennf_transformation,[],[f320]) ).
fof(f931,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X0,X0) ),
inference(flattening,[],[f930]) ).
fof(f932,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(ennf_transformation,[],[f318]) ).
fof(f933,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(flattening,[],[f932]) ).
fof(f934,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f935,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(flattening,[],[f934]) ).
fof(f936,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,[],[f561]) ).
fof(f937,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,[],[f936]) ).
fof(f938,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,[],[f97]) ).
fof(f939,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,[],[f938]) ).
fof(f940,plain,
! [X0] :
( ~ element(X0,omega)
| ( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f941,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,[],[f562]) ).
fof(f942,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,[],[f941]) ).
fof(f943,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,[],[f563]) ).
fof(f944,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,[],[f943]) ).
fof(f945,plain,
! [X0] :
( ~ ordinal(X0)
| ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
inference(ennf_transformation,[],[f231]) ).
fof(f946,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,[],[f96]) ).
fof(f947,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,[],[f946]) ).
fof(f948,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,[],[f87]) ).
fof(f949,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,[],[f948]) ).
fof(f950,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(cast_as_carrier_subset(X0)) ),
inference(ennf_transformation,[],[f215]) ).
fof(f951,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(cast_as_carrier_subset(X0)) ),
inference(flattening,[],[f950]) ).
fof(f952,plain,
! [X0] :
( ~ one_sorted_str(X0)
| element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f140]) ).
fof(f953,plain,
! [X0] :
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = the_carrier(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f954,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,[],[f566]) ).
fof(f955,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,[],[f954]) ).
fof(f956,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ function(X0)
| ~ relation(X0)
| finite(relation_image(X0,X1)) ),
inference(ennf_transformation,[],[f196]) ).
fof(f957,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ function(X0)
| ~ relation(X0)
| finite(relation_image(X0,X1)) ),
inference(flattening,[],[f956]) ).
fof(f958,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(f959,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(f960,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,[],[f959]) ).
fof(f961,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f250]) ).
fof(f962,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(ennf_transformation,[],[f247]) ).
fof(f963,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(flattening,[],[f962]) ).
fof(f968,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(ennf_transformation,[],[f204]) ).
fof(f969,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(flattening,[],[f968]) ).
fof(f970,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,[],[f568]) ).
fof(f971,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,[],[f970]) ).
fof(f972,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f300]) ).
fof(f973,plain,
! [X0,X1] :
( ~ finite(X0)
| finite(set_difference(X0,X1)) ),
inference(ennf_transformation,[],[f194]) ).
fof(f975,plain,
! [X0,X1] :
( ~ finite(X1)
| finite(set_intersection2(X0,X1)) ),
inference(ennf_transformation,[],[f190]) ).
fof(f977,plain,
! [X0] :
( ~ empty(X0)
| finite(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f978,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(f979,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(f980,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,[],[f979]) ).
fof(f981,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
inference(ennf_transformation,[],[f314]) ).
fof(f982,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
inference(flattening,[],[f981]) ).
fof(f983,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X1) = X1 ),
inference(ennf_transformation,[],[f255]) ).
fof(f984,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X1) = X1 ),
inference(flattening,[],[f983]) ).
fof(f985,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_intersection2(X0,X1,X2),powerset(X0)) ),
inference(ennf_transformation,[],[f161]) ).
fof(f986,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_intersection2(X0,X1,X2),powerset(X0)) ),
inference(flattening,[],[f985]) ).
fof(f987,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(f988,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = subset_intersection2(X0,X2,X1) ),
inference(flattening,[],[f987]) ).
fof(f989,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f252]) ).
fof(f990,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f989]) ).
fof(f991,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f200]) ).
fof(f992,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f991]) ).
fof(f993,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(ennf_transformation,[],[f191]) ).
fof(f994,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
inference(flattening,[],[f993]) ).
fof(f995,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f158]) ).
fof(f996,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f995]) ).
fof(f997,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,[],[f114]) ).
fof(f998,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f144]) ).
fof(f999,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(ennf_transformation,[],[f316]) ).
fof(f1000,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(flattening,[],[f999]) ).
fof(f1001,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_difference(X0,X1,X2),powerset(X0)) ),
inference(ennf_transformation,[],[f165]) ).
fof(f1002,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_difference(X0,X1,X2),powerset(X0)) ),
inference(flattening,[],[f1001]) ).
fof(f1003,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,[],[f104]) ).
fof(f1004,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f572]) ).
fof(f1005,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(flattening,[],[f1004]) ).
fof(f1006,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ~ proper_subset(X1,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f1007,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f72]) ).
fof(f1008,plain,
! [X0] :
( ~ empty(X0)
| ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f1009,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f1010,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(flattening,[],[f1009]) ).
fof(f1011,plain,
! [X0] :
( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f1012,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ element(X1,X0)
| ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f1013,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,[],[f85]) ).
fof(f1014,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,[],[f77]) ).
fof(f1015,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,[],[f66]) ).
fof(f1016,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(ennf_transformation,[],[f311]) ).
fof(f1017,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
inference(ennf_transformation,[],[f154]) ).
fof(f1018,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(f1019,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,[],[f1018]) ).
fof(f1022,plain,
! [X0] :
( ~ latt_str(X0)
| ( join_semilatt_str(X0)
& meet_semilatt_str(X0) ) ),
inference(ennf_transformation,[],[f174]) ).
fof(f1023,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,[],[f112]) ).
fof(f1024,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,[],[f1023]) ).
fof(f1025,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
inference(ennf_transformation,[],[f312]) ).
fof(f1026,plain,
! [X0,X1,X2] :
( ~ relation_of2(X2,X0,X1)
| element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
inference(ennf_transformation,[],[f159]) ).
fof(f1027,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f173]) ).
fof(f1028,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,[],[f67]) ).
fof(f1029,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,[],[f1028]) ).
fof(f1030,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(f1031,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(ennf_transformation,[],[f257]) ).
fof(f1032,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f230]) ).
fof(f1033,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
inference(flattening,[],[f1032]) ).
fof(f1034,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f193]) ).
fof(f1035,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(ennf_transformation,[],[f153]) ).
fof(f1036,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(ennf_transformation,[],[f118]) ).
fof(f1037,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(flattening,[],[f1036]) ).
fof(f1038,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,[],[f108]) ).
fof(f1039,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(meet_of_subsets(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f164]) ).
fof(f1040,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f131]) ).
fof(f1041,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f1040]) ).
fof(f1042,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f1043,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f162]) ).
fof(f1044,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(flattening,[],[f1043]) ).
fof(f1045,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f258]) ).
fof(f1046,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f167]) ).
fof(f1047,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,[],[f116]) ).
fof(f1048,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(union_of_subsets(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f160]) ).
fof(f1049,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f137]) ).
fof(f1050,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f1049]) ).
fof(f1051,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,[],[f109]) ).
fof(f1052,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,[],[f1051]) ).
fof(f1053,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,[],[f111]) ).
fof(f1054,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,[],[f1053]) ).
fof(f1055,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f1056,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
inference(flattening,[],[f1055]) ).
fof(f1057,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( is_a_cover_of_carrier(X0,X1)
<=> cast_as_carrier_subset(X0) = union_of_subsets(the_carrier(X0),X1) ) ) ),
inference(ennf_transformation,[],[f113]) ).
fof(f1058,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,[],[f102]) ).
fof(f1059,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,[],[f570]) ).
fof(f1060,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,[],[f571]) ).
fof(f1073,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f1078,plain,
! [X0] :
( ~ meet_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f170]) ).
fof(f1079,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,[],[f138]) ).
fof(f1080,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,[],[f1079]) ).
fof(f1081,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,[],[f124]) ).
fof(f1082,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,[],[f1081]) ).
fof(f1083,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,[],[f90]) ).
fof(f1084,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,[],[f1083]) ).
fof(f1085,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f1086,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,[],[f106]) ).
fof(f1087,plain,
! [X0] :
( ~ relation(X0)
| ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f49]) ).
fof(f1088,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,[],[f115]) ).
fof(f1089,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,[],[f1088]) ).
fof(f1090,plain,
! [X0] :
( ~ relation(X0)
| ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f1091,plain,
! [X0] :
( ~ relation(X0)
| ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f119]) ).
fof(f1092,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(f1158,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,[],[f600]) ).
fof(f1159,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,[],[f1158]) ).
fof(f1160,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ reflexive(X0)
| ! [X2] :
( ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ) )
& ( ( in(sK39(X0),relation_field(X0))
& ~ in(ordered_pair(sK39(X0),sK39(X0)),X0) )
| reflexive(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X1,sK39(X0))],[f1159]) ).
fof(f1161,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,[],[f606]) ).
fof(f1162,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,[],[f1161]) ).
fof(f1163,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(sK41(X0),sK42(X0)),X0)
& in(ordered_pair(sK40(X0),sK41(X0)),X0)
& ~ in(ordered_pair(sK40(X0),sK42(X0)),X0) )
| transitive(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41,sK42]),skolemize(X1,sK40(X0)),skolemize(X2,sK41(X0)),skolemize(X3,sK42(X0))],[f1162]) ).
fof(f1165,plain,
! [X0,X1] :
( ~ relation(X1)
| ( relation(sK43(X0))
& well_orders(sK43(X0),X0) )
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(X2,sK43(X0))],[f608]) ).
fof(f1167,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,[],[f611]) ).
fof(f1168,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,[],[f1167]) ).
fof(f1169,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(sK45(X0),sK44(X0)),X0)
& in(ordered_pair(sK44(X0),sK45(X0)),X0)
& sK44(X0) != sK45(X0) )
| antisymmetric(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44,sK45]),skolemize(X1,sK44(X0)),skolemize(X2,sK45(X0))],[f1168]) ).
fof(f1170,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ in(X2,subset_complement(the_carrier(X0),X1))
| ~ in(X2,X1) )
& ( in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) ) ) ) ) ),
inference(nnf_transformation,[],[f615]) ).
fof(f1171,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,[],[f616]) ).
fof(f1172,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,[],[f1171]) ).
fof(f1173,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(sK47(X0),sK46(X0)),X0)
& ~ in(ordered_pair(sK46(X0),sK47(X0)),X0)
& sK46(X0) != sK47(X0)
& in(sK47(X0),relation_field(X0))
& in(sK46(X0),relation_field(X0)) )
| connected(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46,sK47]),skolemize(X1,sK46(X0)),skolemize(X2,sK47(X0))],[f1172]) ).
fof(f1178,plain,
! [X0,X1] :
( ( in(sK48(X0,X1),X0)
& ~ in(sK48(X0,X1),X1) )
| element(X0,powerset(X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(X2,sK48(X0,X1))],[f618]) ).
fof(f1181,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,[],[f1101]) ).
fof(f1182,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ( sP0(sK49(X0,X1),sK51(X0,X1),X1)
& in(sK49(X0,X1),X0)
& ! [X6] :
( ~ in(X6,sK52(X0,X1))
| in(ordered_pair(sK50(X0,X1),X6),X1) )
& in(sK50(X0,X1),sK52(X0,X1))
& sK49(X0,X1) = sK52(X0,X1)
& in(sK49(X0,X1),X0)
& sK50(X0,X1) != sK51(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49,sK50,sK51,sK52]),skolemize(X2,sK49(X0,X1)),skolemize(X3,sK50(X0,X1)),skolemize(X4,sK51(X0,X1)),skolemize(X5,sK52(X0,X1))],[f1181]) ).
fof(f1183,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,[],[f1100]) ).
fof(f1184,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,[],[f1183]) ).
fof(f1185,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,[],[f1184]) ).
fof(f1186,plain,
! [X0,X1,X2] :
( ~ sP1(X0,X1,X2)
| ! [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X2)
| ( ! [X8] :
( ~ in(X8,sK54(X1,X3,X4))
| in(ordered_pair(X4,X8),X1) )
& in(X4,sK54(X1,X3,X4))
& sK54(X1,X3,X4) = X3
& in(X3,X0)
& in(X3,X0) ) )
& ( ! [X5] :
( ( in(sK53(X1,X4,X5),X5)
& ~ in(ordered_pair(X4,sK53(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,[sK53,sK54]),skolemize(X6,sK53(X1,X4,X5)),skolemize(X7,sK54(X1,X3,X4))],[f1185]) ).
fof(f1190,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| ? [X2] :
( sP1(X0,X1,X2)
& function(X2)
& relation(X2) ) ),
inference(rectify,[],[f1102]) ).
fof(f1191,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| ( sP1(X0,X1,sK56(X0,X1))
& function(sK56(X0,X1))
& relation(sK56(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(X2,sK56(X0,X1))],[f1190]) ).
fof(f1196,plain,
! [X0] :
( ( sK60(X0) = singleton(sK58(X0))
& in(sK58(X0),X0)
& sK59(X0) = singleton(sK58(X0))
& in(sK58(X0),X0)
& sK59(X0) != sK60(X0) )
| sP3(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58,sK59,sK60]),skolemize(X1,sK58(X0)),skolemize(X2,sK59(X0)),skolemize(X3,sK60(X0))],[f1104]) ).
fof(f1197,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,[],[f626]) ).
fof(f1198,plain,
! [X0] :
( ! [X3] :
( ~ in(X3,X0)
| ~ ordinal(X3) )
| ( ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| ordinal_subset(sK61(X0),X2) )
& in(sK61(X0),X0)
& ordinal(sK61(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(X1,sK61(X0))],[f1197]) ).
fof(f1199,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,[],[f1109]) ).
fof(f1200,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,[],[f1199]) ).
fof(f1201,plain,
( ~ sP8
| ( ordinal(sK62)
& ( ~ in(sK62,omega)
| ! [X1] :
( ~ element(X1,powerset(powerset(sK62)))
| ( ! [X3] :
( ~ subset(sK63(X1),X3)
| ~ in(X3,X1)
| sK63(X1) = X3 )
& in(sK63(X1),X1) )
| empty_set = X1 ) )
& in(succ(sK62),omega)
& sP5(sK62) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62,sK63]),skolemize(X0,sK62),skolemize(X2,sK63(X1))],[f1200]) ).
fof(f1202,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,[],[f1108]) ).
fof(f1203,plain,
( ~ sP7
| ( in(empty_set,omega)
& element(sK64,powerset(powerset(empty_set)))
& ! [X1] :
( ( subset(X1,sK65(X1))
& in(sK65(X1),sK64)
& sK65(X1) != X1 )
| ~ in(X1,sK64) )
& empty_set != sK64 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64,sK65]),skolemize(X0,sK64),skolemize(X2,sK65(X1))],[f1202]) ).
fof(f1204,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,[],[f1107]) ).
fof(f1205,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,[],[f1204]) ).
fof(f1206,plain,
( ~ sP6
| ( ordinal(sK66)
& ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,sK66)
| ~ in(X1,omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(X1)))
| ( ! [X4] :
( ~ subset(sK67(X2),X4)
| ~ in(X4,X2)
| sK67(X2) = X4 )
& in(sK67(X2),X2) )
| empty_set = X2 ) )
& being_limit_ordinal(sK66)
& in(sK66,omega)
& sP4(sK66)
& empty_set != sK66 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66,sK67]),skolemize(X0,sK66),skolemize(X3,sK67(X2))],[f1205]) ).
fof(f1207,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,[],[f1106]) ).
fof(f1208,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,[],[f1207]) ).
fof(f1209,plain,
! [X0] :
( ~ sP5(X0)
| ( element(sK68(X0),powerset(powerset(succ(X0))))
& ! [X2] :
( ( subset(X2,sK69(X0,X2))
& in(sK69(X0,X2),sK68(X0))
& sK69(X0,X2) != X2 )
| ~ in(X2,sK68(X0)) )
& empty_set != sK68(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68,sK69]),skolemize(X1,sK68(X0)),skolemize(X3,sK69(X0,X2))],[f1208]) ).
fof(f1213,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,[],[f1110]) ).
fof(f1214,plain,
( sP6
| sP8
| sP7
| ! [X0] :
( ~ ordinal(X0)
| ~ in(X0,omega)
| ! [X1] :
( ~ element(X1,powerset(powerset(X0)))
| ( ! [X3] :
( ~ subset(sK72(X1),X3)
| ~ in(X3,X1)
| sK72(X1) = X3 )
& in(sK72(X1),X1) )
| empty_set = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(X2,sK72(X1))],[f1213]) ).
fof(f1215,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,[],[f630]) ).
fof(f1216,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,[],[f1215]) ).
fof(f1217,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ( ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),sK73(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),sK73(X0,X1,X2)) ) )
& relation(sK73(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(X3,sK73(X0,X1,X2))],[f1216]) ).
fof(f1218,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,[],[f632]) ).
fof(f1219,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,[],[f1218]) ).
fof(f1220,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,[],[f1219]) ).
fof(f1221,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2,X4] :
( ( ~ in(X4,sK74(X0,X1,X2))
| ( ! [X12] :
( ~ in(X12,sK78(X0,X1,X4))
| in(ordered_pair(sK77(X0,X1,X4),X12),X1) )
& in(sK77(X0,X1,X4),sK78(X0,X1,X4))
& sK76(X0,X1,X4) = sK78(X0,X1,X4)
& in(sK76(X0,X1,X4),X0)
& ordered_pair(sK76(X0,X1,X4),sK77(X0,X1,X4)) = X4
& in(X4,cartesian_product2(X0,X2)) ) )
& ( ! [X5,X6] :
( ! [X7] :
( ( in(sK75(X1,X6,X7),X7)
& ~ in(ordered_pair(X6,sK75(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,sK74(X0,X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74,sK75,sK76,sK77,sK78]),skolemize(X3,sK74(X0,X1,X2)),skolemize(X8,sK75(X1,X6,X7)),skolemize(X9,sK76(X0,X1,X4)),skolemize(X10,sK77(X0,X1,X4)),skolemize(X11,sK78(X0,X1,X4))],[f1220]) ).
fof(f1222,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,[],[f341]) ).
fof(f1223,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,[],[f1222]) ).
fof(f1224,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,[],[f1223]) ).
fof(f1225,plain,
! [X0,X1,X3] :
( ( ~ in(X3,sK79(X0,X1))
| ( sK81(X0,X3) = singleton(sK80(X0,X3))
& in(sK80(X0,X3),X0)
& ordered_pair(sK80(X0,X3),sK81(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,sK79(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79,sK80,sK81]),skolemize(X2,sK79(X0,X1)),skolemize(X6,sK80(X0,X3)),skolemize(X7,sK81(X0,X3))],[f1224]) ).
fof(f1226,plain,
! [X0] :
( ~ sP10(X0)
| ? [X1] :
! [X2] :
( ( ~ in(X2,X1)
| sP9(X0,X2) )
& ( ~ sP9(X0,X2)
| in(X2,X1) ) ) ),
inference(nnf_transformation,[],[f1112]) ).
fof(f1227,plain,
! [X0] :
( ~ sP10(X0)
| ! [X2] :
( ( ~ in(X2,sK82(X0))
| sP9(X0,X2) )
& ( ~ sP9(X0,X2)
| in(X2,sK82(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(X1,sK82(X0))],[f1226]) ).
fof(f1232,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,[],[f636]) ).
fof(f1233,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,[],[f1232]) ).
fof(f1234,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,[],[f1233]) ).
fof(f1235,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ! [X3] :
( ( ~ in(X3,sK87(X0,X1))
| ( set_difference(sK88(X0,X1,X3),singleton(X0)) = X3
& in(sK88(X0,X1,X3),X1)
& in(X3,powerset(X0)) ) )
& ( ! [X4] :
( set_difference(X4,singleton(X0)) != X3
| ~ in(X4,X1) )
| ~ in(X3,powerset(X0))
| in(X3,sK87(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87,sK88]),skolemize(X2,sK87(X0,X1)),skolemize(X5,sK88(X0,X1,X3))],[f1234]) ).
fof(f1236,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,[],[f638]) ).
fof(f1237,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,[],[f1236]) ).
fof(f1238,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,[],[f1237]) ).
fof(f1239,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ! [X4] :
( ( ~ in(X4,sK89(X0,X1,X2))
| ( in(ordered_pair(apply(X2,sK90(X1,X2,X4)),apply(X2,sK91(X1,X2,X4))),X1)
& ordered_pair(sK90(X1,X2,X4),sK91(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,sK89(X0,X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89,sK90,sK91]),skolemize(X3,sK89(X0,X1,X2)),skolemize(X7,sK90(X1,X2,X4)),skolemize(X8,sK91(X1,X2,X4))],[f1238]) ).
fof(f1240,plain,
! [X0] :
? [X1] :
! [X2] :
( ( ~ in(X2,X1)
| ( ordinal(X2)
& in(X2,X0) ) )
& ( ~ ordinal(X2)
| ~ in(X2,X0)
| in(X2,X1) ) ),
inference(nnf_transformation,[],[f347]) ).
fof(f1241,plain,
! [X0] :
? [X1] :
! [X2] :
( ( ~ in(X2,X1)
| ( ordinal(X2)
& in(X2,X0) ) )
& ( ~ ordinal(X2)
| ~ in(X2,X0)
| in(X2,X1) ) ),
inference(flattening,[],[f1240]) ).
fof(f1242,plain,
! [X0,X2] :
( ( ~ in(X2,sK92(X0))
| ( ordinal(X2)
& in(X2,X0) ) )
& ( ~ ordinal(X2)
| ~ in(X2,X0)
| in(X2,sK92(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(X1,sK92(X0))],[f1241]) ).
fof(f1243,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,[],[f640]) ).
fof(f1244,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,[],[f1243]) ).
fof(f1245,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ! [X4] :
( ( ~ in(X4,sK93(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,sK93(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(X3,sK93(X1,X2))],[f1244]) ).
fof(f1246,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,[],[f641]) ).
fof(f1247,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,[],[f1246]) ).
fof(f1248,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,[],[f1247]) ).
fof(f1249,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ! [X3] :
( ( ~ in(X3,sK94(X0,X1))
| ( in(sK95(X0,X3),X0)
& sK95(X0,X3) = X3
& ordinal(sK95(X0,X3))
& in(X3,succ(X1)) ) )
& ( ! [X4] :
( ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4) )
| ~ in(X3,succ(X1))
| in(X3,sK94(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94,sK95]),skolemize(X2,sK94(X0,X1)),skolemize(X5,sK95(X0,X3))],[f1248]) ).
fof(f1250,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,[],[f1115]) ).
fof(f1251,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,[],[f1250]) ).
fof(f1252,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| ( ! [X3] :
( ~ in(X3,X0)
| ( ! [X5] :
( ~ in(X5,sK97(X0,X1,X3))
| in(ordered_pair(apply(sK96(X0,X1),X3),X5),X1) )
& in(apply(sK96(X0,X1),X3),sK97(X0,X1,X3))
& sK97(X0,X1,X3) = X3 ) )
& relation_dom(sK96(X0,X1)) = X0
& function(sK96(X0,X1))
& relation(sK96(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96,sK97]),skolemize(X2,sK96(X0,X1)),skolemize(X4,sK97(X0,X1,X3))],[f1251]) ).
fof(f1255,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,[],[f1116]) ).
fof(f1256,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ( ! [X3,X4] :
( ( in(sK104(X1,X3,X4),X4)
& ~ in(ordered_pair(X3,sK104(X1,X3,X4)),X1) )
| ~ in(X3,X4)
| sK103(X0,X1) != X4 )
& in(sK103(X0,X1),X0) )
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103,sK104]),skolemize(X2,sK103(X0,X1)),skolemize(X5,sK104(X1,X3,X4))],[f1255]) ).
fof(f1259,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,[],[f1118]) ).
fof(f1260,plain,
! [X0] :
( ( ! [X4] : singleton(sK109(X0)) != X4
& in(sK109(X0),X0) )
| sP13(X0)
| ( ! [X2] :
( ~ in(X2,X0)
| singleton(X2) = apply(sK108(X0),X2) )
& relation_dom(sK108(X0)) = X0
& function(sK108(X0))
& relation(sK108(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108,sK109]),skolemize(X1,sK108(X0)),skolemize(X3,sK109(X0))],[f1259]) ).
fof(f1261,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,[],[f1120]) ).
fof(f1262,plain,
( ~ sP15
| ( ordinal(sK110)
& ! [X1] :
( ~ ordinal(X1)
| ~ in(X1,sK110)
| ~ in(X1,omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(X1)))
| ( ! [X4] :
( ~ subset(sK111(X2),X4)
| ~ in(X4,X2)
| sK111(X2) = X4 )
& in(sK111(X2),X2) )
| empty_set = X2 ) )
& in(sK110,omega)
& sP14(sK110) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110,sK111]),skolemize(X0,sK110),skolemize(X3,sK111(X2))],[f1261]) ).
fof(f1266,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,[],[f1121]) ).
fof(f1267,plain,
( sP15
| ! [X0] :
( ~ ordinal(X0)
| ~ in(X0,omega)
| ! [X1] :
( ~ element(X1,powerset(powerset(X0)))
| ( ! [X3] :
( ~ subset(sK114(X1),X3)
| ~ in(X3,X1)
| sK114(X1) = X3 )
& in(sK114(X1),X1) )
| empty_set = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(X2,sK114(X1))],[f1266]) ).
fof(f1268,plain,
! [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]),skolemize(X1,sK115(X0))],[f648]) ).
fof(f1269,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,[],[f358]) ).
fof(f1270,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,[],[f1269]) ).
fof(f1271,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,[],[f650]) ).
fof(f1272,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,[],[f1271]) ).
fof(f1273,plain,
! [X0] :
( ! [X5] :
( in(X5,sK116(X0))
| are_equipotent(X5,sK116(X0))
| ~ subset(X5,sK116(X0)) )
& ! [X4] :
( ~ in(X4,sK116(X0))
| in(powerset(X4),sK116(X0)) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,sK116(X0))
| in(X3,sK116(X0)) )
& in(X0,sK116(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(X1,sK116(X0))],[f662]) ).
fof(f1274,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,[],[f666]) ).
fof(f1275,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,[],[f1274]) ).
fof(f1276,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_image(X2,X1))
| ( in(sK117(X0,X1,X2),X1)
& in(ordered_pair(sK117(X0,X1,X2),X0),X2)
& in(sK117(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,[sK117]),skolemize(X4,sK117(X0,X1,X2))],[f1275]) ).
fof(f1277,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,[],[f681]) ).
fof(f1278,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,[],[f1277]) ).
fof(f1279,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_inverse_image(X2,X1))
| ( in(sK118(X0,X1,X2),X1)
& in(ordered_pair(X0,sK118(X0,X1,X2)),X2)
& in(sK118(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,[sK118]),skolemize(X4,sK118(X0,X1,X2))],[f1278]) ).
fof(f1280,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,[],[f685]) ).
fof(f1281,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,[],[f1280]) ).
fof(f1282,plain,
! [X0] :
( ~ finite(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(X0)))
| ( ! [X3] :
( ~ subset(sK119(X1),X3)
| ~ in(X3,X1)
| sK119(X1) = X3 )
& in(sK119(X1),X1) )
| empty_set = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(X2,sK119(X1))],[f695]) ).
fof(f1283,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,[],[f707]) ).
fof(f1284,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,[],[f1283]) ).
fof(f1285,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,[],[f717]) ).
fof(f1286,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,[],[f1285]) ).
fof(f1287,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X1,X0)
| ( ( ( ! [X6] : ~ in(ordered_pair(sK121(X1,X2),X6),X2)
& in(sK121(X1,X2),X1) )
| relation_dom_as_subset(X1,X0,X2) = X1 )
& ( relation_dom_as_subset(X1,X0,X2) != X1
| ! [X3] :
( in(ordered_pair(X3,sK120(X2,X3)),X2)
| ~ in(X3,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120,sK121]),skolemize(X4,sK120(X2,X3)),skolemize(X5,sK121(X1,X2))],[f1286]) ).
fof(f1288,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,[],[f724]) ).
fof(f1289,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,[],[f1288]) ).
fof(f1290,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( ( ( ! [X6] : ~ in(ordered_pair(X6,sK123(X1,X2)),X2)
& in(sK123(X1,X2),X1) )
| relation_rng_as_subset(X0,X1,X2) = X1 )
& ( relation_rng_as_subset(X0,X1,X2) != X1
| ! [X3] :
( in(ordered_pair(sK122(X2,X3),X3),X2)
| ~ in(X3,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122,sK123]),skolemize(X4,sK122(X2,X3)),skolemize(X5,sK123(X1,X2))],[f1289]) ).
fof(f1291,plain,
! [X0] :
( well_orders(sK124(X0),X0)
& relation(sK124(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(X1,sK124(X0))],[f426]) ).
fof(f1292,plain,
! [X0] :
( empty(X0)
| ( function(sK126(X0))
& relation(sK126(X0))
& ! [X3] :
( ~ in(X3,X0)
| in(apply(sK126(X0),X3),X3) )
& relation_dom(sK126(X0)) = X0 )
| ( empty_set = sK125(X0)
& in(sK125(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125,sK126]),skolemize(X1,sK125(X0)),skolemize(X2,sK126(X0))],[f741]) ).
fof(f1293,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) )
& ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f743]) ).
fof(f1294,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( ~ open_subset(X1,X0)
| closed_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f746]) ).
fof(f1295,plain,
! [X0] :
( ( in(sK127(X0),X0)
& ( ~ subset(sK127(X0),X0)
| ~ ordinal(sK127(X0)) ) )
| ordinal(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(X1,sK127(X0))],[f747]) ).
fof(f1296,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ( ordinal(sK128(X0))
& ! [X3] :
( ~ ordinal(X3)
| ~ in(X3,X0)
| ordinal_subset(sK128(X0),X3) )
& in(sK128(X0),X0) )
| empty_set = X0
| ~ subset(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(X2,sK128(X0))],[f751]) ).
fof(f1297,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,[],[f754]) ).
fof(f1298,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,[],[f758]) ).
fof(f1299,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,[],[f1298]) ).
fof(f1300,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,[],[f1299]) ).
fof(f1301,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK129(X0,X1),X0)
& sK129(X0,X1) != apply(X1,sK129(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(X2,sK129(X0,X1))],[f1300]) ).
fof(f1302,plain,
! [X0,X1] :
( ( empty_set != set_difference(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f449]) ).
fof(f1303,plain,
! [X0,X1] :
( ( ~ subset(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f450]) ).
fof(f1304,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,[],[f451]) ).
fof(f1305,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,[],[f1304]) ).
fof(f1306,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,[],[f454]) ).
fof(f1307,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,[],[f1306]) ).
fof(f1308,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) ) )
& ( ( in(sK130(X0,X1),X1)
& in(sK130(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(X2,sK130(X0,X1))],[f764]) ).
fof(f1309,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,[],[f767]) ).
fof(f1310,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,[],[f1309]) ).
fof(f1311,plain,
! [X0] :
( ~ ordinal(X0)
| ( ( ~ being_limit_ordinal(X0)
| ! [X2] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| in(succ(X2),X0) ) )
& ( ( ordinal(sK131(X0))
& in(sK131(X0),X0)
& ~ in(succ(sK131(X0)),X0) )
| being_limit_ordinal(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(X1,sK131(X0))],[f1310]) ).
fof(f1312,plain,
! [X0] :
( ~ ordinal(X0)
| ( ( ~ being_limit_ordinal(X0)
| ! [X2] :
( succ(X2) != X0
| ~ ordinal(X2) ) )
& ( ( ordinal(sK132(X0))
& succ(sK132(X0)) = X0 )
| being_limit_ordinal(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(X1,sK132(X0))],[f768]) ).
fof(f1313,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,[],[f769]) ).
fof(f1314,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,[],[f773]) ).
fof(f1315,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,[],[f1314]) ).
fof(f1316,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(sK133(X0,X1,X2),powerset(the_carrier(X0)))
& subset(X1,sK133(X0,X1,X2))
& closed_subset(sK133(X0,X1,X2),X0)
& ~ in(X2,sK133(X0,X1,X2)) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(X3,sK133(X0,X1,X2))],[f1315]) ).
fof(f1317,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,[],[f777]) ).
fof(f1318,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,[],[f1317]) ).
fof(f1319,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( in(sK134(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(X2,sK134(X0,X1))],[f793]) ).
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(nnf_transformation,[],[f1123]) ).
fof(f1324,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,[],[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) ) )
& ( ? [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,[],[f1324]) ).
fof(f1326,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,sK135(X0,X1),sK136(X0,X1),X1)
| ( sK136(X0,X1) = apply(X1,sK135(X0,X1))
& in(sK135(X0,X1),relation_rng(X0))
& ( sK135(X0,X1) != apply(X0,sK136(X0,X1))
| ~ in(sK136(X0,X1),relation_dom(X0)) ) )
| relation_dom(X1) != relation_rng(X0)
| X1 = function_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135,sK136]),skolemize(X2,sK135(X0,X1)),skolemize(X3,sK136(X0,X1))],[f1325]) ).
fof(f1327,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK137(X0),sK138(X0)),X0)
| X0 = empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137,sK138]),skolemize(X1,sK137(X0)),skolemize(X2,sK138(X0))],[f809]) ).
fof(f1328,plain,
( one_sorted_str(sK139)
& ~ empty_carrier(sK139)
& element(sK140,powerset(powerset(the_carrier(sK139))))
& empty_set = sK140
& is_a_cover_of_carrier(sK139,sK140) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139,sK140]),skolemize(X0,sK139),skolemize(X1,sK140)],[f813]) ).
fof(f1329,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,[],[f814]) ).
fof(f1330,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,[],[f822]) ).
fof(f1331,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) != X0
| ~ in(X1,X0) )
& ( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ) ),
inference(nnf_transformation,[],[f508]) ).
fof(f1332,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,[],[f824]) ).
fof(f1333,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,[],[f1332]) ).
fof(f1334,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,[],[f1333]) ).
fof(f1335,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(sK141(X1,X2),relation_dom(X1))
& apply(X2,sK141(X1,X2)) != apply(X1,sK141(X1,X2)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(X3,sK141(X1,X2))],[f1334]) ).
fof(f1336,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,[],[f833]) ).
fof(f1337,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,[],[f1336]) ).
fof(f1338,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 )
& ( set_difference(X0,X1) != X0
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f524]) ).
fof(f1339,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,[],[f835]) ).
fof(f1340,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,[],[f1339]) ).
fof(f1341,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,[],[f838]) ).
fof(f1342,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,[],[f1341]) ).
fof(f1343,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,[],[f839]) ).
fof(f1344,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ in(X3,sK142(X1))
| ~ in(X3,X1) )
& in(sK142(X1),X1) )
| ~ in(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(X2,sK142(X1))],[f850]) ).
fof(f1345,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f851]) ).
fof(f1346,plain,
! [X0,X1] :
( ( ( in(sK143(X0,X1),X0)
| in(sK143(X0,X1),X1) )
& ( ~ in(sK143(X0,X1),X0)
| ~ in(sK143(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(X2,sK143(X0,X1))],[f1345]) ).
fof(f1347,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,[],[f1125]) ).
fof(f1348,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| ( sP17(sK144(X0,X1),sK146(X0,X1),X1)
& in(sK144(X0,X1),X0)
& ! [X6] :
( ~ in(X6,sK147(X0,X1))
| in(ordered_pair(sK145(X0,X1),X6),X1) )
& in(sK145(X0,X1),sK147(X0,X1))
& sK144(X0,X1) = sK147(X0,X1)
& in(sK144(X0,X1),X0)
& sK145(X0,X1) != sK146(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144,sK145,sK146,sK147]),skolemize(X2,sK144(X0,X1)),skolemize(X3,sK145(X0,X1)),skolemize(X4,sK146(X0,X1)),skolemize(X5,sK147(X0,X1))],[f1347]) ).
fof(f1352,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,[],[f1126]) ).
fof(f1353,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,[],[f1352]) ).
fof(f1354,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ! [X3] :
( ( ~ in(X3,sK149(X0,X1))
| ( ! [X9] :
( ~ in(X9,sK152(X0,X1,X3))
| in(ordered_pair(X3,X9),X1) )
& in(X3,sK152(X0,X1,X3))
& sK151(X0,X1,X3) = sK152(X0,X1,X3)
& in(sK151(X0,X1,X3),X0)
& in(sK151(X0,X1,X3),X0) ) )
& ( ! [X4] :
( ! [X5] :
( ( in(sK150(X1,X3,X5),X5)
& ~ in(ordered_pair(X3,sK150(X1,X3,X5)),X1) )
| ~ in(X3,X5)
| X4 != X5 )
| ~ in(X4,X0)
| ~ in(X4,X0) )
| in(X3,sK149(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149,sK150,sK151,sK152]),skolemize(X2,sK149(X0,X1)),skolemize(X6,sK150(X1,X3,X5)),skolemize(X7,sK151(X0,X1,X3)),skolemize(X8,sK152(X0,X1,X3))],[f1353]) ).
fof(f1355,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,[],[f856]) ).
fof(f1356,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,[],[f1355]) ).
fof(f1357,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK155(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK153(X0,X1),X1)
| in(ordered_pair(sK154(X0,X1),sK153(X0,X1)),X0) )
& ( ~ in(sK153(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK153(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153,sK154,sK155]),skolemize(X2,sK153(X0,X1)),skolemize(X4,sK154(X0,X1)),skolemize(X7,sK155(X0,X5))],[f1356]) ).
fof(f1358,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,[],[f857]) ).
fof(f1359,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,[],[f1358]) ).
fof(f1360,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK158(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK156(X0,X1),X1)
| in(ordered_pair(sK156(X0,X1),sK157(X0,X1)),X0) )
& ( ~ in(sK156(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK156(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156,sK157,sK158]),skolemize(X2,sK156(X0,X1)),skolemize(X4,sK157(X0,X1)),skolemize(X7,sK158(X0,X5))],[f1359]) ).
fof(f1361,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,[],[f858]) ).
fof(f1362,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,[],[f1361]) ).
fof(f1363,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(sK159(X0,X1),sK160(X0,X1)),X0)
& ~ in(ordered_pair(sK159(X0,X1),sK160(X0,X1)),X1) )
| subset(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159,sK160]),skolemize(X2,sK159(X0,X1)),skolemize(X3,sK160(X0,X1))],[f1362]) ).
fof(f1364,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,[],[f859]) ).
fof(f1365,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,[],[f1364]) ).
fof(f1366,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(sK161(X0,X1),sK162(X0,X1)),X0)
| in(ordered_pair(sK161(X0,X1),sK162(X0,X1)),X1) )
& ( ~ in(ordered_pair(sK161(X0,X1),sK162(X0,X1)),X0)
| ~ in(ordered_pair(sK161(X0,X1),sK162(X0,X1)),X1) ) )
| X0 = X1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161,sK162]),skolemize(X2,sK161(X0,X1)),skolemize(X3,sK162(X0,X1))],[f1365]) ).
fof(f1367,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,[],[f860]) ).
fof(f1368,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,[],[f1367]) ).
fof(f1369,plain,
! [X0] :
( ( ~ relation(X0)
| ! [X4] :
( ordered_pair(sK164(X4),sK165(X4)) = X4
| ~ in(X4,X0) ) )
& ( ( ! [X2,X3] : ordered_pair(X2,X3) != sK163(X0)
& in(sK163(X0),X0) )
| relation(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK163,sK164,sK165]),skolemize(X1,sK163(X0)),skolemize(X5,sK164(X4)),skolemize(X6,sK165(X4))],[f1368]) ).
fof(f1370,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,[],[f862]) ).
fof(f1371,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,[],[f1370]) ).
fof(f1372,plain,
! [X0] :
( ( ~ function(X0)
| ! [X4,X5,X6] :
( ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| X5 = X6 ) )
& ( ( in(ordered_pair(sK166(X0),sK168(X0)),X0)
& in(ordered_pair(sK166(X0),sK167(X0)),X0)
& sK167(X0) != sK168(X0) )
| function(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166,sK167,sK168]),skolemize(X1,sK166(X0)),skolemize(X2,sK167(X0)),skolemize(X3,sK168(X0))],[f1371]) ).
fof(f1373,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,[],[f864]) ).
fof(f1374,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,[],[f1373]) ).
fof(f1375,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f1376,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f1375]) ).
fof(f1377,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK169(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(X1,sK169(X0))],[f1376]) ).
fof(f1378,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,[],[f1128]) ).
fof(f1379,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,[],[f1378]) ).
fof(f1380,plain,
! [X0] :
( ~ sP20(X0)
| ( sP19(sK172(X0),X0)
& sK170(X0) = sK172(X0)
& sK174(X0) = singleton(sK173(X0))
& in(sK173(X0),X0)
& sK171(X0) = ordered_pair(sK173(X0),sK174(X0))
& sK170(X0) = sK171(X0)
& sK171(X0) != sK172(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK170,sK171,sK172,sK173,sK174]),skolemize(X1,sK170(X0)),skolemize(X2,sK171(X0)),skolemize(X3,sK172(X0)),skolemize(X4,sK173(X0)),skolemize(X5,sK174(X0))],[f1379]) ).
fof(f1384,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,[],[f1129]) ).
fof(f1385,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,[],[f1384]) ).
fof(f1386,plain,
! [X0,X1] :
( sP20(X0)
| ! [X3] :
( ( ~ in(X3,sK177(X0,X1))
| ( sK180(X0,X3) = singleton(sK179(X0,X3))
& in(sK179(X0,X3),X0)
& ordered_pair(sK179(X0,X3),sK180(X0,X3)) = X3
& sK178(X0,X1,X3) = X3
& in(sK178(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,sK177(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK177,sK178,sK179,sK180]),skolemize(X2,sK177(X0,X1)),skolemize(X7,sK178(X0,X1,X3)),skolemize(X8,sK179(X0,X3)),skolemize(X9,sK180(X0,X3))],[f1385]) ).
fof(f1389,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,[],[f1131]) ).
fof(f1390,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,[],[f1389]) ).
fof(f1391,plain,
! [X0] :
( sP21(X0)
| ! [X2] :
( ( ~ in(X2,sK184(X0))
| ( singleton(sK185(X0,X2)) = X2
& in(sK185(X0,X2),X0)
& in(sK185(X0,X2),X0) ) )
& ( ! [X3] :
( singleton(X3) != X2
| ~ in(X3,X0)
| ~ in(X3,X0) )
| in(X2,sK184(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK184,sK185]),skolemize(X1,sK184(X0)),skolemize(X4,sK185(X0,X2))],[f1390]) ).
fof(f1392,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,[],[f64]) ).
fof(f1393,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,[],[f1392]) ).
fof(f1394,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK186(X0,X1),X1)
| sK186(X0,X1) = X0 )
& ( ~ in(sK186(X0,X1),X1)
| sK186(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(X2,sK186(X0,X1))],[f1393]) ).
fof(f1395,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,[],[f78]) ).
fof(f1396,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,[],[f1395]) ).
fof(f1397,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,[],[f1396]) ).
fof(f1398,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(sK187(X0,X1,X2),X2)
| in(sK187(X0,X1,X2),X1)
| in(sK187(X0,X1,X2),X0) )
& ( ~ in(sK187(X0,X1,X2),X2)
| ( ~ in(sK187(X0,X1,X2),X1)
& ~ in(sK187(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(X3,sK187(X0,X1,X2))],[f1397]) ).
fof(f1399,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set )
& ( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f110]) ).
fof(f1400,plain,
! [X2,X1,X0] :
( ~ sP23(X2,X1,X0)
| ( ( topstr_closure(X0,X1) != X2
| sP22(X0,X1,X2) )
& ( ~ sP22(X0,X1,X2)
| X2 = topstr_closure(X0,X1) ) ) ),
inference(nnf_transformation,[],[f1133]) ).
fof(f1401,plain,
! [X0,X1,X2] :
( ~ sP23(X0,X1,X2)
| ( ( topstr_closure(X2,X1) != X0
| sP22(X2,X1,X0) )
& ( ~ sP22(X2,X1,X0)
| topstr_closure(X2,X1) = X0 ) ) ),
inference(rectify,[],[f1400]) ).
fof(f1406,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,[],[f885]) ).
fof(f1407,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,[],[f1406]) ).
fof(f1408,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,[],[f1407]) ).
fof(f1409,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(sK191(X0,X1,X2),sK192(X0,X1,X2)),X2)
| ( in(ordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),X1)
& in(sK192(X0,X1,X2),X0) ) )
& ( ~ in(ordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),X1)
| ~ in(sK192(X0,X1,X2),X0) ) )
| X2 = relation_rng_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK191,sK192]),skolemize(X3,sK191(X0,X1,X2)),skolemize(X4,sK192(X0,X1,X2))],[f1408]) ).
fof(f1410,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f457]) ).
fof(f1411,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,[],[f886]) ).
fof(f1412,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,[],[f1411]) ).
fof(f1413,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK193(X0,X1),X0)
& ~ in(sK193(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(X2,sK193(X0,X1))],[f1412]) ).
fof(f1414,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,[],[f69]) ).
fof(f1415,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,[],[f1414]) ).
fof(f1416,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK194(X0,X1),X1)
| subset(sK194(X0,X1),X0) )
& ( ~ in(sK194(X0,X1),X1)
| ~ subset(sK194(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(X2,sK194(X0,X1))],[f1415]) ).
fof(f1417,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f1418,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f1417]) ).
fof(f1419,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,[],[f94]) ).
fof(f1420,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,[],[f1419]) ).
fof(f1421,plain,
! [X0,X1] :
( ( ~ equipotent(X0,X1)
| ( relation_rng(sK195(X0,X1)) = X1
& relation_dom(sK195(X0,X1)) = X0
& one_to_one(sK195(X0,X1))
& function(sK195(X0,X1))
& relation(sK195(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,[sK195]),skolemize(X3,sK195(X0,X1))],[f1420]) ).
fof(f1422,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,[],[f95]) ).
fof(f1423,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,[],[f1422]) ).
fof(f1424,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,[],[f1423]) ).
fof(f1425,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(sK196(X0,X1,X2),X2)
| ( ~ in(sK196(X0,X1,X2),X1)
& in(sK196(X0,X1,X2),X0) ) )
& ( ~ in(sK196(X0,X1,X2),X2)
| in(sK196(X0,X1,X2),X1)
| ~ in(sK196(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(X3,sK196(X0,X1,X2))],[f1424]) ).
fof(f1426,plain,
! [X0] :
( empty(sK197(X0))
& element(sK197(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(X1,sK197(X0))],[f297]) ).
fof(f1427,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK198(X0))
& element(sK198(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(X1,sK198(X0))],[f896]) ).
fof(f1428,plain,
! [X0] : element(sK199(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(X1,sK199(X0))],[f188]) ).
fof(f1429,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ( ~ empty(sK200(X0))
& element(sK200(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(X1,sK200(X0))],[f898]) ).
fof(f1430,plain,
( ~ empty_carrier(sK201)
& one_sorted_str(sK201) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(X0,sK201)],[f304]) ).
fof(f1431,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ( ( ~ empty_carrier(X0)
| empty(the_carrier(X0)) )
& ( ~ empty(the_carrier(X0))
| empty_carrier(X0) ) ) ),
inference(nnf_transformation,[],[f901]) ).
fof(f1432,plain,
one_sorted_str(sK202),
inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(X0,sK202)],[f184]) ).
fof(f1433,plain,
! [X0] :
( ( ~ being_limit_ordinal(X0)
| X0 = union(X0) )
& ( union(X0) != X0
| being_limit_ordinal(X0) ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f1434,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,[],[f92]) ).
fof(f1435,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,[],[f1434]) ).
fof(f1436,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK205(X0,X5),X0)
& in(X5,sK205(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK203(X0,X1),X1)
| ( in(sK204(X0,X1),X0)
& in(sK203(X0,X1),sK204(X0,X1)) ) )
& ( ~ in(sK203(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK203(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK203,sK204,sK205]),skolemize(X2,sK203(X0,X1)),skolemize(X4,sK204(X0,X1)),skolemize(X7,sK205(X0,X5))],[f1435]) ).
fof(f1440,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(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,[],[f1136]) ).
fof(f1441,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(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,[],[f1440]) ).
fof(f1442,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(X1,X2)
| ! [X4] :
( ( ~ in(X4,sK213(X0,X1,X2))
| ( in(ordered_pair(apply(X2,sK215(X1,X2,X4)),apply(X2,sK216(X1,X2,X4))),X1)
& ordered_pair(sK215(X1,X2,X4),sK216(X1,X2,X4)) = X4
& sK214(X0,X1,X2,X4) = X4
& in(sK214(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,sK213(X0,X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK213,sK214,sK215,sK216]),skolemize(X3,sK213(X0,X1,X2)),skolemize(X8,sK214(X0,X1,X2,X4)),skolemize(X9,sK215(X1,X2,X4)),skolemize(X10,sK216(X1,X2,X4))],[f1441]) ).
fof(f1443,plain,
! [X1,X0,X2] :
( ~ sP28(X1,X0,X2)
| ? [X14] :
! [X15] :
( ( ~ in(X15,X14)
| sP27(X2,X0,X15,X1) )
& ( ~ sP27(X2,X0,X15,X1)
| in(X15,X14) ) ) ),
inference(nnf_transformation,[],[f1140]) ).
fof(f1444,plain,
! [X0,X1,X2] :
( ~ sP28(X0,X1,X2)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| sP27(X2,X1,X4,X0) )
& ( ~ sP27(X2,X1,X4,X0)
| in(X4,X3) ) ) ),
inference(rectify,[],[f1443]) ).
fof(f1445,plain,
! [X0,X1,X2] :
( ~ sP28(X0,X1,X2)
| ! [X4] :
( ( ~ in(X4,sK217(X0,X1,X2))
| sP27(X2,X1,X4,X0) )
& ( ~ sP27(X2,X1,X4,X0)
| in(X4,sK217(X0,X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(X3,sK217(X0,X1,X2))],[f1444]) ).
fof(f1446,plain,
! [X2,X0,X15,X1] :
( ( ~ sP27(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)) )
| sP27(X2,X0,X15,X1) ) ),
inference(nnf_transformation,[],[f1139]) ).
fof(f1447,plain,
! [X0,X1,X2,X3] :
( ( ~ sP27(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)) )
| sP27(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1446]) ).
fof(f1448,plain,
! [X0,X1,X2,X3] :
( ( ~ sP27(X0,X1,X2,X3)
| ( ! [X13] :
( ~ in(X13,sK222(X1,X2,X3))
| in(ordered_pair(sK221(X1,X2,X3),X13),X3) )
& in(sK221(X1,X2,X3),sK222(X1,X2,X3))
& sK220(X1,X2,X3) = sK222(X1,X2,X3)
& in(sK220(X1,X2,X3),X1)
& ordered_pair(sK220(X1,X2,X3),sK221(X1,X2,X3)) = X2
& sK219(X0,X1,X2,X3) = X2
& in(sK219(X0,X1,X2,X3),cartesian_product2(X1,X0)) ) )
& ( ! [X4] :
( ! [X5,X6] :
( ! [X7] :
( ( in(sK218(X3,X6,X7),X7)
& ~ in(ordered_pair(X6,sK218(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)) )
| sP27(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK218,sK219,sK220,sK221,sK222]),skolemize(X8,sK218(X3,X6,X7)),skolemize(X9,sK219(X0,X1,X2,X3)),skolemize(X10,sK220(X1,X2,X3)),skolemize(X11,sK221(X1,X2,X3)),skolemize(X12,sK222(X1,X2,X3))],[f1447]) ).
fof(f1449,plain,
! [X4,X0,X1] :
( ~ sP26(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,[],[f1138]) ).
fof(f1450,plain,
! [X0,X1,X2] :
( ~ sP26(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,[],[f1449]) ).
fof(f1451,plain,
! [X0,X1,X2] :
( ~ sP26(X0,X1,X2)
| ( ! [X6] :
( ~ in(X6,sK225(X0,X1,X2))
| in(ordered_pair(sK224(X0,X1,X2),X6),X2) )
& in(sK224(X0,X1,X2),sK225(X0,X1,X2))
& sK223(X0,X1,X2) = sK225(X0,X1,X2)
& in(sK223(X0,X1,X2),X1)
& ordered_pair(sK223(X0,X1,X2),sK224(X0,X1,X2)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK223,sK224,sK225]),skolemize(X3,sK223(X0,X1,X2)),skolemize(X4,sK224(X0,X1,X2)),skolemize(X5,sK225(X0,X1,X2))],[f1450]) ).
fof(f1455,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2] :
( ( sP25(sK231(X0,X1),X0,X1)
& sK229(X0,X1) = sK231(X0,X1)
& sP26(sK230(X0,X1),X0,X1)
& sK229(X0,X1) = sK230(X0,X1)
& sK230(X0,X1) != sK231(X0,X1) )
| sP28(X1,X0,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK229,sK230,sK231]),skolemize(X3,sK229(X0,X1)),skolemize(X4,sK230(X0,X1)),skolemize(X5,sK231(X0,X1))],[f1141]) ).
fof(f1456,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,[],[f79]) ).
fof(f1457,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,[],[f1456]) ).
fof(f1458,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ( ordered_pair(sK235(X0,X1,X8),sK236(X0,X1,X8)) = X8
& in(sK236(X0,X1,X8),X1)
& in(sK235(X0,X1,X8),X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ( ( in(sK232(X0,X1,X2),X2)
| ( sK232(X0,X1,X2) = ordered_pair(sK233(X0,X1,X2),sK234(X0,X1,X2))
& in(sK234(X0,X1,X2),X1)
& in(sK233(X0,X1,X2),X0) ) )
& ( ~ in(sK232(X0,X1,X2),X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK232(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK232,sK233,sK234,sK235,sK236]),skolemize(X3,sK232(X0,X1,X2)),skolemize(X6,sK233(X0,X1,X2)),skolemize(X7,sK234(X0,X1,X2)),skolemize(X11,sK235(X0,X1,X8)),skolemize(X12,sK236(X0,X1,X8))],[f1457]) ).
fof(f1459,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,[],[f920]) ).
fof(f1460,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,[],[f1459]) ).
fof(f1461,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,[],[f1460]) ).
fof(f1462,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(sK237(X0,X1,X2),sK238(X0,X1,X2)),X2)
| ( in(ordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),X0)
& in(sK237(X0,X1,X2),X1) ) )
& ( ~ in(ordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),X0)
| ~ in(sK237(X0,X1,X2),X1) ) )
| X2 = relation_dom_restriction(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK237,sK238]),skolemize(X3,sK237(X0,X1,X2)),skolemize(X4,sK238(X0,X1,X2))],[f1461]) ).
fof(f1463,plain,
( function(sK239)
& empty(sK239)
& relation(sK239) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(X0,sK239)],[f293]) ).
fof(f1464,plain,
( function(sK240)
& relation(sK240) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(X0,sK240)],[f282]) ).
fof(f1465,plain,
~ empty(sK241),
inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(X0,sK241)],[f299]) ).
fof(f1466,plain,
( relation(sK242)
& ~ empty(sK242) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(X0,sK242)],[f296]) ).
fof(f1467,plain,
empty(sK243),
inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(X0,sK243)],[f291]) ).
fof(f1468,plain,
( relation(sK244)
& empty(sK244) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(X0,sK244)],[f288]) ).
fof(f1469,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,[],[f926]) ).
fof(f1473,plain,
! [X0] :
( sP29
| ? [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,[],[f1143]) ).
fof(f1474,plain,
! [X0] :
( sP29
| ? [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,[],[f1473]) ).
fof(f1475,plain,
! [X0] :
( sP29
| ! [X2] :
( ( ~ in(X2,sK248(X0))
| ( ordinal(X2)
& sK249(X0,X2) = X2
& in(sK249(X0,X2),X0) ) )
& ( ! [X3] :
( ~ ordinal(X2)
| X2 != X3
| ~ in(X3,X0) )
| in(X2,sK248(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK248,sK249]),skolemize(X1,sK248(X0)),skolemize(X4,sK249(X0,X2))],[f1474]) ).
fof(f1476,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ( ~ ordinal_subset(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| ordinal_subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f933]) ).
fof(f1477,plain,
! [X0] :
( ~ sP32(X0)
| ? [X12] :
! [X13] :
( ( ~ in(X13,X12)
| sP31(X0,X13) )
& ( ~ sP31(X0,X13)
| in(X13,X12) ) ) ),
inference(nnf_transformation,[],[f1146]) ).
fof(f1478,plain,
! [X0] :
( ~ sP32(X0)
| ? [X1] :
! [X2] :
( ( ~ in(X2,X1)
| sP31(X0,X2) )
& ( ~ sP31(X0,X2)
| in(X2,X1) ) ) ),
inference(rectify,[],[f1477]) ).
fof(f1479,plain,
! [X0] :
( ~ sP32(X0)
| ! [X2] :
( ( ~ in(X2,sK250(X0))
| sP31(X0,X2) )
& ( ~ sP31(X0,X2)
| in(X2,sK250(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(X1,sK250(X0))],[f1478]) ).
fof(f1480,plain,
! [X0,X13] :
( ( ~ sP31(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)) )
| sP31(X0,X13) ) ),
inference(nnf_transformation,[],[f1145]) ).
fof(f1481,plain,
! [X0,X1] :
( ( ~ sP31(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)) )
| sP31(X0,X1) ) ),
inference(rectify,[],[f1480]) ).
fof(f1482,plain,
! [X0,X1] :
( ( ~ sP31(X0,X1)
| ( ( ~ in(sK254(X1),omega)
| ! [X9] :
( ~ element(X9,powerset(powerset(sK254(X1))))
| ( ! [X11] :
( ~ subset(sK255(X9),X11)
| ~ in(X11,X9)
| sK255(X9) = X11 )
& in(sK255(X9),X9) )
| empty_set = X9 ) )
& sK254(X1) = X1
& ordinal(sK254(X1))
& sK253(X0,X1) = X1
& in(sK253(X0,X1),succ(X0)) ) )
& ( ! [X2] :
( ! [X3] :
( ( in(X3,omega)
& element(sK251(X3),powerset(powerset(X3)))
& ! [X5] :
( ( subset(X5,sK252(X3,X5))
& in(sK252(X3,X5),sK251(X3))
& sK252(X3,X5) != X5 )
| ~ in(X5,sK251(X3)) )
& empty_set != sK251(X3) )
| X1 != X3
| ~ ordinal(X3) )
| X1 != X2
| ~ in(X2,succ(X0)) )
| sP31(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK251,sK252,sK253,sK254,sK255]),skolemize(X4,sK251(X3)),skolemize(X6,sK252(X3,X5)),skolemize(X7,sK253(X0,X1)),skolemize(X8,sK254(X1)),skolemize(X10,sK255(X9))],[f1481]) ).
fof(f1486,plain,
! [X0] :
( ~ ordinal(X0)
| ( sP30(sK260)
& sK258 = sK260
& ( ~ in(sK261,omega)
| ! [X5] :
( ~ element(X5,powerset(powerset(sK261)))
| ( ! [X7] :
( ~ subset(sK262(X5),X7)
| ~ in(X7,X5)
| sK262(X5) = X7 )
& in(sK262(X5),X5) )
| empty_set = X5 ) )
& sK259 = sK261
& ordinal(sK261)
& sK258 = sK259
& sK259 != sK260 )
| sP32(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK258,sK259,sK260,sK261,sK262]),skolemize(X1,sK258),skolemize(X2,sK259),skolemize(X3,sK260),skolemize(X4,sK261),skolemize(X6,sK262(X5))],[f1147]) ).
fof(f1487,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,[],[f939]) ).
fof(f1488,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,[],[f1487]) ).
fof(f1489,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,[],[f1488]) ).
fof(f1490,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(sK263(X0))
& being_limit_ordinal(sK263(X0))
& in(empty_set,sK263(X0))
& ~ subset(X0,sK263(X0)) )
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| X0 = omega ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(X1,sK263(X0))],[f1489]) ).
fof(f1491,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(f1492,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,[],[f1491]) ).
fof(f1493,plain,
! [X0] :
( ( ~ finite(X0)
| ( in(relation_dom(sK264(X0)),omega)
& relation_rng(sK264(X0)) = X0
& function(sK264(X0))
& relation(sK264(X0)) ) )
& ( ! [X1] :
( ~ in(relation_dom(X1),omega)
| relation_rng(X1) != X0
| ~ function(X1)
| ~ relation(X1) )
| finite(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(X2,sK264(X0))],[f1492]) ).
fof(f1494,plain,
! [X0] :
( ~ sP34(X0)
| ? [X2,X3,X4] :
( sP33(X4,X0)
& X2 = X4
& ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& X2 = X3
& X3 != X4 ) ),
inference(nnf_transformation,[],[f1149]) ).
fof(f1495,plain,
! [X0] :
( ~ sP34(X0)
| ? [X1,X2,X3] :
( sP33(X3,X0)
& X1 = X3
& ? [X4] :
( in(X4,X0)
& X2 = X4
& ordinal(X4) )
& X1 = X2
& X2 != X3 ) ),
inference(rectify,[],[f1494]) ).
fof(f1496,plain,
! [X0] :
( ~ sP34(X0)
| ( sP33(sK267(X0),X0)
& sK265(X0) = sK267(X0)
& in(sK268(X0),X0)
& sK266(X0) = sK268(X0)
& ordinal(sK268(X0))
& sK265(X0) = sK266(X0)
& sK266(X0) != sK267(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK265,sK266,sK267,sK268]),skolemize(X1,sK265(X0)),skolemize(X2,sK266(X0)),skolemize(X3,sK267(X0)),skolemize(X4,sK268(X0))],[f1495]) ).
fof(f1500,plain,
! [X0,X1] :
( ~ ordinal(X1)
| sP34(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,[],[f1150]) ).
fof(f1501,plain,
! [X0,X1] :
( ~ ordinal(X1)
| sP34(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,[],[f1500]) ).
fof(f1502,plain,
! [X0,X1] :
( ~ ordinal(X1)
| sP34(X0)
| ! [X3] :
( ( ~ in(X3,sK270(X0,X1))
| ( in(sK272(X0,X3),X0)
& sK272(X0,X3) = X3
& ordinal(sK272(X0,X3))
& sK271(X0,X1,X3) = X3
& in(sK271(X0,X1,X3),succ(X1)) ) )
& ( ! [X4] :
( ! [X5] :
( ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5) )
| X3 != X4
| ~ in(X4,succ(X1)) )
| in(X3,sK270(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK270,sK271,sK272]),skolemize(X2,sK270(X0,X1)),skolemize(X6,sK271(X0,X1,X3)),skolemize(X7,sK272(X0,X3))],[f1501]) ).
fof(f1506,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP35(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,[],[f1152]) ).
fof(f1507,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP35(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,[],[f1506]) ).
fof(f1508,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP35(X1,X0)
| ! [X3] :
( ( ~ in(X3,sK278(X0,X1))
| ( set_difference(sK280(X0,X1,X3),singleton(X0)) = X3
& in(sK280(X0,X1,X3),X1)
& sK279(X0,X1,X3) = X3
& in(sK279(X0,X1,X3),powerset(X0)) ) )
& ( ! [X4] :
( ! [X5] :
( set_difference(X5,singleton(X0)) != X3
| ~ in(X5,X1) )
| X3 != X4
| ~ in(X4,powerset(X0)) )
| in(X3,sK278(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK278,sK279,sK280]),skolemize(X2,sK278(X0,X1)),skolemize(X6,sK279(X0,X1,X3)),skolemize(X7,sK280(X0,X1,X3))],[f1507]) ).
fof(f1509,plain,
( being_limit_ordinal(sK281)
& ordinal(sK281)
& epsilon_connected(sK281)
& epsilon_transitive(sK281) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(X0,sK281)],[f286]) ).
fof(f1510,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,[],[f947]) ).
fof(f1511,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,[],[f1510]) ).
fof(f1512,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK284(X0,X5)) = X5
& in(sK284(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK282(X0,X1),X1)
| ( sK282(X0,X1) = apply(X0,sK283(X0,X1))
& in(sK283(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK282(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK282(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK282,sK283,sK284]),skolemize(X2,sK282(X0,X1)),skolemize(X4,sK283(X0,X1)),skolemize(X7,sK284(X0,X5))],[f1511]) ).
fof(f1513,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,[],[f949]) ).
fof(f1514,plain,
top_str(sK285),
inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(X0,sK285)],[f183]) ).
fof(f1518,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP36(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,[],[f1154]) ).
fof(f1519,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP36(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,[],[f1518]) ).
fof(f1520,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP36(X1,X2)
| ! [X4] :
( ( ~ in(X4,sK289(X1,X2))
| ( in(relation_image(X2,X4),X1)
& sK290(X1,X2,X4) = X4
& in(sK290(X1,X2,X4),powerset(relation_dom(X2))) ) )
& ( ! [X5] :
( ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2))) )
| in(X4,sK289(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK289,sK290]),skolemize(X3,sK289(X1,X2)),skolemize(X6,sK290(X1,X2,X4))],[f1519]) ).
fof(f1521,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,[],[f958]) ).
fof(f1522,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,[],[f1521]) ).
fof(f1523,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK293(X0,X1,X6),X1)
& in(ordered_pair(sK293(X0,X1,X6),X6),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X7,X6),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK291(X0,X1,X2),X2)
| ( in(sK292(X0,X1,X2),X1)
& in(ordered_pair(sK292(X0,X1,X2),sK291(X0,X1,X2)),X0) ) )
& ( ~ in(sK291(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK291(X0,X1,X2)),X0) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK291,sK292,sK293]),skolemize(X3,sK291(X0,X1,X2)),skolemize(X5,sK292(X0,X1,X2)),skolemize(X8,sK293(X0,X1,X6))],[f1522]) ).
fof(f1524,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,[],[f960]) ).
fof(f1525,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,[],[f1524]) ).
fof(f1526,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1,X2] :
( ( relation_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( apply(X0,sK296(X0,X1,X6)) = X6
& in(sK296(X0,X1,X6),X1)
& in(sK296(X0,X1,X6),relation_dom(X0)) ) )
& ( ! [X7] :
( apply(X0,X7) != X6
| ~ in(X7,X1)
| ~ in(X7,relation_dom(X0)) )
| in(X6,X2) ) ) )
& ( ( ( in(sK294(X0,X1,X2),X2)
| ( sK294(X0,X1,X2) = apply(X0,sK295(X0,X1,X2))
& in(sK295(X0,X1,X2),X1)
& in(sK295(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK294(X0,X1,X2),X2)
| ! [X4] :
( apply(X0,X4) != sK294(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0)) ) ) )
| X2 = relation_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK294,sK295,sK296]),skolemize(X3,sK294(X0,X1,X2)),skolemize(X5,sK295(X0,X1,X2)),skolemize(X8,sK296(X0,X1,X6))],[f1525]) ).
fof(f1527,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,[],[f76]) ).
fof(f1528,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,[],[f1527]) ).
fof(f1529,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,[],[f1528]) ).
fof(f1530,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(sK297(X0,X1,X2),X2)
| sK297(X0,X1,X2) = X1
| sK297(X0,X1,X2) = X0 )
& ( ~ in(sK297(X0,X1,X2),X2)
| ( sK297(X0,X1,X2) != X1
& sK297(X0,X1,X2) != X0 ) ) )
| X2 = unordered_pair(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(X3,sK297(X0,X1,X2))],[f1529]) ).
fof(f1531,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,[],[f86]) ).
fof(f1532,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,[],[f1531]) ).
fof(f1533,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,[],[f1532]) ).
fof(f1534,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(sK298(X0,X1,X2),X2)
| ( in(sK298(X0,X1,X2),X1)
& in(sK298(X0,X1,X2),X0) ) )
& ( ~ in(sK298(X0,X1,X2),X2)
| ~ in(sK298(X0,X1,X2),X1)
| ~ in(sK298(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(X3,sK298(X0,X1,X2))],[f1533]) ).
fof(f1535,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,[],[f317]) ).
fof(f1536,plain,
! [X0,X1] : relation_of2_as_subset(sK299(X0,X1),X0,X1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(X2,sK299(X0,X1))],[f189]) ).
fof(f1537,plain,
! [X0] :
( ! [X7] :
( in(X7,sK300(X0))
| are_equipotent(X7,sK300(X0))
| ~ subset(X7,sK300(X0)) )
& ! [X4] :
( ( ! [X6] :
( ~ subset(X6,X4)
| in(X6,sK301(X0,X4)) )
& in(sK301(X0,X4),sK300(X0)) )
| ~ in(X4,sK300(X0)) )
& ! [X2,X3] :
( ~ subset(X3,X2)
| ~ in(X2,sK300(X0))
| in(X3,sK300(X0)) )
& in(X0,sK300(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK300,sK301]),skolemize(X1,sK300(X0)),skolemize(X5,sK301(X0,X4))],[f971]) ).
fof(f1538,plain,
! [X0,X1] :
( ( ~ equipotent(X0,X1)
| are_equipotent(X0,X1) )
& ( ~ are_equipotent(X0,X1)
| equipotent(X0,X1) ) ),
inference(nnf_transformation,[],[f319]) ).
fof(f1539,plain,
! [X0] :
( empty(X0)
| ( finite(sK302(X0))
& ~ empty(sK302(X0))
& element(sK302(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(X1,sK302(X0))],[f972]) ).
fof(f1540,plain,
( finite(sK303)
& ~ empty(sK303) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(X0,sK303)],[f281]) ).
fof(f1541,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,[],[f978]) ).
fof(f1542,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,[],[f1541]) ).
fof(f1543,plain,
! [X0] :
( ~ relation(X0)
| ! [X1,X2] :
( ( relation_inverse_image(X0,X1) != X2
| ! [X6] :
( ( ~ in(X6,X2)
| ( in(sK306(X0,X1,X6),X1)
& in(ordered_pair(X6,sK306(X0,X1,X6)),X0) ) )
& ( ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) )
| in(X6,X2) ) ) )
& ( ( ( in(sK304(X0,X1,X2),X2)
| ( in(sK305(X0,X1,X2),X1)
& in(ordered_pair(sK304(X0,X1,X2),sK305(X0,X1,X2)),X0) ) )
& ( ~ in(sK304(X0,X1,X2),X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(sK304(X0,X1,X2),X4),X0) ) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK304,sK305,sK306]),skolemize(X3,sK304(X0,X1,X2)),skolemize(X5,sK305(X0,X1,X2)),skolemize(X8,sK306(X0,X1,X6))],[f1542]) ).
fof(f1544,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,[],[f980]) ).
fof(f1545,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,[],[f1544]) ).
fof(f1546,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,[],[f1545]) ).
fof(f1547,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(sK307(X0,X1,X2),X2)
| ( in(apply(X0,sK307(X0,X1,X2)),X1)
& in(sK307(X0,X1,X2),relation_dom(X0)) ) )
& ( ~ in(sK307(X0,X1,X2),X2)
| ~ in(apply(X0,sK307(X0,X1,X2)),X1)
| ~ in(sK307(X0,X1,X2),relation_dom(X0)) ) )
| X2 = relation_inverse_image(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(X3,sK307(X0,X1,X2))],[f1546]) ).
fof(f1548,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,[],[f997]) ).
fof(f1549,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,[],[f1548]) ).
fof(f1550,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(sK311(X0,X1,X7,X8),X8),X1)
& in(ordered_pair(X7,sK311(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(sK308(X0,X1,X2),sK309(X0,X1,X2)),X2)
| ( in(ordered_pair(sK310(X0,X1,X2),sK309(X0,X1,X2)),X1)
& in(ordered_pair(sK308(X0,X1,X2),sK310(X0,X1,X2)),X0) ) )
& ( ~ in(ordered_pair(sK308(X0,X1,X2),sK309(X0,X1,X2)),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,sK309(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK308(X0,X1,X2),X5),X0) ) ) )
| X2 = relation_composition(X0,X1) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK308,sK309,sK310,sK311]),skolemize(X3,sK308(X0,X1,X2)),skolemize(X4,sK309(X0,X1,X2)),skolemize(X6,sK310(X0,X1,X2)),skolemize(X10,sK311(X0,X1,X7,X8))],[f1549]) ).
fof(f1551,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,[],[f1003]) ).
fof(f1552,plain,
! [X0,X1] :
( quasi_total(sK312(X0,X1),X0,X1)
& function(sK312(X0,X1))
& relation(sK312(X0,X1))
& relation_of2(sK312(X0,X1),X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(X2,sK312(X0,X1))],[f283]) ).
fof(f1553,plain,
( ordinal(sK313)
& epsilon_connected(sK313)
& epsilon_transitive(sK313)
& ~ empty(sK313) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(X0,sK313)],[f302]) ).
fof(f1554,plain,
( ordinal(sK314)
& epsilon_connected(sK314)
& epsilon_transitive(sK314)
& empty(sK314)
& one_to_one(sK314)
& function(sK314)
& relation(sK314) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(X0,sK314)],[f294]) ).
fof(f1555,plain,
( ordinal(sK315)
& epsilon_connected(sK315)
& epsilon_transitive(sK315) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(X0,sK315)],[f285]) ).
fof(f1558,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,[],[f1007]) ).
fof(f1559,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f1558]) ).
fof(f1560,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ( in(sK316(X0),X0)
& ~ subset(sK316(X0),X0) )
| epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(X1,sK316(X0))],[f1559]) ).
fof(f1561,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,[],[f1013]) ).
fof(f1562,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,[],[f1561]) ).
fof(f1563,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_well_founded_in(X0,X1)
| ! [X4] :
( ( disjoint(fiber(X0,sK318(X0,X4)),X4)
& in(sK318(X0,X4),X4) )
| empty_set = X4
| ~ subset(X4,X1) ) )
& ( ( ! [X3] :
( ~ disjoint(fiber(X0,X3),sK317(X0,X1))
| ~ in(X3,sK317(X0,X1)) )
& empty_set != sK317(X0,X1)
& subset(sK317(X0,X1),X1) )
| is_well_founded_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK317,sK318]),skolemize(X2,sK317(X0,X1)),skolemize(X5,sK318(X0,X4))],[f1562]) ).
fof(f1564,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,[],[f1014]) ).
fof(f1565,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,[],[f1564]) ).
fof(f1566,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| ! [X3] :
( ( disjoint(fiber(X0,sK320(X0,X3)),X3)
& in(sK320(X0,X3),X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ) )
& ( ( ! [X2] :
( ~ disjoint(fiber(X0,X2),sK319(X0))
| ~ in(X2,sK319(X0)) )
& empty_set != sK319(X0)
& subset(sK319(X0),relation_field(X0)) )
| well_founded_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK319,sK320]),skolemize(X1,sK319(X0)),skolemize(X4,sK320(X0,X3))],[f1565]) ).
fof(f1567,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,[],[f1015]) ).
fof(f1568,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,[],[f1567]) ).
fof(f1569,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,[],[f1568]) ).
fof(f1570,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(sK321(X0,X1,X2),X2)
| ( in(ordered_pair(sK321(X0,X1,X2),X1),X0)
& sK321(X0,X1,X2) != X1 ) )
& ( ~ in(sK321(X0,X1,X2),X2)
| ~ in(ordered_pair(sK321(X0,X1,X2),X1),X0)
| sK321(X0,X1,X2) = X1 ) )
| X2 = fiber(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(X3,sK321(X0,X1,X2))],[f1569]) ).
fof(f1571,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,[],[f1019]) ).
fof(f1573,plain,
latt_str(sK322),
inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(X0,sK322)],[f186]) ).
fof(f1574,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,[],[f1024]) ).
fof(f1575,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,[],[f1574]) ).
fof(f1576,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(sK323(X0),the_carrier(X0))
& element(sK324(X0),the_carrier(X0))
& sK324(X0) != join(X0,meet(X0,sK323(X0),sK324(X0)),sK324(X0)) )
| meet_absorbing(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK323,sK324]),skolemize(X1,sK323(X0)),skolemize(X2,sK324(X0))],[f1575]) ).
fof(f1577,plain,
join_semilatt_str(sK325),
inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(X0,sK325)],[f185]) ).
fof(f1578,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,[],[f1029]) ).
fof(f1579,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,[],[f1578]) ).
fof(f1580,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,[],[f1579]) ).
fof(f1581,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(sK327(X0,X1),X0)
& in(sK326(X0,X1),X0)
& ( in(ordered_pair(sK326(X0,X1),sK327(X0,X1)),X1)
| subset(sK326(X0,X1),sK327(X0,X1)) )
& ( ~ in(ordered_pair(sK326(X0,X1),sK327(X0,X1)),X1)
| ~ subset(sK326(X0,X1),sK327(X0,X1)) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK326,sK327]),skolemize(X2,sK326(X0,X1)),skolemize(X3,sK327(X0,X1))],[f1580]) ).
fof(f1582,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,[],[f1030]) ).
fof(f1583,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,[],[f1582]) ).
fof(f1584,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,[],[f1583]) ).
fof(f1585,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(sK328(X0,X1),sK329(X0,X1)),X1)
| ( sK328(X0,X1) = sK329(X0,X1)
& in(sK328(X0,X1),X0) ) )
& ( ~ in(ordered_pair(sK328(X0,X1),sK329(X0,X1)),X1)
| sK328(X0,X1) != sK329(X0,X1)
| ~ in(sK328(X0,X1),X0) ) )
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK328,sK329]),skolemize(X2,sK328(X0,X1)),skolemize(X3,sK329(X0,X1))],[f1584]) ).
fof(f1586,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,[],[f1038]) ).
fof(f1587,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,[],[f1586]) ).
fof(f1588,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(sK330(X0,X1),sK331(X0,X1)),X1)
| in(ordered_pair(sK331(X0,X1),sK330(X0,X1)),X0) )
& ( ~ in(ordered_pair(sK330(X0,X1),sK331(X0,X1)),X1)
| ~ in(ordered_pair(sK331(X0,X1),sK330(X0,X1)),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK330,sK331]),skolemize(X2,sK330(X0,X1)),skolemize(X3,sK331(X0,X1))],[f1587]) ).
fof(f1589,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,[],[f1047]) ).
fof(f1590,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,[],[f1589]) ).
fof(f1591,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,[],[f1590]) ).
fof(f1592,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(sK332(X0,X1,X2),powerset(X0))
& ( in(sK332(X0,X1,X2),X2)
| in(subset_complement(X0,sK332(X0,X1,X2)),X1) )
& ( ~ in(sK332(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK332(X0,X1,X2)),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(X3,sK332(X0,X1,X2))],[f1591]) ).
fof(f1593,plain,
! [X1,X0,X2] :
( ~ sP38(X1,X0,X2)
| ( ( ~ relation_isomorphism(X0,X1,X2)
| sP37(X2,X0,X1) )
& ( ~ sP37(X2,X0,X1)
| relation_isomorphism(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f1156]) ).
fof(f1594,plain,
! [X0,X1,X2] :
( ~ sP38(X0,X1,X2)
| ( ( ~ relation_isomorphism(X1,X0,X2)
| sP37(X2,X1,X0) )
& ( ~ sP37(X2,X1,X0)
| relation_isomorphism(X1,X0,X2) ) ) ),
inference(rectify,[],[f1593]) ).
fof(f1599,plain,
( one_to_one(sK335)
& function(sK335)
& relation(sK335) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(X0,sK335)],[f301]) ).
fof(f1600,plain,
( empty(sK336)
& one_to_one(sK336)
& function(sK336)
& relation(sK336) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(X0,sK336)],[f287]) ).
fof(f1601,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,[],[f1054]) ).
fof(f1602,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,[],[f1601]) ).
fof(f1603,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,sK337(X0)) = apply(X0,sK338(X0))
& in(sK338(X0),relation_dom(X0))
& in(sK337(X0),relation_dom(X0))
& sK337(X0) != sK338(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK337,sK338]),skolemize(X1,sK337(X0)),skolemize(X2,sK338(X0))],[f1602]) ).
fof(f1604,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( ( ~ is_a_cover_of_carrier(X0,X1)
| cast_as_carrier_subset(X0) = union_of_subsets(the_carrier(X0),X1) )
& ( union_of_subsets(the_carrier(X0),X1) != cast_as_carrier_subset(X0)
| is_a_cover_of_carrier(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f1057]) ).
fof(f1605,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,[],[f1058]) ).
fof(f1606,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,[],[f1605]) ).
fof(f1607,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,[],[f1059]) ).
fof(f1608,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,[],[f1607]) ).
fof(f1609,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(sK339(X0,X1),sK340(X0,X1)) = X0
& sK339(X0,X1) != X1 )
| pair_first(X0) = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK339,sK340]),skolemize(X2,sK339(X0,X1)),skolemize(X3,sK340(X0,X1))],[f1608]) ).
fof(f1610,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,[],[f1060]) ).
fof(f1611,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,[],[f1610]) ).
fof(f1612,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(sK341(X0,X1),sK342(X0,X1)) = X0
& sK342(X0,X1) != X1 )
| pair_second(X0) = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK341,sK342]),skolemize(X2,sK341(X0,X1)),skolemize(X3,sK342(X0,X1))],[f1611]) ).
fof(f1613,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,[],[f1073]) ).
fof(f1614,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,[],[f1613]) ).
fof(f1615,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ( ~ in(sK344(X0),sK343(X0))
& sK343(X0) != sK344(X0)
& ~ in(sK343(X0),sK344(X0))
& in(sK344(X0),X0)
& in(sK343(X0),X0) )
| epsilon_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK343,sK344]),skolemize(X1,sK343(X0)),skolemize(X2,sK344(X0))],[f1614]) ).
fof(f1616,plain,
! [X0] :
( finite(sK345(X0))
& natural(sK345(X0))
& ordinal(sK345(X0))
& epsilon_connected(sK345(X0))
& epsilon_transitive(sK345(X0))
& one_to_one(sK345(X0))
& function(sK345(X0))
& relation(sK345(X0))
& empty(sK345(X0))
& element(sK345(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(X1,sK345(X0))],[f292]) ).
fof(f1617,plain,
( natural(sK346)
& ordinal(sK346)
& epsilon_connected(sK346)
& epsilon_transitive(sK346)
& ~ empty(sK346) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(X0,sK346)],[f280]) ).
fof(f1618,plain,
! [X0,X1] :
( function(sK347(X0,X1))
& relation(sK347(X0,X1))
& relation_of2(sK347(X0,X1),X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(X2,sK347(X0,X1))],[f295]) ).
fof(f1619,plain,
! [X0,X1] : relation_of2(sK348(X0,X1),X0,X1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(X2,sK348(X0,X1))],[f187]) ).
fof(f1620,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(f1621,plain,
meet_semilatt_str(sK349),
inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(X0,sK349)],[f182]) ).
fof(f1622,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,[],[f1084]) ).
fof(f1623,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,[],[f1622]) ).
fof(f1624,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(sK351(X0,X1),sK350(X0,X1)),X0)
& in(ordered_pair(sK350(X0,X1),sK351(X0,X1)),X0)
& in(sK351(X0,X1),X1)
& in(sK350(X0,X1),X1)
& sK350(X0,X1) != sK351(X0,X1) )
| is_antisymmetric_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK350,sK351]),skolemize(X2,sK350(X0,X1)),skolemize(X3,sK351(X0,X1))],[f1623]) ).
fof(f1625,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,[],[f1085]) ).
fof(f1626,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,[],[f1086]) ).
fof(f1627,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,[],[f1626]) ).
fof(f1628,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(sK353(X0,X1),sK352(X0,X1)),X0)
& ~ in(ordered_pair(sK352(X0,X1),sK353(X0,X1)),X0)
& sK352(X0,X1) != sK353(X0,X1)
& in(sK353(X0,X1),X1)
& in(sK352(X0,X1),X1) )
| is_connected_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK352,sK353]),skolemize(X2,sK352(X0,X1)),skolemize(X3,sK353(X0,X1))],[f1627]) ).
fof(f1629,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,[],[f1087]) ).
fof(f1630,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,[],[f1089]) ).
fof(f1631,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,[],[f1630]) ).
fof(f1632,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(sK355(X0,X1),sK356(X0,X1)),X0)
& in(ordered_pair(sK354(X0,X1),sK355(X0,X1)),X0)
& in(sK356(X0,X1),X1)
& in(sK355(X0,X1),X1)
& in(sK354(X0,X1),X1)
& ~ in(ordered_pair(sK354(X0,X1),sK356(X0,X1)),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK354,sK355,sK356]),skolemize(X2,sK354(X0,X1)),skolemize(X3,sK355(X0,X1)),skolemize(X4,sK356(X0,X1))],[f1631]) ).
fof(f1633,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,[],[f1090]) ).
fof(f1634,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,[],[f1091]) ).
fof(f1635,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,[],[f1092]) ).
fof(f1636,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,[],[f1635]) ).
fof(f1637,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_reflexive_in(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| in(ordered_pair(X3,X3),X0) ) )
& ( ( in(sK357(X0,X1),X1)
& ~ in(ordered_pair(sK357(X0,X1),sK357(X0,X1)),X0) )
| is_reflexive_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK357]),skolemize(X2,sK357(X0,X1))],[f1636]) ).
fof(f1638,plain,
( v5_membered(sK358)
& v4_membered(sK358)
& v3_membered(sK358)
& v2_membered(sK358)
& v1_membered(sK358)
& ~ empty(sK358) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK358]),skolemize(X0,sK358)],[f284]) ).
fof(f1639,plain,
! [X2,X0] :
( ~ relation(X0)
| ~ reflexive(X0)
| ~ in(X2,relation_field(X0))
| in(ordered_pair(X2,X2),X0) ),
inference(cnf_transformation,[],[f1160]) ).
fof(f1640,plain,
! [X0] :
( ~ relation(X0)
| in(sK39(X0),relation_field(X0))
| reflexive(X0) ),
inference(cnf_transformation,[],[f1160]) ).
fof(f1641,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK39(X0),sK39(X0)),X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f1160]) ).
fof(f1642,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f261]) ).
fof(f1644,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f602]) ).
fof(f1645,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f603]) ).
fof(f1646,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom(relation_rng_restriction(X0,X1)),relation_dom(X1)) ),
inference(cnf_transformation,[],[f604]) ).
fof(f1647,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,[],[f1163]) ).
fof(f1648,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK41(X0),sK42(X0)),X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f1163]) ).
fof(f1649,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK40(X0),sK41(X0)),X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f1163]) ).
fof(f1650,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK40(X0),sK42(X0)),X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f1163]) ).
fof(f1653,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(sK43(X0))
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1) ),
inference(cnf_transformation,[],[f1165]) ).
fof(f1654,plain,
! [X0,X1] :
( ~ relation(X1)
| well_orders(sK43(X0),X0)
| ~ equipotent(X0,relation_field(X1))
| ~ well_ordering(X1) ),
inference(cnf_transformation,[],[f1165]) ).
fof(f1658,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,[],[f1169]) ).
fof(f1659,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK45(X0),sK44(X0)),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1169]) ).
fof(f1660,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK44(X0),sK45(X0)),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1169]) ).
fof(f1661,plain,
! [X0] :
( ~ relation(X0)
| sK44(X0) != sK45(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1169]) ).
fof(f1662,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ),
inference(cnf_transformation,[],[f613]) ).
fof(f1664,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,the_carrier(X0))
| in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1)) ),
inference(cnf_transformation,[],[f1170]) ).
fof(f1665,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,[],[f1173]) ).
fof(f1666,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK47(X0),sK46(X0)),X0)
| connected(X0) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1667,plain,
! [X0] :
( ~ relation(X0)
| ~ in(ordered_pair(sK46(X0),sK47(X0)),X0)
| connected(X0) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1668,plain,
! [X0] :
( ~ relation(X0)
| sK46(X0) != sK47(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1669,plain,
! [X0] :
( ~ relation(X0)
| in(sK47(X0),relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1670,plain,
! [X0] :
( ~ relation(X0)
| in(sK46(X0),relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1678,plain,
! [X0,X1] :
( in(sK48(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f1679,plain,
! [X0,X1] :
( ~ in(sK48(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f1683,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| sP0(sK49(X0,X1),sK51(X0,X1),X1) ),
inference(cnf_transformation,[],[f1182]) ).
fof(f1684,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| in(sK49(X0,X1),X0) ),
inference(cnf_transformation,[],[f1182]) ).
fof(f1685,plain,
! [X0,X1,X6] :
( ~ sP2(X0,X1)
| ~ in(X6,sK52(X0,X1))
| in(ordered_pair(sK50(X0,X1),X6),X1) ),
inference(cnf_transformation,[],[f1182]) ).
fof(f1686,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| in(sK50(X0,X1),sK52(X0,X1)) ),
inference(cnf_transformation,[],[f1182]) ).
fof(f1687,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| sK49(X0,X1) = sK52(X0,X1) ),
inference(cnf_transformation,[],[f1182]) ).
fof(f1689,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| sK50(X0,X1) != sK51(X0,X1) ),
inference(cnf_transformation,[],[f1182]) ).
fof(f1690,plain,
! [X2,X3,X0,X1,X8,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(ordered_pair(X3,X4),X2)
| ~ in(X8,sK54(X1,X3,X4))
| in(ordered_pair(X4,X8),X1) ),
inference(cnf_transformation,[],[f1186]) ).
fof(f1691,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(ordered_pair(X3,X4),X2)
| in(X4,sK54(X1,X3,X4)) ),
inference(cnf_transformation,[],[f1186]) ).
fof(f1692,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(ordered_pair(X3,X4),X2)
| sK54(X1,X3,X4) = X3 ),
inference(cnf_transformation,[],[f1186]) ).
fof(f1693,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(ordered_pair(X3,X4),X2)
| in(X3,X0) ),
inference(cnf_transformation,[],[f1186]) ).
fof(f1700,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| sP1(X0,X1,sK56(X0,X1)) ),
inference(cnf_transformation,[],[f1191]) ).
fof(f1701,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| function(sK56(X0,X1)) ),
inference(cnf_transformation,[],[f1191]) ).
fof(f1702,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| relation(sK56(X0,X1)) ),
inference(cnf_transformation,[],[f1191]) ).
fof(f1709,plain,
! [X0] :
( sK60(X0) = singleton(sK58(X0))
| sP3(X0) ),
inference(cnf_transformation,[],[f1196]) ).
fof(f1710,plain,
! [X0] :
( in(sK58(X0),X0)
| sP3(X0) ),
inference(cnf_transformation,[],[f1196]) ).
fof(f1711,plain,
! [X0] :
( sK59(X0) = singleton(sK58(X0))
| sP3(X0) ),
inference(cnf_transformation,[],[f1196]) ).
fof(f1713,plain,
! [X0] :
( sK59(X0) != sK60(X0)
| sP3(X0) ),
inference(cnf_transformation,[],[f1196]) ).
fof(f1714,plain,
! [X2,X3,X0] :
( ~ in(X3,X0)
| ~ ordinal(X3)
| ~ ordinal(X2)
| ~ in(X2,X0)
| ordinal_subset(sK61(X0),X2) ),
inference(cnf_transformation,[],[f1198]) ).
fof(f1715,plain,
! [X3,X0] :
( ~ in(X3,X0)
| ~ ordinal(X3)
| in(sK61(X0),X0) ),
inference(cnf_transformation,[],[f1198]) ).
fof(f1716,plain,
! [X3,X0] :
( ~ in(X3,X0)
| ~ ordinal(X3)
| ordinal(sK61(X0)) ),
inference(cnf_transformation,[],[f1198]) ).
fof(f1717,plain,
( ~ sP8
| ordinal(sK62) ),
inference(cnf_transformation,[],[f1201]) ).
fof(f1718,plain,
! [X3,X1] :
( ~ sP8
| ~ in(sK62,omega)
| ~ element(X1,powerset(powerset(sK62)))
| ~ subset(sK63(X1),X3)
| ~ in(X3,X1)
| sK63(X1) = X3
| empty_set = X1 ),
inference(cnf_transformation,[],[f1201]) ).
fof(f1719,plain,
! [X1] :
( ~ sP8
| ~ in(sK62,omega)
| ~ element(X1,powerset(powerset(sK62)))
| in(sK63(X1),X1)
| empty_set = X1 ),
inference(cnf_transformation,[],[f1201]) ).
fof(f1720,plain,
( ~ sP8
| in(succ(sK62),omega) ),
inference(cnf_transformation,[],[f1201]) ).
fof(f1721,plain,
( ~ sP8
| sP5(sK62) ),
inference(cnf_transformation,[],[f1201]) ).
fof(f1723,plain,
( ~ sP7
| element(sK64,powerset(powerset(empty_set))) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1724,plain,
! [X1] :
( ~ sP7
| subset(X1,sK65(X1))
| ~ in(X1,sK64) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1725,plain,
! [X1] :
( ~ sP7
| in(sK65(X1),sK64)
| ~ in(X1,sK64) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1726,plain,
! [X1] :
( ~ sP7
| sK65(X1) != X1
| ~ in(X1,sK64) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1727,plain,
( ~ sP7
| empty_set != sK64 ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1728,plain,
( ~ sP6
| ordinal(sK66) ),
inference(cnf_transformation,[],[f1206]) ).
fof(f1729,plain,
! [X2,X1,X4] :
( ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK66)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(sK67(X2),X4)
| ~ in(X4,X2)
| sK67(X2) = X4
| empty_set = X2 ),
inference(cnf_transformation,[],[f1206]) ).
fof(f1730,plain,
! [X2,X1] :
( ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK66)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| in(sK67(X2),X2)
| empty_set = X2 ),
inference(cnf_transformation,[],[f1206]) ).
fof(f1731,plain,
( ~ sP6
| being_limit_ordinal(sK66) ),
inference(cnf_transformation,[],[f1206]) ).
fof(f1732,plain,
( ~ sP6
| in(sK66,omega) ),
inference(cnf_transformation,[],[f1206]) ).
fof(f1733,plain,
( ~ sP6
| sP4(sK66) ),
inference(cnf_transformation,[],[f1206]) ).
fof(f1734,plain,
( ~ sP6
| empty_set != sK66 ),
inference(cnf_transformation,[],[f1206]) ).
fof(f1735,plain,
! [X0] :
( ~ sP5(X0)
| element(sK68(X0),powerset(powerset(succ(X0)))) ),
inference(cnf_transformation,[],[f1209]) ).
fof(f1736,plain,
! [X2,X0] :
( ~ sP5(X0)
| subset(X2,sK69(X0,X2))
| ~ in(X2,sK68(X0)) ),
inference(cnf_transformation,[],[f1209]) ).
fof(f1737,plain,
! [X2,X0] :
( ~ sP5(X0)
| in(sK69(X0,X2),sK68(X0))
| ~ in(X2,sK68(X0)) ),
inference(cnf_transformation,[],[f1209]) ).
fof(f1738,plain,
! [X2,X0] :
( ~ sP5(X0)
| sK69(X0,X2) != X2
| ~ in(X2,sK68(X0)) ),
inference(cnf_transformation,[],[f1209]) ).
fof(f1739,plain,
! [X0] :
( ~ sP5(X0)
| empty_set != sK68(X0) ),
inference(cnf_transformation,[],[f1209]) ).
fof(f1745,plain,
! [X3,X0,X1] :
( sP6
| sP8
| sP7
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| ~ subset(sK72(X1),X3)
| ~ in(X3,X1)
| sK72(X1) = X3
| empty_set = X1 ),
inference(cnf_transformation,[],[f1214]) ).
fof(f1746,plain,
! [X0,X1] :
( sP6
| sP8
| sP7
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| in(sK72(X1),X1)
| empty_set = X1 ),
inference(cnf_transformation,[],[f1214]) ).
fof(f1747,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(X4,X5),sK73(X0,X1,X2))
| in(ordered_pair(apply(X2,X4),apply(X2,X5)),X1) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1748,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(X4,X5),sK73(X0,X1,X2))
| in(X5,X0) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1749,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(X4,X5),sK73(X0,X1,X2))
| in(X4,X0) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1750,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),sK73(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1751,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| relation(sK73(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1217]) ).
fof(f1752,plain,
! [X2,X0,X1,X4,X12] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK74(X0,X1,X2))
| ~ in(X12,sK78(X0,X1,X4))
| in(ordered_pair(sK77(X0,X1,X4),X12),X1) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1753,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK74(X0,X1,X2))
| in(sK77(X0,X1,X4),sK78(X0,X1,X4)) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1754,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK74(X0,X1,X2))
| sK76(X0,X1,X4) = sK78(X0,X1,X4) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1755,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK74(X0,X1,X2))
| in(sK76(X0,X1,X4),X0) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1756,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK74(X0,X1,X2))
| ordered_pair(sK76(X0,X1,X4),sK77(X0,X1,X4)) = X4 ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1757,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK74(X0,X1,X2))
| in(X4,cartesian_product2(X0,X2)) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1758,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ relation(X1)
| empty(X0)
| in(sK75(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,sK74(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1759,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ relation(X1)
| empty(X0)
| ~ in(ordered_pair(X6,sK75(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,sK74(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1760,plain,
! [X3,X0,X1] :
( ~ in(X3,sK79(X0,X1))
| sK81(X0,X3) = singleton(sK80(X0,X3)) ),
inference(cnf_transformation,[],[f1225]) ).
fof(f1761,plain,
! [X3,X0,X1] :
( ~ in(X3,sK79(X0,X1))
| in(sK80(X0,X3),X0) ),
inference(cnf_transformation,[],[f1225]) ).
fof(f1762,plain,
! [X3,X0,X1] :
( ~ in(X3,sK79(X0,X1))
| ordered_pair(sK80(X0,X3),sK81(X0,X3)) = X3 ),
inference(cnf_transformation,[],[f1225]) ).
fof(f1763,plain,
! [X3,X0,X1] :
( ~ in(X3,sK79(X0,X1))
| in(X3,cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f1225]) ).
fof(f1764,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,sK79(X0,X1)) ),
inference(cnf_transformation,[],[f1225]) ).
fof(f1765,plain,
! [X2,X0] :
( ~ sP10(X0)
| ~ in(X2,sK82(X0))
| sP9(X0,X2) ),
inference(cnf_transformation,[],[f1227]) ).
fof(f1766,plain,
! [X2,X0] :
( ~ sP10(X0)
| ~ sP9(X0,X2)
| in(X2,sK82(X0)) ),
inference(cnf_transformation,[],[f1227]) ).
fof(f1778,plain,
! [X0] :
( ~ ordinal(X0)
| sP10(X0) ),
inference(cnf_transformation,[],[f1113]) ).
fof(f1779,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ~ in(X3,sK87(X0,X1))
| set_difference(sK88(X0,X1,X3),singleton(X0)) = X3 ),
inference(cnf_transformation,[],[f1235]) ).
fof(f1780,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ~ in(X3,sK87(X0,X1))
| in(sK88(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f1235]) ).
fof(f1781,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| ~ in(X3,sK87(X0,X1))
| in(X3,powerset(X0)) ),
inference(cnf_transformation,[],[f1235]) ).
fof(f1782,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,sK87(X0,X1)) ),
inference(cnf_transformation,[],[f1235]) ).
fof(f1783,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK89(X0,X1,X2))
| in(ordered_pair(apply(X2,sK90(X1,X2,X4)),apply(X2,sK91(X1,X2,X4))),X1) ),
inference(cnf_transformation,[],[f1239]) ).
fof(f1784,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK89(X0,X1,X2))
| ordered_pair(sK90(X1,X2,X4),sK91(X1,X2,X4)) = X4 ),
inference(cnf_transformation,[],[f1239]) ).
fof(f1785,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK89(X0,X1,X2))
| in(X4,cartesian_product2(X0,X0)) ),
inference(cnf_transformation,[],[f1239]) ).
fof(f1786,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,sK89(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1239]) ).
fof(f1787,plain,
! [X2,X0] :
( ~ in(X2,sK92(X0))
| ordinal(X2) ),
inference(cnf_transformation,[],[f1242]) ).
fof(f1788,plain,
! [X2,X0] :
( ~ in(X2,sK92(X0))
| in(X2,X0) ),
inference(cnf_transformation,[],[f1242]) ).
fof(f1789,plain,
! [X2,X0] :
( ~ ordinal(X2)
| ~ in(X2,X0)
| in(X2,sK92(X0)) ),
inference(cnf_transformation,[],[f1242]) ).
fof(f1790,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ in(X4,sK93(X1,X2))
| in(relation_image(X2,X4),X1) ),
inference(cnf_transformation,[],[f1245]) ).
fof(f1791,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ in(X4,sK93(X1,X2))
| in(X4,powerset(relation_dom(X2))) ),
inference(cnf_transformation,[],[f1245]) ).
fof(f1792,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,sK93(X1,X2)) ),
inference(cnf_transformation,[],[f1245]) ).
fof(f1793,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ in(X3,sK94(X0,X1))
| in(sK95(X0,X3),X0) ),
inference(cnf_transformation,[],[f1249]) ).
fof(f1794,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ in(X3,sK94(X0,X1))
| sK95(X0,X3) = X3 ),
inference(cnf_transformation,[],[f1249]) ).
fof(f1795,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ in(X3,sK94(X0,X1))
| ordinal(sK95(X0,X3)) ),
inference(cnf_transformation,[],[f1249]) ).
fof(f1796,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ in(X3,sK94(X0,X1))
| in(X3,succ(X1)) ),
inference(cnf_transformation,[],[f1249]) ).
fof(f1797,plain,
! [X3,X0,X1,X4] :
( ~ ordinal(X1)
| ~ in(X4,X0)
| X3 != X4
| ~ ordinal(X4)
| ~ in(X3,succ(X1))
| in(X3,sK94(X0,X1)) ),
inference(cnf_transformation,[],[f1249]) ).
fof(f1798,plain,
! [X3,X0,X1,X5] :
( ~ sP12(X0,X1)
| ~ in(X3,X0)
| ~ in(X5,sK97(X0,X1,X3))
| in(ordered_pair(apply(sK96(X0,X1),X3),X5),X1) ),
inference(cnf_transformation,[],[f1252]) ).
fof(f1799,plain,
! [X3,X0,X1] :
( ~ sP12(X0,X1)
| ~ in(X3,X0)
| in(apply(sK96(X0,X1),X3),sK97(X0,X1,X3)) ),
inference(cnf_transformation,[],[f1252]) ).
fof(f1800,plain,
! [X3,X0,X1] :
( ~ sP12(X0,X1)
| ~ in(X3,X0)
| sK97(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1252]) ).
fof(f1801,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| relation_dom(sK96(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f1252]) ).
fof(f1802,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| function(sK96(X0,X1)) ),
inference(cnf_transformation,[],[f1252]) ).
fof(f1803,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| relation(sK96(X0,X1)) ),
inference(cnf_transformation,[],[f1252]) ).
fof(f1812,plain,
! [X3,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| in(sK104(X1,X3,X4),X4)
| ~ in(X3,X4)
| sK103(X0,X1) != X4
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(cnf_transformation,[],[f1256]) ).
fof(f1813,plain,
! [X3,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(ordered_pair(X3,sK104(X1,X3,X4)),X1)
| ~ in(X3,X4)
| sK103(X0,X1) != X4
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(cnf_transformation,[],[f1256]) ).
fof(f1814,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| in(sK103(X0,X1),X0)
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(cnf_transformation,[],[f1256]) ).
fof(f1819,plain,
! [X2,X0,X4] :
( singleton(sK109(X0)) != X4
| sP13(X0)
| ~ in(X2,X0)
| singleton(X2) = apply(sK108(X0),X2) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f1821,plain,
! [X0,X4] :
( singleton(sK109(X0)) != X4
| sP13(X0)
| relation_dom(sK108(X0)) = X0 ),
inference(cnf_transformation,[],[f1260]) ).
fof(f1823,plain,
! [X0,X4] :
( singleton(sK109(X0)) != X4
| sP13(X0)
| function(sK108(X0)) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f1825,plain,
! [X0,X4] :
( singleton(sK109(X0)) != X4
| sP13(X0)
| relation(sK108(X0)) ),
inference(cnf_transformation,[],[f1260]) ).
fof(f1827,plain,
( ~ sP15
| ordinal(sK110) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f1828,plain,
! [X2,X1,X4] :
( ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK110)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(sK111(X2),X4)
| ~ in(X4,X2)
| sK111(X2) = X4
| empty_set = X2 ),
inference(cnf_transformation,[],[f1262]) ).
fof(f1829,plain,
! [X2,X1] :
( ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK110)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| in(sK111(X2),X2)
| empty_set = X2 ),
inference(cnf_transformation,[],[f1262]) ).
fof(f1830,plain,
( ~ sP15
| in(sK110,omega) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f1831,plain,
( ~ sP15
| sP14(sK110) ),
inference(cnf_transformation,[],[f1262]) ).
fof(f1837,plain,
! [X3,X0,X1] :
( sP15
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| ~ subset(sK114(X1),X3)
| ~ in(X3,X1)
| sK114(X1) = X3
| empty_set = X1 ),
inference(cnf_transformation,[],[f1267]) ).
fof(f1838,plain,
! [X0,X1] :
( sP15
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| in(sK114(X1),X1)
| empty_set = X1 ),
inference(cnf_transformation,[],[f1267]) ).
fof(f1839,plain,
! [X2,X0] :
( ~ in(X2,X0)
| singleton(X2) = apply(sK115(X0),X2) ),
inference(cnf_transformation,[],[f1268]) ).
fof(f1840,plain,
! [X0] : relation_dom(sK115(X0)) = X0,
inference(cnf_transformation,[],[f1268]) ).
fof(f1841,plain,
! [X0] : function(sK115(X0)),
inference(cnf_transformation,[],[f1268]) ).
fof(f1842,plain,
! [X0] : relation(sK115(X0)),
inference(cnf_transformation,[],[f1268]) ).
fof(f1843,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f1270]) ).
fof(f1844,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f1270]) ).
fof(f1846,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f359]) ).
fof(f1847,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f649]) ).
fof(f1848,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f1272]) ).
fof(f1849,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f1272]) ).
fof(f1850,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,[],[f1272]) ).
fof(f1851,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
inference(cnf_transformation,[],[f651]) ).
fof(f1852,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng_restriction(X0,X1),X1) ),
inference(cnf_transformation,[],[f652]) ).
fof(f1853,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
inference(cnf_transformation,[],[f653]) ).
fof(f1854,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
inference(cnf_transformation,[],[f654]) ).
fof(f1855,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f654]) ).
fof(f1856,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
inference(cnf_transformation,[],[f655]) ).
fof(f1857,plain,
! [X2,X3,X0,X1] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(cnf_transformation,[],[f657]) ).
fof(f1859,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| subset(relation_rng(X2),X1) ),
inference(cnf_transformation,[],[f659]) ).
fof(f1860,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| subset(relation_dom(X2),X0) ),
inference(cnf_transformation,[],[f659]) ).
fof(f1861,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f660]) ).
fof(f1862,plain,
! [X0,X5] :
( in(X5,sK116(X0))
| are_equipotent(X5,sK116(X0))
| ~ subset(X5,sK116(X0)) ),
inference(cnf_transformation,[],[f1273]) ).
fof(f1863,plain,
! [X0,X4] :
( ~ in(X4,sK116(X0))
| in(powerset(X4),sK116(X0)) ),
inference(cnf_transformation,[],[f1273]) ).
fof(f1864,plain,
! [X2,X3,X0] :
( ~ subset(X3,X2)
| ~ in(X2,sK116(X0))
| in(X3,sK116(X0)) ),
inference(cnf_transformation,[],[f1273]) ).
fof(f1865,plain,
! [X0] : in(X0,sK116(X0)),
inference(cnf_transformation,[],[f1273]) ).
fof(f1866,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X0,X1)
| finite(X0) ),
inference(cnf_transformation,[],[f664]) ).
fof(f1867,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,[],[f665]) ).
fof(f1868,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(sK117(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1276]) ).
fof(f1869,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(ordered_pair(sK117(X0,X1,X2),X0),X2) ),
inference(cnf_transformation,[],[f1276]) ).
fof(f1870,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(sK117(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[],[f1276]) ).
fof(f1872,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f667]) ).
fof(f1873,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
inference(cnf_transformation,[],[f669]) ).
fof(f1874,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(cnf_transformation,[],[f670]) ).
fof(f1875,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_dom(X1))
| subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ),
inference(cnf_transformation,[],[f672]) ).
fof(f1876,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_image(X0,relation_dom(X0)) ),
inference(cnf_transformation,[],[f673]) ).
fof(f1877,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_rng(X1))
| relation_image(X1,relation_inverse_image(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f675]) ).
fof(f1878,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,[],[f677]) ).
fof(f1880,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,[],[f679]) ).
fof(f1881,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0)) ),
inference(cnf_transformation,[],[f680]) ).
fof(f1882,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(sK118(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1279]) ).
fof(f1883,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(ordered_pair(X0,sK118(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f1279]) ).
fof(f1884,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(sK118(X0,X1,X2),relation_rng(X2)) ),
inference(cnf_transformation,[],[f1279]) ).
fof(f1886,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f682]) ).
fof(f1887,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,[],[f684]) ).
fof(f1888,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f1281]) ).
fof(f1889,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,X2) ),
inference(cnf_transformation,[],[f1281]) ).
fof(f1890,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f1281]) ).
fof(f1891,plain,
! [X0,X1] :
( ~ relation(X1)
| empty_set != relation_inverse_image(X1,X0)
| ~ subset(X0,relation_rng(X1))
| empty_set = X0 ),
inference(cnf_transformation,[],[f687]) ).
fof(f1892,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ subset(X0,X1)
| subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
inference(cnf_transformation,[],[f689]) ).
fof(f1894,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ),
inference(cnf_transformation,[],[f692]) ).
fof(f1895,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_dom_restriction(relation_rng_restriction(X0,X1),X0) ),
inference(cnf_transformation,[],[f693]) ).
fof(f1897,plain,
! [X3,X0,X1] :
( ~ finite(X0)
| ~ element(X1,powerset(powerset(X0)))
| ~ subset(sK119(X1),X3)
| ~ in(X3,X1)
| sK119(X1) = X3
| empty_set = X1 ),
inference(cnf_transformation,[],[f1282]) ).
fof(f1898,plain,
! [X0,X1] :
( ~ finite(X0)
| ~ element(X1,powerset(powerset(X0)))
| in(sK119(X1),X1)
| empty_set = X1 ),
inference(cnf_transformation,[],[f1282]) ).
fof(f1899,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_restriction(X1,X0) = relation_rng_restriction(X0,relation_dom_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f696]) ).
fof(f1900,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f698]) ).
fof(f1901,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f698]) ).
fof(f1902,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f700]) ).
fof(f1903,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f702]) ).
fof(f1904,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f402]) ).
fof(f1907,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_field(relation_restriction(X1,X0)),X0) ),
inference(cnf_transformation,[],[f705]) ).
fof(f1908,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ),
inference(cnf_transformation,[],[f705]) ).
fof(f1909,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,[],[f1284]) ).
fof(f1910,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,[],[f1284]) ).
fof(f1911,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,[],[f1284]) ).
fof(f1912,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,[],[f709]) ).
fof(f1913,plain,
! [X0,X1] :
( ~ epsilon_transitive(X0)
| ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f711]) ).
fof(f1914,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(cnf_transformation,[],[f712]) ).
fof(f1915,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
inference(cnf_transformation,[],[f713]) ).
fof(f1916,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,[],[f715]) ).
fof(f1917,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,[],[f716]) ).
fof(f1918,plain,
! [X2,X0,X1,X6] :
( ~ relation_of2_as_subset(X2,X1,X0)
| ~ in(ordered_pair(sK121(X1,X2),X6),X2)
| relation_dom_as_subset(X1,X0,X2) = X1 ),
inference(cnf_transformation,[],[f1287]) ).
fof(f1919,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X1,X0)
| in(sK121(X1,X2),X1)
| relation_dom_as_subset(X1,X0,X2) = X1 ),
inference(cnf_transformation,[],[f1287]) ).
fof(f1920,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X2,X1,X0)
| relation_dom_as_subset(X1,X0,X2) != X1
| in(ordered_pair(X3,sK120(X2,X3)),X2)
| ~ in(X3,X1) ),
inference(cnf_transformation,[],[f1287]) ).
fof(f1921,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ reflexive(X1)
| reflexive(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f719]) ).
fof(f1922,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,[],[f721]) ).
fof(f1923,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(cnf_transformation,[],[f723]) ).
fof(f1924,plain,
! [X2,X0,X1,X6] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(ordered_pair(X6,sK123(X1,X2)),X2)
| relation_rng_as_subset(X0,X1,X2) = X1 ),
inference(cnf_transformation,[],[f1290]) ).
fof(f1925,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| in(sK123(X1,X2),X1)
| relation_rng_as_subset(X0,X1,X2) = X1 ),
inference(cnf_transformation,[],[f1290]) ).
fof(f1926,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_rng_as_subset(X0,X1,X2) != X1
| in(ordered_pair(sK122(X2,X3),X3),X2)
| ~ in(X3,X1) ),
inference(cnf_transformation,[],[f1290]) ).
fof(f1927,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ connected(X1)
| connected(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f726]) ).
fof(f1928,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
inference(cnf_transformation,[],[f728]) ).
fof(f1929,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ transitive(X1)
| transitive(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f730]) ).
fof(f1930,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(X0,X1)
| subset(relation_rng(X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f732]) ).
fof(f1931,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(X0,X1)
| subset(relation_dom(X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f732]) ).
fof(f1932,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ antisymmetric(X1)
| antisymmetric(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f734]) ).
fof(f1933,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_orders(X1,X0)
| well_ordering(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f736]) ).
fof(f1934,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_orders(X1,X0)
| relation_field(relation_restriction(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f736]) ).
fof(f1935,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ finite(relation_dom(X0))
| finite(relation_rng(X0)) ),
inference(cnf_transformation,[],[f738]) ).
fof(f1936,plain,
! [X0] : well_orders(sK124(X0),X0),
inference(cnf_transformation,[],[f1291]) ).
fof(f1937,plain,
! [X0] : relation(sK124(X0)),
inference(cnf_transformation,[],[f1291]) ).
fof(f1938,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f739]) ).
fof(f1939,plain,
! [X0] :
( empty(X0)
| function(sK126(X0))
| empty_set = sK125(X0) ),
inference(cnf_transformation,[],[f1292]) ).
fof(f1940,plain,
! [X0] :
( empty(X0)
| relation(sK126(X0))
| empty_set = sK125(X0) ),
inference(cnf_transformation,[],[f1292]) ).
fof(f1941,plain,
! [X3,X0] :
( empty(X0)
| ~ in(X3,X0)
| in(apply(sK126(X0),X3),X3)
| empty_set = sK125(X0) ),
inference(cnf_transformation,[],[f1292]) ).
fof(f1942,plain,
! [X0] :
( empty(X0)
| relation_dom(sK126(X0)) = X0
| empty_set = sK125(X0) ),
inference(cnf_transformation,[],[f1292]) ).
fof(f1943,plain,
! [X0] :
( empty(X0)
| function(sK126(X0))
| in(sK125(X0),X0) ),
inference(cnf_transformation,[],[f1292]) ).
fof(f1944,plain,
! [X0] :
( empty(X0)
| relation(sK126(X0))
| in(sK125(X0),X0) ),
inference(cnf_transformation,[],[f1292]) ).
fof(f1945,plain,
! [X3,X0] :
( empty(X0)
| ~ in(X3,X0)
| in(apply(sK126(X0),X3),X3)
| in(sK125(X0),X0) ),
inference(cnf_transformation,[],[f1292]) ).
fof(f1946,plain,
! [X0] :
( empty(X0)
| relation_dom(sK126(X0)) = X0
| in(sK125(X0),X0) ),
inference(cnf_transformation,[],[f1292]) ).
fof(f1947,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f742]) ).
fof(f1948,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f1293]) ).
fof(f1949,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) ),
inference(cnf_transformation,[],[f1293]) ).
fof(f1950,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f434]) ).
fof(f1951,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f435]) ).
fof(f1952,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_field(X2)) ),
inference(cnf_transformation,[],[f745]) ).
fof(f1953,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f745]) ).
fof(f1954,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(X1,X0)
| closed_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f1294]) ).
fof(f1955,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0) ),
inference(cnf_transformation,[],[f1294]) ).
fof(f1956,plain,
! [X0] :
( in(sK127(X0),X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f1295]) ).
fof(f1957,plain,
! [X0] :
( ~ subset(sK127(X0),X0)
| ~ ordinal(sK127(X0))
| ordinal(X0) ),
inference(cnf_transformation,[],[f1295]) ).
fof(f1958,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_founded_relation(X1)
| well_founded_relation(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f749]) ).
fof(f1959,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ordinal(sK128(X0))
| empty_set = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1296]) ).
fof(f1960,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X3)
| ~ in(X3,X0)
| ordinal_subset(sK128(X0),X3)
| empty_set = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1296]) ).
fof(f1961,plain,
! [X0,X1] :
( ~ ordinal(X1)
| in(sK128(X0),X0)
| empty_set = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1296]) ).
fof(f1962,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ well_ordering(X1)
| well_ordering(relation_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f753]) ).
fof(f1963,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal_subset(succ(X0),X1) ),
inference(cnf_transformation,[],[f1297]) ).
fof(f1964,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ ordinal_subset(succ(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f1297]) ).
fof(f1965,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f755]) ).
fof(f1966,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(X0,X1)
| X1 = X3 ),
inference(cnf_transformation,[],[f756]) ).
fof(f1967,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f756]) ).
fof(f1970,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK129(X0,X1),X0)
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1301]) ).
fof(f1971,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| sK129(X0,X1) != apply(X1,sK129(X0,X1))
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1301]) ).
fof(f1972,plain,
! [X0,X1] :
( ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(cnf_transformation,[],[f759]) ).
fof(f1973,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f447]) ).
fof(f1974,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f760]) ).
fof(f1975,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f760]) ).
fof(f1976,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1302]) ).
fof(f1977,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f1302]) ).
fof(f1979,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f1303]) ).
fof(f1980,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f1305]) ).
fof(f1981,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f1305]) ).
fof(f1982,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f1305]) ).
fof(f1983,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ subset(X0,relation_field(X1))
| ~ well_ordering(X1)
| relation_field(relation_restriction(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f762]) ).
fof(f1984,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f453]) ).
fof(f1985,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f1307]) ).
fof(f1988,plain,
! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f763]) ).
fof(f1989,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f458]) ).
fof(f1990,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,X1)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f1308]) ).
fof(f1991,plain,
! [X0,X1] :
( in(sK130(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1308]) ).
fof(f1992,plain,
! [X0,X1] :
( in(sK130(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1308]) ).
fof(f1993,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f765]) ).
fof(f1994,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f461]) ).
fof(f1995,plain,
! [X2,X0] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X2)
| ~ in(X2,X0)
| in(succ(X2),X0) ),
inference(cnf_transformation,[],[f1311]) ).
fof(f1996,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK131(X0))
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1311]) ).
fof(f1997,plain,
! [X0] :
( ~ ordinal(X0)
| in(sK131(X0),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1311]) ).
fof(f1998,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(succ(sK131(X0)),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1311]) ).
fof(f1999,plain,
! [X2,X0] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| succ(X2) != X0
| ~ ordinal(X2) ),
inference(cnf_transformation,[],[f1312]) ).
fof(f2000,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK132(X0))
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1312]) ).
fof(f2001,plain,
! [X0] :
( ~ ordinal(X0)
| succ(sK132(X0)) = X0
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1312]) ).
fof(f2002,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| ~ disjoint(X1,X2)
| subset(X1,subset_complement(X0,X2)) ),
inference(cnf_transformation,[],[f1313]) ).
fof(f2003,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| ~ subset(X1,subset_complement(X0,X2))
| disjoint(X1,X2) ),
inference(cnf_transformation,[],[f1313]) ).
fof(f2004,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ),
inference(cnf_transformation,[],[f770]) ).
fof(f2005,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset(interior(X0,X1),X1) ),
inference(cnf_transformation,[],[f771]) ).
fof(f2006,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,[],[f1316]) ).
fof(f2007,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| element(sK133(X0,X1,X2),powerset(the_carrier(X0)))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f1316]) ).
fof(f2008,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| subset(X1,sK133(X0,X1,X2))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f1316]) ).
fof(f2009,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| closed_subset(sK133(X0,X1,X2),X0)
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f1316]) ).
fof(f2010,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| ~ in(X2,sK133(X0,X1,X2))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f1316]) ).
fof(f2011,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ),
inference(cnf_transformation,[],[f774]) ).
fof(f2013,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,[],[f1318]) ).
fof(f2014,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,[],[f1318]) ).
fof(f2015,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,[],[f1318]) ).
fof(f2016,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,[],[f779]) ).
fof(f2017,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| empty_set != complements_of_subsets(X0,X1)
| empty_set = X1 ),
inference(cnf_transformation,[],[f781]) ).
fof(f2018,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(cnf_transformation,[],[f782]) ).
fof(f2019,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,[],[f784]) ).
fof(f2020,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,[],[f786]) ).
fof(f2021,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset(X1,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f787]) ).
fof(f2022,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,[],[f789]) ).
fof(f2023,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f480]) ).
fof(f2024,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,[],[f791]) ).
fof(f2025,plain,
! [X0] :
( ~ ordinal(X0)
| connected(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f792]) ).
fof(f2026,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f1319]) ).
fof(f2027,plain,
! [X0,X1] :
( in(sK134(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1319]) ).
fof(f2028,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,[],[f795]) ).
fof(f2029,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| topstr_closure(X0,X1) = X1 ),
inference(cnf_transformation,[],[f797]) ).
fof(f2030,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,[],[f799]) ).
fof(f2031,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ antisymmetric(X0)
| antisymmetric(X1) ),
inference(cnf_transformation,[],[f799]) ).
fof(f2032,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ connected(X0)
| connected(X1) ),
inference(cnf_transformation,[],[f799]) ).
fof(f2033,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ transitive(X0)
| transitive(X1) ),
inference(cnf_transformation,[],[f799]) ).
fof(f2034,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation_isomorphism(X0,X1,X2)
| ~ reflexive(X0)
| reflexive(X1) ),
inference(cnf_transformation,[],[f799]) ).
fof(f2040,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,[],[f1326]) ).
fof(f2042,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,[],[f1326]) ).
fof(f2044,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ sP16(X0,sK135(X0,X1),sK136(X0,X1),X1)
| sK136(X0,X1) = apply(X1,sK135(X0,X1))
| relation_dom(X1) != relation_rng(X0)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f1326]) ).
fof(f2045,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ sP16(X0,sK135(X0,X1),sK136(X0,X1),X1)
| in(sK135(X0,X1),relation_rng(X0))
| relation_dom(X1) != relation_rng(X0)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f1326]) ).
fof(f2046,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ sP16(X0,sK135(X0,X1),sK136(X0,X1),X1)
| sK135(X0,X1) != apply(X0,sK136(X0,X1))
| ~ in(sK136(X0,X1),relation_dom(X0))
| relation_dom(X1) != relation_rng(X0)
| function_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f1326]) ).
fof(f2047,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(cnf_transformation,[],[f803]) ).
fof(f2048,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,[],[f805]) ).
fof(f2049,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0)) ),
inference(cnf_transformation,[],[f807]) ).
fof(f2050,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(cnf_transformation,[],[f807]) ).
fof(f2051,plain,
! [X0] :
( ~ relation(X0)
| in(ordered_pair(sK137(X0),sK138(X0)),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f1327]) ).
fof(f2052,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,[],[f811]) ).
fof(f2053,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,[],[f811]) ).
fof(f2054,plain,
one_sorted_str(sK139),
inference(cnf_transformation,[],[f1328]) ).
fof(f2055,plain,
~ empty_carrier(sK139),
inference(cnf_transformation,[],[f1328]) ).
fof(f2056,plain,
element(sK140,powerset(powerset(the_carrier(sK139)))),
inference(cnf_transformation,[],[f1328]) ).
fof(f2057,plain,
empty_set = sK140,
inference(cnf_transformation,[],[f1328]) ).
fof(f2058,plain,
is_a_cover_of_carrier(sK139,sK140),
inference(cnf_transformation,[],[f1328]) ).
fof(f2059,plain,
! [X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| is_well_founded_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1329]) ).
fof(f2060,plain,
! [X0] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1329]) ).
fof(f2061,plain,
! [X0] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f501]) ).
fof(f2062,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f502]) ).
fof(f2063,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f502]) ).
fof(f2064,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f815]) ).
fof(f2065,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| one_to_one(function_inverse(X0)) ),
inference(cnf_transformation,[],[f817]) ).
fof(f2066,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(cnf_transformation,[],[f819]) ).
fof(f2067,plain,
! [X0] :
( ~ relation(X0)
| empty_set != relation_rng(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f821]) ).
fof(f2068,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) != empty_set
| empty_set = X0 ),
inference(cnf_transformation,[],[f821]) ).
fof(f2069,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) != empty_set
| empty_set = relation_rng(X0) ),
inference(cnf_transformation,[],[f1330]) ).
fof(f2070,plain,
! [X0] :
( ~ relation(X0)
| empty_set != relation_rng(X0)
| relation_dom(X0) = empty_set ),
inference(cnf_transformation,[],[f1330]) ).
fof(f2071,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) != X0
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f1331]) ).
fof(f2072,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(cnf_transformation,[],[f1331]) ).
fof(f2075,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| in(sK141(X1,X2),relation_dom(X1))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) = X1 ),
inference(cnf_transformation,[],[f1335]) ).
fof(f2076,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| apply(X2,sK141(X1,X2)) != apply(X1,sK141(X1,X2))
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) = X1 ),
inference(cnf_transformation,[],[f1335]) ).
fof(f2077,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f510]) ).
fof(f2078,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,[],[f826]) ).
fof(f2079,plain,
! [X0] :
( ~ ordinal(X0)
| well_founded_relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f827]) ).
fof(f2080,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f828]) ).
fof(f2081,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,[],[f830]) ).
fof(f2082,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f516]) ).
fof(f2083,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f516]) ).
fof(f2084,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ),
inference(cnf_transformation,[],[f832]) ).
fof(f2085,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,[],[f1337]) ).
fof(f2086,plain,
! [X2,X3,X0,X1] :
( ~ relation(X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f1337]) ).
fof(f2087,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,[],[f1337]) ).
fof(f2088,plain,
! [X0,X1] : pair_second(ordered_pair(X0,X1)) = X1,
inference(cnf_transformation,[],[f520]) ).
fof(f2089,plain,
! [X0,X1] : pair_first(ordered_pair(X0,X1)) = X0,
inference(cnf_transformation,[],[f520]) ).
fof(f2090,plain,
! [X0] :
( ~ ordinal(X0)
| well_ordering(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f834]) ).
fof(f2091,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f523]) ).
fof(f2092,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[],[f1338]) ).
fof(f2093,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1338]) ).
fof(f2094,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f1340]) ).
fof(f2095,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f1340]) ).
fof(f2096,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,[],[f1340]) ).
fof(f2097,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_dom_restriction(X1,X0),X1) ),
inference(cnf_transformation,[],[f836]) ).
fof(f2098,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| apply(X2,X0) = X1 ),
inference(cnf_transformation,[],[f1342]) ).
fof(f2100,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,[],[f1342]) ).
fof(f2101,plain,
! [X0] :
( ~ relation(X0)
| ~ well_orders(X0,relation_field(X0))
| well_ordering(X0) ),
inference(cnf_transformation,[],[f1343]) ).
fof(f2102,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| well_orders(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1343]) ).
fof(f2103,plain,
! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1) ),
inference(cnf_transformation,[],[f841]) ).
fof(f2104,plain,
! [X2,X0,X1] :
( singleton(X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f842]) ).
fof(f2105,plain,
! [X0,X1] :
( ~ relation(X1)
| set_intersection2(relation_dom(X1),X0) = relation_dom(relation_dom_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f843]) ).
fof(f2106,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f844]) ).
fof(f2107,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
inference(cnf_transformation,[],[f845]) ).
fof(f2108,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
inference(cnf_transformation,[],[f846]) ).
fof(f2109,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f536]) ).
fof(f2111,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,[],[f848]) ).
fof(f2113,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,[],[f848]) ).
fof(f2114,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,[],[f848]) ).
fof(f2116,plain,
! [X2,X0,X1] :
( singleton(X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f849]) ).
fof(f2117,plain,
! [X3,X0,X1] :
( ~ in(X3,sK142(X1))
| ~ in(X3,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1344]) ).
fof(f2118,plain,
! [X0,X1] :
( in(sK142(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1344]) ).
fof(f2119,plain,
! [X0,X1] :
( in(sK143(X0,X1),X0)
| in(sK143(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1346]) ).
fof(f2120,plain,
! [X0,X1] :
( ~ in(sK143(X0,X1),X0)
| ~ in(sK143(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1346]) ).
fof(f2121,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f852]) ).
fof(f2122,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f853]) ).
fof(f2123,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| sP17(sK144(X0,X1),sK146(X0,X1),X1) ),
inference(cnf_transformation,[],[f1348]) ).
fof(f2124,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| in(sK144(X0,X1),X0) ),
inference(cnf_transformation,[],[f1348]) ).
fof(f2125,plain,
! [X0,X1,X6] :
( ~ sP18(X0,X1)
| ~ in(X6,sK147(X0,X1))
| in(ordered_pair(sK145(X0,X1),X6),X1) ),
inference(cnf_transformation,[],[f1348]) ).
fof(f2126,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| in(sK145(X0,X1),sK147(X0,X1)) ),
inference(cnf_transformation,[],[f1348]) ).
fof(f2127,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| sK144(X0,X1) = sK147(X0,X1) ),
inference(cnf_transformation,[],[f1348]) ).
fof(f2129,plain,
! [X0,X1] :
( ~ sP18(X0,X1)
| sK145(X0,X1) != sK146(X0,X1) ),
inference(cnf_transformation,[],[f1348]) ).
fof(f2133,plain,
! [X3,X0,X1,X9] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ~ in(X3,sK149(X0,X1))
| ~ in(X9,sK152(X0,X1,X3))
| in(ordered_pair(X3,X9),X1) ),
inference(cnf_transformation,[],[f1354]) ).
fof(f2134,plain,
! [X3,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ~ in(X3,sK149(X0,X1))
| in(X3,sK152(X0,X1,X3)) ),
inference(cnf_transformation,[],[f1354]) ).
fof(f2135,plain,
! [X3,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ~ in(X3,sK149(X0,X1))
| sK151(X0,X1,X3) = sK152(X0,X1,X3) ),
inference(cnf_transformation,[],[f1354]) ).
fof(f2136,plain,
! [X3,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ~ in(X3,sK149(X0,X1))
| in(sK151(X0,X1,X3),X0) ),
inference(cnf_transformation,[],[f1354]) ).
fof(f2141,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK155(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f1357]) ).
fof(f2142,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f1357]) ).
fof(f2143,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK153(X0,X1),X1)
| in(ordered_pair(sK154(X0,X1),sK153(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f1357]) ).
fof(f2144,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK153(X0,X1),X1)
| ~ in(ordered_pair(X3,sK153(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f1357]) ).
fof(f2145,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK158(X0,X5)),X0) ),
inference(cnf_transformation,[],[f1360]) ).
fof(f2146,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f1360]) ).
fof(f2147,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK156(X0,X1),X1)
| in(ordered_pair(sK156(X0,X1),sK157(X0,X1)),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f1360]) ).
fof(f2148,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK156(X0,X1),X1)
| ~ in(ordered_pair(sK156(X0,X1),X3),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f1360]) ).
fof(f2150,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK159(X0,X1),sK160(X0,X1)),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1363]) ).
fof(f2151,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK159(X0,X1),sK160(X0,X1)),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1363]) ).
fof(f2154,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK161(X0,X1),sK162(X0,X1)),X0)
| in(ordered_pair(sK161(X0,X1),sK162(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1366]) ).
fof(f2155,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK161(X0,X1),sK162(X0,X1)),X0)
| ~ in(ordered_pair(sK161(X0,X1),sK162(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1366]) ).
fof(f2156,plain,
! [X0,X4] :
( ~ relation(X0)
| ordered_pair(sK164(X4),sK165(X4)) = X4
| ~ in(X4,X0) ),
inference(cnf_transformation,[],[f1369]) ).
fof(f2157,plain,
! [X2,X3,X0] :
( ordered_pair(X2,X3) != sK163(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f1369]) ).
fof(f2158,plain,
! [X0] :
( in(sK163(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[],[f1369]) ).
fof(f2159,plain,
! [X0,X6,X4,X5] :
( ~ function(X0)
| ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| X5 = X6 ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2160,plain,
! [X0] :
( in(ordered_pair(sK166(X0),sK168(X0)),X0)
| function(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2161,plain,
! [X0] :
( in(ordered_pair(sK166(X0),sK167(X0)),X0)
| function(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2162,plain,
! [X0] :
( sK167(X0) != sK168(X0)
| function(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2163,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f863]) ).
fof(f2164,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1374]) ).
fof(f2165,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| connected(X0) ),
inference(cnf_transformation,[],[f1374]) ).
fof(f2166,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1374]) ).
fof(f2167,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| transitive(X0) ),
inference(cnf_transformation,[],[f1374]) ).
fof(f2168,plain,
! [X0] :
( ~ relation(X0)
| ~ well_ordering(X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f1374]) ).
fof(f2169,plain,
! [X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ),
inference(cnf_transformation,[],[f1374]) ).
fof(f2170,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f865]) ).
fof(f2171,plain,
relation(empty_set),
inference(cnf_transformation,[],[f240]) ).
fof(f2174,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f1377]) ).
fof(f2175,plain,
! [X0] :
( in(sK169(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f1377]) ).
fof(f2176,plain,
! [X0] :
( ~ sP20(X0)
| sP19(sK172(X0),X0) ),
inference(cnf_transformation,[],[f1380]) ).
fof(f2177,plain,
! [X0] :
( ~ sP20(X0)
| sK170(X0) = sK172(X0) ),
inference(cnf_transformation,[],[f1380]) ).
fof(f2178,plain,
! [X0] :
( ~ sP20(X0)
| sK174(X0) = singleton(sK173(X0)) ),
inference(cnf_transformation,[],[f1380]) ).
fof(f2179,plain,
! [X0] :
( ~ sP20(X0)
| in(sK173(X0),X0) ),
inference(cnf_transformation,[],[f1380]) ).
fof(f2180,plain,
! [X0] :
( ~ sP20(X0)
| sK171(X0) = ordered_pair(sK173(X0),sK174(X0)) ),
inference(cnf_transformation,[],[f1380]) ).
fof(f2181,plain,
! [X0] :
( ~ sP20(X0)
| sK170(X0) = sK171(X0) ),
inference(cnf_transformation,[],[f1380]) ).
fof(f2182,plain,
! [X0] :
( ~ sP20(X0)
| sK171(X0) != sK172(X0) ),
inference(cnf_transformation,[],[f1380]) ).
fof(f2186,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK177(X0,X1))
| sK180(X0,X3) = singleton(sK179(X0,X3)) ),
inference(cnf_transformation,[],[f1386]) ).
fof(f2187,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK177(X0,X1))
| in(sK179(X0,X3),X0) ),
inference(cnf_transformation,[],[f1386]) ).
fof(f2188,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK177(X0,X1))
| ordered_pair(sK179(X0,X3),sK180(X0,X3)) = X3 ),
inference(cnf_transformation,[],[f1386]) ).
fof(f2189,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK177(X0,X1))
| sK178(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1386]) ).
fof(f2190,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK177(X0,X1))
| in(sK178(X0,X1,X3),cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f1386]) ).
fof(f2191,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,sK177(X0,X1)) ),
inference(cnf_transformation,[],[f1386]) ).
fof(f2197,plain,
! [X2,X0] :
( sP21(X0)
| ~ in(X2,sK184(X0))
| singleton(sK185(X0,X2)) = X2 ),
inference(cnf_transformation,[],[f1391]) ).
fof(f2198,plain,
! [X2,X0] :
( sP21(X0)
| ~ in(X2,sK184(X0))
| in(sK185(X0,X2),X0) ),
inference(cnf_transformation,[],[f1391]) ).
fof(f2202,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f1394]) ).
fof(f2204,plain,
! [X0,X1] :
( in(sK186(X0,X1),X1)
| sK186(X0,X1) = X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f1394]) ).
fof(f2205,plain,
! [X0,X1] :
( ~ in(sK186(X0,X1),X1)
| sK186(X0,X1) != X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f1394]) ).
fof(f2206,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f399]) ).
fof(f2207,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f555]) ).
fof(f2208,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f871]) ).
fof(f2209,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X1,X0)) ),
inference(cnf_transformation,[],[f872]) ).
fof(f2210,plain,
! [X0,X1] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f873]) ).
fof(f2211,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f875]) ).
fof(f2212,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f1398]) ).
fof(f2213,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f1398]) ).
fof(f2214,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f1398]) ).
fof(f2215,plain,
! [X2,X0,X1] :
( in(sK187(X0,X1,X2),X2)
| in(sK187(X0,X1,X2),X1)
| in(sK187(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1398]) ).
fof(f2216,plain,
! [X2,X0,X1] :
( ~ in(sK187(X0,X1,X2),X2)
| ~ in(sK187(X0,X1,X2),X1)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1398]) ).
fof(f2217,plain,
! [X2,X0,X1] :
( ~ in(sK187(X0,X1,X2),X2)
| ~ in(sK187(X0,X1,X2),X0)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1398]) ).
fof(f2218,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f57]) ).
fof(f2219,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f33]) ).
fof(f2220,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f876]) ).
fof(f2221,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f1399]) ).
fof(f2222,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f1399]) ).
fof(f2223,plain,
! [X2,X0,X1] :
( ~ sP23(X0,X1,X2)
| topstr_closure(X2,X1) != X0
| sP22(X2,X1,X0) ),
inference(cnf_transformation,[],[f1401]) ).
fof(f2224,plain,
! [X2,X0,X1] :
( ~ sP23(X0,X1,X2)
| ~ sP22(X2,X1,X0)
| topstr_closure(X2,X1) = X0 ),
inference(cnf_transformation,[],[f1401]) ).
fof(f2236,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(the_carrier(X0)))
| sP23(X2,X1,X0) ),
inference(cnf_transformation,[],[f1134]) ).
fof(f2237,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f879]) ).
fof(f2238,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f879]) ).
fof(f2239,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f881]) ).
fof(f2240,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| function(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f883]) ).
fof(f2242,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f884]) ).
fof(f2243,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,[],[f1409]) ).
fof(f2244,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,[],[f1409]) ).
fof(f2245,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,[],[f1409]) ).
fof(f2246,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),X2)
| in(ordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),X1)
| relation_rng_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1409]) ).
fof(f2247,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),X2)
| in(sK192(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1409]) ).
fof(f2248,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),X1)
| ~ in(sK192(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1409]) ).
fof(f2249,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1410]) ).
fof(f2250,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1410]) ).
fof(f2252,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2253,plain,
! [X0,X1] :
( in(sK193(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2254,plain,
! [X0,X1] :
( ~ in(sK193(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2255,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f1416]) ).
fof(f2256,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f1416]) ).
fof(f2257,plain,
! [X0,X1] :
( in(sK194(X0,X1),X1)
| subset(sK194(X0,X1),X0)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f1416]) ).
fof(f2258,plain,
! [X0,X1] :
( ~ in(sK194(X0,X1),X1)
| ~ subset(sK194(X0,X1),X0)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f1416]) ).
fof(f2259,plain,
! [X0,X1] :
( X0 != X1
| subset(X1,X0) ),
inference(cnf_transformation,[],[f1418]) ).
fof(f2261,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1418]) ).
fof(f2262,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| equipotent(X1,X0) ),
inference(cnf_transformation,[],[f887]) ).
fof(f2263,plain,
! [X0] : equipotent(X0,X0),
inference(cnf_transformation,[],[f557]) ).
fof(f2264,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| relation_rng(sK195(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f1421]) ).
fof(f2265,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| relation_dom(sK195(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f1421]) ).
fof(f2266,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| one_to_one(sK195(X0,X1)) ),
inference(cnf_transformation,[],[f1421]) ).
fof(f2267,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| function(sK195(X0,X1)) ),
inference(cnf_transformation,[],[f1421]) ).
fof(f2268,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| relation(sK195(X0,X1)) ),
inference(cnf_transformation,[],[f1421]) ).
fof(f2269,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,[],[f1421]) ).
fof(f2270,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f482]) ).
fof(f2271,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f455]) ).
fof(f2272,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_difference(X0,X1)) ),
inference(cnf_transformation,[],[f889]) ).
fof(f2279,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f1425]) ).
fof(f2280,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f1425]) ).
fof(f2281,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f1425]) ).
fof(f2282,plain,
! [X2,X0,X1] :
( in(sK196(X0,X1,X2),X2)
| ~ in(sK196(X0,X1,X2),X1)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1425]) ).
fof(f2283,plain,
! [X2,X0,X1] :
( in(sK196(X0,X1,X2),X2)
| in(sK196(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1425]) ).
fof(f2284,plain,
! [X2,X0,X1] :
( ~ in(sK196(X0,X1,X2),X2)
| in(sK196(X0,X1,X2),X1)
| ~ in(sK196(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1425]) ).
fof(f2285,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f893]) ).
fof(f2286,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f895]) ).
fof(f2287,plain,
! [X0] : empty(sK197(X0)),
inference(cnf_transformation,[],[f1426]) ).
fof(f2288,plain,
! [X0] : element(sK197(X0),powerset(X0)),
inference(cnf_transformation,[],[f1426]) ).
fof(f2289,plain,
! [X0] :
( empty(X0)
| ~ empty(sK198(X0)) ),
inference(cnf_transformation,[],[f1427]) ).
fof(f2290,plain,
! [X0] :
( empty(X0)
| element(sK198(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f1427]) ).
fof(f2291,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f206]) ).
fof(f2292,plain,
! [X0] : element(sK199(X0),X0),
inference(cnf_transformation,[],[f1428]) ).
fof(f2293,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(sK200(X0)) ),
inference(cnf_transformation,[],[f1429]) ).
fof(f2294,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| element(sK200(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1429]) ).
fof(f2295,plain,
~ empty_carrier(sK201),
inference(cnf_transformation,[],[f1430]) ).
fof(f2296,plain,
one_sorted_str(sK201),
inference(cnf_transformation,[],[f1430]) ).
fof(f2298,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ~ empty_carrier(X0)
| empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f1431]) ).
fof(f2299,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1431]) ).
fof(f2300,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f902]) ).
fof(f2301,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f903]) ).
fof(f2302,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) ),
inference(cnf_transformation,[],[f904]) ).
fof(f2303,plain,
one_sorted_str(sK202),
inference(cnf_transformation,[],[f1432]) ).
fof(f2304,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f905]) ).
fof(f2305,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| union_of_subsets(X0,X1) = union(X1) ),
inference(cnf_transformation,[],[f906]) ).
fof(f2306,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(union(X0)) ),
inference(cnf_transformation,[],[f907]) ).
fof(f2307,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(union(X0)) ),
inference(cnf_transformation,[],[f907]) ).
fof(f2308,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(union(X0)) ),
inference(cnf_transformation,[],[f907]) ).
fof(f2309,plain,
! [X0] :
( ~ being_limit_ordinal(X0)
| union(X0) = X0 ),
inference(cnf_transformation,[],[f1433]) ).
fof(f2310,plain,
! [X0] :
( union(X0) != X0
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1433]) ).
fof(f2311,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK205(X0,X5),X0) ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2312,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(X5,sK205(X0,X5)) ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2313,plain,
! [X0,X1,X6,X5] :
( union(X0) != X1
| ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,X1) ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2314,plain,
! [X0,X1] :
( in(sK203(X0,X1),X1)
| in(sK204(X0,X1),X0)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2315,plain,
! [X0,X1] :
( in(sK203(X0,X1),X1)
| in(sK203(X0,X1),sK204(X0,X1))
| union(X0) = X1 ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2316,plain,
! [X3,X0,X1] :
( ~ in(sK203(X0,X1),X1)
| ~ in(X3,X0)
| ~ in(sK203(X0,X1),X3)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2324,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(X1,X2)
| ~ in(X4,sK213(X0,X1,X2))
| in(ordered_pair(apply(X2,sK215(X1,X2,X4)),apply(X2,sK216(X1,X2,X4))),X1) ),
inference(cnf_transformation,[],[f1442]) ).
fof(f2325,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(X1,X2)
| ~ in(X4,sK213(X0,X1,X2))
| ordered_pair(sK215(X1,X2,X4),sK216(X1,X2,X4)) = X4 ),
inference(cnf_transformation,[],[f1442]) ).
fof(f2326,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(X1,X2)
| ~ in(X4,sK213(X0,X1,X2))
| sK214(X0,X1,X2,X4) = X4 ),
inference(cnf_transformation,[],[f1442]) ).
fof(f2327,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(X1,X2)
| ~ in(X4,sK213(X0,X1,X2))
| in(sK214(X0,X1,X2,X4),cartesian_product2(X0,X0)) ),
inference(cnf_transformation,[],[f1442]) ).
fof(f2328,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(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,sK213(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1442]) ).
fof(f2329,plain,
! [X2,X0,X1,X4] :
( ~ sP28(X0,X1,X2)
| ~ in(X4,sK217(X0,X1,X2))
| sP27(X2,X1,X4,X0) ),
inference(cnf_transformation,[],[f1445]) ).
fof(f2330,plain,
! [X2,X0,X1,X4] :
( ~ sP28(X0,X1,X2)
| ~ sP27(X2,X1,X4,X0)
| in(X4,sK217(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1445]) ).
fof(f2331,plain,
! [X2,X3,X0,X1,X13] :
( ~ sP27(X0,X1,X2,X3)
| ~ in(X13,sK222(X1,X2,X3))
| in(ordered_pair(sK221(X1,X2,X3),X13),X3) ),
inference(cnf_transformation,[],[f1448]) ).
fof(f2332,plain,
! [X2,X3,X0,X1] :
( ~ sP27(X0,X1,X2,X3)
| in(sK221(X1,X2,X3),sK222(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1448]) ).
fof(f2333,plain,
! [X2,X3,X0,X1] :
( ~ sP27(X0,X1,X2,X3)
| sK220(X1,X2,X3) = sK222(X1,X2,X3) ),
inference(cnf_transformation,[],[f1448]) ).
fof(f2334,plain,
! [X2,X3,X0,X1] :
( ~ sP27(X0,X1,X2,X3)
| in(sK220(X1,X2,X3),X1) ),
inference(cnf_transformation,[],[f1448]) ).
fof(f2335,plain,
! [X2,X3,X0,X1] :
( ~ sP27(X0,X1,X2,X3)
| ordered_pair(sK220(X1,X2,X3),sK221(X1,X2,X3)) = X2 ),
inference(cnf_transformation,[],[f1448]) ).
fof(f2336,plain,
! [X2,X3,X0,X1] :
( ~ sP27(X0,X1,X2,X3)
| sK219(X0,X1,X2,X3) = X2 ),
inference(cnf_transformation,[],[f1448]) ).
fof(f2337,plain,
! [X2,X3,X0,X1] :
( ~ sP27(X0,X1,X2,X3)
| in(sK219(X0,X1,X2,X3),cartesian_product2(X1,X0)) ),
inference(cnf_transformation,[],[f1448]) ).
fof(f2338,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( in(sK218(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))
| sP27(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1448]) ).
fof(f2339,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ in(ordered_pair(X6,sK218(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))
| sP27(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1448]) ).
fof(f2340,plain,
! [X2,X0,X1,X6] :
( ~ sP26(X0,X1,X2)
| ~ in(X6,sK225(X0,X1,X2))
| in(ordered_pair(sK224(X0,X1,X2),X6),X2) ),
inference(cnf_transformation,[],[f1451]) ).
fof(f2341,plain,
! [X2,X0,X1] :
( ~ sP26(X0,X1,X2)
| in(sK224(X0,X1,X2),sK225(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1451]) ).
fof(f2342,plain,
! [X2,X0,X1] :
( ~ sP26(X0,X1,X2)
| sK223(X0,X1,X2) = sK225(X0,X1,X2) ),
inference(cnf_transformation,[],[f1451]) ).
fof(f2343,plain,
! [X2,X0,X1] :
( ~ sP26(X0,X1,X2)
| in(sK223(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1451]) ).
fof(f2344,plain,
! [X2,X0,X1] :
( ~ sP26(X0,X1,X2)
| ordered_pair(sK223(X0,X1,X2),sK224(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f1451]) ).
fof(f2350,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP25(sK231(X0,X1),X0,X1)
| sP28(X1,X0,X2) ),
inference(cnf_transformation,[],[f1455]) ).
fof(f2351,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sK229(X0,X1) = sK231(X0,X1)
| sP28(X1,X0,X2) ),
inference(cnf_transformation,[],[f1455]) ).
fof(f2352,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP26(sK230(X0,X1),X0,X1)
| sP28(X1,X0,X2) ),
inference(cnf_transformation,[],[f1455]) ).
fof(f2353,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sK229(X0,X1) = sK230(X0,X1)
| sP28(X1,X0,X2) ),
inference(cnf_transformation,[],[f1455]) ).
fof(f2354,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| empty(X0)
| sK230(X0,X1) != sK231(X0,X1)
| sP28(X1,X0,X2) ),
inference(cnf_transformation,[],[f1455]) ).
fof(f2355,plain,
! [X0,X1] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f913]) ).
fof(f2356,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f914]) ).
fof(f2357,plain,
! [X0,X1] :
( ~ relation(X0)
| relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f915]) ).
fof(f2358,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| ordered_pair(sK235(X0,X1,X8),sK236(X0,X1,X8)) = X8 ),
inference(cnf_transformation,[],[f1458]) ).
fof(f2359,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK236(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f1458]) ).
fof(f2360,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK235(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f1458]) ).
fof(f2361,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,[],[f1458]) ).
fof(f2362,plain,
! [X2,X0,X1] :
( in(sK232(X0,X1,X2),X2)
| sK232(X0,X1,X2) = ordered_pair(sK233(X0,X1,X2),sK234(X0,X1,X2))
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1458]) ).
fof(f2363,plain,
! [X2,X0,X1] :
( in(sK232(X0,X1,X2),X2)
| in(sK234(X0,X1,X2),X1)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1458]) ).
fof(f2364,plain,
! [X2,X0,X1] :
( in(sK232(X0,X1,X2),X2)
| in(sK233(X0,X1,X2),X0)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1458]) ).
fof(f2365,plain,
! [X2,X0,X1,X4,X5] :
( ~ in(sK232(X0,X1,X2),X2)
| ordered_pair(X4,X5) != sK232(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1458]) ).
fof(f2366,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f916]) ).
fof(f2367,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f918]) ).
fof(f2369,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f919]) ).
fof(f2370,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,[],[f1462]) ).
fof(f2371,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,[],[f1462]) ).
fof(f2372,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,[],[f1462]) ).
fof(f2373,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(ordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),X2)
| in(ordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),X0)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1462]) ).
fof(f2374,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(ordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),X2)
| in(sK237(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1462]) ).
fof(f2375,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| ~ in(ordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),X2)
| ~ in(ordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),X0)
| ~ in(sK237(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1462]) ).
fof(f2376,plain,
function(sK239),
inference(cnf_transformation,[],[f1463]) ).
fof(f2377,plain,
empty(sK239),
inference(cnf_transformation,[],[f1463]) ).
fof(f2378,plain,
relation(sK239),
inference(cnf_transformation,[],[f1463]) ).
fof(f2379,plain,
function(sK240),
inference(cnf_transformation,[],[f1464]) ).
fof(f2380,plain,
relation(sK240),
inference(cnf_transformation,[],[f1464]) ).
fof(f2381,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f921]) ).
fof(f2382,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f922]) ).
fof(f2383,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f923]) ).
fof(f2385,plain,
~ empty(sK241),
inference(cnf_transformation,[],[f1465]) ).
fof(f2386,plain,
relation(sK242),
inference(cnf_transformation,[],[f1466]) ).
fof(f2387,plain,
~ empty(sK242),
inference(cnf_transformation,[],[f1466]) ).
fof(f2388,plain,
empty(sK243),
inference(cnf_transformation,[],[f1467]) ).
fof(f2389,plain,
relation(sK244),
inference(cnf_transformation,[],[f1468]) ).
fof(f2390,plain,
empty(sK244),
inference(cnf_transformation,[],[f1468]) ).
fof(f2391,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ element(X1,X0)
| empty(X1) ),
inference(cnf_transformation,[],[f1469]) ).
fof(f2392,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| element(X1,X0) ),
inference(cnf_transformation,[],[f1469]) ).
fof(f2393,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| in(X1,X0) ),
inference(cnf_transformation,[],[f1469]) ).
fof(f2395,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f927]) ).
fof(f2401,plain,
! [X2,X0] :
( sP29
| ~ in(X2,sK248(X0))
| ordinal(X2) ),
inference(cnf_transformation,[],[f1475]) ).
fof(f2402,plain,
! [X2,X0] :
( sP29
| ~ in(X2,sK248(X0))
| sK249(X0,X2) = X2 ),
inference(cnf_transformation,[],[f1475]) ).
fof(f2403,plain,
! [X2,X0] :
( sP29
| ~ in(X2,sK248(X0))
| in(sK249(X0,X2),X0) ),
inference(cnf_transformation,[],[f1475]) ).
fof(f2404,plain,
! [X2,X3,X0] :
( sP29
| ~ ordinal(X2)
| X2 != X3
| ~ in(X3,X0)
| in(X2,sK248(X0)) ),
inference(cnf_transformation,[],[f1475]) ).
fof(f2405,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X0,X0) ),
inference(cnf_transformation,[],[f931]) ).
fof(f2406,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1476]) ).
fof(f2407,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ subset(X0,X1)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f1476]) ).
fof(f2408,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f935]) ).
fof(f2409,plain,
! [X2,X0] :
( ~ sP32(X0)
| ~ in(X2,sK250(X0))
| sP31(X0,X2) ),
inference(cnf_transformation,[],[f1479]) ).
fof(f2410,plain,
! [X2,X0] :
( ~ sP32(X0)
| ~ sP31(X0,X2)
| in(X2,sK250(X0)) ),
inference(cnf_transformation,[],[f1479]) ).
fof(f2411,plain,
! [X0,X11,X1,X9] :
( ~ sP31(X0,X1)
| ~ in(sK254(X1),omega)
| ~ element(X9,powerset(powerset(sK254(X1))))
| ~ subset(sK255(X9),X11)
| ~ in(X11,X9)
| sK255(X9) = X11
| empty_set = X9 ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2412,plain,
! [X0,X1,X9] :
( ~ sP31(X0,X1)
| ~ in(sK254(X1),omega)
| ~ element(X9,powerset(powerset(sK254(X1))))
| in(sK255(X9),X9)
| empty_set = X9 ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2413,plain,
! [X0,X1] :
( ~ sP31(X0,X1)
| sK254(X1) = X1 ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2414,plain,
! [X0,X1] :
( ~ sP31(X0,X1)
| ordinal(sK254(X1)) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2415,plain,
! [X0,X1] :
( ~ sP31(X0,X1)
| sK253(X0,X1) = X1 ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2416,plain,
! [X0,X1] :
( ~ sP31(X0,X1)
| in(sK253(X0,X1),succ(X0)) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2417,plain,
! [X2,X3,X0,X1] :
( in(X3,omega)
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP31(X0,X1) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2418,plain,
! [X2,X3,X0,X1] :
( element(sK251(X3),powerset(powerset(X3)))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP31(X0,X1) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2419,plain,
! [X2,X3,X0,X1,X5] :
( subset(X5,sK252(X3,X5))
| ~ in(X5,sK251(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP31(X0,X1) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2420,plain,
! [X2,X3,X0,X1,X5] :
( in(sK252(X3,X5),sK251(X3))
| ~ in(X5,sK251(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP31(X0,X1) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2421,plain,
! [X2,X3,X0,X1,X5] :
( sK252(X3,X5) != X5
| ~ in(X5,sK251(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP31(X0,X1) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2422,plain,
! [X2,X3,X0,X1] :
( empty_set != sK251(X3)
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,succ(X0))
| sP31(X0,X1) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f2427,plain,
! [X0] :
( ~ ordinal(X0)
| sP30(sK260)
| sP32(X0) ),
inference(cnf_transformation,[],[f1486]) ).
fof(f2428,plain,
! [X0] :
( ~ ordinal(X0)
| sK258 = sK260
| sP32(X0) ),
inference(cnf_transformation,[],[f1486]) ).
fof(f2429,plain,
! [X0,X7,X5] :
( ~ ordinal(X0)
| ~ in(sK261,omega)
| ~ element(X5,powerset(powerset(sK261)))
| ~ subset(sK262(X5),X7)
| ~ in(X7,X5)
| sK262(X5) = X7
| empty_set = X5
| sP32(X0) ),
inference(cnf_transformation,[],[f1486]) ).
fof(f2430,plain,
! [X0,X5] :
( ~ ordinal(X0)
| ~ in(sK261,omega)
| ~ element(X5,powerset(powerset(sK261)))
| in(sK262(X5),X5)
| empty_set = X5
| sP32(X0) ),
inference(cnf_transformation,[],[f1486]) ).
fof(f2431,plain,
! [X0] :
( ~ ordinal(X0)
| sK259 = sK261
| sP32(X0) ),
inference(cnf_transformation,[],[f1486]) ).
fof(f2432,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK261)
| sP32(X0) ),
inference(cnf_transformation,[],[f1486]) ).
fof(f2433,plain,
! [X0] :
( ~ ordinal(X0)
| sK258 = sK259
| sP32(X0) ),
inference(cnf_transformation,[],[f1486]) ).
fof(f2434,plain,
! [X0] :
( ~ ordinal(X0)
| sK259 != sK260
| sP32(X0) ),
inference(cnf_transformation,[],[f1486]) ).
fof(f2435,plain,
~ empty(omega),
inference(cnf_transformation,[],[f202]) ).
fof(f2437,plain,
epsilon_connected(omega),
inference(cnf_transformation,[],[f202]) ).
fof(f2438,plain,
epsilon_transitive(omega),
inference(cnf_transformation,[],[f202]) ).
fof(f2439,plain,
! [X2,X0] :
( omega != X0
| ~ ordinal(X2)
| ~ being_limit_ordinal(X2)
| ~ in(empty_set,X2)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2440,plain,
! [X0] :
( omega != X0
| ordinal(X0) ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2441,plain,
! [X0] :
( omega != X0
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2442,plain,
! [X0] :
( omega != X0
| in(empty_set,X0) ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2443,plain,
! [X0] :
( ordinal(sK263(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| omega = X0 ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2444,plain,
! [X0] :
( being_limit_ordinal(sK263(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| omega = X0 ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2445,plain,
! [X0] :
( in(empty_set,sK263(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| omega = X0 ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2446,plain,
! [X0] :
( ~ subset(X0,sK263(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(empty_set,X0)
| omega = X0 ),
inference(cnf_transformation,[],[f1490]) ).
fof(f2447,plain,
! [X0] :
( ~ finite(X0)
| in(relation_dom(sK264(X0)),omega) ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2448,plain,
! [X0] :
( ~ finite(X0)
| relation_rng(sK264(X0)) = X0 ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2449,plain,
! [X0] :
( ~ finite(X0)
| function(sK264(X0)) ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2450,plain,
! [X0] :
( ~ finite(X0)
| relation(sK264(X0)) ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2451,plain,
! [X0,X1] :
( ~ in(relation_dom(X1),omega)
| relation_rng(X1) != X0
| ~ function(X1)
| ~ relation(X1)
| finite(X0) ),
inference(cnf_transformation,[],[f1493]) ).
fof(f2453,plain,
! [X0] :
( ~ element(X0,omega)
| ordinal(X0) ),
inference(cnf_transformation,[],[f940]) ).
fof(f2454,plain,
! [X0] :
( ~ element(X0,omega)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f940]) ).
fof(f2455,plain,
! [X0] :
( ~ element(X0,omega)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f940]) ).
fof(f2456,plain,
! [X0] :
( ~ sP34(X0)
| sP33(sK267(X0),X0) ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2457,plain,
! [X0] :
( ~ sP34(X0)
| sK265(X0) = sK267(X0) ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2458,plain,
! [X0] :
( ~ sP34(X0)
| in(sK268(X0),X0) ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2459,plain,
! [X0] :
( ~ sP34(X0)
| sK266(X0) = sK268(X0) ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2460,plain,
! [X0] :
( ~ sP34(X0)
| ordinal(sK268(X0)) ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2461,plain,
! [X0] :
( ~ sP34(X0)
| sK265(X0) = sK266(X0) ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2462,plain,
! [X0] :
( ~ sP34(X0)
| sK266(X0) != sK267(X0) ),
inference(cnf_transformation,[],[f1496]) ).
fof(f2466,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP34(X0)
| ~ in(X3,sK270(X0,X1))
| in(sK272(X0,X3),X0) ),
inference(cnf_transformation,[],[f1502]) ).
fof(f2467,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP34(X0)
| ~ in(X3,sK270(X0,X1))
| sK272(X0,X3) = X3 ),
inference(cnf_transformation,[],[f1502]) ).
fof(f2468,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP34(X0)
| ~ in(X3,sK270(X0,X1))
| ordinal(sK272(X0,X3)) ),
inference(cnf_transformation,[],[f1502]) ).
fof(f2469,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP34(X0)
| ~ in(X3,sK270(X0,X1))
| sK271(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1502]) ).
fof(f2470,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP34(X0)
| ~ in(X3,sK270(X0,X1))
| in(sK271(X0,X1,X3),succ(X1)) ),
inference(cnf_transformation,[],[f1502]) ).
fof(f2471,plain,
! [X3,X0,X1,X4,X5] :
( ~ ordinal(X1)
| sP34(X0)
| ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5)
| X3 != X4
| ~ in(X4,succ(X1))
| in(X3,sK270(X0,X1)) ),
inference(cnf_transformation,[],[f1502]) ).
fof(f2479,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP35(X1,X0)
| ~ in(X3,sK278(X0,X1))
| set_difference(sK280(X0,X1,X3),singleton(X0)) = X3 ),
inference(cnf_transformation,[],[f1508]) ).
fof(f2480,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP35(X1,X0)
| ~ in(X3,sK278(X0,X1))
| in(sK280(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f1508]) ).
fof(f2481,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP35(X1,X0)
| ~ in(X3,sK278(X0,X1))
| sK279(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f1508]) ).
fof(f2482,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP35(X1,X0)
| ~ in(X3,sK278(X0,X1))
| in(sK279(X0,X1,X3),powerset(X0)) ),
inference(cnf_transformation,[],[f1508]) ).
fof(f2483,plain,
! [X3,X0,X1,X4,X5] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP35(X1,X0)
| set_difference(X5,singleton(X0)) != X3
| ~ in(X5,X1)
| X3 != X4
| ~ in(X4,powerset(X0))
| in(X3,sK278(X0,X1)) ),
inference(cnf_transformation,[],[f1508]) ).
fof(f2484,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(succ(X0)) ),
inference(cnf_transformation,[],[f945]) ).
fof(f2485,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(succ(X0)) ),
inference(cnf_transformation,[],[f945]) ).
fof(f2486,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(succ(X0)) ),
inference(cnf_transformation,[],[f945]) ).
fof(f2488,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[],[f201]) ).
fof(f2489,plain,
being_limit_ordinal(sK281),
inference(cnf_transformation,[],[f1509]) ).
fof(f2490,plain,
ordinal(sK281),
inference(cnf_transformation,[],[f1509]) ).
fof(f2491,plain,
epsilon_connected(sK281),
inference(cnf_transformation,[],[f1509]) ).
fof(f2492,plain,
epsilon_transitive(sK281),
inference(cnf_transformation,[],[f1509]) ).
fof(f2493,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| apply(X0,sK284(X0,X5)) = X5 ),
inference(cnf_transformation,[],[f1512]) ).
fof(f2494,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(sK284(X0,X5),relation_dom(X0)) ),
inference(cnf_transformation,[],[f1512]) ).
fof(f2495,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,[],[f1512]) ).
fof(f2496,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK282(X0,X1),X1)
| sK282(X0,X1) = apply(X0,sK283(X0,X1))
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f1512]) ).
fof(f2497,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK282(X0,X1),X1)
| in(sK283(X0,X1),relation_dom(X0))
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f1512]) ).
fof(f2498,plain,
! [X3,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK282(X0,X1),X1)
| apply(X0,X3) != sK282(X0,X1)
| ~ in(X3,relation_dom(X0))
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f1512]) ).
fof(f2499,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| empty_set = X2 ),
inference(cnf_transformation,[],[f1513]) ).
fof(f2503,plain,
top_str(sK285),
inference(cnf_transformation,[],[f1514]) ).
fof(f2504,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(cast_as_carrier_subset(X0)) ),
inference(cnf_transformation,[],[f951]) ).
fof(f2505,plain,
! [X0] :
( ~ one_sorted_str(X0)
| element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f952]) ).
fof(f2506,plain,
! [X0] :
( ~ one_sorted_str(X0)
| the_carrier(X0) = cast_as_carrier_subset(X0) ),
inference(cnf_transformation,[],[f953]) ).
fof(f2512,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP36(X1,X2)
| ~ in(X4,sK289(X1,X2))
| in(relation_image(X2,X4),X1) ),
inference(cnf_transformation,[],[f1520]) ).
fof(f2513,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP36(X1,X2)
| ~ in(X4,sK289(X1,X2))
| sK290(X1,X2,X4) = X4 ),
inference(cnf_transformation,[],[f1520]) ).
fof(f2514,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP36(X1,X2)
| ~ in(X4,sK289(X1,X2))
| in(sK290(X1,X2,X4),powerset(relation_dom(X2))) ),
inference(cnf_transformation,[],[f1520]) ).
fof(f2515,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP36(X1,X2)
| ~ in(relation_image(X2,X4),X1)
| X4 != X5
| ~ in(X5,powerset(relation_dom(X2)))
| in(X4,sK289(X1,X2)) ),
inference(cnf_transformation,[],[f1520]) ).
fof(f2516,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ function(X0)
| ~ relation(X0)
| finite(relation_image(X0,X1)) ),
inference(cnf_transformation,[],[f957]) ).
fof(f2517,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK293(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f1523]) ).
fof(f2518,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(sK293(X0,X1,X6),X6),X0) ),
inference(cnf_transformation,[],[f1523]) ).
fof(f2519,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,[],[f1523]) ).
fof(f2520,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK291(X0,X1,X2),X2)
| in(sK292(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1523]) ).
fof(f2521,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK291(X0,X1,X2),X2)
| in(ordered_pair(sK292(X0,X1,X2),sK291(X0,X1,X2)),X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1523]) ).
fof(f2522,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK291(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(ordered_pair(X4,sK291(X0,X1,X2)),X0)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1523]) ).
fof(f2523,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| apply(X0,sK296(X0,X1,X6)) = X6 ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2524,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK296(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2525,plain,
! [X2,X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK296(X0,X1,X6),relation_dom(X0)) ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2526,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,[],[f1526]) ).
fof(f2527,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK294(X0,X1,X2),X2)
| sK294(X0,X1,X2) = apply(X0,sK295(X0,X1,X2))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2528,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK294(X0,X1,X2),X2)
| in(sK295(X0,X1,X2),X1)
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2529,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK294(X0,X1,X2),X2)
| in(sK295(X0,X1,X2),relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2530,plain,
! [X2,X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK294(X0,X1,X2),X2)
| apply(X0,X4) != sK294(X0,X1,X2)
| ~ in(X4,X1)
| ~ in(X4,relation_dom(X0))
| relation_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1526]) ).
fof(f2531,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f233]) ).
fof(f2532,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f101]) ).
fof(f2533,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| ~ in(X4,X2)
| X1 = X4
| X0 = X4 ),
inference(cnf_transformation,[],[f1530]) ).
fof(f2534,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X1 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f1530]) ).
fof(f2535,plain,
! [X2,X0,X1,X4] :
( unordered_pair(X0,X1) != X2
| X0 != X4
| in(X4,X2) ),
inference(cnf_transformation,[],[f1530]) ).
fof(f2536,plain,
! [X2,X0,X1] :
( in(sK297(X0,X1,X2),X2)
| sK297(X0,X1,X2) = X1
| sK297(X0,X1,X2) = X0
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1530]) ).
fof(f2537,plain,
! [X2,X0,X1] :
( ~ in(sK297(X0,X1,X2),X2)
| sK297(X0,X1,X2) != X1
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1530]) ).
fof(f2538,plain,
! [X2,X0,X1] :
( ~ in(sK297(X0,X1,X2),X2)
| sK297(X0,X1,X2) != X0
| unordered_pair(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1530]) ).
fof(f2539,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f32]) ).
fof(f2540,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_rng(X0)) ),
inference(cnf_transformation,[],[f961]) ).
fof(f2541,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f961]) ).
fof(f2542,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f963]) ).
fof(f2543,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f431]) ).
fof(f2551,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f969]) ).
fof(f2552,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f1534]) ).
fof(f2554,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f1534]) ).
fof(f2555,plain,
! [X2,X0,X1] :
( in(sK298(X0,X1,X2),X2)
| in(sK298(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1534]) ).
fof(f2556,plain,
! [X2,X0,X1] :
( in(sK298(X0,X1,X2),X2)
| in(sK298(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1534]) ).
fof(f2557,plain,
! [X2,X0,X1] :
( ~ in(sK298(X0,X1,X2),X2)
| ~ in(sK298(X0,X1,X2),X1)
| ~ in(sK298(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1534]) ).
fof(f2558,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f35]) ).
fof(f2559,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f1535]) ).
fof(f2560,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f1535]) ).
fof(f2561,plain,
! [X0,X1] : relation_of2_as_subset(sK299(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1536]) ).
fof(f2562,plain,
! [X0,X7] :
( in(X7,sK300(X0))
| are_equipotent(X7,sK300(X0))
| ~ subset(X7,sK300(X0)) ),
inference(cnf_transformation,[],[f1537]) ).
fof(f2563,plain,
! [X0,X6,X4] :
( ~ subset(X6,X4)
| in(X6,sK301(X0,X4))
| ~ in(X4,sK300(X0)) ),
inference(cnf_transformation,[],[f1537]) ).
fof(f2564,plain,
! [X0,X4] :
( in(sK301(X0,X4),sK300(X0))
| ~ in(X4,sK300(X0)) ),
inference(cnf_transformation,[],[f1537]) ).
fof(f2565,plain,
! [X2,X3,X0] :
( ~ subset(X3,X2)
| ~ in(X2,sK300(X0))
| in(X3,sK300(X0)) ),
inference(cnf_transformation,[],[f1537]) ).
fof(f2566,plain,
! [X0] : in(X0,sK300(X0)),
inference(cnf_transformation,[],[f1537]) ).
fof(f2567,plain,
! [X0,X1] :
( ~ equipotent(X0,X1)
| are_equipotent(X0,X1) ),
inference(cnf_transformation,[],[f1538]) ).
fof(f2568,plain,
! [X0,X1] :
( ~ are_equipotent(X0,X1)
| equipotent(X0,X1) ),
inference(cnf_transformation,[],[f1538]) ).
fof(f2569,plain,
! [X0] :
( empty(X0)
| finite(sK302(X0)) ),
inference(cnf_transformation,[],[f1539]) ).
fof(f2570,plain,
! [X0] :
( empty(X0)
| ~ empty(sK302(X0)) ),
inference(cnf_transformation,[],[f1539]) ).
fof(f2571,plain,
! [X0] :
( empty(X0)
| element(sK302(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f1539]) ).
fof(f2572,plain,
finite(sK303),
inference(cnf_transformation,[],[f1540]) ).
fof(f2573,plain,
~ empty(sK303),
inference(cnf_transformation,[],[f1540]) ).
fof(f2574,plain,
! [X0] : finite(singleton(X0)),
inference(cnf_transformation,[],[f198]) ).
fof(f2576,plain,
! [X0,X1] :
( ~ finite(X0)
| finite(set_difference(X0,X1)) ),
inference(cnf_transformation,[],[f973]) ).
fof(f2578,plain,
! [X0,X1] :
( ~ finite(X1)
| finite(set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f975]) ).
fof(f2580,plain,
! [X0] :
( ~ empty(X0)
| finite(X0) ),
inference(cnf_transformation,[],[f977]) ).
fof(f2581,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(sK306(X0,X1,X6),X1) ),
inference(cnf_transformation,[],[f1543]) ).
fof(f2582,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(ordered_pair(X6,sK306(X0,X1,X6)),X0) ),
inference(cnf_transformation,[],[f1543]) ).
fof(f2583,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,[],[f1543]) ).
fof(f2584,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK304(X0,X1,X2),X2)
| in(sK305(X0,X1,X2),X1)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1543]) ).
fof(f2585,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK304(X0,X1,X2),X2)
| in(ordered_pair(sK304(X0,X1,X2),sK305(X0,X1,X2)),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1543]) ).
fof(f2586,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK304(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(ordered_pair(sK304(X0,X1,X2),X4),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1543]) ).
fof(f2587,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,[],[f1547]) ).
fof(f2588,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,[],[f1547]) ).
fof(f2589,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,[],[f1547]) ).
fof(f2590,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK307(X0,X1,X2),X2)
| in(apply(X0,sK307(X0,X1,X2)),X1)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1547]) ).
fof(f2591,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(sK307(X0,X1,X2),X2)
| in(sK307(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1547]) ).
fof(f2592,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(sK307(X0,X1,X2),X2)
| ~ in(apply(X0,sK307(X0,X1,X2)),X1)
| ~ in(sK307(X0,X1,X2),relation_dom(X0))
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1547]) ).
fof(f2593,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
inference(cnf_transformation,[],[f982]) ).
fof(f2594,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X1) = X1 ),
inference(cnf_transformation,[],[f984]) ).
fof(f2595,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_intersection2(X0,X1,X2),powerset(X0)) ),
inference(cnf_transformation,[],[f986]) ).
fof(f2596,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,[],[f988]) ).
fof(f2597,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f990]) ).
fof(f2598,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| empty(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f990]) ).
fof(f2599,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f992]) ).
fof(f2600,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f992]) ).
fof(f2601,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f994]) ).
fof(f2602,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ empty(X0)
| empty(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f994]) ).
fof(f2603,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f996]) ).
fof(f2604,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(sK311(X0,X1,X7,X8),X8),X1) ),
inference(cnf_transformation,[],[f1550]) ).
fof(f2605,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,sK311(X0,X1,X7,X8)),X0) ),
inference(cnf_transformation,[],[f1550]) ).
fof(f2606,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,[],[f1550]) ).
fof(f2607,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK308(X0,X1,X2),sK309(X0,X1,X2)),X2)
| in(ordered_pair(sK310(X0,X1,X2),sK309(X0,X1,X2)),X1)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1550]) ).
fof(f2608,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK308(X0,X1,X2),sK309(X0,X1,X2)),X2)
| in(ordered_pair(sK308(X0,X1,X2),sK310(X0,X1,X2)),X0)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1550]) ).
fof(f2609,plain,
! [X2,X0,X1,X5] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(sK308(X0,X1,X2),sK309(X0,X1,X2)),X2)
| ~ in(ordered_pair(X5,sK309(X0,X1,X2)),X1)
| ~ in(ordered_pair(sK308(X0,X1,X2),X5),X0)
| relation_composition(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1550]) ).
fof(f2610,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f998]) ).
fof(f2611,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(cnf_transformation,[],[f1000]) ).
fof(f2612,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_difference(X0,X1,X2),powerset(X0)) ),
inference(cnf_transformation,[],[f1002]) ).
fof(f2613,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,[],[f1551]) ).
fof(f2614,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,[],[f1551]) ).
fof(f2615,plain,
! [X0,X1] : quasi_total(sK312(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1552]) ).
fof(f2616,plain,
! [X0,X1] : function(sK312(X0,X1)),
inference(cnf_transformation,[],[f1552]) ).
fof(f2617,plain,
! [X0,X1] : relation(sK312(X0,X1)),
inference(cnf_transformation,[],[f1552]) ).
fof(f2618,plain,
! [X0,X1] : relation_of2(sK312(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1552]) ).
fof(f2619,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f569]) ).
fof(f2620,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f1005]) ).
fof(f2621,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ~ proper_subset(X1,X0) ),
inference(cnf_transformation,[],[f1006]) ).
fof(f2622,plain,
ordinal(sK313),
inference(cnf_transformation,[],[f1553]) ).
fof(f2623,plain,
epsilon_connected(sK313),
inference(cnf_transformation,[],[f1553]) ).
fof(f2624,plain,
epsilon_transitive(sK313),
inference(cnf_transformation,[],[f1553]) ).
fof(f2625,plain,
~ empty(sK313),
inference(cnf_transformation,[],[f1553]) ).
fof(f2626,plain,
ordinal(sK314),
inference(cnf_transformation,[],[f1554]) ).
fof(f2627,plain,
epsilon_connected(sK314),
inference(cnf_transformation,[],[f1554]) ).
fof(f2628,plain,
epsilon_transitive(sK314),
inference(cnf_transformation,[],[f1554]) ).
fof(f2629,plain,
empty(sK314),
inference(cnf_transformation,[],[f1554]) ).
fof(f2630,plain,
one_to_one(sK314),
inference(cnf_transformation,[],[f1554]) ).
fof(f2631,plain,
function(sK314),
inference(cnf_transformation,[],[f1554]) ).
fof(f2632,plain,
relation(sK314),
inference(cnf_transformation,[],[f1554]) ).
fof(f2633,plain,
ordinal(sK315),
inference(cnf_transformation,[],[f1555]) ).
fof(f2634,plain,
epsilon_connected(sK315),
inference(cnf_transformation,[],[f1555]) ).
fof(f2635,plain,
epsilon_transitive(sK315),
inference(cnf_transformation,[],[f1555]) ).
fof(f2639,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| ~ in(X2,X0)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f1560]) ).
fof(f2640,plain,
! [X0] :
( in(sK316(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f1560]) ).
fof(f2641,plain,
! [X0] :
( ~ subset(sK316(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f1560]) ).
fof(f2642,plain,
! [X0] :
( ~ empty(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f1008]) ).
fof(f2643,plain,
! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1008]) ).
fof(f2644,plain,
! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f1008]) ).
fof(f2645,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f1010]) ).
fof(f2646,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1011]) ).
fof(f2647,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f1011]) ).
fof(f2648,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ element(X1,X0)
| ordinal(X1) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f2649,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ element(X1,X0)
| epsilon_connected(X1) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f2650,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ element(X1,X0)
| epsilon_transitive(X1) ),
inference(cnf_transformation,[],[f1012]) ).
fof(f2651,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| disjoint(fiber(X0,sK318(X0,X4)),X4)
| empty_set = X4
| ~ subset(X4,X1) ),
inference(cnf_transformation,[],[f1563]) ).
fof(f2652,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| in(sK318(X0,X4),X4)
| empty_set = X4
| ~ subset(X4,X1) ),
inference(cnf_transformation,[],[f1563]) ).
fof(f2653,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ disjoint(fiber(X0,X3),sK317(X0,X1))
| ~ in(X3,sK317(X0,X1))
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f1563]) ).
fof(f2654,plain,
! [X0,X1] :
( ~ relation(X0)
| empty_set != sK317(X0,X1)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f1563]) ).
fof(f2655,plain,
! [X0,X1] :
( ~ relation(X0)
| subset(sK317(X0,X1),X1)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f1563]) ).
fof(f2656,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| disjoint(fiber(X0,sK320(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f1566]) ).
fof(f2657,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| in(sK320(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f1566]) ).
fof(f2658,plain,
! [X2,X0] :
( ~ relation(X0)
| ~ disjoint(fiber(X0,X2),sK319(X0))
| ~ in(X2,sK319(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1566]) ).
fof(f2659,plain,
! [X0] :
( ~ relation(X0)
| empty_set != sK319(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1566]) ).
fof(f2660,plain,
! [X0] :
( ~ relation(X0)
| subset(sK319(X0),relation_field(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f1566]) ).
fof(f2661,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| fiber(X0,X1) != X2
| ~ in(X4,X2)
| in(ordered_pair(X4,X1),X0) ),
inference(cnf_transformation,[],[f1570]) ).
fof(f2662,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| fiber(X0,X1) != X2
| ~ in(X4,X2)
| X1 != X4 ),
inference(cnf_transformation,[],[f1570]) ).
fof(f2663,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,[],[f1570]) ).
fof(f2664,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK321(X0,X1,X2),X2)
| in(ordered_pair(sK321(X0,X1,X2),X1),X0)
| fiber(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1570]) ).
fof(f2665,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK321(X0,X1,X2),X2)
| sK321(X0,X1,X2) != X1
| fiber(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1570]) ).
fof(f2666,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ in(sK321(X0,X1,X2),X2)
| ~ in(ordered_pair(sK321(X0,X1,X2),X1),X0)
| sK321(X0,X1,X2) = X1
| fiber(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1570]) ).
fof(f2667,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(cnf_transformation,[],[f1016]) ).
fof(f2668,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
inference(cnf_transformation,[],[f1017]) ).
fof(f2669,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,[],[f1571]) ).
fof(f2670,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,[],[f1571]) ).
fof(f2671,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,[],[f1571]) ).
fof(f2672,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,[],[f1571]) ).
fof(f2673,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,[],[f1571]) ).
fof(f2674,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,[],[f1571]) ).
fof(f2677,plain,
latt_str(sK322),
inference(cnf_transformation,[],[f1573]) ).
fof(f2678,plain,
! [X0] :
( ~ latt_str(X0)
| join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f1022]) ).
fof(f2679,plain,
! [X0] :
( ~ latt_str(X0)
| meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f1022]) ).
fof(f2680,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,[],[f1576]) ).
fof(f2681,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| element(sK323(X0),the_carrier(X0))
| meet_absorbing(X0) ),
inference(cnf_transformation,[],[f1576]) ).
fof(f2682,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| element(sK324(X0),the_carrier(X0))
| meet_absorbing(X0) ),
inference(cnf_transformation,[],[f1576]) ).
fof(f2683,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| sK324(X0) != join(X0,meet(X0,sK323(X0),sK324(X0)),sK324(X0))
| meet_absorbing(X0) ),
inference(cnf_transformation,[],[f1576]) ).
fof(f2684,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_rng(X2) = relation_rng_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1025]) ).
fof(f2685,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f1026]) ).
fof(f2686,plain,
join_semilatt_str(sK325),
inference(cnf_transformation,[],[f1577]) ).
fof(f2687,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f1027]) ).
fof(f2688,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f2689,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,[],[f1581]) ).
fof(f2690,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,[],[f1581]) ).
fof(f2691,plain,
! [X0,X1] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| relation_field(X1) = X0 ),
inference(cnf_transformation,[],[f1581]) ).
fof(f2692,plain,
! [X0,X1] :
( ~ relation(X1)
| in(sK327(X0,X1),X0)
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1581]) ).
fof(f2693,plain,
! [X0,X1] :
( ~ relation(X1)
| in(sK326(X0,X1),X0)
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1581]) ).
fof(f2694,plain,
! [X0,X1] :
( ~ relation(X1)
| in(ordered_pair(sK326(X0,X1),sK327(X0,X1)),X1)
| subset(sK326(X0,X1),sK327(X0,X1))
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1581]) ).
fof(f2695,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(ordered_pair(sK326(X0,X1),sK327(X0,X1)),X1)
| ~ subset(sK326(X0,X1),sK327(X0,X1))
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1581]) ).
fof(f2696,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f213]) ).
fof(f2697,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f213]) ).
fof(f2698,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f163]) ).
fof(f2699,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| X4 = X5 ),
inference(cnf_transformation,[],[f1585]) ).
fof(f2700,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| in(X4,X0) ),
inference(cnf_transformation,[],[f1585]) ).
fof(f2701,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,[],[f1585]) ).
fof(f2702,plain,
! [X0,X1] :
( ~ relation(X1)
| in(ordered_pair(sK328(X0,X1),sK329(X0,X1)),X1)
| sK328(X0,X1) = sK329(X0,X1)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1585]) ).
fof(f2703,plain,
! [X0,X1] :
( ~ relation(X1)
| in(ordered_pair(sK328(X0,X1),sK329(X0,X1)),X1)
| in(sK328(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1585]) ).
fof(f2704,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(ordered_pair(sK328(X0,X1),sK329(X0,X1)),X1)
| sK328(X0,X1) != sK329(X0,X1)
| ~ in(sK328(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f1585]) ).
fof(f2705,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(cnf_transformation,[],[f1031]) ).
fof(f2706,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| function(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1033]) ).
fof(f2708,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1034]) ).
fof(f2709,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1034]) ).
fof(f2710,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f1035]) ).
fof(f2711,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_inverse(X0) = function_inverse(X0) ),
inference(cnf_transformation,[],[f1037]) ).
fof(f2712,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,[],[f1588]) ).
fof(f2713,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,[],[f1588]) ).
fof(f2714,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK330(X0,X1),sK331(X0,X1)),X1)
| in(ordered_pair(sK331(X0,X1),sK330(X0,X1)),X0)
| relation_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f1588]) ).
fof(f2715,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK330(X0,X1),sK331(X0,X1)),X1)
| ~ in(ordered_pair(sK331(X0,X1),sK330(X0,X1)),X0)
| relation_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f1588]) ).
fof(f2716,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(meet_of_subsets(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f1039]) ).
fof(f2717,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(interior(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1041]) ).
fof(f2718,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ),
inference(cnf_transformation,[],[f1042]) ).
fof(f2719,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f1044]) ).
fof(f2720,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f1045]) ).
fof(f2721,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1046]) ).
fof(f2722,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,[],[f1592]) ).
fof(f2723,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,[],[f1592]) ).
fof(f2724,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| element(sK332(X0,X1,X2),powerset(X0))
| complements_of_subsets(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1592]) ).
fof(f2725,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| in(sK332(X0,X1,X2),X2)
| in(subset_complement(X0,sK332(X0,X1,X2)),X1)
| complements_of_subsets(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1592]) ).
fof(f2726,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| ~ in(sK332(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK332(X0,X1,X2)),X1)
| complements_of_subsets(X0,X1) = X2 ),
inference(cnf_transformation,[],[f1592]) ).
fof(f2727,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(union_of_subsets(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f1048]) ).
fof(f2728,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f142]) ).
fof(f2729,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f91]) ).
fof(f2730,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f1050]) ).
fof(f2731,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f1050]) ).
fof(f2732,plain,
! [X2,X0,X1] :
( ~ sP38(X0,X1,X2)
| ~ relation_isomorphism(X1,X0,X2)
| sP37(X2,X1,X0) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2733,plain,
! [X2,X0,X1] :
( ~ sP38(X0,X1,X2)
| ~ sP37(X2,X1,X0)
| relation_isomorphism(X1,X0,X2) ),
inference(cnf_transformation,[],[f1594]) ).
fof(f2745,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| sP38(X1,X0,X2) ),
inference(cnf_transformation,[],[f1157]) ).
fof(f2746,plain,
one_to_one(sK335),
inference(cnf_transformation,[],[f1599]) ).
fof(f2747,plain,
function(sK335),
inference(cnf_transformation,[],[f1599]) ).
fof(f2748,plain,
relation(sK335),
inference(cnf_transformation,[],[f1599]) ).
fof(f2749,plain,
empty(sK336),
inference(cnf_transformation,[],[f1600]) ).
fof(f2750,plain,
one_to_one(sK336),
inference(cnf_transformation,[],[f1600]) ).
fof(f2751,plain,
function(sK336),
inference(cnf_transformation,[],[f1600]) ).
fof(f2752,plain,
relation(sK336),
inference(cnf_transformation,[],[f1600]) ).
fof(f2753,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,[],[f1603]) ).
fof(f2754,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK337(X0)) = apply(X0,sK338(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1603]) ).
fof(f2755,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK338(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1603]) ).
fof(f2756,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK337(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1603]) ).
fof(f2757,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK337(X0) != sK338(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1603]) ).
fof(f2758,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1056]) ).
fof(f2761,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ is_a_cover_of_carrier(X0,X1)
| union_of_subsets(the_carrier(X0),X1) = cast_as_carrier_subset(X0) ),
inference(cnf_transformation,[],[f1604]) ).
fof(f2763,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f1606]) ).
fof(f2764,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1606]) ).
fof(f2765,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1606]) ).
fof(f2766,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1606]) ).
fof(f2767,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ well_orders(X0,X1)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f1606]) ).
fof(f2768,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,[],[f1606]) ).
fof(f2769,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,[],[f1609]) ).
fof(f2770,plain,
! [X0,X1,X6,X7] :
( ordered_pair(X6,X7) != X0
| ordered_pair(sK339(X0,X1),sK340(X0,X1)) = X0
| pair_first(X0) = X1 ),
inference(cnf_transformation,[],[f1609]) ).
fof(f2771,plain,
! [X0,X1,X6,X7] :
( ordered_pair(X6,X7) != X0
| sK339(X0,X1) != X1
| pair_first(X0) = X1 ),
inference(cnf_transformation,[],[f1609]) ).
fof(f2772,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,[],[f1612]) ).
fof(f2773,plain,
! [X0,X1,X6,X7] :
( ordered_pair(X6,X7) != X0
| ordered_pair(sK341(X0,X1),sK342(X0,X1)) = X0
| pair_second(X0) = X1 ),
inference(cnf_transformation,[],[f1612]) ).
fof(f2774,plain,
! [X0,X1,X6,X7] :
( ordered_pair(X6,X7) != X0
| sK342(X0,X1) != X1
| pair_second(X0) = X1 ),
inference(cnf_transformation,[],[f1612]) ).
fof(f2806,plain,
! [X3,X0,X4] :
( ~ epsilon_connected(X0)
| in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f1615]) ).
fof(f2807,plain,
! [X0] :
( ~ in(sK344(X0),sK343(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1615]) ).
fof(f2808,plain,
! [X0] :
( sK343(X0) != sK344(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1615]) ).
fof(f2809,plain,
! [X0] :
( ~ in(sK343(X0),sK344(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1615]) ).
fof(f2810,plain,
! [X0] :
( in(sK344(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1615]) ).
fof(f2811,plain,
! [X0] :
( in(sK343(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f1615]) ).
fof(f2812,plain,
! [X0] : finite(sK345(X0)),
inference(cnf_transformation,[],[f1616]) ).
fof(f2814,plain,
! [X0] : ordinal(sK345(X0)),
inference(cnf_transformation,[],[f1616]) ).
fof(f2815,plain,
! [X0] : epsilon_connected(sK345(X0)),
inference(cnf_transformation,[],[f1616]) ).
fof(f2816,plain,
! [X0] : epsilon_transitive(sK345(X0)),
inference(cnf_transformation,[],[f1616]) ).
fof(f2817,plain,
! [X0] : one_to_one(sK345(X0)),
inference(cnf_transformation,[],[f1616]) ).
fof(f2818,plain,
! [X0] : function(sK345(X0)),
inference(cnf_transformation,[],[f1616]) ).
fof(f2819,plain,
! [X0] : relation(sK345(X0)),
inference(cnf_transformation,[],[f1616]) ).
fof(f2820,plain,
! [X0] : empty(sK345(X0)),
inference(cnf_transformation,[],[f1616]) ).
fof(f2821,plain,
! [X0] : element(sK345(X0),powerset(X0)),
inference(cnf_transformation,[],[f1616]) ).
fof(f2823,plain,
ordinal(sK346),
inference(cnf_transformation,[],[f1617]) ).
fof(f2824,plain,
epsilon_connected(sK346),
inference(cnf_transformation,[],[f1617]) ).
fof(f2825,plain,
epsilon_transitive(sK346),
inference(cnf_transformation,[],[f1617]) ).
fof(f2826,plain,
~ empty(sK346),
inference(cnf_transformation,[],[f1617]) ).
fof(f2836,plain,
! [X0,X1] : function(sK347(X0,X1)),
inference(cnf_transformation,[],[f1618]) ).
fof(f2837,plain,
! [X0,X1] : relation(sK347(X0,X1)),
inference(cnf_transformation,[],[f1618]) ).
fof(f2838,plain,
! [X0,X1] : relation_of2(sK347(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1618]) ).
fof(f2839,plain,
! [X0,X1] : relation_of2(sK348(X0,X1),X0,X1),
inference(cnf_transformation,[],[f1619]) ).
fof(f2840,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| subset(X2,cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f1620]) ).
fof(f2841,plain,
! [X2,X0,X1] :
( ~ subset(X2,cartesian_product2(X0,X1))
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f1620]) ).
fof(f2842,plain,
meet_semilatt_str(sK349),
inference(cnf_transformation,[],[f1621]) ).
fof(f2843,plain,
! [X0] :
( ~ meet_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f1078]) ).
fof(f2844,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,[],[f1080]) ).
fof(f2845,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,[],[f1082]) ).
fof(f2846,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,[],[f1624]) ).
fof(f2847,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK351(X0,X1),sK350(X0,X1)),X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1624]) ).
fof(f2848,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK350(X0,X1),sK351(X0,X1)),X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1624]) ).
fof(f2849,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK351(X0,X1),X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1624]) ).
fof(f2850,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK350(X0,X1),X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1624]) ).
fof(f2851,plain,
! [X0,X1] :
( ~ relation(X0)
| sK350(X0,X1) != sK351(X0,X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f1624]) ).
fof(f2852,plain,
! [X0] :
( ~ relation(X0)
| ~ antisymmetric(X0)
| is_antisymmetric_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1625]) ).
fof(f2853,plain,
! [X0] :
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1625]) ).
fof(f2854,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,[],[f1628]) ).
fof(f2855,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK353(X0,X1),sK352(X0,X1)),X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1628]) ).
fof(f2856,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK352(X0,X1),sK353(X0,X1)),X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1628]) ).
fof(f2857,plain,
! [X0,X1] :
( ~ relation(X0)
| sK352(X0,X1) != sK353(X0,X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1628]) ).
fof(f2858,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK353(X0,X1),X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1628]) ).
fof(f2859,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK352(X0,X1),X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f1628]) ).
fof(f2860,plain,
! [X0] :
( ~ relation(X0)
| ~ connected(X0)
| is_connected_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1629]) ).
fof(f2861,plain,
! [X0] :
( ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f1629]) ).
fof(f2862,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,[],[f1632]) ).
fof(f2863,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK355(X0,X1),sK356(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1632]) ).
fof(f2864,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK354(X0,X1),sK355(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1632]) ).
fof(f2865,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK356(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1632]) ).
fof(f2866,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK355(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1632]) ).
fof(f2867,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK354(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1632]) ).
fof(f2868,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK354(X0,X1),sK356(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f1632]) ).
fof(f2869,plain,
! [X0] :
( ~ relation(X0)
| ~ transitive(X0)
| is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1633]) ).
fof(f2870,plain,
! [X0] :
( ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0) ),
inference(cnf_transformation,[],[f1633]) ).
fof(f2871,plain,
! [X0] :
( ~ relation(X0)
| ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1634]) ).
fof(f2872,plain,
! [X0] :
( ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0) ),
inference(cnf_transformation,[],[f1634]) ).
fof(f2873,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ is_reflexive_in(X0,X1)
| ~ in(X3,X1)
| in(ordered_pair(X3,X3),X0) ),
inference(cnf_transformation,[],[f1637]) ).
fof(f2874,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK357(X0,X1),X1)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f1637]) ).
fof(f2875,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK357(X0,X1),sK357(X0,X1)),X0)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f1637]) ).
fof(f2881,plain,
~ empty(sK358),
inference(cnf_transformation,[],[f1638]) ).
fof(f2887,plain,
empty(empty_set),
inference(cnf_transformation,[],[f246]) ).
fof(f2914,plain,
! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f2218,f2077]) ).
fof(f2915,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f2532,f2077]) ).
fof(f2916,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK39(X0),sK39(X0)),unordered_pair(sK39(X0),sK39(X0))),X0)
| reflexive(X0) ),
inference(definition_unfolding,[],[f1641,f2915]) ).
fof(f2917,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,[],[f1639,f2915]) ).
fof(f2918,plain,
! [X0] : unordered_pair(X0,X0) != sK140,
inference(definition_unfolding,[],[f1642,f2057,f2077]) ).
fof(f2920,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f1644,f2077]) ).
fof(f2921,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f1645,f2077]) ).
fof(f2922,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK40(X0),sK42(X0)),unordered_pair(sK40(X0),sK40(X0))),X0)
| transitive(X0) ),
inference(definition_unfolding,[],[f1650,f2915]) ).
fof(f2923,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK40(X0),sK41(X0)),unordered_pair(sK40(X0),sK40(X0))),X0)
| transitive(X0) ),
inference(definition_unfolding,[],[f1649,f2915]) ).
fof(f2924,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK41(X0),sK42(X0)),unordered_pair(sK41(X0),sK41(X0))),X0)
| transitive(X0) ),
inference(definition_unfolding,[],[f1648,f2915]) ).
fof(f2925,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,[],[f1647,f2915,f2915,f2915]) ).
fof(f2930,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK44(X0),sK45(X0)),unordered_pair(sK44(X0),sK44(X0))),X0)
| antisymmetric(X0) ),
inference(definition_unfolding,[],[f1660,f2915]) ).
fof(f2931,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK45(X0),sK44(X0)),unordered_pair(sK45(X0),sK45(X0))),X0)
| antisymmetric(X0) ),
inference(definition_unfolding,[],[f1659,f2915]) ).
fof(f2932,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,[],[f1658,f2915,f2915]) ).
fof(f2933,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0) ),
inference(definition_unfolding,[],[f1662,f2077]) ).
fof(f2934,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK46(X0),sK47(X0)),unordered_pair(sK46(X0),sK46(X0))),X0)
| connected(X0) ),
inference(definition_unfolding,[],[f1667,f2915]) ).
fof(f2935,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK47(X0),sK46(X0)),unordered_pair(sK47(X0),sK47(X0))),X0)
| connected(X0) ),
inference(definition_unfolding,[],[f1666,f2915]) ).
fof(f2936,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,[],[f1665,f2915,f2915]) ).
fof(f2943,plain,
! [X0,X1,X6] :
( ~ sP2(X0,X1)
| ~ in(X6,sK52(X0,X1))
| in(unordered_pair(unordered_pair(sK50(X0,X1),X6),unordered_pair(sK50(X0,X1),sK50(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1685,f2915]) ).
fof(f2947,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,[],[f1693,f2915]) ).
fof(f2948,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X2)
| sK54(X1,X3,X4) = X3 ),
inference(definition_unfolding,[],[f1692,f2915]) ).
fof(f2949,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X2)
| in(X4,sK54(X1,X3,X4)) ),
inference(definition_unfolding,[],[f1691,f2915]) ).
fof(f2950,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,sK54(X1,X3,X4))
| in(unordered_pair(unordered_pair(X4,X8),unordered_pair(X4,X4)),X1) ),
inference(definition_unfolding,[],[f1690,f2915,f2915]) ).
fof(f2956,plain,
! [X0] :
( sK59(X0) = unordered_pair(sK58(X0),sK58(X0))
| sP3(X0) ),
inference(definition_unfolding,[],[f1711,f2077]) ).
fof(f2957,plain,
! [X0] :
( sK60(X0) = unordered_pair(sK58(X0),sK58(X0))
| sP3(X0) ),
inference(definition_unfolding,[],[f1709,f2077]) ).
fof(f2958,plain,
( ~ sP8
| in(set_union2(sK62,unordered_pair(sK62,sK62)),omega) ),
inference(definition_unfolding,[],[f1720,f2914]) ).
fof(f2959,plain,
! [X1] :
( ~ sP8
| ~ in(sK62,omega)
| ~ element(X1,powerset(powerset(sK62)))
| in(sK63(X1),X1)
| sK140 = X1 ),
inference(definition_unfolding,[],[f1719,f2057]) ).
fof(f2960,plain,
! [X3,X1] :
( ~ sP8
| ~ in(sK62,omega)
| ~ element(X1,powerset(powerset(sK62)))
| ~ subset(sK63(X1),X3)
| ~ in(X3,X1)
| sK63(X1) = X3
| sK140 = X1 ),
inference(definition_unfolding,[],[f1718,f2057]) ).
fof(f2961,plain,
( ~ sP7
| sK64 != sK140 ),
inference(definition_unfolding,[],[f1727,f2057]) ).
fof(f2962,plain,
( ~ sP7
| element(sK64,powerset(powerset(sK140))) ),
inference(definition_unfolding,[],[f1723,f2057]) ).
fof(f2964,plain,
( ~ sP6
| sK66 != sK140 ),
inference(definition_unfolding,[],[f1734,f2057]) ).
fof(f2965,plain,
! [X2,X1] :
( ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK66)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| in(sK67(X2),X2)
| sK140 = X2 ),
inference(definition_unfolding,[],[f1730,f2057]) ).
fof(f2966,plain,
! [X2,X1,X4] :
( ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK66)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(sK67(X2),X4)
| ~ in(X4,X2)
| sK67(X2) = X4
| sK140 = X2 ),
inference(definition_unfolding,[],[f1729,f2057]) ).
fof(f2967,plain,
! [X0] :
( ~ sP5(X0)
| sK68(X0) != sK140 ),
inference(definition_unfolding,[],[f1739,f2057]) ).
fof(f2968,plain,
! [X0] :
( ~ sP5(X0)
| element(sK68(X0),powerset(powerset(set_union2(X0,unordered_pair(X0,X0))))) ),
inference(definition_unfolding,[],[f1735,f2914]) ).
fof(f2970,plain,
! [X0,X1] :
( sP6
| sP8
| sP7
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| in(sK72(X1),X1)
| sK140 = X1 ),
inference(definition_unfolding,[],[f1746,f2057]) ).
fof(f2971,plain,
! [X3,X0,X1] :
( sP6
| sP8
| sP7
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| ~ subset(sK72(X1),X3)
| ~ in(X3,X1)
| sK72(X1) = X3
| sK140 = X1 ),
inference(definition_unfolding,[],[f1745,f2057]) ).
fof(f2972,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)),sK73(X0,X1,X2)) ),
inference(definition_unfolding,[],[f1750,f2915,f2915]) ).
fof(f2973,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK73(X0,X1,X2))
| in(X4,X0) ),
inference(definition_unfolding,[],[f1749,f2915]) ).
fof(f2974,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK73(X0,X1,X2))
| in(X5,X0) ),
inference(definition_unfolding,[],[f1748,f2915]) ).
fof(f2975,plain,
! [X2,X0,X1,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),sK73(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,[],[f1747,f2915,f2915]) ).
fof(f2976,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ relation(X1)
| empty(X0)
| ~ in(unordered_pair(unordered_pair(X6,sK75(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,sK74(X0,X1,X2)) ),
inference(definition_unfolding,[],[f1759,f2915,f2915]) ).
fof(f2977,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ relation(X1)
| empty(X0)
| in(sK75(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,sK74(X0,X1,X2)) ),
inference(definition_unfolding,[],[f1758,f2915]) ).
fof(f2978,plain,
! [X2,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK74(X0,X1,X2))
| unordered_pair(unordered_pair(sK76(X0,X1,X4),sK77(X0,X1,X4)),unordered_pair(sK76(X0,X1,X4),sK76(X0,X1,X4))) = X4 ),
inference(definition_unfolding,[],[f1756,f2915]) ).
fof(f2979,plain,
! [X2,X0,X1,X4,X12] :
( ~ relation(X1)
| empty(X0)
| ~ in(X4,sK74(X0,X1,X2))
| ~ in(X12,sK78(X0,X1,X4))
| in(unordered_pair(unordered_pair(sK77(X0,X1,X4),X12),unordered_pair(sK77(X0,X1,X4),sK77(X0,X1,X4))),X1) ),
inference(definition_unfolding,[],[f1752,f2915]) ).
fof(f2980,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,sK79(X0,X1)) ),
inference(definition_unfolding,[],[f1764,f2915,f2077]) ).
fof(f2981,plain,
! [X3,X0,X1] :
( ~ in(X3,sK79(X0,X1))
| unordered_pair(unordered_pair(sK80(X0,X3),sK81(X0,X3)),unordered_pair(sK80(X0,X3),sK80(X0,X3))) = X3 ),
inference(definition_unfolding,[],[f1762,f2915]) ).
fof(f2982,plain,
! [X3,X0,X1] :
( ~ in(X3,sK79(X0,X1))
| sK81(X0,X3) = unordered_pair(sK80(X0,X3),sK80(X0,X3)) ),
inference(definition_unfolding,[],[f1760,f2077]) ).
fof(f2992,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,sK87(X0,X1)) ),
inference(definition_unfolding,[],[f1782,f2077,f2914]) ).
fof(f2993,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| ~ in(X3,sK87(X0,X1))
| in(X3,powerset(X0)) ),
inference(definition_unfolding,[],[f1781,f2914]) ).
fof(f2994,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| ~ in(X3,sK87(X0,X1))
| in(sK88(X0,X1,X3),X1) ),
inference(definition_unfolding,[],[f1780,f2914]) ).
fof(f2995,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| ~ in(X3,sK87(X0,X1))
| set_difference(sK88(X0,X1,X3),unordered_pair(X0,X0)) = X3 ),
inference(definition_unfolding,[],[f1779,f2077,f2914]) ).
fof(f2996,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,sK89(X0,X1,X2)) ),
inference(definition_unfolding,[],[f1786,f2915,f2915]) ).
fof(f2997,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK89(X0,X1,X2))
| unordered_pair(unordered_pair(sK90(X1,X2,X4),sK91(X1,X2,X4)),unordered_pair(sK90(X1,X2,X4),sK90(X1,X2,X4))) = X4 ),
inference(definition_unfolding,[],[f1784,f2915]) ).
fof(f2998,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X4,sK89(X0,X1,X2))
| in(unordered_pair(unordered_pair(apply(X2,sK90(X1,X2,X4)),apply(X2,sK91(X1,X2,X4))),unordered_pair(apply(X2,sK90(X1,X2,X4)),apply(X2,sK90(X1,X2,X4)))),X1) ),
inference(definition_unfolding,[],[f1783,f2915]) ).
fof(f2999,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,sK94(X0,X1)) ),
inference(definition_unfolding,[],[f1797,f2914]) ).
fof(f3000,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ in(X3,sK94(X0,X1))
| in(X3,set_union2(X1,unordered_pair(X1,X1))) ),
inference(definition_unfolding,[],[f1796,f2914]) ).
fof(f3001,plain,
! [X3,X0,X1,X5] :
( ~ sP12(X0,X1)
| ~ in(X3,X0)
| ~ in(X5,sK97(X0,X1,X3))
| in(unordered_pair(unordered_pair(apply(sK96(X0,X1),X3),X5),unordered_pair(apply(sK96(X0,X1),X3),apply(sK96(X0,X1),X3))),X1) ),
inference(definition_unfolding,[],[f1798,f2915]) ).
fof(f3004,plain,
! [X3,X0,X1,X4] :
( ~ relation(X1)
| empty(X0)
| ~ in(unordered_pair(unordered_pair(X3,sK104(X1,X3,X4)),unordered_pair(X3,X3)),X1)
| ~ in(X3,X4)
| sK103(X0,X1) != X4
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(definition_unfolding,[],[f1813,f2915]) ).
fof(f3007,plain,
! [X0,X4] :
( unordered_pair(sK109(X0),sK109(X0)) != X4
| sP13(X0)
| relation(sK108(X0)) ),
inference(definition_unfolding,[],[f1825,f2077]) ).
fof(f3008,plain,
! [X0,X4] :
( unordered_pair(sK109(X0),sK109(X0)) != X4
| sP13(X0)
| function(sK108(X0)) ),
inference(definition_unfolding,[],[f1823,f2077]) ).
fof(f3009,plain,
! [X0,X4] :
( unordered_pair(sK109(X0),sK109(X0)) != X4
| sP13(X0)
| relation_dom(sK108(X0)) = X0 ),
inference(definition_unfolding,[],[f1821,f2077]) ).
fof(f3011,plain,
! [X2,X0,X4] :
( unordered_pair(sK109(X0),sK109(X0)) != X4
| sP13(X0)
| ~ in(X2,X0)
| apply(sK108(X0),X2) = unordered_pair(X2,X2) ),
inference(definition_unfolding,[],[f1819,f2077,f2077]) ).
fof(f3012,plain,
! [X2,X1] :
( ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK110)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| in(sK111(X2),X2)
| sK140 = X2 ),
inference(definition_unfolding,[],[f1829,f2057]) ).
fof(f3013,plain,
! [X2,X1,X4] :
( ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK110)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(sK111(X2),X4)
| ~ in(X4,X2)
| sK111(X2) = X4
| sK140 = X2 ),
inference(definition_unfolding,[],[f1828,f2057]) ).
fof(f3015,plain,
! [X0,X1] :
( sP15
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| in(sK114(X1),X1)
| sK140 = X1 ),
inference(definition_unfolding,[],[f1838,f2057]) ).
fof(f3016,plain,
! [X3,X0,X1] :
( sP15
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| ~ subset(sK114(X1),X3)
| ~ in(X3,X1)
| sK114(X1) = X3
| sK140 = X1 ),
inference(definition_unfolding,[],[f1837,f2057]) ).
fof(f3017,plain,
! [X2,X0] :
( ~ in(X2,X0)
| apply(sK115(X0),X2) = unordered_pair(X2,X2) ),
inference(definition_unfolding,[],[f1839,f2077]) ).
fof(f3019,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,[],[f1844,f2915]) ).
fof(f3020,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,[],[f1843,f2915]) ).
fof(f3021,plain,
! [X0] : in(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f1846,f2914]) ).
fof(f3022,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,[],[f1856,f2023]) ).
fof(f3024,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(unordered_pair(unordered_pair(sK117(X0,X1,X2),X0),unordered_pair(sK117(X0,X1,X2),sK117(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f1869,f2915]) ).
fof(f3025,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,[],[f1874,f2023]) ).
fof(f3028,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| in(unordered_pair(unordered_pair(X0,sK118(X0,X1,X2)),unordered_pair(X0,X0)),X2) ),
inference(definition_unfolding,[],[f1883,f2915]) ).
fof(f3029,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_inverse_image(X1,X0) != sK140
| ~ subset(X0,relation_rng(X1))
| sK140 = X0 ),
inference(definition_unfolding,[],[f1891,f2057,f2057]) ).
fof(f3031,plain,
! [X0,X1] :
( ~ finite(X0)
| ~ element(X1,powerset(powerset(X0)))
| in(sK119(X1),X1)
| sK140 = X1 ),
inference(definition_unfolding,[],[f1898,f2057]) ).
fof(f3032,plain,
! [X3,X0,X1] :
( ~ finite(X0)
| ~ element(X1,powerset(powerset(X0)))
| ~ subset(sK119(X1),X3)
| ~ in(X3,X1)
| sK119(X1) = X3
| sK140 = X1 ),
inference(definition_unfolding,[],[f1897,f2057]) ).
fof(f3033,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(definition_unfolding,[],[f1902,f2023]) ).
fof(f3034,plain,
powerset(sK140) = unordered_pair(sK140,sK140),
inference(definition_unfolding,[],[f1904,f2057,f2077,f2057]) ).
fof(f3037,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))
| sK140 = X1 ),
inference(definition_unfolding,[],[f1912,f2057]) ).
fof(f3038,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,sK120(X2,X3)),unordered_pair(X3,X3)),X2)
| ~ in(X3,X1) ),
inference(definition_unfolding,[],[f1920,f2915]) ).
fof(f3039,plain,
! [X2,X0,X1,X6] :
( ~ relation_of2_as_subset(X2,X1,X0)
| ~ in(unordered_pair(unordered_pair(sK121(X1,X2),X6),unordered_pair(sK121(X1,X2),sK121(X1,X2))),X2)
| relation_dom_as_subset(X1,X0,X2) = X1 ),
inference(definition_unfolding,[],[f1918,f2915]) ).
fof(f3040,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(sK122(X2,X3),X3),unordered_pair(sK122(X2,X3),sK122(X2,X3))),X2)
| ~ in(X3,X1) ),
inference(definition_unfolding,[],[f1926,f2915]) ).
fof(f3041,plain,
! [X2,X0,X1,X6] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ~ in(unordered_pair(unordered_pair(X6,sK123(X1,X2)),unordered_pair(X6,X6)),X2)
| relation_rng_as_subset(X0,X1,X2) = X1 ),
inference(definition_unfolding,[],[f1924,f2915]) ).
fof(f3042,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,[],[f1938,f2023,f2023]) ).
fof(f3043,plain,
! [X0] :
( empty(X0)
| relation_dom(sK126(X0)) = X0
| sK125(X0) = sK140 ),
inference(definition_unfolding,[],[f1942,f2057]) ).
fof(f3044,plain,
! [X3,X0] :
( empty(X0)
| ~ in(X3,X0)
| in(apply(sK126(X0),X3),X3)
| sK125(X0) = sK140 ),
inference(definition_unfolding,[],[f1941,f2057]) ).
fof(f3045,plain,
! [X0] :
( empty(X0)
| relation(sK126(X0))
| sK125(X0) = sK140 ),
inference(definition_unfolding,[],[f1940,f2057]) ).
fof(f3046,plain,
! [X0] :
( empty(X0)
| function(sK126(X0))
| sK125(X0) = sK140 ),
inference(definition_unfolding,[],[f1939,f2057]) ).
fof(f3047,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,set_difference(X0,X1)) = X0 ),
inference(definition_unfolding,[],[f1947,f2023]) ).
fof(f3048,plain,
! [X0] : subset(sK140,X0),
inference(definition_unfolding,[],[f1951,f2057]) ).
fof(f3049,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,[],[f1953,f2915]) ).
fof(f3050,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,[],[f1952,f2915]) ).
fof(f3051,plain,
! [X0,X1] :
( ~ ordinal(X1)
| in(sK128(X0),X0)
| sK140 = X0
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1961,f2057]) ).
fof(f3052,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X3)
| ~ in(X3,X0)
| ordinal_subset(sK128(X0),X3)
| sK140 = X0
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1960,f2057]) ).
fof(f3053,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ordinal(sK128(X0))
| sK140 = X0
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f1959,f2057]) ).
fof(f3054,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f1964,f2914]) ).
fof(f3055,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal_subset(set_union2(X0,unordered_pair(X0,X0)),X1) ),
inference(definition_unfolding,[],[f1963,f2914]) ).
fof(f3056,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,[],[f1967,f2915,f2915]) ).
fof(f3057,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,[],[f1966,f2915,f2915]) ).
fof(f3058,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK140 ),
inference(definition_unfolding,[],[f1977,f2057]) ).
fof(f3059,plain,
! [X0,X1] :
( set_difference(X0,X1) != sK140
| subset(X0,X1) ),
inference(definition_unfolding,[],[f1976,f2057]) ).
fof(f3060,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f1979,f2077]) ).
fof(f3064,plain,
! [X0,X1] :
( ~ subset(X0,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = X0
| sK140 = X0 ),
inference(definition_unfolding,[],[f1985,f2057,f2077,f2077]) ).
fof(f3065,plain,
! [X0] :
( ~ subset(X0,sK140)
| sK140 = X0 ),
inference(definition_unfolding,[],[f1993,f2057,f2057]) ).
fof(f3066,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(set_union2(sK131(X0),unordered_pair(sK131(X0),sK131(X0))),X0)
| being_limit_ordinal(X0) ),
inference(definition_unfolding,[],[f1998,f2914]) ).
fof(f3067,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,[],[f1995,f2914]) ).
fof(f3068,plain,
! [X0] :
( ~ ordinal(X0)
| set_union2(sK132(X0),unordered_pair(sK132(X0),sK132(X0))) = X0
| being_limit_ordinal(X0) ),
inference(definition_unfolding,[],[f2001,f2914]) ).
fof(f3069,plain,
! [X2,X0] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| set_union2(X2,unordered_pair(X2,X2)) != X0
| ~ ordinal(X2) ),
inference(definition_unfolding,[],[f1999,f2914]) ).
fof(f3070,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| sK140 = X1
| ~ in(apply(X3,X4),X2)
| ~ in(X4,X0)
| in(X4,relation_inverse_image(X3,X2)) ),
inference(definition_unfolding,[],[f2015,f2057]) ).
fof(f3071,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| sK140 = X1
| ~ in(X4,relation_inverse_image(X3,X2))
| in(X4,X0) ),
inference(definition_unfolding,[],[f2014,f2057]) ).
fof(f3072,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(X3,X0,X1)
| ~ quasi_total(X3,X0,X1)
| ~ function(X3)
| sK140 = X1
| ~ in(X4,relation_inverse_image(X3,X2))
| in(apply(X3,X4),X2) ),
inference(definition_unfolding,[],[f2013,f2057]) ).
fof(f3073,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) != sK140
| sK140 = X1 ),
inference(definition_unfolding,[],[f2017,f2057,f2057]) ).
fof(f3074,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(unordered_pair(X0,X0),X1) = X1 ),
inference(definition_unfolding,[],[f2018,f2077]) ).
fof(f3075,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| sK140 = X1
| subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ),
inference(definition_unfolding,[],[f2020,f2057]) ).
fof(f3076,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| sK140 = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ),
inference(definition_unfolding,[],[f2022,f2057]) ).
fof(f3077,plain,
! [X0,X1] :
( in(sK134(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f2027,f2023]) ).
fof(f3078,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f2026,f2023]) ).
fof(f3079,plain,
! [X2,X0,X1] :
( sK140 = X0
| ~ element(X1,powerset(X0))
| ~ element(X2,X0)
| in(X2,X1)
| in(X2,subset_complement(X0,X1)) ),
inference(definition_unfolding,[],[f2028,f2057]) ).
fof(f3080,plain,
! [X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK137(X0),sK138(X0)),unordered_pair(sK137(X0),sK137(X0))),X0)
| sK140 = X0 ),
inference(definition_unfolding,[],[f2051,f2057,f2915]) ).
fof(f3081,plain,
sK140 = relation_dom(sK140),
inference(definition_unfolding,[],[f2063,f2057,f2057]) ).
fof(f3082,plain,
sK140 = relation_rng(sK140),
inference(definition_unfolding,[],[f2062,f2057,f2057]) ).
fof(f3083,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) != sK140
| sK140 = X0 ),
inference(definition_unfolding,[],[f2068,f2057,f2057]) ).
fof(f3084,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) != sK140
| sK140 = X0 ),
inference(definition_unfolding,[],[f2067,f2057,f2057]) ).
fof(f3085,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) != sK140
| relation_dom(X0) = sK140 ),
inference(definition_unfolding,[],[f2070,f2057,f2057]) ).
fof(f3086,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) != sK140
| relation_rng(X0) = sK140 ),
inference(definition_unfolding,[],[f2069,f2057,f2057]) ).
fof(f3087,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) = X0 ),
inference(definition_unfolding,[],[f2072,f2077]) ).
fof(f3088,plain,
! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) != X0
| ~ in(X1,X0) ),
inference(definition_unfolding,[],[f2071,f2077]) ).
fof(f3089,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| apply(X2,sK141(X1,X2)) != apply(X1,sK141(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,[],[f2076,f2023]) ).
fof(f3090,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| in(sK141(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,[],[f2075,f2023]) ).
fof(f3092,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))
| sK140 = X1 ),
inference(definition_unfolding,[],[f2078,f2057]) ).
fof(f3093,plain,
! [X0,X1] :
( ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1))
| X0 = X1 ),
inference(definition_unfolding,[],[f2080,f2077,f2077]) ).
fof(f3094,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,[],[f2087,f2915,f2915]) ).
fof(f3095,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,[],[f2086,f2915]) ).
fof(f3096,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,[],[f2085,f2915,f2915]) ).
fof(f3097,plain,
! [X0,X1] : pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0,
inference(definition_unfolding,[],[f2089,f2915]) ).
fof(f3098,plain,
! [X0,X1] : pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1,
inference(definition_unfolding,[],[f2088,f2915]) ).
fof(f3099,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,[],[f2100,f2915]) ).
fof(f3101,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,[],[f2098,f2915]) ).
fof(f3102,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(definition_unfolding,[],[f2104,f2077]) ).
fof(f3103,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,[],[f2105,f2023]) ).
fof(f3105,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)
| sK140 = X1 ),
inference(definition_unfolding,[],[f2114,f2057]) ).
fof(f3106,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)
| sK140 = X1 ),
inference(definition_unfolding,[],[f2113,f2057]) ).
fof(f3108,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)
| sK140 != X0 ),
inference(definition_unfolding,[],[f2111,f2057]) ).
fof(f3110,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X0) != unordered_pair(X1,X2)
| X1 = X2 ),
inference(definition_unfolding,[],[f2116,f2077]) ).
fof(f3111,plain,
! [X0,X1,X6] :
( ~ sP18(X0,X1)
| ~ in(X6,sK147(X0,X1))
| in(unordered_pair(unordered_pair(sK145(X0,X1),X6),unordered_pair(sK145(X0,X1),sK145(X0,X1))),X1) ),
inference(definition_unfolding,[],[f2125,f2915]) ).
fof(f3114,plain,
! [X3,X0,X1,X9] :
( ~ relation(X1)
| empty(X0)
| sP18(X0,X1)
| ~ in(X3,sK149(X0,X1))
| ~ in(X9,sK152(X0,X1,X3))
| in(unordered_pair(unordered_pair(X3,X9),unordered_pair(X3,X3)),X1) ),
inference(definition_unfolding,[],[f2133,f2915]) ).
fof(f3116,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK153(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(X3,sK153(X0,X1)),unordered_pair(X3,X3)),X0)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f2144,f2915]) ).
fof(f3117,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK153(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK154(X0,X1),sK153(X0,X1)),unordered_pair(sK154(X0,X1),sK154(X0,X1))),X0)
| relation_rng(X0) = X1 ),
inference(definition_unfolding,[],[f2143,f2915]) ).
fof(f3118,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,[],[f2142,f2915]) ).
fof(f3119,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(sK155(X0,X5),X5),unordered_pair(sK155(X0,X5),sK155(X0,X5))),X0) ),
inference(definition_unfolding,[],[f2141,f2915]) ).
fof(f3120,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK156(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(sK156(X0,X1),X3),unordered_pair(sK156(X0,X1),sK156(X0,X1))),X0)
| relation_dom(X0) = X1 ),
inference(definition_unfolding,[],[f2148,f2915]) ).
fof(f3121,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK156(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK156(X0,X1),sK157(X0,X1)),unordered_pair(sK156(X0,X1),sK156(X0,X1))),X0)
| relation_dom(X0) = X1 ),
inference(definition_unfolding,[],[f2147,f2915]) ).
fof(f3122,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,[],[f2146,f2915]) ).
fof(f3123,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(unordered_pair(unordered_pair(X5,sK158(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(definition_unfolding,[],[f2145,f2915]) ).
fof(f3124,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK159(X0,X1),sK160(X0,X1)),unordered_pair(sK159(X0,X1),sK159(X0,X1))),X1)
| subset(X0,X1) ),
inference(definition_unfolding,[],[f2151,f2915]) ).
fof(f3125,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK159(X0,X1),sK160(X0,X1)),unordered_pair(sK159(X0,X1),sK159(X0,X1))),X0)
| subset(X0,X1) ),
inference(definition_unfolding,[],[f2150,f2915]) ).
fof(f3127,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK161(X0,X1),sK162(X0,X1)),unordered_pair(sK161(X0,X1),sK161(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK161(X0,X1),sK162(X0,X1)),unordered_pair(sK161(X0,X1),sK161(X0,X1))),X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f2155,f2915,f2915]) ).
fof(f3128,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK161(X0,X1),sK162(X0,X1)),unordered_pair(sK161(X0,X1),sK161(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK161(X0,X1),sK162(X0,X1)),unordered_pair(sK161(X0,X1),sK161(X0,X1))),X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f2154,f2915,f2915]) ).
fof(f3131,plain,
! [X2,X3,X0] :
( sK163(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| relation(X0) ),
inference(definition_unfolding,[],[f2157,f2915]) ).
fof(f3132,plain,
! [X0,X4] :
( ~ relation(X0)
| unordered_pair(unordered_pair(sK164(X4),sK165(X4)),unordered_pair(sK164(X4),sK164(X4))) = X4
| ~ in(X4,X0) ),
inference(definition_unfolding,[],[f2156,f2915]) ).
fof(f3133,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK166(X0),sK167(X0)),unordered_pair(sK166(X0),sK166(X0))),X0)
| function(X0) ),
inference(definition_unfolding,[],[f2161,f2915]) ).
fof(f3134,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK166(X0),sK168(X0)),unordered_pair(sK166(X0),sK166(X0))),X0)
| function(X0) ),
inference(definition_unfolding,[],[f2160,f2915]) ).
fof(f3135,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,[],[f2159,f2915,f2915]) ).
fof(f3136,plain,
! [X0] :
( ~ empty(X0)
| sK140 = X0 ),
inference(definition_unfolding,[],[f2170,f2057]) ).
fof(f3138,plain,
relation(sK140),
inference(definition_unfolding,[],[f2171,f2057]) ).
fof(f3140,plain,
! [X0] :
( in(sK169(X0),X0)
| sK140 = X0 ),
inference(definition_unfolding,[],[f2175,f2057]) ).
fof(f3141,plain,
! [X2,X0] :
( sK140 != X0
| ~ in(X2,X0) ),
inference(definition_unfolding,[],[f2174,f2057]) ).
fof(f3142,plain,
! [X0] :
( ~ sP20(X0)
| sK171(X0) = unordered_pair(unordered_pair(sK173(X0),sK174(X0)),unordered_pair(sK173(X0),sK173(X0))) ),
inference(definition_unfolding,[],[f2180,f2915]) ).
fof(f3143,plain,
! [X0] :
( ~ sP20(X0)
| sK174(X0) = unordered_pair(sK173(X0),sK173(X0)) ),
inference(definition_unfolding,[],[f2178,f2077]) ).
fof(f3146,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,sK177(X0,X1)) ),
inference(definition_unfolding,[],[f2191,f2915,f2077]) ).
fof(f3147,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK177(X0,X1))
| unordered_pair(unordered_pair(sK179(X0,X3),sK180(X0,X3)),unordered_pair(sK179(X0,X3),sK179(X0,X3))) = X3 ),
inference(definition_unfolding,[],[f2188,f2915]) ).
fof(f3148,plain,
! [X3,X0,X1] :
( sP20(X0)
| ~ in(X3,sK177(X0,X1))
| sK180(X0,X3) = unordered_pair(sK179(X0,X3),sK179(X0,X3)) ),
inference(definition_unfolding,[],[f2186,f2077]) ).
fof(f3152,plain,
! [X2,X0] :
( sP21(X0)
| ~ in(X2,sK184(X0))
| unordered_pair(sK185(X0,X2),sK185(X0,X2)) = X2 ),
inference(definition_unfolding,[],[f2197,f2077]) ).
fof(f3154,plain,
! [X0,X1] :
( ~ in(sK186(X0,X1),X1)
| sK186(X0,X1) != X0
| unordered_pair(X0,X0) = X1 ),
inference(definition_unfolding,[],[f2205,f2077]) ).
fof(f3155,plain,
! [X0,X1] :
( in(sK186(X0,X1),X1)
| sK186(X0,X1) = X0
| unordered_pair(X0,X0) = X1 ),
inference(definition_unfolding,[],[f2204,f2077]) ).
fof(f3157,plain,
! [X3,X0,X1] :
( unordered_pair(X0,X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(definition_unfolding,[],[f2202,f2077]) ).
fof(f3158,plain,
! [X0] : set_union2(X0,sK140) = X0,
inference(definition_unfolding,[],[f2206,f2057]) ).
fof(f3159,plain,
! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) != sK140
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f2222,f2023,f2057]) ).
fof(f3160,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,set_difference(X0,X1)) = sK140 ),
inference(definition_unfolding,[],[f2221,f2023,f2057]) ).
fof(f3161,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),unordered_pair(sK191(X0,X1,X2),sK191(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),unordered_pair(sK191(X0,X1,X2),sK191(X0,X1,X2))),X1)
| ~ in(sK192(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2248,f2915,f2915]) ).
fof(f3162,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),unordered_pair(sK191(X0,X1,X2),sK191(X0,X1,X2))),X2)
| in(sK192(X0,X1,X2),X0)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2247,f2915]) ).
fof(f3163,plain,
! [X2,X0,X1] :
( ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),unordered_pair(sK191(X0,X1,X2),sK191(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),unordered_pair(sK191(X0,X1,X2),sK191(X0,X1,X2))),X1)
| relation_rng_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2246,f2915,f2915]) ).
fof(f3164,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,[],[f2245,f2915,f2915]) ).
fof(f3165,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,[],[f2244,f2915]) ).
fof(f3166,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,[],[f2243,f2915,f2915]) ).
fof(f3167,plain,
! [X0] : sK140 = set_difference(sK140,X0),
inference(definition_unfolding,[],[f2270,f2057,f2057]) ).
fof(f3168,plain,
! [X0] : set_difference(X0,sK140) = X0,
inference(definition_unfolding,[],[f2271,f2057]) ).
fof(f3173,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(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,sK213(X0,X1,X2)) ),
inference(definition_unfolding,[],[f2328,f2915,f2915]) ).
fof(f3174,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(X1,X2)
| ~ in(X4,sK213(X0,X1,X2))
| unordered_pair(unordered_pair(sK215(X1,X2,X4),sK216(X1,X2,X4)),unordered_pair(sK215(X1,X2,X4),sK215(X1,X2,X4))) = X4 ),
inference(definition_unfolding,[],[f2325,f2915]) ).
fof(f3175,plain,
! [X2,X0,X1,X4] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(X1,X2)
| ~ in(X4,sK213(X0,X1,X2))
| in(unordered_pair(unordered_pair(apply(X2,sK215(X1,X2,X4)),apply(X2,sK216(X1,X2,X4))),unordered_pair(apply(X2,sK215(X1,X2,X4)),apply(X2,sK215(X1,X2,X4)))),X1) ),
inference(definition_unfolding,[],[f2324,f2915]) ).
fof(f3176,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ in(unordered_pair(unordered_pair(X6,sK218(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))
| sP27(X0,X1,X2,X3) ),
inference(definition_unfolding,[],[f2339,f2915,f2915]) ).
fof(f3177,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( in(sK218(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))
| sP27(X0,X1,X2,X3) ),
inference(definition_unfolding,[],[f2338,f2915]) ).
fof(f3178,plain,
! [X2,X3,X0,X1] :
( ~ sP27(X0,X1,X2,X3)
| unordered_pair(unordered_pair(sK220(X1,X2,X3),sK221(X1,X2,X3)),unordered_pair(sK220(X1,X2,X3),sK220(X1,X2,X3))) = X2 ),
inference(definition_unfolding,[],[f2335,f2915]) ).
fof(f3179,plain,
! [X2,X3,X0,X1,X13] :
( ~ sP27(X0,X1,X2,X3)
| ~ in(X13,sK222(X1,X2,X3))
| in(unordered_pair(unordered_pair(sK221(X1,X2,X3),X13),unordered_pair(sK221(X1,X2,X3),sK221(X1,X2,X3))),X3) ),
inference(definition_unfolding,[],[f2331,f2915]) ).
fof(f3180,plain,
! [X2,X0,X1] :
( ~ sP26(X0,X1,X2)
| unordered_pair(unordered_pair(sK223(X0,X1,X2),sK224(X0,X1,X2)),unordered_pair(sK223(X0,X1,X2),sK223(X0,X1,X2))) = X0 ),
inference(definition_unfolding,[],[f2344,f2915]) ).
fof(f3181,plain,
! [X2,X0,X1,X6] :
( ~ sP26(X0,X1,X2)
| ~ in(X6,sK225(X0,X1,X2))
| in(unordered_pair(unordered_pair(sK224(X0,X1,X2),X6),unordered_pair(sK224(X0,X1,X2),sK224(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f2340,f2915]) ).
fof(f3184,plain,
! [X0,X1] :
( ~ relation(X0)
| relation_restriction(X0,X1) = set_difference(X0,set_difference(X0,cartesian_product2(X1,X1))) ),
inference(definition_unfolding,[],[f2357,f2023]) ).
fof(f3185,plain,
! [X2,X0,X1,X4,X5] :
( ~ in(sK232(X0,X1,X2),X2)
| sK232(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,[],[f2365,f2915]) ).
fof(f3186,plain,
! [X2,X0,X1] :
( in(sK232(X0,X1,X2),X2)
| sK232(X0,X1,X2) = unordered_pair(unordered_pair(sK233(X0,X1,X2),sK234(X0,X1,X2)),unordered_pair(sK233(X0,X1,X2),sK233(X0,X1,X2)))
| cartesian_product2(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2362,f2915]) ).
fof(f3187,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,[],[f2361,f2915]) ).
fof(f3188,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| unordered_pair(unordered_pair(sK235(X0,X1,X8),sK236(X0,X1,X8)),unordered_pair(sK235(X0,X1,X8),sK235(X0,X1,X8))) = X8 ),
inference(definition_unfolding,[],[f2358,f2915]) ).
fof(f3189,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),unordered_pair(sK237(X0,X1,X2),sK237(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),unordered_pair(sK237(X0,X1,X2),sK237(X0,X1,X2))),X0)
| ~ in(sK237(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2375,f2915,f2915]) ).
fof(f3190,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),unordered_pair(sK237(X0,X1,X2),sK237(X0,X1,X2))),X2)
| in(sK237(X0,X1,X2),X1)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2374,f2915]) ).
fof(f3191,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),unordered_pair(sK237(X0,X1,X2),sK237(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),unordered_pair(sK237(X0,X1,X2),sK237(X0,X1,X2))),X0)
| relation_dom_restriction(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2373,f2915,f2915]) ).
fof(f3192,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,[],[f2372,f2915,f2915]) ).
fof(f3193,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,[],[f2371,f2915]) ).
fof(f3194,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,[],[f2370,f2915,f2915]) ).
fof(f3195,plain,
! [X2,X3,X0,X1] :
( sK140 != sK251(X3)
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X1) ),
inference(definition_unfolding,[],[f2422,f2914,f2057]) ).
fof(f3196,plain,
! [X2,X3,X0,X1,X5] :
( sK252(X3,X5) != X5
| ~ in(X5,sK251(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X1) ),
inference(definition_unfolding,[],[f2421,f2914]) ).
fof(f3197,plain,
! [X2,X3,X0,X1,X5] :
( in(sK252(X3,X5),sK251(X3))
| ~ in(X5,sK251(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X1) ),
inference(definition_unfolding,[],[f2420,f2914]) ).
fof(f3198,plain,
! [X2,X3,X0,X1,X5] :
( subset(X5,sK252(X3,X5))
| ~ in(X5,sK251(X3))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X1) ),
inference(definition_unfolding,[],[f2419,f2914]) ).
fof(f3199,plain,
! [X2,X3,X0,X1] :
( element(sK251(X3),powerset(powerset(X3)))
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X1) ),
inference(definition_unfolding,[],[f2418,f2914]) ).
fof(f3200,plain,
! [X2,X3,X0,X1] :
( in(X3,omega)
| X1 != X3
| ~ ordinal(X3)
| X1 != X2
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X1) ),
inference(definition_unfolding,[],[f2417,f2914]) ).
fof(f3201,plain,
! [X0,X1] :
( ~ sP31(X0,X1)
| in(sK253(X0,X1),set_union2(X0,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f2416,f2914]) ).
fof(f3202,plain,
! [X0,X1,X9] :
( ~ sP31(X0,X1)
| ~ in(sK254(X1),omega)
| ~ element(X9,powerset(powerset(sK254(X1))))
| in(sK255(X9),X9)
| sK140 = X9 ),
inference(definition_unfolding,[],[f2412,f2057]) ).
fof(f3203,plain,
! [X0,X11,X1,X9] :
( ~ sP31(X0,X1)
| ~ in(sK254(X1),omega)
| ~ element(X9,powerset(powerset(sK254(X1))))
| ~ subset(sK255(X9),X11)
| ~ in(X11,X9)
| sK255(X9) = X11
| sK140 = X9 ),
inference(definition_unfolding,[],[f2411,f2057]) ).
fof(f3206,plain,
! [X0,X5] :
( ~ ordinal(X0)
| ~ in(sK261,omega)
| ~ element(X5,powerset(powerset(sK261)))
| in(sK262(X5),X5)
| sK140 = X5
| sP32(X0) ),
inference(definition_unfolding,[],[f2430,f2057]) ).
fof(f3207,plain,
! [X0,X7,X5] :
( ~ ordinal(X0)
| ~ in(sK261,omega)
| ~ element(X5,powerset(powerset(sK261)))
| ~ subset(sK262(X5),X7)
| ~ in(X7,X5)
| sK262(X5) = X7
| sK140 = X5
| sP32(X0) ),
inference(definition_unfolding,[],[f2429,f2057]) ).
fof(f3208,plain,
! [X0] :
( ~ subset(X0,sK263(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(sK140,X0)
| omega = X0 ),
inference(definition_unfolding,[],[f2446,f2057]) ).
fof(f3209,plain,
! [X0] :
( in(sK140,sK263(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(sK140,X0)
| omega = X0 ),
inference(definition_unfolding,[],[f2445,f2057,f2057]) ).
fof(f3210,plain,
! [X0] :
( being_limit_ordinal(sK263(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(sK140,X0)
| omega = X0 ),
inference(definition_unfolding,[],[f2444,f2057]) ).
fof(f3211,plain,
! [X0] :
( ordinal(sK263(X0))
| ~ ordinal(X0)
| ~ being_limit_ordinal(X0)
| ~ in(sK140,X0)
| omega = X0 ),
inference(definition_unfolding,[],[f2443,f2057]) ).
fof(f3212,plain,
! [X0] :
( omega != X0
| in(sK140,X0) ),
inference(definition_unfolding,[],[f2442,f2057]) ).
fof(f3213,plain,
! [X2,X0] :
( omega != X0
| ~ ordinal(X2)
| ~ being_limit_ordinal(X2)
| ~ in(sK140,X2)
| subset(X0,X2) ),
inference(definition_unfolding,[],[f2439,f2057]) ).
fof(f3214,plain,
! [X3,X0,X1,X4,X5] :
( ~ ordinal(X1)
| sP34(X0)
| ~ in(X5,X0)
| X3 != X5
| ~ ordinal(X5)
| X3 != X4
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1)))
| in(X3,sK270(X0,X1)) ),
inference(definition_unfolding,[],[f2471,f2914]) ).
fof(f3215,plain,
! [X3,X0,X1] :
( ~ ordinal(X1)
| sP34(X0)
| ~ in(X3,sK270(X0,X1))
| in(sK271(X0,X1,X3),set_union2(X1,unordered_pair(X1,X1))) ),
inference(definition_unfolding,[],[f2470,f2914]) ).
fof(f3218,plain,
! [X3,X0,X1,X4,X5] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP35(X1,X0)
| set_difference(X5,unordered_pair(X0,X0)) != X3
| ~ in(X5,X1)
| X3 != X4
| ~ in(X4,powerset(X0))
| in(X3,sK278(X0,X1)) ),
inference(definition_unfolding,[],[f2483,f2077,f2914]) ).
fof(f3219,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP35(X1,X0)
| ~ in(X3,sK278(X0,X1))
| in(sK279(X0,X1,X3),powerset(X0)) ),
inference(definition_unfolding,[],[f2482,f2914]) ).
fof(f3220,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP35(X1,X0)
| ~ in(X3,sK278(X0,X1))
| sK279(X0,X1,X3) = X3 ),
inference(definition_unfolding,[],[f2481,f2914]) ).
fof(f3221,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP35(X1,X0)
| ~ in(X3,sK278(X0,X1))
| in(sK280(X0,X1,X3),X1) ),
inference(definition_unfolding,[],[f2480,f2914]) ).
fof(f3222,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP35(X1,X0)
| ~ in(X3,sK278(X0,X1))
| set_difference(sK280(X0,X1,X3),unordered_pair(X0,X0)) = X3 ),
inference(definition_unfolding,[],[f2479,f2077,f2914]) ).
fof(f3224,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(set_union2(X0,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f2486,f2914]) ).
fof(f3225,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(set_union2(X0,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f2485,f2914]) ).
fof(f3226,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f2484,f2914]) ).
fof(f3227,plain,
! [X0] : ~ empty(set_union2(X0,unordered_pair(X0,X0))),
inference(definition_unfolding,[],[f2488,f2914]) ).
fof(f3231,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| sK140 = X2 ),
inference(definition_unfolding,[],[f2499,f2057]) ).
fof(f3232,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK291(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(X4,sK291(X0,X1,X2)),unordered_pair(X4,X4)),X0)
| relation_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2522,f2915]) ).
fof(f3233,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK291(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK292(X0,X1,X2),sK291(X0,X1,X2)),unordered_pair(sK292(X0,X1,X2),sK292(X0,X1,X2))),X0)
| relation_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2521,f2915]) ).
fof(f3234,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,[],[f2519,f2915]) ).
fof(f3235,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_image(X0,X1) != X2
| ~ in(X6,X2)
| in(unordered_pair(unordered_pair(sK293(X0,X1,X6),X6),unordered_pair(sK293(X0,X1,X6),sK293(X0,X1,X6))),X0) ),
inference(definition_unfolding,[],[f2518,f2915]) ).
fof(f3236,plain,
! [X0] : sK140 = set_difference(X0,set_difference(X0,sK140)),
inference(definition_unfolding,[],[f2543,f2057,f2023,f2057]) ).
fof(f3244,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f2551,f2023]) ).
fof(f3245,plain,
! [X2,X0,X1] :
( ~ in(sK298(X0,X1,X2),X2)
| ~ in(sK298(X0,X1,X2),X1)
| ~ in(sK298(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f2557,f2023]) ).
fof(f3246,plain,
! [X2,X0,X1] :
( in(sK298(X0,X1,X2),X2)
| in(sK298(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f2556,f2023]) ).
fof(f3247,plain,
! [X2,X0,X1] :
( in(sK298(X0,X1,X2),X2)
| in(sK298(X0,X1,X2),X1)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f2555,f2023]) ).
fof(f3248,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,[],[f2554,f2023]) ).
fof(f3250,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,set_difference(X0,X1)) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(definition_unfolding,[],[f2552,f2023]) ).
fof(f3251,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f2558,f2023,f2023]) ).
fof(f3253,plain,
! [X0] : finite(unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f2574,f2077]) ).
fof(f3255,plain,
! [X0,X1] :
( ~ finite(X1)
| finite(set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f2578,f2023]) ).
fof(f3256,plain,
! [X2,X0,X1,X4] :
( ~ relation(X0)
| ~ in(sK304(X0,X1,X2),X2)
| ~ in(X4,X1)
| ~ in(unordered_pair(unordered_pair(sK304(X0,X1,X2),X4),unordered_pair(sK304(X0,X1,X2),sK304(X0,X1,X2))),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2586,f2915]) ).
fof(f3257,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK304(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK304(X0,X1,X2),sK305(X0,X1,X2)),unordered_pair(sK304(X0,X1,X2),sK304(X0,X1,X2))),X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2585,f2915]) ).
fof(f3258,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,[],[f2583,f2915]) ).
fof(f3259,plain,
! [X2,X0,X1,X6] :
( ~ relation(X0)
| relation_inverse_image(X0,X1) != X2
| ~ in(X6,X2)
| in(unordered_pair(unordered_pair(X6,sK306(X0,X1,X6)),unordered_pair(X6,X6)),X0) ),
inference(definition_unfolding,[],[f2582,f2915]) ).
fof(f3260,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,[],[f2593,f2023]) ).
fof(f3261,plain,
! [X2,X0,X1,X5] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(sK308(X0,X1,X2),sK309(X0,X1,X2)),unordered_pair(sK308(X0,X1,X2),sK308(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(X5,sK309(X0,X1,X2)),unordered_pair(X5,X5)),X1)
| ~ in(unordered_pair(unordered_pair(sK308(X0,X1,X2),X5),unordered_pair(sK308(X0,X1,X2),sK308(X0,X1,X2))),X0)
| relation_composition(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2609,f2915,f2915,f2915]) ).
fof(f3262,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK308(X0,X1,X2),sK309(X0,X1,X2)),unordered_pair(sK308(X0,X1,X2),sK308(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK308(X0,X1,X2),sK310(X0,X1,X2)),unordered_pair(sK308(X0,X1,X2),sK308(X0,X1,X2))),X0)
| relation_composition(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2608,f2915,f2915]) ).
fof(f3263,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK308(X0,X1,X2),sK309(X0,X1,X2)),unordered_pair(sK308(X0,X1,X2),sK308(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK310(X0,X1,X2),sK309(X0,X1,X2)),unordered_pair(sK310(X0,X1,X2),sK310(X0,X1,X2))),X1)
| relation_composition(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2607,f2915,f2915]) ).
fof(f3264,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,[],[f2606,f2915,f2915,f2915]) ).
fof(f3265,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,sK311(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0) ),
inference(definition_unfolding,[],[f2605,f2915,f2915]) ).
fof(f3266,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(sK311(X0,X1,X7,X8),X8),unordered_pair(sK311(X0,X1,X7,X8),sK311(X0,X1,X7,X8))),X1) ),
inference(definition_unfolding,[],[f2604,f2915,f2915]) ).
fof(f3267,plain,
! [X0,X1] :
( ~ relation(X0)
| sK140 != sK317(X0,X1)
| is_well_founded_in(X0,X1) ),
inference(definition_unfolding,[],[f2654,f2057]) ).
fof(f3268,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| in(sK318(X0,X4),X4)
| sK140 = X4
| ~ subset(X4,X1) ),
inference(definition_unfolding,[],[f2652,f2057]) ).
fof(f3269,plain,
! [X0,X1,X4] :
( ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| disjoint(fiber(X0,sK318(X0,X4)),X4)
| sK140 = X4
| ~ subset(X4,X1) ),
inference(definition_unfolding,[],[f2651,f2057]) ).
fof(f3270,plain,
! [X0] :
( ~ relation(X0)
| sK140 != sK319(X0)
| well_founded_relation(X0) ),
inference(definition_unfolding,[],[f2659,f2057]) ).
fof(f3271,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| in(sK320(X0,X3),X3)
| sK140 = X3
| ~ subset(X3,relation_field(X0)) ),
inference(definition_unfolding,[],[f2657,f2057]) ).
fof(f3272,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| disjoint(fiber(X0,sK320(X0,X3)),X3)
| sK140 = X3
| ~ subset(X3,relation_field(X0)) ),
inference(definition_unfolding,[],[f2656,f2057]) ).
fof(f3273,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ in(sK321(X0,X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(sK321(X0,X1,X2),X1),unordered_pair(sK321(X0,X1,X2),sK321(X0,X1,X2))),X0)
| sK321(X0,X1,X2) = X1
| fiber(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2666,f2915]) ).
fof(f3274,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(sK321(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK321(X0,X1,X2),X1),unordered_pair(sK321(X0,X1,X2),sK321(X0,X1,X2))),X0)
| fiber(X0,X1) = X2 ),
inference(definition_unfolding,[],[f2664,f2915]) ).
fof(f3275,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,[],[f2663,f2915]) ).
fof(f3276,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,[],[f2661,f2915]) ).
fof(f3277,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| sK140 != X0
| relation_dom_as_subset(X0,X1,X2) != X0
| quasi_total(X2,X0,X1) ),
inference(definition_unfolding,[],[f2674,f2057]) ).
fof(f3278,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| sK140 = X1
| relation_dom_as_subset(X0,X1,X2) != X0
| quasi_total(X2,X0,X1) ),
inference(definition_unfolding,[],[f2673,f2057]) ).
fof(f3279,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| sK140 != X0
| ~ quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = X0 ),
inference(definition_unfolding,[],[f2672,f2057]) ).
fof(f3280,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| sK140 = X1
| ~ quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = X0 ),
inference(definition_unfolding,[],[f2671,f2057]) ).
fof(f3281,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| sK140 != X1
| sK140 != X2
| quasi_total(X2,X0,X1)
| sK140 = X0 ),
inference(definition_unfolding,[],[f2670,f2057,f2057,f2057]) ).
fof(f3282,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| sK140 != X1
| ~ quasi_total(X2,X0,X1)
| sK140 = X2
| sK140 = X0 ),
inference(definition_unfolding,[],[f2669,f2057,f2057,f2057]) ).
fof(f3283,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK326(X0,X1),sK327(X0,X1)),unordered_pair(sK326(X0,X1),sK326(X0,X1))),X1)
| ~ subset(sK326(X0,X1),sK327(X0,X1))
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(definition_unfolding,[],[f2695,f2915]) ).
fof(f3284,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK326(X0,X1),sK327(X0,X1)),unordered_pair(sK326(X0,X1),sK326(X0,X1))),X1)
| subset(sK326(X0,X1),sK327(X0,X1))
| relation_field(X1) != X0
| inclusion_relation(X0) = X1 ),
inference(definition_unfolding,[],[f2694,f2915]) ).
fof(f3285,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,[],[f2690,f2915]) ).
fof(f3286,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,[],[f2689,f2915]) ).
fof(f3287,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK328(X0,X1),sK329(X0,X1)),unordered_pair(sK328(X0,X1),sK328(X0,X1))),X1)
| sK328(X0,X1) != sK329(X0,X1)
| ~ in(sK328(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f2704,f2915]) ).
fof(f3288,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK328(X0,X1),sK329(X0,X1)),unordered_pair(sK328(X0,X1),sK328(X0,X1))),X1)
| in(sK328(X0,X1),X0)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f2703,f2915]) ).
fof(f3289,plain,
! [X0,X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK328(X0,X1),sK329(X0,X1)),unordered_pair(sK328(X0,X1),sK328(X0,X1))),X1)
| sK328(X0,X1) = sK329(X0,X1)
| identity_relation(X0) = X1 ),
inference(definition_unfolding,[],[f2702,f2915]) ).
fof(f3290,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,[],[f2701,f2915]) ).
fof(f3291,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,[],[f2700,f2915]) ).
fof(f3292,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,[],[f2699,f2915]) ).
fof(f3293,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK330(X0,X1),sK331(X0,X1)),unordered_pair(sK330(X0,X1),sK330(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK331(X0,X1),sK330(X0,X1)),unordered_pair(sK331(X0,X1),sK331(X0,X1))),X0)
| relation_inverse(X0) = X1 ),
inference(definition_unfolding,[],[f2715,f2915,f2915]) ).
fof(f3294,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK330(X0,X1),sK331(X0,X1)),unordered_pair(sK330(X0,X1),sK330(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK331(X0,X1),sK330(X0,X1)),unordered_pair(sK331(X0,X1),sK331(X0,X1))),X0)
| relation_inverse(X0) = X1 ),
inference(definition_unfolding,[],[f2714,f2915,f2915]) ).
fof(f3295,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,[],[f2713,f2915,f2915]) ).
fof(f3296,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,[],[f2712,f2915,f2915]) ).
fof(f3305,plain,
! [X0,X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| sK339(X0,X1) != X1
| pair_first(X0) = X1 ),
inference(definition_unfolding,[],[f2771,f2915]) ).
fof(f3306,plain,
! [X0,X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| unordered_pair(unordered_pair(sK339(X0,X1),sK340(X0,X1)),unordered_pair(sK339(X0,X1),sK339(X0,X1))) = X0
| pair_first(X0) = X1 ),
inference(definition_unfolding,[],[f2770,f2915,f2915]) ).
fof(f3307,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,[],[f2769,f2915,f2915]) ).
fof(f3308,plain,
! [X0,X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| sK342(X0,X1) != X1
| pair_second(X0) = X1 ),
inference(definition_unfolding,[],[f2774,f2915]) ).
fof(f3309,plain,
! [X0,X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0
| unordered_pair(unordered_pair(sK341(X0,X1),sK342(X0,X1)),unordered_pair(sK341(X0,X1),sK341(X0,X1))) = X0
| pair_second(X0) = X1 ),
inference(definition_unfolding,[],[f2773,f2915,f2915]) ).
fof(f3310,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,[],[f2772,f2915,f2915]) ).
fof(f3330,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK350(X0,X1),sK351(X0,X1)),unordered_pair(sK350(X0,X1),sK350(X0,X1))),X0)
| is_antisymmetric_in(X0,X1) ),
inference(definition_unfolding,[],[f2848,f2915]) ).
fof(f3331,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK351(X0,X1),sK350(X0,X1)),unordered_pair(sK351(X0,X1),sK351(X0,X1))),X0)
| is_antisymmetric_in(X0,X1) ),
inference(definition_unfolding,[],[f2847,f2915]) ).
fof(f3332,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,[],[f2846,f2915,f2915]) ).
fof(f3333,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK352(X0,X1),sK353(X0,X1)),unordered_pair(sK352(X0,X1),sK352(X0,X1))),X0)
| is_connected_in(X0,X1) ),
inference(definition_unfolding,[],[f2856,f2915]) ).
fof(f3334,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK353(X0,X1),sK352(X0,X1)),unordered_pair(sK353(X0,X1),sK353(X0,X1))),X0)
| is_connected_in(X0,X1) ),
inference(definition_unfolding,[],[f2855,f2915]) ).
fof(f3335,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,[],[f2854,f2915,f2915]) ).
fof(f3336,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK354(X0,X1),sK356(X0,X1)),unordered_pair(sK354(X0,X1),sK354(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f2868,f2915]) ).
fof(f3337,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK354(X0,X1),sK355(X0,X1)),unordered_pair(sK354(X0,X1),sK354(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f2864,f2915]) ).
fof(f3338,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK355(X0,X1),sK356(X0,X1)),unordered_pair(sK355(X0,X1),sK355(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f2863,f2915]) ).
fof(f3339,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,[],[f2862,f2915,f2915,f2915]) ).
fof(f3340,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK357(X0,X1),sK357(X0,X1)),unordered_pair(sK357(X0,X1),sK357(X0,X1))),X0)
| is_reflexive_in(X0,X1) ),
inference(definition_unfolding,[],[f2875,f2915]) ).
fof(f3341,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,[],[f2873,f2915]) ).
fof(f3342,plain,
empty(sK140),
inference(definition_unfolding,[],[f2887,f2057]) ).
fof(f3363,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ relation(X1)
| empty(X0)
| ~ in(unordered_pair(unordered_pair(X6,sK75(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)),sK74(X0,X1,X2)) ),
inference(equality_resolution,[],[f2976]) ).
fof(f3364,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X1)
| empty(X0)
| ~ in(unordered_pair(unordered_pair(X6,sK75(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)),sK74(X0,X1,X2)) ),
inference(equality_resolution,[],[f3363]) ).
fof(f3365,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ relation(X1)
| empty(X0)
| in(sK75(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)),sK74(X0,X1,X2)) ),
inference(equality_resolution,[],[f2977]) ).
fof(f3366,plain,
! [X2,X0,X1,X6,X7] :
( ~ relation(X1)
| empty(X0)
| in(sK75(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)),sK74(X0,X1,X2)) ),
inference(equality_resolution,[],[f3365]) ).
fof(f3367,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)),sK79(X0,X1)) ),
inference(equality_resolution,[],[f2980]) ).
fof(f3368,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)),sK79(X0,X1)) ),
inference(equality_resolution,[],[f3367]) ).
fof(f3375,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)),sK87(X0,X1)) ),
inference(equality_resolution,[],[f2992]) ).
fof(f3376,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)),sK89(X0,X1,X2)) ),
inference(equality_resolution,[],[f2996]) ).
fof(f3377,plain,
! [X0,X1,X4] :
( ~ ordinal(X1)
| ~ in(X4,X0)
| ~ ordinal(X4)
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1)))
| in(X4,sK94(X0,X1)) ),
inference(equality_resolution,[],[f2999]) ).
fof(f3378,plain,
! [X3,X0,X1] :
( ~ relation(X1)
| empty(X0)
| ~ in(unordered_pair(unordered_pair(X3,sK104(X1,X3,sK103(X0,X1))),unordered_pair(X3,X3)),X1)
| ~ in(X3,sK103(X0,X1))
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(equality_resolution,[],[f3004]) ).
fof(f3379,plain,
! [X3,X0,X1] :
( ~ relation(X1)
| empty(X0)
| in(sK104(X1,X3,sK103(X0,X1)),sK103(X0,X1))
| ~ in(X3,sK103(X0,X1))
| sP11(X0,X1)
| sP12(X0,X1) ),
inference(equality_resolution,[],[f1812]) ).
fof(f3380,plain,
! [X0] :
( sP13(X0)
| relation(sK108(X0)) ),
inference(equality_resolution,[],[f3007]) ).
fof(f3381,plain,
! [X0] :
( sP13(X0)
| function(sK108(X0)) ),
inference(equality_resolution,[],[f3008]) ).
fof(f3382,plain,
! [X0] :
( sP13(X0)
| relation_dom(sK108(X0)) = X0 ),
inference(equality_resolution,[],[f3009]) ).
fof(f3383,plain,
! [X2,X0] :
( sP13(X0)
| ~ in(X2,X0)
| apply(sK108(X0),X2) = unordered_pair(X2,X2) ),
inference(equality_resolution,[],[f3011]) ).
fof(f3384,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| sK129(relation_dom(X1),X1) != apply(X1,sK129(relation_dom(X1),X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f1971]) ).
fof(f3385,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK129(relation_dom(X1),X1),relation_dom(X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f1970]) ).
fof(f3390,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,[],[f3069]) ).
fof(f3395,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,[],[f2042]) ).
fof(f3396,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,[],[f3395]) ).
fof(f3399,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,[],[f2040]) ).
fof(f3402,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,[],[f3099]) ).
fof(f3404,plain,
! [X2,X3,X1] :
( ~ relation_of2_as_subset(X3,sK140,X1)
| ~ quasi_total(X3,sK140,X1)
| ~ function(X3)
| ~ subset(X1,X2)
| quasi_total(X3,sK140,X2) ),
inference(equality_resolution,[],[f3108]) ).
fof(f3408,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,[],[f3118]) ).
fof(f3409,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK155(X0,X5),X5),unordered_pair(sK155(X0,X5),sK155(X0,X5))),X0) ),
inference(equality_resolution,[],[f3119]) ).
fof(f3410,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,[],[f3122]) ).
fof(f3411,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(unordered_pair(unordered_pair(X5,sK158(X0,X5)),unordered_pair(X5,X5)),X0) ),
inference(equality_resolution,[],[f3123]) ).
fof(f3414,plain,
! [X2] : ~ in(X2,sK140),
inference(equality_resolution,[],[f3141]) ).
fof(f3415,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,sK177(X0,X1)) ),
inference(equality_resolution,[],[f3146]) ).
fof(f3416,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)),sK177(X0,X1)) ),
inference(equality_resolution,[],[f3415]) ).
fof(f3417,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)),sK177(X0,X1)) ),
inference(equality_resolution,[],[f3416]) ).
fof(f3421,plain,
! [X3,X0] :
( ~ in(X3,unordered_pair(X0,X0))
| X0 = X3 ),
inference(equality_resolution,[],[f3157]) ).
fof(f3422,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f2214]) ).
fof(f3423,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f2213]) ).
fof(f3424,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f2212]) ).
fof(f3425,plain,
! [X2,X1] :
( ~ sP23(topstr_closure(X2,X1),X1,X2)
| sP22(X2,X1,topstr_closure(X2,X1)) ),
inference(equality_resolution,[],[f2223]) ).
fof(f3426,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,[],[f3164]) ).
fof(f3427,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,[],[f3165]) ).
fof(f3428,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,[],[f3166]) ).
fof(f3429,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f2256]) ).
fof(f3430,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f2255]) ).
fof(f3432,plain,
! [X1] : subset(X1,X1),
inference(equality_resolution,[],[f2259]) ).
fof(f3433,plain,
! [X2,X1] :
( relation_rng(X2) != X1
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2)
| equipotent(relation_dom(X2),X1) ),
inference(equality_resolution,[],[f2269]) ).
fof(f3434,plain,
! [X2] :
( ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2)
| equipotent(relation_dom(X2),relation_rng(X2)) ),
inference(equality_resolution,[],[f3433]) ).
fof(f3435,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f2281]) ).
fof(f3436,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f2280]) ).
fof(f3437,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f2279]) ).
fof(f3438,plain,
! [X0,X6,X5] :
( ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,union(X0)) ),
inference(equality_resolution,[],[f2313]) ).
fof(f3439,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(X5,sK205(X0,X5)) ),
inference(equality_resolution,[],[f2312]) ).
fof(f3440,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK205(X0,X5),X0) ),
inference(equality_resolution,[],[f2311]) ).
fof(f3441,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(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,sK213(X0,X1,X2)) ),
inference(equality_resolution,[],[f3173]) ).
fof(f3442,plain,
! [X2,X0,X1,X6,X7] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(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)),sK213(X0,X1,X2)) ),
inference(equality_resolution,[],[f3441]) ).
fof(f3443,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( ~ in(unordered_pair(unordered_pair(X6,sK218(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))
| sP27(X0,X1,X4,X3) ),
inference(equality_resolution,[],[f3176]) ).
fof(f3444,plain,
! [X3,X0,X1,X6,X7,X5] :
( ~ in(unordered_pair(unordered_pair(X6,sK218(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))
| sP27(X0,X1,unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X3) ),
inference(equality_resolution,[],[f3443]) ).
fof(f3445,plain,
! [X3,X0,X1,X6,X7] :
( ~ in(unordered_pair(unordered_pair(X6,sK218(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))
| sP27(X0,X1,unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X3) ),
inference(equality_resolution,[],[f3444]) ).
fof(f3446,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( in(sK218(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))
| sP27(X0,X1,X4,X3) ),
inference(equality_resolution,[],[f3177]) ).
fof(f3447,plain,
! [X3,X0,X1,X6,X7,X5] :
( in(sK218(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))
| sP27(X0,X1,unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X3) ),
inference(equality_resolution,[],[f3446]) ).
fof(f3448,plain,
! [X3,X0,X1,X6,X7] :
( in(sK218(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))
| sP27(X0,X1,unordered_pair(unordered_pair(X7,X6),unordered_pair(X7,X7)),X3) ),
inference(equality_resolution,[],[f3447]) ).
fof(f3449,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,[],[f3187]) ).
fof(f3450,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,[],[f3449]) ).
fof(f3451,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK235(X0,X1,X8),X0) ),
inference(equality_resolution,[],[f2360]) ).
fof(f3452,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK236(X0,X1,X8),X1) ),
inference(equality_resolution,[],[f2359]) ).
fof(f3453,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(sK235(X0,X1,X8),sK236(X0,X1,X8)),unordered_pair(sK235(X0,X1,X8),sK235(X0,X1,X8))) = X8 ),
inference(equality_resolution,[],[f3188]) ).
fof(f3454,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,[],[f3192]) ).
fof(f3455,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,[],[f3193]) ).
fof(f3456,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,[],[f3194]) ).
fof(f3457,plain,
! [X3,X0] :
( sP29
| ~ ordinal(X3)
| ~ in(X3,X0)
| in(X3,sK248(X0)) ),
inference(equality_resolution,[],[f2404]) ).
fof(f3458,plain,
! [X2,X3,X0] :
( sK140 != sK251(X3)
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X2) ),
inference(equality_resolution,[],[f3195]) ).
fof(f3459,plain,
! [X3,X0] :
( sK140 != sK251(X3)
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X3) ),
inference(equality_resolution,[],[f3458]) ).
fof(f3460,plain,
! [X2,X3,X0,X5] :
( sK252(X3,X5) != X5
| ~ in(X5,sK251(X3))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X2) ),
inference(equality_resolution,[],[f3196]) ).
fof(f3461,plain,
! [X3,X0,X5] :
( sK252(X3,X5) != X5
| ~ in(X5,sK251(X3))
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X3) ),
inference(equality_resolution,[],[f3460]) ).
fof(f3462,plain,
! [X2,X3,X0,X5] :
( in(sK252(X3,X5),sK251(X3))
| ~ in(X5,sK251(X3))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X2) ),
inference(equality_resolution,[],[f3197]) ).
fof(f3463,plain,
! [X3,X0,X5] :
( in(sK252(X3,X5),sK251(X3))
| ~ in(X5,sK251(X3))
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X3) ),
inference(equality_resolution,[],[f3462]) ).
fof(f3464,plain,
! [X2,X3,X0,X5] :
( subset(X5,sK252(X3,X5))
| ~ in(X5,sK251(X3))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X2) ),
inference(equality_resolution,[],[f3198]) ).
fof(f3465,plain,
! [X3,X0,X5] :
( subset(X5,sK252(X3,X5))
| ~ in(X5,sK251(X3))
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X3) ),
inference(equality_resolution,[],[f3464]) ).
fof(f3466,plain,
! [X2,X3,X0] :
( element(sK251(X3),powerset(powerset(X3)))
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X2) ),
inference(equality_resolution,[],[f3199]) ).
fof(f3467,plain,
! [X3,X0] :
( element(sK251(X3),powerset(powerset(X3)))
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X3) ),
inference(equality_resolution,[],[f3466]) ).
fof(f3468,plain,
! [X2,X3,X0] :
( in(X3,omega)
| X2 != X3
| ~ ordinal(X3)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X2) ),
inference(equality_resolution,[],[f3200]) ).
fof(f3469,plain,
! [X3,X0] :
( in(X3,omega)
| ~ ordinal(X3)
| ~ in(X3,set_union2(X0,unordered_pair(X0,X0)))
| sP31(X0,X3) ),
inference(equality_resolution,[],[f3468]) ).
fof(f3470,plain,
in(sK140,omega),
inference(equality_resolution,[],[f3212]) ).
fof(f3471,plain,
being_limit_ordinal(omega),
inference(equality_resolution,[],[f2441]) ).
fof(f3472,plain,
ordinal(omega),
inference(equality_resolution,[],[f2440]) ).
fof(f3473,plain,
! [X2] :
( ~ ordinal(X2)
| ~ being_limit_ordinal(X2)
| ~ in(sK140,X2)
| subset(omega,X2) ),
inference(equality_resolution,[],[f3213]) ).
fof(f3474,plain,
! [X1] :
( ~ in(relation_dom(X1),omega)
| ~ function(X1)
| ~ relation(X1)
| finite(relation_rng(X1)) ),
inference(equality_resolution,[],[f2451]) ).
fof(f3475,plain,
! [X0,X1,X4,X5] :
( ~ ordinal(X1)
| sP34(X0)
| ~ in(X5,X0)
| X4 != X5
| ~ ordinal(X5)
| ~ in(X4,set_union2(X1,unordered_pair(X1,X1)))
| in(X4,sK270(X0,X1)) ),
inference(equality_resolution,[],[f3214]) ).
fof(f3476,plain,
! [X0,X1,X5] :
( ~ ordinal(X1)
| sP34(X0)
| ~ in(X5,X0)
| ~ ordinal(X5)
| ~ in(X5,set_union2(X1,unordered_pair(X1,X1)))
| in(X5,sK270(X0,X1)) ),
inference(equality_resolution,[],[f3475]) ).
fof(f3477,plain,
! [X0,X1,X4,X5] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP35(X1,X0)
| set_difference(X5,unordered_pair(X0,X0)) != X4
| ~ in(X5,X1)
| ~ in(X4,powerset(X0))
| in(X4,sK278(X0,X1)) ),
inference(equality_resolution,[],[f3218]) ).
fof(f3478,plain,
! [X0,X1,X5] :
( ~ element(X1,powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ ordinal(X0)
| sP35(X1,X0)
| ~ in(X5,X1)
| ~ in(set_difference(X5,unordered_pair(X0,X0)),powerset(X0))
| in(set_difference(X5,unordered_pair(X0,X0)),sK278(X0,X1)) ),
inference(equality_resolution,[],[f3477]) ).
fof(f3479,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,[],[f2495]) ).
fof(f3480,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f3479]) ).
fof(f3481,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(sK284(X0,X5),relation_dom(X0)) ),
inference(equality_resolution,[],[f2494]) ).
fof(f3482,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| apply(X0,sK284(X0,X5)) = X5 ),
inference(equality_resolution,[],[f2493]) ).
fof(f3485,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) = sK140 ),
inference(equality_resolution,[],[f3231]) ).
fof(f3486,plain,
! [X2,X0,X1,X5] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP36(X1,X2)
| ~ in(relation_image(X2,X5),X1)
| ~ in(X5,powerset(relation_dom(X2)))
| in(X5,sK289(X1,X2)) ),
inference(equality_resolution,[],[f2515]) ).
fof(f3487,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,[],[f3234]) ).
fof(f3488,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(unordered_pair(unordered_pair(sK293(X0,X1,X6),X6),unordered_pair(sK293(X0,X1,X6),sK293(X0,X1,X6))),X0) ),
inference(equality_resolution,[],[f3235]) ).
fof(f3489,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK293(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f2517]) ).
fof(f3490,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,[],[f2526]) ).
fof(f3491,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,[],[f3490]) ).
fof(f3492,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK296(X0,X1,X6),relation_dom(X0)) ),
inference(equality_resolution,[],[f2525]) ).
fof(f3493,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| in(sK296(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f2524]) ).
fof(f3494,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_image(X0,X1))
| apply(X0,sK296(X0,X1,X6)) = X6 ),
inference(equality_resolution,[],[f2523]) ).
fof(f3495,plain,
! [X2,X1,X4] :
( unordered_pair(X4,X1) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f2535]) ).
fof(f3496,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f3495]) ).
fof(f3497,plain,
! [X2,X0,X4] :
( unordered_pair(X0,X4) != X2
| in(X4,X2) ),
inference(equality_resolution,[],[f2534]) ).
fof(f3498,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f3497]) ).
fof(f3499,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f2533]) ).
fof(f3500,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,set_difference(X0,X1))) ),
inference(equality_resolution,[],[f3248]) ).
fof(f3502,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,set_difference(X0,X1)))
| in(X4,X1) ),
inference(equality_resolution,[],[f3250]) ).
fof(f3503,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,[],[f3258]) ).
fof(f3504,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(unordered_pair(unordered_pair(X6,sK306(X0,X1,X6)),unordered_pair(X6,X6)),X0) ),
inference(equality_resolution,[],[f3259]) ).
fof(f3505,plain,
! [X0,X1,X6] :
( ~ relation(X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(sK306(X0,X1,X6),X1) ),
inference(equality_resolution,[],[f2581]) ).
fof(f3506,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,[],[f2589]) ).
fof(f3507,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(X4,relation_dom(X0)) ),
inference(equality_resolution,[],[f2588]) ).
fof(f3508,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X4,relation_inverse_image(X0,X1))
| in(apply(X0,X4),X1) ),
inference(equality_resolution,[],[f2587]) ).
fof(f3509,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,[],[f3264]) ).
fof(f3510,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,sK311(X0,X1,X7,X8)),unordered_pair(X7,X7)),X0) ),
inference(equality_resolution,[],[f3265]) ).
fof(f3511,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(sK311(X0,X1,X7,X8),X8),unordered_pair(sK311(X0,X1,X7,X8),sK311(X0,X1,X7,X8))),X1) ),
inference(equality_resolution,[],[f3266]) ).
fof(f3512,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,[],[f3275]) ).
fof(f3513,plain,
! [X2,X0,X4] :
( ~ relation(X0)
| fiber(X0,X4) != X2
| ~ in(X4,X2) ),
inference(equality_resolution,[],[f2662]) ).
fof(f3514,plain,
! [X0,X4] :
( ~ relation(X0)
| ~ in(X4,fiber(X0,X4)) ),
inference(equality_resolution,[],[f3513]) ).
fof(f3515,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,[],[f3276]) ).
fof(f3516,plain,
! [X2,X1] :
( ~ relation_of2_as_subset(X2,sK140,X1)
| sK140 != relation_dom_as_subset(sK140,X1,X2)
| quasi_total(X2,sK140,X1) ),
inference(equality_resolution,[],[f3277]) ).
fof(f3517,plain,
! [X2,X1] :
( ~ relation_of2_as_subset(X2,sK140,X1)
| ~ quasi_total(X2,sK140,X1)
| sK140 = relation_dom_as_subset(sK140,X1,X2) ),
inference(equality_resolution,[],[f3279]) ).
fof(f3518,plain,
! [X0,X1] :
( ~ relation_of2_as_subset(sK140,X0,X1)
| sK140 != X1
| quasi_total(sK140,X0,X1)
| sK140 = X0 ),
inference(equality_resolution,[],[f3281]) ).
fof(f3519,plain,
! [X0] :
( ~ relation_of2_as_subset(sK140,X0,sK140)
| quasi_total(sK140,X0,sK140)
| sK140 = X0 ),
inference(equality_resolution,[],[f3518]) ).
fof(f3520,plain,
! [X2,X0] :
( ~ relation_of2_as_subset(X2,X0,sK140)
| ~ quasi_total(X2,X0,sK140)
| sK140 = X2
| sK140 = X0 ),
inference(equality_resolution,[],[f3282]) ).
fof(f3521,plain,
! [X1] :
( ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK326(relation_field(X1),X1),sK327(relation_field(X1),X1)),unordered_pair(sK326(relation_field(X1),X1),sK326(relation_field(X1),X1))),X1)
| ~ subset(sK326(relation_field(X1),X1),sK327(relation_field(X1),X1))
| inclusion_relation(relation_field(X1)) = X1 ),
inference(equality_resolution,[],[f3283]) ).
fof(f3522,plain,
! [X1] :
( ~ relation(X1)
| in(unordered_pair(unordered_pair(sK326(relation_field(X1),X1),sK327(relation_field(X1),X1)),unordered_pair(sK326(relation_field(X1),X1),sK326(relation_field(X1),X1))),X1)
| subset(sK326(relation_field(X1),X1),sK327(relation_field(X1),X1))
| inclusion_relation(relation_field(X1)) = X1 ),
inference(equality_resolution,[],[f3284]) ).
fof(f3523,plain,
! [X1] :
( ~ relation(X1)
| in(sK326(relation_field(X1),X1),relation_field(X1))
| inclusion_relation(relation_field(X1)) = X1 ),
inference(equality_resolution,[],[f2693]) ).
fof(f3524,plain,
! [X1] :
( ~ relation(X1)
| in(sK327(relation_field(X1),X1),relation_field(X1))
| inclusion_relation(relation_field(X1)) = X1 ),
inference(equality_resolution,[],[f2692]) ).
fof(f3525,plain,
! [X0] :
( ~ relation(inclusion_relation(X0))
| relation_field(inclusion_relation(X0)) = X0 ),
inference(equality_resolution,[],[f2691]) ).
fof(f3526,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,[],[f3285]) ).
fof(f3527,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,[],[f3286]) ).
fof(f3528,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,[],[f3290]) ).
fof(f3529,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,[],[f3528]) ).
fof(f3530,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,[],[f3291]) ).
fof(f3531,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,[],[f3292]) ).
fof(f3532,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,[],[f3295]) ).
fof(f3533,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,[],[f3296]) ).
fof(f3534,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,[],[f2723]) ).
fof(f3535,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,[],[f2722]) ).
fof(f3536,plain,
! [X1,X6,X7] :
( sK339(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,[],[f3305]) ).
fof(f3537,plain,
! [X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) = unordered_pair(unordered_pair(sK339(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK340(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)),unordered_pair(sK339(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK339(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,[],[f3306]) ).
fof(f3538,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,[],[f3307]) ).
fof(f3539,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,[],[f3538]) ).
fof(f3540,plain,
! [X1,X6,X7] :
( sK342(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,[],[f3308]) ).
fof(f3541,plain,
! [X1,X6,X7] :
( unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) = unordered_pair(unordered_pair(sK341(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK342(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1)),unordered_pair(sK341(unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)),X1),sK341(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,[],[f3309]) ).
fof(f3542,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,[],[f3310]) ).
fof(f3543,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,[],[f3542]) ).
tcf(c_49,plain,
! [X0: $i] :
( reflexive(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK39(X0),sK39(X0)),unordered_pair(sK39(X0),sK39(X0))),X0) ),
inference(cnf_transformation,[],[f2916]) ).
tcf(c_50,plain,
! [X0: $i] :
( reflexive(X0)
| in(sK39(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1640]) ).
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,[],[f2917]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] : unordered_pair(X0,X0) != sK140,
inference(cnf_transformation,[],[f2918]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(cnf_transformation,[],[f2920]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| disjoint(unordered_pair(X0,X0),X1) ),
inference(cnf_transformation,[],[f2921]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_rng_restriction(X1,X0)),relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1646]) ).
tcf(c_57,plain,
! [X0: $i] :
( transitive(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK40(X0),sK42(X0)),unordered_pair(sK40(X0),sK40(X0))),X0) ),
inference(cnf_transformation,[],[f2922]) ).
tcf(c_58,plain,
! [X0: $i] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK40(X0),sK41(X0)),unordered_pair(sK40(X0),sK40(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2923]) ).
tcf(c_59,plain,
! [X0: $i] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK41(X0),sK42(X0)),unordered_pair(sK41(X0),sK41(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2924]) ).
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,[],[f2925]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( well_orders(sK43(X0),X0)
| ~ well_ordering(X1)
| ~ relation(X1)
| ~ equipotent(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f1654]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( relation(sK43(X0))
| ~ well_ordering(X1)
| ~ relation(X1)
| ~ equipotent(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f1653]) ).
tcf(c_68,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ relation(X0)
| ( sK44(X0) != sK45(X0) ) ),
inference(cnf_transformation,[],[f1661]) ).
tcf(c_69,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK44(X0),sK45(X0)),unordered_pair(sK44(X0),sK44(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2930]) ).
tcf(c_70,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK45(X0),sK44(X0)),unordered_pair(sK45(X0),sK45(X0))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2931]) ).
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,[],[f2932]) ).
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,[],[f2933]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| in(X2,X0)
| in(X2,subset_complement(the_carrier(X1),X0))
| ~ one_sorted_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f1664]) ).
tcf(c_75,plain,
! [X0: $i] :
( connected(X0)
| in(sK46(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1670]) ).
tcf(c_76,plain,
! [X0: $i] :
( connected(X0)
| in(sK47(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1669]) ).
tcf(c_77,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ( sK46(X0) != sK47(X0) ) ),
inference(cnf_transformation,[],[f1668]) ).
tcf(c_78,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK46(X0),sK47(X0)),unordered_pair(sK46(X0),sK46(X0))),X0) ),
inference(cnf_transformation,[],[f2934]) ).
tcf(c_79,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK47(X0),sK46(X0)),unordered_pair(sK47(X0),sK47(X0))),X0) ),
inference(cnf_transformation,[],[f2935]) ).
tcf(c_80,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,[],[f2936]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ in(sK48(X0,X1),X1) ),
inference(cnf_transformation,[],[f1679]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| in(sK48(X0,X1),X0) ),
inference(cnf_transformation,[],[f1678]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( ~ sP2(X0,X1)
| ( sK50(X0,X1) != sK51(X0,X1) ) ),
inference(cnf_transformation,[],[f1689]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ( sK49(X0,X1) = sK52(X0,X1) )
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1687]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( in(sK50(X0,X1),sK52(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1686]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK50(X1,X2),X0),unordered_pair(sK50(X1,X2),sK50(X1,X2))),X2)
| ~ sP2(X1,X2)
| ~ in(X0,sK52(X1,X2)) ),
inference(cnf_transformation,[],[f2943]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( in(sK49(X0,X1),X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1684]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( sP0(sK49(X0,X1),sK51(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1683]) ).
tcf(c_100,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,sK53(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3544]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK53(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,[],[f3545]) ).
tcf(c_103,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,[],[f2947]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK54(X4,X0,X1) = X0 )
| ~ sP1(X3,X4,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f2948]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X1,sK54(X4,X0,X1))
| ~ sP1(X3,X4,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f2949]) ).
tcf(c_106,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,sK54(X4,X0,X1))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f2950]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| sP2(X1,X0)
| relation(sK56(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1702]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| sP2(X1,X0)
| function(sK56(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1701]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| sP2(X1,X0)
| sP1(X1,X0,sK56(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1700]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK57(X1))
| ~ sP3(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3546]) ).
tcf(c_119,plain,
! [X0: $i] :
( sP3(X0)
| ( sK59(X0) != sK60(X0) ) ),
inference(cnf_transformation,[],[f1713]) ).
tcf(c_121,plain,
! [X0: $i] :
( sP3(X0)
| ( unordered_pair(sK58(X0),sK58(X0)) = sK59(X0) ) ),
inference(cnf_transformation,[],[f2956]) ).
tcf(c_122,plain,
! [X0: $i] :
( sP3(X0)
| in(sK58(X0),X0) ),
inference(cnf_transformation,[],[f1710]) ).
tcf(c_123,plain,
! [X0: $i] :
( sP3(X0)
| ( unordered_pair(sK58(X0),sK58(X0)) = sK60(X0) ) ),
inference(cnf_transformation,[],[f2957]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( ordinal(sK61(X1))
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1716]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( in(sK61(X1),X1)
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1715]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK61(X1),X0)
| ~ ordinal(X2)
| ~ ordinal(X0)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1714]) ).
tcf(c_127,plain,
( sP5(sK62)
| ~ sP8 ),
inference(cnf_transformation,[],[f1721]) ).
tcf(c_128,plain,
( in(set_union2(sK62,unordered_pair(sK62,sK62)),omega)
| ~ sP8 ),
inference(cnf_transformation,[],[f2958]) ).
tcf(c_129,negated_conjecture,
! [X0: $i] :
( in(sK63(X0),X0)
| ( X0 = sK140 )
| ~ sP8
| ~ in(sK62,omega)
| ~ element(X0,powerset(powerset(sK62))) ),
inference(cnf_transformation,[],[f2959]) ).
tcf(c_130,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK63(X0) = X1 )
| ~ sP8
| ~ in(sK62,omega)
| ~ in(X1,X0)
| ~ subset(sK63(X0),X1)
| ~ element(X0,powerset(powerset(sK62))) ),
inference(cnf_transformation,[],[f2960]) ).
tcf(c_131,plain,
( ordinal(sK62)
| ~ sP8 ),
inference(cnf_transformation,[],[f1717]) ).
tcf(c_132,negated_conjecture,
( ~ sP7
| ( sK140 != sK64 ) ),
inference(cnf_transformation,[],[f2961]) ).
tcf(c_133,plain,
! [X0: $i] :
( ~ sP7
| ~ in(X0,sK64)
| ( sK65(X0) != X0 ) ),
inference(cnf_transformation,[],[f1726]) ).
tcf(c_134,plain,
! [X0: $i] :
( in(sK65(X0),sK64)
| ~ sP7
| ~ in(X0,sK64) ),
inference(cnf_transformation,[],[f1725]) ).
tcf(c_135,plain,
! [X0: $i] :
( subset(X0,sK65(X0))
| ~ sP7
| ~ in(X0,sK64) ),
inference(cnf_transformation,[],[f1724]) ).
tcf(c_136,negated_conjecture,
( element(sK64,powerset(powerset(sK140)))
| ~ sP7 ),
inference(cnf_transformation,[],[f2962]) ).
tcf(c_138,negated_conjecture,
( ~ sP6
| ( sK140 != sK66 ) ),
inference(cnf_transformation,[],[f2964]) ).
tcf(c_139,plain,
( sP4(sK66)
| ~ sP6 ),
inference(cnf_transformation,[],[f1733]) ).
tcf(c_140,plain,
( in(sK66,omega)
| ~ sP6 ),
inference(cnf_transformation,[],[f1732]) ).
tcf(c_141,plain,
( being_limit_ordinal(sK66)
| ~ sP6 ),
inference(cnf_transformation,[],[f1731]) ).
tcf(c_142,negated_conjecture,
! [X0: $i,X1: $i] :
( in(sK67(X0),X0)
| ( X0 = sK140 )
| ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK66)
| ~ in(X1,omega)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2965]) ).
tcf(c_143,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sK140 )
| ( sK67(X0) = X2 )
| ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK66)
| ~ in(X1,omega)
| ~ in(X2,X0)
| ~ subset(sK67(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2966]) ).
tcf(c_144,plain,
( ordinal(sK66)
| ~ sP6 ),
inference(cnf_transformation,[],[f1728]) ).
tcf(c_145,negated_conjecture,
! [X0: $i] :
( ~ sP5(X0)
| ( sK68(X0) != sK140 ) ),
inference(cnf_transformation,[],[f2967]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] :
( ~ sP5(X0)
| ~ in(X1,sK68(X0))
| ( sK69(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f1738]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( in(sK69(X1,X0),sK68(X1))
| ~ sP5(X1)
| ~ in(X0,sK68(X1)) ),
inference(cnf_transformation,[],[f1737]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK69(X1,X0))
| ~ sP5(X1)
| ~ in(X0,sK68(X1)) ),
inference(cnf_transformation,[],[f1736]) ).
tcf(c_149,plain,
! [X0: $i] :
( element(sK68(X0),powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f2968]) ).
tcf(c_155,negated_conjecture,
! [X0: $i,X1: $i] :
( sP6
| sP7
| sP8
| in(sK72(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2970]) ).
tcf(c_156,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( sP6
| sP7
| sP8
| ( X0 = sK140 )
| ( sK72(X0) = X2 )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ in(X2,X0)
| ~ subset(sK72(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2971]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(sK73(X2,X1,X0))
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1751]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK73(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,[],[f2972]) ).
tcf(c_159,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)),sK73(X2,X3,X4)) ),
inference(cnf_transformation,[],[f2973]) ).
tcf(c_160,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)),sK73(X2,X3,X4)) ),
inference(cnf_transformation,[],[f2974]) ).
tcf(c_161,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)),sK73(X2,X3,X4)) ),
inference(cnf_transformation,[],[f2975]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( empty(X3)
| in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),sK74(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,sK75(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3364]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( empty(X2)
| in(sK75(X4,X1,X0),X0)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK74(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,[],[f3366]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| in(X0,cartesian_product2(X1,X3))
| ~ relation(X2)
| ~ in(X0,sK74(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1757]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| ( unordered_pair(unordered_pair(sK76(X1,X2,X0),sK77(X1,X2,X0)),unordered_pair(sK76(X1,X2,X0),sK76(X1,X2,X0))) = X0 )
| ~ relation(X2)
| ~ in(X0,sK74(X1,X2,X3)) ),
inference(cnf_transformation,[],[f2978]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| in(sK76(X1,X2,X0),X1)
| ~ relation(X2)
| ~ in(X0,sK74(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1755]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| ( sK76(X1,X2,X0) = sK78(X1,X2,X0) )
| ~ relation(X2)
| ~ in(X0,sK74(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1754]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| in(sK77(X1,X2,X0),sK78(X1,X2,X0))
| ~ relation(X2)
| ~ in(X0,sK74(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1753]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( empty(X1)
| in(unordered_pair(unordered_pair(sK77(X1,X2,X0),X4),unordered_pair(sK77(X1,X2,X0),sK77(X1,X2,X0))),X2)
| ~ relation(X2)
| ~ in(X4,sK78(X1,X2,X0))
| ~ in(X0,sK74(X1,X2,X3)) ),
inference(cnf_transformation,[],[f2979]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK79(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,[],[f3368]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,cartesian_product2(X1,X2))
| ~ in(X0,sK79(X1,X2)) ),
inference(cnf_transformation,[],[f1763]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK80(X1,X0),sK81(X1,X0)),unordered_pair(sK80(X1,X0),sK80(X1,X0))) = X0 )
| ~ in(X0,sK79(X1,X2)) ),
inference(cnf_transformation,[],[f2981]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK80(X1,X0),X1)
| ~ in(X0,sK79(X1,X2)) ),
inference(cnf_transformation,[],[f1761]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(sK80(X1,X0),sK80(X1,X0)) = sK81(X1,X0) )
| ~ in(X0,sK79(X1,X2)) ),
inference(cnf_transformation,[],[f2982]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( in(X1,sK82(X0))
| ~ sP10(X0)
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f1766]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( sP9(X1,X0)
| ~ sP10(X1)
| ~ in(X0,sK82(X1)) ),
inference(cnf_transformation,[],[f1765]) ).
tcf(c_188,plain,
! [X0: $i] :
( sP10(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1778]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_difference(X2,unordered_pair(X1,X1)),sK87(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,[],[f3375]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,powerset(X1))
| ~ ordinal(X1)
| ~ in(X2,sK87(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f2993]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK88(X1,X0,X2),X0)
| ~ ordinal(X1)
| ~ in(X2,sK87(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f2994]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(sK88(X1,X0,X2),unordered_pair(X1,X1)) = X2 )
| ~ ordinal(X1)
| ~ in(X2,sK87(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f2995]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK89(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,[],[f3376]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,cartesian_product2(X1,X1))
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK89(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1785]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK90(X2,X3,X0),sK91(X2,X3,X0)),unordered_pair(sK90(X2,X3,X0),sK90(X2,X3,X0))) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK89(X1,X2,X3)) ),
inference(cnf_transformation,[],[f2997]) ).
tcf(c_196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(apply(X3,sK90(X2,X3,X0)),apply(X3,sK91(X2,X3,X0))),unordered_pair(apply(X3,sK90(X2,X3,X0)),apply(X3,sK90(X2,X3,X0)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK89(X1,X2,X3)) ),
inference(cnf_transformation,[],[f2998]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i] :
( in(X0,sK92(X1))
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1789]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(X0,sK92(X1)) ),
inference(cnf_transformation,[],[f1788]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ in(X0,sK92(X1)) ),
inference(cnf_transformation,[],[f1787]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,sK93(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,[],[f1792]) ).
tcf(c_201,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,sK93(X1,X2)) ),
inference(cnf_transformation,[],[f1791]) ).
tcf(c_202,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,sK93(X1,X2)) ),
inference(cnf_transformation,[],[f1790]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,sK94(X2,X1))
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X2)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3377]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X0,sK94(X1,X2)) ),
inference(cnf_transformation,[],[f3000]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK95(X1,X0))
| ~ ordinal(X2)
| ~ in(X0,sK94(X1,X2)) ),
inference(cnf_transformation,[],[f1795]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK95(X1,X0) = X0 )
| ~ ordinal(X2)
| ~ in(X0,sK94(X1,X2)) ),
inference(cnf_transformation,[],[f1794]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK95(X1,X0),X1)
| ~ ordinal(X2)
| ~ in(X0,sK94(X1,X2)) ),
inference(cnf_transformation,[],[f1793]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i] :
( relation(sK96(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f1803]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] :
( function(sK96(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f1802]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK96(X0,X1)) = X0 )
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f1801]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK97(X1,X2,X0) = X0 )
| ~ sP12(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1800]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK96(X1,X2),X0),sK97(X1,X2,X0))
| ~ sP12(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1799]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(apply(sK96(X1,X2),X3),X0),unordered_pair(apply(sK96(X1,X2),X3),apply(sK96(X1,X2),X3))),X2)
| ~ sP12(X1,X2)
| ~ in(X3,X1)
| ~ in(X0,sK97(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3001]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| sP11(X1,X0)
| sP12(X1,X0)
| in(sK103(X1,X0),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1814]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| sP11(X2,X1)
| sP12(X2,X1)
| ~ relation(X1)
| ~ in(X0,sK103(X2,X1))
| ~ in(unordered_pair(unordered_pair(X0,sK104(X1,X0,sK103(X2,X1))),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3378]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP11(X1,X2)
| sP12(X1,X2)
| in(sK104(X2,X0,sK103(X1,X2)),sK103(X1,X2))
| ~ relation(X2)
| ~ in(X0,sK103(X1,X2)) ),
inference(cnf_transformation,[],[f3379]) ).
tcf(c_230,plain,
! [X0: $i] :
( sP13(X0)
| relation(sK108(X0)) ),
inference(cnf_transformation,[],[f3380]) ).
tcf(c_232,plain,
! [X0: $i] :
( sP13(X0)
| function(sK108(X0)) ),
inference(cnf_transformation,[],[f3381]) ).
tcf(c_234,plain,
! [X0: $i] :
( sP13(X0)
| ( relation_dom(sK108(X0)) = X0 ) ),
inference(cnf_transformation,[],[f3382]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( sP13(X1)
| ( apply(sK108(X1),X0) = unordered_pair(X0,X0) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3383]) ).
tcf(c_237,plain,
( sP14(sK110)
| ~ sP15 ),
inference(cnf_transformation,[],[f1831]) ).
tcf(c_238,plain,
( in(sK110,omega)
| ~ sP15 ),
inference(cnf_transformation,[],[f1830]) ).
tcf(c_239,negated_conjecture,
! [X0: $i,X1: $i] :
( in(sK111(X0),X0)
| ( X0 = sK140 )
| ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK110)
| ~ in(X1,omega)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f3012]) ).
tcf(c_240,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sK140 )
| ( sK111(X0) = X2 )
| ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK110)
| ~ in(X1,omega)
| ~ in(X2,X0)
| ~ subset(sK111(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f3013]) ).
tcf(c_241,plain,
( ordinal(sK110)
| ~ sP15 ),
inference(cnf_transformation,[],[f1827]) ).
tcf(c_247,negated_conjecture,
! [X0: $i,X1: $i] :
( sP15
| in(sK114(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f3015]) ).
tcf(c_248,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( sP15
| ( X0 = sK140 )
| ( sK114(X0) = X2 )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ in(X2,X0)
| ~ subset(sK114(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f3016]) ).
tcf(c_249,plain,
! [X0: $i] : relation(sK115(X0)),
inference(cnf_transformation,[],[f1842]) ).
tcf(c_250,plain,
! [X0: $i] : function(sK115(X0)),
inference(cnf_transformation,[],[f1841]) ).
tcf(c_251,plain,
! [X0: $i] : relation_dom(sK115(X0)) = X0,
inference(cnf_transformation,[],[f1840]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] :
( ( apply(sK115(X1),X0) = unordered_pair(X0,X0) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3017]) ).
tcf(c_254,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,[],[f3019]) ).
tcf(c_255,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,[],[f3020]) ).
tcf(c_256,plain,
! [X0: $i] : in(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(cnf_transformation,[],[f3021]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( X0 = X2 )
| ( unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
inference(cnf_transformation,[],[f1847]) ).
tcf(c_258,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,[],[f1850]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f1849]) ).
tcf(c_260,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,[],[f1848]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1851]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng_restriction(X1,X0),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1852]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1853]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1855]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1854]) ).
tcf(c_266,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,[],[f3022]) ).
tcf(c_267,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,[],[f1857]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1860]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(X0),X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1859]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1861]) ).
tcf(c_272,plain,
! [X0: $i] : in(X0,sK116(X0)),
inference(cnf_transformation,[],[f1865]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK116(X1))
| ~ subset(X2,X0)
| ~ in(X0,sK116(X1)) ),
inference(cnf_transformation,[],[f1864]) ).
tcf(c_274,plain,
! [X0: $i,X1: $i] :
( in(powerset(X0),sK116(X1))
| ~ in(X0,sK116(X1)) ),
inference(cnf_transformation,[],[f1863]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i] :
( are_equipotent(X0,sK116(X1))
| in(X0,sK116(X1))
| ~ subset(X0,sK116(X1)) ),
inference(cnf_transformation,[],[f1862]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1866]) ).
tcf(c_277,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,[],[f1867]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK117(X0,X2,X1),relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f1870]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK117(X0,X2,X1),X0),unordered_pair(sK117(X0,X2,X1),sK117(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3024]) ).
tcf(c_281,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK117(X0,X2,X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f1868]) ).
tcf(c_282,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(X0,X1),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1872]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(X0,relation_inverse_image(X0,X1)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1873]) ).
tcf(c_284,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,[],[f3025]) ).
tcf(c_285,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,[],[f1875]) ).
tcf(c_286,plain,
! [X0: $i] :
( ( relation_image(X0,relation_dom(X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1876]) ).
tcf(c_287,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,[],[f1877]) ).
tcf(c_288,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,[],[f1878]) ).
tcf(c_290,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,[],[f1880]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,relation_rng(X0)) = relation_rng(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1881]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK118(X0,X2,X1),relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f1884]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK118(X0,X2,X1)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f3028]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK118(X0,X2,X1),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f1882]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(X0,X1),relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1886]) ).
tcf(c_297,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,[],[f1887]) ).
tcf(c_298,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,[],[f1890]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(X1)
| ~ in(X0,relation_restriction(X1,X2)) ),
inference(cnf_transformation,[],[f1889]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,cartesian_product2(X2,X2))
| ~ relation(X1)
| ~ in(X0,relation_restriction(X1,X2)) ),
inference(cnf_transformation,[],[f1888]) ).
tcf(c_301,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ~ relation(X0)
| ~ subset(X1,relation_rng(X0))
| ( relation_inverse_image(X0,X1) != sK140 ) ),
inference(cnf_transformation,[],[f3029]) ).
tcf(c_302,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,[],[f1892]) ).
tcf(c_304,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,[],[f1894]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(relation_rng_restriction(X1,X0),X1) = relation_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1895]) ).
tcf(c_307,negated_conjecture,
! [X0: $i,X1: $i] :
( in(sK119(X0),X0)
| ( X0 = sK140 )
| ~ finite(X1)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f3031]) ).
tcf(c_308,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sK140 )
| ( sK119(X0) = X2 )
| ~ finite(X1)
| ~ in(X2,X0)
| ~ subset(sK119(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f3032]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X1,relation_dom_restriction(X0,X1)) = relation_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1899]) ).
tcf(c_310,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,[],[f1901]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_field(relation_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f1900]) ).
tcf(c_312,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,[],[f3033]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1903]) ).
tcf(c_314,negated_conjecture,
unordered_pair(sK140,sK140) = powerset(sK140),
inference(cnf_transformation,[],[f3034]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i] :
( subset(relation_field(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1908]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i] :
( subset(relation_field(relation_restriction(X0,X1)),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1907]) ).
tcf(c_319,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,[],[f1911]) ).
tcf(c_320,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,[],[f1910]) ).
tcf(c_321,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,[],[f1909]) ).
tcf(c_322,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = sK140 )
| ( 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,[],[f3037]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ epsilon_transitive(X0)
| ~ ordinal(X1)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f1913]) ).
tcf(c_324,plain,
! [X0: $i] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1914]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(fiber(relation_restriction(X0,X1),X2),fiber(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1915]) ).
tcf(c_326,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,[],[f1916]) ).
tcf(c_327,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,[],[f1917]) ).
tcf(c_328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X3,sK120(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,[],[f3038]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK121(X1,X0),X1)
| ( relation_dom_as_subset(X1,X2,X0) = X1 )
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1919]) ).
tcf(c_330,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(sK121(X0,X1),X2),unordered_pair(sK121(X0,X1),sK121(X0,X1))),X1) ),
inference(cnf_transformation,[],[f3039]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ reflexive(X0) ),
inference(cnf_transformation,[],[f1921]) ).
tcf(c_332,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,[],[f1922]) ).
tcf(c_333,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1923]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK122(X2,X3),X3),unordered_pair(sK122(X2,X3),sK122(X2,X3))),X2)
| ~ in(X3,X1)
| ~ relation_of2_as_subset(X2,X0,X1)
| ( relation_rng_as_subset(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f3040]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK123(X2,X0),X2)
| ( relation_rng_as_subset(X1,X2,X0) = X2 )
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1925]) ).
tcf(c_336,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,sK123(X1,X2)),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3041]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1927]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1928]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i] :
( transitive(relation_restriction(X0,X1))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1929]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1931]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1930]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i] :
( antisymmetric(relation_restriction(X0,X1))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1932]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i] :
( ( relation_field(relation_restriction(X0,X1)) = X1 )
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f1934]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i] :
( well_ordering(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f1933]) ).
tcf(c_345,plain,
! [X0: $i] :
( finite(relation_rng(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ finite(relation_dom(X0)) ),
inference(cnf_transformation,[],[f1935]) ).
tcf(c_346,plain,
! [X0: $i] : relation(sK124(X0)),
inference(cnf_transformation,[],[f1937]) ).
tcf(c_347,plain,
! [X0: $i] : well_orders(sK124(X0),X0),
inference(cnf_transformation,[],[f1936]) ).
tcf(c_348,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,[],[f3042]) ).
tcf(c_349,plain,
! [X0: $i] :
( empty(X0)
| in(sK125(X0),X0)
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(cnf_transformation,[],[f1946]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(sK125(X1),X1)
| in(apply(sK126(X1),X0),X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1945]) ).
tcf(c_351,plain,
! [X0: $i] :
( empty(X0)
| relation(sK126(X0))
| in(sK125(X0),X0) ),
inference(cnf_transformation,[],[f1944]) ).
tcf(c_352,plain,
! [X0: $i] :
( empty(X0)
| function(sK126(X0))
| in(sK125(X0),X0) ),
inference(cnf_transformation,[],[f1943]) ).
tcf(c_353,negated_conjecture,
! [X0: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(cnf_transformation,[],[f3043]) ).
tcf(c_354,negated_conjecture,
! [X0: $i,X1: $i] :
( empty(X1)
| in(apply(sK126(X1),X0),X0)
| ( sK125(X1) = sK140 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3044]) ).
tcf(c_355,negated_conjecture,
! [X0: $i] :
( empty(X0)
| relation(sK126(X0))
| ( sK125(X0) = sK140 ) ),
inference(cnf_transformation,[],[f3045]) ).
tcf(c_356,negated_conjecture,
! [X0: $i] :
( empty(X0)
| function(sK126(X0))
| ( sK125(X0) = sK140 ) ),
inference(cnf_transformation,[],[f3046]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X0 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3047]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f1949]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_complement(the_carrier(X1),X0),X1)
| ~ top_str(X1)
| ~ closed_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f1948]) ).
tcf(c_360,plain,
! [X0: $i] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f1950]) ).
tcf(c_361,negated_conjecture,
! [X0: $i] : subset(sK140,X0),
inference(cnf_transformation,[],[f3048]) ).
tcf(c_362,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,[],[f3049]) ).
tcf(c_363,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,[],[f3050]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i] :
( open_subset(X1,X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f1955]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] :
( closed_subset(subset_complement(the_carrier(X1),X0),X1)
| ~ top_str(X1)
| ~ open_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f1954]) ).
tcf(c_366,plain,
! [X0: $i] :
( ordinal(X0)
| ~ ordinal(sK127(X0))
| ~ subset(sK127(X0),X0) ),
inference(cnf_transformation,[],[f1957]) ).
tcf(c_367,plain,
! [X0: $i] :
( ordinal(X0)
| in(sK127(X0),X0) ),
inference(cnf_transformation,[],[f1956]) ).
tcf(c_368,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(relation_restriction(X0,X1))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1958]) ).
tcf(c_369,negated_conjecture,
! [X0: $i,X1: $i] :
( in(sK128(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3051]) ).
tcf(c_370,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(X1),X0)
| ( X1 = sK140 )
| ~ ordinal(X2)
| ~ ordinal(X0)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3052]) ).
tcf(c_371,negated_conjecture,
! [X0: $i,X1: $i] :
( ordinal(sK128(X0))
| ( X0 = sK140 )
| ~ ordinal(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3053]) ).
tcf(c_372,plain,
! [X0: $i,X1: $i] :
( well_ordering(relation_restriction(X0,X1))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1962]) ).
tcf(c_373,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,[],[f3054]) ).
tcf(c_374,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,[],[f3055]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1965]) ).
tcf(c_376,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,[],[f3056]) ).
tcf(c_377,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,[],[f3057]) ).
tcf(c_378,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0)
| ( apply(X0,sK129(relation_dom(X0),X0)) != sK129(relation_dom(X0),X0) ) ),
inference(cnf_transformation,[],[f3384]) ).
tcf(c_379,plain,
! [X0: $i] :
( in(sK129(relation_dom(X0),X0),relation_dom(X0))
| ( identity_relation(relation_dom(X0)) = X0 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3385]) ).
tcf(c_382,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1972]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f1973]) ).
tcf(c_384,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1975]) ).
tcf(c_385,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(X0)) = relation_dom(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1974]) ).
tcf(c_386,negated_conjecture,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = sK140 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3058]) ).
tcf(c_387,negated_conjecture,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(X0,X1) != sK140 ) ),
inference(cnf_transformation,[],[f3059]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3060]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(unordered_pair(X0,X2),X1)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1982]) ).
tcf(c_391,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f1981]) ).
tcf(c_392,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f1980]) ).
tcf(c_393,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,[],[f1983]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(cnf_transformation,[],[f1984]) ).
tcf(c_397,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( unordered_pair(X1,X1) = X0 )
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f3064]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1988]) ).
tcf(c_399,plain,
! [X0: $i] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f1989]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK130(X0,X1),X0) ),
inference(cnf_transformation,[],[f1992]) ).
tcf(c_401,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK130(X0,X1),X1) ),
inference(cnf_transformation,[],[f1991]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1990]) ).
tcf(c_403,negated_conjecture,
! [X0: $i] :
( ( X0 = sK140 )
| ~ subset(X0,sK140) ),
inference(cnf_transformation,[],[f3065]) ).
tcf(c_404,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[],[f1994]) ).
tcf(c_405,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(set_union2(sK131(X0),unordered_pair(sK131(X0),sK131(X0))),X0) ),
inference(cnf_transformation,[],[f3066]) ).
tcf(c_406,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| in(sK131(X0),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1997]) ).
tcf(c_407,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ordinal(sK131(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1996]) ).
tcf(c_408,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,[],[f3067]) ).
tcf(c_409,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ( set_union2(sK132(X0),unordered_pair(sK132(X0),sK132(X0))) = X0 )
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f3068]) ).
tcf(c_410,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ordinal(sK132(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2000]) ).
tcf(c_411,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,[],[f3390]) ).
tcf(c_412,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,[],[f2003]) ).
tcf(c_413,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,[],[f2002]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2004]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i] :
( subset(interior(X1,X0),X0)
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2005]) ).
tcf(c_416,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,sK133(X1,X2,X0)) ),
inference(cnf_transformation,[],[f2010]) ).
tcf(c_417,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X1,X0))
| closed_subset(sK133(X1,X0,X2),X1)
| ~ top_str(X1)
| ~ in(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2009]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X1,X0))
| subset(X0,sK133(X1,X0,X2))
| ~ top_str(X1)
| ~ in(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2008]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X1,X0))
| element(sK133(X1,X0,X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ in(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2007]) ).
tcf(c_420,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,[],[f2006]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2011]) ).
tcf(c_423,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X1,relation_inverse_image(X0,X2))
| ( X4 = sK140 )
| ~ 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,[],[f3070]) ).
tcf(c_424,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,X3)
| ( X4 = sK140 )
| ~ function(X1)
| ~ quasi_total(X1,X3,X4)
| ~ relation_of2_as_subset(X1,X3,X4)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f3071]) ).
tcf(c_425,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,X0),X2)
| ( X4 = sK140 )
| ~ function(X1)
| ~ quasi_total(X1,X3,X4)
| ~ relation_of2_as_subset(X1,X3,X4)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f3072]) ).
tcf(c_426,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,[],[f2016]) ).
tcf(c_427,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ~ element(X1,powerset(powerset(X0)))
| ( complements_of_subsets(X0,X1) != sK140 ) ),
inference(cnf_transformation,[],[f3073]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i] :
( ( set_union2(unordered_pair(X0,X0),X1) = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3074]) ).
tcf(c_429,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,[],[f2019]) ).
tcf(c_430,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( 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,[],[f3075]) ).
tcf(c_431,plain,
! [X0: $i,X1: $i] :
( subset(X0,topstr_closure(X1,X0))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2021]) ).
tcf(c_432,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( 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,[],[f3076]) ).
tcf(c_433,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,[],[f2024]) ).
tcf(c_434,plain,
! [X0: $i] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2025]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK134(X0,X1),set_difference(X0,set_difference(X0,X1))) ),
inference(cnf_transformation,[],[f3077]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(cnf_transformation,[],[f3078]) ).
tcf(c_437,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X2,subset_complement(X1,X0))
| ( X1 = sK140 )
| ~ element(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f3079]) ).
tcf(c_438,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,[],[f2029]) ).
tcf(c_439,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,[],[f2034]) ).
tcf(c_440,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,[],[f2033]) ).
tcf(c_441,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,[],[f2032]) ).
tcf(c_442,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,[],[f2031]) ).
tcf(c_443,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,[],[f2030]) ).
tcf(c_449,plain,
! [X0: $i,X1: $i] :
( ( function_inverse(X0) = X1 )
| ~ one_to_one(X0)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK136(X0,X1),relation_dom(X0))
| ~ sP16(X0,sK135(X0,X1),sK136(X0,X1),X1)
| ( relation_dom(X1) != relation_rng(X0) )
| ( apply(X0,sK136(X0,X1)) != sK135(X0,X1) ) ),
inference(cnf_transformation,[],[f2046]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i] :
( in(sK135(X1,X0),relation_rng(X1))
| ( function_inverse(X1) = X0 )
| ~ one_to_one(X1)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ sP16(X1,sK135(X1,X0),sK136(X1,X0),X0)
| ( relation_dom(X0) != relation_rng(X1) ) ),
inference(cnf_transformation,[],[f2045]) ).
tcf(c_451,plain,
! [X0: $i,X1: $i] :
( ( function_inverse(X1) = X0 )
| ( apply(X0,sK135(X1,X0)) = sK136(X1,X0) )
| ~ one_to_one(X1)
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ sP16(X1,sK135(X1,X0),sK136(X1,X0),X0)
| ( relation_dom(X0) != relation_rng(X1) ) ),
inference(cnf_transformation,[],[f2044]) ).
tcf(c_453,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,[],[f3396]) ).
tcf(c_455,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,[],[f3399]) ).
tcf(c_456,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ element(X2,powerset(X1))
| ~ in(X0,subset_complement(X1,X2)) ),
inference(cnf_transformation,[],[f2047]) ).
tcf(c_457,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,[],[f2048]) ).
tcf(c_458,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(X0)) = relation_rng(X0) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2050]) ).
tcf(c_459,plain,
! [X0: $i] :
( ( relation_rng(function_inverse(X0)) = relation_dom(X0) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2049]) ).
tcf(c_460,negated_conjecture,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK137(X0),sK138(X0)),unordered_pair(sK137(X0),sK137(X0))),X0)
| ( X0 = sK140 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3080]) ).
tcf(c_461,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,[],[f2053]) ).
tcf(c_462,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,[],[f2052]) ).
tcf(c_463,negated_conjecture,
is_a_cover_of_carrier(sK139,sK140),
inference(cnf_transformation,[],[f2058]) ).
tcf(c_464,negated_conjecture,
element(sK140,powerset(powerset(the_carrier(sK139)))),
inference(cnf_transformation,[],[f2056]) ).
tcf(c_465,negated_conjecture,
~ empty_carrier(sK139),
inference(cnf_transformation,[],[f2055]) ).
tcf(c_466,negated_conjecture,
one_sorted_str(sK139),
inference(cnf_transformation,[],[f2054]) ).
tcf(c_467,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2060]) ).
tcf(c_468,plain,
! [X0: $i] :
( is_well_founded_in(X0,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2059]) ).
tcf(c_469,plain,
! [X0: $i] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f2061]) ).
tcf(c_470,negated_conjecture,
relation_dom(sK140) = sK140,
inference(cnf_transformation,[],[f3081]) ).
tcf(c_471,negated_conjecture,
relation_rng(sK140) = sK140,
inference(cnf_transformation,[],[f3082]) ).
tcf(c_472,plain,
! [X0: $i,X1: $i] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2064]) ).
tcf(c_473,plain,
! [X0: $i] :
( one_to_one(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2065]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X2,X1)
| ~ subset(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f2066]) ).
tcf(c_475,negated_conjecture,
! [X0: $i] :
( ( X0 = sK140 )
| ~ relation(X0)
| ( relation_dom(X0) != sK140 ) ),
inference(cnf_transformation,[],[f3083]) ).
tcf(c_476,negated_conjecture,
! [X0: $i] :
( ( X0 = sK140 )
| ~ relation(X0)
| ( relation_rng(X0) != sK140 ) ),
inference(cnf_transformation,[],[f3084]) ).
tcf(c_477,negated_conjecture,
! [X0: $i] :
( ( relation_dom(X0) = sK140 )
| ~ relation(X0)
| ( relation_rng(X0) != sK140 ) ),
inference(cnf_transformation,[],[f3085]) ).
tcf(c_478,negated_conjecture,
! [X0: $i] :
( ( relation_rng(X0) = sK140 )
| ~ relation(X0)
| ( relation_dom(X0) != sK140 ) ),
inference(cnf_transformation,[],[f3086]) ).
tcf(c_479,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( set_difference(X0,unordered_pair(X1,X1)) = X0 ) ),
inference(cnf_transformation,[],[f3087]) ).
tcf(c_480,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ( set_difference(X0,unordered_pair(X1,X1)) != X0 ) ),
inference(cnf_transformation,[],[f3088]) ).
tcf(c_481,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(X1,X2) = X0 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ( apply(X0,sK141(X0,X1)) != apply(X1,sK141(X0,X1)) )
| ( set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2)) != relation_dom(X0) ) ),
inference(cnf_transformation,[],[f3089]) ).
tcf(c_482,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK141(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,[],[f3090]) ).
tcf(c_485,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,X3),relation_rng(X0))
| ( X2 = sK140 )
| ~ function(X0)
| ~ in(X3,X1)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f3092]) ).
tcf(c_486,plain,
! [X0: $i] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2079]) ).
tcf(c_487,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f3093]) ).
tcf(c_488,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,[],[f2081]) ).
tcf(c_489,plain,
! [X0: $i] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f2083]) ).
tcf(c_490,plain,
! [X0: $i] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f2082]) ).
tcf(c_491,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,[],[f2084]) ).
tcf(c_492,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,[],[f3094]) ).
tcf(c_493,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,[],[f3095]) ).
tcf(c_494,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,[],[f3096]) ).
tcf(c_495,plain,
! [X0: $i,X1: $i] : pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0,
inference(cnf_transformation,[],[f3097]) ).
tcf(c_496,plain,
! [X0: $i,X1: $i] : pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1,
inference(cnf_transformation,[],[f3098]) ).
tcf(c_497,plain,
! [X0: $i] :
( well_ordering(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2090]) ).
tcf(c_498,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f2091]) ).
tcf(c_499,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f2093]) ).
tcf(c_500,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f2092]) ).
tcf(c_501,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,[],[f2096]) ).
tcf(c_502,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f2095]) ).
tcf(c_503,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,[],[f2094]) ).
tcf(c_504,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom_restriction(X0,X1),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2097]) ).
tcf(c_505,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,[],[f3402]) ).
tcf(c_507,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,[],[f3101]) ).
tcf(c_508,plain,
! [X0: $i] :
( well_orders(X0,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2102]) ).
tcf(c_509,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ relation(X0)
| ~ well_orders(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2101]) ).
tcf(c_510,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2103]) ).
tcf(c_511,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(cnf_transformation,[],[f3102]) ).
tcf(c_512,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,[],[f3103]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2106]) ).
tcf(c_514,plain,
! [X0: $i,X1: $i] :
( ( relation_composition(identity_relation(X1),X0) = relation_dom_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2107]) ).
tcf(c_515,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng(relation_dom_restriction(X0,X1)),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2108]) ).
tcf(c_516,plain,
! [X0: $i] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f2109]) ).
tcf(c_517,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( quasi_total(X0,X1,X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ subset(X2,X3)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f3105]) ).
tcf(c_518,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2_as_subset(X0,X1,X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ subset(X2,X3)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f3106]) ).
tcf(c_519,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(X0,sK140,X2)
| ~ function(X0)
| ~ subset(X1,X2)
| ~ quasi_total(X0,sK140,X1)
| ~ relation_of2_as_subset(X0,sK140,X1) ),
inference(cnf_transformation,[],[f3404]) ).
tcf(c_521,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
inference(cnf_transformation,[],[f3110]) ).
tcf(c_522,plain,
! [X0: $i,X1: $i] :
( in(sK142(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2118]) ).
tcf(c_523,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(X0,X1)
| ~ in(X0,sK142(X1)) ),
inference(cnf_transformation,[],[f2117]) ).
tcf(c_524,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK143(X0,X1),X1)
| ~ in(sK143(X0,X1),X0) ),
inference(cnf_transformation,[],[f2120]) ).
tcf(c_525,plain,
! [X0: $i,X1: $i] :
( in(sK143(X0,X1),X1)
| in(sK143(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f2119]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2121]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2122]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i] :
( ~ sP18(X0,X1)
| ( sK145(X0,X1) != sK146(X0,X1) ) ),
inference(cnf_transformation,[],[f2129]) ).
tcf(c_530,plain,
! [X0: $i,X1: $i] :
( ( sK144(X0,X1) = sK147(X0,X1) )
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f2127]) ).
tcf(c_531,plain,
! [X0: $i,X1: $i] :
( in(sK145(X0,X1),sK147(X0,X1))
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f2126]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK145(X1,X2),X0),unordered_pair(sK145(X1,X2),sK145(X1,X2))),X2)
| ~ sP18(X1,X2)
| ~ in(X0,sK147(X1,X2)) ),
inference(cnf_transformation,[],[f3111]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i] :
( in(sK144(X0,X1),X0)
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f2124]) ).
tcf(c_534,plain,
! [X0: $i,X1: $i] :
( sP17(sK144(X0,X1),sK146(X0,X1),X1)
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f2123]) ).
tcf(c_538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X3)
| sP18(X3,X1)
| in(X0,sK149(X3,X1))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,sK150(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3547]) ).
tcf(c_539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| sP18(X1,X3)
| in(X2,sK149(X1,X3))
| in(sK150(X3,X2,X0),X0)
| ~ relation(X3)
| ~ in(X2,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3548]) ).
tcf(c_541,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP18(X1,X2)
| in(sK151(X1,X2,X0),X1)
| ~ relation(X2)
| ~ in(X0,sK149(X1,X2)) ),
inference(cnf_transformation,[],[f2136]) ).
tcf(c_542,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP18(X1,X2)
| ( sK151(X1,X2,X0) = sK152(X1,X2,X0) )
| ~ relation(X2)
| ~ in(X0,sK149(X1,X2)) ),
inference(cnf_transformation,[],[f2135]) ).
tcf(c_543,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP18(X1,X2)
| in(X0,sK152(X1,X2,X0))
| ~ relation(X2)
| ~ in(X0,sK149(X1,X2)) ),
inference(cnf_transformation,[],[f2134]) ).
tcf(c_544,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,sK149(X1,X2))
| ~ in(X0,sK152(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3114]) ).
tcf(c_546,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(X1) = X2 )
| ~ relation(X1)
| ~ in(sK153(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X0,sK153(X1,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3116]) ).
tcf(c_547,plain,
! [X0: $i,X1: $i] :
( in(sK153(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK154(X0,X1),sK153(X0,X1)),unordered_pair(sK154(X0,X1),sK154(X0,X1))),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3117]) ).
tcf(c_548,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,[],[f3408]) ).
tcf(c_549,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK155(X1,X0),X0),unordered_pair(sK155(X1,X0),sK155(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f3409]) ).
tcf(c_550,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X0) = X1 )
| ~ relation(X0)
| ~ in(sK156(X0,X1),X1)
| ~ in(unordered_pair(unordered_pair(sK156(X0,X1),X2),unordered_pair(sK156(X0,X1),sK156(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3120]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i] :
( in(sK156(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK156(X0,X1),sK157(X0,X1)),unordered_pair(sK156(X0,X1),sK156(X0,X1))),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3121]) ).
tcf(c_552,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,[],[f3410]) ).
tcf(c_553,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK158(X1,X0)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f3411]) ).
tcf(c_554,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK159(X0,X1),sK160(X0,X1)),unordered_pair(sK159(X0,X1),sK159(X0,X1))),X1) ),
inference(cnf_transformation,[],[f3124]) ).
tcf(c_555,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK159(X0,X1),sK160(X0,X1)),unordered_pair(sK159(X0,X1),sK159(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3125]) ).
tcf(c_557,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK161(X0,X1),sK162(X0,X1)),unordered_pair(sK161(X0,X1),sK161(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK161(X0,X1),sK162(X0,X1)),unordered_pair(sK161(X0,X1),sK161(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3127]) ).
tcf(c_558,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK161(X0,X1),sK162(X0,X1)),unordered_pair(sK161(X0,X1),sK161(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK161(X0,X1),sK162(X0,X1)),unordered_pair(sK161(X0,X1),sK161(X0,X1))),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3128]) ).
tcf(c_561,plain,
! [X0: $i] :
( relation(X0)
| in(sK163(X0),X0) ),
inference(cnf_transformation,[],[f2158]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X2)
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != sK163(X2) ) ),
inference(cnf_transformation,[],[f3131]) ).
tcf(c_563,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK164(X0),sK165(X0)),unordered_pair(sK164(X0),sK164(X0))) = X0 )
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3132]) ).
tcf(c_564,plain,
! [X0: $i] :
( function(X0)
| ( sK167(X0) != sK168(X0) ) ),
inference(cnf_transformation,[],[f2162]) ).
tcf(c_565,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK166(X0),sK167(X0)),unordered_pair(sK166(X0),sK166(X0))),X0) ),
inference(cnf_transformation,[],[f3133]) ).
tcf(c_566,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK166(X0),sK168(X0)),unordered_pair(sK166(X0),sK166(X0))),X0) ),
inference(cnf_transformation,[],[f3134]) ).
tcf(c_567,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,[],[f3135]) ).
tcf(c_568,plain,
! [X0: $i] :
( ( set_union2(relation_dom(X0),relation_rng(X0)) = relation_field(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2163]) ).
tcf(c_569,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ relation(X0)
| ~ reflexive(X0) ),
inference(cnf_transformation,[],[f2169]) ).
tcf(c_570,plain,
! [X0: $i] :
( reflexive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2168]) ).
tcf(c_571,plain,
! [X0: $i] :
( transitive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2167]) ).
tcf(c_572,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2166]) ).
tcf(c_573,plain,
! [X0: $i] :
( connected(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2165]) ).
tcf(c_574,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2164]) ).
tcf(c_575,negated_conjecture,
! [X0: $i] :
( ( X0 = sK140 )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f3136]) ).
tcf(c_577,negated_conjecture,
relation(sK140),
inference(cnf_transformation,[],[f3138]) ).
tcf(c_579,negated_conjecture,
! [X0: $i] :
( in(sK169(X0),X0)
| ( X0 = sK140 ) ),
inference(cnf_transformation,[],[f3140]) ).
tcf(c_580,negated_conjecture,
! [X0: $i] : ~ in(X0,sK140),
inference(cnf_transformation,[],[f3414]) ).
tcf(c_581,plain,
! [X0: $i] :
( ~ sP20(X0)
| ( sK171(X0) != sK172(X0) ) ),
inference(cnf_transformation,[],[f2182]) ).
tcf(c_582,plain,
! [X0: $i] :
( ( sK171(X0) = sK170(X0) )
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f2181]) ).
tcf(c_583,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK173(X0),sK174(X0)),unordered_pair(sK173(X0),sK173(X0))) = sK171(X0) )
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f3142]) ).
tcf(c_584,plain,
! [X0: $i] :
( in(sK173(X0),X0)
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f2179]) ).
tcf(c_585,plain,
! [X0: $i] :
( ( unordered_pair(sK173(X0),sK173(X0)) = sK174(X0) )
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f3143]) ).
tcf(c_586,plain,
! [X0: $i] :
( ( sK172(X0) = sK170(X0) )
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f2177]) ).
tcf(c_587,plain,
! [X0: $i] :
( sP19(sK172(X0),X0)
| ~ sP20(X0) ),
inference(cnf_transformation,[],[f2176]) ).
tcf(c_591,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK177(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,[],[f3417]) ).
tcf(c_592,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| in(sK178(X1,X2,X0),cartesian_product2(X1,X2))
| ~ in(X0,sK177(X1,X2)) ),
inference(cnf_transformation,[],[f2190]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| ( sK178(X1,X2,X0) = X0 )
| ~ in(X0,sK177(X1,X2)) ),
inference(cnf_transformation,[],[f2189]) ).
tcf(c_594,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| ( unordered_pair(unordered_pair(sK179(X1,X0),sK180(X1,X0)),unordered_pair(sK179(X1,X0),sK179(X1,X0))) = X0 )
| ~ in(X0,sK177(X1,X2)) ),
inference(cnf_transformation,[],[f3147]) ).
tcf(c_595,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| in(sK179(X1,X0),X1)
| ~ in(X0,sK177(X1,X2)) ),
inference(cnf_transformation,[],[f2187]) ).
tcf(c_596,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| ( unordered_pair(sK179(X1,X0),sK179(X1,X0)) = sK180(X1,X0) )
| ~ in(X0,sK177(X1,X2)) ),
inference(cnf_transformation,[],[f3148]) ).
tcf(c_602,plain,
! [X0: $i,X1: $i] :
( sP21(X1)
| in(unordered_pair(X0,X0),sK184(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3551]) ).
tcf(c_604,plain,
! [X0: $i,X1: $i] :
( sP21(X1)
| in(sK185(X1,X0),X1)
| ~ in(X0,sK184(X1)) ),
inference(cnf_transformation,[],[f2198]) ).
tcf(c_605,plain,
! [X0: $i,X1: $i] :
( sP21(X1)
| ( unordered_pair(sK185(X1,X0),sK185(X1,X0)) = X0 )
| ~ in(X0,sK184(X1)) ),
inference(cnf_transformation,[],[f3152]) ).
tcf(c_607,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = X1 )
| ~ in(sK186(X0,X1),X1)
| ( sK186(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f3154]) ).
tcf(c_608,plain,
! [X0: $i,X1: $i] :
( in(sK186(X0,X1),X1)
| ( sK186(X0,X1) = X0 )
| ( unordered_pair(X0,X0) = X1 ) ),
inference(cnf_transformation,[],[f3155]) ).
tcf(c_610,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(cnf_transformation,[],[f3421]) ).
tcf(c_611,negated_conjecture,
! [X0: $i] : set_union2(X0,sK140) = X0,
inference(cnf_transformation,[],[f3158]) ).
tcf(c_612,plain,
! [X0: $i] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f2207]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2208]) ).
tcf(c_614,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f2209]) ).
tcf(c_615,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(set_union2(X0,X1)) ),
inference(cnf_transformation,[],[f2210]) ).
tcf(c_616,plain,
! [X0: $i,X1: $i] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2211]) ).
tcf(c_617,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK187(X0,X1,X2),X2)
| ~ in(sK187(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f2217]) ).
tcf(c_618,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_union2(X0,X1) = X2 )
| ~ in(sK187(X0,X1,X2),X2)
| ~ in(sK187(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f2216]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK187(X0,X1,X2),X2)
| in(sK187(X0,X1,X2),X1)
| in(sK187(X0,X1,X2),X0)
| ( set_union2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f2215]) ).
tcf(c_620,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3422]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3423]) ).
tcf(c_622,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f3424]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2219]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f2220]) ).
tcf(c_625,negated_conjecture,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,set_difference(X0,X1)) != sK140 ) ),
inference(cnf_transformation,[],[f3159]) ).
tcf(c_626,negated_conjecture,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = sK140 )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f3160]) ).
tcf(c_627,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( topstr_closure(X0,X1) = X2 )
| ~ sP23(X2,X1,X0)
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f2224]) ).
tcf(c_628,plain,
! [X0: $i,X1: $i] :
( sP22(X0,X1,topstr_closure(X0,X1))
| ~ sP23(topstr_closure(X0,X1),X1,X0) ),
inference(cnf_transformation,[],[f3425]) ).
tcf(c_640,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP23(X0,X2,X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2236]) ).
tcf(c_641,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2238]) ).
tcf(c_642,plain,
! [X0: $i] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2237]) ).
tcf(c_643,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f2239]) ).
tcf(c_645,plain,
! [X0: $i,X1: $i] :
( function(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2240]) ).
tcf(c_646,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2242]) ).
tcf(c_647,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ in(sK192(X0,X1,X2),X0)
| ~ in(unordered_pair(unordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),unordered_pair(sK191(X0,X1,X2),sK191(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2)),unordered_pair(sK191(X0,X1,X2),sK191(X0,X1,X2))),X1) ),
inference(cnf_transformation,[],[f3161]) ).
tcf(c_648,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK192(X2,X1,X0),X2)
| in(unordered_pair(unordered_pair(sK191(X2,X1,X0),sK192(X2,X1,X0)),unordered_pair(sK191(X2,X1,X0),sK191(X2,X1,X0))),X0)
| ( relation_rng_restriction(X2,X1) = X0 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3162]) ).
tcf(c_649,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK191(X2,X1,X0),sK192(X2,X1,X0)),unordered_pair(sK191(X2,X1,X0),sK191(X2,X1,X0))),X1)
| in(unordered_pair(unordered_pair(sK191(X2,X1,X0),sK192(X2,X1,X0)),unordered_pair(sK191(X2,X1,X0),sK191(X2,X1,X0))),X0)
| ( relation_rng_restriction(X2,X1) = X0 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3163]) ).
tcf(c_650,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,[],[f3426]) ).
tcf(c_651,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,[],[f3427]) ).
tcf(c_652,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,[],[f3428]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2250]) ).
tcf(c_654,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2249]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK193(X0,X1),X1) ),
inference(cnf_transformation,[],[f2254]) ).
tcf(c_657,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK193(X0,X1),X0) ),
inference(cnf_transformation,[],[f2253]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2252]) ).
tcf(c_659,plain,
! [X0: $i,X1: $i] :
( ( powerset(X0) = X1 )
| ~ subset(sK194(X0,X1),X0)
| ~ in(sK194(X0,X1),X1) ),
inference(cnf_transformation,[],[f2258]) ).
tcf(c_660,plain,
! [X0: $i,X1: $i] :
( subset(sK194(X0,X1),X0)
| in(sK194(X0,X1),X1)
| ( powerset(X0) = X1 ) ),
inference(cnf_transformation,[],[f2257]) ).
tcf(c_661,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3429]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f3430]) ).
tcf(c_663,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2261]) ).
tcf(c_665,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f3432]) ).
tcf(c_666,plain,
! [X0: $i,X1: $i] :
( equipotent(X1,X0)
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2262]) ).
tcf(c_667,plain,
! [X0: $i] : equipotent(X0,X0),
inference(cnf_transformation,[],[f2263]) ).
tcf(c_668,plain,
! [X0: $i] :
( equipotent(relation_dom(X0),relation_rng(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3434]) ).
tcf(c_669,plain,
! [X0: $i,X1: $i] :
( relation(sK195(X0,X1))
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2268]) ).
tcf(c_670,plain,
! [X0: $i,X1: $i] :
( function(sK195(X0,X1))
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2267]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK195(X0,X1))
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2266]) ).
tcf(c_672,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK195(X0,X1)) = X0 )
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2265]) ).
tcf(c_673,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK195(X0,X1)) = X1 )
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2264]) ).
tcf(c_674,negated_conjecture,
! [X0: $i] : set_difference(sK140,X0) = sK140,
inference(cnf_transformation,[],[f3167]) ).
tcf(c_675,negated_conjecture,
! [X0: $i] : set_difference(X0,sK140) = X0,
inference(cnf_transformation,[],[f3168]) ).
tcf(c_676,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2272]) ).
tcf(c_683,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK196(X0,X1,X2),X1)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK196(X0,X1,X2),X2)
| ~ in(sK196(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f2284]) ).
tcf(c_684,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK196(X0,X1,X2),X2)
| in(sK196(X0,X1,X2),X0)
| ( set_difference(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f2283]) ).
tcf(c_685,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK196(X0,X1,X2),X2)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK196(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f2282]) ).
tcf(c_686,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3435]) ).
tcf(c_687,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f3436]) ).
tcf(c_688,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f3437]) ).
tcf(c_689,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2285]) ).
tcf(c_690,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2286]) ).
tcf(c_691,plain,
! [X0: $i] : element(sK197(X0),powerset(X0)),
inference(cnf_transformation,[],[f2288]) ).
tcf(c_692,plain,
! [X0: $i] : empty(sK197(X0)),
inference(cnf_transformation,[],[f2287]) ).
tcf(c_693,plain,
! [X0: $i] :
( empty(X0)
| element(sK198(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f2290]) ).
tcf(c_694,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK198(X0)) ),
inference(cnf_transformation,[],[f2289]) ).
tcf(c_695,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f2291]) ).
tcf(c_696,plain,
! [X0: $i] : element(sK199(X0),X0),
inference(cnf_transformation,[],[f2292]) ).
tcf(c_697,plain,
! [X0: $i] :
( empty_carrier(X0)
| element(sK200(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f2294]) ).
tcf(c_698,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(sK200(X0)) ),
inference(cnf_transformation,[],[f2293]) ).
tcf(c_699,plain,
one_sorted_str(sK201),
inference(cnf_transformation,[],[f2296]) ).
tcf(c_700,plain,
~ empty_carrier(sK201),
inference(cnf_transformation,[],[f2295]) ).
tcf(c_702,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f2299]) ).
tcf(c_703,plain,
! [X0: $i] :
( empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| ~ empty_carrier(X0) ),
inference(cnf_transformation,[],[f2298]) ).
tcf(c_704,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2300]) ).
tcf(c_705,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2301]) ).
tcf(c_706,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2302]) ).
tcf(c_707,plain,
one_sorted_str(sK202),
inference(cnf_transformation,[],[f2303]) ).
tcf(c_708,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f2304]) ).
tcf(c_709,plain,
! [X0: $i,X1: $i] :
( ( union_of_subsets(X1,X0) = union(X0) )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2305]) ).
tcf(c_710,plain,
! [X0: $i] :
( epsilon_transitive(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2308]) ).
tcf(c_711,plain,
! [X0: $i] :
( epsilon_connected(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2307]) ).
tcf(c_712,plain,
! [X0: $i] :
( ordinal(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2306]) ).
tcf(c_713,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ( union(X0) != X0 ) ),
inference(cnf_transformation,[],[f2310]) ).
tcf(c_714,plain,
! [X0: $i] :
( ( union(X0) = X0 )
| ~ being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f2309]) ).
tcf(c_715,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( union(X0) = X1 )
| ~ in(X2,X0)
| ~ in(sK203(X0,X1),X2)
| ~ in(sK203(X0,X1),X1) ),
inference(cnf_transformation,[],[f2316]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i] :
( in(sK203(X0,X1),X1)
| in(sK203(X0,X1),sK204(X0,X1))
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f2315]) ).
tcf(c_717,plain,
! [X0: $i,X1: $i] :
( in(sK204(X0,X1),X0)
| in(sK203(X0,X1),X1)
| ( union(X0) = X1 ) ),
inference(cnf_transformation,[],[f2314]) ).
tcf(c_718,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,union(X1))
| ~ in(X2,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3438]) ).
tcf(c_719,plain,
! [X0: $i,X1: $i] :
( in(X0,sK205(X1,X0))
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f3439]) ).
tcf(c_720,plain,
! [X0: $i,X1: $i] :
( in(sK205(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f3440]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP24(X3,X0)
| in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK213(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,[],[f3442]) ).
tcf(c_729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP24(X2,X3)
| in(sK214(X1,X2,X3,X0),cartesian_product2(X1,X1))
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK213(X1,X2,X3)) ),
inference(cnf_transformation,[],[f2327]) ).
tcf(c_730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP24(X2,X3)
| ( sK214(X1,X2,X3,X0) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK213(X1,X2,X3)) ),
inference(cnf_transformation,[],[f2326]) ).
tcf(c_731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP24(X2,X3)
| ( unordered_pair(unordered_pair(sK215(X2,X3,X0),sK216(X2,X3,X0)),unordered_pair(sK215(X2,X3,X0),sK215(X2,X3,X0))) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK213(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3174]) ).
tcf(c_732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP24(X2,X3)
| in(unordered_pair(unordered_pair(apply(X3,sK215(X2,X3,X0)),apply(X3,sK216(X2,X3,X0))),unordered_pair(apply(X3,sK215(X2,X3,X0)),apply(X3,sK215(X2,X3,X0)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK213(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3175]) ).
tcf(c_733,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,sK217(X3,X1,X0))
| ~ sP28(X3,X1,X0)
| ~ sP27(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2330]) ).
tcf(c_734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP27(X3,X2,X0,X1)
| ~ sP28(X1,X2,X3)
| ~ in(X0,sK217(X1,X2,X3)) ),
inference(cnf_transformation,[],[f2329]) ).
tcf(c_735,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP27(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,sK218(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3445]) ).
tcf(c_736,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK218(X4,X1,X0),X0)
| sP27(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,[],[f3448]) ).
tcf(c_737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK219(X0,X1,X2,X3),cartesian_product2(X1,X0))
| ~ sP27(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2337]) ).
tcf(c_738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK219(X0,X1,X2,X3) = X2 )
| ~ sP27(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2336]) ).
tcf(c_739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK220(X1,X2,X3),sK221(X1,X2,X3)),unordered_pair(sK220(X1,X2,X3),sK220(X1,X2,X3))) = X2 )
| ~ sP27(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3178]) ).
tcf(c_740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK220(X1,X2,X3),X1)
| ~ sP27(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2334]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK220(X1,X2,X3) = sK222(X1,X2,X3) )
| ~ sP27(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2333]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK221(X1,X2,X3),sK222(X1,X2,X3))
| ~ sP27(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2332]) ).
tcf(c_743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(sK221(X1,X2,X3),X0),unordered_pair(sK221(X1,X2,X3),sK221(X1,X2,X3))),X3)
| ~ sP27(X4,X1,X2,X3)
| ~ in(X0,sK222(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3179]) ).
tcf(c_744,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK223(X0,X1,X2),sK224(X0,X1,X2)),unordered_pair(sK223(X0,X1,X2),sK223(X0,X1,X2))) = X0 )
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f3180]) ).
tcf(c_745,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK223(X0,X1,X2),X1)
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f2343]) ).
tcf(c_746,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK223(X0,X1,X2) = sK225(X0,X1,X2) )
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f2342]) ).
tcf(c_747,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK224(X0,X1,X2),sK225(X0,X1,X2))
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f2341]) ).
tcf(c_748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK224(X1,X2,X3),X0),unordered_pair(sK224(X1,X2,X3),sK224(X1,X2,X3))),X3)
| ~ sP26(X1,X2,X3)
| ~ in(X0,sK225(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3181]) ).
tcf(c_754,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| sP28(X1,X0,X2)
| ~ relation(X1)
| ( sK230(X0,X1) != sK231(X0,X1) ) ),
inference(cnf_transformation,[],[f2354]) ).
tcf(c_755,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP28(X0,X1,X2)
| ( sK230(X1,X0) = sK229(X1,X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2353]) ).
tcf(c_756,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP28(X0,X1,X2)
| sP26(sK230(X1,X0),X1,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2352]) ).
tcf(c_757,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP28(X0,X1,X2)
| ( sK231(X1,X0) = sK229(X1,X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2351]) ).
tcf(c_758,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| sP28(X0,X1,X2)
| sP25(sK231(X1,X0),X1,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2350]) ).
tcf(c_759,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| empty(X0)
| ~ empty(cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f2355]) ).
tcf(c_760,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f2356]) ).
tcf(c_761,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,cartesian_product2(X1,X1))) = relation_restriction(X0,X1) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3184]) ).
tcf(c_762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cartesian_product2(X2,X3) = X4 )
| ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(sK232(X2,X3,X4),X4)
| ( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != sK232(X2,X3,X4) ) ),
inference(cnf_transformation,[],[f3185]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK233(X0,X1,X2),X0)
| in(sK232(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f2364]) ).
tcf(c_764,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK234(X0,X1,X2),X1)
| in(sK232(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f2363]) ).
tcf(c_765,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK232(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK233(X0,X1,X2),sK234(X0,X1,X2)),unordered_pair(sK233(X0,X1,X2),sK233(X0,X1,X2))) = sK232(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f3186]) ).
tcf(c_766,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,[],[f3450]) ).
tcf(c_767,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK235(X1,X2,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f3451]) ).
tcf(c_768,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK236(X1,X2,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f3452]) ).
tcf(c_769,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK235(X1,X2,X0),sK236(X1,X2,X0)),unordered_pair(sK235(X1,X2,X0),sK235(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f3453]) ).
tcf(c_770,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f2366]) ).
tcf(c_772,plain,
! [X0: $i,X1: $i] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2367]) ).
tcf(c_773,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2369]) ).
tcf(c_774,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK237(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),unordered_pair(sK237(X0,X1,X2),sK237(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2)),unordered_pair(sK237(X0,X1,X2),sK237(X0,X1,X2))),X0) ),
inference(cnf_transformation,[],[f3189]) ).
tcf(c_775,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK237(X0,X2,X1),X2)
| in(unordered_pair(unordered_pair(sK237(X0,X2,X1),sK238(X0,X2,X1)),unordered_pair(sK237(X0,X2,X1),sK237(X0,X2,X1))),X1)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3190]) ).
tcf(c_776,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK237(X0,X2,X1),sK238(X0,X2,X1)),unordered_pair(sK237(X0,X2,X1),sK237(X0,X2,X1))),X1)
| in(unordered_pair(unordered_pair(sK237(X0,X2,X1),sK238(X0,X2,X1)),unordered_pair(sK237(X0,X2,X1),sK237(X0,X2,X1))),X0)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3191]) ).
tcf(c_777,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,[],[f3454]) ).
tcf(c_778,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,[],[f3455]) ).
tcf(c_779,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,[],[f3456]) ).
tcf(c_780,plain,
relation(sK239),
inference(cnf_transformation,[],[f2378]) ).
tcf(c_781,plain,
empty(sK239),
inference(cnf_transformation,[],[f2377]) ).
tcf(c_782,plain,
function(sK239),
inference(cnf_transformation,[],[f2376]) ).
tcf(c_783,plain,
relation(sK240),
inference(cnf_transformation,[],[f2380]) ).
tcf(c_784,plain,
function(sK240),
inference(cnf_transformation,[],[f2379]) ).
tcf(c_785,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2381]) ).
tcf(c_786,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2382]) ).
tcf(c_787,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2383]) ).
tcf(c_789,plain,
~ empty(sK241),
inference(cnf_transformation,[],[f2385]) ).
tcf(c_790,plain,
~ empty(sK242),
inference(cnf_transformation,[],[f2387]) ).
tcf(c_791,plain,
relation(sK242),
inference(cnf_transformation,[],[f2386]) ).
tcf(c_792,plain,
empty(sK243),
inference(cnf_transformation,[],[f2388]) ).
tcf(c_793,plain,
empty(sK244),
inference(cnf_transformation,[],[f2390]) ).
tcf(c_794,plain,
relation(sK244),
inference(cnf_transformation,[],[f2389]) ).
tcf(c_796,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f2393]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2392]) ).
tcf(c_798,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f2391]) ).
tcf(c_799,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2395]) ).
tcf(c_805,plain,
! [X0: $i,X1: $i] :
( sP29
| in(X0,sK248(X1))
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f3457]) ).
tcf(c_806,plain,
! [X0: $i,X1: $i] :
( sP29
| in(sK249(X1,X0),X1)
| ~ in(X0,sK248(X1)) ),
inference(cnf_transformation,[],[f2403]) ).
tcf(c_807,plain,
! [X0: $i,X1: $i] :
( sP29
| ( sK249(X1,X0) = X0 )
| ~ in(X0,sK248(X1)) ),
inference(cnf_transformation,[],[f2402]) ).
tcf(c_808,plain,
! [X0: $i,X1: $i] :
( sP29
| ordinal(X0)
| ~ in(X0,sK248(X1)) ),
inference(cnf_transformation,[],[f2401]) ).
tcf(c_809,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2405]) ).
tcf(c_810,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2407]) ).
tcf(c_811,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f2406]) ).
tcf(c_812,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2408]) ).
tcf(c_813,plain,
! [X0: $i,X1: $i] :
( in(X1,sK250(X0))
| ~ sP32(X0)
| ~ sP31(X0,X1) ),
inference(cnf_transformation,[],[f2410]) ).
tcf(c_814,plain,
! [X0: $i,X1: $i] :
( sP31(X1,X0)
| ~ sP32(X1)
| ~ in(X0,sK250(X1)) ),
inference(cnf_transformation,[],[f2409]) ).
tcf(c_815,negated_conjecture,
! [X0: $i,X1: $i] :
( sP31(X1,X0)
| ~ ordinal(X0)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1)))
| ( sK251(X0) != sK140 ) ),
inference(cnf_transformation,[],[f3459]) ).
tcf(c_816,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP31(X2,X0)
| ~ ordinal(X0)
| ~ in(X1,sK251(X0))
| ~ in(X0,set_union2(X2,unordered_pair(X2,X2)))
| ( sK252(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f3461]) ).
tcf(c_817,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP31(X1,X0)
| in(sK252(X0,X2),sK251(X0))
| ~ ordinal(X0)
| ~ in(X2,sK251(X0))
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3463]) ).
tcf(c_818,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP31(X1,X0)
| subset(X2,sK252(X0,X2))
| ~ ordinal(X0)
| ~ in(X2,sK251(X0))
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3465]) ).
tcf(c_819,plain,
! [X0: $i,X1: $i] :
( sP31(X1,X0)
| element(sK251(X0),powerset(powerset(X0)))
| ~ ordinal(X0)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3467]) ).
tcf(c_820,plain,
! [X0: $i,X1: $i] :
( in(X0,omega)
| sP31(X1,X0)
| ~ ordinal(X0)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3469]) ).
tcf(c_821,plain,
! [X0: $i,X1: $i] :
( in(sK253(X0,X1),set_union2(X0,unordered_pair(X0,X0)))
| ~ sP31(X0,X1) ),
inference(cnf_transformation,[],[f3201]) ).
tcf(c_822,plain,
! [X0: $i,X1: $i] :
( ( sK253(X0,X1) = X1 )
| ~ sP31(X0,X1) ),
inference(cnf_transformation,[],[f2415]) ).
tcf(c_823,plain,
! [X0: $i,X1: $i] :
( ordinal(sK254(X1))
| ~ sP31(X0,X1) ),
inference(cnf_transformation,[],[f2414]) ).
tcf(c_824,plain,
! [X0: $i,X1: $i] :
( ( sK254(X1) = X1 )
| ~ sP31(X0,X1) ),
inference(cnf_transformation,[],[f2413]) ).
tcf(c_825,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( in(sK255(X0),X0)
| ( X0 = sK140 )
| ~ sP31(X2,X1)
| ~ in(sK254(X1),omega)
| ~ element(X0,powerset(powerset(sK254(X1)))) ),
inference(cnf_transformation,[],[f3202]) ).
tcf(c_826,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = sK140 )
| ( sK255(X0) = X2 )
| ~ sP31(X3,X1)
| ~ in(X2,X0)
| ~ in(sK254(X1),omega)
| ~ subset(sK255(X0),X2)
| ~ element(X0,powerset(powerset(sK254(X1)))) ),
inference(cnf_transformation,[],[f3203]) ).
tcf(c_831,plain,
! [X0: $i] :
( sP32(X0)
| ~ ordinal(X0)
| ( sK259 != sK260 ) ),
inference(cnf_transformation,[],[f2434]) ).
tcf(c_832,plain,
! [X0: $i] :
( sP32(X0)
| ( sK259 = sK258 )
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2433]) ).
tcf(c_833,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2432]) ).
tcf(c_834,plain,
! [X0: $i] :
( sP32(X0)
| ( sK259 = sK261 )
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2431]) ).
tcf(c_835,negated_conjecture,
! [X0: $i,X1: $i] :
( sP32(X1)
| in(sK262(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(X1)
| ~ in(sK261,omega)
| ~ element(X0,powerset(powerset(sK261))) ),
inference(cnf_transformation,[],[f3206]) ).
tcf(c_836,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( sP32(X2)
| ( X0 = sK140 )
| ( sK262(X0) = X1 )
| ~ ordinal(X2)
| ~ in(sK261,omega)
| ~ in(X1,X0)
| ~ subset(sK262(X0),X1)
| ~ element(X0,powerset(powerset(sK261))) ),
inference(cnf_transformation,[],[f3207]) ).
tcf(c_837,plain,
! [X0: $i] :
( sP32(X0)
| ( sK260 = sK258 )
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2428]) ).
tcf(c_838,plain,
! [X0: $i] :
( sP30(sK260)
| sP32(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2427]) ).
tcf(c_839,plain,
epsilon_transitive(omega),
inference(cnf_transformation,[],[f2438]) ).
tcf(c_840,plain,
epsilon_connected(omega),
inference(cnf_transformation,[],[f2437]) ).
tcf(c_842,plain,
~ empty(omega),
inference(cnf_transformation,[],[f2435]) ).
tcf(c_843,negated_conjecture,
! [X0: $i] :
( ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0)
| ~ subset(X0,sK263(X0)) ),
inference(cnf_transformation,[],[f3208]) ).
tcf(c_844,negated_conjecture,
! [X0: $i] :
( in(sK140,sK263(X0))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(cnf_transformation,[],[f3209]) ).
tcf(c_845,negated_conjecture,
! [X0: $i] :
( being_limit_ordinal(sK263(X0))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(cnf_transformation,[],[f3210]) ).
tcf(c_846,negated_conjecture,
! [X0: $i] :
( ordinal(sK263(X0))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(cnf_transformation,[],[f3211]) ).
tcf(c_847,negated_conjecture,
in(sK140,omega),
inference(cnf_transformation,[],[f3470]) ).
tcf(c_848,plain,
being_limit_ordinal(omega),
inference(cnf_transformation,[],[f3471]) ).
tcf(c_849,plain,
ordinal(omega),
inference(cnf_transformation,[],[f3472]) ).
tcf(c_850,negated_conjecture,
! [X0: $i] :
( subset(omega,X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(cnf_transformation,[],[f3473]) ).
tcf(c_851,plain,
! [X0: $i] :
( finite(relation_rng(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),omega) ),
inference(cnf_transformation,[],[f3474]) ).
tcf(c_852,plain,
! [X0: $i] :
( relation(sK264(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2450]) ).
tcf(c_853,plain,
! [X0: $i] :
( function(sK264(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2449]) ).
tcf(c_854,plain,
! [X0: $i] :
( ( relation_rng(sK264(X0)) = X0 )
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2448]) ).
tcf(c_855,plain,
! [X0: $i] :
( in(relation_dom(sK264(X0)),omega)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2447]) ).
tcf(c_856,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ element(X0,omega) ),
inference(cnf_transformation,[],[f2455]) ).
tcf(c_857,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ element(X0,omega) ),
inference(cnf_transformation,[],[f2454]) ).
tcf(c_858,plain,
! [X0: $i] :
( ordinal(X0)
| ~ element(X0,omega) ),
inference(cnf_transformation,[],[f2453]) ).
tcf(c_860,plain,
! [X0: $i] :
( ~ sP34(X0)
| ( sK266(X0) != sK267(X0) ) ),
inference(cnf_transformation,[],[f2462]) ).
tcf(c_861,plain,
! [X0: $i] :
( ( sK266(X0) = sK265(X0) )
| ~ sP34(X0) ),
inference(cnf_transformation,[],[f2461]) ).
tcf(c_862,plain,
! [X0: $i] :
( ordinal(sK268(X0))
| ~ sP34(X0) ),
inference(cnf_transformation,[],[f2460]) ).
tcf(c_863,plain,
! [X0: $i] :
( ( sK266(X0) = sK268(X0) )
| ~ sP34(X0) ),
inference(cnf_transformation,[],[f2459]) ).
tcf(c_864,plain,
! [X0: $i] :
( in(sK268(X0),X0)
| ~ sP34(X0) ),
inference(cnf_transformation,[],[f2458]) ).
tcf(c_865,plain,
! [X0: $i] :
( ( sK267(X0) = sK265(X0) )
| ~ sP34(X0) ),
inference(cnf_transformation,[],[f2457]) ).
tcf(c_866,plain,
! [X0: $i] :
( sP33(sK267(X0),X0)
| ~ sP34(X0) ),
inference(cnf_transformation,[],[f2456]) ).
tcf(c_870,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X2)
| in(X0,sK270(X2,X1))
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X2)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3476]) ).
tcf(c_871,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X1)
| in(sK271(X1,X2,X0),set_union2(X2,unordered_pair(X2,X2)))
| ~ ordinal(X2)
| ~ in(X0,sK270(X1,X2)) ),
inference(cnf_transformation,[],[f3215]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X1)
| ( sK271(X1,X2,X0) = X0 )
| ~ ordinal(X2)
| ~ in(X0,sK270(X1,X2)) ),
inference(cnf_transformation,[],[f2469]) ).
tcf(c_873,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X1)
| ordinal(sK272(X1,X0))
| ~ ordinal(X2)
| ~ in(X0,sK270(X1,X2)) ),
inference(cnf_transformation,[],[f2468]) ).
tcf(c_874,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X1)
| ( sK272(X1,X0) = X0 )
| ~ ordinal(X2)
| ~ in(X0,sK270(X1,X2)) ),
inference(cnf_transformation,[],[f2467]) ).
tcf(c_875,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP34(X1)
| in(sK272(X1,X0),X1)
| ~ ordinal(X2)
| ~ in(X0,sK270(X1,X2)) ),
inference(cnf_transformation,[],[f2466]) ).
tcf(c_883,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP35(X0,X1)
| in(set_difference(X2,unordered_pair(X1,X1)),sK278(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,[],[f3478]) ).
tcf(c_884,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP35(X0,X1)
| in(sK279(X1,X0,X2),powerset(X1))
| ~ ordinal(X1)
| ~ in(X2,sK278(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3219]) ).
tcf(c_885,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP35(X0,X1)
| ( sK279(X1,X0,X2) = X2 )
| ~ ordinal(X1)
| ~ in(X2,sK278(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3220]) ).
tcf(c_886,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP35(X0,X1)
| in(sK280(X1,X0,X2),X0)
| ~ ordinal(X1)
| ~ in(X2,sK278(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3221]) ).
tcf(c_887,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP35(X0,X1)
| ( set_difference(sK280(X1,X0,X2),unordered_pair(X1,X1)) = X2 )
| ~ ordinal(X1)
| ~ in(X2,sK278(X1,X0))
| ~ element(X0,powerset(powerset(set_union2(X1,unordered_pair(X1,X1))))) ),
inference(cnf_transformation,[],[f3222]) ).
tcf(c_889,plain,
! [X0: $i] :
( epsilon_transitive(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f3224]) ).
tcf(c_890,plain,
! [X0: $i] :
( epsilon_connected(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f3225]) ).
tcf(c_891,plain,
! [X0: $i] :
( ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f3226]) ).
tcf(c_892,plain,
! [X0: $i] : ~ empty(set_union2(X0,unordered_pair(X0,X0))),
inference(cnf_transformation,[],[f3227]) ).
tcf(c_893,plain,
epsilon_transitive(sK281),
inference(cnf_transformation,[],[f2492]) ).
tcf(c_894,plain,
epsilon_connected(sK281),
inference(cnf_transformation,[],[f2491]) ).
tcf(c_895,plain,
ordinal(sK281),
inference(cnf_transformation,[],[f2490]) ).
tcf(c_896,plain,
being_limit_ordinal(sK281),
inference(cnf_transformation,[],[f2489]) ).
tcf(c_897,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(X0) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(sK282(X0,X2),X2)
| ( apply(X0,X1) != sK282(X0,X2) ) ),
inference(cnf_transformation,[],[f2498]) ).
tcf(c_898,plain,
! [X0: $i,X1: $i] :
( in(sK282(X0,X1),X1)
| in(sK283(X0,X1),relation_dom(X0))
| ( relation_rng(X0) = X1 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2497]) ).
tcf(c_899,plain,
! [X0: $i,X1: $i] :
( in(sK282(X0,X1),X1)
| ( relation_rng(X0) = X1 )
| ( apply(X0,sK283(X0,X1)) = sK282(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2496]) ).
tcf(c_900,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f3480]) ).
tcf(c_901,plain,
! [X0: $i,X1: $i] :
( in(sK284(X1,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f3481]) ).
tcf(c_902,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK284(X1,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f3482]) ).
tcf(c_906,negated_conjecture,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(X0))
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3485]) ).
tcf(c_907,plain,
top_str(sK285),
inference(cnf_transformation,[],[f2503]) ).
tcf(c_908,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(cast_as_carrier_subset(X0)) ),
inference(cnf_transformation,[],[f2504]) ).
tcf(c_909,plain,
! [X0: $i] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f2505]) ).
tcf(c_910,plain,
! [X0: $i] :
( ( the_carrier(X0) = cast_as_carrier_subset(X0) )
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f2506]) ).
tcf(c_916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP36(X2,X0)
| in(X1,sK289(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,[],[f3486]) ).
tcf(c_917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP36(X1,X2)
| in(sK290(X1,X2,X0),powerset(relation_dom(X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X3)))
| ~ in(X0,sK289(X1,X2)) ),
inference(cnf_transformation,[],[f2514]) ).
tcf(c_918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP36(X1,X2)
| ( sK290(X1,X2,X0) = X0 )
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X3)))
| ~ in(X0,sK289(X1,X2)) ),
inference(cnf_transformation,[],[f2513]) ).
tcf(c_919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP36(X1,X2)
| in(relation_image(X2,X0),X1)
| ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X3)))
| ~ in(X0,sK289(X1,X2)) ),
inference(cnf_transformation,[],[f2512]) ).
tcf(c_920,plain,
! [X0: $i,X1: $i] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2516]) ).
tcf(c_921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_image(X1,X2) = X3 )
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(sK291(X1,X2,X3),X3)
| ~ in(unordered_pair(unordered_pair(X0,sK291(X1,X2,X3)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f3232]) ).
tcf(c_922,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK291(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK292(X0,X1,X2),sK291(X0,X1,X2)),unordered_pair(sK292(X0,X1,X2),sK292(X0,X1,X2))),X0)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3233]) ).
tcf(c_923,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK292(X0,X1,X2),X1)
| in(sK291(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2520]) ).
tcf(c_924,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,[],[f3487]) ).
tcf(c_925,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK293(X1,X2,X0),X0),unordered_pair(sK293(X1,X2,X0),sK293(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3488]) ).
tcf(c_926,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK293(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3489]) ).
tcf(c_927,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(sK294(X0,X1,X2),X2)
| ( sK294(X0,X1,X2) != apply(X0,X3) ) ),
inference(cnf_transformation,[],[f2530]) ).
tcf(c_928,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK294(X0,X1,X2),X2)
| in(sK295(X0,X1,X2),relation_dom(X0))
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2529]) ).
tcf(c_929,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK295(X0,X1,X2),X1)
| in(sK294(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2528]) ).
tcf(c_930,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK294(X0,X1,X2),X2)
| ( relation_image(X0,X1) = X2 )
| ( apply(X0,sK295(X0,X1,X2)) = sK294(X0,X1,X2) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2527]) ).
tcf(c_931,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,[],[f3491]) ).
tcf(c_932,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK296(X1,X2,X0),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3492]) ).
tcf(c_933,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK296(X1,X2,X0),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3493]) ).
tcf(c_934,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X1,sK296(X1,X2,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(cnf_transformation,[],[f3494]) ).
tcf(c_935,plain,
! [X0: $i,X1: $i] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f2531]) ).
tcf(c_936,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X1) = X2 )
| ~ in(sK297(X0,X1,X2),X2)
| ( sK297(X0,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2538]) ).
tcf(c_937,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(X0,X1) = X2 )
| ~ in(sK297(X0,X1,X2),X2)
| ( sK297(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f2537]) ).
tcf(c_938,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK297(X0,X1,X2),X2)
| ( unordered_pair(X0,X1) = X2 )
| ( sK297(X0,X1,X2) = X1 )
| ( sK297(X0,X1,X2) = X0 ) ),
inference(cnf_transformation,[],[f2536]) ).
tcf(c_939,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f3496]) ).
tcf(c_940,plain,
! [X0: $i,X1: $i] : in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f3498]) ).
tcf(c_941,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f3499]) ).
tcf(c_942,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2539]) ).
tcf(c_943,plain,
! [X0: $i] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2541]) ).
tcf(c_944,plain,
! [X0: $i] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2540]) ).
tcf(c_945,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f2542]) ).
tcf(c_946,negated_conjecture,
! [X0: $i] : set_difference(X0,set_difference(X0,sK140)) = sK140,
inference(cnf_transformation,[],[f3236]) ).
tcf(c_954,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3244]) ).
tcf(c_955,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ in(sK298(X0,X1,X2),X2)
| ~ in(sK298(X0,X1,X2),X1)
| ~ in(sK298(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f3245]) ).
tcf(c_956,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK298(X0,X1,X2),X2)
| in(sK298(X0,X1,X2),X0)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f3246]) ).
tcf(c_957,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK298(X0,X1,X2),X2)
| in(sK298(X0,X1,X2),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f3247]) ).
tcf(c_958,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,[],[f3500]) ).
tcf(c_960,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_difference(X1,set_difference(X1,X2))) ),
inference(cnf_transformation,[],[f3502]) ).
tcf(c_961,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(cnf_transformation,[],[f3251]) ).
tcf(c_962,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f2560]) ).
tcf(c_963,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f2559]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i] : relation_of2_as_subset(sK299(X0,X1),X0,X1),
inference(cnf_transformation,[],[f2561]) ).
tcf(c_965,plain,
! [X0: $i] : in(X0,sK300(X0)),
inference(cnf_transformation,[],[f2566]) ).
tcf(c_966,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK300(X1))
| ~ subset(X2,X0)
| ~ in(X0,sK300(X1)) ),
inference(cnf_transformation,[],[f2565]) ).
tcf(c_967,plain,
! [X0: $i,X1: $i] :
( in(sK301(X1,X0),sK300(X1))
| ~ in(X0,sK300(X1)) ),
inference(cnf_transformation,[],[f2564]) ).
tcf(c_968,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK301(X1,X0))
| ~ subset(X2,X0)
| ~ in(X0,sK300(X1)) ),
inference(cnf_transformation,[],[f2563]) ).
tcf(c_969,plain,
! [X0: $i,X1: $i] :
( are_equipotent(X0,sK300(X1))
| in(X0,sK300(X1))
| ~ subset(X0,sK300(X1)) ),
inference(cnf_transformation,[],[f2562]) ).
tcf(c_970,plain,
! [X0: $i,X1: $i] :
( equipotent(X0,X1)
| ~ are_equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2568]) ).
tcf(c_971,plain,
! [X0: $i,X1: $i] :
( are_equipotent(X0,X1)
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[],[f2567]) ).
tcf(c_972,plain,
! [X0: $i] :
( empty(X0)
| element(sK302(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f2571]) ).
tcf(c_973,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK302(X0)) ),
inference(cnf_transformation,[],[f2570]) ).
tcf(c_974,plain,
! [X0: $i] :
( empty(X0)
| finite(sK302(X0)) ),
inference(cnf_transformation,[],[f2569]) ).
tcf(c_975,plain,
~ empty(sK303),
inference(cnf_transformation,[],[f2573]) ).
tcf(c_976,plain,
finite(sK303),
inference(cnf_transformation,[],[f2572]) ).
tcf(c_978,plain,
! [X0: $i] : finite(unordered_pair(X0,X0)),
inference(cnf_transformation,[],[f3253]) ).
tcf(c_979,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f2576]) ).
tcf(c_981,plain,
! [X0: $i,X1: $i] :
( finite(set_difference(X1,set_difference(X1,X0)))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f3255]) ).
tcf(c_983,plain,
! [X0: $i] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2580]) ).
tcf(c_984,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0)
| ~ in(X3,X1)
| ~ in(sK304(X0,X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(sK304(X0,X1,X2),X3),unordered_pair(sK304(X0,X1,X2),sK304(X0,X1,X2))),X0) ),
inference(cnf_transformation,[],[f3256]) ).
tcf(c_985,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK304(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK304(X0,X1,X2),sK305(X0,X1,X2)),unordered_pair(sK304(X0,X1,X2),sK304(X0,X1,X2))),X0)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3257]) ).
tcf(c_986,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK305(X0,X1,X2),X1)
| in(sK304(X0,X1,X2),X2)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2584]) ).
tcf(c_987,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,[],[f3503]) ).
tcf(c_988,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK306(X1,X2,X0)),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f3504]) ).
tcf(c_989,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK306(X1,X2,X0),X2)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(cnf_transformation,[],[f3505]) ).
tcf(c_990,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK307(X0,X1,X2),X2)
| ~ in(sK307(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK307(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f2592]) ).
tcf(c_991,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK307(X0,X1,X2),X2)
| in(sK307(X0,X1,X2),relation_dom(X0))
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2591]) ).
tcf(c_992,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK307(X0,X1,X2),X2)
| in(apply(X0,sK307(X0,X1,X2)),X1)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2590]) ).
tcf(c_993,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,[],[f3506]) ).
tcf(c_994,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,[],[f3507]) ).
tcf(c_995,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,[],[f3508]) ).
tcf(c_996,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,[],[f3260]) ).
tcf(c_997,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset_intersection2(X1,X2,X2) = X2 )
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2594]) ).
tcf(c_998,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,[],[f2595]) ).
tcf(c_999,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,[],[f2596]) ).
tcf(c_1000,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2598]) ).
tcf(c_1001,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2597]) ).
tcf(c_1002,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2600]) ).
tcf(c_1003,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2599]) ).
tcf(c_1004,plain,
! [X0: $i,X1: $i] :
( empty(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2602]) ).
tcf(c_1005,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ empty(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2601]) ).
tcf(c_1006,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2603]) ).
tcf(c_1007,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,sK309(X0,X1,X2)),unordered_pair(X3,X3)),X1)
| ~ in(unordered_pair(unordered_pair(sK308(X0,X1,X2),X3),unordered_pair(sK308(X0,X1,X2),sK308(X0,X1,X2))),X0)
| ~ in(unordered_pair(unordered_pair(sK308(X0,X1,X2),sK309(X0,X1,X2)),unordered_pair(sK308(X0,X1,X2),sK308(X0,X1,X2))),X2) ),
inference(cnf_transformation,[],[f3261]) ).
tcf(c_1008,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK308(X0,X2,X1),sK310(X0,X2,X1)),unordered_pair(sK308(X0,X2,X1),sK308(X0,X2,X1))),X0)
| in(unordered_pair(unordered_pair(sK308(X0,X2,X1),sK309(X0,X2,X1)),unordered_pair(sK308(X0,X2,X1),sK308(X0,X2,X1))),X1)
| ( relation_composition(X0,X2) = X1 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3262]) ).
tcf(c_1009,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK310(X0,X2,X1),sK309(X0,X2,X1)),unordered_pair(sK310(X0,X2,X1),sK310(X0,X2,X1))),X2)
| in(unordered_pair(unordered_pair(sK308(X0,X2,X1),sK309(X0,X2,X1)),unordered_pair(sK308(X0,X2,X1),sK308(X0,X2,X1))),X1)
| ( relation_composition(X0,X2) = X1 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3263]) ).
tcf(c_1010,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,[],[f3509]) ).
tcf(c_1011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,sK311(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,[],[f3510]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK311(X2,X3,X0,X1),X1),unordered_pair(sK311(X2,X3,X0,X1),sK311(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,[],[f3511]) ).
tcf(c_1013,plain,
! [X0: $i,X1: $i] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2610]) ).
tcf(c_1014,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,[],[f2611]) ).
tcf(c_1015,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,[],[f2612]) ).
tcf(c_1016,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,[],[f2614]) ).
tcf(c_1017,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,[],[f2613]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i] : relation_of2(sK312(X0,X1),X0,X1),
inference(cnf_transformation,[],[f2618]) ).
tcf(c_1019,plain,
! [X0: $i,X1: $i] : relation(sK312(X0,X1)),
inference(cnf_transformation,[],[f2617]) ).
tcf(c_1020,plain,
! [X0: $i,X1: $i] : function(sK312(X0,X1)),
inference(cnf_transformation,[],[f2616]) ).
tcf(c_1021,plain,
! [X0: $i,X1: $i] : quasi_total(sK312(X0,X1),X0,X1),
inference(cnf_transformation,[],[f2615]) ).
tcf(c_1022,plain,
! [X0: $i] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f2619]) ).
tcf(c_1023,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,X1)
| ( X0 = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f2620]) ).
tcf(c_1024,plain,
! [X0: $i,X1: $i] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f2621]) ).
tcf(c_1025,plain,
~ empty(sK313),
inference(cnf_transformation,[],[f2625]) ).
tcf(c_1026,plain,
epsilon_transitive(sK313),
inference(cnf_transformation,[],[f2624]) ).
tcf(c_1027,plain,
epsilon_connected(sK313),
inference(cnf_transformation,[],[f2623]) ).
tcf(c_1028,plain,
ordinal(sK313),
inference(cnf_transformation,[],[f2622]) ).
tcf(c_1029,plain,
relation(sK314),
inference(cnf_transformation,[],[f2632]) ).
tcf(c_1030,plain,
function(sK314),
inference(cnf_transformation,[],[f2631]) ).
tcf(c_1031,plain,
one_to_one(sK314),
inference(cnf_transformation,[],[f2630]) ).
tcf(c_1032,plain,
empty(sK314),
inference(cnf_transformation,[],[f2629]) ).
tcf(c_1033,plain,
epsilon_transitive(sK314),
inference(cnf_transformation,[],[f2628]) ).
tcf(c_1034,plain,
epsilon_connected(sK314),
inference(cnf_transformation,[],[f2627]) ).
tcf(c_1035,plain,
ordinal(sK314),
inference(cnf_transformation,[],[f2626]) ).
tcf(c_1036,plain,
epsilon_transitive(sK315),
inference(cnf_transformation,[],[f2635]) ).
tcf(c_1037,plain,
epsilon_connected(sK315),
inference(cnf_transformation,[],[f2634]) ).
tcf(c_1038,plain,
ordinal(sK315),
inference(cnf_transformation,[],[f2633]) ).
tcf(c_1042,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK316(X0),X0) ),
inference(cnf_transformation,[],[f2641]) ).
tcf(c_1043,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK316(X0),X0) ),
inference(cnf_transformation,[],[f2640]) ).
tcf(c_1044,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ epsilon_transitive(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2639]) ).
tcf(c_1045,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2644]) ).
tcf(c_1046,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2643]) ).
tcf(c_1047,plain,
! [X0: $i] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2642]) ).
tcf(c_1048,plain,
! [X0: $i] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f2645]) ).
tcf(c_1049,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2647]) ).
tcf(c_1050,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f2646]) ).
tcf(c_1051,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ~ ordinal(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f2650]) ).
tcf(c_1052,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| ~ ordinal(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f2649]) ).
tcf(c_1053,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f2648]) ).
tcf(c_1054,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(X0,X1)
| subset(sK317(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2655]) ).
tcf(c_1055,negated_conjecture,
! [X0: $i,X1: $i] :
( is_well_founded_in(X0,X1)
| ~ relation(X0)
| ( sK317(X0,X1) != sK140 ) ),
inference(cnf_transformation,[],[f3267]) ).
tcf(c_1056,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_well_founded_in(X0,X2)
| ~ relation(X0)
| ~ in(X1,sK317(X0,X2))
| ~ disjoint(fiber(X0,X1),sK317(X0,X2)) ),
inference(cnf_transformation,[],[f2653]) ).
tcf(c_1057,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X2,X0),X0)
| ( X0 = sK140 )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3268]) ).
tcf(c_1058,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X2,sK318(X2,X0)),X0)
| ( X0 = sK140 )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f3269]) ).
tcf(c_1059,plain,
! [X0: $i] :
( well_founded_relation(X0)
| subset(sK319(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2660]) ).
tcf(c_1060,negated_conjecture,
! [X0: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ( sK319(X0) != sK140 ) ),
inference(cnf_transformation,[],[f3270]) ).
tcf(c_1061,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ~ in(X1,sK319(X0))
| ~ disjoint(fiber(X0,X1),sK319(X0)) ),
inference(cnf_transformation,[],[f2658]) ).
tcf(c_1062,negated_conjecture,
! [X0: $i,X1: $i] :
( in(sK320(X1,X0),X0)
| ( X0 = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f3271]) ).
tcf(c_1063,negated_conjecture,
! [X0: $i,X1: $i] :
( disjoint(fiber(X1,sK320(X1,X0)),X0)
| ( X0 = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f3272]) ).
tcf(c_1064,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( fiber(X0,X1) = X2 )
| ( sK321(X0,X1,X2) = X1 )
| ~ relation(X0)
| ~ in(sK321(X0,X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(sK321(X0,X1,X2),X1),unordered_pair(sK321(X0,X1,X2),sK321(X0,X1,X2))),X0) ),
inference(cnf_transformation,[],[f3273]) ).
tcf(c_1065,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK321(X0,X1,X2),X2)
| ( fiber(X0,X1) = X2 )
| ~ relation(X0)
| ( sK321(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f2665]) ).
tcf(c_1066,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK321(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK321(X0,X1,X2),X1),unordered_pair(sK321(X0,X1,X2),sK321(X0,X1,X2))),X0)
| ( fiber(X0,X1) = X2 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3274]) ).
tcf(c_1067,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,[],[f3512]) ).
tcf(c_1068,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ in(X0,fiber(X1,X0)) ),
inference(cnf_transformation,[],[f3514]) ).
tcf(c_1069,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,[],[f3515]) ).
tcf(c_1070,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,[],[f2667]) ).
tcf(c_1071,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,[],[f2668]) ).
tcf(c_1072,negated_conjecture,
! [X0: $i,X1: $i] :
( quasi_total(X1,sK140,X0)
| ~ relation_of2_as_subset(X1,sK140,X0)
| ( relation_dom_as_subset(sK140,X0,X1) != sK140 ) ),
inference(cnf_transformation,[],[f3516]) ).
tcf(c_1073,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(X2,X0,X1)
| ( X1 = sK140 )
| ~ relation_of2_as_subset(X2,X0,X1)
| ( relation_dom_as_subset(X0,X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f3278]) ).
tcf(c_1074,negated_conjecture,
! [X0: $i,X1: $i] :
( ( relation_dom_as_subset(sK140,X1,X0) = sK140 )
| ~ quasi_total(X0,sK140,X1)
| ~ relation_of2_as_subset(X0,sK140,X1) ),
inference(cnf_transformation,[],[f3517]) ).
tcf(c_1075,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = sK140 )
| ( relation_dom_as_subset(X1,X2,X0) = X1 )
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f3280]) ).
tcf(c_1076,negated_conjecture,
! [X0: $i] :
( quasi_total(sK140,X0,sK140)
| ( X0 = sK140 )
| ~ relation_of2_as_subset(sK140,X0,sK140) ),
inference(cnf_transformation,[],[f3519]) ).
tcf(c_1077,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( X0 = sK140 )
| ~ quasi_total(X0,X1,sK140)
| ~ relation_of2_as_subset(X0,X1,sK140) ),
inference(cnf_transformation,[],[f3520]) ).
tcf(c_1080,plain,
latt_str(sK322),
inference(cnf_transformation,[],[f2677]) ).
tcf(c_1081,plain,
! [X0: $i] :
( meet_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f2679]) ).
tcf(c_1082,plain,
! [X0: $i] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f2678]) ).
tcf(c_1083,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| ( join(X0,meet(X0,sK323(X0),sK324(X0)),sK324(X0)) != sK324(X0) ) ),
inference(cnf_transformation,[],[f2683]) ).
tcf(c_1084,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| element(sK324(X0),the_carrier(X0))
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f2682]) ).
tcf(c_1085,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| element(sK323(X0),the_carrier(X0))
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f2681]) ).
tcf(c_1086,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,[],[f2680]) ).
tcf(c_1087,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,[],[f2684]) ).
tcf(c_1088,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,[],[f2685]) ).
tcf(c_1089,plain,
join_semilatt_str(sK325),
inference(cnf_transformation,[],[f2686]) ).
tcf(c_1090,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f2687]) ).
tcf(c_1091,plain,
! [X0: $i] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f2688]) ).
tcf(c_1092,plain,
! [X0: $i] :
( ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0)
| ~ subset(sK326(relation_field(X0),X0),sK327(relation_field(X0),X0))
| ~ in(unordered_pair(unordered_pair(sK326(relation_field(X0),X0),sK327(relation_field(X0),X0)),unordered_pair(sK326(relation_field(X0),X0),sK326(relation_field(X0),X0))),X0) ),
inference(cnf_transformation,[],[f3521]) ).
tcf(c_1093,plain,
! [X0: $i] :
( subset(sK326(relation_field(X0),X0),sK327(relation_field(X0),X0))
| in(unordered_pair(unordered_pair(sK326(relation_field(X0),X0),sK327(relation_field(X0),X0)),unordered_pair(sK326(relation_field(X0),X0),sK326(relation_field(X0),X0))),X0)
| ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3522]) ).
tcf(c_1094,plain,
! [X0: $i] :
( in(sK326(relation_field(X0),X0),relation_field(X0))
| ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3523]) ).
tcf(c_1095,plain,
! [X0: $i] :
( in(sK327(relation_field(X0),X0),relation_field(X0))
| ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3524]) ).
tcf(c_1096,plain,
! [X0: $i] :
( ( relation_field(inclusion_relation(X0)) = X0 )
| ~ relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f3525]) ).
tcf(c_1097,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,[],[f3526]) ).
tcf(c_1098,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,[],[f3527]) ).
tcf(c_1099,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f2697]) ).
tcf(c_1100,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f2696]) ).
tcf(c_1101,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f2698]) ).
tcf(c_1102,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ~ relation(X1)
| ~ in(sK328(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK328(X0,X1),sK329(X0,X1)),unordered_pair(sK328(X0,X1),sK328(X0,X1))),X1)
| ( sK328(X0,X1) != sK329(X0,X1) ) ),
inference(cnf_transformation,[],[f3287]) ).
tcf(c_1103,plain,
! [X0: $i,X1: $i] :
( in(sK328(X1,X0),X1)
| in(unordered_pair(unordered_pair(sK328(X1,X0),sK329(X1,X0)),unordered_pair(sK328(X1,X0),sK328(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3288]) ).
tcf(c_1104,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK328(X1,X0),sK329(X1,X0)),unordered_pair(sK328(X1,X0),sK328(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ( sK328(X1,X0) = sK329(X1,X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3289]) ).
tcf(c_1105,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,[],[f3529]) ).
tcf(c_1106,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,[],[f3530]) ).
tcf(c_1107,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,[],[f3531]) ).
tcf(c_1108,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2705]) ).
tcf(c_1110,plain,
! [X0: $i] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2706]) ).
tcf(c_1111,plain,
! [X0: $i] :
( empty(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2709]) ).
tcf(c_1112,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f2708]) ).
tcf(c_1113,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2710]) ).
tcf(c_1114,plain,
! [X0: $i] :
( ( relation_inverse(X0) = function_inverse(X0) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2711]) ).
tcf(c_1115,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK330(X0,X1),sK331(X0,X1)),unordered_pair(sK330(X0,X1),sK330(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK331(X0,X1),sK330(X0,X1)),unordered_pair(sK331(X0,X1),sK331(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3293]) ).
tcf(c_1116,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK330(X0,X1),sK331(X0,X1)),unordered_pair(sK330(X0,X1),sK330(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK331(X0,X1),sK330(X0,X1)),unordered_pair(sK331(X0,X1),sK331(X0,X1))),X0)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3294]) ).
tcf(c_1117,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,[],[f3532]) ).
tcf(c_1118,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,[],[f3533]) ).
tcf(c_1119,plain,
! [X0: $i,X1: $i] :
( element(meet_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2716]) ).
tcf(c_1120,plain,
! [X0: $i,X1: $i] :
( element(interior(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2717]) ).
tcf(c_1121,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X0))) = interior(X1,X0) )
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2718]) ).
tcf(c_1122,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,[],[f2719]) ).
tcf(c_1123,plain,
! [X0: $i,X1: $i] :
( ( complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 )
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2720]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2721]) ).
tcf(c_1125,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( complements_of_subsets(X0,X1) = X2 )
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(sK332(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK332(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f2726]) ).
tcf(c_1126,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK332(X1,X2,X0),X0)
| in(subset_complement(X1,sK332(X1,X2,X0)),X2)
| ( complements_of_subsets(X1,X2) = X0 )
| ~ element(X2,powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2725]) ).
tcf(c_1127,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK332(X1,X2,X0),powerset(X1))
| ( complements_of_subsets(X1,X2) = X0 )
| ~ element(X2,powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2724]) ).
tcf(c_1128,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,[],[f3534]) ).
tcf(c_1129,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,[],[f3535]) ).
tcf(c_1130,plain,
! [X0: $i,X1: $i] :
( element(union_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2727]) ).
tcf(c_1131,plain,
! [X0: $i] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f2728]) ).
tcf(c_1132,plain,
! [X0: $i] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f2729]) ).
tcf(c_1133,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2731]) ).
tcf(c_1134,plain,
! [X0: $i] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2730]) ).
tcf(c_1135,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_isomorphism(X1,X2,X0)
| ~ sP38(X2,X1,X0)
| ~ sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f2733]) ).
tcf(c_1136,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP37(X2,X0,X1)
| ~ sP38(X1,X0,X2)
| ~ relation_isomorphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f2732]) ).
tcf(c_1148,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP38(X2,X0,X1)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2745]) ).
tcf(c_1149,plain,
relation(sK335),
inference(cnf_transformation,[],[f2748]) ).
tcf(c_1150,plain,
function(sK335),
inference(cnf_transformation,[],[f2747]) ).
tcf(c_1151,plain,
one_to_one(sK335),
inference(cnf_transformation,[],[f2746]) ).
tcf(c_1152,plain,
relation(sK336),
inference(cnf_transformation,[],[f2752]) ).
tcf(c_1153,plain,
function(sK336),
inference(cnf_transformation,[],[f2751]) ).
tcf(c_1154,plain,
one_to_one(sK336),
inference(cnf_transformation,[],[f2750]) ).
tcf(c_1155,plain,
empty(sK336),
inference(cnf_transformation,[],[f2749]) ).
tcf(c_1156,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( sK337(X0) != sK338(X0) ) ),
inference(cnf_transformation,[],[f2757]) ).
tcf(c_1157,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK337(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2756]) ).
tcf(c_1158,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK338(X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2755]) ).
tcf(c_1159,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK337(X0)) = apply(X0,sK338(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2754]) ).
tcf(c_1160,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,[],[f2753]) ).
tcf(c_1161,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2758]) ).
tcf(c_1163,plain,
! [X0: $i,X1: $i] :
( ( union_of_subsets(the_carrier(X1),X0) = cast_as_carrier_subset(X1) )
| ~ one_sorted_str(X1)
| ~ is_a_cover_of_carrier(X1,X0)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f2761]) ).
tcf(c_1164,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,[],[f2768]) ).
tcf(c_1165,plain,
! [X0: $i,X1: $i] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f2767]) ).
tcf(c_1166,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f2766]) ).
tcf(c_1167,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f2765]) ).
tcf(c_1168,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f2764]) ).
tcf(c_1169,plain,
! [X0: $i,X1: $i] :
( is_well_founded_in(X0,X1)
| ~ relation(X0)
| ~ well_orders(X0,X1) ),
inference(cnf_transformation,[],[f2763]) ).
tcf(c_1170,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(cnf_transformation,[],[f3536]) ).
tcf(c_1171,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( unordered_pair(unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK340(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(cnf_transformation,[],[f3537]) ).
tcf(c_1172,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,[],[f3539]) ).
tcf(c_1173,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( sK342(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(cnf_transformation,[],[f3540]) ).
tcf(c_1174,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( unordered_pair(unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK342(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2))) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) ) ),
inference(cnf_transformation,[],[f3541]) ).
tcf(c_1175,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,[],[f3543]) ).
tcf(c_1207,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK343(X0),X0) ),
inference(cnf_transformation,[],[f2811]) ).
tcf(c_1208,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK344(X0),X0) ),
inference(cnf_transformation,[],[f2810]) ).
tcf(c_1209,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK343(X0),sK344(X0)) ),
inference(cnf_transformation,[],[f2809]) ).
tcf(c_1210,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK343(X0) != sK344(X0) ) ),
inference(cnf_transformation,[],[f2808]) ).
tcf(c_1211,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK344(X0),sK343(X0)) ),
inference(cnf_transformation,[],[f2807]) ).
tcf(c_1212,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,[],[f2806]) ).
tcf(c_1213,plain,
! [X0: $i] : element(sK345(X0),powerset(X0)),
inference(cnf_transformation,[],[f2821]) ).
tcf(c_1214,plain,
! [X0: $i] : empty(sK345(X0)),
inference(cnf_transformation,[],[f2820]) ).
tcf(c_1215,plain,
! [X0: $i] : relation(sK345(X0)),
inference(cnf_transformation,[],[f2819]) ).
tcf(c_1216,plain,
! [X0: $i] : function(sK345(X0)),
inference(cnf_transformation,[],[f2818]) ).
tcf(c_1217,plain,
! [X0: $i] : one_to_one(sK345(X0)),
inference(cnf_transformation,[],[f2817]) ).
tcf(c_1218,plain,
! [X0: $i] : epsilon_transitive(sK345(X0)),
inference(cnf_transformation,[],[f2816]) ).
tcf(c_1219,plain,
! [X0: $i] : epsilon_connected(sK345(X0)),
inference(cnf_transformation,[],[f2815]) ).
tcf(c_1220,plain,
! [X0: $i] : ordinal(sK345(X0)),
inference(cnf_transformation,[],[f2814]) ).
tcf(c_1222,plain,
! [X0: $i] : finite(sK345(X0)),
inference(cnf_transformation,[],[f2812]) ).
tcf(c_1223,plain,
~ empty(sK346),
inference(cnf_transformation,[],[f2826]) ).
tcf(c_1224,plain,
epsilon_transitive(sK346),
inference(cnf_transformation,[],[f2825]) ).
tcf(c_1225,plain,
epsilon_connected(sK346),
inference(cnf_transformation,[],[f2824]) ).
tcf(c_1226,plain,
ordinal(sK346),
inference(cnf_transformation,[],[f2823]) ).
tcf(c_1236,plain,
! [X0: $i,X1: $i] : relation_of2(sK347(X0,X1),X0,X1),
inference(cnf_transformation,[],[f2838]) ).
tcf(c_1237,plain,
! [X0: $i,X1: $i] : relation(sK347(X0,X1)),
inference(cnf_transformation,[],[f2837]) ).
tcf(c_1238,plain,
! [X0: $i,X1: $i] : function(sK347(X0,X1)),
inference(cnf_transformation,[],[f2836]) ).
tcf(c_1239,plain,
! [X0: $i,X1: $i] : relation_of2(sK348(X0,X1),X0,X1),
inference(cnf_transformation,[],[f2839]) ).
tcf(c_1240,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f2841]) ).
tcf(c_1241,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,cartesian_product2(X1,X2))
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f2840]) ).
tcf(c_1242,plain,
meet_semilatt_str(sK349),
inference(cnf_transformation,[],[f2842]) ).
tcf(c_1243,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f2843]) ).
tcf(c_1244,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,[],[f2844]) ).
tcf(c_1245,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,[],[f2845]) ).
tcf(c_1246,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| ~ relation(X0)
| ( sK350(X0,X1) != sK351(X0,X1) ) ),
inference(cnf_transformation,[],[f2851]) ).
tcf(c_1247,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(sK350(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2850]) ).
tcf(c_1248,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(sK351(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2849]) ).
tcf(c_1249,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK350(X0,X1),sK351(X0,X1)),unordered_pair(sK350(X0,X1),sK350(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3330]) ).
tcf(c_1250,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK351(X0,X1),sK350(X0,X1)),unordered_pair(sK351(X0,X1),sK351(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3331]) ).
tcf(c_1251,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,[],[f3332]) ).
tcf(c_1252,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2853]) ).
tcf(c_1253,plain,
! [X0: $i] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2852]) ).
tcf(c_1254,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| in(sK352(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2859]) ).
tcf(c_1255,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| in(sK353(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2858]) ).
tcf(c_1256,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ( sK352(X0,X1) != sK353(X0,X1) ) ),
inference(cnf_transformation,[],[f2857]) ).
tcf(c_1257,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK352(X0,X1),sK353(X0,X1)),unordered_pair(sK352(X0,X1),sK352(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3333]) ).
tcf(c_1258,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK353(X0,X1),sK352(X0,X1)),unordered_pair(sK353(X0,X1),sK353(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3334]) ).
tcf(c_1259,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,[],[f3335]) ).
tcf(c_1260,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2861]) ).
tcf(c_1261,plain,
! [X0: $i] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2860]) ).
tcf(c_1262,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK354(X0,X1),sK356(X0,X1)),unordered_pair(sK354(X0,X1),sK354(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3336]) ).
tcf(c_1263,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(sK354(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2867]) ).
tcf(c_1264,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(sK355(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2866]) ).
tcf(c_1265,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(sK356(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2865]) ).
tcf(c_1266,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK354(X0,X1),sK355(X0,X1)),unordered_pair(sK354(X0,X1),sK354(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3337]) ).
tcf(c_1267,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK355(X0,X1),sK356(X0,X1)),unordered_pair(sK355(X0,X1),sK355(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f3338]) ).
tcf(c_1268,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,[],[f3339]) ).
tcf(c_1269,plain,
! [X0: $i] :
( transitive(X0)
| ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2870]) ).
tcf(c_1270,plain,
! [X0: $i] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2869]) ).
tcf(c_1271,plain,
! [X0: $i] :
( reflexive(X0)
| ~ relation(X0)
| ~ is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f2872]) ).
tcf(c_1272,plain,
! [X0: $i] :
( is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0)
| ~ reflexive(X0) ),
inference(cnf_transformation,[],[f2871]) ).
tcf(c_1273,plain,
! [X0: $i,X1: $i] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK357(X0,X1),sK357(X0,X1)),unordered_pair(sK357(X0,X1),sK357(X0,X1))),X0) ),
inference(cnf_transformation,[],[f3340]) ).
tcf(c_1274,plain,
! [X0: $i,X1: $i] :
( is_reflexive_in(X0,X1)
| in(sK357(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f2874]) ).
tcf(c_1275,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,[],[f3341]) ).
tcf(c_1276,plain,
~ empty(sK358),
inference(cnf_transformation,[],[f2881]) ).
tcf(c_1282,negated_conjecture,
empty(sK140),
inference(cnf_transformation,[],[f3342]) ).
tcf(c_1357,plain,
( ordinal(sK140)
| ~ empty(sK140) ),
inference(instantiation,[status(thm)],[c_1047]) ).
tcf(c_1360,plain,
( finite(sK140)
| ~ empty(sK140) ),
inference(instantiation,[status(thm)],[c_983]) ).
tcf(c_1363,plain,
( function(sK140)
| ~ empty(sK140) ),
inference(instantiation,[status(thm)],[c_785]) ).
tcf(c_2144,plain,
! [X0: $i] : relation_field(inclusion_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_1096,c_1091,c_1096]) ).
tcf(c_2153,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1161,c_799,c_785,c_1161]) ).
tcf(c_2170,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1002,c_1006]) ).
tcf(c_2172,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| in(apply(sK126(X1),X0),X0)
| in(sK125(X1),X1) ),
inference(global_subsumption_just,[status(thm)],[c_350,c_787,c_350]) ).
tcf(c_2173,plain,
! [X0: $i,X1: $i] :
( in(sK125(X1),X1)
| in(apply(sK126(X1),X0),X0)
| ~ in(X0,X1) ),
inference(renaming,[status(thm)],[c_2172]) ).
tcf(c_2176,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| ( sK125(X1) = sK140 )
| in(apply(sK126(X1),X0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_354,c_787,c_354]) ).
tcf(c_2177,negated_conjecture,
! [X0: $i,X1: $i] :
( in(apply(sK126(X1),X0),X0)
| ( sK125(X1) = sK140 )
| ~ in(X0,X1) ),
inference(renaming,[status(thm)],[c_2176]) ).
tcf(c_2178,plain,
! [X0: $i] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(global_subsumption_just,[status(thm)],[c_411,c_891,c_411]) ).
tcf(c_2181,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_374,c_333,c_374]) ).
tcf(c_2191,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_408,c_333,c_408]) ).
tcf(c_2195,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_455,c_1134,c_1133,c_455]) ).
tcf(c_2200,negated_conjecture,
! [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_518,c_297]) ).
tcf(c_2204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ in(X0,X1)
| ~ in(X2,X0)
| ~ relation(X3)
| in(sK150(X3,X2,X0),X0)
| in(X2,sK149(X1,X3))
| sP18(X1,X3) ),
inference(global_subsumption_just,[status(thm)],[c_539,c_787,c_539]) ).
tcf(c_2205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP18(X1,X3)
| in(X2,sK149(X1,X3))
| in(sK150(X3,X2,X0),X0)
| ~ relation(X3)
| ~ in(X2,X0)
| ~ in(X0,X1) ),
inference(renaming,[status(thm)],[c_2204]) ).
tcf(c_2210,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_1175,c_496]) ).
tcf(c_2212,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_1172,c_495]) ).
tcf(c_2220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK218(X4,X1,X0),X0)
| sP27(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_736,c_254,c_736]) ).
tcf(c_2222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( empty(X2)
| in(sK75(X4,X1,X0),X0)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK74(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_163,c_254,c_163]) ).
tcf(c_2238,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_653]) ).
tcf(c_2242,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_962]) ).
tcf(c_2308,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_773]) ).
tcf(c_2320,plain,
! [X0: $i,X1: $i] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_646]) ).
tcf(c_2328,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(prop_impl_just,[status(thm)],[c_1113]) ).
tcf(c_2340,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_254]) ).
tcf(c_2341,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_2340]) ).
tcf(c_2364,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_787]) ).
tcf(c_2390,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_653,c_704]) ).
tcf(c_2392,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_653,c_705]) ).
tcf(c_2394,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_653,c_706]) ).
tcf(c_2396,plain,
! [X0: $i,X1: $i] :
( ~ in(sK48(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_654,c_88]) ).
tcf(c_2397,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK48(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_2396]) ).
tcf(c_2398,plain,
! [X0: $i,X1: $i] :
( in(sK48(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_654,c_89]) ).
tcf(c_2399,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK48(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_2398]) ).
tcf(c_2412,plain,
! [X0: $i] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_708]) ).
tcf(c_2413,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(renaming,[status(thm)],[c_2412]) ).
tcf(c_2414,plain,
! [X0: $i] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_1090]) ).
tcf(c_2415,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(renaming,[status(thm)],[c_2414]) ).
tcf(c_2416,plain,
! [X0: $i] :
( ~ meet_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_1243]) ).
tcf(c_2417,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ meet_semilatt_str(X0) ),
inference(renaming,[status(thm)],[c_2416]) ).
tcf(c_2496,plain,
! [X0: $i] :
( sP10(X0)
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_188]) ).
tcf(c_2530,plain,
( sP5(sK62)
| ~ sP8 ),
inference(prop_impl_just,[status(thm)],[c_127]) ).
tcf(c_2544,plain,
( sP4(sK66)
| ~ sP6 ),
inference(prop_impl_just,[status(thm)],[c_139]) ).
tcf(c_2560,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_1124]) ).
tcf(c_2564,plain,
! [X0: $i] :
( ~ sP5(X0)
| ( sK68(X0) != sK140 ) ),
inference(prop_impl_just,[status(thm)],[c_145]) ).
tcf(c_2568,plain,
! [X0: $i] :
( element(sK68(X0),powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ sP5(X0) ),
inference(prop_impl_just,[status(thm)],[c_149]) ).
tcf(c_2578,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK166(X0),sK167(X0)),unordered_pair(sK166(X0),sK166(X0))),X0)
| function(X0) ),
inference(prop_impl_just,[status(thm)],[c_565]) ).
tcf(c_2579,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK166(X0),sK167(X0)),unordered_pair(sK166(X0),sK166(X0))),X0) ),
inference(renaming,[status(thm)],[c_2578]) ).
tcf(c_2580,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK166(X0),sK168(X0)),unordered_pair(sK166(X0),sK166(X0))),X0)
| function(X0) ),
inference(prop_impl_just,[status(thm)],[c_566]) ).
tcf(c_2581,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK166(X0),sK168(X0)),unordered_pair(sK166(X0),sK166(X0))),X0) ),
inference(renaming,[status(thm)],[c_2580]) ).
tcf(c_2586,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK80(X1,X0),sK81(X1,X0)),unordered_pair(sK80(X1,X0),sK80(X1,X0))) = X0 )
| ~ in(X0,sK79(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_172]) ).
tcf(c_2596,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK235(X1,X2,X0),sK236(X1,X2,X0)),unordered_pair(sK235(X1,X2,X0),sK235(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_769]) ).
tcf(c_2648,plain,
( sP14(sK110)
| ~ sP15 ),
inference(prop_impl_just,[status(thm)],[c_237]) ).
tcf(c_2780,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK173(X0),sK174(X0)),unordered_pair(sK173(X0),sK173(X0))) = sK171(X0) )
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_583]) ).
tcf(c_2788,plain,
! [X0: $i] :
( sP19(sK172(X0),X0)
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_587]) ).
tcf(c_2816,plain,
! [X0: $i,X1: $i] :
( sP22(X0,X1,topstr_closure(X0,X1))
| ~ sP23(topstr_closure(X0,X1),X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_628]) ).
tcf(c_2906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK220(X1,X2,X3),sK221(X1,X2,X3)),unordered_pair(sK220(X1,X2,X3),sK220(X1,X2,X3))) = X2 )
| ~ sP27(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_739]) ).
tcf(c_2914,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK223(X0,X1,X2),sK224(X0,X1,X2)),unordered_pair(sK223(X0,X1,X2),sK223(X0,X1,X2))) = X0 )
| ~ sP26(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_744]) ).
tcf(c_2934,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_962,c_760]) ).
tcf(c_2935,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_2934]) ).
tcf(c_2984,plain,
! [X0: $i] :
( sP33(sK267(X0),X0)
| ~ sP34(X0) ),
inference(prop_impl_just,[status(thm)],[c_866]) ).
tcf(c_3024,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_962,c_269]) ).
tcf(c_3026,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(X0),X2)
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_962,c_270]) ).
tcf(c_3040,plain,
! [X0: $i,X1: $i] :
( equipotent(X1,X0)
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_970,c_666]) ).
tcf(c_3042,plain,
! [X0: $i,X1: $i] :
( relation(sK195(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_970,c_669]) ).
tcf(c_3044,plain,
! [X0: $i,X1: $i] :
( function(sK195(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_970,c_670]) ).
tcf(c_3046,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK195(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_970,c_671]) ).
tcf(c_3048,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK195(X0,X1)) = X0 )
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_970,c_672]) ).
tcf(c_3050,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK195(X0,X1)) = X1 )
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_970,c_673]) ).
tcf(c_3076,plain,
! [X0: $i] :
( ~ latt_str(X0)
| join_semilatt_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_1082]) ).
tcf(c_3077,plain,
! [X0: $i] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(renaming,[status(thm)],[c_3076]) ).
tcf(c_3082,plain,
! [X0: $i] :
( meet_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_1081]) ).
tcf(c_3094,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(prop_impl_just,[status(thm)],[c_1170]) ).
tcf(c_3096,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( sK342(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(prop_impl_just,[status(thm)],[c_1173]) ).
tcf(c_3712,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK342(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK341(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_1174]) ).
tcf(c_3713,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( unordered_pair(unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK342(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK341(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_3712]) ).
tcf(c_3716,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK340(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK339(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_1171]) ).
tcf(c_3717,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X2 )
| ( unordered_pair(unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK340(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK339(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_3716]) ).
tcf(c_5396,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_288,c_2242]) ).
tcf(c_5397,negated_conjecture,
! [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_2200,c_2242]) ).
tcf(c_5398,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X2 = sK140 )
| ( 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_322,c_2242]) ).
tcf(c_5399,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK121(X1,X0),X1)
| ( relation_dom_as_subset(X1,X2,X0) = X1 )
| ~ relation_of2(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_329,c_2242]) ).
tcf(c_5400,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK123(X2,X0),X2)
| ( relation_rng_as_subset(X1,X2,X0) = X2 )
| ~ relation_of2(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_335,c_2242]) ).
tcf(c_5401,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_412,c_2238]) ).
tcf(c_5402,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_413,c_2238]) ).
tcf(c_5403,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X2,subset_complement(X1,X0))
| ( X1 = sK140 )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_437,c_2238]) ).
tcf(c_5404,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,X3),relation_rng(X0))
| ( X2 = sK140 )
| ~ function(X0)
| ~ in(X3,X1)
| ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_485,c_2242]) ).
tcf(c_5405,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( quasi_total(X0,X1,X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ subset(X2,X3)
| ~ relation_of2(X0,X1,X2)
| ~ quasi_total(X0,X1,X2) ),
inference(bin_hyper_res,[status(thm)],[c_517,c_2242]) ).
tcf(c_5406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_689,c_2238]) ).
tcf(c_5407,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_690,c_2238]) ).
tcf(c_5409,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_996,c_2238]) ).
tcf(c_5410,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_997,c_2238]) ).
tcf(c_5411,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_998,c_2238]) ).
tcf(c_5412,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_999,c_2238]) ).
tcf(c_5413,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_1014,c_2238]) ).
tcf(c_5414,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_1015,c_2238]) ).
tcf(c_5415,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = sK140 )
| ( 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_1075,c_2242]) ).
tcf(c_5606,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_1098,c_1091]) ).
tcf(c_5607,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_1097,c_1091]) ).
tcf(c_5610,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_1107,c_1099]) ).
tcf(c_5611,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_1106,c_1099]) ).
tcf(c_5612,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_1105,c_1099]) ).
tcf(c_5903,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_1118,c_2328]) ).
tcf(c_5904,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_1117,c_2328]) ).
tcf(c_6047,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_778,c_2308]) ).
tcf(c_6048,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_779,c_2308]) ).
tcf(c_6049,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_777,c_2308]) ).
tcf(c_6056,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_651,c_2320]) ).
tcf(c_6057,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_652,c_2320]) ).
tcf(c_6058,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_650,c_2320]) ).
tcf(c_6073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP18(X3,X1)
| in(X0,sK149(X3,X1))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,sK150(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_538,c_2364]) ).
tcf(c_6074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),sK74(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,sK75(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_162,c_2364]) ).
tcf(c_7039,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_1129,c_2560]) ).
tcf(c_7040,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_1128,c_2560]) ).
tcf(c_7131,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK79(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_170,c_2341]) ).
tcf(c_7132,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| in(unordered_pair(unordered_pair(X0,unordered_pair(X0,X0)),unordered_pair(X0,X0)),sK177(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_591,c_2341]) ).
tcf(c_7133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP27(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,sK218(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_735,c_2341]) ).
tcf(c_7134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),sK74(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,sK75(X1,X0,X2)),unordered_pair(X0,X0)),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6074,c_2341]) ).
tcf(c_7475,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_453,c_1133]) ).
tcf(c_7483,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_7475,c_1134]) ).
tcf(c_7851,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,sK311(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_1011,c_2170]) ).
tcf(c_7852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK311(X2,X3,X0,X1),X1),unordered_pair(sK311(X2,X3,X0,X1),sK311(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_1012,c_2170]) ).
tcf(c_7853,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_1010,c_2170]) ).
tcf(c_12479,plain,
! [X0: $i] : element(X0,powerset(X0)),
inference(light_normalisation,[status(thm)],[c_1131,c_1132]) ).
tcf(c_12910,plain,
! [X0: $i] : set_difference(X0,X0) = sK140,
inference(light_normalisation,[status(thm)],[c_946,c_675]) ).
tcf(c_15157,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK166(X0),sK166(X0)),unordered_pair(sK166(X0),sK168(X0))),X0) ),
inference(demodulation,[status(thm)],[c_2581,c_942]) ).
tcf(c_15164,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK166(X0),sK166(X0)),unordered_pair(sK166(X0),sK167(X0))),X0) ),
inference(demodulation,[status(thm)],[c_2579,c_942]) ).
tcf(c_15847,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK173(X0),sK173(X0)),unordered_pair(sK173(X0),sK174(X0))) = sK171(X0) )
| ~ sP20(X0) ),
inference(demodulation,[status(thm)],[c_2780,c_942]) ).
tcf(c_15926,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK44(X0),sK45(X0)),unordered_pair(sK45(X0),sK45(X0))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_70,c_942]) ).
tcf(c_15936,plain,
! [X0: $i] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK44(X0),sK44(X0)),unordered_pair(sK44(X0),sK45(X0))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_69,c_942]) ).
tcf(c_15946,plain,
! [X0: $i] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK41(X0),sK41(X0)),unordered_pair(sK41(X0),sK42(X0))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_59,c_942]) ).
tcf(c_15956,plain,
! [X0: $i] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK40(X0),sK40(X0)),unordered_pair(sK40(X0),sK41(X0))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_58,c_942]) ).
tcf(c_16060,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK158(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(demodulation,[status(thm)],[c_553,c_942]) ).
tcf(c_16146,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sK57(X1))
| ~ sP3(X1)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_115,c_942]) ).
tcf(c_16162,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK46(X0),sK47(X0)),unordered_pair(sK47(X0),sK47(X0))),X0) ),
inference(demodulation,[status(thm)],[c_79,c_942]) ).
tcf(c_16172,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK46(X0),sK46(X0)),unordered_pair(sK46(X0),sK47(X0))),X0) ),
inference(demodulation,[status(thm)],[c_78,c_942]) ).
tcf(c_16182,plain,
! [X0: $i] :
( transitive(X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK40(X0),sK40(X0)),unordered_pair(sK40(X0),sK42(X0))),X0) ),
inference(demodulation,[status(thm)],[c_57,c_942]) ).
tcf(c_16344,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))),X0)
| ( X0 = sK140 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_460,c_942]) ).
tcf(c_16464,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK306(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_988,c_942]) ).
tcf(c_16534,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK164(X0),sK164(X0)),unordered_pair(sK164(X0),sK165(X0))) = X0 )
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_563,c_942]) ).
tcf(c_16590,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK118(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_294,c_942]) ).
tcf(c_16795,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_505,c_942]) ).
tcf(c_16954,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK355(X0,X1),sK355(X0,X1)),unordered_pair(sK355(X0,X1),sK356(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1267,c_942]) ).
tcf(c_16964,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK354(X0,X1),sK354(X0,X1)),unordered_pair(sK354(X0,X1),sK355(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1266,c_942]) ).
tcf(c_16974,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK350(X0,X1),sK351(X0,X1)),unordered_pair(sK351(X0,X1),sK351(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1250,c_942]) ).
tcf(c_16984,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK350(X0,X1),sK350(X0,X1)),unordered_pair(sK350(X0,X1),sK351(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1249,c_942]) ).
tcf(c_17030,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(X0,sK155(X1,X0)),unordered_pair(sK155(X1,X0),sK155(X1,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(demodulation,[status(thm)],[c_549,c_942]) ).
tcf(c_17142,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK354(X0,X1),sK354(X0,X1)),unordered_pair(sK354(X0,X1),sK356(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_1262,c_942]) ).
tcf(c_17152,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK352(X0,X1),sK353(X0,X1)),unordered_pair(sK353(X0,X1),sK353(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_1258,c_942]) ).
tcf(c_17162,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK352(X0,X1),sK352(X0,X1)),unordered_pair(sK352(X0,X1),sK353(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_1257,c_942]) ).
tcf(c_17172,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sK342(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(light_normalisation,[status(thm)],[c_3096,c_2210]) ).
tcf(c_17179,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(light_normalisation,[status(thm)],[c_3094,c_2212]) ).
tcf(c_17248,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( 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_432,c_1132]) ).
tcf(c_17258,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( 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_430,c_1132]) ).
tcf(c_17294,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK80(X1,X0),sK80(X1,X0)),unordered_pair(sK80(X1,X0),sK81(X1,X0))) = X0 )
| ~ in(X0,sK79(X1,X2)) ),
inference(demodulation,[status(thm)],[c_2586,c_942]) ).
tcf(c_17583,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| ( unordered_pair(unordered_pair(sK179(X1,X0),sK179(X1,X0)),unordered_pair(sK179(X1,X0),sK180(X1,X0))) = X0 )
| ~ in(X0,sK177(X1,X2)) ),
inference(demodulation,[status(thm)],[c_594,c_942]) ).
tcf(c_17593,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK159(X0,X1),sK159(X0,X1)),unordered_pair(sK159(X0,X1),sK160(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_555,c_942]) ).
tcf(c_17646,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sK79(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_7131,c_942]) ).
tcf(c_17689,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK293(X1,X2,X0)),unordered_pair(sK293(X1,X2,X0),sK293(X1,X2,X0))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_925,c_942]) ).
tcf(c_17706,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK223(X0,X1,X2),sK223(X0,X1,X2)),unordered_pair(sK223(X0,X1,X2),sK224(X0,X1,X2))) = X0 )
| ~ sP26(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_2914,c_942]) ).
tcf(c_17733,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK159(X0,X1),sK159(X0,X1)),unordered_pair(sK159(X0,X1),sK160(X0,X1))),X1) ),
inference(demodulation,[status(thm)],[c_554,c_942]) ).
tcf(c_17768,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,sK117(X0,X2,X1)),unordered_pair(sK117(X0,X2,X1),sK117(X0,X2,X1))),X1)
| ~ relation(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(demodulation,[status(thm)],[c_280,c_942]) ).
tcf(c_17868,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK235(X1,X2,X0),sK235(X1,X2,X0)),unordered_pair(sK235(X1,X2,X0),sK236(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(demodulation,[status(thm)],[c_2596,c_942]) ).
tcf(c_17875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK220(X1,X2,X3),sK220(X1,X2,X3)),unordered_pair(sK220(X1,X2,X3),sK221(X1,X2,X3))) = X2 )
| ~ sP27(X0,X1,X2,X3) ),
inference(demodulation,[status(thm)],[c_2906,c_942]) ).
tcf(c_17912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,sK120(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_328,c_942]) ).
tcf(c_17935,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP20(X1)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sK177(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_7132,c_942]) ).
tcf(c_18031,plain,
! [X0: $i,X1: $i] :
( in(sK328(X1,X0),X1)
| in(unordered_pair(unordered_pair(sK328(X1,X0),sK328(X1,X0)),unordered_pair(sK328(X1,X0),sK329(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1103,c_942]) ).
tcf(c_18066,plain,
! [X0: $i,X1: $i] :
( in(sK156(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK156(X0,X1),sK156(X0,X1)),unordered_pair(sK156(X0,X1),sK157(X0,X1))),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_551,c_942]) ).
tcf(c_18087,plain,
! [X0: $i,X1: $i] :
( in(sK153(X0,X1),X1)
| in(unordered_pair(unordered_pair(sK153(X0,X1),sK154(X0,X1)),unordered_pair(sK154(X0,X1),sK154(X0,X1))),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_547,c_942]) ).
tcf(c_18158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK311(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_7851,c_942]) ).
tcf(c_18221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP18(X3,X1)
| in(X0,sK149(X3,X1))
| ~ relation(X1)
| ~ in(X2,X3)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK150(X1,X0,X2))),X1) ),
inference(demodulation,[status(thm)],[c_6073,c_942]) ).
tcf(c_18312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X3,sK122(X2,X3)),unordered_pair(sK122(X2,X3),sK122(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_334,c_942]) ).
tcf(c_18341,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| sP11(X2,X1)
| sP12(X2,X1)
| ~ relation(X1)
| ~ in(X0,sK103(X2,X1))
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK104(X1,X0,sK103(X2,X1)))),X1) ),
inference(demodulation,[status(thm)],[c_223,c_942]) ).
tcf(c_18368,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK328(X1,X0),sK328(X1,X0)),unordered_pair(sK328(X1,X0),sK329(X1,X0))),X0)
| ( identity_relation(X1) = X0 )
| ( sK328(X1,X0) = sK329(X1,X0) )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1104,c_942]) ).
tcf(c_18381,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK321(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(X1,sK321(X0,X1,X2)),unordered_pair(sK321(X0,X1,X2),sK321(X0,X1,X2))),X0)
| ( fiber(X0,X1) = X2 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1066,c_942]) ).
tcf(c_18482,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(X1)
| ( unordered_pair(unordered_pair(sK76(X1,X2,X0),sK76(X1,X2,X0)),unordered_pair(sK76(X1,X2,X0),sK77(X1,X2,X0))) = X0 )
| ~ relation(X2)
| ~ in(X0,sK74(X1,X2,X3)) ),
inference(demodulation,[status(thm)],[c_165,c_942]) ).
tcf(c_18535,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,sK53(X1,X0,X2))),X1) ),
inference(demodulation,[status(thm)],[c_100,c_942]) ).
tcf(c_18573,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK304(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK304(X0,X1,X2),sK304(X0,X1,X2)),unordered_pair(sK304(X0,X1,X2),sK305(X0,X1,X2))),X0)
| ( relation_inverse_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_985,c_942]) ).
tcf(c_18586,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK291(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK291(X0,X1,X2),sK292(X0,X1,X2)),unordered_pair(sK292(X0,X1,X2),sK292(X0,X1,X2))),X0)
| ( relation_image(X0,X1) = X2 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_922,c_942]) ).
tcf(c_18645,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK232(X0,X1,X2),X2)
| ( cartesian_product2(X0,X1) = X2 )
| ( unordered_pair(unordered_pair(sK233(X0,X1,X2),sK233(X0,X1,X2)),unordered_pair(sK233(X0,X1,X2),sK234(X0,X1,X2))) = sK232(X0,X1,X2) ) ),
inference(demodulation,[status(thm)],[c_765,c_942]) ).
tcf(c_18743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK90(X2,X3,X0),sK90(X2,X3,X0)),unordered_pair(sK90(X2,X3,X0),sK91(X2,X3,X0))) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK89(X1,X2,X3)) ),
inference(demodulation,[status(thm)],[c_195,c_942]) ).
tcf(c_18773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X1,sK311(X2,X3,X0,X1)),unordered_pair(sK311(X2,X3,X0,X1),sK311(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_7852,c_942]) ).
tcf(c_18828,plain,
! [X0: $i] :
( subset(sK326(relation_field(X0),X0),sK327(relation_field(X0),X0))
| in(unordered_pair(unordered_pair(sK326(relation_field(X0),X0),sK326(relation_field(X0),X0)),unordered_pair(sK326(relation_field(X0),X0),sK327(relation_field(X0),X0))),X0)
| ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1093,c_942]) ).
tcf(c_18851,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK237(X0,X2,X1),X2)
| in(unordered_pair(unordered_pair(sK237(X0,X2,X1),sK237(X0,X2,X1)),unordered_pair(sK237(X0,X2,X1),sK238(X0,X2,X1))),X1)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_775,c_942]) ).
tcf(c_18867,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK192(X2,X1,X0),X2)
| in(unordered_pair(unordered_pair(sK191(X2,X1,X0),sK191(X2,X1,X0)),unordered_pair(sK191(X2,X1,X0),sK192(X2,X1,X0))),X0)
| ( relation_rng_restriction(X2,X1) = X0 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_648,c_942]) ).
tcf(c_18893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP27(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,sK218(X1,X0,X2))),X1) ),
inference(demodulation,[status(thm)],[c_7133,c_942]) ).
tcf(c_18906,plain,
! [X0: $i,X1: $i] :
( ( identity_relation(X0) = X1 )
| ~ relation(X1)
| ~ in(sK328(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK328(X0,X1),sK328(X0,X1)),unordered_pair(sK328(X0,X1),sK329(X0,X1))),X1)
| ( sK328(X0,X1) != sK329(X0,X1) ) ),
inference(demodulation,[status(thm)],[c_1102,c_942]) ).
tcf(c_18922,plain,
! [X0: $i] :
( ( inclusion_relation(relation_field(X0)) = X0 )
| ~ relation(X0)
| ~ subset(sK326(relation_field(X0),X0),sK327(relation_field(X0),X0))
| ~ in(unordered_pair(unordered_pair(sK326(relation_field(X0),X0),sK326(relation_field(X0),X0)),unordered_pair(sK326(relation_field(X0),X0),sK327(relation_field(X0),X0))),X0) ),
inference(demodulation,[status(thm)],[c_1092,c_942]) ).
tcf(c_18935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP24(X2,X3)
| ( unordered_pair(unordered_pair(sK215(X2,X3,X0),sK215(X2,X3,X0)),unordered_pair(sK215(X2,X3,X0),sK216(X2,X3,X0))) = X0 )
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK213(X1,X2,X3)) ),
inference(demodulation,[status(thm)],[c_731,c_942]) ).
tcf(c_18964,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( fiber(X1,X0) = X2 )
| ( sK321(X1,X0,X2) = X0 )
| ~ relation(X1)
| ~ in(sK321(X1,X0,X2),X2)
| ~ in(unordered_pair(unordered_pair(X0,sK321(X1,X0,X2)),unordered_pair(sK321(X1,X0,X2),sK321(X1,X0,X2))),X1) ),
inference(demodulation,[status(thm)],[c_1064,c_942]) ).
tcf(c_19012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),sK74(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,sK75(X1,X0,X2))),X1) ),
inference(demodulation,[status(thm)],[c_7134,c_942]) ).
tcf(c_19028,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK161(X0,X1),sK161(X0,X1)),unordered_pair(sK161(X0,X1),sK162(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK161(X0,X1),sK161(X0,X1)),unordered_pair(sK161(X0,X1),sK162(X0,X1))),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_558,c_942]) ).
tcf(c_19044,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK331(X0,X1),sK330(X0,X1)),unordered_pair(sK330(X0,X1),sK330(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK331(X0,X1),sK331(X0,X1)),unordered_pair(sK331(X0,X1),sK330(X0,X1))),X0)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1116,c_942]) ).
tcf(c_19060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(apply(X3,sK90(X2,X3,X0)),apply(X3,sK90(X2,X3,X0))),unordered_pair(apply(X3,sK90(X2,X3,X0)),apply(X3,sK91(X2,X3,X0)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK89(X1,X2,X3)) ),
inference(demodulation,[status(thm)],[c_196,c_942]) ).
tcf(c_19076,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK161(X0,X1),sK161(X0,X1)),unordered_pair(sK161(X0,X1),sK162(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK161(X0,X1),sK161(X0,X1)),unordered_pair(sK161(X0,X1),sK162(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_557,c_942]) ).
tcf(c_19092,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK331(X0,X1),sK330(X0,X1)),unordered_pair(sK330(X0,X1),sK330(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK331(X0,X1),sK331(X0,X1)),unordered_pair(sK331(X0,X1),sK330(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_1115,c_942]) ).
tcf(c_19156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP24(X2,X3)
| in(unordered_pair(unordered_pair(apply(X3,sK215(X2,X3,X0)),apply(X3,sK215(X2,X3,X0))),unordered_pair(apply(X3,sK215(X2,X3,X0)),apply(X3,sK216(X2,X3,X0)))),X2)
| ~ function(X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(X0,sK213(X1,X2,X3)) ),
inference(demodulation,[status(thm)],[c_732,c_942]) ).
tcf(c_19225,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK237(X0,X2,X1),sK237(X0,X2,X1)),unordered_pair(sK237(X0,X2,X1),sK238(X0,X2,X1))),X1)
| in(unordered_pair(unordered_pair(sK237(X0,X2,X1),sK237(X0,X2,X1)),unordered_pair(sK237(X0,X2,X1),sK238(X0,X2,X1))),X0)
| ( relation_dom_restriction(X0,X2) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_776,c_942]) ).
tcf(c_19255,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK191(X2,X1,X0),sK191(X2,X1,X0)),unordered_pair(sK191(X2,X1,X0),sK192(X2,X1,X0))),X1)
| in(unordered_pair(unordered_pair(sK191(X2,X1,X0),sK191(X2,X1,X0)),unordered_pair(sK191(X2,X1,X0),sK192(X2,X1,X0))),X0)
| ( relation_rng_restriction(X2,X1) = X0 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_649,c_942]) ).
tcf(c_19291,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK309(X0,X2,X1),sK310(X0,X2,X1)),unordered_pair(sK310(X0,X2,X1),sK310(X0,X2,X1))),X2)
| in(unordered_pair(unordered_pair(sK308(X0,X2,X1),sK308(X0,X2,X1)),unordered_pair(sK308(X0,X2,X1),sK309(X0,X2,X1))),X1)
| ( relation_composition(X0,X2) = X1 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1009,c_942]) ).
tcf(c_19310,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK308(X0,X2,X1),sK308(X0,X2,X1)),unordered_pair(sK308(X0,X2,X1),sK310(X0,X2,X1))),X0)
| in(unordered_pair(unordered_pair(sK308(X0,X2,X1),sK308(X0,X2,X1)),unordered_pair(sK308(X0,X2,X1),sK309(X0,X2,X1))),X1)
| ( relation_composition(X0,X2) = X1 )
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_1008,c_942]) ).
tcf(c_19329,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK342(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK341(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_3713,c_2210]) ).
tcf(c_19330,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK342(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_19329,c_942]) ).
tcf(c_19337,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK340(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK339(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_3717,c_2212]) ).
tcf(c_19338,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK340(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_19337,c_942]) ).
tcf(c_19345,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X0)
| ~ in(sK237(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK237(X0,X1,X2),sK237(X0,X1,X2)),unordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK237(X0,X1,X2),sK237(X0,X1,X2)),unordered_pair(sK237(X0,X1,X2),sK238(X0,X1,X2))),X0) ),
inference(demodulation,[status(thm)],[c_774,c_942]) ).
tcf(c_19364,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng_restriction(X0,X1) = X2 )
| ~ relation(X2)
| ~ relation(X1)
| ~ in(sK192(X0,X1,X2),X0)
| ~ in(unordered_pair(unordered_pair(sK191(X0,X1,X2),sK191(X0,X1,X2)),unordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK191(X0,X1,X2),sK191(X0,X1,X2)),unordered_pair(sK191(X0,X1,X2),sK192(X0,X1,X2))),X1) ),
inference(demodulation,[status(thm)],[c_647,c_942]) ).
tcf(c_19383,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,sK309(X0,X1,X2)),unordered_pair(X3,X3)),X1)
| ~ in(unordered_pair(unordered_pair(sK308(X0,X1,X2),X3),unordered_pair(sK308(X0,X1,X2),sK308(X0,X1,X2))),X0)
| ~ in(unordered_pair(unordered_pair(sK308(X0,X1,X2),sK308(X0,X1,X2)),unordered_pair(sK308(X0,X1,X2),sK309(X0,X1,X2))),X2) ),
inference(demodulation,[status(thm)],[c_1007,c_942]) ).
tcf(c_19632,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK82(X1))
| ~ ordinal(X0)
| ~ sP9(X1,X2)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2496,c_175]) ).
tcf(c_19633,plain,
! [X0: $i,X1: $i] :
( in(X1,sK82(X0))
| ~ ordinal(X0)
| ~ sP9(X0,X1) ),
inference(unflattening,[status(thm)],[c_19632]) ).
tcf(c_19644,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP9(X1,X2)
| ~ ordinal(X0)
| ~ in(X2,sK82(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2496,c_176]) ).
tcf(c_19645,plain,
! [X0: $i,X1: $i] :
( sP9(X1,X0)
| ~ ordinal(X1)
| ~ in(X0,sK82(X1)) ),
inference(unflattening,[status(thm)],[c_19644]) ).
tcf(c_19802,plain,
! [X0: $i,X1: $i] :
( ( union_of_subsets(the_carrier(X1),X0) = cast_as_carrier_subset(X1) )
| ~ one_sorted_str(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1))))
| ( X1 != sK139 )
| ( X0 != sK140 ) ),
inference(resolution_lifted,[status(thm)],[c_463,c_1163]) ).
tcf(c_19803,plain,
( ( union_of_subsets(the_carrier(sK139),sK140) = cast_as_carrier_subset(sK139) )
| ~ one_sorted_str(sK139)
| ~ element(sK140,powerset(powerset(the_carrier(sK139)))) ),
inference(unflattening,[status(thm)],[c_19802]) ).
tcf(c_19804,plain,
union_of_subsets(the_carrier(sK139),sK140) = cast_as_carrier_subset(sK139),
inference(global_subsumption_just,[status(thm)],[c_19803,c_466,c_464,c_19803]) ).
tcf(c_19812,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( topstr_closure(X3,X5) = X1 )
| ~ top_str(X2)
| ~ sP22(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_640,c_627]) ).
tcf(c_19813,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( topstr_closure(X1,X2) = X0 )
| ~ top_str(X1)
| ~ sP22(X1,X2,X0)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(unflattening,[status(thm)],[c_19812]) ).
tcf(c_19830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sP22(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_640,c_2816]) ).
tcf(c_19831,plain,
! [X0: $i,X1: $i] :
( sP22(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_19830]) ).
tcf(c_19841,plain,
! [X0: $i,X1: $i] :
( sP22(X1,X0,topstr_closure(X1,X0))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19831,c_1122]) ).
tcf(c_19973,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)
| ~ sP37(X0,X2,X4)
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1135,c_1148]) ).
tcf(c_19974,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_isomorphism(X1,X2,X0)
| ~ function(X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ sP37(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_19973]) ).
tcf(c_19994,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sP37(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_1136,c_1148]) ).
tcf(c_19995,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP37(X2,X0,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation_isomorphism(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_19994]) ).
tcf(c_20027,plain,
! [X0: $i] :
( element(sK68(X0),powerset(powerset(set_union2(X0,unordered_pair(X0,X0)))))
| ~ sP8
| ( X0 != sK62 ) ),
inference(resolution_lifted,[status(thm)],[c_2530,c_2568]) ).
tcf(c_20028,plain,
( element(sK68(sK62),powerset(powerset(set_union2(sK62,unordered_pair(sK62,sK62)))))
| ~ sP8 ),
inference(unflattening,[status(thm)],[c_20027]) ).
tcf(c_20035,plain,
! [X0: $i,X1: $i] :
( ~ sP8
| ~ in(X1,sK68(X0))
| ( X0 != sK62 )
| ( sK69(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2530,c_146]) ).
tcf(c_20036,plain,
! [X0: $i] :
( ~ sP8
| ~ in(X0,sK68(sK62))
| ( sK69(sK62,X0) != X0 ) ),
inference(unflattening,[status(thm)],[c_20035]) ).
tcf(c_20047,plain,
! [X0: $i] :
( ~ sP8
| ( X0 != sK62 )
| ( sK68(X0) != sK140 ) ),
inference(resolution_lifted,[status(thm)],[c_2530,c_2564]) ).
tcf(c_20048,plain,
( ~ sP8
| ( sK68(sK62) != sK140 ) ),
inference(unflattening,[status(thm)],[c_20047]) ).
tcf(c_20055,plain,
! [X0: $i,X1: $i] :
( subset(X1,sK69(X0,X1))
| ~ sP8
| ~ in(X1,sK68(X0))
| ( X0 != sK62 ) ),
inference(resolution_lifted,[status(thm)],[c_2530,c_148]) ).
tcf(c_20056,plain,
! [X0: $i] :
( subset(X0,sK69(sK62,X0))
| ~ sP8
| ~ in(X0,sK68(sK62)) ),
inference(unflattening,[status(thm)],[c_20055]) ).
tcf(c_20067,plain,
! [X0: $i,X1: $i] :
( in(sK69(X0,X1),sK68(X0))
| ~ sP8
| ~ in(X1,sK68(X0))
| ( X0 != sK62 ) ),
inference(resolution_lifted,[status(thm)],[c_2530,c_147]) ).
tcf(c_20068,plain,
! [X0: $i] :
( in(sK69(sK62,X0),sK68(sK62))
| ~ sP8
| ~ in(X0,sK68(sK62)) ),
inference(unflattening,[status(thm)],[c_20067]) ).
tcf(c_20222,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| element(sK323(X0),the_carrier(X0))
| ( X0 != sK322 ) ),
inference(resolution_lifted,[status(thm)],[c_1080,c_1085]) ).
tcf(c_20223,plain,
( meet_absorbing(sK322)
| empty_carrier(sK322)
| element(sK323(sK322),the_carrier(sK322)) ),
inference(unflattening,[status(thm)],[c_20222]) ).
tcf(c_20233,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| element(sK324(X0),the_carrier(X0))
| ( X0 != sK322 ) ),
inference(resolution_lifted,[status(thm)],[c_1080,c_1084]) ).
tcf(c_20234,plain,
( meet_absorbing(sK322)
| empty_carrier(sK322)
| element(sK324(sK322),the_carrier(sK322)) ),
inference(unflattening,[status(thm)],[c_20233]) ).
tcf(c_20244,plain,
! [X0: $i] :
( meet_absorbing(X0)
| empty_carrier(X0)
| ( X0 != sK322 )
| ( join(X0,meet(X0,sK323(X0),sK324(X0)),sK324(X0)) != sK324(X0) ) ),
inference(resolution_lifted,[status(thm)],[c_1080,c_1083]) ).
tcf(c_20245,plain,
( meet_absorbing(sK322)
| empty_carrier(sK322)
| ( join(sK322,meet(sK322,sK323(sK322),sK324(sK322)),sK324(sK322)) != sK324(sK322) ) ),
inference(unflattening,[status(thm)],[c_20244]) ).
tcf(c_20255,plain,
! [X0: $i] :
( join_semilatt_str(X0)
| ( X0 != sK322 ) ),
inference(resolution_lifted,[status(thm)],[c_1080,c_3077]) ).
tcf(c_20256,plain,
join_semilatt_str(sK322),
inference(unflattening,[status(thm)],[c_20255]) ).
tcf(c_20260,plain,
! [X0: $i] :
( meet_semilatt_str(X0)
| ( X0 != sK322 ) ),
inference(resolution_lifted,[status(thm)],[c_1080,c_3082]) ).
tcf(c_20261,plain,
meet_semilatt_str(sK322),
inference(unflattening,[status(thm)],[c_20260]) ).
tcf(c_20265,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 != sK322 ) ),
inference(resolution_lifted,[status(thm)],[c_1080,c_1086]) ).
tcf(c_20266,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK322)
| ( join(sK322,meet(sK322,X1,X0),X0) = X0 )
| ~ meet_absorbing(sK322)
| ~ element(X1,the_carrier(sK322))
| ~ element(X0,the_carrier(sK322)) ),
inference(unflattening,[status(thm)],[c_20265]) ).
tcf(c_20299,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK325 ) ),
inference(resolution_lifted,[status(thm)],[c_2415,c_1089]) ).
tcf(c_20300,plain,
one_sorted_str(sK325),
inference(unflattening,[status(thm)],[c_20299]) ).
tcf(c_20304,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK322 ) ),
inference(resolution_lifted,[status(thm)],[c_2415,c_20256]) ).
tcf(c_20305,plain,
one_sorted_str(sK322),
inference(unflattening,[status(thm)],[c_20304]) ).
tcf(c_20309,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 != sK325 ) ),
inference(resolution_lifted,[status(thm)],[c_1089,c_1245]) ).
tcf(c_20310,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK325)
| element(join(sK325,X1,X0),the_carrier(sK325))
| ~ element(X1,the_carrier(sK325))
| ~ element(X0,the_carrier(sK325)) ),
inference(unflattening,[status(thm)],[c_20309]) ).
tcf(c_20323,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 != sK322 ) ),
inference(resolution_lifted,[status(thm)],[c_1245,c_20256]) ).
tcf(c_20324,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK322)
| element(join(sK322,X1,X0),the_carrier(sK322))
| ~ element(X1,the_carrier(sK322))
| ~ element(X0,the_carrier(sK322)) ),
inference(unflattening,[status(thm)],[c_20323]) ).
tcf(c_20348,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK349 ) ),
inference(resolution_lifted,[status(thm)],[c_2417,c_1242]) ).
tcf(c_20349,plain,
one_sorted_str(sK349),
inference(unflattening,[status(thm)],[c_20348]) ).
tcf(c_20355,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 != sK349 ) ),
inference(resolution_lifted,[status(thm)],[c_1242,c_1244]) ).
tcf(c_20356,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK349)
| element(meet(sK349,X1,X0),the_carrier(sK349))
| ~ element(X1,the_carrier(sK349))
| ~ element(X0,the_carrier(sK349)) ),
inference(unflattening,[status(thm)],[c_20355]) ).
tcf(c_20369,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 != sK322 ) ),
inference(resolution_lifted,[status(thm)],[c_1244,c_20261]) ).
tcf(c_20370,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK322)
| element(meet(sK322,X1,X0),the_carrier(sK322))
| ~ element(X1,the_carrier(sK322))
| ~ element(X0,the_carrier(sK322)) ),
inference(unflattening,[status(thm)],[c_20369]) ).
tcf(c_22200,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 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_1016,c_907]) ).
tcf(c_22201,plain,
! [X0: $i] :
( closed_subset(X0,sK285)
| ~ element(X0,powerset(the_carrier(sK285)))
| ~ open_subset(subset_difference(the_carrier(sK285),cast_as_carrier_subset(sK285),X0),sK285) ),
inference(unflattening,[status(thm)],[c_22200]) ).
tcf(c_22212,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_2413,c_907]) ).
tcf(c_22213,plain,
one_sorted_str(sK285),
inference(unflattening,[status(thm)],[c_22212]) ).
tcf(c_22217,plain,
! [X0: $i,X1: $i] :
( open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_364,c_907]) ).
tcf(c_22218,plain,
! [X0: $i] :
( open_subset(X0,sK285)
| ~ element(X0,powerset(the_carrier(sK285)))
| ~ closed_subset(subset_complement(the_carrier(sK285),X0),sK285) ),
inference(unflattening,[status(thm)],[c_22217]) ).
tcf(c_22229,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_358,c_907]) ).
tcf(c_22230,plain,
! [X0: $i] :
( closed_subset(X0,sK285)
| ~ element(X0,powerset(the_carrier(sK285)))
| ~ open_subset(subset_complement(the_carrier(sK285),X0),sK285) ),
inference(unflattening,[status(thm)],[c_22229]) ).
tcf(c_22241,plain,
! [X0: $i,X1: $i] :
( sP22(X0,X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_19841,c_907]) ).
tcf(c_22242,plain,
! [X0: $i] :
( sP22(sK285,X0,topstr_closure(sK285,X0))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22241]) ).
tcf(c_22250,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( topstr_closure(X0,X2) = X1 )
| ~ sP22(X0,X2,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_19813,c_907]) ).
tcf(c_22251,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(sK285,X1) = X0 )
| ~ sP22(sK285,X1,X0)
| ~ element(X1,powerset(the_carrier(sK285)))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22250]) ).
tcf(c_22265,plain,
! [X0: $i,X1: $i] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_1122,c_907]) ).
tcf(c_22266,plain,
! [X0: $i] :
( element(topstr_closure(sK285,X0),powerset(the_carrier(sK285)))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22265]) ).
tcf(c_22274,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) = interior(X0,X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_1121,c_907]) ).
tcf(c_22275,plain,
! [X0: $i] :
( ( subset_complement(the_carrier(sK285),topstr_closure(sK285,subset_complement(the_carrier(sK285),X0))) = interior(sK285,X0) )
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22274]) ).
tcf(c_22283,plain,
! [X0: $i,X1: $i] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_1120,c_907]) ).
tcf(c_22284,plain,
! [X0: $i] :
( element(interior(sK285,X0),powerset(the_carrier(sK285)))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22283]) ).
tcf(c_22292,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 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_1017,c_907]) ).
tcf(c_22293,plain,
! [X0: $i] :
( open_subset(subset_difference(the_carrier(sK285),cast_as_carrier_subset(sK285),X0),sK285)
| ~ closed_subset(X0,sK285)
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22292]) ).
tcf(c_22304,plain,
! [X0: $i,X1: $i] :
( ( topstr_closure(X0,X1) = X1 )
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_438,c_907]) ).
tcf(c_22305,plain,
! [X0: $i] :
( ( topstr_closure(sK285,X0) = X0 )
| ~ closed_subset(X0,sK285)
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22304]) ).
tcf(c_22316,plain,
! [X0: $i,X1: $i] :
( subset(X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_431,c_907]) ).
tcf(c_22317,plain,
! [X0: $i] :
( subset(X0,topstr_closure(sK285,X0))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22316]) ).
tcf(c_22325,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 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_420,c_907]) ).
tcf(c_22326,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ closed_subset(X2,sK285)
| ~ subset(X1,X2)
| ~ in(X0,the_carrier(sK285))
| ~ element(X2,powerset(the_carrier(sK285)))
| ~ element(X1,powerset(the_carrier(sK285)))
| ~ in(X0,topstr_closure(sK285,X1)) ),
inference(unflattening,[status(thm)],[c_22325]) ).
tcf(c_22349,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X0,X1))
| element(sK133(X0,X1,X2),powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_419,c_907]) ).
tcf(c_22350,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK285,X0))
| element(sK133(sK285,X0,X1),powerset(the_carrier(sK285)))
| ~ in(X1,the_carrier(sK285))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22349]) ).
tcf(c_22364,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X0,X1))
| subset(X1,sK133(X0,X1,X2))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_418,c_907]) ).
tcf(c_22365,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK285,X0))
| subset(X0,sK133(sK285,X0,X1))
| ~ in(X1,the_carrier(sK285))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22364]) ).
tcf(c_22379,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X0,X1))
| closed_subset(sK133(X0,X1,X2),X0)
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_417,c_907]) ).
tcf(c_22380,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK285,X0))
| closed_subset(sK133(sK285,X0,X1),sK285)
| ~ in(X1,the_carrier(sK285))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22379]) ).
tcf(c_22394,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,sK133(X0,X2,X1))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_416,c_907]) ).
tcf(c_22395,plain,
! [X0: $i,X1: $i] :
( in(X0,topstr_closure(sK285,X1))
| ~ in(X0,the_carrier(sK285))
| ~ element(X1,powerset(the_carrier(sK285)))
| ~ in(X0,sK133(sK285,X1,X0)) ),
inference(unflattening,[status(thm)],[c_22394]) ).
tcf(c_22409,plain,
! [X0: $i,X1: $i] :
( subset(interior(X0,X1),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_415,c_907]) ).
tcf(c_22410,plain,
! [X0: $i] :
( subset(interior(sK285,X0),X0)
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22409]) ).
tcf(c_22418,plain,
! [X0: $i,X1: $i] :
( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_365,c_907]) ).
tcf(c_22419,plain,
! [X0: $i] :
( closed_subset(subset_complement(the_carrier(sK285),X0),sK285)
| ~ open_subset(X0,sK285)
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22418]) ).
tcf(c_22430,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK285 ) ),
inference(resolution_lifted,[status(thm)],[c_359,c_907]) ).
tcf(c_22431,plain,
! [X0: $i] :
( open_subset(subset_complement(the_carrier(sK285),X0),sK285)
| ~ closed_subset(X0,sK285)
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(unflattening,[status(thm)],[c_22430]) ).
tcf(c_37626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = sK140 )
| ( relation_dom_as_subset(X3,X4,X2) = X3 )
| ~ quasi_total(X2,X3,X4)
| ( X1 != X4 )
| ( X0 != X3 )
| ( sK312(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_5415,c_1018]) ).
tcf(c_37627,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( relation_dom_as_subset(X0,X1,sK312(X0,X1)) = X0 )
| ~ quasi_total(sK312(X0,X1),X0,X1) ),
inference(unflattening,[status(thm)],[c_37626]) ).
tcf(c_37629,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( relation_dom_as_subset(X0,X1,sK312(X0,X1)) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_37627,c_1021,c_37627]) ).
tcf(c_44338,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_653]) ).
tcf(c_47136,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_5402,c_44338]) ).
tcf(c_47137,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_5409,c_44338]) ).
tcf(c_47138,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_5410,c_44338]) ).
tcf(c_47139,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_5411,c_44338]) ).
tcf(c_47140,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_5412,c_44338]) ).
tcf(c_47141,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_5413,c_44338]) ).
tcf(c_47142,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_5414,c_44338]) ).
tcf(c_47143,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_7039,c_44338]) ).
tcf(c_84096,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_5611]) ).
tcf(c_84097,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_84096]) ).
tcf(c_84120,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_5612]) ).
tcf(c_84144,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2390]) ).
tcf(c_84146,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2392]) ).
tcf(c_84148,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X1,X0) = subset_complement(X1,X0) )
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2394]) ).
tcf(c_84150,plain,
! [X0: $i,X1: $i] :
( ~ in(sK48(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2397]) ).
tcf(c_84151,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK48(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_84150]) ).
tcf(c_84152,plain,
! [X0: $i,X1: $i] :
( in(sK48(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2399]) ).
tcf(c_84153,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK48(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_84152]) ).
tcf(c_84200,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0) ),
inference(prop_impl_just,[status(thm)],[c_2153]) ).
tcf(c_84236,plain,
! [X0: $i] :
( ~ being_limit_ordinal(set_union2(X0,unordered_pair(X0,X0)))
| ~ ordinal(X0) ),
inference(prop_impl_just,[status(thm)],[c_2178]) ).
tcf(c_84237,plain,
! [X0: $i] :
( ~ ordinal(X0)
| ~ being_limit_ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(renaming,[status(thm)],[c_84236]) ).
tcf(c_84268,plain,
( element(sK68(sK62),powerset(powerset(set_union2(sK62,unordered_pair(sK62,sK62)))))
| ~ sP8 ),
inference(prop_impl_just,[status(thm)],[c_20028]) ).
tcf(c_84270,plain,
( ( sK68(sK62) != sK140 )
| ~ sP8 ),
inference(prop_impl_just,[status(thm)],[c_20048]) ).
tcf(c_84271,plain,
( ~ sP8
| ( sK68(sK62) != sK140 ) ),
inference(renaming,[status(thm)],[c_84270]) ).
tcf(c_84306,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK166(X0),sK166(X0)),unordered_pair(sK166(X0),sK168(X0))),X0)
| function(X0) ),
inference(prop_impl_just,[status(thm)],[c_15157]) ).
tcf(c_84307,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK166(X0),sK166(X0)),unordered_pair(sK166(X0),sK168(X0))),X0) ),
inference(renaming,[status(thm)],[c_84306]) ).
tcf(c_84308,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK166(X0),sK166(X0)),unordered_pair(sK166(X0),sK167(X0))),X0)
| function(X0) ),
inference(prop_impl_just,[status(thm)],[c_15164]) ).
tcf(c_84309,plain,
! [X0: $i] :
( function(X0)
| in(unordered_pair(unordered_pair(sK166(X0),sK166(X0)),unordered_pair(sK166(X0),sK167(X0))),X0) ),
inference(renaming,[status(thm)],[c_84308]) ).
tcf(c_84316,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK80(X1,X0),sK80(X1,X0)),unordered_pair(sK80(X1,X0),sK81(X1,X0))) = X0 )
| ~ in(X0,sK79(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_17294]) ).
tcf(c_84322,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK235(X1,X2,X0),sK235(X1,X2,X0)),unordered_pair(sK235(X1,X2,X0),sK236(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_17868]) ).
tcf(c_84500,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK173(X0),sK173(X0)),unordered_pair(sK173(X0),sK174(X0))) = sK171(X0) )
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_15847]) ).
tcf(c_84570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( unordered_pair(unordered_pair(sK220(X1,X2,X3),sK220(X1,X2,X3)),unordered_pair(sK220(X1,X2,X3),sK221(X1,X2,X3))) = X2 )
| ~ sP27(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_17875]) ).
tcf(c_84578,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK223(X0,X1,X2),sK223(X0,X1,X2)),unordered_pair(sK223(X0,X1,X2),sK224(X0,X1,X2))) = X0 )
| ~ sP26(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_17706]) ).
tcf(c_84592,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_2935]) ).
tcf(c_84593,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_84592]) ).
tcf(c_84674,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_3024]) ).
tcf(c_84676,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_rng(X0),X2)
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_3026]) ).
tcf(c_84690,plain,
! [X0: $i,X1: $i] :
( equipotent(X1,X0)
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3040]) ).
tcf(c_84692,plain,
! [X0: $i,X1: $i] :
( relation(sK195(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3042]) ).
tcf(c_84694,plain,
! [X0: $i,X1: $i] :
( function(sK195(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3044]) ).
tcf(c_84696,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK195(X0,X1))
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3046]) ).
tcf(c_84698,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK195(X0,X1)) = X0 )
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3048]) ).
tcf(c_84700,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK195(X0,X1)) = X1 )
| ~ are_equipotent(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_3050]) ).
tcf(c_84726,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_5610]) ).
tcf(c_84738,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(prop_impl_just,[status(thm)],[c_17179]) ).
tcf(c_84740,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( sK342(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) != X2 ) ),
inference(prop_impl_just,[status(thm)],[c_17172]) ).
tcf(c_85108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK342(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_19330]) ).
tcf(c_85109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( unordered_pair(unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK341(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK342(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_85108]) ).
tcf(c_85122,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK340(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_19338]) ).
tcf(c_85123,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( unordered_pair(unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)),unordered_pair(sK339(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2),sK340(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_85122]) ).
tcf(c_85174,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),sK79(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_17646]) ).
tcf(c_85218,plain,
! [X0: $i] :
( sP22(sK285,X0,topstr_closure(sK285,X0))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(prop_impl_just,[status(thm)],[c_22242]) ).
tcf(c_85220,plain,
! [X0: $i] :
( element(topstr_closure(sK285,X0),powerset(the_carrier(sK285)))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(prop_impl_just,[status(thm)],[c_22266]) ).
tcf(c_85222,plain,
! [X0: $i] :
( ( subset_complement(the_carrier(sK285),topstr_closure(sK285,subset_complement(the_carrier(sK285),X0))) = interior(sK285,X0) )
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(prop_impl_just,[status(thm)],[c_22275]) ).
tcf(c_85224,plain,
! [X0: $i] :
( element(interior(sK285,X0),powerset(the_carrier(sK285)))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(prop_impl_just,[status(thm)],[c_22284]) ).
tcf(c_85226,plain,
! [X0: $i] :
( subset(X0,topstr_closure(sK285,X0))
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(prop_impl_just,[status(thm)],[c_22317]) ).
tcf(c_85228,plain,
! [X0: $i] :
( subset(interior(sK285,X0),X0)
| ~ element(X0,powerset(the_carrier(sK285))) ),
inference(prop_impl_just,[status(thm)],[c_22410]) ).
tcf(c_123587,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_13
| ( join(sK322,meet(sK322,X0,X1),X1) = X1 )
| ~ element(X1,the_carrier(sK322))
| ~ element(X0,the_carrier(sK322)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_20266]) ).
tcf(c_123588,plain,
( iPr_def_13
| empty_carrier(sK322)
| ~ meet_absorbing(sK322) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_20266]) ).
tcf(c_123589,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_14
| ( sK262(X0) = X1 )
| ( X0 = sK140 )
| ~ in(X1,X0)
| ~ subset(sK262(X0),X1)
| ~ element(X0,powerset(powerset(sK261))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_836]) ).
tcf(c_123590,negated_conjecture,
( iPr_def_14
| iPr_def_10
| ~ in(sK261,omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_836]) ).
tcf(c_123591,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_15
| ( X0 = sK140 )
| in(sK262(X0),X0)
| ~ element(X0,powerset(powerset(sK261))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_15])],[c_835]) ).
tcf(c_123592,negated_conjecture,
( iPr_def_15
| iPr_def_10
| ~ in(sK261,omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_835]) ).
tcf(c_123593,plain,
! [X0: $i] :
( ~ iPr_def_16
| ~ ordinal(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_16])],[c_809]) ).
tcf(c_123594,plain,
! [X0: $i] :
( ~ iPr_def_17
| ~ ordinal(X0)
| ordinal_subset(X0,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_17])],[c_809]) ).
tcf(c_123595,plain,
( iPr_def_17
| iPr_def_16 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_809]) ).
tcf(c_123596,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_18
| ( sK72(X0) = X2 )
| ( X0 = sK140 )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ in(X2,X0)
| ~ subset(sK72(X0),X2)
| ~ element(X0,powerset(powerset(X1))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_18])],[c_156]) ).
tcf(c_123597,negated_conjecture,
( iPr_def_18
| sP6
| sP7
| sP8 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_156]) ).
tcf(c_123598,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_19
| ( X0 = sK140 )
| ~ ordinal(X1)
| in(sK72(X0),X0)
| ~ in(X1,omega)
| ~ element(X0,powerset(powerset(X1))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_19])],[c_155]) ).
tcf(c_123599,negated_conjecture,
( iPr_def_19
| sP6
| sP7
| sP8 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_155]) ).
tcf(c_123600,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_20
| ( sK63(X0) = X1 )
| ( X0 = sK140 )
| ~ in(X1,X0)
| ~ subset(sK63(X0),X1)
| ~ element(X0,powerset(powerset(sK62))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_20])],[c_130]) ).
tcf(c_123601,negated_conjecture,
( iPr_def_20
| ~ sP8
| ~ in(sK62,omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_130]) ).
tcf(c_123602,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_21
| ( X0 = sK140 )
| in(sK63(X0),X0)
| ~ element(X0,powerset(powerset(sK62))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_21])],[c_129]) ).
tcf(c_123603,negated_conjecture,
( iPr_def_21
| ~ sP8
| ~ in(sK62,omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_129]) ).
tcf(c_123764,plain,
( ~ iPr_def_16
| ~ ordinal(sK140) ),
inference(instantiation,[status(thm)],[c_123593]) ).
tcf(c_144206,plain,
powerset(sK140) != sK140,
inference(superposition,[status(thm)],[c_314,c_52]) ).
tcf(c_144212,plain,
sK140 = sK239,
inference(superposition,[status(thm)],[c_781,c_575]) ).
tcf(c_144213,plain,
sK140 = sK243,
inference(superposition,[status(thm)],[c_792,c_575]) ).
tcf(c_144214,plain,
sK140 = sK244,
inference(superposition,[status(thm)],[c_793,c_575]) ).
tcf(c_144215,plain,
function(sK140),
inference(demodulation,[status(thm)],[c_782,c_144212]) ).
tcf(c_144265,plain,
! [X0: $i] :
( subset(X0,sK140)
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_675,c_387]) ).
tcf(c_144275,plain,
sK140 = sK314,
inference(superposition,[status(thm)],[c_1032,c_575]) ).
tcf(c_144277,plain,
one_to_one(sK140),
inference(demodulation,[status(thm)],[c_1031,c_144275]) ).
tcf(c_144280,plain,
epsilon_transitive(sK140),
inference(light_normalisation,[status(thm)],[c_1033,c_144275]) ).
tcf(c_144281,plain,
epsilon_connected(sK140),
inference(light_normalisation,[status(thm)],[c_1034,c_144275]) ).
tcf(c_144282,plain,
ordinal(sK140),
inference(light_normalisation,[status(thm)],[c_1035,c_144275]) ).
tcf(c_144287,plain,
! [X0: $i] : disjoint(sK140,X0),
inference(superposition,[status(thm)],[c_674,c_625]) ).
tcf(c_144289,plain,
! [X0: $i] :
( disjoint(X0,sK140)
| ( set_difference(X0,X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_675,c_625]) ).
tcf(c_144290,plain,
! [X0: $i] :
( disjoint(X0,X0)
| ( set_difference(X0,sK140) != sK140 ) ),
inference(superposition,[status(thm)],[c_12910,c_625]) ).
tcf(c_144291,plain,
! [X0: $i] :
( disjoint(X0,X0)
| ( X0 != sK140 ) ),
inference(light_normalisation,[status(thm)],[c_144290,c_675]) ).
tcf(c_144294,plain,
! [X0: $i] : disjoint(X0,sK140),
inference(ground_joinability,[status(thm)],[c_144289,c_12910]) ).
tcf(c_144306,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_575]) ).
tcf(c_144332,plain,
( subset(omega,omega)
| ~ being_limit_ordinal(omega)
| ~ ordinal(omega) ),
inference(superposition,[status(thm)],[c_847,c_850]) ).
tcf(c_144333,plain,
subset(omega,omega),
inference(forward_subsumption_resolution,[status(thm)],[c_144332,c_848,c_849]) ).
tcf(c_144346,plain,
sK140 = sK336,
inference(superposition,[status(thm)],[c_1155,c_575]) ).
tcf(c_144395,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_2177,c_580]) ).
tcf(c_144405,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( unordered_pair(sK140,sK140) = X0 )
| ~ subset(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_314,c_397]) ).
tcf(c_144406,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( powerset(sK140) = X0 )
| ~ subset(X0,powerset(sK140)) ),
inference(light_normalisation,[status(thm)],[c_144405,c_314]) ).
tcf(c_144418,plain,
! [X0: $i] :
( in(X0,sK140)
| ( apply(sK140,X0) = sK140 )
| ~ function(sK140)
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_470,c_906]) ).
tcf(c_144419,plain,
! [X0: $i] :
( subset(omega,relation_dom(X0))
| ( apply(X0,sK140) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ being_limit_ordinal(relation_dom(X0))
| ~ ordinal(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_906,c_850]) ).
tcf(c_144420,plain,
! [X0: $i] :
( ( apply(sK140,X0) = sK140 )
| ~ function(sK140) ),
inference(forward_subsumption_resolution,[status(thm)],[c_144418,c_580,c_577]) ).
tcf(c_144454,plain,
( in(sK119(sK64),sK64)
| ( sK140 = sK64 )
| ~ sP7
| ~ finite(sK140) ),
inference(superposition,[status(thm)],[c_136,c_307]) ).
tcf(c_144477,plain,
! [X0: $i] :
( being_limit_ordinal(sK263(relation_dom(X0)))
| ( relation_dom(X0) = omega )
| ( apply(X0,sK140) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ being_limit_ordinal(relation_dom(X0))
| ~ ordinal(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_906,c_845]) ).
tcf(c_144496,plain,
! [X0: $i] :
( ordinal(sK263(relation_dom(X0)))
| ( relation_dom(X0) = omega )
| ( apply(X0,sK140) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ being_limit_ordinal(relation_dom(X0))
| ~ ordinal(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_906,c_846]) ).
tcf(c_144516,plain,
iPr_def_17,
inference(global_subsumption_just,[status(thm)],[c_123595,c_1282,c_1357,c_123764,c_123595]) ).
tcf(c_144528,plain,
! [X0: $i] :
( ordinal(sK263(sK263(X0)))
| ( X0 = omega )
| ( sK263(X0) = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ being_limit_ordinal(sK263(X0))
| ~ ordinal(sK263(X0))
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_846]) ).
tcf(c_144529,plain,
! [X0: $i] :
( being_limit_ordinal(sK263(sK263(X0)))
| ( X0 = omega )
| ( sK263(X0) = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ being_limit_ordinal(sK263(X0))
| ~ ordinal(sK263(X0))
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_845]) ).
tcf(c_144530,plain,
! [X0: $i] :
( subset(omega,sK263(X0))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ being_limit_ordinal(sK263(X0))
| ~ ordinal(sK263(X0))
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_850]) ).
tcf(c_144580,plain,
( ( sK140 = omega )
| ~ being_limit_ordinal(sK140)
| ~ ordinal(sK140)
| ~ in(sK140,sK140) ),
inference(superposition,[status(thm)],[c_361,c_843]) ).
tcf(c_144619,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,X1),X1)
| ( X1 = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_665,c_1057]) ).
tcf(c_144620,plain,
! [X0: $i] :
( in(sK128(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_665,c_369]) ).
tcf(c_144621,plain,
! [X0: $i] :
( ordinal(sK128(X0))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_665,c_371]) ).
tcf(c_144635,plain,
! [X0: $i] : sK197(X0) = sK140,
inference(superposition,[status(thm)],[c_692,c_575]) ).
tcf(c_144638,plain,
( ( sK125(sK241) = sK140 )
| ( relation_dom(sK126(sK241)) = sK241 ) ),
inference(superposition,[status(thm)],[c_353,c_789]) ).
tcf(c_144641,plain,
( ( sK125(sK242) = sK140 )
| ( relation_dom(sK126(sK242)) = sK242 ) ),
inference(superposition,[status(thm)],[c_353,c_790]) ).
tcf(c_144644,plain,
( ( sK125(omega) = sK140 )
| ( relation_dom(sK126(omega)) = omega ) ),
inference(superposition,[status(thm)],[c_353,c_842]) ).
tcf(c_144647,plain,
( ( sK125(sK303) = sK140 )
| ( relation_dom(sK126(sK303)) = sK303 ) ),
inference(superposition,[status(thm)],[c_353,c_975]) ).
tcf(c_144660,plain,
! [X0: $i,X1: $i] :
( in(sK140,X1)
| ordinal(sK263(subset_complement(X0,X1)))
| ( X0 = sK140 )
| ( subset_complement(X0,X1) = omega )
| ~ element(sK140,X0)
| ~ subset(X1,X0)
| ~ being_limit_ordinal(subset_complement(X0,X1))
| ~ ordinal(subset_complement(X0,X1)) ),
inference(superposition,[status(thm)],[c_5403,c_846]) ).
tcf(c_144661,plain,
! [X0: $i,X1: $i] :
( in(sK140,X1)
| being_limit_ordinal(sK263(subset_complement(X0,X1)))
| ( X0 = sK140 )
| ( subset_complement(X0,X1) = omega )
| ~ element(sK140,X0)
| ~ subset(X1,X0)
| ~ being_limit_ordinal(subset_complement(X0,X1))
| ~ ordinal(subset_complement(X0,X1)) ),
inference(superposition,[status(thm)],[c_5403,c_845]) ).
tcf(c_144662,plain,
! [X0: $i,X1: $i] :
( in(sK140,X1)
| subset(omega,subset_complement(X0,X1))
| ( X0 = sK140 )
| ~ element(sK140,X0)
| ~ subset(X1,X0)
| ~ being_limit_ordinal(subset_complement(X0,X1))
| ~ ordinal(subset_complement(X0,X1)) ),
inference(superposition,[status(thm)],[c_5403,c_850]) ).
tcf(c_144724,plain,
( sP15
| in(sK114(sK64),sK64)
| ( sK140 = sK64 )
| ~ sP7
| ~ ordinal(sK140)
| ~ in(sK140,omega) ),
inference(superposition,[status(thm)],[c_136,c_247]) ).
tcf(c_144726,plain,
( sP15
| in(sK114(sK64),sK64)
| ( sK140 = sK64 )
| ~ sP7 ),
inference(forward_subsumption_resolution,[status(thm)],[c_144724,c_144282,c_847]) ).
tcf(c_144744,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(X1),X0)
| ( X1 = sK140 )
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_665,c_370]) ).
tcf(c_144761,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,X1)),X1)
| ( X1 = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_665,c_1058]) ).
tcf(c_144776,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( set_difference(fiber(X1,sK320(X1,X0)),set_difference(fiber(X1,sK320(X1,X0)),X0)) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1063,c_626]) ).
tcf(c_144788,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_906]) ).
tcf(c_144797,plain,
( ( sK125(sK313) = sK140 )
| ( relation_dom(sK126(sK313)) = sK313 ) ),
inference(superposition,[status(thm)],[c_353,c_1025]) ).
tcf(c_144800,plain,
! [X0: $i] : sK345(X0) = sK140,
inference(superposition,[status(thm)],[c_1214,c_575]) ).
tcf(c_144818,plain,
( in(sK72(sK64),sK64)
| ( sK140 = sK64 )
| ~ iPr_def_19
| ~ sP7
| ~ ordinal(sK140)
| ~ in(sK140,omega) ),
inference(superposition,[status(thm)],[c_136,c_123598]) ).
tcf(c_144820,plain,
( in(sK72(sK64),sK64)
| ( sK140 = sK64 )
| ~ iPr_def_19
| ~ sP7 ),
inference(forward_subsumption_resolution,[status(thm)],[c_144818,c_144282,c_847]) ).
tcf(c_144869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(sK126(X2),relation_inverse_image(X0,X1)),X3)
| ( X4 = sK140 )
| ( sK125(X2) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ in(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_2177,c_424]) ).
tcf(c_144870,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK169(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ( relation_inverse_image(X0,X3) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_579,c_424]) ).
tcf(c_144871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK320(X2,relation_inverse_image(X0,X1)),X3)
| ( X4 = sK140 )
| ( relation_inverse_image(X0,X1) = sK140 )
| ~ well_founded_relation(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ subset(relation_inverse_image(X0,X1),relation_field(X2)) ),
inference(superposition,[status(thm)],[c_1062,c_424]) ).
tcf(c_144932,plain,
( in(sK67(sK64),sK64)
| ( sK140 = sK64 )
| ~ sP6
| ~ sP7
| ~ ordinal(sK140)
| ~ in(sK140,sK66)
| ~ in(sK140,omega) ),
inference(superposition,[status(thm)],[c_136,c_142]) ).
tcf(c_144934,plain,
( in(sK67(sK64),sK64)
| ( sK140 = sK64 )
| ~ sP6
| ~ sP7
| ~ in(sK140,sK66) ),
inference(forward_subsumption_resolution,[status(thm)],[c_144932,c_144282,c_847]) ).
tcf(c_144943,plain,
finite(sK140),
inference(light_normalisation,[status(thm)],[c_1222,c_144800]) ).
tcf(c_144944,plain,
( ( sK125(sK346) = sK140 )
| ( relation_dom(sK126(sK346)) = sK346 ) ),
inference(superposition,[status(thm)],[c_353,c_1223]) ).
tcf(c_144947,plain,
( ( sK125(sK358) = sK140 )
| ( relation_dom(sK126(sK358)) = sK358 ) ),
inference(superposition,[status(thm)],[c_353,c_1276]) ).
tcf(c_144950,plain,
! [X0: $i] : set_difference(sK140,set_difference(sK140,X0)) = sK140,
inference(superposition,[status(thm)],[c_144287,c_626]) ).
tcf(c_144951,plain,
set_difference(sK140,sK140) = sK140,
inference(light_normalisation,[status(thm)],[c_144950,c_674]) ).
tcf(c_144952,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,sK140)) = sK140,
inference(superposition,[status(thm)],[c_144294,c_626]) ).
tcf(c_144968,plain,
( in(sK111(sK64),sK64)
| ( sK140 = sK64 )
| ~ sP15
| ~ sP7
| ~ ordinal(sK140)
| ~ in(sK140,sK110)
| ~ in(sK140,omega) ),
inference(superposition,[status(thm)],[c_136,c_239]) ).
tcf(c_144970,plain,
( in(sK111(sK64),sK64)
| ( sK140 = sK64 )
| ~ sP15
| ~ sP7
| ~ in(sK140,sK110) ),
inference(forward_subsumption_resolution,[status(thm)],[c_144968,c_144282,c_847]) ).
tcf(c_144988,plain,
! [X0: $i] :
( ( sK140 = sK64 )
| ( sK119(sK64) = X0 )
| ~ sP7
| ~ finite(sK140)
| ~ in(X0,sK64)
| ~ subset(sK119(sK64),X0) ),
inference(superposition,[status(thm)],[c_136,c_308]) ).
tcf(c_144990,plain,
! [X0: $i] :
( ( sK140 = sK64 )
| ( sK119(sK64) = X0 )
| ~ sP7
| ~ in(X0,sK64)
| ~ subset(sK119(sK64),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_144988,c_144943]) ).
tcf(c_145021,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,apply(sK126(X2),relation_inverse_image(X0,X1))),X1)
| ( X4 = sK140 )
| ( sK125(X2) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ in(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_2177,c_425]) ).
tcf(c_145022,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK169(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ( relation_inverse_image(X0,X3) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_579,c_425]) ).
tcf(c_145023,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK320(X2,relation_inverse_image(X0,X1))),X1)
| ( X4 = sK140 )
| ( relation_inverse_image(X0,X1) = sK140 )
| ~ well_founded_relation(X2)
| ~ function(X0)
| ~ relation(X2)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ subset(relation_inverse_image(X0,X1),relation_field(X2)) ),
inference(superposition,[status(thm)],[c_1062,c_425]) ).
tcf(c_145062,plain,
! [X0: $i] :
( sP15
| ( sK140 = sK64 )
| ( sK114(sK64) = X0 )
| ~ sP7
| ~ ordinal(sK140)
| ~ in(sK140,omega)
| ~ in(X0,sK64)
| ~ subset(sK114(sK64),X0) ),
inference(superposition,[status(thm)],[c_136,c_248]) ).
tcf(c_145064,plain,
! [X0: $i] :
( sP15
| ( sK140 = sK64 )
| ( sK114(sK64) = X0 )
| ~ sP7
| ~ in(X0,sK64)
| ~ subset(sK114(sK64),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_145062,c_144282,c_847]) ).
tcf(c_145086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X3,relation_inverse_image(X0,relation_dom(X4)))
| ( X2 = sK140 )
| ( apply(X4,apply(X0,X3)) = sK140 )
| ~ function(X4)
| ~ function(X0)
| ~ relation(X4)
| ~ in(X3,X1)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_906,c_423]) ).
tcf(c_145087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,relation_inverse_image(sK126(X0),X3))
| ( X2 = sK140 )
| ( sK125(X0) = sK140 )
| ~ function(sK126(X0))
| ~ in(X3,X1)
| ~ in(X3,X0)
| ~ quasi_total(sK126(X0),X1,X2)
| ~ relation_of2_as_subset(sK126(X0),X1,X2) ),
inference(superposition,[status(thm)],[c_2177,c_423]) ).
tcf(c_145088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(apply(X0,X1),X5)
| in(X1,relation_inverse_image(X0,subset_complement(X2,X5)))
| ( X4 = sK140 )
| ( X2 = sK140 )
| ~ function(X0)
| ~ subset(X5,X2)
| ~ in(X1,X3)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ element(apply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_5403,c_423]) ).
tcf(c_145132,plain,
! [X0: $i] :
( ( sK140 = sK64 )
| ( sK72(sK64) = X0 )
| ~ iPr_def_18
| ~ sP7
| ~ ordinal(sK140)
| ~ in(sK140,omega)
| ~ in(X0,sK64)
| ~ subset(sK72(sK64),X0) ),
inference(superposition,[status(thm)],[c_136,c_123596]) ).
tcf(c_145134,plain,
! [X0: $i] :
( ( sK140 = sK64 )
| ( sK72(sK64) = X0 )
| ~ iPr_def_18
| ~ sP7
| ~ in(X0,sK64)
| ~ subset(sK72(sK64),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_145132,c_144282,c_847]) ).
tcf(c_145172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,relation_inverse_image(X0,sK116(apply(X0,X3))))
| ( X2 = sK140 )
| ~ function(X0)
| ~ in(X3,X1)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_272,c_423]) ).
tcf(c_145173,plain,
( ordinal(sK263(sK116(sK140)))
| ( sK116(sK140) = omega )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_272,c_846]) ).
tcf(c_145174,plain,
( being_limit_ordinal(sK263(sK116(sK140)))
| ( sK116(sK140) = omega )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_272,c_845]) ).
tcf(c_145175,plain,
( subset(omega,sK116(sK140))
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_272,c_850]) ).
tcf(c_145193,plain,
! [X0: $i] :
( ( sK125(powerset(X0)) = sK140 )
| ( relation_dom(sK126(powerset(X0))) = powerset(X0) ) ),
inference(superposition,[status(thm)],[c_353,c_695]) ).
tcf(c_145229,plain,
! [X0: $i] :
( ( sK140 = sK64 )
| ( sK67(sK64) = X0 )
| ~ sP6
| ~ sP7
| ~ ordinal(sK140)
| ~ in(sK140,sK66)
| ~ in(sK140,omega)
| ~ in(X0,sK64)
| ~ subset(sK67(sK64),X0) ),
inference(superposition,[status(thm)],[c_136,c_143]) ).
tcf(c_145231,plain,
! [X0: $i] :
( ( sK140 = sK64 )
| ( sK67(sK64) = X0 )
| ~ sP6
| ~ sP7
| ~ in(sK140,sK66)
| ~ in(X0,sK64)
| ~ subset(sK67(sK64),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_145229,c_144282,c_847]) ).
tcf(c_145258,plain,
! [X0: $i] :
( ( sK140 = sK64 )
| ( sK111(sK64) = X0 )
| ~ sP15
| ~ sP7
| ~ ordinal(sK140)
| ~ in(sK140,sK110)
| ~ in(sK140,omega)
| ~ in(X0,sK64)
| ~ subset(sK111(sK64),X0) ),
inference(superposition,[status(thm)],[c_136,c_240]) ).
tcf(c_145260,plain,
! [X0: $i] :
( ( sK140 = sK64 )
| ( sK111(sK64) = X0 )
| ~ sP15
| ~ sP7
| ~ in(sK140,sK110)
| ~ in(X0,sK64)
| ~ subset(sK111(sK64),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_145258,c_144282,c_847]) ).
tcf(c_145337,plain,
! [X0: $i] :
( in(X0,sK241)
| ( sK125(sK241) = sK140 )
| ( apply(sK126(sK241),X0) = sK140 )
| ~ function(sK126(sK241))
| ~ relation(sK126(sK241)) ),
inference(superposition,[status(thm)],[c_144638,c_906]) ).
tcf(c_145338,plain,
( ( sK125(sK241) = sK140 )
| ( relation_rng(sK126(sK241)) = sK140 )
| ~ relation(sK126(sK241))
| ( sK140 != sK241 ) ),
inference(superposition,[status(thm)],[c_144638,c_478]) ).
tcf(c_145339,plain,
( ( sK126(sK241) = sK140 )
| ( sK125(sK241) = sK140 )
| ~ relation(sK126(sK241))
| ( sK140 != sK241 ) ),
inference(superposition,[status(thm)],[c_144638,c_475]) ).
tcf(c_145354,plain,
! [X0: $i] :
( ( sK199(powerset(powerset(sK62))) = sK140 )
| ( sK63(sK199(powerset(powerset(sK62)))) = X0 )
| ~ iPr_def_20
| ~ in(X0,sK199(powerset(powerset(sK62))))
| ~ subset(sK63(sK199(powerset(powerset(sK62)))),X0) ),
inference(superposition,[status(thm)],[c_696,c_123600]) ).
tcf(c_145355,plain,
( in(sK63(sK199(powerset(powerset(sK62)))),sK199(powerset(powerset(sK62))))
| ( sK199(powerset(powerset(sK62))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_696,c_123602]) ).
tcf(c_145356,plain,
! [X0: $i,X1: $i] :
( ( sK199(powerset(powerset(X0))) = sK140 )
| ( sK111(sK199(powerset(powerset(X0)))) = X1 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega)
| ~ in(X1,sK199(powerset(powerset(X0))))
| ~ subset(sK111(sK199(powerset(powerset(X0)))),X1) ),
inference(superposition,[status(thm)],[c_696,c_240]) ).
tcf(c_145357,plain,
! [X0: $i,X1: $i] :
( ( sK199(powerset(powerset(X0))) = sK140 )
| ( sK67(sK199(powerset(powerset(X0)))) = X1 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega)
| ~ in(X1,sK199(powerset(powerset(X0))))
| ~ subset(sK67(sK199(powerset(powerset(X0)))),X1) ),
inference(superposition,[status(thm)],[c_696,c_143]) ).
tcf(c_145358,plain,
! [X0: $i,X1: $i] :
( ( sK199(powerset(powerset(X0))) = sK140 )
| ( sK72(sK199(powerset(powerset(X0)))) = X1 )
| ~ iPr_def_18
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK199(powerset(powerset(X0))))
| ~ subset(sK72(sK199(powerset(powerset(X0)))),X1) ),
inference(superposition,[status(thm)],[c_696,c_123596]) ).
tcf(c_145359,plain,
! [X0: $i,X1: $i] :
( sP15
| ( sK199(powerset(powerset(X0))) = sK140 )
| ( sK114(sK199(powerset(powerset(X0)))) = X1 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK199(powerset(powerset(X0))))
| ~ subset(sK114(sK199(powerset(powerset(X0)))),X1) ),
inference(superposition,[status(thm)],[c_696,c_248]) ).
tcf(c_145360,plain,
! [X0: $i,X1: $i] :
( ( sK199(powerset(powerset(X0))) = sK140 )
| ( sK119(sK199(powerset(powerset(X0)))) = X1 )
| ~ finite(X0)
| ~ in(X1,sK199(powerset(powerset(X0))))
| ~ subset(sK119(sK199(powerset(powerset(X0)))),X1) ),
inference(superposition,[status(thm)],[c_696,c_308]) ).
tcf(c_145361,plain,
! [X0: $i] :
( in(sK111(sK199(powerset(powerset(X0)))),sK199(powerset(powerset(X0))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_696,c_239]) ).
tcf(c_145362,plain,
! [X0: $i] :
( in(sK67(sK199(powerset(powerset(X0)))),sK199(powerset(powerset(X0))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_696,c_142]) ).
tcf(c_145363,plain,
! [X0: $i] :
( in(sK72(sK199(powerset(powerset(X0)))),sK199(powerset(powerset(X0))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_696,c_123598]) ).
tcf(c_145364,plain,
! [X0: $i] :
( sP15
| in(sK114(sK199(powerset(powerset(X0)))),sK199(powerset(powerset(X0))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_696,c_247]) ).
tcf(c_145365,plain,
! [X0: $i] :
( in(sK119(sK199(powerset(powerset(X0)))),sK199(powerset(powerset(X0))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_696,c_307]) ).
tcf(c_145368,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK199(powerset(powerset(sK254(X0)))) = sK140 )
| ( sK255(sK199(powerset(powerset(sK254(X0))))) = X1 )
| ~ sP31(X2,X0)
| ~ in(sK254(X0),omega)
| ~ in(X1,sK199(powerset(powerset(sK254(X0)))))
| ~ subset(sK255(sK199(powerset(powerset(sK254(X0))))),X1) ),
inference(superposition,[status(thm)],[c_696,c_826]) ).
tcf(c_145369,plain,
! [X0: $i,X1: $i] :
( in(sK255(sK199(powerset(powerset(sK254(X0))))),sK199(powerset(powerset(sK254(X0)))))
| ( sK199(powerset(powerset(sK254(X0)))) = sK140 )
| ~ sP31(X1,X0)
| ~ in(sK254(X0),omega) ),
inference(superposition,[status(thm)],[c_696,c_825]) ).
tcf(c_145370,plain,
! [X0: $i] :
( ( sK199(powerset(powerset(sK261))) = sK140 )
| ( sK262(sK199(powerset(powerset(sK261)))) = X0 )
| ~ iPr_def_14
| ~ in(X0,sK199(powerset(powerset(sK261))))
| ~ subset(sK262(sK199(powerset(powerset(sK261)))),X0) ),
inference(superposition,[status(thm)],[c_696,c_123589]) ).
tcf(c_145371,plain,
( in(sK262(sK199(powerset(powerset(sK261)))),sK199(powerset(powerset(sK261))))
| ( sK199(powerset(powerset(sK261))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_696,c_123591]) ).
tcf(c_145500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,relation_inverse_image(X0,sK300(apply(X0,X3))))
| ( X2 = sK140 )
| ~ function(X0)
| ~ in(X3,X1)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_965,c_423]) ).
tcf(c_145501,plain,
( ordinal(sK263(sK300(sK140)))
| ( sK300(sK140) = omega )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_965,c_846]) ).
tcf(c_145502,plain,
( being_limit_ordinal(sK263(sK300(sK140)))
| ( sK300(sK140) = omega )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_965,c_845]) ).
tcf(c_145503,plain,
( subset(omega,sK300(sK140))
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_965,c_850]) ).
tcf(c_145521,plain,
finite(powerset(sK140)),
inference(superposition,[status(thm)],[c_314,c_978]) ).
tcf(c_145526,plain,
subset(sK140,sK140),
inference(equality_resolution,[status(thm)],[c_144265]) ).
tcf(c_145531,plain,
disjoint(sK140,sK140),
inference(equality_resolution,[status(thm)],[c_144291]) ).
tcf(c_145536,plain,
sK125(omega) = sK140,
inference(superposition,[status(thm)],[c_847,c_144395]) ).
tcf(c_145537,plain,
sK125(sK116(sK140)) = sK140,
inference(superposition,[status(thm)],[c_272,c_144395]) ).
tcf(c_145538,plain,
! [X0: $i] :
( ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,sK140) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_144395]) ).
tcf(c_145539,plain,
! [X0: $i,X1: $i] :
( in(sK140,X0)
| ( X1 = sK140 )
| ( sK125(subset_complement(X1,X0)) = sK140 )
| ~ element(sK140,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5403,c_144395]) ).
tcf(c_145540,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK263(X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_144395]) ).
tcf(c_145541,plain,
sK125(sK300(sK140)) = sK140,
inference(superposition,[status(thm)],[c_965,c_144395]) ).
tcf(c_145556,plain,
! [X0: $i] : apply(sK140,X0) = sK140,
inference(global_subsumption_just,[status(thm)],[c_144420,c_1282,c_1363,c_144420]) ).
tcf(c_145559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,relation_inverse_image(sK140,X3))
| ( X1 = sK140 )
| ~ function(sK140)
| ~ in(sK140,X3)
| ~ in(X2,X0)
| ~ quasi_total(sK140,X0,X1)
| ~ relation_of2_as_subset(sK140,X0,X1) ),
inference(superposition,[status(thm)],[c_145556,c_423]) ).
tcf(c_145560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,relation_inverse_image(sK140,X3))
| ( X1 = sK140 )
| ~ in(sK140,X3)
| ~ in(X2,X0)
| ~ quasi_total(sK140,X0,X1)
| ~ relation_of2_as_subset(sK140,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_145559,c_144215]) ).
tcf(c_145584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK128(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ( relation_inverse_image(X0,X3) = sK140 )
| ~ function(X0)
| ~ ordinal(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_144620,c_425]) ).
tcf(c_145585,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK128(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ( relation_inverse_image(X0,X3) = sK140 )
| ~ function(X0)
| ~ ordinal(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_144620,c_424]) ).
tcf(c_145605,plain,
! [X0: $i] :
( in(X0,sK242)
| ( sK125(sK242) = sK140 )
| ( apply(sK126(sK242),X0) = sK140 )
| ~ function(sK126(sK242))
| ~ relation(sK126(sK242)) ),
inference(superposition,[status(thm)],[c_144641,c_906]) ).
tcf(c_145606,plain,
( ( sK125(sK242) = sK140 )
| ( relation_rng(sK126(sK242)) = sK140 )
| ~ relation(sK126(sK242))
| ( sK140 != sK242 ) ),
inference(superposition,[status(thm)],[c_144641,c_478]) ).
tcf(c_145607,plain,
( ( sK126(sK242) = sK140 )
| ( sK125(sK242) = sK140 )
| ~ relation(sK126(sK242))
| ( sK140 != sK242 ) ),
inference(superposition,[status(thm)],[c_144641,c_475]) ).
tcf(c_145624,plain,
! [X0: $i] :
( ( powerset(sK62) = sK140 )
| ( sK63(powerset(sK62)) = X0 )
| ~ iPr_def_20
| ~ in(X0,powerset(sK62))
| ~ subset(sK63(powerset(sK62)),X0) ),
inference(superposition,[status(thm)],[c_12479,c_123600]) ).
tcf(c_145625,plain,
( in(sK63(powerset(sK62)),powerset(sK62))
| ( powerset(sK62) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_12479,c_123602]) ).
tcf(c_145626,plain,
! [X0: $i,X1: $i] :
( ( powerset(X0) = sK140 )
| ( sK111(powerset(X0)) = X1 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega)
| ~ in(X1,powerset(X0))
| ~ subset(sK111(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_12479,c_240]) ).
tcf(c_145627,plain,
! [X0: $i,X1: $i] :
( ( powerset(X0) = sK140 )
| ( sK67(powerset(X0)) = X1 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega)
| ~ in(X1,powerset(X0))
| ~ subset(sK67(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_12479,c_143]) ).
tcf(c_145628,plain,
! [X0: $i,X1: $i] :
( ( powerset(X0) = sK140 )
| ( sK72(powerset(X0)) = X1 )
| ~ iPr_def_18
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,powerset(X0))
| ~ subset(sK72(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_12479,c_123596]) ).
tcf(c_145629,plain,
! [X0: $i,X1: $i] :
( sP15
| ( powerset(X0) = sK140 )
| ( sK114(powerset(X0)) = X1 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,powerset(X0))
| ~ subset(sK114(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_12479,c_248]) ).
tcf(c_145630,plain,
! [X0: $i,X1: $i] :
( ( powerset(X0) = sK140 )
| ( sK119(powerset(X0)) = X1 )
| ~ finite(X0)
| ~ in(X1,powerset(X0))
| ~ subset(sK119(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_12479,c_308]) ).
tcf(c_145631,plain,
! [X0: $i] :
( in(sK111(powerset(X0)),powerset(X0))
| ( powerset(X0) = sK140 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_12479,c_239]) ).
tcf(c_145632,plain,
! [X0: $i] :
( in(sK67(powerset(X0)),powerset(X0))
| ( powerset(X0) = sK140 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_12479,c_142]) ).
tcf(c_145633,plain,
! [X0: $i] :
( in(sK72(powerset(X0)),powerset(X0))
| ( powerset(X0) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_12479,c_123598]) ).
tcf(c_145634,plain,
! [X0: $i] :
( sP15
| in(sK114(powerset(X0)),powerset(X0))
| ( powerset(X0) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_12479,c_247]) ).
tcf(c_145635,plain,
! [X0: $i] :
( in(sK119(powerset(X0)),powerset(X0))
| ( powerset(X0) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_12479,c_307]) ).
tcf(c_145638,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(sK254(X0)) = sK140 )
| ( sK255(powerset(sK254(X0))) = X1 )
| ~ sP31(X2,X0)
| ~ in(sK254(X0),omega)
| ~ in(X1,powerset(sK254(X0)))
| ~ subset(sK255(powerset(sK254(X0))),X1) ),
inference(superposition,[status(thm)],[c_12479,c_826]) ).
tcf(c_145639,plain,
! [X0: $i,X1: $i] :
( in(sK255(powerset(sK254(X0))),powerset(sK254(X0)))
| ( powerset(sK254(X0)) = sK140 )
| ~ sP31(X1,X0)
| ~ in(sK254(X0),omega) ),
inference(superposition,[status(thm)],[c_12479,c_825]) ).
tcf(c_145640,plain,
! [X0: $i] :
( ( powerset(sK261) = sK140 )
| ( sK262(powerset(sK261)) = X0 )
| ~ iPr_def_14
| ~ in(X0,powerset(sK261))
| ~ subset(sK262(powerset(sK261)),X0) ),
inference(superposition,[status(thm)],[c_12479,c_123589]) ).
tcf(c_145641,plain,
( in(sK262(powerset(sK261)),powerset(sK261))
| ( powerset(sK261) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_12479,c_123591]) ).
tcf(c_145774,plain,
! [X0: $i] :
( in(X0,sK303)
| ( sK125(sK303) = sK140 )
| ( apply(sK126(sK303),X0) = sK140 )
| ~ function(sK126(sK303))
| ~ relation(sK126(sK303)) ),
inference(superposition,[status(thm)],[c_144647,c_906]) ).
tcf(c_145775,plain,
( ( sK125(sK303) = sK140 )
| ( relation_rng(sK126(sK303)) = sK140 )
| ~ relation(sK126(sK303))
| ( sK140 != sK303 ) ),
inference(superposition,[status(thm)],[c_144647,c_478]) ).
tcf(c_145776,plain,
( ( sK126(sK303) = sK140 )
| ( sK125(sK303) = sK140 )
| ~ relation(sK126(sK303))
| ( sK140 != sK303 ) ),
inference(superposition,[status(thm)],[c_144647,c_475]) ).
tcf(c_145791,plain,
( sP15
| in(sK114(sK64),sK64)
| ~ sP7 ),
inference(global_subsumption_just,[status(thm)],[c_144726,c_132,c_144726]) ).
tcf(c_145803,plain,
! [X0: $i] :
( in(X0,sK313)
| ( sK125(sK313) = sK140 )
| ( apply(sK126(sK313),X0) = sK140 )
| ~ function(sK126(sK313))
| ~ relation(sK126(sK313)) ),
inference(superposition,[status(thm)],[c_144797,c_906]) ).
tcf(c_145804,plain,
( ( sK125(sK313) = sK140 )
| ( relation_rng(sK126(sK313)) = sK140 )
| ~ relation(sK126(sK313))
| ( sK140 != sK313 ) ),
inference(superposition,[status(thm)],[c_144797,c_478]) ).
tcf(c_145805,plain,
( ( sK126(sK313) = sK140 )
| ( sK125(sK313) = sK140 )
| ~ relation(sK126(sK313))
| ( sK140 != sK313 ) ),
inference(superposition,[status(thm)],[c_144797,c_475]) ).
tcf(c_145824,plain,
! [X0: $i] :
( in(X0,sK346)
| ( sK125(sK346) = sK140 )
| ( apply(sK126(sK346),X0) = sK140 )
| ~ function(sK126(sK346))
| ~ relation(sK126(sK346)) ),
inference(superposition,[status(thm)],[c_144944,c_906]) ).
tcf(c_145825,plain,
( ( sK125(sK346) = sK140 )
| ( relation_rng(sK126(sK346)) = sK140 )
| ~ relation(sK126(sK346))
| ( sK140 != sK346 ) ),
inference(superposition,[status(thm)],[c_144944,c_478]) ).
tcf(c_145826,plain,
( ( sK126(sK346) = sK140 )
| ( sK125(sK346) = sK140 )
| ~ relation(sK126(sK346))
| ( sK140 != sK346 ) ),
inference(superposition,[status(thm)],[c_144944,c_475]) ).
tcf(c_145845,plain,
! [X0: $i] :
( in(X0,sK358)
| ( sK125(sK358) = sK140 )
| ( apply(sK126(sK358),X0) = sK140 )
| ~ function(sK126(sK358))
| ~ relation(sK126(sK358)) ),
inference(superposition,[status(thm)],[c_144947,c_906]) ).
tcf(c_145846,plain,
( ( sK125(sK358) = sK140 )
| ( relation_rng(sK126(sK358)) = sK140 )
| ~ relation(sK126(sK358))
| ( sK140 != sK358 ) ),
inference(superposition,[status(thm)],[c_144947,c_478]) ).
tcf(c_145847,plain,
( ( sK126(sK358) = sK140 )
| ( sK125(sK358) = sK140 )
| ~ relation(sK126(sK358))
| ( sK140 != sK358 ) ),
inference(superposition,[status(thm)],[c_144947,c_475]) ).
tcf(c_145862,plain,
( in(sK72(sK64),sK64)
| ~ sP7
| ~ iPr_def_19 ),
inference(global_subsumption_just,[status(thm)],[c_144820,c_132,c_144820]) ).
tcf(c_145863,plain,
( in(sK72(sK64),sK64)
| ~ iPr_def_19
| ~ sP7 ),
inference(renaming,[status(thm)],[c_145862]) ).
tcf(c_145876,plain,
! [X0: $i] :
( disjoint(fiber(X0,sK318(X0,omega)),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140))
| ~ is_well_founded_in(X0,sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145175,c_1058]) ).
tcf(c_145877,plain,
! [X0: $i] :
( in(sK318(X0,omega),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140))
| ~ is_well_founded_in(X0,sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145175,c_1057]) ).
tcf(c_145878,plain,
( in(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145175,c_369]) ).
tcf(c_145879,plain,
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145175,c_371]) ).
tcf(c_145880,plain,
( ( set_difference(omega,sK116(sK140)) = sK140 )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145175,c_386]) ).
tcf(c_145881,plain,
! [X0: $i] :
( ordinal_subset(sK128(omega),X0)
| ( sK140 = omega )
| ~ ordinal(X0)
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140))
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145175,c_370]) ).
tcf(c_145920,plain,
! [X0: $i] :
( disjoint(fiber(X0,sK318(X0,omega)),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140))
| ~ is_well_founded_in(X0,sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145503,c_1058]) ).
tcf(c_145921,plain,
! [X0: $i] :
( in(sK318(X0,omega),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140))
| ~ is_well_founded_in(X0,sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145503,c_1057]) ).
tcf(c_145922,plain,
( in(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145503,c_369]) ).
tcf(c_145923,plain,
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145503,c_371]) ).
tcf(c_145924,plain,
( ( set_difference(omega,sK300(sK140)) = sK140 )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145503,c_386]) ).
tcf(c_145925,plain,
! [X0: $i] :
( ordinal_subset(sK128(omega),X0)
| ( sK140 = omega )
| ~ ordinal(X0)
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140))
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145503,c_370]) ).
tcf(c_145962,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(X0))
| ( sK125(powerset(X0)) = sK140 )
| ( apply(sK126(powerset(X0)),X1) = sK140 )
| ~ function(sK126(powerset(X0)))
| ~ relation(sK126(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145193,c_906]) ).
tcf(c_145963,plain,
! [X0: $i] :
( ( sK125(powerset(X0)) = sK140 )
| ( relation_rng(sK126(powerset(X0))) = sK140 )
| ~ relation(sK126(powerset(X0)))
| ( powerset(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_145193,c_478]) ).
tcf(c_145964,plain,
! [X0: $i] :
( ( sK126(powerset(X0)) = sK140 )
| ( sK125(powerset(X0)) = sK140 )
| ~ relation(sK126(powerset(X0)))
| ( powerset(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_145193,c_475]) ).
tcf(c_146006,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,set_difference(X1,X2))),set_difference(X1,X2))
| ( set_difference(X1,X2) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_383,c_1058]) ).
tcf(c_146007,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,set_difference(X1,X2)),set_difference(X1,X2))
| ( set_difference(X1,X2) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_383,c_1057]) ).
tcf(c_146008,plain,
! [X0: $i,X1: $i] :
( in(sK128(set_difference(X0,X1)),set_difference(X0,X1))
| ( set_difference(X0,X1) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_383,c_369]) ).
tcf(c_146009,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(set_difference(X0,X1)))
| ( set_difference(X0,X1) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_383,c_371]) ).
tcf(c_146010,plain,
! [X0: $i,X1: $i] : set_difference(set_difference(X0,X1),X0) = sK140,
inference(superposition,[status(thm)],[c_383,c_386]) ).
tcf(c_146011,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),X1) = sK140 )
| ( set_difference(unordered_pair(X0,X0),X1) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_383,c_397]) ).
tcf(c_146012,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(set_difference(X1,X2)),X0)
| ( set_difference(X1,X2) = sK140 )
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_383,c_370]) ).
tcf(c_146038,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,X1)),X1)
| ( X1 = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_498,c_1058]) ).
tcf(c_146039,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,X1),X1)
| ( X1 = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_498,c_1057]) ).
tcf(c_146040,plain,
! [X0: $i,X1: $i] :
( in(sK128(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_498,c_369]) ).
tcf(c_146041,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(X0))
| ( X0 = sK140 )
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_498,c_371]) ).
tcf(c_146042,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_union2(X0,X1)) = sK140,
inference(superposition,[status(thm)],[c_498,c_386]) ).
tcf(c_146043,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(X0),X2)
| ( X0 = sK140 )
| ~ ordinal(X2)
| ~ in(X2,X0)
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_498,c_370]) ).
tcf(c_146068,plain,
! [X0: $i,X1: $i] : set_difference(sK140,set_difference(X0,X1)) = sK140,
inference(superposition,[status(thm)],[c_146010,c_146010]) ).
tcf(c_146070,plain,
! [X0: $i,X1: $i] : subset(sK140,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_146010,c_383]) ).
tcf(c_146071,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(X0,X1),X0)
| ( set_difference(set_difference(X0,X1),sK140) != sK140 ) ),
inference(superposition,[status(thm)],[c_146010,c_625]) ).
tcf(c_146080,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_union2(X0,X1))
| ( set_difference(X0,sK140) != sK140 ) ),
inference(superposition,[status(thm)],[c_146042,c_625]) ).
tcf(c_146082,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,set_union2(X0,X1))
| ( X0 != sK140 ) ),
inference(light_normalisation,[status(thm)],[c_146080,c_675]) ).
tcf(c_146090,plain,
! [X0: $i] : disjoint(sK140,set_union2(sK140,X0)),
inference(equality_resolution,[status(thm)],[c_146082]) ).
tcf(c_146098,plain,
( in(sK119(sK64),sK64)
| ~ sP7 ),
inference(global_subsumption_just,[status(thm)],[c_144454,c_1282,c_1360,c_132,c_144454]) ).
tcf(c_146123,plain,
! [X0: $i] : element(sK140,powerset(X0)),
inference(light_normalisation,[status(thm)],[c_691,c_144635]) ).
tcf(c_146146,plain,
! [X0: $i] :
( function(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_785]) ).
tcf(c_146155,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_799]) ).
tcf(c_146160,plain,
! [X0: $i,X1: $i] :
( ( sK125(unordered_pair(X0,X1)) = sK140 )
| ( relation_dom(sK126(unordered_pair(X0,X1))) = unordered_pair(X0,X1) ) ),
inference(superposition,[status(thm)],[c_353,c_935]) ).
tcf(c_146161,plain,
~ empty(powerset(sK140)),
inference(superposition,[status(thm)],[c_314,c_935]) ).
tcf(c_146165,plain,
in(sK140,powerset(sK140)),
inference(superposition,[status(thm)],[c_314,c_939]) ).
tcf(c_146166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X3,relation_inverse_image(X0,unordered_pair(apply(X0,X3),X4)))
| ( X2 = sK140 )
| ~ function(X0)
| ~ in(X3,X1)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_939,c_423]) ).
tcf(c_146167,plain,
! [X0: $i] : sK125(unordered_pair(sK140,X0)) = sK140,
inference(superposition,[status(thm)],[c_939,c_144395]) ).
tcf(c_146168,plain,
! [X0: $i] :
( ordinal(sK263(unordered_pair(sK140,X0)))
| ( unordered_pair(sK140,X0) = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_939,c_846]) ).
tcf(c_146169,plain,
! [X0: $i] :
( being_limit_ordinal(sK263(unordered_pair(sK140,X0)))
| ( unordered_pair(sK140,X0) = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_939,c_845]) ).
tcf(c_146170,plain,
! [X0: $i] :
( subset(omega,unordered_pair(sK140,X0))
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_939,c_850]) ).
tcf(c_146192,plain,
sK125(powerset(sK140)) = sK140,
inference(superposition,[status(thm)],[c_146165,c_144395]) ).
tcf(c_146193,plain,
( ordinal(sK263(powerset(sK140)))
| ( powerset(sK140) = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146165,c_846]) ).
tcf(c_146194,plain,
( being_limit_ordinal(sK263(powerset(sK140)))
| ( powerset(sK140) = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146165,c_845]) ).
tcf(c_146195,plain,
( subset(omega,powerset(sK140))
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146165,c_850]) ).
tcf(c_146208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X3,relation_inverse_image(X0,unordered_pair(X4,apply(X0,X3))))
| ( X2 = sK140 )
| ~ function(X0)
| ~ in(X3,X1)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_940,c_423]) ).
tcf(c_146209,plain,
! [X0: $i] : sK125(unordered_pair(X0,sK140)) = sK140,
inference(superposition,[status(thm)],[c_940,c_144395]) ).
tcf(c_146210,plain,
! [X0: $i] :
( ordinal(sK263(unordered_pair(X0,sK140)))
| ( unordered_pair(X0,sK140) = omega )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_940,c_846]) ).
tcf(c_146211,plain,
! [X0: $i] :
( being_limit_ordinal(sK263(unordered_pair(X0,sK140)))
| ( unordered_pair(X0,sK140) = omega )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_940,c_845]) ).
tcf(c_146212,plain,
! [X0: $i] :
( subset(omega,unordered_pair(X0,sK140))
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_940,c_850]) ).
tcf(c_146240,plain,
! [X0: $i] :
( disjoint(fiber(X0,sK318(X0,omega)),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140))
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146195,c_1058]) ).
tcf(c_146241,plain,
! [X0: $i] :
( in(sK318(X0,omega),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140))
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146195,c_1057]) ).
tcf(c_146242,plain,
( in(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146195,c_369]) ).
tcf(c_146243,plain,
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146195,c_371]) ).
tcf(c_146244,plain,
( ( set_difference(omega,powerset(sK140)) = sK140 )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146195,c_386]) ).
tcf(c_146245,plain,
! [X0: $i] :
( ordinal_subset(sK128(omega),X0)
| ( sK140 = omega )
| ~ ordinal(X0)
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140))
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_146195,c_370]) ).
tcf(c_146297,plain,
! [X0: $i] :
( ( set_difference(powerset(sK140),X0) = sK140 )
| ( set_difference(powerset(sK140),X0) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_383,c_144406]) ).
tcf(c_146299,plain,
( ( sK140 = omega )
| ( powerset(sK140) = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146195,c_144406]) ).
tcf(c_146320,plain,
! [X0: $i] :
( ordinal(sK128(X0))
| ( set_difference(X0,sK140) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_675,c_146009]) ).
tcf(c_146330,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(X0,X1),X0)
| ( set_difference(X0,X1) != sK140 ) ),
inference(demodulation,[status(thm)],[c_146071,c_675]) ).
tcf(c_146337,plain,
! [X0: $i] : disjoint(set_difference(sK140,X0),sK140),
inference(superposition,[status(thm)],[c_674,c_146330]) ).
tcf(c_146338,plain,
! [X0: $i] :
( disjoint(set_difference(X0,sK140),X0)
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_675,c_146330]) ).
tcf(c_146339,plain,
! [X0: $i] : disjoint(set_difference(X0,X0),X0),
inference(superposition,[status(thm)],[c_12910,c_146330]) ).
tcf(c_146340,plain,
! [X0: $i,X1: $i] : disjoint(set_difference(set_difference(X0,X1),X0),set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_146010,c_146330]) ).
tcf(c_146341,plain,
! [X0: $i,X1: $i] : disjoint(set_difference(X0,set_union2(X0,X1)),X0),
inference(superposition,[status(thm)],[c_146042,c_146330]) ).
tcf(c_146345,plain,
! [X0: $i,X1: $i] : disjoint(sK140,set_difference(X0,X1)),
inference(light_normalisation,[status(thm)],[c_146340,c_146010]) ).
tcf(c_146359,plain,
! [X0: $i] :
( finite(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_983]) ).
tcf(c_146369,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_1045]) ).
tcf(c_146379,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_1046]) ).
tcf(c_146389,plain,
! [X0: $i] :
( ordinal(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_1047]) ).
tcf(c_146399,plain,
( epsilon_transitive(sK62)
| ~ sP8 ),
inference(superposition,[status(thm)],[c_131,c_1049]) ).
tcf(c_146400,plain,
( epsilon_transitive(sK66)
| ~ sP6 ),
inference(superposition,[status(thm)],[c_144,c_1049]) ).
tcf(c_146401,plain,
( epsilon_transitive(sK110)
| ~ sP15 ),
inference(superposition,[status(thm)],[c_241,c_1049]) ).
tcf(c_146402,plain,
! [X0: $i] :
( epsilon_transitive(sK128(X0))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_144621,c_1049]) ).
tcf(c_146411,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK128(set_difference(X0,X1)))
| ( set_difference(X0,X1) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_146009,c_1049]) ).
tcf(c_146466,plain,
! [X0: $i,X1: $i] :
( in(sK128(X0),X0)
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_146389,c_146040]) ).
tcf(c_146467,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(X0))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_146389,c_146041]) ).
tcf(c_146507,plain,
( subset(omega,powerset(sK140))
| ~ being_limit_ordinal(unordered_pair(sK140,sK140))
| ~ ordinal(unordered_pair(sK140,sK140)) ),
inference(superposition,[status(thm)],[c_314,c_146170]) ).
tcf(c_146508,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,omega)),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(unordered_pair(sK140,X1))
| ~ ordinal(unordered_pair(sK140,X1))
| ~ is_well_founded_in(X0,unordered_pair(sK140,X1)) ),
inference(superposition,[status(thm)],[c_146170,c_1058]) ).
tcf(c_146509,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,omega),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(unordered_pair(sK140,X1))
| ~ ordinal(unordered_pair(sK140,X1))
| ~ is_well_founded_in(X0,unordered_pair(sK140,X1)) ),
inference(superposition,[status(thm)],[c_146170,c_1057]) ).
tcf(c_146510,plain,
! [X0: $i] :
( in(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146170,c_369]) ).
tcf(c_146511,plain,
! [X0: $i] :
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146170,c_371]) ).
tcf(c_146512,plain,
! [X0: $i] :
( ( set_difference(omega,unordered_pair(sK140,X0)) = sK140 )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146170,c_386]) ).
tcf(c_146513,plain,
( ( sK140 = omega )
| ( unordered_pair(sK140,sK140) = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,sK140))
| ~ ordinal(unordered_pair(sK140,sK140)) ),
inference(superposition,[status(thm)],[c_146170,c_397]) ).
tcf(c_146514,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(omega),X1)
| ( sK140 = omega )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146170,c_370]) ).
tcf(c_146558,plain,
! [X0: $i] :
( ( set_difference(powerset(sK140),X0) = powerset(sK140) )
| ( set_difference(unordered_pair(sK140,sK140),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_314,c_146011]) ).
tcf(c_146560,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ( set_difference(unordered_pair(X0,X0),X1) = sK140 )
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_146011,c_146009]) ).
tcf(c_146561,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),X1) = sK140 )
| ( set_difference(unordered_pair(X0,X0),unordered_pair(X0,X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146011,c_146010]) ).
tcf(c_146562,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),unordered_pair(X0,X0))
| ( set_difference(unordered_pair(X0,X0),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_146011,c_383]) ).
tcf(c_146563,plain,
! [X0: $i,X1: $i] :
( disjoint(unordered_pair(X0,X0),X1)
| ( set_difference(unordered_pair(X0,X0),X1) = sK140 )
| ( set_difference(unordered_pair(X0,X0),unordered_pair(X0,X0)) != sK140 ) ),
inference(superposition,[status(thm)],[c_146011,c_625]) ).
tcf(c_146566,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = sK140 )
| ( set_difference(unordered_pair(X0,X0),unordered_pair(X0,X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146011,c_12910]) ).
tcf(c_146567,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = sK140 )
| ( set_difference(unordered_pair(X0,X0),set_union2(unordered_pair(X0,X0),X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146011,c_146042]) ).
tcf(c_146572,plain,
! [X0: $i,X1: $i] :
( disjoint(unordered_pair(X0,X0),X1)
| ( set_difference(unordered_pair(X0,X0),X1) = sK140 ) ),
inference(ground_joinability,[status(thm)],[c_146563,c_12910]) ).
tcf(c_146582,plain,
( epsilon_connected(sK62)
| ~ sP8 ),
inference(superposition,[status(thm)],[c_131,c_1050]) ).
tcf(c_146583,plain,
( epsilon_connected(sK66)
| ~ sP6 ),
inference(superposition,[status(thm)],[c_144,c_1050]) ).
tcf(c_146584,plain,
( epsilon_connected(sK110)
| ~ sP15 ),
inference(superposition,[status(thm)],[c_241,c_1050]) ).
tcf(c_146585,plain,
! [X0: $i] :
( epsilon_connected(sK128(X0))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_144621,c_1050]) ).
tcf(c_146594,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK128(set_difference(X0,X1)))
| ( set_difference(X0,X1) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_146009,c_1050]) ).
tcf(c_146616,plain,
! [X0: $i] :
( one_to_one(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_84200]) ).
tcf(c_146650,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,omega)),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(unordered_pair(X1,sK140))
| ~ ordinal(unordered_pair(X1,sK140))
| ~ is_well_founded_in(X0,unordered_pair(X1,sK140)) ),
inference(superposition,[status(thm)],[c_146212,c_1058]) ).
tcf(c_146651,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,omega),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(unordered_pair(X1,sK140))
| ~ ordinal(unordered_pair(X1,sK140))
| ~ is_well_founded_in(X0,unordered_pair(X1,sK140)) ),
inference(superposition,[status(thm)],[c_146212,c_1057]) ).
tcf(c_146652,plain,
! [X0: $i] :
( in(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146212,c_369]) ).
tcf(c_146653,plain,
! [X0: $i] :
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146212,c_371]) ).
tcf(c_146654,plain,
! [X0: $i] :
( ( set_difference(omega,unordered_pair(X0,sK140)) = sK140 )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146212,c_386]) ).
tcf(c_146656,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(omega),X1)
| ( sK140 = omega )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146212,c_370]) ).
tcf(c_146708,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X1,sK318(X0,relation_inverse_image(X1,X2))),X2)
| ( X4 = sK140 )
| ( relation_inverse_image(X1,X2) = sK140 )
| ~ function(X1)
| ~ relation(X0)
| ~ quasi_total(X1,X3,X4)
| ~ relation_of2_as_subset(X1,X3,X4)
| ~ is_well_founded_in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_144619,c_425]) ).
tcf(c_146709,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK318(X0,relation_inverse_image(X1,X2)),X3)
| ( X4 = sK140 )
| ( relation_inverse_image(X1,X2) = sK140 )
| ~ function(X1)
| ~ relation(X0)
| ~ quasi_total(X1,X3,X4)
| ~ relation_of2_as_subset(X1,X3,X4)
| ~ is_well_founded_in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_144619,c_424]) ).
tcf(c_146727,plain,
( in(sK67(sK64),sK64)
| ~ in(sK140,sK66)
| ~ sP7
| ~ sP6 ),
inference(global_subsumption_just,[status(thm)],[c_144934,c_132,c_144934]) ).
tcf(c_146728,plain,
( in(sK67(sK64),sK64)
| ~ sP6
| ~ sP7
| ~ in(sK140,sK66) ),
inference(renaming,[status(thm)],[c_146727]) ).
tcf(c_146737,plain,
( in(sK111(sK64),sK64)
| ~ in(sK140,sK110)
| ~ sP7
| ~ sP15 ),
inference(global_subsumption_just,[status(thm)],[c_144970,c_132,c_144970]) ).
tcf(c_146738,plain,
( in(sK111(sK64),sK64)
| ~ sP15
| ~ sP7
| ~ in(sK140,sK110) ),
inference(renaming,[status(thm)],[c_146737]) ).
tcf(c_146759,plain,
( ( sK125(unordered_pair(sK140,sK140)) = sK140 )
| ( relation_dom(sK126(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_314,c_146160]) ).
tcf(c_146760,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,unordered_pair(X0,X1))
| ( sK125(unordered_pair(X0,X1)) = sK140 )
| ( apply(sK126(unordered_pair(X0,X1)),X2) = sK140 )
| ~ function(sK126(unordered_pair(X0,X1)))
| ~ relation(sK126(unordered_pair(X0,X1))) ),
inference(superposition,[status(thm)],[c_146160,c_906]) ).
tcf(c_146761,plain,
! [X0: $i,X1: $i] :
( ( sK125(unordered_pair(X0,X1)) = sK140 )
| ( relation_rng(sK126(unordered_pair(X0,X1))) = sK140 )
| ~ relation(sK126(unordered_pair(X0,X1)))
| ( unordered_pair(X0,X1) != sK140 ) ),
inference(superposition,[status(thm)],[c_146160,c_478]) ).
tcf(c_146762,plain,
! [X0: $i,X1: $i] :
( ( sK126(unordered_pair(X0,X1)) = sK140 )
| ( sK125(unordered_pair(X0,X1)) = sK140 )
| ~ relation(sK126(unordered_pair(X0,X1)))
| ( unordered_pair(X0,X1) != sK140 ) ),
inference(superposition,[status(thm)],[c_146160,c_475]) ).
tcf(c_146789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP3(relation_inverse_image(X0,X3))
| in(apply(X0,sK58(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_122,c_425]) ).
tcf(c_146790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP3(relation_inverse_image(X0,X3))
| in(sK58(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_122,c_424]) ).
tcf(c_146791,plain,
sP3(sK140),
inference(superposition,[status(thm)],[c_122,c_580]) ).
tcf(c_146804,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( apply(sK115(X0),X1) = sK140 )
| ~ function(sK115(X0))
| ~ relation(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_906]) ).
tcf(c_146805,plain,
! [X0: $i] :
( ( relation_rng(sK115(X0)) = sK140 )
| ~ relation(sK115(X0))
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_251,c_478]) ).
tcf(c_146806,plain,
! [X0: $i] :
( ( sK115(X0) = sK140 )
| ~ relation(sK115(X0))
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_251,c_475]) ).
tcf(c_146807,plain,
! [X0: $i] :
( ( sK115(X0) = sK140 )
| ( X0 != sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_146806,c_249]) ).
tcf(c_146810,plain,
! [X0: $i] :
( ( relation_rng(sK115(X0)) = sK140 )
| ( X0 != sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_146805,c_249]) ).
tcf(c_146813,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( apply(sK115(X0),X1) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_146804,c_250,c_249]) ).
tcf(c_146872,plain,
( epsilon_connected(sK263(sK116(sK140)))
| ( sK116(sK140) = omega )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145173,c_1050]) ).
tcf(c_146873,plain,
( epsilon_transitive(sK263(sK116(sK140)))
| ( sK116(sK140) = omega )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145173,c_1049]) ).
tcf(c_146904,plain,
( epsilon_connected(sK263(sK300(sK140)))
| ( sK300(sK140) = omega )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145501,c_1050]) ).
tcf(c_146905,plain,
( epsilon_transitive(sK263(sK300(sK140)))
| ( sK300(sK140) = omega )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145501,c_1049]) ).
tcf(c_146941,plain,
! [X0: $i] :
( in(sK128(X0),X0)
| ( set_difference(X0,sK140) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_675,c_146008]) ).
tcf(c_146944,plain,
! [X0: $i,X1: $i] :
( in(sK128(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ( set_difference(unordered_pair(X0,X0),X1) = sK140 )
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_146011,c_146008]) ).
tcf(c_146956,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ordinal(relation_inverse_image(X0,X3))
| in(apply(X0,sK127(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_367,c_425]) ).
tcf(c_146957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ordinal(relation_inverse_image(X0,X3))
| in(sK127(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_367,c_424]) ).
tcf(c_146979,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( apply(identity_relation(X0),X1) = sK140 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_906]) ).
tcf(c_146980,plain,
! [X0: $i] :
( ( relation_rng(identity_relation(X0)) = sK140 )
| ~ relation(identity_relation(X0))
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_489,c_478]) ).
tcf(c_146981,plain,
! [X0: $i] :
( ( identity_relation(X0) = sK140 )
| ~ relation(identity_relation(X0))
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_489,c_475]) ).
tcf(c_146982,plain,
! [X0: $i] :
( ( identity_relation(X0) = sK140 )
| ( X0 != sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_146981,c_1101]) ).
tcf(c_146986,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( apply(identity_relation(X0),X1) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_146979,c_1100,c_1101]) ).
tcf(c_146991,plain,
~ iPr_def_16,
inference(global_subsumption_just,[status(thm)],[c_123593,c_1282,c_1357,c_123764]) ).
tcf(c_146993,plain,
! [X0: $i] :
( ( relation_dom(identity_relation(X0)) = sK140 )
| ~ relation(identity_relation(X0))
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_490,c_477]) ).
tcf(c_147008,plain,
( epsilon_connected(sK263(powerset(sK140)))
| ( powerset(sK140) = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146193,c_1050]) ).
tcf(c_147009,plain,
( epsilon_transitive(sK263(powerset(sK140)))
| ( powerset(sK140) = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146193,c_1049]) ).
tcf(c_147041,plain,
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ ordinal(powerset(sK140))
| ~ being_limit_ordinal(unordered_pair(sK140,sK140)) ),
inference(superposition,[status(thm)],[c_314,c_146511]) ).
tcf(c_147053,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(X1),X0)
| ( X1 = sK140 )
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_144744,c_333,c_144744]) ).
tcf(c_147071,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( set_difference(fiber(X0,sK318(X0,X1)),set_difference(fiber(X0,sK318(X0,X1)),X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144761,c_626]) ).
tcf(c_147085,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,sK140) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_146146,c_145538]) ).
tcf(c_147086,plain,
! [X0: $i] :
( sP13(X0)
| ( sK125(relation_dom(sK108(X0))) = sK140 )
| ( apply(sK108(X0),sK140) = sK140 )
| ~ relation(sK108(X0)) ),
inference(superposition,[status(thm)],[c_232,c_145538]) ).
tcf(c_147087,plain,
! [X0: $i] :
( ( sK125(relation_dom(sK115(X0))) = sK140 )
| ( apply(sK115(X0),sK140) = sK140 )
| ~ relation(sK115(X0)) ),
inference(superposition,[status(thm)],[c_250,c_145538]) ).
tcf(c_147088,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( sK125(relation_dom(sK126(X0))) = sK140 )
| ( apply(sK126(X0),sK140) = sK140 )
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_356,c_145538]) ).
tcf(c_147089,plain,
! [X0: $i] :
( ( sK125(relation_dom(identity_relation(X0))) = sK140 )
| ( apply(identity_relation(X0),sK140) = sK140 )
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1100,c_145538]) ).
tcf(c_147090,plain,
( ( sK125(relation_dom(sK240)) = sK140 )
| ( apply(sK240,sK140) = sK140 )
| ~ relation(sK240) ),
inference(superposition,[status(thm)],[c_784,c_145538]) ).
tcf(c_147091,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(sK312(X0,X1))) = sK140 )
| ( apply(sK312(X0,X1),sK140) = sK140 )
| ~ relation(sK312(X0,X1)) ),
inference(superposition,[status(thm)],[c_1020,c_145538]) ).
tcf(c_147092,plain,
( ( sK125(relation_dom(sK335)) = sK140 )
| ( apply(sK335,sK140) = sK140 )
| ~ relation(sK335) ),
inference(superposition,[status(thm)],[c_1150,c_145538]) ).
tcf(c_147093,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(sK347(X0,X1))) = sK140 )
| ( apply(sK347(X0,X1),sK140) = sK140 )
| ~ relation(sK347(X0,X1)) ),
inference(superposition,[status(thm)],[c_1238,c_145538]) ).
tcf(c_147094,plain,
( ( sK125(relation_dom(sK140)) = sK140 )
| ( apply(sK140,sK140) = sK140 )
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_144215,c_145538]) ).
tcf(c_147095,plain,
( ( sK125(sK140) = sK140 )
| ( apply(sK140,sK140) = sK140 )
| ~ relation(sK140) ),
inference(light_normalisation,[status(thm)],[c_147094,c_470]) ).
tcf(c_147096,plain,
( ( sK125(relation_dom(sK335)) = sK140 )
| ( apply(sK335,sK140) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147092,c_1149]) ).
tcf(c_147099,plain,
( ( sK125(relation_dom(sK240)) = sK140 )
| ( apply(sK240,sK140) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147090,c_783]) ).
tcf(c_147102,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( apply(identity_relation(X0),sK140) = sK140 )
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_147089,c_489]) ).
tcf(c_147103,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( apply(identity_relation(X0),sK140) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147102,c_1101]) ).
tcf(c_147106,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( apply(sK115(X0),sK140) = sK140 )
| ~ relation(sK115(X0)) ),
inference(light_normalisation,[status(thm)],[c_147087,c_251]) ).
tcf(c_147107,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( apply(sK115(X0),sK140) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147106,c_249]) ).
tcf(c_147114,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(sK347(X0,X1))) = sK140 )
| ( apply(sK347(X0,X1),sK140) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147093,c_1237]) ).
tcf(c_147117,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(sK312(X0,X1))) = sK140 )
| ( apply(sK312(X0,X1),sK140) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147091,c_1019]) ).
tcf(c_147153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation(relation_inverse_image(X0,X3))
| in(apply(X0,sK163(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_561,c_425]) ).
tcf(c_147154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation(relation_inverse_image(X0,X3))
| in(sK163(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_561,c_424]) ).
tcf(c_147177,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_641]) ).
tcf(c_147178,plain,
! [X0: $i] :
( empty(X0)
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_641]) ).
tcf(c_147179,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_641]) ).
tcf(c_147181,plain,
( empty(sK241)
| ( sK125(sK241) = sK140 )
| ~ empty(sK126(sK241)) ),
inference(superposition,[status(thm)],[c_144638,c_641]) ).
tcf(c_147182,plain,
( empty(sK242)
| ( sK125(sK242) = sK140 )
| ~ empty(sK126(sK242)) ),
inference(superposition,[status(thm)],[c_144641,c_641]) ).
tcf(c_147183,plain,
( empty(sK303)
| ( sK125(sK303) = sK140 )
| ~ empty(sK126(sK303)) ),
inference(superposition,[status(thm)],[c_144647,c_641]) ).
tcf(c_147184,plain,
( empty(sK313)
| ( sK125(sK313) = sK140 )
| ~ empty(sK126(sK313)) ),
inference(superposition,[status(thm)],[c_144797,c_641]) ).
tcf(c_147185,plain,
( empty(sK346)
| ( sK125(sK346) = sK140 )
| ~ empty(sK126(sK346)) ),
inference(superposition,[status(thm)],[c_144944,c_641]) ).
tcf(c_147186,plain,
( empty(sK358)
| ( sK125(sK358) = sK140 )
| ~ empty(sK126(sK358)) ),
inference(superposition,[status(thm)],[c_144947,c_641]) ).
tcf(c_147187,plain,
! [X0: $i] :
( empty(powerset(X0))
| ( sK125(powerset(X0)) = sK140 )
| ~ empty(sK126(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145193,c_641]) ).
tcf(c_147188,plain,
! [X0: $i,X1: $i] :
( empty(unordered_pair(X0,X1))
| ( sK125(unordered_pair(X0,X1)) = sK140 )
| ~ empty(sK126(unordered_pair(X0,X1))) ),
inference(superposition,[status(thm)],[c_146160,c_641]) ).
tcf(c_147189,plain,
! [X0: $i] :
( one_to_one(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_641,c_84200]) ).
tcf(c_147190,plain,
! [X0: $i] :
( ordinal(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_641,c_1047]) ).
tcf(c_147191,plain,
! [X0: $i] :
( epsilon_connected(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_641,c_1046]) ).
tcf(c_147192,plain,
! [X0: $i] :
( epsilon_transitive(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_641,c_1045]) ).
tcf(c_147193,plain,
! [X0: $i] :
( finite(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_641,c_983]) ).
tcf(c_147195,plain,
! [X0: $i] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_641,c_785]) ).
tcf(c_147196,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_641,c_575]) ).
tcf(c_147215,plain,
( ( sK125(sK358) = sK140 )
| ~ empty(sK126(sK358)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147186,c_1276]) ).
tcf(c_147218,plain,
( ( sK125(sK346) = sK140 )
| ~ empty(sK126(sK346)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147185,c_1223]) ).
tcf(c_147221,plain,
( ( sK125(sK313) = sK140 )
| ~ empty(sK126(sK313)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147184,c_1025]) ).
tcf(c_147224,plain,
( ( sK125(sK303) = sK140 )
| ~ empty(sK126(sK303)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147183,c_975]) ).
tcf(c_147227,plain,
( ( sK125(sK242) = sK140 )
| ~ empty(sK126(sK242)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147182,c_790]) ).
tcf(c_147230,plain,
( ( sK125(sK241) = sK140 )
| ~ empty(sK126(sK241)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147181,c_789]) ).
tcf(c_147233,plain,
! [X0: $i] :
( ( sK125(powerset(X0)) = sK140 )
| ~ empty(sK126(powerset(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147187,c_695]) ).
tcf(c_147240,plain,
! [X0: $i,X1: $i] :
( ( sK125(unordered_pair(X0,X1)) = sK140 )
| ~ empty(sK126(unordered_pair(X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147188,c_935]) ).
tcf(c_147253,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_642]) ).
tcf(c_147254,plain,
! [X0: $i] :
( relation(X0)
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_642]) ).
tcf(c_147255,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_642]) ).
tcf(c_147277,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_353,c_694]) ).
tcf(c_147285,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_516,c_710]) ).
tcf(c_147293,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_516,c_711]) ).
tcf(c_147301,plain,
! [X0: $i] :
( ordinal(X0)
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_516,c_712]) ).
tcf(c_147316,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_147196]) ).
tcf(c_147318,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_641,c_147196]) ).
tcf(c_147331,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_147196]) ).
tcf(c_147332,plain,
! [X0: $i] :
( one_to_one(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_84200]) ).
tcf(c_147333,plain,
! [X0: $i] :
( ordinal(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_1047]) ).
tcf(c_147334,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_1046]) ).
tcf(c_147335,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_1045]) ).
tcf(c_147336,plain,
! [X0: $i] :
( finite(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_983]) ).
tcf(c_147337,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_799]) ).
tcf(c_147338,plain,
! [X0: $i] :
( function(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_785]) ).
tcf(c_147339,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_575]) ).
tcf(c_147340,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK198(sK198(X0))) = sK140 )
| ( relation_dom(sK126(sK198(sK198(X0)))) = sK198(sK198(X0)) ) ),
inference(superposition,[status(thm)],[c_147277,c_694]) ).
tcf(c_147341,plain,
! [X0: $i] :
( ( sK125(sK198(powerset(X0))) = sK140 )
| ( relation_dom(sK126(sK198(powerset(X0)))) = sK198(powerset(X0)) ) ),
inference(superposition,[status(thm)],[c_147277,c_695]) ).
tcf(c_147342,plain,
( ( sK125(sK198(sK241)) = sK140 )
| ( relation_dom(sK126(sK198(sK241))) = sK198(sK241) ) ),
inference(superposition,[status(thm)],[c_147277,c_789]) ).
tcf(c_147343,plain,
( ( sK125(sK198(sK242)) = sK140 )
| ( relation_dom(sK126(sK198(sK242))) = sK198(sK242) ) ),
inference(superposition,[status(thm)],[c_147277,c_790]) ).
tcf(c_147344,plain,
( ( sK125(sK198(omega)) = sK140 )
| ( relation_dom(sK126(sK198(omega))) = sK198(omega) ) ),
inference(superposition,[status(thm)],[c_147277,c_842]) ).
tcf(c_147345,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ( relation_dom(sK126(sK198(unordered_pair(X0,X1)))) = sK198(unordered_pair(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_147277,c_935]) ).
tcf(c_147346,plain,
( ( sK125(sK198(sK303)) = sK140 )
| ( relation_dom(sK126(sK198(sK303))) = sK198(sK303) ) ),
inference(superposition,[status(thm)],[c_147277,c_975]) ).
tcf(c_147347,plain,
( ( sK125(sK198(sK313)) = sK140 )
| ( relation_dom(sK126(sK198(sK313))) = sK198(sK313) ) ),
inference(superposition,[status(thm)],[c_147277,c_1025]) ).
tcf(c_147348,plain,
( ( sK125(sK198(sK346)) = sK140 )
| ( relation_dom(sK126(sK198(sK346))) = sK198(sK346) ) ),
inference(superposition,[status(thm)],[c_147277,c_1223]) ).
tcf(c_147349,plain,
( ( sK125(sK198(sK358)) = sK140 )
| ( relation_dom(sK126(sK198(sK358))) = sK198(sK358) ) ),
inference(superposition,[status(thm)],[c_147277,c_1276]) ).
tcf(c_147410,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_642]) ).
tcf(c_147411,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_641]) ).
tcf(c_147412,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_906]) ).
tcf(c_147413,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ( relation_rng(sK126(X0)) = sK140 )
| ~ relation(sK126(X0))
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_147316,c_478]) ).
tcf(c_147414,plain,
! [X0: $i] :
( ( sK126(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ~ relation(sK126(X0))
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_147316,c_475]) ).
tcf(c_147448,plain,
( in(sK128(omega),omega)
| ( sK140 = omega )
| ~ ordinal(powerset(sK140))
| ~ being_limit_ordinal(unordered_pair(sK140,sK140)) ),
inference(superposition,[status(thm)],[c_314,c_146510]) ).
tcf(c_147456,plain,
( ( set_difference(omega,unordered_pair(sK140,sK140)) = sK140 )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(unordered_pair(sK140,sK140)) ),
inference(superposition,[status(thm)],[c_314,c_146512]) ).
tcf(c_147481,plain,
! [X0: $i] :
( relation(sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_642]) ).
tcf(c_147482,plain,
! [X0: $i] :
( empty(sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_641]) ).
tcf(c_147483,plain,
! [X0: $i,X1: $i] :
( in(X1,sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_906]) ).
tcf(c_147484,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( relation_rng(sK126(sK198(X0))) = sK140 )
| ~ relation(sK126(sK198(X0)))
| ( sK198(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147339,c_478]) ).
tcf(c_147485,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK126(sK198(X0)) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ relation(sK126(sK198(X0)))
| ( sK198(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147339,c_475]) ).
tcf(c_147527,plain,
! [X0: $i] :
( ( sK125(relation_dom(sK264(X0))) = sK140 )
| ( apply(sK264(X0),sK140) = sK140 )
| ~ finite(X0)
| ~ relation(sK264(X0)) ),
inference(superposition,[status(thm)],[c_853,c_145538]) ).
tcf(c_147537,plain,
epsilon_transitive(sK199(omega)),
inference(superposition,[status(thm)],[c_696,c_856]) ).
tcf(c_147542,plain,
epsilon_connected(sK199(omega)),
inference(superposition,[status(thm)],[c_696,c_857]) ).
tcf(c_147611,plain,
! [X0: $i] :
( in(sK128(powerset(sK140)),powerset(sK140))
| ( set_difference(powerset(sK140),X0) = sK140 )
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146297,c_146008]) ).
tcf(c_147613,plain,
! [X0: $i] :
( ordinal(sK128(powerset(sK140)))
| ( set_difference(powerset(sK140),X0) = sK140 )
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146297,c_146009]) ).
tcf(c_147614,plain,
! [X0: $i] :
( ( set_difference(powerset(sK140),X0) = sK140 )
| ( set_difference(powerset(sK140),powerset(sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146297,c_146010]) ).
tcf(c_147615,plain,
! [X0: $i] :
( subset(powerset(sK140),powerset(sK140))
| ( set_difference(powerset(sK140),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_146297,c_383]) ).
tcf(c_147616,plain,
! [X0: $i] :
( disjoint(powerset(sK140),X0)
| ( set_difference(powerset(sK140),X0) = sK140 )
| ( set_difference(powerset(sK140),powerset(sK140)) != sK140 ) ),
inference(superposition,[status(thm)],[c_146297,c_625]) ).
tcf(c_147619,plain,
( ( powerset(sK140) = sK140 )
| ( set_difference(powerset(sK140),powerset(sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146297,c_12910]) ).
tcf(c_147620,plain,
! [X0: $i] :
( ( powerset(sK140) = sK140 )
| ( set_difference(powerset(sK140),set_union2(powerset(sK140),X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146297,c_146042]) ).
tcf(c_147627,plain,
! [X0: $i] :
( disjoint(powerset(sK140),X0)
| ( set_difference(powerset(sK140),X0) = sK140 ) ),
inference(ground_joinability,[status(thm)],[c_147616,c_12910]) ).
tcf(c_147637,plain,
ordinal(sK199(omega)),
inference(superposition,[status(thm)],[c_696,c_858]) ).
tcf(c_147642,plain,
! [X0: $i] :
( epsilon_connected(sK268(X0))
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_862,c_1050]) ).
tcf(c_147643,plain,
! [X0: $i] :
( epsilon_transitive(sK268(X0))
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_862,c_1049]) ).
tcf(c_147661,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_943,c_147196]) ).
tcf(c_147662,plain,
! [X0: $i] :
( one_to_one(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_943,c_84200]) ).
tcf(c_147663,plain,
! [X0: $i] :
( ordinal(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_943,c_1047]) ).
tcf(c_147664,plain,
! [X0: $i] :
( epsilon_connected(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_943,c_1046]) ).
tcf(c_147665,plain,
! [X0: $i] :
( epsilon_transitive(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_943,c_1045]) ).
tcf(c_147666,plain,
! [X0: $i] :
( finite(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_943,c_983]) ).
tcf(c_147668,plain,
! [X0: $i] :
( function(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_943,c_785]) ).
tcf(c_147669,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_943,c_575]) ).
tcf(c_147708,plain,
! [X0: $i,X1: $i] :
( quasi_total(sK299(sK140,X0),sK140,X1)
| ~ subset(X0,X1)
| ~ function(sK299(sK140,X0))
| ~ quasi_total(sK299(sK140,X0),sK140,X0) ),
inference(superposition,[status(thm)],[c_964,c_519]) ).
tcf(c_147709,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK299(X0,sK140) = sK140 )
| ~ quasi_total(sK299(X0,sK140),X0,sK140) ),
inference(superposition,[status(thm)],[c_964,c_1077]) ).
tcf(c_147721,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK198(sK302(X0))) = sK140 )
| ( relation_dom(sK126(sK198(sK302(X0)))) = sK198(sK302(X0)) ) ),
inference(superposition,[status(thm)],[c_147277,c_973]) ).
tcf(c_147722,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_353,c_973]) ).
tcf(c_147733,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_147669]) ).
tcf(c_147734,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_147669]) ).
tcf(c_147736,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_641,c_147669]) ).
tcf(c_147737,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_943,c_147669]) ).
tcf(c_147756,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_147669]) ).
tcf(c_147757,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_147196]) ).
tcf(c_147758,plain,
! [X0: $i] :
( one_to_one(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_84200]) ).
tcf(c_147759,plain,
! [X0: $i] :
( ordinal(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_1047]) ).
tcf(c_147760,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_1046]) ).
tcf(c_147761,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_1045]) ).
tcf(c_147762,plain,
! [X0: $i] :
( finite(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_983]) ).
tcf(c_147763,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_799]) ).
tcf(c_147764,plain,
! [X0: $i] :
( function(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_785]) ).
tcf(c_147765,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_575]) ).
tcf(c_147766,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK302(sK198(X0))) = sK140 )
| ( relation_dom(sK126(sK302(sK198(X0)))) = sK302(sK198(X0)) ) ),
inference(superposition,[status(thm)],[c_147722,c_694]) ).
tcf(c_147767,plain,
! [X0: $i] :
( ( sK125(sK302(powerset(X0))) = sK140 )
| ( relation_dom(sK126(sK302(powerset(X0)))) = sK302(powerset(X0)) ) ),
inference(superposition,[status(thm)],[c_147722,c_695]) ).
tcf(c_147768,plain,
( ( sK125(sK302(sK241)) = sK140 )
| ( relation_dom(sK126(sK302(sK241))) = sK302(sK241) ) ),
inference(superposition,[status(thm)],[c_147722,c_789]) ).
tcf(c_147769,plain,
( ( sK125(sK302(sK242)) = sK140 )
| ( relation_dom(sK126(sK302(sK242))) = sK302(sK242) ) ),
inference(superposition,[status(thm)],[c_147722,c_790]) ).
tcf(c_147770,plain,
( ( sK125(sK302(omega)) = sK140 )
| ( relation_dom(sK126(sK302(omega))) = sK302(omega) ) ),
inference(superposition,[status(thm)],[c_147722,c_842]) ).
tcf(c_147771,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK302(unordered_pair(X0,X1))) = sK140 )
| ( relation_dom(sK126(sK302(unordered_pair(X0,X1)))) = sK302(unordered_pair(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_147722,c_935]) ).
tcf(c_147772,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK302(sK302(X0))) = sK140 )
| ( relation_dom(sK126(sK302(sK302(X0)))) = sK302(sK302(X0)) ) ),
inference(superposition,[status(thm)],[c_147722,c_973]) ).
tcf(c_147773,plain,
( ( sK125(sK302(sK303)) = sK140 )
| ( relation_dom(sK126(sK302(sK303))) = sK302(sK303) ) ),
inference(superposition,[status(thm)],[c_147722,c_975]) ).
tcf(c_147774,plain,
( ( sK125(sK302(sK313)) = sK140 )
| ( relation_dom(sK126(sK302(sK313))) = sK302(sK313) ) ),
inference(superposition,[status(thm)],[c_147722,c_1025]) ).
tcf(c_147775,plain,
( ( sK125(sK302(sK346)) = sK140 )
| ( relation_dom(sK126(sK302(sK346))) = sK302(sK346) ) ),
inference(superposition,[status(thm)],[c_147722,c_1223]) ).
tcf(c_147776,plain,
( ( sK125(sK302(sK358)) = sK140 )
| ( relation_dom(sK126(sK302(sK358))) = sK302(sK358) ) ),
inference(superposition,[status(thm)],[c_147722,c_1276]) ).
tcf(c_147843,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_642]) ).
tcf(c_147844,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_641]) ).
tcf(c_147845,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_906]) ).
tcf(c_147846,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ( relation_rng(sK126(X0)) = sK140 )
| ~ relation(sK126(X0))
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_147734,c_478]) ).
tcf(c_147847,plain,
! [X0: $i] :
( ( sK126(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ~ relation(sK126(X0))
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_147734,c_475]) ).
tcf(c_147884,plain,
! [X0: $i] :
( relation(sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_642]) ).
tcf(c_147885,plain,
! [X0: $i] :
( empty(sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_641]) ).
tcf(c_147886,plain,
! [X0: $i,X1: $i] :
( in(X1,sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_906]) ).
tcf(c_147887,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( relation_rng(sK126(sK302(X0))) = sK140 )
| ~ relation(sK126(sK302(X0)))
| ( sK302(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147765,c_478]) ).
tcf(c_147888,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK126(sK302(X0)) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ relation(sK126(sK302(X0)))
| ( sK302(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147765,c_475]) ).
tcf(c_147927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,unordered_pair(unordered_pair(sK137(relation_inverse_image(X0,X3)),sK137(relation_inverse_image(X0,X3))),unordered_pair(sK137(relation_inverse_image(X0,X3)),sK138(relation_inverse_image(X0,X3))))),X3)
| ( X2 = sK140 )
| ( relation_inverse_image(X0,X3) = sK140 )
| ~ function(X0)
| ~ relation(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_16344,c_425]) ).
tcf(c_147928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK137(relation_inverse_image(X0,X3)),sK137(relation_inverse_image(X0,X3))),unordered_pair(sK137(relation_inverse_image(X0,X3)),sK138(relation_inverse_image(X0,X3)))),X1)
| ( X2 = sK140 )
| ( relation_inverse_image(X0,X3) = sK140 )
| ~ function(X0)
| ~ relation(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_16344,c_424]) ).
tcf(c_147956,plain,
sK115(sK140) = sK140,
inference(equality_resolution,[status(thm)],[c_146807]) ).
tcf(c_147957,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = sK140 )
| ( apply(relation_composition(sK312(X0,X1),X3),X2) = apply(X3,apply(sK312(X0,X1),X2)) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X2,X0)
| ~ function(sK312(X0,X1))
| ~ quasi_total(sK312(X0,X1),X0,X1) ),
inference(superposition,[status(thm)],[c_1018,c_5398]) ).
tcf(c_147958,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK312(X0,X1),X2),relation_rng(sK312(X0,X1)))
| ( X1 = sK140 )
| ~ in(X2,X0)
| ~ function(sK312(X0,X1))
| ~ quasi_total(sK312(X0,X1),X0,X1) ),
inference(superposition,[status(thm)],[c_1018,c_5404]) ).
tcf(c_147959,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( relation_dom_as_subset(X0,X1,sK312(X0,X1)) = X0 )
| ~ quasi_total(sK312(X0,X1),X0,X1) ),
inference(superposition,[status(thm)],[c_1018,c_5415]) ).
tcf(c_147960,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(sK312(X2,X0),X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1018,c_5397]) ).
tcf(c_147966,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK312(X0,X1),X2),relation_rng(sK312(X0,X1)))
| ( X1 = sK140 )
| ~ in(X2,X0)
| ~ quasi_total(sK312(X0,X1),X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147958,c_1020]) ).
tcf(c_147971,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = sK140 )
| ( apply(relation_composition(sK312(X0,X1),X3),X2) = apply(X3,apply(sK312(X0,X1),X2)) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X2,X0)
| ~ quasi_total(sK312(X0,X1),X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147957,c_1020]) ).
tcf(c_147978,plain,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(sK312(X0,X1),X0,X2)
| ( X1 = sK140 )
| ~ subset(X1,X2)
| ~ function(sK312(X0,X1))
| ~ relation_of2(sK312(X0,X1),X0,X1) ),
inference(superposition,[status(thm)],[c_1021,c_5405]) ).
tcf(c_147979,plain,
! [X0: $i] :
( ( relation_dom_as_subset(sK140,X0,sK312(sK140,X0)) = sK140 )
| ~ relation_of2_as_subset(sK312(sK140,X0),sK140,X0) ),
inference(superposition,[status(thm)],[c_1021,c_1074]) ).
tcf(c_147982,plain,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(sK312(X2,X0),X2,X1)
| ( X0 = sK140 )
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_147978,c_1020,c_1018]) ).
tcf(c_147991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(relation_inverse_image(X0,X3))
| in(apply(X0,sK316(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1043,c_425]) ).
tcf(c_147992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_transitive(relation_inverse_image(X0,X3))
| in(sK316(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1043,c_424]) ).
tcf(c_148010,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1111,c_147669]) ).
tcf(c_148011,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1111,c_147196]) ).
tcf(c_148012,plain,
! [X0: $i] :
( one_to_one(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1111,c_84200]) ).
tcf(c_148013,plain,
! [X0: $i] :
( ordinal(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1111,c_1047]) ).
tcf(c_148014,plain,
! [X0: $i] :
( epsilon_connected(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1111,c_1046]) ).
tcf(c_148015,plain,
! [X0: $i] :
( epsilon_transitive(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1111,c_1045]) ).
tcf(c_148016,plain,
! [X0: $i] :
( finite(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1111,c_983]) ).
tcf(c_148018,plain,
! [X0: $i] :
( function(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1111,c_785]) ).
tcf(c_148019,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1111,c_575]) ).
tcf(c_148062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(relation_inverse_image(X0,X3))
| in(apply(X0,sK343(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1207,c_425]) ).
tcf(c_148063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(relation_inverse_image(X0,X3))
| in(sK343(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1207,c_424]) ).
tcf(c_148081,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_148019]) ).
tcf(c_148082,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_148019]) ).
tcf(c_148083,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_148019]) ).
tcf(c_148084,plain,
relation_inverse(sK140) = sK140,
inference(superposition,[status(thm)],[c_1282,c_148019]) ).
tcf(c_148085,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_641,c_148019]) ).
tcf(c_148086,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_943,c_148019]) ).
tcf(c_148087,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1111,c_148019]) ).
tcf(c_148113,plain,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(sK312(sK140,X0),sK140,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ function(sK312(sK140,X0))
| ~ quasi_total(sK312(sK140,X0),sK140,X1) ),
inference(superposition,[status(thm)],[c_147960,c_519]) ).
tcf(c_148114,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK312(X0,X1) = sK140 )
| ~ subset(X1,sK140)
| ~ quasi_total(sK312(X0,X1),X0,sK140) ),
inference(superposition,[status(thm)],[c_147960,c_1077]) ).
tcf(c_148119,plain,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(sK312(sK140,X0),sK140,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ quasi_total(sK312(sK140,X0),sK140,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_148113,c_1020]) ).
tcf(c_148128,plain,
! [X0: $i] :
( ( relation_dom_as_subset(sK140,X0,sK312(sK140,X0)) = sK140 )
| ~ subset(X0,X0) ),
inference(superposition,[status(thm)],[c_147960,c_147979]) ).
tcf(c_148129,plain,
! [X0: $i] : relation_dom_as_subset(sK140,X0,sK312(sK140,X0)) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_148128,c_665]) ).
tcf(c_148137,plain,
! [X0: $i] :
( relation(X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_642]) ).
tcf(c_148138,plain,
! [X0: $i] :
( empty(X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_641]) ).
tcf(c_148139,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_906]) ).
tcf(c_148140,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_rng(sK126(X0)) = sK140 )
| ~ relation(sK126(X0))
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_148083,c_478]) ).
tcf(c_148141,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK126(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ~ relation(sK126(X0))
| ( X0 != sK140 ) ),
inference(superposition,[status(thm)],[c_148083,c_475]) ).
tcf(c_148183,plain,
( ( sK116(sK140) = omega )
| ( sK125(sK263(sK116(sK140))) = sK140 )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_272,c_145540]) ).
tcf(c_148184,plain,
! [X0: $i] :
( ( relation_dom(X0) = omega )
| ( apply(X0,sK140) = sK140 )
| ( sK125(sK263(relation_dom(X0))) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ being_limit_ordinal(relation_dom(X0))
| ~ ordinal(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_906,c_145540]) ).
tcf(c_148185,plain,
! [X0: $i,X1: $i] :
( in(sK140,X1)
| ( X0 = sK140 )
| ( subset_complement(X0,X1) = omega )
| ( sK125(sK263(subset_complement(X0,X1))) = sK140 )
| ~ element(sK140,X0)
| ~ subset(X1,X0)
| ~ being_limit_ordinal(subset_complement(X0,X1))
| ~ ordinal(subset_complement(X0,X1)) ),
inference(superposition,[status(thm)],[c_5403,c_145540]) ).
tcf(c_148186,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK263(X0) = omega )
| ( sK125(sK263(sK263(X0))) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ being_limit_ordinal(sK263(X0))
| ~ ordinal(sK263(X0))
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_145540]) ).
tcf(c_148187,plain,
! [X0: $i] :
( ( unordered_pair(sK140,X0) = omega )
| ( sK125(sK263(unordered_pair(sK140,X0))) = sK140 )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_939,c_145540]) ).
tcf(c_148188,plain,
! [X0: $i] :
( ( unordered_pair(X0,sK140) = omega )
| ( sK125(sK263(unordered_pair(X0,sK140))) = sK140 )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_940,c_145540]) ).
tcf(c_148189,plain,
( ( sK300(sK140) = omega )
| ( sK125(sK263(sK300(sK140))) = sK140 )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_965,c_145540]) ).
tcf(c_148190,plain,
( ( powerset(sK140) = omega )
| ( sK125(sK263(powerset(sK140))) = sK140 )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146165,c_145540]) ).
tcf(c_148247,plain,
relation_rng(sK115(sK140)) = sK140,
inference(equality_resolution,[status(thm)],[c_146810]) ).
tcf(c_148253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(relation_inverse_image(X0,X3))
| in(apply(X0,sK344(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1208,c_425]) ).
tcf(c_148254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( epsilon_connected(relation_inverse_image(X0,X3))
| in(sK344(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1208,c_424]) ).
tcf(c_148268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = sK140 )
| ( apply(relation_composition(sK347(X0,X1),X3),X2) = apply(X3,apply(sK347(X0,X1),X2)) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X2,X0)
| ~ function(sK347(X0,X1))
| ~ quasi_total(sK347(X0,X1),X0,X1) ),
inference(superposition,[status(thm)],[c_1236,c_5398]) ).
tcf(c_148269,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK347(X0,X1),X2),relation_rng(sK347(X0,X1)))
| ( X1 = sK140 )
| ~ in(X2,X0)
| ~ function(sK347(X0,X1))
| ~ quasi_total(sK347(X0,X1),X0,X1) ),
inference(superposition,[status(thm)],[c_1236,c_5404]) ).
tcf(c_148270,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( relation_dom_as_subset(X0,X1,sK347(X0,X1)) = X0 )
| ~ quasi_total(sK347(X0,X1),X0,X1) ),
inference(superposition,[status(thm)],[c_1236,c_5415]) ).
tcf(c_148271,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(sK347(X2,X0),X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1236,c_5397]) ).
tcf(c_148277,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK347(X0,X1),X2),relation_rng(sK347(X0,X1)))
| ( X1 = sK140 )
| ~ in(X2,X0)
| ~ quasi_total(sK347(X0,X1),X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_148269,c_1238]) ).
tcf(c_148282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = sK140 )
| ( apply(relation_composition(sK347(X0,X1),X3),X2) = apply(X3,apply(sK347(X0,X1),X2)) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X2,X0)
| ~ quasi_total(sK347(X0,X1),X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_148268,c_1238]) ).
tcf(c_148289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = sK140 )
| ( apply(relation_composition(sK348(X0,X1),X3),X2) = apply(X3,apply(sK348(X0,X1),X2)) )
| ~ function(X3)
| ~ relation(X3)
| ~ in(X2,X0)
| ~ function(sK348(X0,X1))
| ~ quasi_total(sK348(X0,X1),X0,X1) ),
inference(superposition,[status(thm)],[c_1239,c_5398]) ).
tcf(c_148290,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK348(X0,X1),X2),relation_rng(sK348(X0,X1)))
| ( X1 = sK140 )
| ~ in(X2,X0)
| ~ function(sK348(X0,X1))
| ~ quasi_total(sK348(X0,X1),X0,X1) ),
inference(superposition,[status(thm)],[c_1239,c_5404]) ).
tcf(c_148291,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( relation_dom_as_subset(X0,X1,sK348(X0,X1)) = X0 )
| ~ quasi_total(sK348(X0,X1),X0,X1) ),
inference(superposition,[status(thm)],[c_1239,c_5415]) ).
tcf(c_148292,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(sK348(X2,X0),X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1239,c_5397]) ).
tcf(c_148342,plain,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(sK347(sK140,X0),sK140,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ function(sK347(sK140,X0))
| ~ quasi_total(sK347(sK140,X0),sK140,X1) ),
inference(superposition,[status(thm)],[c_148271,c_519]) ).
tcf(c_148343,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK347(X0,X1) = sK140 )
| ~ subset(X1,sK140)
| ~ quasi_total(sK347(X0,X1),X0,sK140) ),
inference(superposition,[status(thm)],[c_148271,c_1077]) ).
tcf(c_148348,plain,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(sK347(sK140,X0),sK140,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ quasi_total(sK347(sK140,X0),sK140,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_148342,c_1238]) ).
tcf(c_148357,plain,
! [X0: $i,X1: $i,X2: $i] :
( quasi_total(sK348(sK140,X0),sK140,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ function(sK348(sK140,X0))
| ~ quasi_total(sK348(sK140,X0),sK140,X1) ),
inference(superposition,[status(thm)],[c_148292,c_519]) ).
tcf(c_148358,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK348(X0,X1) = sK140 )
| ~ subset(X1,sK140)
| ~ quasi_total(sK348(X0,X1),X0,sK140) ),
inference(superposition,[status(thm)],[c_148292,c_1077]) ).
tcf(c_148424,plain,
identity_relation(sK140) = sK140,
inference(equality_resolution,[status(thm)],[c_146982]) ).
tcf(c_148429,plain,
! [X0: $i] :
( sP3(sK92(X0))
| ordinal(sK58(sK92(X0))) ),
inference(superposition,[status(thm)],[c_122,c_199]) ).
tcf(c_148430,plain,
! [X0: $i,X1: $i] :
( ordinal(apply(sK126(X1),sK92(X0)))
| ( sK125(X1) = sK140 )
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_2177,c_199]) ).
tcf(c_148431,plain,
! [X0: $i] :
( ordinal(sK92(X0))
| ordinal(sK127(sK92(X0))) ),
inference(superposition,[status(thm)],[c_367,c_199]) ).
tcf(c_148432,plain,
! [X0: $i] :
( ordinal(sK128(sK92(X0)))
| ( sK92(X0) = sK140 )
| ~ ordinal(sK92(X0)) ),
inference(superposition,[status(thm)],[c_144620,c_199]) ).
tcf(c_148433,plain,
! [X0: $i] :
( relation(sK92(X0))
| ordinal(sK163(sK92(X0))) ),
inference(superposition,[status(thm)],[c_561,c_199]) ).
tcf(c_148434,plain,
! [X0: $i] :
( ordinal(sK169(sK92(X0)))
| ( sK92(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_579,c_199]) ).
tcf(c_148435,plain,
! [X0: $i] :
( epsilon_transitive(sK92(X0))
| ordinal(sK316(sK92(X0))) ),
inference(superposition,[status(thm)],[c_1043,c_199]) ).
tcf(c_148436,plain,
! [X0: $i,X1: $i] :
( ordinal(sK320(X1,sK92(X0)))
| ( sK92(X0) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(sK92(X0),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_199]) ).
tcf(c_148437,plain,
! [X0: $i] :
( epsilon_connected(sK92(X0))
| ordinal(sK343(sK92(X0))) ),
inference(superposition,[status(thm)],[c_1207,c_199]) ).
tcf(c_148438,plain,
! [X0: $i] :
( epsilon_connected(sK92(X0))
| ordinal(sK344(sK92(X0))) ),
inference(superposition,[status(thm)],[c_1208,c_199]) ).
tcf(c_148439,plain,
! [X0: $i] :
( ordinal(unordered_pair(unordered_pair(sK137(sK92(X0)),sK137(sK92(X0))),unordered_pair(sK137(sK92(X0)),sK138(sK92(X0)))))
| ( sK92(X0) = sK140 )
| ~ relation(sK92(X0)) ),
inference(superposition,[status(thm)],[c_16344,c_199]) ).
tcf(c_148440,plain,
! [X0: $i,X1: $i] :
( ordinal(sK318(X0,sK92(X1)))
| ( sK92(X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,sK92(X1)) ),
inference(superposition,[status(thm)],[c_144619,c_199]) ).
tcf(c_148508,plain,
in(sK140,set_union2(sK140,powerset(sK140))),
inference(superposition,[status(thm)],[c_314,c_256]) ).
tcf(c_148509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,relation_inverse_image(X0,set_union2(apply(X0,X3),unordered_pair(apply(X0,X3),apply(X0,X3)))))
| ( X2 = sK140 )
| ~ function(X0)
| ~ in(X3,X1)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_256,c_423]) ).
tcf(c_148510,plain,
( ( set_union2(sK140,unordered_pair(sK140,sK140)) = omega )
| ( sK125(sK263(set_union2(sK140,unordered_pair(sK140,sK140)))) = sK140 )
| ~ being_limit_ordinal(set_union2(sK140,unordered_pair(sK140,sK140)))
| ~ ordinal(set_union2(sK140,unordered_pair(sK140,sK140))) ),
inference(superposition,[status(thm)],[c_256,c_145540]) ).
tcf(c_148511,plain,
sK125(set_union2(sK140,unordered_pair(sK140,sK140))) = sK140,
inference(superposition,[status(thm)],[c_256,c_144395]) ).
tcf(c_148512,plain,
( ordinal(sK263(set_union2(sK140,unordered_pair(sK140,sK140))))
| ( set_union2(sK140,unordered_pair(sK140,sK140)) = omega )
| ~ being_limit_ordinal(set_union2(sK140,unordered_pair(sK140,sK140)))
| ~ ordinal(set_union2(sK140,unordered_pair(sK140,sK140))) ),
inference(superposition,[status(thm)],[c_256,c_846]) ).
tcf(c_148513,plain,
( being_limit_ordinal(sK263(set_union2(sK140,unordered_pair(sK140,sK140))))
| ( set_union2(sK140,unordered_pair(sK140,sK140)) = omega )
| ~ being_limit_ordinal(set_union2(sK140,unordered_pair(sK140,sK140)))
| ~ ordinal(set_union2(sK140,unordered_pair(sK140,sK140))) ),
inference(superposition,[status(thm)],[c_256,c_845]) ).
tcf(c_148514,plain,
( subset(omega,set_union2(sK140,unordered_pair(sK140,sK140)))
| ~ being_limit_ordinal(set_union2(sK140,unordered_pair(sK140,sK140)))
| ~ ordinal(set_union2(sK140,unordered_pair(sK140,sK140))) ),
inference(superposition,[status(thm)],[c_256,c_850]) ).
tcf(c_148515,plain,
sK125(set_union2(sK140,powerset(sK140))) = sK140,
inference(light_normalisation,[status(thm)],[c_148511,c_314]) ).
tcf(c_148516,plain,
( subset(omega,set_union2(sK140,powerset(sK140)))
| ~ being_limit_ordinal(set_union2(sK140,powerset(sK140)))
| ~ ordinal(set_union2(sK140,powerset(sK140))) ),
inference(light_normalisation,[status(thm)],[c_148514,c_314]) ).
tcf(c_148520,plain,
( being_limit_ordinal(sK263(set_union2(sK140,powerset(sK140))))
| ( set_union2(sK140,powerset(sK140)) = omega )
| ~ being_limit_ordinal(set_union2(sK140,powerset(sK140)))
| ~ ordinal(set_union2(sK140,powerset(sK140))) ),
inference(light_normalisation,[status(thm)],[c_148513,c_314]) ).
tcf(c_148525,plain,
( ordinal(sK263(set_union2(sK140,powerset(sK140))))
| ( set_union2(sK140,powerset(sK140)) = omega )
| ~ being_limit_ordinal(set_union2(sK140,powerset(sK140)))
| ~ ordinal(set_union2(sK140,powerset(sK140))) ),
inference(light_normalisation,[status(thm)],[c_148512,c_314]) ).
tcf(c_148530,plain,
( ( set_union2(sK140,powerset(sK140)) = omega )
| ( sK125(sK263(set_union2(sK140,powerset(sK140)))) = sK140 )
| ~ being_limit_ordinal(set_union2(sK140,powerset(sK140)))
| ~ ordinal(set_union2(sK140,powerset(sK140))) ),
inference(light_normalisation,[status(thm)],[c_148510,c_314]) ).
tcf(c_148545,plain,
! [X0: $i] :
( sP3(X0)
| element(sK58(X0),X0) ),
inference(superposition,[status(thm)],[c_122,c_526]) ).
tcf(c_148546,plain,
element(sK140,omega),
inference(superposition,[status(thm)],[c_847,c_526]) ).
tcf(c_148547,plain,
( element(sK66,omega)
| ~ sP6 ),
inference(superposition,[status(thm)],[c_140,c_526]) ).
tcf(c_148549,plain,
( element(sK110,omega)
| ~ sP15 ),
inference(superposition,[status(thm)],[c_238,c_526]) ).
tcf(c_148550,plain,
! [X0: $i] : element(X0,set_union2(X0,unordered_pair(X0,X0))),
inference(superposition,[status(thm)],[c_256,c_526]) ).
tcf(c_148551,plain,
! [X0: $i] : element(X0,sK116(X0)),
inference(superposition,[status(thm)],[c_272,c_526]) ).
tcf(c_148552,plain,
! [X0: $i,X1: $i] :
( element(X1,relation_dom(X0))
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_526]) ).
tcf(c_148553,plain,
! [X0: $i,X1: $i] :
( element(apply(sK126(X1),X0),X0)
| ( sK125(X1) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2177,c_526]) ).
tcf(c_148554,plain,
! [X0: $i] :
( ordinal(X0)
| element(sK127(X0),X0) ),
inference(superposition,[status(thm)],[c_367,c_526]) ).
tcf(c_148555,plain,
! [X0: $i] :
( element(sK128(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_144620,c_526]) ).
tcf(c_148556,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| element(X2,subset_complement(X1,X0))
| ( X1 = sK140 )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5403,c_526]) ).
tcf(c_148557,plain,
! [X0: $i] :
( relation(X0)
| element(sK163(X0),X0) ),
inference(superposition,[status(thm)],[c_561,c_526]) ).
tcf(c_148558,plain,
! [X0: $i] :
( element(sK169(X0),X0)
| ( X0 = sK140 ) ),
inference(superposition,[status(thm)],[c_579,c_526]) ).
tcf(c_148559,plain,
! [X0: $i] :
( element(sK140,sK263(X0))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_526]) ).
tcf(c_148560,plain,
! [X0: $i,X1: $i] : element(X0,unordered_pair(X0,X1)),
inference(superposition,[status(thm)],[c_939,c_526]) ).
tcf(c_148561,plain,
! [X0: $i,X1: $i] : element(X0,unordered_pair(X1,X0)),
inference(superposition,[status(thm)],[c_940,c_526]) ).
tcf(c_148562,plain,
! [X0: $i] : element(X0,sK300(X0)),
inference(superposition,[status(thm)],[c_965,c_526]) ).
tcf(c_148563,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| element(sK316(X0),X0) ),
inference(superposition,[status(thm)],[c_1043,c_526]) ).
tcf(c_148564,plain,
! [X0: $i,X1: $i] :
( element(sK320(X1,X0),X0)
| ( X0 = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_526]) ).
tcf(c_148565,plain,
! [X0: $i] :
( epsilon_connected(X0)
| element(sK343(X0),X0) ),
inference(superposition,[status(thm)],[c_1207,c_526]) ).
tcf(c_148566,plain,
! [X0: $i] :
( epsilon_connected(X0)
| element(sK344(X0),X0) ),
inference(superposition,[status(thm)],[c_1208,c_526]) ).
tcf(c_148567,plain,
element(sK140,powerset(sK140)),
inference(superposition,[status(thm)],[c_146165,c_526]) ).
tcf(c_148568,plain,
! [X0: $i] :
( element(unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))),X0)
| ( X0 = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16344,c_526]) ).
tcf(c_148569,plain,
( element(sK119(sK64),sK64)
| ~ sP7 ),
inference(superposition,[status(thm)],[c_146098,c_526]) ).
tcf(c_148570,plain,
! [X0: $i,X1: $i] :
( element(sK318(X0,X1),X1)
| ( X1 = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144619,c_526]) ).
tcf(c_148571,plain,
( sP15
| element(sK114(sK64),sK64)
| ~ sP7 ),
inference(superposition,[status(thm)],[c_145791,c_526]) ).
tcf(c_148572,plain,
( element(sK72(sK64),sK64)
| ~ iPr_def_19
| ~ sP7 ),
inference(superposition,[status(thm)],[c_145863,c_526]) ).
tcf(c_148573,plain,
( element(sK67(sK64),sK64)
| ~ sP6
| ~ sP7
| ~ in(sK140,sK66) ),
inference(superposition,[status(thm)],[c_146728,c_526]) ).
tcf(c_148574,plain,
( element(sK111(sK64),sK64)
| ~ sP15
| ~ sP7
| ~ in(sK140,sK110) ),
inference(superposition,[status(thm)],[c_146738,c_526]) ).
tcf(c_148575,plain,
( element(sK63(sK199(powerset(powerset(sK62)))),sK199(powerset(powerset(sK62))))
| ( sK199(powerset(powerset(sK62))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145355,c_526]) ).
tcf(c_148576,plain,
! [X0: $i] :
( element(sK119(sK199(powerset(powerset(X0)))),sK199(powerset(powerset(X0))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145365,c_526]) ).
tcf(c_148577,plain,
( element(sK262(sK199(powerset(powerset(sK261)))),sK199(powerset(powerset(sK261))))
| ( sK199(powerset(powerset(sK261))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145371,c_526]) ).
tcf(c_148578,plain,
( element(sK63(powerset(sK62)),powerset(sK62))
| ( powerset(sK62) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145625,c_526]) ).
tcf(c_148579,plain,
! [X0: $i] :
( element(sK72(powerset(X0)),powerset(X0))
| ( powerset(X0) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145633,c_526]) ).
tcf(c_148580,plain,
! [X0: $i] :
( sP15
| element(sK114(powerset(X0)),powerset(X0))
| ( powerset(X0) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145634,c_526]) ).
tcf(c_148581,plain,
! [X0: $i] :
( element(sK119(powerset(X0)),powerset(X0))
| ( powerset(X0) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145635,c_526]) ).
tcf(c_148582,plain,
( element(sK262(powerset(sK261)),powerset(sK261))
| ( powerset(sK261) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145641,c_526]) ).
tcf(c_148583,plain,
( element(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146242,c_526]) ).
tcf(c_148584,plain,
( element(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145922,c_526]) ).
tcf(c_148585,plain,
( element(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145878,c_526]) ).
tcf(c_148586,plain,
! [X0: $i,X1: $i] :
( element(sK128(set_difference(X0,X1)),set_difference(X0,X1))
| ( set_difference(X0,X1) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_146008,c_526]) ).
tcf(c_148713,plain,
element(sK140,set_union2(sK140,powerset(sK140))),
inference(superposition,[status(thm)],[c_148508,c_526]) ).
tcf(c_148723,plain,
! [X0: $i] :
( ( powerset(powerset(sK62)) = sK140 )
| ( sK169(powerset(powerset(sK62))) = sK140 )
| ( sK63(sK169(powerset(powerset(sK62)))) = X0 )
| ~ iPr_def_20
| ~ in(X0,sK169(powerset(powerset(sK62))))
| ~ subset(sK63(sK169(powerset(powerset(sK62)))),X0) ),
inference(superposition,[status(thm)],[c_148558,c_123600]) ).
tcf(c_148724,plain,
( in(sK63(sK169(powerset(powerset(sK62)))),sK169(powerset(powerset(sK62))))
| ( powerset(powerset(sK62)) = sK140 )
| ( sK169(powerset(powerset(sK62))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_148558,c_123602]) ).
tcf(c_148725,plain,
! [X0: $i,X1: $i] :
( ( powerset(powerset(X0)) = sK140 )
| ( sK169(powerset(powerset(X0))) = sK140 )
| ( sK111(sK169(powerset(powerset(X0)))) = X1 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega)
| ~ in(X1,sK169(powerset(powerset(X0))))
| ~ subset(sK111(sK169(powerset(powerset(X0)))),X1) ),
inference(superposition,[status(thm)],[c_148558,c_240]) ).
tcf(c_148726,plain,
! [X0: $i,X1: $i] :
( ( powerset(powerset(X0)) = sK140 )
| ( sK169(powerset(powerset(X0))) = sK140 )
| ( sK67(sK169(powerset(powerset(X0)))) = X1 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega)
| ~ in(X1,sK169(powerset(powerset(X0))))
| ~ subset(sK67(sK169(powerset(powerset(X0)))),X1) ),
inference(superposition,[status(thm)],[c_148558,c_143]) ).
tcf(c_148727,plain,
! [X0: $i,X1: $i] :
( ( powerset(powerset(X0)) = sK140 )
| ( sK169(powerset(powerset(X0))) = sK140 )
| ( sK72(sK169(powerset(powerset(X0)))) = X1 )
| ~ iPr_def_18
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK169(powerset(powerset(X0))))
| ~ subset(sK72(sK169(powerset(powerset(X0)))),X1) ),
inference(superposition,[status(thm)],[c_148558,c_123596]) ).
tcf(c_148728,plain,
! [X0: $i,X1: $i] :
( sP15
| ( powerset(powerset(X0)) = sK140 )
| ( sK169(powerset(powerset(X0))) = sK140 )
| ( sK114(sK169(powerset(powerset(X0)))) = X1 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK169(powerset(powerset(X0))))
| ~ subset(sK114(sK169(powerset(powerset(X0)))),X1) ),
inference(superposition,[status(thm)],[c_148558,c_248]) ).
tcf(c_148729,plain,
! [X0: $i,X1: $i] :
( ( powerset(powerset(X0)) = sK140 )
| ( sK169(powerset(powerset(X0))) = sK140 )
| ( sK119(sK169(powerset(powerset(X0)))) = X1 )
| ~ finite(X0)
| ~ in(X1,sK169(powerset(powerset(X0))))
| ~ subset(sK119(sK169(powerset(powerset(X0)))),X1) ),
inference(superposition,[status(thm)],[c_148558,c_308]) ).
tcf(c_148730,plain,
! [X0: $i] :
( in(sK111(sK169(powerset(powerset(X0)))),sK169(powerset(powerset(X0))))
| ( powerset(powerset(X0)) = sK140 )
| ( sK169(powerset(powerset(X0))) = sK140 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_148558,c_239]) ).
tcf(c_148731,plain,
! [X0: $i] :
( in(sK67(sK169(powerset(powerset(X0)))),sK169(powerset(powerset(X0))))
| ( powerset(powerset(X0)) = sK140 )
| ( sK169(powerset(powerset(X0))) = sK140 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_148558,c_142]) ).
tcf(c_148732,plain,
! [X0: $i] :
( in(sK72(sK169(powerset(powerset(X0)))),sK169(powerset(powerset(X0))))
| ( powerset(powerset(X0)) = sK140 )
| ( sK169(powerset(powerset(X0))) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_148558,c_123598]) ).
tcf(c_148733,plain,
! [X0: $i] :
( sP15
| in(sK114(sK169(powerset(powerset(X0)))),sK169(powerset(powerset(X0))))
| ( powerset(powerset(X0)) = sK140 )
| ( sK169(powerset(powerset(X0))) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_148558,c_247]) ).
tcf(c_148734,plain,
! [X0: $i] :
( in(sK119(sK169(powerset(powerset(X0)))),sK169(powerset(powerset(X0))))
| ( powerset(powerset(X0)) = sK140 )
| ( sK169(powerset(powerset(X0))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_148558,c_307]) ).
tcf(c_148737,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(powerset(sK254(X0))) = sK140 )
| ( sK169(powerset(powerset(sK254(X0)))) = sK140 )
| ( sK255(sK169(powerset(powerset(sK254(X0))))) = X1 )
| ~ sP31(X2,X0)
| ~ in(sK254(X0),omega)
| ~ in(X1,sK169(powerset(powerset(sK254(X0)))))
| ~ subset(sK255(sK169(powerset(powerset(sK254(X0))))),X1) ),
inference(superposition,[status(thm)],[c_148558,c_826]) ).
tcf(c_148738,plain,
! [X0: $i,X1: $i] :
( in(sK255(sK169(powerset(powerset(sK254(X0))))),sK169(powerset(powerset(sK254(X0)))))
| ( powerset(powerset(sK254(X0))) = sK140 )
| ( sK169(powerset(powerset(sK254(X0)))) = sK140 )
| ~ sP31(X1,X0)
| ~ in(sK254(X0),omega) ),
inference(superposition,[status(thm)],[c_148558,c_825]) ).
tcf(c_148739,plain,
! [X0: $i] :
( ( powerset(powerset(sK261)) = sK140 )
| ( sK169(powerset(powerset(sK261))) = sK140 )
| ( sK262(sK169(powerset(powerset(sK261)))) = X0 )
| ~ iPr_def_14
| ~ in(X0,sK169(powerset(powerset(sK261))))
| ~ subset(sK262(sK169(powerset(powerset(sK261)))),X0) ),
inference(superposition,[status(thm)],[c_148558,c_123589]) ).
tcf(c_148740,plain,
( in(sK262(sK169(powerset(powerset(sK261)))),sK169(powerset(powerset(sK261))))
| ( powerset(powerset(sK261)) = sK140 )
| ( sK169(powerset(powerset(sK261))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_148558,c_123591]) ).
tcf(c_148741,plain,
( ordinal(sK169(omega))
| ( sK140 = omega ) ),
inference(superposition,[status(thm)],[c_148558,c_858]) ).
tcf(c_148742,plain,
( epsilon_connected(sK169(omega))
| ( sK140 = omega ) ),
inference(superposition,[status(thm)],[c_148558,c_857]) ).
tcf(c_148743,plain,
( epsilon_transitive(sK169(omega))
| ( sK140 = omega ) ),
inference(superposition,[status(thm)],[c_148558,c_856]) ).
tcf(c_148889,plain,
! [X0: $i] :
( epsilon_connected(sK169(sK92(X0)))
| ( sK92(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_148434,c_1050]) ).
tcf(c_148890,plain,
! [X0: $i] :
( epsilon_transitive(sK169(sK92(X0)))
| ( sK92(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_148434,c_1049]) ).
tcf(c_148908,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(sK62))) = sK140 )
| ( sK63(apply(sK126(X0),powerset(powerset(sK62)))) = X1 )
| ~ iPr_def_20
| ~ in(powerset(powerset(sK62)),X0)
| ~ in(X1,apply(sK126(X0),powerset(powerset(sK62))))
| ~ subset(sK63(apply(sK126(X0),powerset(powerset(sK62)))),X1) ),
inference(superposition,[status(thm)],[c_148553,c_123600]) ).
tcf(c_148909,plain,
! [X0: $i] :
( in(sK63(apply(sK126(X0),powerset(powerset(sK62)))),apply(sK126(X0),powerset(powerset(sK62))))
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(sK62))) = sK140 )
| ~ iPr_def_21
| ~ in(powerset(powerset(sK62)),X0) ),
inference(superposition,[status(thm)],[c_148553,c_123602]) ).
tcf(c_148910,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(X1))) = sK140 )
| ( sK111(apply(sK126(X0),powerset(powerset(X1)))) = X2 )
| ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK110)
| ~ in(X1,omega)
| ~ in(powerset(powerset(X1)),X0)
| ~ in(X2,apply(sK126(X0),powerset(powerset(X1))))
| ~ subset(sK111(apply(sK126(X0),powerset(powerset(X1)))),X2) ),
inference(superposition,[status(thm)],[c_148553,c_240]) ).
tcf(c_148911,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(X1))) = sK140 )
| ( sK67(apply(sK126(X0),powerset(powerset(X1)))) = X2 )
| ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK66)
| ~ in(X1,omega)
| ~ in(powerset(powerset(X1)),X0)
| ~ in(X2,apply(sK126(X0),powerset(powerset(X1))))
| ~ subset(sK67(apply(sK126(X0),powerset(powerset(X1)))),X2) ),
inference(superposition,[status(thm)],[c_148553,c_143]) ).
tcf(c_148912,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(X1))) = sK140 )
| ( sK72(apply(sK126(X0),powerset(powerset(X1)))) = X2 )
| ~ iPr_def_18
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ in(powerset(powerset(X1)),X0)
| ~ in(X2,apply(sK126(X0),powerset(powerset(X1))))
| ~ subset(sK72(apply(sK126(X0),powerset(powerset(X1)))),X2) ),
inference(superposition,[status(thm)],[c_148553,c_123596]) ).
tcf(c_148913,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP15
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(X1))) = sK140 )
| ( sK114(apply(sK126(X0),powerset(powerset(X1)))) = X2 )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ in(powerset(powerset(X1)),X0)
| ~ in(X2,apply(sK126(X0),powerset(powerset(X1))))
| ~ subset(sK114(apply(sK126(X0),powerset(powerset(X1)))),X2) ),
inference(superposition,[status(thm)],[c_148553,c_248]) ).
tcf(c_148914,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(X1))) = sK140 )
| ( sK119(apply(sK126(X0),powerset(powerset(X1)))) = X2 )
| ~ finite(X1)
| ~ in(powerset(powerset(X1)),X0)
| ~ in(X2,apply(sK126(X0),powerset(powerset(X1))))
| ~ subset(sK119(apply(sK126(X0),powerset(powerset(X1)))),X2) ),
inference(superposition,[status(thm)],[c_148553,c_308]) ).
tcf(c_148915,plain,
! [X0: $i,X1: $i] :
( in(sK111(apply(sK126(X1),powerset(powerset(X0)))),apply(sK126(X1),powerset(powerset(X0))))
| ( sK125(X1) = sK140 )
| ( apply(sK126(X1),powerset(powerset(X0))) = sK140 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega)
| ~ in(powerset(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_148553,c_239]) ).
tcf(c_148916,plain,
! [X0: $i,X1: $i] :
( in(sK67(apply(sK126(X1),powerset(powerset(X0)))),apply(sK126(X1),powerset(powerset(X0))))
| ( sK125(X1) = sK140 )
| ( apply(sK126(X1),powerset(powerset(X0))) = sK140 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega)
| ~ in(powerset(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_148553,c_142]) ).
tcf(c_148917,plain,
! [X0: $i,X1: $i] :
( in(sK72(apply(sK126(X1),powerset(powerset(X0)))),apply(sK126(X1),powerset(powerset(X0))))
| ( sK125(X1) = sK140 )
| ( apply(sK126(X1),powerset(powerset(X0))) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(powerset(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_148553,c_123598]) ).
tcf(c_148918,plain,
! [X0: $i,X1: $i] :
( sP15
| in(sK114(apply(sK126(X1),powerset(powerset(X0)))),apply(sK126(X1),powerset(powerset(X0))))
| ( sK125(X1) = sK140 )
| ( apply(sK126(X1),powerset(powerset(X0))) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(powerset(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_148553,c_247]) ).
tcf(c_148919,plain,
! [X0: $i,X1: $i] :
( in(sK119(apply(sK126(X1),powerset(powerset(X0)))),apply(sK126(X1),powerset(powerset(X0))))
| ( sK125(X1) = sK140 )
| ( apply(sK126(X1),powerset(powerset(X0))) = sK140 )
| ~ finite(X0)
| ~ in(powerset(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_148553,c_307]) ).
tcf(c_148922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(sK254(X1)))) = sK140 )
| ( sK255(apply(sK126(X0),powerset(powerset(sK254(X1))))) = X2 )
| ~ sP31(X3,X1)
| ~ in(sK254(X1),omega)
| ~ in(powerset(powerset(sK254(X1))),X0)
| ~ in(X2,apply(sK126(X0),powerset(powerset(sK254(X1)))))
| ~ subset(sK255(apply(sK126(X0),powerset(powerset(sK254(X1))))),X2) ),
inference(superposition,[status(thm)],[c_148553,c_826]) ).
tcf(c_148923,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK255(apply(sK126(X1),powerset(powerset(sK254(X0))))),apply(sK126(X1),powerset(powerset(sK254(X0)))))
| ( sK125(X1) = sK140 )
| ( apply(sK126(X1),powerset(powerset(sK254(X0)))) = sK140 )
| ~ sP31(X2,X0)
| ~ in(sK254(X0),omega)
| ~ in(powerset(powerset(sK254(X0))),X1) ),
inference(superposition,[status(thm)],[c_148553,c_825]) ).
tcf(c_148924,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(sK261))) = sK140 )
| ( sK262(apply(sK126(X0),powerset(powerset(sK261)))) = X1 )
| ~ iPr_def_14
| ~ in(powerset(powerset(sK261)),X0)
| ~ in(X1,apply(sK126(X0),powerset(powerset(sK261))))
| ~ subset(sK262(apply(sK126(X0),powerset(powerset(sK261)))),X1) ),
inference(superposition,[status(thm)],[c_148553,c_123589]) ).
tcf(c_148925,plain,
! [X0: $i] :
( in(sK262(apply(sK126(X0),powerset(powerset(sK261)))),apply(sK126(X0),powerset(powerset(sK261))))
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(sK261))) = sK140 )
| ~ iPr_def_15
| ~ in(powerset(powerset(sK261)),X0) ),
inference(superposition,[status(thm)],[c_148553,c_123591]) ).
tcf(c_148926,plain,
! [X0: $i] :
( ordinal(apply(sK126(X0),omega))
| ( sK125(X0) = sK140 )
| ~ in(omega,X0) ),
inference(superposition,[status(thm)],[c_148553,c_858]) ).
tcf(c_148927,plain,
! [X0: $i] :
( epsilon_connected(apply(sK126(X0),omega))
| ( sK125(X0) = sK140 )
| ~ in(omega,X0) ),
inference(superposition,[status(thm)],[c_148553,c_857]) ).
tcf(c_148928,plain,
! [X0: $i] :
( epsilon_transitive(apply(sK126(X0),omega))
| ( sK125(X0) = sK140 )
| ~ in(omega,X0) ),
inference(superposition,[status(thm)],[c_148553,c_856]) ).
tcf(c_149104,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(apply(sK126(X1),sK92(X0)))
| ( sK125(X1) = sK140 )
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_148430,c_1050]) ).
tcf(c_149105,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(apply(sK126(X1),sK92(X0)))
| ( sK125(X1) = sK140 )
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_148430,c_1049]) ).
tcf(c_149128,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ( apply(sK115(X0),X1) = sK140 )
| ~ function(sK115(X0))
| ~ relation(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_148552]) ).
tcf(c_149129,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_148552]) ).
tcf(c_149130,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_148552]) ).
tcf(c_149131,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_148552]) ).
tcf(c_149132,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_148552]) ).
tcf(c_149133,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ( apply(identity_relation(X0),X1) = sK140 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_148552]) ).
tcf(c_149135,plain,
! [X0: $i] :
( element(X0,sK241)
| ( sK125(sK241) = sK140 )
| ( apply(sK126(sK241),X0) = sK140 )
| ~ function(sK126(sK241))
| ~ relation(sK126(sK241)) ),
inference(superposition,[status(thm)],[c_144638,c_148552]) ).
tcf(c_149136,plain,
! [X0: $i] :
( element(X0,sK242)
| ( sK125(sK242) = sK140 )
| ( apply(sK126(sK242),X0) = sK140 )
| ~ function(sK126(sK242))
| ~ relation(sK126(sK242)) ),
inference(superposition,[status(thm)],[c_144641,c_148552]) ).
tcf(c_149137,plain,
! [X0: $i] :
( element(X0,sK303)
| ( sK125(sK303) = sK140 )
| ( apply(sK126(sK303),X0) = sK140 )
| ~ function(sK126(sK303))
| ~ relation(sK126(sK303)) ),
inference(superposition,[status(thm)],[c_144647,c_148552]) ).
tcf(c_149138,plain,
! [X0: $i] :
( element(X0,sK313)
| ( sK125(sK313) = sK140 )
| ( apply(sK126(sK313),X0) = sK140 )
| ~ function(sK126(sK313))
| ~ relation(sK126(sK313)) ),
inference(superposition,[status(thm)],[c_144797,c_148552]) ).
tcf(c_149139,plain,
! [X0: $i] :
( element(X0,sK346)
| ( sK125(sK346) = sK140 )
| ( apply(sK126(sK346),X0) = sK140 )
| ~ function(sK126(sK346))
| ~ relation(sK126(sK346)) ),
inference(superposition,[status(thm)],[c_144944,c_148552]) ).
tcf(c_149140,plain,
! [X0: $i] :
( element(X0,sK358)
| ( sK125(sK358) = sK140 )
| ( apply(sK126(sK358),X0) = sK140 )
| ~ function(sK126(sK358))
| ~ relation(sK126(sK358)) ),
inference(superposition,[status(thm)],[c_144947,c_148552]) ).
tcf(c_149141,plain,
! [X0: $i,X1: $i] :
( element(X1,powerset(X0))
| ( sK125(powerset(X0)) = sK140 )
| ( apply(sK126(powerset(X0)),X1) = sK140 )
| ~ function(sK126(powerset(X0)))
| ~ relation(sK126(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145193,c_148552]) ).
tcf(c_149142,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,unordered_pair(X0,X1))
| ( sK125(unordered_pair(X0,X1)) = sK140 )
| ( apply(sK126(unordered_pair(X0,X1)),X2) = sK140 )
| ~ function(sK126(unordered_pair(X0,X1)))
| ~ relation(sK126(unordered_pair(X0,X1))) ),
inference(superposition,[status(thm)],[c_146160,c_148552]) ).
tcf(c_149143,plain,
! [X0: $i,X1: $i] :
( element(X1,sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_148552]) ).
tcf(c_149144,plain,
! [X0: $i,X1: $i] :
( element(X1,sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_148552]) ).
tcf(c_149145,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ( apply(identity_relation(X0),X1) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149133,c_1100,c_1101]) ).
tcf(c_149148,plain,
! [X0: $i,X1: $i] :
( element(X1,X0)
| ( apply(sK115(X0),X1) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149128,c_250,c_249]) ).
tcf(c_149241,plain,
! [X0: $i] :
( disjoint(fiber(X0,sK318(X0,omega)),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(set_union2(sK140,powerset(sK140)))
| ~ ordinal(set_union2(sK140,powerset(sK140)))
| ~ is_well_founded_in(X0,set_union2(sK140,powerset(sK140))) ),
inference(superposition,[status(thm)],[c_148516,c_1058]) ).
tcf(c_149242,plain,
! [X0: $i] :
( in(sK318(X0,omega),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(set_union2(sK140,powerset(sK140)))
| ~ ordinal(set_union2(sK140,powerset(sK140)))
| ~ is_well_founded_in(X0,set_union2(sK140,powerset(sK140))) ),
inference(superposition,[status(thm)],[c_148516,c_1057]) ).
tcf(c_149243,plain,
( in(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(set_union2(sK140,powerset(sK140)))
| ~ ordinal(set_union2(sK140,powerset(sK140))) ),
inference(superposition,[status(thm)],[c_148516,c_369]) ).
tcf(c_149244,plain,
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ being_limit_ordinal(set_union2(sK140,powerset(sK140)))
| ~ ordinal(set_union2(sK140,powerset(sK140))) ),
inference(superposition,[status(thm)],[c_148516,c_371]) ).
tcf(c_149245,plain,
( ( set_difference(omega,set_union2(sK140,powerset(sK140))) = sK140 )
| ~ being_limit_ordinal(set_union2(sK140,powerset(sK140)))
| ~ ordinal(set_union2(sK140,powerset(sK140))) ),
inference(superposition,[status(thm)],[c_148516,c_386]) ).
tcf(c_149246,plain,
! [X0: $i] :
( ordinal_subset(sK128(omega),X0)
| ( sK140 = omega )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ being_limit_ordinal(set_union2(sK140,powerset(sK140)))
| ~ ordinal(set_union2(sK140,powerset(sK140))) ),
inference(superposition,[status(thm)],[c_148516,c_370]) ).
tcf(c_149287,plain,
! [X0: $i] :
( element(sK173(X0),X0)
| ~ sP20(X0) ),
inference(superposition,[status(thm)],[c_584,c_526]) ).
tcf(c_149288,plain,
! [X0: $i] :
( ordinal(sK173(sK92(X0)))
| ~ sP20(sK92(X0)) ),
inference(superposition,[status(thm)],[c_584,c_199]) ).
tcf(c_149289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK173(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ sP20(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_584,c_425]) ).
tcf(c_149290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK173(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ sP20(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_584,c_424]) ).
tcf(c_149291,plain,
~ sP20(sK140),
inference(superposition,[status(thm)],[c_584,c_580]) ).
tcf(c_149339,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(sK302(set_union2(X0,X1))) = sK140 )
| ( relation_dom(sK126(sK302(set_union2(X0,X1)))) = sK302(set_union2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_147722,c_614]) ).
tcf(c_149340,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(sK198(set_union2(X0,X1))) = sK140 )
| ( relation_dom(sK126(sK198(set_union2(X0,X1)))) = sK198(set_union2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_147277,c_614]) ).
tcf(c_149341,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_353,c_614]) ).
tcf(c_149357,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(sK302(set_union2(X0,X1))) = sK140 )
| ( relation_dom(sK126(sK302(set_union2(X0,X1)))) = sK302(set_union2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_147722,c_615]) ).
tcf(c_149358,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(sK198(set_union2(X0,X1))) = sK140 )
| ( relation_dom(sK126(sK198(set_union2(X0,X1)))) = sK198(set_union2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_147277,c_615]) ).
tcf(c_149359,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_353,c_615]) ).
tcf(c_149407,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X1) = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_148019]) ).
tcf(c_149408,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(X1) = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_147669]) ).
tcf(c_149409,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X1) = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_147196]) ).
tcf(c_149410,plain,
! [X0: $i,X1: $i] :
( one_to_one(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_84200]) ).
tcf(c_149411,plain,
! [X0: $i,X1: $i] :
( ordinal(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_1047]) ).
tcf(c_149412,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_1046]) ).
tcf(c_149413,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_1045]) ).
tcf(c_149414,plain,
! [X0: $i,X1: $i] :
( finite(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_983]) ).
tcf(c_149415,plain,
! [X0: $i,X1: $i] :
( relation(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_799]) ).
tcf(c_149416,plain,
! [X0: $i,X1: $i] :
( function(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_785]) ).
tcf(c_149417,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_575]) ).
tcf(c_149418,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| ( sK125(set_union2(X0,set_union2(X1,X2))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,set_union2(X1,X2)))) = set_union2(X0,set_union2(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_149341,c_615]) ).
tcf(c_149419,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| ( sK125(set_union2(X0,set_union2(X1,X2))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,set_union2(X1,X2)))) = set_union2(X0,set_union2(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_149341,c_614]) ).
tcf(c_149420,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(set_union2(X0,sK198(X1))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK198(X1)))) = set_union2(X0,sK198(X1)) ) ),
inference(superposition,[status(thm)],[c_149341,c_694]) ).
tcf(c_149421,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(X0,powerset(X1))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,powerset(X1)))) = set_union2(X0,powerset(X1)) ) ),
inference(superposition,[status(thm)],[c_149341,c_695]) ).
tcf(c_149422,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,sK241)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK241))) = set_union2(X0,sK241) ) ),
inference(superposition,[status(thm)],[c_149341,c_789]) ).
tcf(c_149423,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,sK242)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK242))) = set_union2(X0,sK242) ) ),
inference(superposition,[status(thm)],[c_149341,c_790]) ).
tcf(c_149424,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,omega)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,omega))) = set_union2(X0,omega) ) ),
inference(superposition,[status(thm)],[c_149341,c_842]) ).
tcf(c_149425,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(set_union2(X0,unordered_pair(X1,X2))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,unordered_pair(X1,X2)))) = set_union2(X0,unordered_pair(X1,X2)) ) ),
inference(superposition,[status(thm)],[c_149341,c_935]) ).
tcf(c_149426,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(set_union2(X0,sK302(X1))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK302(X1)))) = set_union2(X0,sK302(X1)) ) ),
inference(superposition,[status(thm)],[c_149341,c_973]) ).
tcf(c_149427,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,sK303)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK303))) = set_union2(X0,sK303) ) ),
inference(superposition,[status(thm)],[c_149341,c_975]) ).
tcf(c_149428,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,sK313)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK313))) = set_union2(X0,sK313) ) ),
inference(superposition,[status(thm)],[c_149341,c_1025]) ).
tcf(c_149429,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,sK346)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK346))) = set_union2(X0,sK346) ) ),
inference(superposition,[status(thm)],[c_149341,c_1223]) ).
tcf(c_149430,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,sK358)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK358))) = set_union2(X0,sK358) ) ),
inference(superposition,[status(thm)],[c_149341,c_1276]) ).
tcf(c_149512,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_148019]) ).
tcf(c_149513,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_147669]) ).
tcf(c_149514,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_147196]) ).
tcf(c_149515,plain,
! [X0: $i,X1: $i] :
( one_to_one(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_84200]) ).
tcf(c_149516,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_1047]) ).
tcf(c_149517,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_1046]) ).
tcf(c_149518,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_1045]) ).
tcf(c_149519,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_983]) ).
tcf(c_149520,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_799]) ).
tcf(c_149521,plain,
! [X0: $i,X1: $i] :
( function(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_785]) ).
tcf(c_149522,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_575]) ).
tcf(c_149523,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ( sK125(set_union2(set_union2(X0,X1),X2)) = sK140 )
| ( relation_dom(sK126(set_union2(set_union2(X0,X1),X2))) = set_union2(set_union2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_149359,c_615]) ).
tcf(c_149524,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| ( sK125(set_union2(set_union2(X0,X1),X2)) = sK140 )
| ( relation_dom(sK126(set_union2(set_union2(X0,X1),X2))) = set_union2(set_union2(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_149359,c_614]) ).
tcf(c_149525,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(set_union2(sK198(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(sK198(X0),X1))) = set_union2(sK198(X0),X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_694]) ).
tcf(c_149526,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(powerset(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(powerset(X0),X1))) = set_union2(powerset(X0),X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_695]) ).
tcf(c_149527,plain,
! [X0: $i] :
( ( sK125(set_union2(sK241,X0)) = sK140 )
| ( relation_dom(sK126(set_union2(sK241,X0))) = set_union2(sK241,X0) ) ),
inference(superposition,[status(thm)],[c_149359,c_789]) ).
tcf(c_149528,plain,
! [X0: $i] :
( ( sK125(set_union2(sK242,X0)) = sK140 )
| ( relation_dom(sK126(set_union2(sK242,X0))) = set_union2(sK242,X0) ) ),
inference(superposition,[status(thm)],[c_149359,c_790]) ).
tcf(c_149529,plain,
! [X0: $i] :
( ( sK125(set_union2(omega,X0)) = sK140 )
| ( relation_dom(sK126(set_union2(omega,X0))) = set_union2(omega,X0) ) ),
inference(superposition,[status(thm)],[c_149359,c_842]) ).
tcf(c_149530,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(set_union2(unordered_pair(X0,X1),X2)) = sK140 )
| ( relation_dom(sK126(set_union2(unordered_pair(X0,X1),X2))) = set_union2(unordered_pair(X0,X1),X2) ) ),
inference(superposition,[status(thm)],[c_149359,c_935]) ).
tcf(c_149531,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(set_union2(sK302(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(sK302(X0),X1))) = set_union2(sK302(X0),X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_973]) ).
tcf(c_149532,plain,
! [X0: $i] :
( ( sK125(set_union2(sK303,X0)) = sK140 )
| ( relation_dom(sK126(set_union2(sK303,X0))) = set_union2(sK303,X0) ) ),
inference(superposition,[status(thm)],[c_149359,c_975]) ).
tcf(c_149533,plain,
! [X0: $i] :
( ( sK125(set_union2(sK313,X0)) = sK140 )
| ( relation_dom(sK126(set_union2(sK313,X0))) = set_union2(sK313,X0) ) ),
inference(superposition,[status(thm)],[c_149359,c_1025]) ).
tcf(c_149534,plain,
! [X0: $i] :
( ( sK125(set_union2(sK346,X0)) = sK140 )
| ( relation_dom(sK126(set_union2(sK346,X0))) = set_union2(sK346,X0) ) ),
inference(superposition,[status(thm)],[c_149359,c_1223]) ).
tcf(c_149535,plain,
! [X0: $i] :
( ( sK125(set_union2(sK358,X0)) = sK140 )
| ( relation_dom(sK126(set_union2(sK358,X0))) = set_union2(sK358,X0) ) ),
inference(superposition,[status(thm)],[c_149359,c_1276]) ).
tcf(c_149618,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(X1),X0)
| ( X1 = sK140 )
| ( sK125(set_union2(X1,X2)) = sK140 )
| ( relation_dom(sK126(set_union2(X1,X2))) = set_union2(X1,X2) )
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_146389,c_146043]) ).
tcf(c_149627,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( relation_dom_as_subset(X0,X1,sK312(X0,X1)) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_147959,c_37629]) ).
tcf(c_149634,plain,
! [X0: $i] :
( quasi_total(sK312(sK140,X0),sK140,X0)
| ( X0 = sK140 )
| ~ relation_of2_as_subset(sK312(sK140,X0),sK140,X0) ),
inference(superposition,[status(thm)],[c_149627,c_1072]) ).
tcf(c_149655,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,fiber(X1,sK320(X1,X0)))
| ( X0 = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1063,c_624]) ).
tcf(c_149658,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,fiber(X0,sK318(X0,X1)))
| ( X1 = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144761,c_624]) ).
tcf(c_149676,plain,
! [X0: $i] :
( empty(powerset(sK62))
| ( sK198(powerset(sK62)) = sK140 )
| ( sK63(sK198(powerset(sK62))) = X0 )
| ~ iPr_def_20
| ~ in(X0,sK198(powerset(sK62)))
| ~ subset(sK63(sK198(powerset(sK62))),X0) ),
inference(superposition,[status(thm)],[c_693,c_123600]) ).
tcf(c_149677,plain,
( empty(powerset(sK62))
| in(sK63(sK198(powerset(sK62))),sK198(powerset(sK62)))
| ( sK198(powerset(sK62)) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_693,c_123602]) ).
tcf(c_149678,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| ( sK198(powerset(X0)) = sK140 )
| ( sK111(sK198(powerset(X0))) = X1 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega)
| ~ in(X1,sK198(powerset(X0)))
| ~ subset(sK111(sK198(powerset(X0))),X1) ),
inference(superposition,[status(thm)],[c_693,c_240]) ).
tcf(c_149679,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| ( sK198(powerset(X0)) = sK140 )
| ( sK67(sK198(powerset(X0))) = X1 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega)
| ~ in(X1,sK198(powerset(X0)))
| ~ subset(sK67(sK198(powerset(X0))),X1) ),
inference(superposition,[status(thm)],[c_693,c_143]) ).
tcf(c_149680,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| ( sK198(powerset(X0)) = sK140 )
| ( sK72(sK198(powerset(X0))) = X1 )
| ~ iPr_def_18
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK198(powerset(X0)))
| ~ subset(sK72(sK198(powerset(X0))),X1) ),
inference(superposition,[status(thm)],[c_693,c_123596]) ).
tcf(c_149681,plain,
! [X0: $i,X1: $i] :
( sP15
| empty(powerset(X0))
| ( sK198(powerset(X0)) = sK140 )
| ( sK114(sK198(powerset(X0))) = X1 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK198(powerset(X0)))
| ~ subset(sK114(sK198(powerset(X0))),X1) ),
inference(superposition,[status(thm)],[c_693,c_248]) ).
tcf(c_149682,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| ( sK198(powerset(X0)) = sK140 )
| ( sK119(sK198(powerset(X0))) = X1 )
| ~ finite(X0)
| ~ in(X1,sK198(powerset(X0)))
| ~ subset(sK119(sK198(powerset(X0))),X1) ),
inference(superposition,[status(thm)],[c_693,c_308]) ).
tcf(c_149683,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(sK111(sK198(powerset(X0))),sK198(powerset(X0)))
| ( sK198(powerset(X0)) = sK140 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_693,c_239]) ).
tcf(c_149684,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(sK67(sK198(powerset(X0))),sK198(powerset(X0)))
| ( sK198(powerset(X0)) = sK140 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_693,c_142]) ).
tcf(c_149685,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(sK72(sK198(powerset(X0))),sK198(powerset(X0)))
| ( sK198(powerset(X0)) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_693,c_123598]) ).
tcf(c_149686,plain,
! [X0: $i] :
( sP15
| empty(powerset(X0))
| in(sK114(sK198(powerset(X0))),sK198(powerset(X0)))
| ( sK198(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_693,c_247]) ).
tcf(c_149687,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(sK119(sK198(powerset(X0))),sK198(powerset(X0)))
| ( sK198(powerset(X0)) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_693,c_307]) ).
tcf(c_149690,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(sK254(X0)))
| ( sK198(powerset(sK254(X0))) = sK140 )
| ( sK255(sK198(powerset(sK254(X0)))) = X1 )
| ~ sP31(X2,X0)
| ~ in(sK254(X0),omega)
| ~ in(X1,sK198(powerset(sK254(X0))))
| ~ subset(sK255(sK198(powerset(sK254(X0)))),X1) ),
inference(superposition,[status(thm)],[c_693,c_826]) ).
tcf(c_149691,plain,
! [X0: $i,X1: $i] :
( empty(powerset(sK254(X0)))
| in(sK255(sK198(powerset(sK254(X0)))),sK198(powerset(sK254(X0))))
| ( sK198(powerset(sK254(X0))) = sK140 )
| ~ sP31(X1,X0)
| ~ in(sK254(X0),omega) ),
inference(superposition,[status(thm)],[c_693,c_825]) ).
tcf(c_149692,plain,
! [X0: $i] :
( empty(powerset(sK261))
| ( sK198(powerset(sK261)) = sK140 )
| ( sK262(sK198(powerset(sK261))) = X0 )
| ~ iPr_def_14
| ~ in(X0,sK198(powerset(sK261)))
| ~ subset(sK262(sK198(powerset(sK261))),X0) ),
inference(superposition,[status(thm)],[c_693,c_123589]) ).
tcf(c_149693,plain,
( empty(powerset(sK261))
| in(sK262(sK198(powerset(sK261))),sK198(powerset(sK261)))
| ( sK198(powerset(sK261)) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_693,c_123591]) ).
tcf(c_149695,plain,
( in(sK262(sK198(powerset(sK261))),sK198(powerset(sK261)))
| ( sK198(powerset(sK261)) = sK140 )
| ~ iPr_def_15 ),
inference(forward_subsumption_resolution,[status(thm)],[c_149693,c_695]) ).
tcf(c_149699,plain,
( in(sK63(sK198(powerset(sK62))),sK198(powerset(sK62)))
| ( sK198(powerset(sK62)) = sK140 )
| ~ iPr_def_21 ),
inference(forward_subsumption_resolution,[status(thm)],[c_149677,c_695]) ).
tcf(c_149703,plain,
! [X0: $i] :
( in(sK119(sK198(powerset(X0))),sK198(powerset(X0)))
| ( sK198(powerset(X0)) = sK140 )
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149687,c_695]) ).
tcf(c_149711,plain,
! [X0: $i] :
( sP15
| in(sK114(sK198(powerset(X0))),sK198(powerset(X0)))
| ( sK198(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149686,c_695]) ).
tcf(c_149717,plain,
! [X0: $i] :
( in(sK72(sK198(powerset(X0))),sK198(powerset(X0)))
| ( sK198(powerset(X0)) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149685,c_695]) ).
tcf(c_149723,plain,
! [X0: $i,X1: $i] :
( in(sK255(sK198(powerset(sK254(X0)))),sK198(powerset(sK254(X0))))
| ( sK198(powerset(sK254(X0))) = sK140 )
| ~ sP31(X1,X0)
| ~ in(sK254(X0),omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149691,c_695]) ).
tcf(c_149733,plain,
! [X0: $i] :
( in(sK67(sK198(powerset(X0))),sK198(powerset(X0)))
| ( sK198(powerset(X0)) = sK140 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149684,c_695]) ).
tcf(c_149740,plain,
! [X0: $i] :
( in(sK111(sK198(powerset(X0))),sK198(powerset(X0)))
| ( sK198(powerset(X0)) = sK140 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149683,c_695]) ).
tcf(c_149747,plain,
! [X0: $i] :
( ( sK198(powerset(sK261)) = sK140 )
| ( sK262(sK198(powerset(sK261))) = X0 )
| ~ iPr_def_14
| ~ in(X0,sK198(powerset(sK261)))
| ~ subset(sK262(sK198(powerset(sK261))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149692,c_695]) ).
tcf(c_149753,plain,
! [X0: $i] :
( ( sK198(powerset(sK62)) = sK140 )
| ( sK63(sK198(powerset(sK62))) = X0 )
| ~ iPr_def_20
| ~ in(X0,sK198(powerset(sK62)))
| ~ subset(sK63(sK198(powerset(sK62))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149676,c_695]) ).
tcf(c_149759,plain,
! [X0: $i,X1: $i] :
( ( sK198(powerset(X0)) = sK140 )
| ( sK119(sK198(powerset(X0))) = X1 )
| ~ finite(X0)
| ~ in(X1,sK198(powerset(X0)))
| ~ subset(sK119(sK198(powerset(X0))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149682,c_695]) ).
tcf(c_149765,plain,
! [X0: $i,X1: $i] :
( sP15
| ( sK198(powerset(X0)) = sK140 )
| ( sK114(sK198(powerset(X0))) = X1 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK198(powerset(X0)))
| ~ subset(sK114(sK198(powerset(X0))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149681,c_695]) ).
tcf(c_149773,plain,
! [X0: $i,X1: $i] :
( ( sK198(powerset(X0)) = sK140 )
| ( sK72(sK198(powerset(X0))) = X1 )
| ~ iPr_def_18
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK198(powerset(X0)))
| ~ subset(sK72(sK198(powerset(X0))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149680,c_695]) ).
tcf(c_149781,plain,
! [X0: $i,X1: $i] :
( ( sK198(powerset(X0)) = sK140 )
| ( sK67(sK198(powerset(X0))) = X1 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega)
| ~ in(X1,sK198(powerset(X0)))
| ~ subset(sK67(sK198(powerset(X0))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149679,c_695]) ).
tcf(c_149790,plain,
! [X0: $i,X1: $i] :
( ( sK198(powerset(X0)) = sK140 )
| ( sK111(sK198(powerset(X0))) = X1 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega)
| ~ in(X1,sK198(powerset(X0)))
| ~ subset(sK111(sK198(powerset(X0))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149678,c_695]) ).
tcf(c_149799,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK198(powerset(sK254(X0))) = sK140 )
| ( sK255(sK198(powerset(sK254(X0)))) = X1 )
| ~ sP31(X2,X0)
| ~ in(sK254(X0),omega)
| ~ in(X1,sK198(powerset(sK254(X0))))
| ~ subset(sK255(sK198(powerset(sK254(X0)))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149690,c_695]) ).
tcf(c_149868,plain,
! [X0: $i,X1: $i] :
( ( powerset(powerset(sK62)) = sK140 )
| ( sK320(X0,powerset(powerset(sK62))) = sK140 )
| ( sK63(sK320(X0,powerset(powerset(sK62)))) = X1 )
| ~ iPr_def_20
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ subset(powerset(powerset(sK62)),relation_field(X0))
| ~ in(X1,sK320(X0,powerset(powerset(sK62))))
| ~ subset(sK63(sK320(X0,powerset(powerset(sK62)))),X1) ),
inference(superposition,[status(thm)],[c_148564,c_123600]) ).
tcf(c_149869,plain,
! [X0: $i] :
( in(sK63(sK320(X0,powerset(powerset(sK62)))),sK320(X0,powerset(powerset(sK62))))
| ( powerset(powerset(sK62)) = sK140 )
| ( sK320(X0,powerset(powerset(sK62))) = sK140 )
| ~ iPr_def_21
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ subset(powerset(powerset(sK62)),relation_field(X0)) ),
inference(superposition,[status(thm)],[c_148564,c_123602]) ).
tcf(c_149870,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(powerset(X1)) = sK140 )
| ( sK320(X0,powerset(powerset(X1))) = sK140 )
| ( sK111(sK320(X0,powerset(powerset(X1)))) = X2 )
| ~ sP15
| ~ well_founded_relation(X0)
| ~ ordinal(X1)
| ~ relation(X0)
| ~ in(X1,sK110)
| ~ in(X1,omega)
| ~ subset(powerset(powerset(X1)),relation_field(X0))
| ~ in(X2,sK320(X0,powerset(powerset(X1))))
| ~ subset(sK111(sK320(X0,powerset(powerset(X1)))),X2) ),
inference(superposition,[status(thm)],[c_148564,c_240]) ).
tcf(c_149871,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(powerset(X1)) = sK140 )
| ( sK320(X0,powerset(powerset(X1))) = sK140 )
| ( sK67(sK320(X0,powerset(powerset(X1)))) = X2 )
| ~ sP6
| ~ well_founded_relation(X0)
| ~ ordinal(X1)
| ~ relation(X0)
| ~ in(X1,sK66)
| ~ in(X1,omega)
| ~ subset(powerset(powerset(X1)),relation_field(X0))
| ~ in(X2,sK320(X0,powerset(powerset(X1))))
| ~ subset(sK67(sK320(X0,powerset(powerset(X1)))),X2) ),
inference(superposition,[status(thm)],[c_148564,c_143]) ).
tcf(c_149872,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(powerset(X1)) = sK140 )
| ( sK320(X0,powerset(powerset(X1))) = sK140 )
| ( sK72(sK320(X0,powerset(powerset(X1)))) = X2 )
| ~ iPr_def_18
| ~ well_founded_relation(X0)
| ~ ordinal(X1)
| ~ relation(X0)
| ~ in(X1,omega)
| ~ subset(powerset(powerset(X1)),relation_field(X0))
| ~ in(X2,sK320(X0,powerset(powerset(X1))))
| ~ subset(sK72(sK320(X0,powerset(powerset(X1)))),X2) ),
inference(superposition,[status(thm)],[c_148564,c_123596]) ).
tcf(c_149873,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP15
| ( powerset(powerset(X1)) = sK140 )
| ( sK320(X0,powerset(powerset(X1))) = sK140 )
| ( sK114(sK320(X0,powerset(powerset(X1)))) = X2 )
| ~ well_founded_relation(X0)
| ~ ordinal(X1)
| ~ relation(X0)
| ~ in(X1,omega)
| ~ subset(powerset(powerset(X1)),relation_field(X0))
| ~ in(X2,sK320(X0,powerset(powerset(X1))))
| ~ subset(sK114(sK320(X0,powerset(powerset(X1)))),X2) ),
inference(superposition,[status(thm)],[c_148564,c_248]) ).
tcf(c_149874,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(powerset(X1)) = sK140 )
| ( sK320(X0,powerset(powerset(X1))) = sK140 )
| ( sK119(sK320(X0,powerset(powerset(X1)))) = X2 )
| ~ well_founded_relation(X0)
| ~ finite(X1)
| ~ relation(X0)
| ~ subset(powerset(powerset(X1)),relation_field(X0))
| ~ in(X2,sK320(X0,powerset(powerset(X1))))
| ~ subset(sK119(sK320(X0,powerset(powerset(X1)))),X2) ),
inference(superposition,[status(thm)],[c_148564,c_308]) ).
tcf(c_149875,plain,
! [X0: $i,X1: $i] :
( in(sK111(sK320(X1,powerset(powerset(X0)))),sK320(X1,powerset(powerset(X0))))
| ( powerset(powerset(X0)) = sK140 )
| ( sK320(X1,powerset(powerset(X0))) = sK140 )
| ~ sP15
| ~ well_founded_relation(X1)
| ~ ordinal(X0)
| ~ relation(X1)
| ~ in(X0,sK110)
| ~ in(X0,omega)
| ~ subset(powerset(powerset(X0)),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_148564,c_239]) ).
tcf(c_149876,plain,
! [X0: $i,X1: $i] :
( in(sK67(sK320(X1,powerset(powerset(X0)))),sK320(X1,powerset(powerset(X0))))
| ( powerset(powerset(X0)) = sK140 )
| ( sK320(X1,powerset(powerset(X0))) = sK140 )
| ~ sP6
| ~ well_founded_relation(X1)
| ~ ordinal(X0)
| ~ relation(X1)
| ~ in(X0,sK66)
| ~ in(X0,omega)
| ~ subset(powerset(powerset(X0)),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_148564,c_142]) ).
tcf(c_149877,plain,
! [X0: $i,X1: $i] :
( in(sK72(sK320(X1,powerset(powerset(X0)))),sK320(X1,powerset(powerset(X0))))
| ( powerset(powerset(X0)) = sK140 )
| ( sK320(X1,powerset(powerset(X0))) = sK140 )
| ~ iPr_def_19
| ~ well_founded_relation(X1)
| ~ ordinal(X0)
| ~ relation(X1)
| ~ in(X0,omega)
| ~ subset(powerset(powerset(X0)),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_148564,c_123598]) ).
tcf(c_149878,plain,
! [X0: $i,X1: $i] :
( sP15
| in(sK114(sK320(X1,powerset(powerset(X0)))),sK320(X1,powerset(powerset(X0))))
| ( powerset(powerset(X0)) = sK140 )
| ( sK320(X1,powerset(powerset(X0))) = sK140 )
| ~ well_founded_relation(X1)
| ~ ordinal(X0)
| ~ relation(X1)
| ~ in(X0,omega)
| ~ subset(powerset(powerset(X0)),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_148564,c_247]) ).
tcf(c_149879,plain,
! [X0: $i,X1: $i] :
( in(sK119(sK320(X1,powerset(powerset(X0)))),sK320(X1,powerset(powerset(X0))))
| ( powerset(powerset(X0)) = sK140 )
| ( sK320(X1,powerset(powerset(X0))) = sK140 )
| ~ well_founded_relation(X1)
| ~ finite(X0)
| ~ relation(X1)
| ~ subset(powerset(powerset(X0)),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_148564,c_307]) ).
tcf(c_149882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( powerset(powerset(sK254(X1))) = sK140 )
| ( sK320(X0,powerset(powerset(sK254(X1)))) = sK140 )
| ( sK255(sK320(X0,powerset(powerset(sK254(X1))))) = X2 )
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ sP31(X3,X1)
| ~ in(sK254(X1),omega)
| ~ subset(powerset(powerset(sK254(X1))),relation_field(X0))
| ~ in(X2,sK320(X0,powerset(powerset(sK254(X1)))))
| ~ subset(sK255(sK320(X0,powerset(powerset(sK254(X1))))),X2) ),
inference(superposition,[status(thm)],[c_148564,c_826]) ).
tcf(c_149883,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK255(sK320(X1,powerset(powerset(sK254(X0))))),sK320(X1,powerset(powerset(sK254(X0)))))
| ( powerset(powerset(sK254(X0))) = sK140 )
| ( sK320(X1,powerset(powerset(sK254(X0)))) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ sP31(X2,X0)
| ~ in(sK254(X0),omega)
| ~ subset(powerset(powerset(sK254(X0))),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_148564,c_825]) ).
tcf(c_149884,plain,
! [X0: $i,X1: $i] :
( ( powerset(powerset(sK261)) = sK140 )
| ( sK320(X0,powerset(powerset(sK261))) = sK140 )
| ( sK262(sK320(X0,powerset(powerset(sK261)))) = X1 )
| ~ iPr_def_14
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ subset(powerset(powerset(sK261)),relation_field(X0))
| ~ in(X1,sK320(X0,powerset(powerset(sK261))))
| ~ subset(sK262(sK320(X0,powerset(powerset(sK261)))),X1) ),
inference(superposition,[status(thm)],[c_148564,c_123589]) ).
tcf(c_149885,plain,
! [X0: $i] :
( in(sK262(sK320(X0,powerset(powerset(sK261)))),sK320(X0,powerset(powerset(sK261))))
| ( powerset(powerset(sK261)) = sK140 )
| ( sK320(X0,powerset(powerset(sK261))) = sK140 )
| ~ iPr_def_15
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ subset(powerset(powerset(sK261)),relation_field(X0)) ),
inference(superposition,[status(thm)],[c_148564,c_123591]) ).
tcf(c_149886,plain,
! [X0: $i] :
( ordinal(sK320(X0,omega))
| ( sK140 = omega )
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ subset(omega,relation_field(X0)) ),
inference(superposition,[status(thm)],[c_148564,c_858]) ).
tcf(c_149887,plain,
! [X0: $i] :
( epsilon_connected(sK320(X0,omega))
| ( sK140 = omega )
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ subset(omega,relation_field(X0)) ),
inference(superposition,[status(thm)],[c_148564,c_857]) ).
tcf(c_149888,plain,
! [X0: $i] :
( epsilon_transitive(sK320(X0,omega))
| ( sK140 = omega )
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ subset(omega,relation_field(X0)) ),
inference(superposition,[status(thm)],[c_148564,c_856]) ).
tcf(c_150111,plain,
! [X0: $i] :
( sP15
| ~ subset(sK114(sK64),X0)
| ~ in(X0,sK64)
| ~ sP7
| ( sK114(sK64) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_145064,c_132,c_145064]) ).
tcf(c_150112,plain,
! [X0: $i] :
( sP15
| ( sK114(sK64) = X0 )
| ~ sP7
| ~ in(X0,sK64)
| ~ subset(sK114(sK64),X0) ),
inference(renaming,[status(thm)],[c_150111]) ).
tcf(c_150124,plain,
! [X0: $i] :
( sP15
| ( set_union2(sK114(sK64),X0) = sK114(sK64) )
| ~ sP7
| ~ in(set_union2(sK114(sK64),X0),sK64) ),
inference(superposition,[status(thm)],[c_498,c_150112]) ).
tcf(c_150139,plain,
( ordinal(sK263(powerset(sK140)))
| ( unordered_pair(sK140,sK140) = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,sK140))
| ~ ordinal(unordered_pair(sK140,sK140)) ),
inference(superposition,[status(thm)],[c_314,c_146168]) ).
tcf(c_150140,plain,
! [X0: $i] :
( epsilon_connected(sK263(unordered_pair(sK140,X0)))
| ( unordered_pair(sK140,X0) = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146168,c_1050]) ).
tcf(c_150141,plain,
! [X0: $i] :
( epsilon_transitive(sK263(unordered_pair(sK140,X0)))
| ( unordered_pair(sK140,X0) = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146168,c_1049]) ).
tcf(c_150168,plain,
( being_limit_ordinal(sK263(powerset(sK140)))
| ( unordered_pair(sK140,sK140) = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,sK140))
| ~ ordinal(unordered_pair(sK140,sK140)) ),
inference(superposition,[status(thm)],[c_314,c_146169]) ).
tcf(c_150179,plain,
! [X0: $i] :
( epsilon_connected(sK263(unordered_pair(X0,sK140)))
| ( unordered_pair(X0,sK140) = omega )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146210,c_1050]) ).
tcf(c_150180,plain,
! [X0: $i] :
( epsilon_transitive(sK263(unordered_pair(X0,sK140)))
| ( unordered_pair(X0,sK140) = omega )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146210,c_1049]) ).
tcf(c_150208,plain,
( ( sK125(sK140) = sK140 )
| ( apply(sK140,sK140) = sK140 ) ),
inference(superposition,[status(thm)],[c_148424,c_147103]) ).
tcf(c_150209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK140,relation_inverse_image(identity_relation(X0),X3))
| ( X2 = sK140 )
| ( sK125(X0) = sK140 )
| ~ function(identity_relation(X0))
| ~ in(sK140,X3)
| ~ in(sK140,X1)
| ~ quasi_total(identity_relation(X0),X1,X2)
| ~ relation_of2_as_subset(identity_relation(X0),X1,X2) ),
inference(superposition,[status(thm)],[c_147103,c_423]) ).
tcf(c_150210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK140,relation_inverse_image(identity_relation(X0),X3))
| ( X2 = sK140 )
| ( sK125(X0) = sK140 )
| ~ in(sK140,X3)
| ~ in(sK140,X1)
| ~ quasi_total(identity_relation(X0),X1,X2)
| ~ relation_of2_as_subset(identity_relation(X0),X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_150209,c_1100]) ).
tcf(c_150222,plain,
! [X0: $i] :
( sP3(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_122,c_787]) ).
tcf(c_150228,plain,
! [X0: $i] : ~ empty(sK116(X0)),
inference(superposition,[status(thm)],[c_272,c_787]) ).
tcf(c_150229,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_906,c_787]) ).
tcf(c_150230,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ~ empty(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2177,c_787]) ).
tcf(c_150232,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ~ ordinal(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_144620,c_787]) ).
tcf(c_150233,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ( X0 = sK140 )
| ~ element(X2,X0)
| ~ subset(X1,X0)
| ~ empty(subset_complement(X0,X1)) ),
inference(superposition,[status(thm)],[c_5403,c_787]) ).
tcf(c_150236,plain,
! [X0: $i] :
( ~ sP20(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_584,c_787]) ).
tcf(c_150238,plain,
! [X0: $i] :
( ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ empty(sK263(X0))
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_787]) ).
tcf(c_150241,plain,
! [X0: $i] : ~ empty(sK300(X0)),
inference(superposition,[status(thm)],[c_965,c_787]) ).
tcf(c_150243,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ~ well_founded_relation(X1)
| ~ empty(X0)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_787]) ).
tcf(c_150248,plain,
( ~ sP7
| ~ empty(sK64) ),
inference(superposition,[status(thm)],[c_146098,c_787]) ).
tcf(c_150249,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ~ empty(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144619,c_787]) ).
tcf(c_150254,plain,
( ( sK199(powerset(powerset(sK62))) = sK140 )
| ~ iPr_def_21
| ~ empty(sK199(powerset(powerset(sK62)))) ),
inference(superposition,[status(thm)],[c_145355,c_787]) ).
tcf(c_150255,plain,
! [X0: $i] :
( ( sK199(powerset(powerset(X0))) = sK140 )
| ~ finite(X0)
| ~ empty(sK199(powerset(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_145365,c_787]) ).
tcf(c_150256,plain,
( ( sK199(powerset(powerset(sK261))) = sK140 )
| ~ iPr_def_15
| ~ empty(sK199(powerset(powerset(sK261)))) ),
inference(superposition,[status(thm)],[c_145371,c_787]) ).
tcf(c_150257,plain,
( ( powerset(sK62) = sK140 )
| ~ iPr_def_21
| ~ empty(powerset(sK62)) ),
inference(superposition,[status(thm)],[c_145625,c_787]) ).
tcf(c_150261,plain,
( ( powerset(sK261) = sK140 )
| ~ iPr_def_15
| ~ empty(powerset(sK261)) ),
inference(superposition,[status(thm)],[c_145641,c_787]) ).
tcf(c_150265,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ empty(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_146008,c_787]) ).
tcf(c_150266,plain,
~ empty(set_union2(sK140,powerset(sK140))),
inference(superposition,[status(thm)],[c_148508,c_787]) ).
tcf(c_150335,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_146389,c_833]) ).
tcf(c_150336,plain,
( sP32(sK62)
| ordinal(sK261)
| ~ sP8 ),
inference(superposition,[status(thm)],[c_131,c_833]) ).
tcf(c_150337,plain,
( sP32(sK66)
| ordinal(sK261)
| ~ sP6 ),
inference(superposition,[status(thm)],[c_144,c_833]) ).
tcf(c_150338,plain,
( sP32(sK110)
| ordinal(sK261)
| ~ sP15 ),
inference(superposition,[status(thm)],[c_241,c_833]) ).
tcf(c_150339,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK128(X0))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_144621,c_833]) ).
tcf(c_150340,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(union(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_712,c_833]) ).
tcf(c_150343,plain,
( sP32(omega)
| ordinal(sK261) ),
inference(superposition,[status(thm)],[c_849,c_833]) ).
tcf(c_150344,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK268(X0))
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_862,c_833]) ).
tcf(c_150345,plain,
( sP32(sK281)
| ordinal(sK261) ),
inference(superposition,[status(thm)],[c_895,c_833]) ).
tcf(c_150346,plain,
( sP32(sK313)
| ordinal(sK261) ),
inference(superposition,[status(thm)],[c_1028,c_833]) ).
tcf(c_150347,plain,
( sP32(sK315)
| ordinal(sK261) ),
inference(superposition,[status(thm)],[c_1038,c_833]) ).
tcf(c_150348,plain,
( sP32(sK346)
| ordinal(sK261) ),
inference(superposition,[status(thm)],[c_1226,c_833]) ).
tcf(c_150349,plain,
( sP32(sK140)
| ordinal(sK261) ),
inference(superposition,[status(thm)],[c_144282,c_833]) ).
tcf(c_150350,plain,
( ordinal(sK261)
| sP32(sK263(sK116(sK140)))
| ( sK116(sK140) = omega )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145173,c_833]) ).
tcf(c_150351,plain,
( ordinal(sK261)
| sP32(sK263(sK300(sK140)))
| ( sK300(sK140) = omega )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145501,c_833]) ).
tcf(c_150352,plain,
! [X0: $i,X1: $i] :
( ordinal(sK261)
| sP32(sK128(set_difference(X0,X1)))
| ( set_difference(X0,X1) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_146009,c_833]) ).
tcf(c_150353,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK263(unordered_pair(sK140,X0)))
| ( unordered_pair(sK140,X0) = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146168,c_833]) ).
tcf(c_150354,plain,
( ordinal(sK261)
| sP32(sK263(powerset(sK140)))
| ( powerset(sK140) = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146193,c_833]) ).
tcf(c_150355,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK263(unordered_pair(X0,sK140)))
| ( unordered_pair(X0,sK140) = omega )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146210,c_833]) ).
tcf(c_150356,plain,
( ordinal(sK261)
| sP32(sK199(omega)) ),
inference(superposition,[status(thm)],[c_147637,c_833]) ).
tcf(c_150357,plain,
! [X0: $i,X1: $i] :
( ordinal(sK261)
| sP32(apply(sK126(X1),sK92(X0)))
| ( sK125(X1) = sK140 )
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_148430,c_833]) ).
tcf(c_150358,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK169(sK92(X0)))
| ( sK92(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_148434,c_833]) ).
tcf(c_150443,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(sK116(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(sK116(X0),X1))) = set_union2(sK116(X0),X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_150228]) ).
tcf(c_150444,plain,
! [X0: $i] :
( ( sK125(sK302(sK116(X0))) = sK140 )
| ( relation_dom(sK126(sK302(sK116(X0)))) = sK302(sK116(X0)) ) ),
inference(superposition,[status(thm)],[c_147722,c_150228]) ).
tcf(c_150445,plain,
! [X0: $i] :
( ( sK125(sK198(sK116(X0))) = sK140 )
| ( relation_dom(sK126(sK198(sK116(X0)))) = sK198(sK116(X0)) ) ),
inference(superposition,[status(thm)],[c_147277,c_150228]) ).
tcf(c_150446,plain,
! [X0: $i] :
( ( sK125(sK116(X0)) = sK140 )
| ( relation_dom(sK126(sK116(X0))) = sK116(X0) ) ),
inference(superposition,[status(thm)],[c_353,c_150228]) ).
tcf(c_150447,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(X0,sK116(X1))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK116(X1)))) = set_union2(X0,sK116(X1)) ) ),
inference(superposition,[status(thm)],[c_149341,c_150228]) ).
tcf(c_150462,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(sK300(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(sK300(X0),X1))) = set_union2(sK300(X0),X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_150241]) ).
tcf(c_150463,plain,
! [X0: $i] :
( ( sK125(sK302(sK300(X0))) = sK140 )
| ( relation_dom(sK126(sK302(sK300(X0)))) = sK302(sK300(X0)) ) ),
inference(superposition,[status(thm)],[c_147722,c_150241]) ).
tcf(c_150464,plain,
! [X0: $i] :
( ( sK125(sK198(sK300(X0))) = sK140 )
| ( relation_dom(sK126(sK198(sK300(X0)))) = sK198(sK300(X0)) ) ),
inference(superposition,[status(thm)],[c_147277,c_150241]) ).
tcf(c_150465,plain,
! [X0: $i] :
( ( sK125(sK300(X0)) = sK140 )
| ( relation_dom(sK126(sK300(X0))) = sK300(X0) ) ),
inference(superposition,[status(thm)],[c_353,c_150241]) ).
tcf(c_150466,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(X0,sK300(X1))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK300(X1)))) = set_union2(X0,sK300(X1)) ) ),
inference(superposition,[status(thm)],[c_149341,c_150241]) ).
tcf(c_150495,plain,
! [X0: $i] :
( sP3(X0)
| ( sK125(X0) = sK140 )
| ~ empty(sK58(X0)) ),
inference(superposition,[status(thm)],[c_122,c_150230]) ).
tcf(c_150500,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,unordered_pair(X0,X0))) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_256,c_150230]) ).
tcf(c_150501,plain,
! [X0: $i] :
( ( sK125(sK116(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_272,c_150230]) ).
tcf(c_150502,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,X1) = sK140 )
| ~ empty(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_150230]) ).
tcf(c_150503,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ~ in(X1,X0)
| ~ empty(apply(sK126(X0),X1)) ),
inference(superposition,[status(thm)],[c_2177,c_150230]) ).
tcf(c_150504,plain,
! [X0: $i] :
( ordinal(X0)
| ( sK125(X0) = sK140 )
| ~ empty(sK127(X0)) ),
inference(superposition,[status(thm)],[c_367,c_150230]) ).
tcf(c_150505,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ ordinal(X0)
| ~ empty(sK128(X0)) ),
inference(superposition,[status(thm)],[c_144620,c_150230]) ).
tcf(c_150506,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(subset_complement(X1,X0)) = sK140 )
| ~ empty(X2)
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5403,c_150230]) ).
tcf(c_150507,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(X0) = sK140 )
| ~ empty(sK163(X0)) ),
inference(superposition,[status(thm)],[c_561,c_150230]) ).
tcf(c_150508,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK169(X0)) ),
inference(superposition,[status(thm)],[c_579,c_150230]) ).
tcf(c_150509,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ~ sP20(X0)
| ~ empty(sK173(X0)) ),
inference(superposition,[status(thm)],[c_584,c_150230]) ).
tcf(c_150511,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK263(X0)) = sK140 )
| ~ empty(sK140)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_150230]) ).
tcf(c_150512,plain,
! [X0: $i,X1: $i] :
( ( sK125(unordered_pair(X0,X1)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_939,c_150230]) ).
tcf(c_150513,plain,
! [X0: $i,X1: $i] :
( ( sK125(unordered_pair(X1,X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_940,c_150230]) ).
tcf(c_150514,plain,
! [X0: $i] :
( ( sK125(sK300(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_965,c_150230]) ).
tcf(c_150515,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( sK125(X0) = sK140 )
| ~ empty(sK316(X0)) ),
inference(superposition,[status(thm)],[c_1043,c_150230]) ).
tcf(c_150516,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ empty(sK320(X1,X0))
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_150230]) ).
tcf(c_150517,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(X0) = sK140 )
| ~ empty(sK343(X0)) ),
inference(superposition,[status(thm)],[c_1207,c_150230]) ).
tcf(c_150518,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(X0) = sK140 )
| ~ empty(sK344(X0)) ),
inference(superposition,[status(thm)],[c_1208,c_150230]) ).
tcf(c_150520,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ relation(X0)
| ~ empty(unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0)))) ),
inference(superposition,[status(thm)],[c_16344,c_150230]) ).
tcf(c_150521,plain,
( ( sK125(sK64) = sK140 )
| ~ sP7
| ~ empty(sK119(sK64)) ),
inference(superposition,[status(thm)],[c_146098,c_150230]) ).
tcf(c_150522,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| ~ empty(sK318(X0,X1)) ),
inference(superposition,[status(thm)],[c_144619,c_150230]) ).
tcf(c_150523,plain,
( sP15
| ( sK125(sK64) = sK140 )
| ~ sP7
| ~ empty(sK114(sK64)) ),
inference(superposition,[status(thm)],[c_145791,c_150230]) ).
tcf(c_150524,plain,
( ( sK125(sK64) = sK140 )
| ~ iPr_def_19
| ~ sP7
| ~ empty(sK72(sK64)) ),
inference(superposition,[status(thm)],[c_145863,c_150230]) ).
tcf(c_150525,plain,
( ( sK125(sK64) = sK140 )
| ~ sP6
| ~ sP7
| ~ empty(sK67(sK64))
| ~ in(sK140,sK66) ),
inference(superposition,[status(thm)],[c_146728,c_150230]) ).
tcf(c_150526,plain,
( ( sK125(sK64) = sK140 )
| ~ sP15
| ~ sP7
| ~ empty(sK111(sK64))
| ~ in(sK140,sK110) ),
inference(superposition,[status(thm)],[c_146738,c_150230]) ).
tcf(c_150527,plain,
( ( sK199(powerset(powerset(sK62))) = sK140 )
| ( sK125(sK199(powerset(powerset(sK62)))) = sK140 )
| ~ iPr_def_21
| ~ empty(sK63(sK199(powerset(powerset(sK62))))) ),
inference(superposition,[status(thm)],[c_145355,c_150230]) ).
tcf(c_150528,plain,
! [X0: $i] :
( ( sK199(powerset(powerset(X0))) = sK140 )
| ( sK125(sK199(powerset(powerset(X0)))) = sK140 )
| ~ finite(X0)
| ~ empty(sK119(sK199(powerset(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_145365,c_150230]) ).
tcf(c_150529,plain,
( ( sK199(powerset(powerset(sK261))) = sK140 )
| ( sK125(sK199(powerset(powerset(sK261)))) = sK140 )
| ~ iPr_def_15
| ~ empty(sK262(sK199(powerset(powerset(sK261))))) ),
inference(superposition,[status(thm)],[c_145371,c_150230]) ).
tcf(c_150530,plain,
( ( powerset(sK62) = sK140 )
| ( sK125(powerset(sK62)) = sK140 )
| ~ iPr_def_21
| ~ empty(sK63(powerset(sK62))) ),
inference(superposition,[status(thm)],[c_145625,c_150230]) ).
tcf(c_150531,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ( sK125(powerset(X0)) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ empty(sK72(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145633,c_150230]) ).
tcf(c_150532,plain,
! [X0: $i] :
( sP15
| ( powerset(X0) = sK140 )
| ( sK125(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ empty(sK114(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145634,c_150230]) ).
tcf(c_150533,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ( sK125(powerset(X0)) = sK140 )
| ~ finite(X0)
| ~ empty(sK119(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145635,c_150230]) ).
tcf(c_150534,plain,
( ( powerset(sK261) = sK140 )
| ( sK125(powerset(sK261)) = sK140 )
| ~ iPr_def_15
| ~ empty(sK262(powerset(sK261))) ),
inference(superposition,[status(thm)],[c_145641,c_150230]) ).
tcf(c_150538,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = sK140 )
| ( sK125(set_difference(X0,X1)) = sK140 )
| ~ ordinal(X0)
| ~ empty(sK128(set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_146008,c_150230]) ).
tcf(c_150684,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(set_union2(sK169(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(sK169(X0),X1))) = set_union2(sK169(X0),X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_150508]) ).
tcf(c_150685,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK302(sK169(X0))) = sK140 )
| ( relation_dom(sK126(sK302(sK169(X0)))) = sK302(sK169(X0)) ) ),
inference(superposition,[status(thm)],[c_147722,c_150508]) ).
tcf(c_150686,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK198(sK169(X0))) = sK140 )
| ( relation_dom(sK126(sK198(sK169(X0)))) = sK198(sK169(X0)) ) ),
inference(superposition,[status(thm)],[c_147277,c_150508]) ).
tcf(c_150687,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK169(X0)) = sK140 )
| ( relation_dom(sK126(sK169(X0))) = sK169(X0) ) ),
inference(superposition,[status(thm)],[c_353,c_150508]) ).
tcf(c_150688,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( sK125(set_union2(X0,sK169(X1))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK169(X1)))) = set_union2(X0,sK169(X1)) ) ),
inference(superposition,[status(thm)],[c_149341,c_150508]) ).
tcf(c_150713,plain,
! [X0: $i,X1: $i] :
( element(X1,sK116(X0))
| ( sK125(sK116(X0)) = sK140 )
| ( apply(sK126(sK116(X0)),X1) = sK140 )
| ~ function(sK126(sK116(X0)))
| ~ relation(sK126(sK116(X0))) ),
inference(superposition,[status(thm)],[c_150446,c_148552]) ).
tcf(c_150715,plain,
! [X0: $i] :
( empty(sK116(X0))
| ( sK125(sK116(X0)) = sK140 )
| ~ empty(sK126(sK116(X0))) ),
inference(superposition,[status(thm)],[c_150446,c_641]) ).
tcf(c_150716,plain,
! [X0: $i,X1: $i] :
( in(X1,sK116(X0))
| ( sK125(sK116(X0)) = sK140 )
| ( apply(sK126(sK116(X0)),X1) = sK140 )
| ~ function(sK126(sK116(X0)))
| ~ relation(sK126(sK116(X0))) ),
inference(superposition,[status(thm)],[c_150446,c_906]) ).
tcf(c_150717,plain,
! [X0: $i] :
( ( sK125(sK116(X0)) = sK140 )
| ( relation_rng(sK126(sK116(X0))) = sK140 )
| ~ relation(sK126(sK116(X0)))
| ( sK116(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_150446,c_478]) ).
tcf(c_150718,plain,
! [X0: $i] :
( ( sK126(sK116(X0)) = sK140 )
| ( sK125(sK116(X0)) = sK140 )
| ~ relation(sK126(sK116(X0)))
| ( sK116(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_150446,c_475]) ).
tcf(c_150719,plain,
! [X0: $i] :
( ( sK125(sK116(X0)) = sK140 )
| ~ empty(sK126(sK116(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_150715,c_150228]) ).
tcf(c_150744,plain,
! [X0: $i,X1: $i] :
( element(X1,sK300(X0))
| ( sK125(sK300(X0)) = sK140 )
| ( apply(sK126(sK300(X0)),X1) = sK140 )
| ~ function(sK126(sK300(X0)))
| ~ relation(sK126(sK300(X0))) ),
inference(superposition,[status(thm)],[c_150465,c_148552]) ).
tcf(c_150746,plain,
! [X0: $i] :
( empty(sK300(X0))
| ( sK125(sK300(X0)) = sK140 )
| ~ empty(sK126(sK300(X0))) ),
inference(superposition,[status(thm)],[c_150465,c_641]) ).
tcf(c_150747,plain,
! [X0: $i,X1: $i] :
( in(X1,sK300(X0))
| ( sK125(sK300(X0)) = sK140 )
| ( apply(sK126(sK300(X0)),X1) = sK140 )
| ~ function(sK126(sK300(X0)))
| ~ relation(sK126(sK300(X0))) ),
inference(superposition,[status(thm)],[c_150465,c_906]) ).
tcf(c_150748,plain,
! [X0: $i] :
( ( sK125(sK300(X0)) = sK140 )
| ( relation_rng(sK126(sK300(X0))) = sK140 )
| ~ relation(sK126(sK300(X0)))
| ( sK300(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_150465,c_478]) ).
tcf(c_150749,plain,
! [X0: $i] :
( ( sK126(sK300(X0)) = sK140 )
| ( sK125(sK300(X0)) = sK140 )
| ~ relation(sK126(sK300(X0)))
| ( sK300(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_150465,c_475]) ).
tcf(c_150750,plain,
! [X0: $i] :
( ( sK125(sK300(X0)) = sK140 )
| ~ empty(sK126(sK300(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_150746,c_150241]) ).
tcf(c_150771,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ~ empty(relation_dom(X0))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_150229,c_785,c_643,c_150229]) ).
tcf(c_150772,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(renaming,[status(thm)],[c_150771]) ).
tcf(c_150779,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,X2) = sK140 )
| ( sK125(set_union2(relation_dom(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(relation_dom(X0),X1))) = set_union2(relation_dom(X0),X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_149359,c_150772]) ).
tcf(c_150780,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ( sK125(sK302(relation_dom(X0))) = sK140 )
| ( relation_dom(sK126(sK302(relation_dom(X0)))) = sK302(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_147722,c_150772]) ).
tcf(c_150781,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ( sK125(sK198(relation_dom(X0))) = sK140 )
| ( relation_dom(sK126(sK198(relation_dom(X0)))) = sK198(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_147277,c_150772]) ).
tcf(c_150782,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,X1) = sK140 )
| ( relation_dom(sK126(relation_dom(X0))) = relation_dom(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_353,c_150772]) ).
tcf(c_150783,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,X2) = sK140 )
| ( sK125(set_union2(X1,relation_dom(X0))) = sK140 )
| ( relation_dom(sK126(set_union2(X1,relation_dom(X0)))) = set_union2(X1,relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_149341,c_150772]) ).
tcf(c_150784,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_641,c_150772]) ).
tcf(c_150785,plain,
! [X0: $i,X1: $i] :
( ( apply(sK115(X0),X1) = sK140 )
| ~ empty(X0)
| ~ relation(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_150772]) ).
tcf(c_150786,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ empty(X0)
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_150772]) ).
tcf(c_150787,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ empty(X0)
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_150772]) ).
tcf(c_150788,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ empty(X0)
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_150772]) ).
tcf(c_150789,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ empty(X0)
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_150772]) ).
tcf(c_150790,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),X1) = sK140 )
| ~ empty(X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_150772]) ).
tcf(c_150800,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ empty(sK198(X0))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_150772]) ).
tcf(c_150801,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ empty(sK302(X0))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_150772]) ).
tcf(c_150807,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),X1) = sK140 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_150790,c_1101]) ).
tcf(c_150810,plain,
! [X0: $i,X1: $i] :
( ( apply(sK115(X0),X1) = sK140 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_150785,c_249]) ).
tcf(c_150875,plain,
! [X0: $i,X1: $i] :
( ( X0 = omega )
| ( sK125(set_union2(sK263(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(sK263(X0),X1))) = set_union2(sK263(X0),X1) )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_149359,c_150238]) ).
tcf(c_150876,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK302(sK263(X0))) = sK140 )
| ( relation_dom(sK126(sK302(sK263(X0)))) = sK302(sK263(X0)) )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_147722,c_150238]) ).
tcf(c_150877,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK198(sK263(X0))) = sK140 )
| ( relation_dom(sK126(sK198(sK263(X0)))) = sK198(sK263(X0)) )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_147277,c_150238]) ).
tcf(c_150878,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK263(X0)) = sK140 )
| ( relation_dom(sK126(sK263(X0))) = sK263(X0) )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_353,c_150238]) ).
tcf(c_150879,plain,
! [X0: $i,X1: $i] :
( ( X0 = omega )
| ( sK125(set_union2(X1,sK263(X0))) = sK140 )
| ( relation_dom(sK126(set_union2(X1,sK263(X0)))) = set_union2(X1,sK263(X0)) )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_149341,c_150238]) ).
tcf(c_150922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(set_union2(subset_complement(X1,X0),X3)) = sK140 )
| ( relation_dom(sK126(set_union2(subset_complement(X1,X0),X3))) = set_union2(subset_complement(X1,X0),X3) )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_149359,c_150233]) ).
tcf(c_150923,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(sK302(subset_complement(X1,X0))) = sK140 )
| ( relation_dom(sK126(sK302(subset_complement(X1,X0)))) = sK302(subset_complement(X1,X0)) )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_147722,c_150233]) ).
tcf(c_150924,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(sK198(subset_complement(X1,X0))) = sK140 )
| ( relation_dom(sK126(sK198(subset_complement(X1,X0)))) = sK198(subset_complement(X1,X0)) )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_147277,c_150233]) ).
tcf(c_150925,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(subset_complement(X1,X0)) = sK140 )
| ( relation_dom(sK126(subset_complement(X1,X0))) = subset_complement(X1,X0) )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_353,c_150233]) ).
tcf(c_150926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(set_union2(X3,subset_complement(X1,X0))) = sK140 )
| ( relation_dom(sK126(set_union2(X3,subset_complement(X1,X0)))) = set_union2(X3,subset_complement(X1,X0)) )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_149341,c_150233]) ).
tcf(c_150962,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK140,relation_inverse_image(sK115(X0),X3))
| ( X2 = sK140 )
| ( sK125(X0) = sK140 )
| ~ function(sK115(X0))
| ~ in(sK140,X3)
| ~ in(sK140,X1)
| ~ quasi_total(sK115(X0),X1,X2)
| ~ relation_of2_as_subset(sK115(X0),X1,X2) ),
inference(superposition,[status(thm)],[c_147107,c_423]) ).
tcf(c_150963,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK140,relation_inverse_image(sK115(X0),X3))
| ( X2 = sK140 )
| ( sK125(X0) = sK140 )
| ~ in(sK140,X3)
| ~ in(sK140,X1)
| ~ quasi_total(sK115(X0),X1,X2)
| ~ relation_of2_as_subset(sK115(X0),X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_150962,c_250]) ).
tcf(c_150975,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ~ sP34(X0)
| ~ empty(sK268(X0)) ),
inference(superposition,[status(thm)],[c_864,c_150230]) ).
tcf(c_150976,plain,
! [X0: $i] :
( ~ sP34(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_864,c_787]) ).
tcf(c_150977,plain,
! [X0: $i] :
( element(sK268(X0),X0)
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_864,c_526]) ).
tcf(c_150978,plain,
! [X0: $i] :
( ordinal(sK268(sK92(X0)))
| ~ sP34(sK92(X0)) ),
inference(superposition,[status(thm)],[c_864,c_199]) ).
tcf(c_150979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK268(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ sP34(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_864,c_425]) ).
tcf(c_150980,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK268(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ sP34(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_864,c_424]) ).
tcf(c_150981,plain,
~ sP34(sK140),
inference(superposition,[status(thm)],[c_864,c_580]) ).
tcf(c_151004,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(set_union2(X0,unordered_pair(X0,X0)),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(set_union2(X0,unordered_pair(X0,X0)),X1))) = set_union2(set_union2(X0,unordered_pair(X0,X0)),X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_892]) ).
tcf(c_151005,plain,
! [X0: $i] :
( ( sK125(sK302(set_union2(X0,unordered_pair(X0,X0)))) = sK140 )
| ( relation_dom(sK126(sK302(set_union2(X0,unordered_pair(X0,X0))))) = sK302(set_union2(X0,unordered_pair(X0,X0))) ) ),
inference(superposition,[status(thm)],[c_147722,c_892]) ).
tcf(c_151006,plain,
! [X0: $i] :
( ( sK125(sK198(set_union2(X0,unordered_pair(X0,X0)))) = sK140 )
| ( relation_dom(sK126(sK198(set_union2(X0,unordered_pair(X0,X0))))) = sK198(set_union2(X0,unordered_pair(X0,X0))) ) ),
inference(superposition,[status(thm)],[c_147277,c_892]) ).
tcf(c_151007,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,unordered_pair(X0,X0))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,unordered_pair(X0,X0)))) = set_union2(X0,unordered_pair(X0,X0)) ) ),
inference(superposition,[status(thm)],[c_353,c_892]) ).
tcf(c_151008,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(X0,set_union2(X1,unordered_pair(X1,X1)))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,set_union2(X1,unordered_pair(X1,X1))))) = set_union2(X0,set_union2(X1,unordered_pair(X1,X1))) ) ),
inference(superposition,[status(thm)],[c_149341,c_892]) ).
tcf(c_151032,plain,
! [X0: $i] : are_equipotent(X0,X0),
inference(superposition,[status(thm)],[c_667,c_971]) ).
tcf(c_151050,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(set_union2(apply(sK126(X1),X0),X2)) = sK140 )
| ( relation_dom(sK126(set_union2(apply(sK126(X1),X0),X2))) = set_union2(apply(sK126(X1),X0),X2) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_149359,c_150503]) ).
tcf(c_151051,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK302(apply(sK126(X1),X0))) = sK140 )
| ( relation_dom(sK126(sK302(apply(sK126(X1),X0)))) = sK302(apply(sK126(X1),X0)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_147722,c_150503]) ).
tcf(c_151052,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK198(apply(sK126(X1),X0))) = sK140 )
| ( relation_dom(sK126(sK198(apply(sK126(X1),X0)))) = sK198(apply(sK126(X1),X0)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_147277,c_150503]) ).
tcf(c_151053,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(apply(sK126(X1),X0)) = sK140 )
| ( relation_dom(sK126(apply(sK126(X1),X0))) = apply(sK126(X1),X0) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_353,c_150503]) ).
tcf(c_151054,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(set_union2(X2,apply(sK126(X1),X0))) = sK140 )
| ( relation_dom(sK126(set_union2(X2,apply(sK126(X1),X0)))) = set_union2(X2,apply(sK126(X1),X0)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_149341,c_150503]) ).
tcf(c_151088,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK312(X0,sK140) = sK140 )
| ~ subset(sK140,sK140) ),
inference(superposition,[status(thm)],[c_1021,c_148114]) ).
tcf(c_151089,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK312(X0,sK140) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151088,c_361]) ).
tcf(c_151098,plain,
! [X0: $i] :
( quasi_total(sK140,X0,sK140)
| ( X0 = sK140 ) ),
inference(superposition,[status(thm)],[c_151089,c_1021]) ).
tcf(c_151099,plain,
! [X0: $i] :
( relation_of2(sK140,X0,sK140)
| ( X0 = sK140 ) ),
inference(superposition,[status(thm)],[c_151089,c_1018]) ).
tcf(c_151102,plain,
! [X0: $i,X1: $i] :
( relation_of2_as_subset(sK140,X1,X0)
| ( X1 = sK140 )
| ~ subset(sK140,X0) ),
inference(superposition,[status(thm)],[c_151089,c_147960]) ).
tcf(c_151107,plain,
! [X0: $i,X1: $i] :
( relation_of2_as_subset(sK140,X0,X1)
| ( X0 = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151102,c_361]) ).
tcf(c_151146,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( sK125(set_union2(X0,X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_612,c_149417]) ).
tcf(c_151147,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( apply(sK126(set_union2(X0,X1)),X2) = sK140 )
| ~ empty(set_union2(X0,X1))
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_150772]) ).
tcf(c_151148,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( apply(sK126(set_union2(X0,X1)),X2) = sK140 )
| ~ function(sK126(set_union2(X0,X1)))
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_148552]) ).
tcf(c_151149,plain,
! [X0: $i,X1: $i] :
( relation(set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_642]) ).
tcf(c_151150,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_641]) ).
tcf(c_151151,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( apply(sK126(set_union2(X0,X1)),X2) = sK140 )
| ~ function(sK126(set_union2(X0,X1)))
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_906]) ).
tcf(c_151152,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_rng(sK126(set_union2(X0,X1))) = sK140 )
| ~ relation(sK126(set_union2(X0,X1)))
| ( set_union2(X0,X1) != sK140 ) ),
inference(superposition,[status(thm)],[c_149417,c_478]) ).
tcf(c_151153,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( sK126(set_union2(X0,X1)) = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ relation(sK126(set_union2(X0,X1)))
| ( set_union2(X0,X1) != sK140 ) ),
inference(superposition,[status(thm)],[c_149417,c_475]) ).
tcf(c_151198,plain,
! [X0: $i] :
( empty(powerset(sK62))
| ( sK302(powerset(sK62)) = sK140 )
| ( sK63(sK302(powerset(sK62))) = X0 )
| ~ iPr_def_20
| ~ in(X0,sK302(powerset(sK62)))
| ~ subset(sK63(sK302(powerset(sK62))),X0) ),
inference(superposition,[status(thm)],[c_972,c_123600]) ).
tcf(c_151199,plain,
( empty(powerset(sK62))
| in(sK63(sK302(powerset(sK62))),sK302(powerset(sK62)))
| ( sK302(powerset(sK62)) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_972,c_123602]) ).
tcf(c_151200,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| ( sK302(powerset(X0)) = sK140 )
| ( sK111(sK302(powerset(X0))) = X1 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega)
| ~ in(X1,sK302(powerset(X0)))
| ~ subset(sK111(sK302(powerset(X0))),X1) ),
inference(superposition,[status(thm)],[c_972,c_240]) ).
tcf(c_151201,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| ( sK302(powerset(X0)) = sK140 )
| ( sK67(sK302(powerset(X0))) = X1 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega)
| ~ in(X1,sK302(powerset(X0)))
| ~ subset(sK67(sK302(powerset(X0))),X1) ),
inference(superposition,[status(thm)],[c_972,c_143]) ).
tcf(c_151202,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| ( sK302(powerset(X0)) = sK140 )
| ( sK72(sK302(powerset(X0))) = X1 )
| ~ iPr_def_18
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK302(powerset(X0)))
| ~ subset(sK72(sK302(powerset(X0))),X1) ),
inference(superposition,[status(thm)],[c_972,c_123596]) ).
tcf(c_151203,plain,
! [X0: $i,X1: $i] :
( sP15
| empty(powerset(X0))
| ( sK302(powerset(X0)) = sK140 )
| ( sK114(sK302(powerset(X0))) = X1 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK302(powerset(X0)))
| ~ subset(sK114(sK302(powerset(X0))),X1) ),
inference(superposition,[status(thm)],[c_972,c_248]) ).
tcf(c_151204,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X0))
| ( sK302(powerset(X0)) = sK140 )
| ( sK119(sK302(powerset(X0))) = X1 )
| ~ finite(X0)
| ~ in(X1,sK302(powerset(X0)))
| ~ subset(sK119(sK302(powerset(X0))),X1) ),
inference(superposition,[status(thm)],[c_972,c_308]) ).
tcf(c_151205,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(sK111(sK302(powerset(X0))),sK302(powerset(X0)))
| ( sK302(powerset(X0)) = sK140 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_972,c_239]) ).
tcf(c_151206,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(sK67(sK302(powerset(X0))),sK302(powerset(X0)))
| ( sK302(powerset(X0)) = sK140 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_972,c_142]) ).
tcf(c_151207,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(sK72(sK302(powerset(X0))),sK302(powerset(X0)))
| ( sK302(powerset(X0)) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_972,c_123598]) ).
tcf(c_151208,plain,
! [X0: $i] :
( sP15
| empty(powerset(X0))
| in(sK114(sK302(powerset(X0))),sK302(powerset(X0)))
| ( sK302(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_972,c_247]) ).
tcf(c_151209,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(sK119(sK302(powerset(X0))),sK302(powerset(X0)))
| ( sK302(powerset(X0)) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_972,c_307]) ).
tcf(c_151212,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(sK254(X0)))
| ( sK302(powerset(sK254(X0))) = sK140 )
| ( sK255(sK302(powerset(sK254(X0)))) = X1 )
| ~ sP31(X2,X0)
| ~ in(sK254(X0),omega)
| ~ in(X1,sK302(powerset(sK254(X0))))
| ~ subset(sK255(sK302(powerset(sK254(X0)))),X1) ),
inference(superposition,[status(thm)],[c_972,c_826]) ).
tcf(c_151213,plain,
! [X0: $i,X1: $i] :
( empty(powerset(sK254(X0)))
| in(sK255(sK302(powerset(sK254(X0)))),sK302(powerset(sK254(X0))))
| ( sK302(powerset(sK254(X0))) = sK140 )
| ~ sP31(X1,X0)
| ~ in(sK254(X0),omega) ),
inference(superposition,[status(thm)],[c_972,c_825]) ).
tcf(c_151214,plain,
! [X0: $i] :
( empty(powerset(sK261))
| ( sK302(powerset(sK261)) = sK140 )
| ( sK262(sK302(powerset(sK261))) = X0 )
| ~ iPr_def_14
| ~ in(X0,sK302(powerset(sK261)))
| ~ subset(sK262(sK302(powerset(sK261))),X0) ),
inference(superposition,[status(thm)],[c_972,c_123589]) ).
tcf(c_151215,plain,
( empty(powerset(sK261))
| in(sK262(sK302(powerset(sK261))),sK302(powerset(sK261)))
| ( sK302(powerset(sK261)) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_972,c_123591]) ).
tcf(c_151217,plain,
( in(sK262(sK302(powerset(sK261))),sK302(powerset(sK261)))
| ( sK302(powerset(sK261)) = sK140 )
| ~ iPr_def_15 ),
inference(forward_subsumption_resolution,[status(thm)],[c_151215,c_695]) ).
tcf(c_151221,plain,
( in(sK63(sK302(powerset(sK62))),sK302(powerset(sK62)))
| ( sK302(powerset(sK62)) = sK140 )
| ~ iPr_def_21 ),
inference(forward_subsumption_resolution,[status(thm)],[c_151199,c_695]) ).
tcf(c_151225,plain,
! [X0: $i] :
( in(sK119(sK302(powerset(X0))),sK302(powerset(X0)))
| ( sK302(powerset(X0)) = sK140 )
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151209,c_695]) ).
tcf(c_151233,plain,
! [X0: $i] :
( sP15
| in(sK114(sK302(powerset(X0))),sK302(powerset(X0)))
| ( sK302(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151208,c_695]) ).
tcf(c_151239,plain,
! [X0: $i] :
( in(sK72(sK302(powerset(X0))),sK302(powerset(X0)))
| ( sK302(powerset(X0)) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151207,c_695]) ).
tcf(c_151245,plain,
! [X0: $i,X1: $i] :
( in(sK255(sK302(powerset(sK254(X0)))),sK302(powerset(sK254(X0))))
| ( sK302(powerset(sK254(X0))) = sK140 )
| ~ sP31(X1,X0)
| ~ in(sK254(X0),omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151213,c_695]) ).
tcf(c_151255,plain,
! [X0: $i] :
( in(sK67(sK302(powerset(X0))),sK302(powerset(X0)))
| ( sK302(powerset(X0)) = sK140 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151206,c_695]) ).
tcf(c_151262,plain,
! [X0: $i] :
( in(sK111(sK302(powerset(X0))),sK302(powerset(X0)))
| ( sK302(powerset(X0)) = sK140 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151205,c_695]) ).
tcf(c_151269,plain,
! [X0: $i] :
( ( sK302(powerset(sK261)) = sK140 )
| ( sK262(sK302(powerset(sK261))) = X0 )
| ~ iPr_def_14
| ~ in(X0,sK302(powerset(sK261)))
| ~ subset(sK262(sK302(powerset(sK261))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151214,c_695]) ).
tcf(c_151275,plain,
! [X0: $i] :
( ( sK302(powerset(sK62)) = sK140 )
| ( sK63(sK302(powerset(sK62))) = X0 )
| ~ iPr_def_20
| ~ in(X0,sK302(powerset(sK62)))
| ~ subset(sK63(sK302(powerset(sK62))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151198,c_695]) ).
tcf(c_151281,plain,
! [X0: $i,X1: $i] :
( ( sK302(powerset(X0)) = sK140 )
| ( sK119(sK302(powerset(X0))) = X1 )
| ~ finite(X0)
| ~ in(X1,sK302(powerset(X0)))
| ~ subset(sK119(sK302(powerset(X0))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151204,c_695]) ).
tcf(c_151287,plain,
! [X0: $i,X1: $i] :
( sP15
| ( sK302(powerset(X0)) = sK140 )
| ( sK114(sK302(powerset(X0))) = X1 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK302(powerset(X0)))
| ~ subset(sK114(sK302(powerset(X0))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151203,c_695]) ).
tcf(c_151295,plain,
! [X0: $i,X1: $i] :
( ( sK302(powerset(X0)) = sK140 )
| ( sK72(sK302(powerset(X0))) = X1 )
| ~ iPr_def_18
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(X1,sK302(powerset(X0)))
| ~ subset(sK72(sK302(powerset(X0))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151202,c_695]) ).
tcf(c_151303,plain,
! [X0: $i,X1: $i] :
( ( sK302(powerset(X0)) = sK140 )
| ( sK67(sK302(powerset(X0))) = X1 )
| ~ sP6
| ~ ordinal(X0)
| ~ in(X0,sK66)
| ~ in(X0,omega)
| ~ in(X1,sK302(powerset(X0)))
| ~ subset(sK67(sK302(powerset(X0))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151201,c_695]) ).
tcf(c_151312,plain,
! [X0: $i,X1: $i] :
( ( sK302(powerset(X0)) = sK140 )
| ( sK111(sK302(powerset(X0))) = X1 )
| ~ sP15
| ~ ordinal(X0)
| ~ in(X0,sK110)
| ~ in(X0,omega)
| ~ in(X1,sK302(powerset(X0)))
| ~ subset(sK111(sK302(powerset(X0))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151200,c_695]) ).
tcf(c_151321,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK302(powerset(sK254(X0))) = sK140 )
| ( sK255(sK302(powerset(sK254(X0)))) = X1 )
| ~ sP31(X2,X0)
| ~ in(sK254(X0),omega)
| ~ in(X1,sK302(powerset(sK254(X0))))
| ~ subset(sK255(sK302(powerset(sK254(X0)))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151212,c_695]) ).
tcf(c_151382,plain,
! [X0: $i,X1: $i] :
( sP3(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_150222]) ).
tcf(c_151383,plain,
! [X0: $i] :
( sP3(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( relation_dom(sK126(sK302(X0))) = sK302(X0) ) ),
inference(superposition,[status(thm)],[c_147722,c_150222]) ).
tcf(c_151384,plain,
! [X0: $i] :
( sP3(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( relation_dom(sK126(sK198(X0))) = sK198(X0) ) ),
inference(superposition,[status(thm)],[c_147277,c_150222]) ).
tcf(c_151385,plain,
! [X0: $i] :
( sP3(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_353,c_150222]) ).
tcf(c_151386,plain,
! [X0: $i,X1: $i] :
( sP3(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_149341,c_150222]) ).
tcf(c_151388,plain,
! [X0: $i] :
( sP3(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_641,c_150222]) ).
tcf(c_151389,plain,
! [X0: $i] :
( sP3(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_943,c_150222]) ).
tcf(c_151390,plain,
! [X0: $i] :
( sP3(relation_inverse(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1111,c_150222]) ).
tcf(c_151419,plain,
! [X0: $i] :
( ( sK125(set_union2(sK64,X0)) = sK140 )
| ( relation_dom(sK126(set_union2(sK64,X0))) = set_union2(sK64,X0) )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_149359,c_150248]) ).
tcf(c_151420,plain,
( ( sK125(sK302(sK64)) = sK140 )
| ( relation_dom(sK126(sK302(sK64))) = sK302(sK64) )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_147722,c_150248]) ).
tcf(c_151421,plain,
( ( sK125(sK198(sK64)) = sK140 )
| ( relation_dom(sK126(sK198(sK64))) = sK198(sK64) )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_147277,c_150248]) ).
tcf(c_151422,plain,
( ( sK125(sK64) = sK140 )
| ( relation_dom(sK126(sK64)) = sK64 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_353,c_150248]) ).
tcf(c_151423,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,sK64)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK64))) = set_union2(X0,sK64) )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_149341,c_150248]) ).
tcf(c_151459,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( sK125(set_union2(X0,sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_611,c_149522]) ).
tcf(c_151461,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( apply(sK126(set_union2(X0,X1)),X2) = sK140 )
| ~ empty(set_union2(X0,X1))
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_150772]) ).
tcf(c_151462,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( apply(sK126(set_union2(X0,X1)),X2) = sK140 )
| ~ function(sK126(set_union2(X0,X1)))
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_148552]) ).
tcf(c_151463,plain,
! [X0: $i,X1: $i] :
( relation(set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_642]) ).
tcf(c_151464,plain,
! [X0: $i,X1: $i] :
( empty(set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_641]) ).
tcf(c_151465,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( apply(sK126(set_union2(X0,X1)),X2) = sK140 )
| ~ function(sK126(set_union2(X0,X1)))
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_906]) ).
tcf(c_151466,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_rng(sK126(set_union2(X0,X1))) = sK140 )
| ~ relation(sK126(set_union2(X0,X1)))
| ( set_union2(X0,X1) != sK140 ) ),
inference(superposition,[status(thm)],[c_149522,c_478]) ).
tcf(c_151467,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK126(set_union2(X0,X1)) = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ relation(sK126(set_union2(X0,X1)))
| ( set_union2(X0,X1) != sK140 ) ),
inference(superposition,[status(thm)],[c_149522,c_475]) ).
tcf(c_151515,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( sK125(relation_dom(X0)) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( apply(X0,X1) = sK140 )
| ~ empty(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_146146,c_150502]) ).
tcf(c_151516,plain,
! [X0: $i,X1: $i] :
( sP13(X0)
| ( sK125(relation_dom(sK108(X0))) = sK140 )
| ( apply(sK108(X0),X1) = sK140 )
| ~ empty(X1)
| ~ relation(sK108(X0)) ),
inference(superposition,[status(thm)],[c_232,c_150502]) ).
tcf(c_151517,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(sK115(X0))) = sK140 )
| ( apply(sK115(X0),X1) = sK140 )
| ~ empty(X1)
| ~ relation(sK115(X0)) ),
inference(superposition,[status(thm)],[c_250,c_150502]) ).
tcf(c_151518,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( sK125(relation_dom(sK126(X0))) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ empty(X1)
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_356,c_150502]) ).
tcf(c_151519,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(identity_relation(X0))) = sK140 )
| ( apply(identity_relation(X0),X1) = sK140 )
| ~ empty(X1)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1100,c_150502]) ).
tcf(c_151520,plain,
! [X0: $i] :
( ( sK125(relation_dom(sK240)) = sK140 )
| ( apply(sK240,X0) = sK140 )
| ~ relation(sK240)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_784,c_150502]) ).
tcf(c_151521,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(sK264(X0))) = sK140 )
| ( apply(sK264(X0),X1) = sK140 )
| ~ finite(X0)
| ~ empty(X1)
| ~ relation(sK264(X0)) ),
inference(superposition,[status(thm)],[c_853,c_150502]) ).
tcf(c_151522,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(relation_dom(sK312(X0,X1))) = sK140 )
| ( apply(sK312(X0,X1),X2) = sK140 )
| ~ empty(X2)
| ~ relation(sK312(X0,X1)) ),
inference(superposition,[status(thm)],[c_1020,c_150502]) ).
tcf(c_151523,plain,
! [X0: $i] :
( ( sK125(relation_dom(sK335)) = sK140 )
| ( apply(sK335,X0) = sK140 )
| ~ relation(sK335)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1150,c_150502]) ).
tcf(c_151524,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(relation_dom(sK347(X0,X1))) = sK140 )
| ( apply(sK347(X0,X1),X2) = sK140 )
| ~ empty(X2)
| ~ relation(sK347(X0,X1)) ),
inference(superposition,[status(thm)],[c_1238,c_150502]) ).
tcf(c_151526,plain,
! [X0: $i] :
( ( sK125(relation_dom(sK335)) = sK140 )
| ( apply(sK335,X0) = sK140 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151523,c_1149]) ).
tcf(c_151530,plain,
! [X0: $i] :
( ( sK125(relation_dom(sK240)) = sK140 )
| ( apply(sK240,X0) = sK140 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151520,c_783]) ).
tcf(c_151534,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( apply(identity_relation(X0),X1) = sK140 )
| ~ empty(X1)
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_151519,c_489]) ).
tcf(c_151535,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( apply(identity_relation(X1),X0) = sK140 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151534,c_1101]) ).
tcf(c_151539,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( apply(sK115(X0),X1) = sK140 )
| ~ empty(X1)
| ~ relation(sK115(X0)) ),
inference(light_normalisation,[status(thm)],[c_151517,c_251]) ).
tcf(c_151540,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( apply(sK115(X1),X0) = sK140 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151539,c_249]) ).
tcf(c_151549,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(relation_dom(sK347(X1,X2))) = sK140 )
| ( apply(sK347(X1,X2),X0) = sK140 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151524,c_1237]) ).
tcf(c_151553,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(relation_dom(sK312(X1,X2))) = sK140 )
| ( apply(sK312(X1,X2),X0) = sK140 )
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151522,c_1019]) ).
tcf(c_151579,plain,
! [X0: $i] :
( ~ subset(sK72(sK64),X0)
| ~ in(X0,sK64)
| ~ sP7
| ~ iPr_def_18
| ( sK72(sK64) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_145134,c_132,c_145134]) ).
tcf(c_151580,plain,
! [X0: $i] :
( ( sK72(sK64) = X0 )
| ~ iPr_def_18
| ~ sP7
| ~ in(X0,sK64)
| ~ subset(sK72(sK64),X0) ),
inference(renaming,[status(thm)],[c_151579]) ).
tcf(c_151592,plain,
! [X0: $i] :
( ( set_union2(sK72(sK64),X0) = sK72(sK64) )
| ~ iPr_def_18
| ~ sP7
| ~ in(set_union2(sK72(sK64),X0),sK64) ),
inference(superposition,[status(thm)],[c_498,c_151580]) ).
tcf(c_151609,plain,
! [X0: $i] :
( in(sK140,sK140)
| ( X0 = sK140 )
| ( sK125(subset_complement(X0,sK140)) = sK140 )
| ~ element(sK140,X0) ),
inference(superposition,[status(thm)],[c_361,c_145539]) ).
tcf(c_151610,plain,
! [X0: $i,X1: $i] :
( in(sK140,set_difference(X0,X1))
| ( X0 = sK140 )
| ( sK125(subset_complement(X0,set_difference(X0,X1))) = sK140 )
| ~ element(sK140,X0) ),
inference(superposition,[status(thm)],[c_383,c_145539]) ).
tcf(c_151611,plain,
! [X0: $i,X1: $i] :
( in(sK140,X0)
| ( set_union2(X0,X1) = sK140 )
| ( sK125(subset_complement(set_union2(X0,X1),X0)) = sK140 )
| ~ element(sK140,set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_498,c_145539]) ).
tcf(c_151612,plain,
! [X0: $i] :
( in(sK140,X0)
| ( X0 = sK140 )
| ( sK125(subset_complement(X0,X0)) = sK140 )
| ~ element(sK140,X0) ),
inference(superposition,[status(thm)],[c_665,c_145539]) ).
tcf(c_151623,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(subset_complement(X0,sK140)) = sK140 )
| ~ element(sK140,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151609,c_580]) ).
tcf(c_151641,plain,
( ( sK140 = omega )
| ( sK125(subset_complement(omega,sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_148546,c_151623]) ).
tcf(c_151642,plain,
( ( powerset(sK140) = sK140 )
| ( sK125(subset_complement(powerset(sK140),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_12479,c_151623]) ).
tcf(c_151643,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ( sK125(subset_complement(powerset(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146123,c_151623]) ).
tcf(c_151644,plain,
( ( sK116(sK140) = sK140 )
| ( sK125(subset_complement(sK116(sK140),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_148551,c_151623]) ).
tcf(c_151645,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK140 )
| ( apply(X0,sK140) = sK140 )
| ( sK125(subset_complement(relation_dom(X0),sK140)) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_148552,c_151623]) ).
tcf(c_151646,plain,
! [X0: $i,X1: $i] :
( in(sK140,X0)
| ( X1 = sK140 )
| ( subset_complement(X1,X0) = sK140 )
| ( sK125(subset_complement(subset_complement(X1,X0),sK140)) = sK140 )
| ~ element(sK140,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_148556,c_151623]) ).
tcf(c_151647,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK263(X0) = sK140 )
| ( sK125(subset_complement(sK263(X0),sK140)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_148559,c_151623]) ).
tcf(c_151648,plain,
! [X0: $i] :
( ( unordered_pair(sK140,X0) = sK140 )
| ( sK125(subset_complement(unordered_pair(sK140,X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_148560,c_151623]) ).
tcf(c_151649,plain,
! [X0: $i] :
( ( unordered_pair(X0,sK140) = sK140 )
| ( sK125(subset_complement(unordered_pair(X0,sK140),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_148561,c_151623]) ).
tcf(c_151650,plain,
( ( sK300(sK140) = sK140 )
| ( sK125(subset_complement(sK300(sK140),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_148562,c_151623]) ).
tcf(c_151659,plain,
sK125(subset_complement(powerset(sK140),sK140)) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_151642,c_144206]) ).
tcf(c_151697,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,sK140),sK140)
| ( set_difference(sK140,X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,sK140) ),
inference(superposition,[status(thm)],[c_674,c_146007]) ).
tcf(c_151698,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,X1),X1)
| ( set_difference(X1,sK140) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_675,c_146007]) ).
tcf(c_151699,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,sK140),sK140)
| ( set_difference(X1,X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_12910,c_146007]) ).
tcf(c_151700,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,sK140),sK140)
| ( set_difference(set_difference(X1,X2),X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_146010,c_146007]) ).
tcf(c_151701,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,unordered_pair(X1,X1)),unordered_pair(X1,X1))
| ( set_difference(unordered_pair(X1,X1),X2) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_146011,c_146007]) ).
tcf(c_151702,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,sK140),sK140)
| ( set_difference(X1,set_union2(X1,X2)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_146042,c_146007]) ).
tcf(c_151703,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,powerset(sK140)),powerset(sK140))
| ( set_difference(powerset(sK140),X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146297,c_146007]) ).
tcf(c_151704,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X1,X2) = sK140 )
| ( sK125(set_difference(X1,X2)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1)
| ~ empty(sK318(X0,set_difference(X1,X2))) ),
inference(superposition,[status(thm)],[c_146007,c_150230]) ).
tcf(c_151705,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,X1) = sK140 )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X0)
| ~ empty(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_146007,c_787]) ).
tcf(c_151706,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(sK318(X0,set_difference(X1,X2)),set_difference(X1,X2))
| ( set_difference(X1,X2) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_146007,c_526]) ).
tcf(c_151738,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(relation_dom(sK140)) = sK140 )
| ( apply(sK312(X0,sK140),sK140) = sK140 ) ),
inference(superposition,[status(thm)],[c_151089,c_147117]) ).
tcf(c_151739,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(sK140) = sK140 )
| ( apply(sK312(X0,sK140),sK140) = sK140 ) ),
inference(light_normalisation,[status(thm)],[c_151738,c_470]) ).
tcf(c_151756,plain,
! [X0: $i] :
( in(sK140,X0)
| disjoint(powerset(sK140),X0) ),
inference(superposition,[status(thm)],[c_314,c_55]) ).
tcf(c_151757,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| disjoint(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_55,c_624]) ).
tcf(c_151758,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_55,c_626]) ).
tcf(c_151772,plain,
! [X0: $i] :
( sP3(sK92(X0))
| in(sK58(sK92(X0)),X0) ),
inference(superposition,[status(thm)],[c_122,c_198]) ).
tcf(c_151774,plain,
! [X0: $i,X1: $i] :
( in(apply(sK126(X1),sK92(X0)),X0)
| ( sK125(X1) = sK140 )
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_2177,c_198]) ).
tcf(c_151775,plain,
! [X0: $i] :
( ordinal(sK92(X0))
| in(sK127(sK92(X0)),X0) ),
inference(superposition,[status(thm)],[c_367,c_198]) ).
tcf(c_151776,plain,
! [X0: $i] :
( in(sK128(sK92(X0)),X0)
| ( sK92(X0) = sK140 )
| ~ ordinal(sK92(X0)) ),
inference(superposition,[status(thm)],[c_144620,c_198]) ).
tcf(c_151777,plain,
! [X0: $i] :
( relation(sK92(X0))
| in(sK163(sK92(X0)),X0) ),
inference(superposition,[status(thm)],[c_561,c_198]) ).
tcf(c_151778,plain,
! [X0: $i] :
( in(sK169(sK92(X0)),X0)
| ( sK92(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_579,c_198]) ).
tcf(c_151779,plain,
! [X0: $i] :
( in(sK173(sK92(X0)),X0)
| ~ sP20(sK92(X0)) ),
inference(superposition,[status(thm)],[c_584,c_198]) ).
tcf(c_151781,plain,
! [X0: $i] :
( in(sK268(sK92(X0)),X0)
| ~ sP34(sK92(X0)) ),
inference(superposition,[status(thm)],[c_864,c_198]) ).
tcf(c_151782,plain,
! [X0: $i] :
( epsilon_transitive(sK92(X0))
| in(sK316(sK92(X0)),X0) ),
inference(superposition,[status(thm)],[c_1043,c_198]) ).
tcf(c_151783,plain,
! [X0: $i,X1: $i] :
( in(sK320(X1,sK92(X0)),X0)
| ( sK92(X0) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(sK92(X0),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_198]) ).
tcf(c_151784,plain,
! [X0: $i] :
( epsilon_connected(sK92(X0))
| in(sK343(sK92(X0)),X0) ),
inference(superposition,[status(thm)],[c_1207,c_198]) ).
tcf(c_151785,plain,
! [X0: $i] :
( epsilon_connected(sK92(X0))
| in(sK344(sK92(X0)),X0) ),
inference(superposition,[status(thm)],[c_1208,c_198]) ).
tcf(c_151786,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK137(sK92(X0)),sK137(sK92(X0))),unordered_pair(sK137(sK92(X0)),sK138(sK92(X0)))),X0)
| ( sK92(X0) = sK140 )
| ~ relation(sK92(X0)) ),
inference(superposition,[status(thm)],[c_16344,c_198]) ).
tcf(c_151787,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,sK92(X1)),X1)
| ( sK92(X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,sK92(X1)) ),
inference(superposition,[status(thm)],[c_144619,c_198]) ).
tcf(c_151858,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(set_union2(sK115(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(sK115(X0),X1))) = set_union2(sK115(X0),X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_147177]) ).
tcf(c_151859,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK302(sK115(X0))) = sK140 )
| ( relation_dom(sK126(sK302(sK115(X0)))) = sK302(sK115(X0)) ) ),
inference(superposition,[status(thm)],[c_147722,c_147177]) ).
tcf(c_151860,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK198(sK115(X0))) = sK140 )
| ( relation_dom(sK126(sK198(sK115(X0)))) = sK198(sK115(X0)) ) ),
inference(superposition,[status(thm)],[c_147277,c_147177]) ).
tcf(c_151861,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_353,c_147177]) ).
tcf(c_151862,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(set_union2(X0,sK115(X1))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK115(X1)))) = set_union2(X0,sK115(X1)) ) ),
inference(superposition,[status(thm)],[c_149341,c_147177]) ).
tcf(c_151883,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(set_union2(identity_relation(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(identity_relation(X0),X1))) = set_union2(identity_relation(X0),X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_147179]) ).
tcf(c_151884,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK302(identity_relation(X0))) = sK140 )
| ( relation_dom(sK126(sK302(identity_relation(X0)))) = sK302(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_147722,c_147179]) ).
tcf(c_151885,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK198(identity_relation(X0))) = sK140 )
| ( relation_dom(sK126(sK198(identity_relation(X0)))) = sK198(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_147277,c_147179]) ).
tcf(c_151886,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_353,c_147179]) ).
tcf(c_151887,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(set_union2(X0,identity_relation(X1))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,identity_relation(X1)))) = set_union2(X0,identity_relation(X1)) ) ),
inference(superposition,[status(thm)],[c_149341,c_147179]) ).
tcf(c_151908,plain,
! [X0: $i] :
( in(sK140,X0)
| disjoint(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_151756,c_624]) ).
tcf(c_151909,plain,
! [X0: $i] :
( in(sK140,X0)
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151756,c_626]) ).
tcf(c_151920,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( sK92(X0) = sK140 )
| ~ empty(sK169(sK92(X0))) ),
inference(superposition,[status(thm)],[c_151778,c_150230]) ).
tcf(c_151921,plain,
! [X0: $i] :
( ( sK92(X0) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_151778,c_787]) ).
tcf(c_151922,plain,
! [X0: $i] :
( element(sK169(sK92(X0)),X0)
| ( sK92(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_151778,c_526]) ).
tcf(c_151923,plain,
! [X0: $i] :
( in(sK169(sK92(sK92(X0))),X0)
| ( sK92(sK92(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151778,c_198]) ).
tcf(c_151924,plain,
! [X0: $i] :
( ordinal(sK169(sK92(sK92(X0))))
| ( sK92(sK92(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151778,c_199]) ).
tcf(c_151925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK169(sK92(relation_inverse_image(X0,X3)))),X3)
| ( X2 = sK140 )
| ( sK92(relation_inverse_image(X0,X3)) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_151778,c_425]) ).
tcf(c_151926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK169(sK92(relation_inverse_image(X0,X3))),X1)
| ( X2 = sK140 )
| ( sK92(relation_inverse_image(X0,X3)) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_151778,c_424]) ).
tcf(c_151927,plain,
sK92(sK140) = sK140,
inference(superposition,[status(thm)],[c_151778,c_580]) ).
tcf(c_151954,plain,
! [X0: $i] :
( ordinal(apply(sK126(X0),sK140))
| ( sK125(X0) = sK140 )
| ~ in(sK92(sK140),X0) ),
inference(superposition,[status(thm)],[c_151927,c_148430]) ).
tcf(c_151964,plain,
! [X0: $i] :
( ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_151909,c_787]) ).
tcf(c_151965,plain,
! [X0: $i] :
( element(sK140,X0)
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151909,c_526]) ).
tcf(c_151966,plain,
! [X0: $i] :
( in(sK140,X0)
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),sK92(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151909,c_198]) ).
tcf(c_151968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK140),X3)
| ( X2 = sK140 )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),relation_inverse_image(X0,X3))) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_151909,c_425]) ).
tcf(c_151969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK140,X1)
| ( X2 = sK140 )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),relation_inverse_image(X0,X3))) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_151909,c_424]) ).
tcf(c_151970,plain,
set_difference(powerset(sK140),set_difference(powerset(sK140),sK140)) = sK140,
inference(superposition,[status(thm)],[c_151909,c_580]) ).
tcf(c_151971,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK263(X0)) = sK140 )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151909,c_145540]) ).
tcf(c_151972,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151909,c_144395]) ).
tcf(c_151973,plain,
! [X0: $i] :
( ordinal(sK263(X0))
| ( X0 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151909,c_846]) ).
tcf(c_151974,plain,
! [X0: $i] :
( being_limit_ordinal(sK263(X0))
| ( X0 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151909,c_845]) ).
tcf(c_151975,plain,
! [X0: $i] :
( subset(omega,X0)
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151909,c_850]) ).
tcf(c_152025,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_151758,c_150230]) ).
tcf(c_152026,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X1,X1),set_difference(unordered_pair(X1,X1),X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_151758,c_787]) ).
tcf(c_152027,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_526]) ).
tcf(c_152028,plain,
( iPr_def_21
| ( set_difference(unordered_pair(sK62,sK62),set_difference(unordered_pair(sK62,sK62),omega)) = sK140 )
| ~ sP8 ),
inference(superposition,[status(thm)],[c_151758,c_123603]) ).
tcf(c_152029,plain,
( iPr_def_20
| ( set_difference(unordered_pair(sK62,sK62),set_difference(unordered_pair(sK62,sK62),omega)) = sK140 )
| ~ sP8 ),
inference(superposition,[status(thm)],[c_151758,c_123601]) ).
tcf(c_152030,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),sK92(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_198]) ).
tcf(c_152031,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),sK92(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_199]) ).
tcf(c_152032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,X3),X4)
| ( X2 = sK140 )
| ( set_difference(unordered_pair(X3,X3),set_difference(unordered_pair(X3,X3),relation_inverse_image(X0,X4))) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_151758,c_425]) ).
tcf(c_152033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X3,X1)
| ( X2 = sK140 )
| ( set_difference(unordered_pair(X3,X3),set_difference(unordered_pair(X3,X3),relation_inverse_image(X0,X4))) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_151758,c_424]) ).
tcf(c_152034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X3,relation_inverse_image(X0,X4))
| ( X2 = sK140 )
| ( set_difference(unordered_pair(apply(X0,X3),apply(X0,X3)),set_difference(unordered_pair(apply(X0,X3),apply(X0,X3)),X4)) = sK140 )
| ~ function(X0)
| ~ in(X3,X1)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_151758,c_423]) ).
tcf(c_152035,plain,
! [X0: $i] : set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),sK140)) = sK140,
inference(superposition,[status(thm)],[c_151758,c_580]) ).
tcf(c_152036,plain,
( iPr_def_15
| iPr_def_10
| ( set_difference(unordered_pair(sK261,sK261),set_difference(unordered_pair(sK261,sK261),omega)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_123592]) ).
tcf(c_152037,plain,
( iPr_def_14
| iPr_def_10
| ( set_difference(unordered_pair(sK261,sK261),set_difference(unordered_pair(sK261,sK261),omega)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_123590]) ).
tcf(c_152038,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK263(X0)) = sK140 )
| ( set_difference(unordered_pair(sK140,sK140),set_difference(unordered_pair(sK140,sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151758,c_145540]) ).
tcf(c_152039,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( set_difference(unordered_pair(sK140,sK140),set_difference(unordered_pair(sK140,sK140),X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_144395]) ).
tcf(c_152040,plain,
! [X0: $i] :
( ordinal(sK263(X0))
| ( X0 = omega )
| ( set_difference(unordered_pair(sK140,sK140),set_difference(unordered_pair(sK140,sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151758,c_846]) ).
tcf(c_152041,plain,
! [X0: $i] :
( being_limit_ordinal(sK263(X0))
| ( X0 = omega )
| ( set_difference(unordered_pair(sK140,sK140),set_difference(unordered_pair(sK140,sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151758,c_845]) ).
tcf(c_152042,plain,
! [X0: $i] :
( subset(omega,X0)
| ( set_difference(unordered_pair(sK140,sK140),set_difference(unordered_pair(sK140,sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151758,c_850]) ).
tcf(c_152117,plain,
( iPr_def_15
| iPr_def_10
| ( set_difference(omega,set_difference(omega,unordered_pair(sK261,sK261))) = sK140 ) ),
inference(demodulation,[status(thm)],[c_152036,c_961]) ).
tcf(c_152133,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ empty(sK198(X0))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_150772]) ).
tcf(c_152134,plain,
! [X0: $i,X1: $i] :
( element(X1,sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_148552]) ).
tcf(c_152135,plain,
! [X0: $i] :
( relation(sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_642]) ).
tcf(c_152136,plain,
! [X0: $i] :
( empty(sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_641]) ).
tcf(c_152137,plain,
! [X0: $i,X1: $i] :
( in(X1,sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_906]) ).
tcf(c_152138,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( relation_rng(sK126(sK198(X0))) = sK140 )
| ~ relation(sK126(sK198(X0)))
| ( sK198(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147331,c_478]) ).
tcf(c_152139,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK126(sK198(X0)) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ relation(sK126(sK198(X0)))
| ( sK198(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147331,c_475]) ).
tcf(c_152189,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(relation_dom(sK96(X0,X1))) = sK140 )
| ( apply(sK96(X0,X1),X2) = sK140 )
| ~ empty(X2)
| ~ sP12(X0,X1)
| ~ relation(sK96(X0,X1)) ),
inference(superposition,[status(thm)],[c_209,c_150502]) ).
tcf(c_152190,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(sK96(X0,X1))) = sK140 )
| ( apply(sK96(X0,X1),sK140) = sK140 )
| ~ sP12(X0,X1)
| ~ relation(sK96(X0,X1)) ),
inference(superposition,[status(thm)],[c_209,c_145538]) ).
tcf(c_152214,plain,
! [X0: $i,X1: $i] :
( in(sK140,relation_rng_restriction(X1,X0))
| ( X0 = sK140 )
| ( sK125(subset_complement(X0,relation_rng_restriction(X1,X0))) = sK140 )
| ~ relation(X0)
| ~ element(sK140,X0) ),
inference(superposition,[status(thm)],[c_262,c_145539]) ).
tcf(c_152215,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,relation_rng_restriction(X2,X1))),relation_rng_restriction(X2,X1))
| ( relation_rng_restriction(X2,X1) = sK140 )
| ~ relation(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_262,c_1058]) ).
tcf(c_152216,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,relation_rng_restriction(X2,X1)),relation_rng_restriction(X2,X1))
| ( relation_rng_restriction(X2,X1) = sK140 )
| ~ relation(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_262,c_1057]) ).
tcf(c_152217,plain,
! [X0: $i,X1: $i] :
( in(sK128(relation_rng_restriction(X1,X0)),relation_rng_restriction(X1,X0))
| ( relation_rng_restriction(X1,X0) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_262,c_369]) ).
tcf(c_152218,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(relation_rng_restriction(X1,X0)))
| ( relation_rng_restriction(X1,X0) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_262,c_371]) ).
tcf(c_152219,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng_restriction(X1,X0),X0) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_262,c_386]) ).
tcf(c_152220,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X1,unordered_pair(X0,X0)) = sK140 )
| ( relation_rng_restriction(X1,unordered_pair(X0,X0)) = unordered_pair(X0,X0) )
| ~ relation(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_262,c_397]) ).
tcf(c_152221,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(relation_rng_restriction(X1,X2)),X0)
| ( relation_rng_restriction(X1,X2) = sK140 )
| ~ ordinal(X2)
| ~ ordinal(X0)
| ~ relation(X2)
| ~ in(X0,relation_rng_restriction(X1,X2)) ),
inference(superposition,[status(thm)],[c_262,c_370]) ).
tcf(c_152222,plain,
! [X0: $i] :
( ( relation_rng_restriction(X0,sK140) = sK140 )
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_262,c_403]) ).
tcf(c_152223,plain,
! [X0: $i] :
( ( relation_rng_restriction(X0,powerset(sK140)) = sK140 )
| ( relation_rng_restriction(X0,powerset(sK140)) = powerset(sK140) )
| ~ relation(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_262,c_144406]) ).
tcf(c_152224,plain,
! [X0: $i] : relation_rng_restriction(X0,sK140) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_152222,c_577]) ).
tcf(c_152279,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_147189]) ).
tcf(c_152280,plain,
! [X0: $i] :
( one_to_one(X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_147189]) ).
tcf(c_152281,plain,
! [X0: $i] :
( one_to_one(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_147189]) ).
tcf(c_152282,plain,
! [X0: $i] :
( one_to_one(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_147189]) ).
tcf(c_152283,plain,
! [X0: $i] :
( one_to_one(X0)
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_147189]) ).
tcf(c_152284,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_147189]) ).
tcf(c_152294,plain,
! [X0: $i,X1: $i] :
( one_to_one(set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_147189]) ).
tcf(c_152295,plain,
! [X0: $i,X1: $i] :
( one_to_one(set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_147189]) ).
tcf(c_152296,plain,
! [X0: $i] :
( one_to_one(sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_147189]) ).
tcf(c_152297,plain,
! [X0: $i] :
( one_to_one(sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_147189]) ).
tcf(c_152298,plain,
! [X0: $i] :
( one_to_one(sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_147189]) ).
tcf(c_152358,plain,
! [X0: $i] :
( ordinal(X0)
| ~ empty(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_147190]) ).
tcf(c_152359,plain,
! [X0: $i] :
( ordinal(X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_147190]) ).
tcf(c_152360,plain,
! [X0: $i] :
( ordinal(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_147190]) ).
tcf(c_152361,plain,
! [X0: $i] :
( ordinal(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_147190]) ).
tcf(c_152362,plain,
! [X0: $i] :
( ordinal(X0)
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_147190]) ).
tcf(c_152363,plain,
! [X0: $i] :
( ordinal(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_147190]) ).
tcf(c_152373,plain,
! [X0: $i,X1: $i] :
( ordinal(set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_147190]) ).
tcf(c_152374,plain,
! [X0: $i,X1: $i] :
( ordinal(set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_147190]) ).
tcf(c_152375,plain,
! [X0: $i] :
( ordinal(sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_147190]) ).
tcf(c_152376,plain,
! [X0: $i] :
( ordinal(sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_147190]) ).
tcf(c_152377,plain,
! [X0: $i] :
( ordinal(sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_147190]) ).
tcf(c_152380,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_147190,c_833]) ).
tcf(c_152451,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ empty(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_147191]) ).
tcf(c_152452,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_147191]) ).
tcf(c_152453,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_147191]) ).
tcf(c_152454,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_147191]) ).
tcf(c_152455,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_147191]) ).
tcf(c_152456,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_147191]) ).
tcf(c_152466,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_147191]) ).
tcf(c_152467,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_147191]) ).
tcf(c_152468,plain,
! [X0: $i] :
( epsilon_connected(sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_147191]) ).
tcf(c_152469,plain,
! [X0: $i] :
( epsilon_connected(sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_147191]) ).
tcf(c_152470,plain,
! [X0: $i] :
( epsilon_connected(sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_147191]) ).
tcf(c_152528,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ empty(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_147192]) ).
tcf(c_152529,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_147192]) ).
tcf(c_152530,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_147192]) ).
tcf(c_152531,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_147192]) ).
tcf(c_152532,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_147192]) ).
tcf(c_152533,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_147192]) ).
tcf(c_152543,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_147192]) ).
tcf(c_152544,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_147192]) ).
tcf(c_152545,plain,
! [X0: $i] :
( epsilon_transitive(sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_147192]) ).
tcf(c_152546,plain,
! [X0: $i] :
( epsilon_transitive(sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_147192]) ).
tcf(c_152547,plain,
! [X0: $i] :
( epsilon_transitive(sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_147192]) ).
tcf(c_152598,plain,
( subset(sK140,sK140)
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_152224,c_262]) ).
tcf(c_152604,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( relation_dom(sK126(X1)) = X1 )
| ( set_difference(relation_rng_restriction(X0,X1),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_146155,c_152219]) ).
tcf(c_152606,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng_restriction(X2,sK96(X0,X1)),sK96(X0,X1)) = sK140 )
| ~ sP12(X0,X1) ),
inference(superposition,[status(thm)],[c_208,c_152219]) ).
tcf(c_152607,plain,
! [X0: $i,X1: $i] :
( sP13(X1)
| ( set_difference(relation_rng_restriction(X0,sK108(X1)),sK108(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_230,c_152219]) ).
tcf(c_152608,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng_restriction(X0,sK115(X1)),sK115(X1)) = sK140,
inference(superposition,[status(thm)],[c_249,c_152219]) ).
tcf(c_152609,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng_restriction(X0,sK124(X1)),sK124(X1)) = sK140,
inference(superposition,[status(thm)],[c_346,c_152219]) ).
tcf(c_152610,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_355,c_152219]) ).
tcf(c_152611,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng_restriction(X0,identity_relation(X1)),identity_relation(X1)) = sK140,
inference(superposition,[status(thm)],[c_1101,c_152219]) ).
tcf(c_152612,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng_restriction(X1,relation_dom_restriction(X0,X2)),relation_dom_restriction(X0,X2)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_773,c_152219]) ).
tcf(c_152613,plain,
! [X0: $i] : set_difference(relation_rng_restriction(X0,sK140),sK140) = sK140,
inference(superposition,[status(thm)],[c_577,c_152219]) ).
tcf(c_152614,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng_restriction(X1,relation_dom(X0)),relation_dom(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_642,c_152219]) ).
tcf(c_152615,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng_restriction(X1,relation_rng_restriction(X2,X0)),relation_rng_restriction(X2,X0)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_646,c_152219]) ).
tcf(c_152616,plain,
! [X0: $i] : set_difference(relation_rng_restriction(X0,sK240),sK240) = sK140,
inference(superposition,[status(thm)],[c_783,c_152219]) ).
tcf(c_152617,plain,
! [X0: $i] : set_difference(relation_rng_restriction(X0,sK242),sK242) = sK140,
inference(superposition,[status(thm)],[c_791,c_152219]) ).
tcf(c_152618,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng_restriction(X1,sK264(X0)),sK264(X0)) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_852,c_152219]) ).
tcf(c_152619,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng_restriction(X1,relation_rng(X0)),relation_rng(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_944,c_152219]) ).
tcf(c_152620,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng_restriction(X1,relation_restriction(X0,X2)),relation_restriction(X0,X2)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1013,c_152219]) ).
tcf(c_152621,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_rng_restriction(X0,sK312(X1,X2)),sK312(X1,X2)) = sK140,
inference(superposition,[status(thm)],[c_1019,c_152219]) ).
tcf(c_152622,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng_restriction(X0,inclusion_relation(X1)),inclusion_relation(X1)) = sK140,
inference(superposition,[status(thm)],[c_1091,c_152219]) ).
tcf(c_152623,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng_restriction(X1,relation_inverse(X0)),relation_inverse(X0)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1113,c_152219]) ).
tcf(c_152624,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng_restriction(X1,relation_inverse(X0)),relation_inverse(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1112,c_152219]) ).
tcf(c_152625,plain,
! [X0: $i] : set_difference(relation_rng_restriction(X0,sK335),sK335) = sK140,
inference(superposition,[status(thm)],[c_1149,c_152219]) ).
tcf(c_152626,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_rng_restriction(X0,sK347(X1,X2)),sK347(X1,X2)) = sK140,
inference(superposition,[status(thm)],[c_1237,c_152219]) ).
tcf(c_152742,plain,
( iPr_def_14
| iPr_def_10
| ( set_difference(omega,set_difference(omega,unordered_pair(sK261,sK261))) = sK140 ) ),
inference(demodulation,[status(thm)],[c_152037,c_961]) ).
tcf(c_152752,plain,
( iPr_def_21
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 )
| ~ sP8 ),
inference(demodulation,[status(thm)],[c_152028,c_961]) ).
tcf(c_152762,plain,
( iPr_def_21
| iPr_def_19
| sP6
| sP7
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_123599,c_152752]) ).
tcf(c_152763,plain,
( iPr_def_21
| iPr_def_18
| sP6
| sP7
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_123597,c_152752]) ).
tcf(c_152784,plain,
( iPr_def_21
| iPr_def_19
| sP6
| ( sK125(sK64) = sK140 )
| ( relation_dom(sK126(sK64)) = sK64 )
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152762,c_151422]) ).
tcf(c_152801,plain,
( iPr_def_21
| iPr_def_18
| sP6
| ( sK125(sK64) = sK140 )
| ( relation_dom(sK126(sK64)) = sK64 )
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152763,c_151422]) ).
tcf(c_152808,plain,
( iPr_def_20
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 )
| ~ sP8 ),
inference(demodulation,[status(thm)],[c_152029,c_961]) ).
tcf(c_152818,plain,
( iPr_def_20
| iPr_def_19
| sP6
| sP7
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_123599,c_152808]) ).
tcf(c_152819,plain,
( iPr_def_20
| iPr_def_18
| sP6
| sP7
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_123597,c_152808]) ).
tcf(c_152840,plain,
( iPr_def_20
| iPr_def_19
| sP6
| ( sK125(sK64) = sK140 )
| ( relation_dom(sK126(sK64)) = sK64 )
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152818,c_151422]) ).
tcf(c_152851,plain,
! [X0: $i] :
( epsilon_transitive(sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ~ empty(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_147192]) ).
tcf(c_152852,plain,
! [X0: $i] :
( epsilon_connected(sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ~ empty(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_147191]) ).
tcf(c_152853,plain,
! [X0: $i] :
( ordinal(sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ~ empty(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_147190]) ).
tcf(c_152854,plain,
! [X0: $i] :
( one_to_one(sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ~ empty(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_147189]) ).
tcf(c_152855,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK198(powerset(X0))) = sK140 )
| ( apply(sK126(sK198(powerset(X0))),X1) = sK140 )
| ~ empty(sK198(powerset(X0)))
| ~ relation(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_150772]) ).
tcf(c_152856,plain,
! [X0: $i,X1: $i] :
( element(X1,sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ( apply(sK126(sK198(powerset(X0))),X1) = sK140 )
| ~ function(sK126(sK198(powerset(X0))))
| ~ relation(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_148552]) ).
tcf(c_152857,plain,
! [X0: $i] :
( relation(sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ~ empty(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_642]) ).
tcf(c_152858,plain,
! [X0: $i] :
( empty(sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ~ empty(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_641]) ).
tcf(c_152859,plain,
! [X0: $i,X1: $i] :
( in(X1,sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ( apply(sK126(sK198(powerset(X0))),X1) = sK140 )
| ~ function(sK126(sK198(powerset(X0))))
| ~ relation(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_906]) ).
tcf(c_152860,plain,
! [X0: $i] :
( ( sK125(sK198(powerset(X0))) = sK140 )
| ( relation_rng(sK126(sK198(powerset(X0)))) = sK140 )
| ~ relation(sK126(sK198(powerset(X0))))
| ( sK198(powerset(X0)) != sK140 ) ),
inference(superposition,[status(thm)],[c_147341,c_478]) ).
tcf(c_152861,plain,
! [X0: $i] :
( ( sK126(sK198(powerset(X0))) = sK140 )
| ( sK125(sK198(powerset(X0))) = sK140 )
| ~ relation(sK126(sK198(powerset(X0))))
| ( sK198(powerset(X0)) != sK140 ) ),
inference(superposition,[status(thm)],[c_147341,c_475]) ).
tcf(c_152917,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( sK125(X0) = sK140 )
| ~ empty(sK130(X0,X1)) ),
inference(superposition,[status(thm)],[c_400,c_150230]) ).
tcf(c_152918,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_400,c_787]) ).
tcf(c_152919,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| element(sK130(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_400,c_526]) ).
tcf(c_152920,plain,
! [X0: $i,X1: $i] :
( disjoint(sK92(X0),X1)
| in(sK130(sK92(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_400,c_198]) ).
tcf(c_152921,plain,
! [X0: $i,X1: $i] :
( disjoint(sK92(X0),X1)
| ordinal(sK130(sK92(X0),X1)) ),
inference(superposition,[status(thm)],[c_400,c_199]) ).
tcf(c_152922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( disjoint(relation_inverse_image(X0,X3),X4)
| in(apply(X0,sK130(relation_inverse_image(X0,X3),X4)),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_400,c_425]) ).
tcf(c_152923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( disjoint(relation_inverse_image(X0,X3),X4)
| in(sK130(relation_inverse_image(X0,X3),X4),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_400,c_424]) ).
tcf(c_152954,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( sK125(X1) = sK140 )
| ~ empty(sK130(X0,X1)) ),
inference(superposition,[status(thm)],[c_401,c_150230]) ).
tcf(c_152955,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_401,c_787]) ).
tcf(c_152956,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| element(sK130(X0,X1),X1) ),
inference(superposition,[status(thm)],[c_401,c_526]) ).
tcf(c_152957,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,sK92(X1))
| in(sK130(X0,sK92(X1)),X1) ),
inference(superposition,[status(thm)],[c_401,c_198]) ).
tcf(c_152958,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,sK92(X1))
| ordinal(sK130(X0,sK92(X1))) ),
inference(superposition,[status(thm)],[c_401,c_199]) ).
tcf(c_152959,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( disjoint(X3,relation_inverse_image(X0,X4))
| in(apply(X0,sK130(X3,relation_inverse_image(X0,X4))),X4)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_401,c_425]) ).
tcf(c_152960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( disjoint(X3,relation_inverse_image(X0,X4))
| in(sK130(X3,relation_inverse_image(X0,X4)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_401,c_424]) ).
tcf(c_152993,plain,
! [X0: $i] :
( ordinal(sK261)
| being_limit_ordinal(X0)
| sP32(sK131(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_407,c_833]) ).
tcf(c_152994,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| epsilon_connected(sK131(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_407,c_1050]) ).
tcf(c_152995,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| epsilon_transitive(sK131(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_407,c_1049]) ).
tcf(c_153021,plain,
! [X0: $i] :
( ordinal(sK261)
| being_limit_ordinal(X0)
| sP32(sK132(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_410,c_833]) ).
tcf(c_153022,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| epsilon_connected(sK132(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_410,c_1050]) ).
tcf(c_153023,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| epsilon_transitive(sK132(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_410,c_1049]) ).
tcf(c_153047,plain,
! [X0: $i] :
( finite(X0)
| ~ empty(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_147193]) ).
tcf(c_153048,plain,
! [X0: $i] :
( finite(X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_147193]) ).
tcf(c_153049,plain,
! [X0: $i] :
( finite(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_147193]) ).
tcf(c_153050,plain,
! [X0: $i] :
( finite(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_147193]) ).
tcf(c_153051,plain,
! [X0: $i] :
( finite(X0)
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_147193]) ).
tcf(c_153052,plain,
! [X0: $i] :
( finite(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_147193]) ).
tcf(c_153062,plain,
! [X0: $i,X1: $i] :
( finite(set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_147193]) ).
tcf(c_153063,plain,
! [X0: $i,X1: $i] :
( finite(set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_147193]) ).
tcf(c_153064,plain,
! [X0: $i] :
( finite(sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_147193]) ).
tcf(c_153065,plain,
! [X0: $i] :
( finite(sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_147193]) ).
tcf(c_153066,plain,
! [X0: $i] :
( finite(sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ~ empty(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_147193]) ).
tcf(c_153067,plain,
! [X0: $i] :
( finite(sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_147193]) ).
tcf(c_153179,plain,
! [X0: $i] :
( function(X0)
| ~ empty(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_147195]) ).
tcf(c_153180,plain,
! [X0: $i] :
( function(X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_147195]) ).
tcf(c_153181,plain,
! [X0: $i] :
( function(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_147195]) ).
tcf(c_153182,plain,
! [X0: $i] :
( function(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_147195]) ).
tcf(c_153183,plain,
! [X0: $i] :
( function(X0)
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_147195]) ).
tcf(c_153184,plain,
! [X0: $i] :
( function(X0)
| ~ empty(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_147195]) ).
tcf(c_153194,plain,
! [X0: $i,X1: $i] :
( function(set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_147195]) ).
tcf(c_153195,plain,
! [X0: $i,X1: $i] :
( function(set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_147195]) ).
tcf(c_153196,plain,
! [X0: $i] :
( function(sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_147195]) ).
tcf(c_153197,plain,
! [X0: $i] :
( function(sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_147195]) ).
tcf(c_153198,plain,
! [X0: $i] :
( function(sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ~ empty(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_147195]) ).
tcf(c_153199,plain,
! [X0: $i] :
( function(sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_147195]) ).
tcf(c_153202,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(relation_dom(X0))) = sK140 )
| ( apply(relation_dom(X0),X1) = sK140 )
| ~ empty(X1)
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_147195,c_150502]) ).
tcf(c_153203,plain,
! [X0: $i] :
( ( sK125(relation_dom(relation_dom(X0))) = sK140 )
| ( apply(relation_dom(X0),sK140) = sK140 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_147195,c_145538]) ).
tcf(c_153262,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| ( sK125(set_union2(sK115(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(sK115(X0),X1))) = set_union2(sK115(X0),X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_147253]) ).
tcf(c_153263,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(sK302(sK115(X0))) = sK140 )
| ( relation_dom(sK126(sK302(sK115(X0)))) = sK302(sK115(X0)) ) ),
inference(superposition,[status(thm)],[c_147722,c_147253]) ).
tcf(c_153264,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(sK198(sK115(X0))) = sK140 )
| ( relation_dom(sK126(sK198(sK115(X0)))) = sK198(sK115(X0)) ) ),
inference(superposition,[status(thm)],[c_147277,c_147253]) ).
tcf(c_153265,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_353,c_147253]) ).
tcf(c_153266,plain,
! [X0: $i,X1: $i] :
( relation(X1)
| ( sK125(set_union2(X0,sK115(X1))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,sK115(X1)))) = set_union2(X0,sK115(X1)) ) ),
inference(superposition,[status(thm)],[c_149341,c_147253]) ).
tcf(c_153287,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| ( sK125(set_union2(identity_relation(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(identity_relation(X0),X1))) = set_union2(identity_relation(X0),X1) ) ),
inference(superposition,[status(thm)],[c_149359,c_147255]) ).
tcf(c_153288,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(sK302(identity_relation(X0))) = sK140 )
| ( relation_dom(sK126(sK302(identity_relation(X0)))) = sK302(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_147722,c_147255]) ).
tcf(c_153289,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(sK198(identity_relation(X0))) = sK140 )
| ( relation_dom(sK126(sK198(identity_relation(X0)))) = sK198(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_147277,c_147255]) ).
tcf(c_153290,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_353,c_147255]) ).
tcf(c_153291,plain,
! [X0: $i,X1: $i] :
( relation(X1)
| ( sK125(set_union2(X0,identity_relation(X1))) = sK140 )
| ( relation_dom(sK126(set_union2(X0,identity_relation(X1)))) = set_union2(X0,identity_relation(X1)) ) ),
inference(superposition,[status(thm)],[c_149341,c_147255]) ).
tcf(c_153318,plain,
( iPr_def_20
| iPr_def_18
| sP6
| ( sK125(sK64) = sK140 )
| ( relation_dom(sK126(sK64)) = sK64 )
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152819,c_151422]) ).
tcf(c_153331,plain,
! [X0: $i] :
( sP3(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_151861,c_150222]) ).
tcf(c_153332,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_151861,c_148019]) ).
tcf(c_153333,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_151861,c_147669]) ).
tcf(c_153334,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_151861,c_147196]) ).
tcf(c_153335,plain,
! [X0: $i] :
( one_to_one(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_151861,c_84200]) ).
tcf(c_153336,plain,
! [X0: $i] :
( ordinal(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_151861,c_1047]) ).
tcf(c_153337,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_151861,c_1046]) ).
tcf(c_153338,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_151861,c_1045]) ).
tcf(c_153339,plain,
! [X0: $i] :
( finite(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_151861,c_983]) ).
tcf(c_153341,plain,
! [X0: $i] :
( function(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_151861,c_785]) ).
tcf(c_153342,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_151861,c_575]) ).
tcf(c_153343,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(sK115(set_union2(X0,X1))) = sK140 )
| ( relation_dom(sK126(sK115(set_union2(X0,X1)))) = sK115(set_union2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_151861,c_615]) ).
tcf(c_153344,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(sK115(set_union2(X0,X1))) = sK140 )
| ( relation_dom(sK126(sK115(set_union2(X0,X1)))) = sK115(set_union2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_151861,c_614]) ).
tcf(c_153345,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ( sK125(sK115(relation_dom(X0))) = sK140 )
| ( relation_dom(sK126(sK115(relation_dom(X0)))) = sK115(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_151861,c_150772]) ).
tcf(c_153346,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK115(sK198(X0))) = sK140 )
| ( relation_dom(sK126(sK115(sK198(X0)))) = sK115(sK198(X0)) ) ),
inference(superposition,[status(thm)],[c_151861,c_694]) ).
tcf(c_153347,plain,
! [X0: $i] :
( ( sK125(sK115(powerset(X0))) = sK140 )
| ( relation_dom(sK126(sK115(powerset(X0)))) = sK115(powerset(X0)) ) ),
inference(superposition,[status(thm)],[c_151861,c_695]) ).
tcf(c_153348,plain,
( ( sK125(sK115(sK241)) = sK140 )
| ( relation_dom(sK126(sK115(sK241))) = sK115(sK241) ) ),
inference(superposition,[status(thm)],[c_151861,c_789]) ).
tcf(c_153349,plain,
( ( sK125(sK115(sK242)) = sK140 )
| ( relation_dom(sK126(sK115(sK242))) = sK115(sK242) ) ),
inference(superposition,[status(thm)],[c_151861,c_790]) ).
tcf(c_153350,plain,
( ( sK125(sK115(omega)) = sK140 )
| ( relation_dom(sK126(sK115(omega))) = sK115(omega) ) ),
inference(superposition,[status(thm)],[c_151861,c_842]) ).
tcf(c_153351,plain,
! [X0: $i] :
( ( sK125(sK115(set_union2(X0,unordered_pair(X0,X0)))) = sK140 )
| ( relation_dom(sK126(sK115(set_union2(X0,unordered_pair(X0,X0))))) = sK115(set_union2(X0,unordered_pair(X0,X0))) ) ),
inference(superposition,[status(thm)],[c_151861,c_892]) ).
tcf(c_153352,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK115(unordered_pair(X0,X1))) = sK140 )
| ( relation_dom(sK126(sK115(unordered_pair(X0,X1)))) = sK115(unordered_pair(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_151861,c_935]) ).
tcf(c_153353,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK115(sK302(X0))) = sK140 )
| ( relation_dom(sK126(sK115(sK302(X0)))) = sK115(sK302(X0)) ) ),
inference(superposition,[status(thm)],[c_151861,c_973]) ).
tcf(c_153354,plain,
( ( sK125(sK115(sK303)) = sK140 )
| ( relation_dom(sK126(sK115(sK303))) = sK115(sK303) ) ),
inference(superposition,[status(thm)],[c_151861,c_975]) ).
tcf(c_153355,plain,
( ( sK125(sK115(sK313)) = sK140 )
| ( relation_dom(sK126(sK115(sK313))) = sK115(sK313) ) ),
inference(superposition,[status(thm)],[c_151861,c_1025]) ).
tcf(c_153356,plain,
( ( sK125(sK115(sK346)) = sK140 )
| ( relation_dom(sK126(sK115(sK346))) = sK115(sK346) ) ),
inference(superposition,[status(thm)],[c_151861,c_1223]) ).
tcf(c_153357,plain,
( ( sK125(sK115(sK358)) = sK140 )
| ( relation_dom(sK126(sK115(sK358))) = sK115(sK358) ) ),
inference(superposition,[status(thm)],[c_151861,c_1276]) ).
tcf(c_153358,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(sK115(sK115(X0))) = sK140 )
| ( relation_dom(sK126(sK115(sK115(X0)))) = sK115(sK115(X0)) ) ),
inference(superposition,[status(thm)],[c_151861,c_147253]) ).
tcf(c_153359,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK115(sK115(X0))) = sK140 )
| ( relation_dom(sK126(sK115(sK115(X0)))) = sK115(sK115(X0)) ) ),
inference(superposition,[status(thm)],[c_151861,c_147177]) ).
tcf(c_153360,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(sK115(identity_relation(X0))) = sK140 )
| ( relation_dom(sK126(sK115(identity_relation(X0)))) = sK115(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_151861,c_147255]) ).
tcf(c_153361,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK115(identity_relation(X0))) = sK140 )
| ( relation_dom(sK126(sK115(identity_relation(X0)))) = sK115(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_151861,c_147179]) ).
tcf(c_153362,plain,
! [X0: $i] :
( ( sK125(sK115(sK116(X0))) = sK140 )
| ( relation_dom(sK126(sK115(sK116(X0)))) = sK115(sK116(X0)) ) ),
inference(superposition,[status(thm)],[c_151861,c_150228]) ).
tcf(c_153363,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(sK115(subset_complement(X1,X0))) = sK140 )
| ( relation_dom(sK126(sK115(subset_complement(X1,X0)))) = sK115(subset_complement(X1,X0)) )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_151861,c_150233]) ).
tcf(c_153364,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK115(sK263(X0))) = sK140 )
| ( relation_dom(sK126(sK115(sK263(X0)))) = sK115(sK263(X0)) )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_151861,c_150238]) ).
tcf(c_153365,plain,
! [X0: $i] :
( ( sK125(sK115(sK300(X0))) = sK140 )
| ( relation_dom(sK126(sK115(sK300(X0)))) = sK115(sK300(X0)) ) ),
inference(superposition,[status(thm)],[c_151861,c_150241]) ).
tcf(c_153366,plain,
( ( sK125(sK115(sK64)) = sK140 )
| ( relation_dom(sK126(sK115(sK64))) = sK115(sK64) )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_151861,c_150248]) ).
tcf(c_153367,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK115(apply(sK126(X1),X0))) = sK140 )
| ( relation_dom(sK126(sK115(apply(sK126(X1),X0)))) = sK115(apply(sK126(X1),X0)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_151861,c_150503]) ).
tcf(c_153368,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK115(sK169(X0))) = sK140 )
| ( relation_dom(sK126(sK115(sK169(X0)))) = sK115(sK169(X0)) ) ),
inference(superposition,[status(thm)],[c_151861,c_150508]) ).
tcf(c_153508,plain,
! [X0: $i] :
( sP3(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_151886,c_150222]) ).
tcf(c_153509,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_151886,c_148019]) ).
tcf(c_153510,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_151886,c_147669]) ).
tcf(c_153511,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_151886,c_147196]) ).
tcf(c_153512,plain,
! [X0: $i] :
( one_to_one(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_151886,c_84200]) ).
tcf(c_153513,plain,
! [X0: $i] :
( ordinal(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_151886,c_1047]) ).
tcf(c_153514,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_151886,c_1046]) ).
tcf(c_153515,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_151886,c_1045]) ).
tcf(c_153516,plain,
! [X0: $i] :
( finite(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_151886,c_983]) ).
tcf(c_153518,plain,
! [X0: $i] :
( function(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_151886,c_785]) ).
tcf(c_153519,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_151886,c_575]) ).
tcf(c_153520,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(identity_relation(set_union2(X0,X1))) = sK140 )
| ( relation_dom(sK126(identity_relation(set_union2(X0,X1)))) = identity_relation(set_union2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_151886,c_615]) ).
tcf(c_153521,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(identity_relation(set_union2(X0,X1))) = sK140 )
| ( relation_dom(sK126(identity_relation(set_union2(X0,X1)))) = identity_relation(set_union2(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_151886,c_614]) ).
tcf(c_153522,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ( sK125(identity_relation(relation_dom(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(relation_dom(X0)))) = identity_relation(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_151886,c_150772]) ).
tcf(c_153523,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(identity_relation(sK198(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(sK198(X0)))) = identity_relation(sK198(X0)) ) ),
inference(superposition,[status(thm)],[c_151886,c_694]) ).
tcf(c_153524,plain,
! [X0: $i] :
( ( sK125(identity_relation(powerset(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(powerset(X0)))) = identity_relation(powerset(X0)) ) ),
inference(superposition,[status(thm)],[c_151886,c_695]) ).
tcf(c_153525,plain,
( ( sK125(identity_relation(sK241)) = sK140 )
| ( relation_dom(sK126(identity_relation(sK241))) = identity_relation(sK241) ) ),
inference(superposition,[status(thm)],[c_151886,c_789]) ).
tcf(c_153526,plain,
( ( sK125(identity_relation(sK242)) = sK140 )
| ( relation_dom(sK126(identity_relation(sK242))) = identity_relation(sK242) ) ),
inference(superposition,[status(thm)],[c_151886,c_790]) ).
tcf(c_153527,plain,
( ( sK125(identity_relation(omega)) = sK140 )
| ( relation_dom(sK126(identity_relation(omega))) = identity_relation(omega) ) ),
inference(superposition,[status(thm)],[c_151886,c_842]) ).
tcf(c_153528,plain,
! [X0: $i] :
( ( sK125(identity_relation(set_union2(X0,unordered_pair(X0,X0)))) = sK140 )
| ( relation_dom(sK126(identity_relation(set_union2(X0,unordered_pair(X0,X0))))) = identity_relation(set_union2(X0,unordered_pair(X0,X0))) ) ),
inference(superposition,[status(thm)],[c_151886,c_892]) ).
tcf(c_153529,plain,
! [X0: $i,X1: $i] :
( ( sK125(identity_relation(unordered_pair(X0,X1))) = sK140 )
| ( relation_dom(sK126(identity_relation(unordered_pair(X0,X1)))) = identity_relation(unordered_pair(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_151886,c_935]) ).
tcf(c_153530,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(identity_relation(sK302(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(sK302(X0)))) = identity_relation(sK302(X0)) ) ),
inference(superposition,[status(thm)],[c_151886,c_973]) ).
tcf(c_153531,plain,
( ( sK125(identity_relation(sK303)) = sK140 )
| ( relation_dom(sK126(identity_relation(sK303))) = identity_relation(sK303) ) ),
inference(superposition,[status(thm)],[c_151886,c_975]) ).
tcf(c_153532,plain,
( ( sK125(identity_relation(sK313)) = sK140 )
| ( relation_dom(sK126(identity_relation(sK313))) = identity_relation(sK313) ) ),
inference(superposition,[status(thm)],[c_151886,c_1025]) ).
tcf(c_153533,plain,
( ( sK125(identity_relation(sK346)) = sK140 )
| ( relation_dom(sK126(identity_relation(sK346))) = identity_relation(sK346) ) ),
inference(superposition,[status(thm)],[c_151886,c_1223]) ).
tcf(c_153534,plain,
( ( sK125(identity_relation(sK358)) = sK140 )
| ( relation_dom(sK126(identity_relation(sK358))) = identity_relation(sK358) ) ),
inference(superposition,[status(thm)],[c_151886,c_1276]) ).
tcf(c_153535,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(identity_relation(sK115(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(sK115(X0)))) = identity_relation(sK115(X0)) ) ),
inference(superposition,[status(thm)],[c_151886,c_147253]) ).
tcf(c_153536,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(identity_relation(sK115(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(sK115(X0)))) = identity_relation(sK115(X0)) ) ),
inference(superposition,[status(thm)],[c_151886,c_147177]) ).
tcf(c_153537,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(identity_relation(identity_relation(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(identity_relation(X0)))) = identity_relation(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_151886,c_147255]) ).
tcf(c_153538,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(identity_relation(identity_relation(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(identity_relation(X0)))) = identity_relation(identity_relation(X0)) ) ),
inference(superposition,[status(thm)],[c_151886,c_147179]) ).
tcf(c_153539,plain,
! [X0: $i] :
( ( sK125(identity_relation(sK116(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(sK116(X0)))) = identity_relation(sK116(X0)) ) ),
inference(superposition,[status(thm)],[c_151886,c_150228]) ).
tcf(c_153540,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(identity_relation(subset_complement(X1,X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(subset_complement(X1,X0)))) = identity_relation(subset_complement(X1,X0)) )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_151886,c_150233]) ).
tcf(c_153541,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(identity_relation(sK263(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(sK263(X0)))) = identity_relation(sK263(X0)) )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_151886,c_150238]) ).
tcf(c_153542,plain,
! [X0: $i] :
( ( sK125(identity_relation(sK300(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(sK300(X0)))) = identity_relation(sK300(X0)) ) ),
inference(superposition,[status(thm)],[c_151886,c_150241]) ).
tcf(c_153543,plain,
( ( sK125(identity_relation(sK64)) = sK140 )
| ( relation_dom(sK126(identity_relation(sK64))) = identity_relation(sK64) )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_151886,c_150248]) ).
tcf(c_153544,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(identity_relation(apply(sK126(X1),X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(apply(sK126(X1),X0)))) = identity_relation(apply(sK126(X1),X0)) )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_151886,c_150503]) ).
tcf(c_153545,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(identity_relation(sK169(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(sK169(X0)))) = identity_relation(sK169(X0)) ) ),
inference(superposition,[status(thm)],[c_151886,c_150508]) ).
tcf(c_153701,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK115(X1)) = sK140 )
| ( relation_dom(sK126(sK115(X1))) = sK115(X1) )
| ( set_difference(relation_rng_restriction(X0,X1),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_153265,c_152219]) ).
tcf(c_153712,plain,
! [X0: $i,X1: $i] :
( ( sK125(identity_relation(X1)) = sK140 )
| ( relation_dom(sK126(identity_relation(X1))) = identity_relation(X1) )
| ( set_difference(relation_rng_restriction(X0,X1),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_153290,c_152219]) ).
tcf(c_153723,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(sK140) = sK140 )
| ( apply(sK140,sK140) = sK140 ) ),
inference(superposition,[status(thm)],[c_151089,c_151739]) ).
tcf(c_153724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK140,relation_inverse_image(sK312(X0,sK140),X3))
| ( X2 = sK140 )
| ( X0 = sK140 )
| ( sK125(sK140) = sK140 )
| ~ in(sK140,X3)
| ~ in(sK140,X1)
| ~ function(sK312(X0,sK140))
| ~ quasi_total(sK312(X0,sK140),X1,X2)
| ~ relation_of2_as_subset(sK312(X0,sK140),X1,X2) ),
inference(superposition,[status(thm)],[c_151739,c_423]) ).
tcf(c_153725,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK140,relation_inverse_image(sK312(X0,sK140),X3))
| ( X2 = sK140 )
| ( X0 = sK140 )
| ( sK125(sK140) = sK140 )
| ~ in(sK140,X3)
| ~ in(sK140,X1)
| ~ quasi_total(sK312(X0,sK140),X1,X2)
| ~ relation_of2_as_subset(sK312(X0,sK140),X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_153724,c_1020]) ).
tcf(c_153740,plain,
! [X0: $i] :
( in(apply(sK126(X0),sK140),sK140)
| ( sK125(X0) = sK140 )
| ~ in(sK92(sK140),X0) ),
inference(superposition,[status(thm)],[c_151927,c_151774]) ).
tcf(c_153741,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ~ in(sK92(X1),X0)
| ~ empty(apply(sK126(X0),sK92(X1))) ),
inference(superposition,[status(thm)],[c_151774,c_150230]) ).
tcf(c_153742,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ~ empty(X0)
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_151774,c_787]) ).
tcf(c_153743,plain,
! [X0: $i,X1: $i] :
( element(apply(sK126(X1),sK92(X0)),X0)
| ( sK125(X1) = sK140 )
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_151774,c_526]) ).
tcf(c_153744,plain,
! [X0: $i,X1: $i] :
( in(apply(sK126(X1),sK92(sK92(X0))),X0)
| ( sK125(X1) = sK140 )
| ~ in(sK92(sK92(X0)),X1) ),
inference(superposition,[status(thm)],[c_151774,c_198]) ).
tcf(c_153745,plain,
! [X0: $i,X1: $i] :
( ordinal(apply(sK126(X1),sK92(sK92(X0))))
| ( sK125(X1) = sK140 )
| ~ in(sK92(sK92(X0)),X1) ),
inference(superposition,[status(thm)],[c_151774,c_199]) ).
tcf(c_153746,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,apply(sK126(X2),sK92(relation_inverse_image(X0,X1)))),X1)
| ( X4 = sK140 )
| ( sK125(X2) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ in(sK92(relation_inverse_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_151774,c_425]) ).
tcf(c_153747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(sK126(X2),sK92(relation_inverse_image(X0,X1))),X3)
| ( X4 = sK140 )
| ( sK125(X2) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ in(sK92(relation_inverse_image(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_151774,c_424]) ).
tcf(c_153748,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK92(X3),relation_inverse_image(sK126(X0),X3))
| ( X2 = sK140 )
| ( sK125(X0) = sK140 )
| ~ function(sK126(X0))
| ~ in(sK92(X3),X1)
| ~ in(sK92(X3),X0)
| ~ quasi_total(sK126(X0),X1,X2)
| ~ relation_of2_as_subset(sK126(X0),X1,X2) ),
inference(superposition,[status(thm)],[c_151774,c_423]) ).
tcf(c_153749,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ~ in(sK92(sK140),X0) ),
inference(superposition,[status(thm)],[c_151774,c_580]) ).
tcf(c_153754,plain,
! [X0: $i] :
( in(apply(sK126(X0),sK140),sK140)
| ( sK125(X0) = sK140 )
| ~ in(sK140,X0) ),
inference(light_normalisation,[status(thm)],[c_153740,c_151927]) ).
tcf(c_153813,plain,
! [X0: $i,X1: $i] :
( ordinal(sK261)
| sP32(sK128(relation_rng_restriction(X1,X0)))
| ( relation_rng_restriction(X1,X0) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152218,c_833]) ).
tcf(c_153814,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK128(relation_rng_restriction(X1,X0)))
| ( relation_rng_restriction(X1,X0) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152218,c_1050]) ).
tcf(c_153815,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK128(relation_rng_restriction(X1,X0)))
| ( relation_rng_restriction(X1,X0) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152218,c_1049]) ).
tcf(c_153839,plain,
( function(sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ~ empty(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_147195]) ).
tcf(c_153840,plain,
( finite(sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ~ empty(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_147193]) ).
tcf(c_153841,plain,
( epsilon_transitive(sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ~ empty(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_147192]) ).
tcf(c_153842,plain,
( epsilon_connected(sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ~ empty(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_147191]) ).
tcf(c_153843,plain,
( ordinal(sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ~ empty(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_147190]) ).
tcf(c_153844,plain,
( one_to_one(sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ~ empty(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_147189]) ).
tcf(c_153845,plain,
! [X0: $i] :
( ( sK125(sK198(sK241)) = sK140 )
| ( apply(sK126(sK198(sK241)),X0) = sK140 )
| ~ empty(sK198(sK241))
| ~ relation(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_150772]) ).
tcf(c_153846,plain,
! [X0: $i] :
( element(X0,sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ( apply(sK126(sK198(sK241)),X0) = sK140 )
| ~ function(sK126(sK198(sK241)))
| ~ relation(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_148552]) ).
tcf(c_153847,plain,
( relation(sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ~ empty(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_642]) ).
tcf(c_153848,plain,
( empty(sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ~ empty(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_641]) ).
tcf(c_153849,plain,
! [X0: $i] :
( in(X0,sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ( apply(sK126(sK198(sK241)),X0) = sK140 )
| ~ function(sK126(sK198(sK241)))
| ~ relation(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_906]) ).
tcf(c_153850,plain,
( ( sK125(sK198(sK241)) = sK140 )
| ( relation_rng(sK126(sK198(sK241))) = sK140 )
| ~ relation(sK126(sK198(sK241)))
| ( sK198(sK241) != sK140 ) ),
inference(superposition,[status(thm)],[c_147342,c_478]) ).
tcf(c_153851,plain,
( ( sK126(sK198(sK241)) = sK140 )
| ( sK125(sK198(sK241)) = sK140 )
| ~ relation(sK126(sK198(sK241)))
| ( sK198(sK241) != sK140 ) ),
inference(superposition,[status(thm)],[c_147342,c_475]) ).
tcf(c_153930,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(X0,relation_rng_restriction(X1,X0)) ),
inference(superposition,[status(thm)],[c_262,c_472]) ).
tcf(c_153931,plain,
! [X0: $i] : ~ proper_subset(X0,sK140),
inference(superposition,[status(thm)],[c_361,c_472]) ).
tcf(c_153932,plain,
! [X0: $i,X1: $i] : ~ proper_subset(X0,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_383,c_472]) ).
tcf(c_153933,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),X0),
inference(superposition,[status(thm)],[c_498,c_472]) ).
tcf(c_153935,plain,
( ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140))
| ~ proper_subset(sK116(sK140),omega) ),
inference(superposition,[status(thm)],[c_145175,c_472]) ).
tcf(c_153936,plain,
( ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140))
| ~ proper_subset(sK300(sK140),omega) ),
inference(superposition,[status(thm)],[c_145503,c_472]) ).
tcf(c_153937,plain,
! [X0: $i] :
( ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0))
| ~ proper_subset(unordered_pair(sK140,X0),omega) ),
inference(superposition,[status(thm)],[c_146170,c_472]) ).
tcf(c_153938,plain,
( ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140))
| ~ proper_subset(powerset(sK140),omega) ),
inference(superposition,[status(thm)],[c_146195,c_472]) ).
tcf(c_153939,plain,
! [X0: $i] :
( ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140))
| ~ proper_subset(unordered_pair(X0,sK140),omega) ),
inference(superposition,[status(thm)],[c_146212,c_472]) ).
tcf(c_153940,plain,
( ~ being_limit_ordinal(set_union2(sK140,powerset(sK140)))
| ~ ordinal(set_union2(sK140,powerset(sK140)))
| ~ proper_subset(set_union2(sK140,powerset(sK140)),omega) ),
inference(superposition,[status(thm)],[c_148516,c_472]) ).
tcf(c_153987,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(X0,relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_504,c_472]) ).
tcf(c_153988,plain,
! [X0: $i,X1: $i] :
( in(sK140,relation_dom_restriction(X0,X1))
| ( X0 = sK140 )
| ( sK125(subset_complement(X0,relation_dom_restriction(X0,X1))) = sK140 )
| ~ relation(X0)
| ~ element(sK140,X0) ),
inference(superposition,[status(thm)],[c_504,c_145539]) ).
tcf(c_153989,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,relation_dom_restriction(X1,X2))),relation_dom_restriction(X1,X2))
| ( relation_dom_restriction(X1,X2) = sK140 )
| ~ relation(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_504,c_1058]) ).
tcf(c_153990,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,relation_dom_restriction(X1,X2)),relation_dom_restriction(X1,X2))
| ( relation_dom_restriction(X1,X2) = sK140 )
| ~ relation(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_504,c_1057]) ).
tcf(c_153991,plain,
! [X0: $i,X1: $i] :
( in(sK128(relation_dom_restriction(X0,X1)),relation_dom_restriction(X0,X1))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_504,c_369]) ).
tcf(c_153992,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(relation_dom_restriction(X0,X1)))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_504,c_371]) ).
tcf(c_153993,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom_restriction(X0,X1),X0) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_504,c_386]) ).
tcf(c_153994,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(unordered_pair(X0,X0),X1) = sK140 )
| ( relation_dom_restriction(unordered_pair(X0,X0),X1) = unordered_pair(X0,X0) )
| ~ relation(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_504,c_397]) ).
tcf(c_153995,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(relation_dom_restriction(X1,X2)),X0)
| ( relation_dom_restriction(X1,X2) = sK140 )
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ relation(X1)
| ~ in(X0,relation_dom_restriction(X1,X2)) ),
inference(superposition,[status(thm)],[c_504,c_370]) ).
tcf(c_153996,plain,
! [X0: $i] :
( ( relation_dom_restriction(sK140,X0) = sK140 )
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_504,c_403]) ).
tcf(c_153997,plain,
! [X0: $i] :
( ( relation_dom_restriction(powerset(sK140),X0) = sK140 )
| ( relation_dom_restriction(powerset(sK140),X0) = powerset(sK140) )
| ~ relation(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_504,c_144406]) ).
tcf(c_153998,plain,
! [X0: $i] : relation_dom_restriction(sK140,X0) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_153996,c_577]) ).
tcf(c_154059,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ proper_subset(union(X0),X1) ),
inference(superposition,[status(thm)],[c_513,c_472]) ).
tcf(c_154060,plain,
! [X0: $i,X1: $i] :
( in(sK140,X1)
| ( union(X0) = sK140 )
| ( sK125(subset_complement(union(X0),X1)) = sK140 )
| ~ in(X1,X0)
| ~ element(sK140,union(X0)) ),
inference(superposition,[status(thm)],[c_513,c_145539]) ).
tcf(c_154061,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,X2)),X2)
| ( X2 = sK140 )
| ~ relation(X0)
| ~ in(X2,X1)
| ~ is_well_founded_in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_513,c_1058]) ).
tcf(c_154062,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,X2),X2)
| ( X2 = sK140 )
| ~ relation(X0)
| ~ in(X2,X1)
| ~ is_well_founded_in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_513,c_1057]) ).
tcf(c_154063,plain,
! [X0: $i,X1: $i] :
( in(sK128(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_513,c_369]) ).
tcf(c_154064,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(X0))
| ( X0 = sK140 )
| ~ ordinal(union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_513,c_371]) ).
tcf(c_154065,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,union(X1)) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_513,c_386]) ).
tcf(c_154066,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(X0),X2)
| ( X0 = sK140 )
| ~ ordinal(X2)
| ~ ordinal(union(X1))
| ~ in(X2,X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_513,c_370]) ).
tcf(c_154067,plain,
! [X0: $i] :
( epsilon_transitive(union(X0))
| ~ in(sK316(union(X0)),X0) ),
inference(superposition,[status(thm)],[c_513,c_1042]) ).
tcf(c_154068,plain,
! [X0: $i] :
( sP15
| ( union(X0) = sK114(sK64) )
| ~ sP7
| ~ in(sK114(sK64),X0)
| ~ in(union(X0),sK64) ),
inference(superposition,[status(thm)],[c_513,c_150112]) ).
tcf(c_154069,plain,
! [X0: $i] :
( ( union(X0) = sK72(sK64) )
| ~ iPr_def_18
| ~ sP7
| ~ in(sK72(sK64),X0)
| ~ in(union(X0),sK64) ),
inference(superposition,[status(thm)],[c_513,c_151580]) ).
tcf(c_154122,plain,
! [X0: $i,X1: $i] :
( in(sK142(X1),X1)
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_522]) ).
tcf(c_154123,plain,
! [X0: $i] :
( sP3(X0)
| in(sK142(X0),X0) ),
inference(superposition,[status(thm)],[c_122,c_522]) ).
tcf(c_154124,plain,
in(sK142(omega),omega),
inference(superposition,[status(thm)],[c_847,c_522]) ).
tcf(c_154128,plain,
! [X0: $i] : in(sK142(set_union2(X0,unordered_pair(X0,X0))),set_union2(X0,unordered_pair(X0,X0))),
inference(superposition,[status(thm)],[c_256,c_522]) ).
tcf(c_154129,plain,
! [X0: $i] : in(sK142(sK116(X0)),sK116(X0)),
inference(superposition,[status(thm)],[c_272,c_522]) ).
tcf(c_154130,plain,
! [X0: $i,X1: $i] :
( in(sK142(relation_dom(X0)),relation_dom(X0))
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_522]) ).
tcf(c_154131,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ( sK125(X1) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2177,c_522]) ).
tcf(c_154132,plain,
! [X0: $i] :
( ordinal(X0)
| in(sK142(X0),X0) ),
inference(superposition,[status(thm)],[c_367,c_522]) ).
tcf(c_154134,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK142(X0),X0) ),
inference(superposition,[status(thm)],[c_400,c_522]) ).
tcf(c_154135,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| in(sK142(X0),X0) ),
inference(superposition,[status(thm)],[c_401,c_522]) ).
tcf(c_154136,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(sK142(subset_complement(X1,X0)),subset_complement(X1,X0))
| ( X1 = sK140 )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5403,c_522]) ).
tcf(c_154137,plain,
! [X0: $i] :
( relation(X0)
| in(sK142(X0),X0) ),
inference(superposition,[status(thm)],[c_561,c_522]) ).
tcf(c_154138,plain,
! [X0: $i] :
( in(sK142(X0),X0)
| ( X0 = sK140 ) ),
inference(superposition,[status(thm)],[c_579,c_522]) ).
tcf(c_154139,plain,
! [X0: $i] :
( in(sK142(X0),X0)
| ~ sP20(X0) ),
inference(superposition,[status(thm)],[c_584,c_522]) ).
tcf(c_154141,plain,
! [X0: $i] :
( in(sK142(X0),X0)
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151909,c_522]) ).
tcf(c_154142,plain,
! [X0: $i] :
( in(sK142(sK263(X0)),sK263(X0))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_522]) ).
tcf(c_154143,plain,
! [X0: $i] :
( in(sK142(X0),X0)
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_864,c_522]) ).
tcf(c_154144,plain,
! [X0: $i,X1: $i] : in(sK142(unordered_pair(X0,X1)),unordered_pair(X0,X1)),
inference(superposition,[status(thm)],[c_939,c_522]) ).
tcf(c_154146,plain,
! [X0: $i] : in(sK142(sK300(X0)),sK300(X0)),
inference(superposition,[status(thm)],[c_965,c_522]) ).
tcf(c_154147,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK142(X0),X0) ),
inference(superposition,[status(thm)],[c_1043,c_522]) ).
tcf(c_154149,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK142(X0),X0) ),
inference(superposition,[status(thm)],[c_1207,c_522]) ).
tcf(c_154151,plain,
in(sK142(powerset(sK140)),powerset(sK140)),
inference(superposition,[status(thm)],[c_146165,c_522]) ).
tcf(c_154153,plain,
( in(sK142(sK64),sK64)
| ~ sP7 ),
inference(superposition,[status(thm)],[c_146098,c_522]) ).
tcf(c_154154,plain,
! [X0: $i,X1: $i] :
( in(sK142(X1),X1)
| ( X1 = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144619,c_522]) ).
tcf(c_154156,plain,
( in(sK142(sK64),sK64)
| ~ iPr_def_19
| ~ sP7 ),
inference(superposition,[status(thm)],[c_145863,c_522]) ).
tcf(c_154157,plain,
( in(sK142(sK64),sK64)
| ~ sP6
| ~ sP7
| ~ in(sK140,sK66) ),
inference(superposition,[status(thm)],[c_146728,c_522]) ).
tcf(c_154158,plain,
( in(sK142(sK64),sK64)
| ~ sP15
| ~ sP7
| ~ in(sK140,sK110) ),
inference(superposition,[status(thm)],[c_146738,c_522]) ).
tcf(c_154159,plain,
( in(sK142(sK199(powerset(powerset(sK62)))),sK199(powerset(powerset(sK62))))
| ( sK199(powerset(powerset(sK62))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145355,c_522]) ).
tcf(c_154160,plain,
! [X0: $i] :
( in(sK142(sK199(powerset(powerset(X0)))),sK199(powerset(powerset(X0))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145365,c_522]) ).
tcf(c_154161,plain,
( in(sK142(sK199(powerset(powerset(sK261)))),sK199(powerset(powerset(sK261))))
| ( sK199(powerset(powerset(sK261))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145371,c_522]) ).
tcf(c_154162,plain,
( in(sK142(powerset(sK62)),powerset(sK62))
| ( powerset(sK62) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145625,c_522]) ).
tcf(c_154163,plain,
! [X0: $i] :
( in(sK142(powerset(X0)),powerset(X0))
| ( powerset(X0) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145633,c_522]) ).
tcf(c_154164,plain,
! [X0: $i] :
( sP15
| in(sK142(powerset(X0)),powerset(X0))
| ( powerset(X0) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145634,c_522]) ).
tcf(c_154165,plain,
! [X0: $i] :
( in(sK142(powerset(X0)),powerset(X0))
| ( powerset(X0) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145635,c_522]) ).
tcf(c_154166,plain,
( in(sK142(powerset(sK261)),powerset(sK261))
| ( powerset(sK261) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145641,c_522]) ).
tcf(c_154170,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK142(set_difference(X1,X2)),set_difference(X1,X2))
| ( set_difference(X1,X2) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_146007,c_522]) ).
tcf(c_154171,plain,
! [X0: $i,X1: $i] :
( in(sK142(set_difference(X0,X1)),set_difference(X0,X1))
| ( set_difference(X0,X1) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_146008,c_522]) ).
tcf(c_154172,plain,
in(sK142(set_union2(sK140,powerset(sK140))),set_union2(sK140,powerset(sK140))),
inference(superposition,[status(thm)],[c_148508,c_522]) ).
tcf(c_154173,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ( sK125(X1) = sK140 )
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_151774,c_522]) ).
tcf(c_154174,plain,
! [X0: $i] :
( in(sK142(X0),X0)
| ( sK92(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_151778,c_522]) ).
tcf(c_154340,plain,
element(sK142(omega),omega),
inference(superposition,[status(thm)],[c_154124,c_526]) ).
tcf(c_154341,plain,
ordinal(sK142(omega)),
inference(superposition,[status(thm)],[c_154340,c_858]) ).
tcf(c_154342,plain,
epsilon_connected(sK142(omega)),
inference(superposition,[status(thm)],[c_154340,c_857]) ).
tcf(c_154343,plain,
epsilon_transitive(sK142(omega)),
inference(superposition,[status(thm)],[c_154340,c_856]) ).
tcf(c_154344,plain,
( ordinal(sK261)
| sP32(sK142(omega)) ),
inference(superposition,[status(thm)],[c_154341,c_833]) ).
tcf(c_154359,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(sK142(X0)) ),
inference(superposition,[status(thm)],[c_154138,c_150230]) ).
tcf(c_154361,plain,
! [X0: $i] :
( element(sK142(X0),X0)
| ( X0 = sK140 ) ),
inference(superposition,[status(thm)],[c_154138,c_526]) ).
tcf(c_154362,plain,
! [X0: $i] :
( in(sK142(sK92(X0)),X0)
| ( sK92(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_154138,c_198]) ).
tcf(c_154363,plain,
! [X0: $i] :
( ordinal(sK142(sK92(X0)))
| ( sK92(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_154138,c_199]) ).
tcf(c_154364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK142(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ( relation_inverse_image(X0,X3) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_154138,c_425]) ).
tcf(c_154365,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK142(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ( relation_inverse_image(X0,X3) = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_154138,c_424]) ).
tcf(c_154392,plain,
! [X0: $i,X1: $i] :
( ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) )
| ( set_difference(relation_dom_restriction(X0,X1),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_153290,c_153993]) ).
tcf(c_154393,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) )
| ( set_difference(relation_dom_restriction(X0,X1),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_153265,c_153993]) ).
tcf(c_154394,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( set_difference(relation_dom_restriction(X0,X1),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_146155,c_153993]) ).
tcf(c_154396,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_dom_restriction(sK96(X0,X1),X2),sK96(X0,X1)) = sK140 )
| ~ sP12(X0,X1) ),
inference(superposition,[status(thm)],[c_208,c_153993]) ).
tcf(c_154397,plain,
! [X0: $i,X1: $i] :
( sP13(X0)
| ( set_difference(relation_dom_restriction(sK108(X0),X1),sK108(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_230,c_153993]) ).
tcf(c_154398,plain,
! [X0: $i,X1: $i] : set_difference(relation_dom_restriction(sK115(X0),X1),sK115(X0)) = sK140,
inference(superposition,[status(thm)],[c_249,c_153993]) ).
tcf(c_154399,plain,
! [X0: $i,X1: $i] : set_difference(relation_dom_restriction(sK124(X0),X1),sK124(X0)) = sK140,
inference(superposition,[status(thm)],[c_346,c_153993]) ).
tcf(c_154400,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_355,c_153993]) ).
tcf(c_154401,plain,
! [X0: $i,X1: $i] : set_difference(relation_dom_restriction(identity_relation(X0),X1),identity_relation(X0)) = sK140,
inference(superposition,[status(thm)],[c_1101,c_153993]) ).
tcf(c_154402,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_dom_restriction(relation_dom_restriction(X0,X1),X2),relation_dom_restriction(X0,X1)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_773,c_153993]) ).
tcf(c_154403,plain,
! [X0: $i] : set_difference(relation_dom_restriction(sK140,X0),sK140) = sK140,
inference(superposition,[status(thm)],[c_577,c_153993]) ).
tcf(c_154404,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom_restriction(relation_dom(X0),X1),relation_dom(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_642,c_153993]) ).
tcf(c_154405,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_dom_restriction(relation_rng_restriction(X1,X0),X2),relation_rng_restriction(X1,X0)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_646,c_153993]) ).
tcf(c_154406,plain,
! [X0: $i] : set_difference(relation_dom_restriction(sK240,X0),sK240) = sK140,
inference(superposition,[status(thm)],[c_783,c_153993]) ).
tcf(c_154407,plain,
! [X0: $i] : set_difference(relation_dom_restriction(sK242,X0),sK242) = sK140,
inference(superposition,[status(thm)],[c_791,c_153993]) ).
tcf(c_154408,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom_restriction(sK264(X0),X1),sK264(X0)) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_852,c_153993]) ).
tcf(c_154409,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom_restriction(relation_rng(X0),X1),relation_rng(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_944,c_153993]) ).
tcf(c_154410,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_dom_restriction(relation_restriction(X0,X1),X2),relation_restriction(X0,X1)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1013,c_153993]) ).
tcf(c_154411,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_dom_restriction(sK312(X0,X1),X2),sK312(X0,X1)) = sK140,
inference(superposition,[status(thm)],[c_1019,c_153993]) ).
tcf(c_154412,plain,
! [X0: $i,X1: $i] : set_difference(relation_dom_restriction(inclusion_relation(X0),X1),inclusion_relation(X0)) = sK140,
inference(superposition,[status(thm)],[c_1091,c_153993]) ).
tcf(c_154413,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom_restriction(relation_inverse(X0),X1),relation_inverse(X0)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1113,c_153993]) ).
tcf(c_154414,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom_restriction(relation_inverse(X0),X1),relation_inverse(X0)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1112,c_153993]) ).
tcf(c_154415,plain,
! [X0: $i] : set_difference(relation_dom_restriction(sK335,X0),sK335) = sK140,
inference(superposition,[status(thm)],[c_1149,c_153993]) ).
tcf(c_154416,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_dom_restriction(sK347(X0,X1),X2),sK347(X0,X1)) = sK140,
inference(superposition,[status(thm)],[c_1237,c_153993]) ).
tcf(c_154500,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,union(X1)) = sK140 )
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_154065]) ).
tcf(c_154501,plain,
! [X0: $i] :
( sP3(X0)
| ( set_difference(sK58(X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_122,c_154065]) ).
tcf(c_154502,plain,
set_difference(sK140,union(omega)) = sK140,
inference(superposition,[status(thm)],[c_847,c_154065]) ).
tcf(c_154503,plain,
( ( set_difference(sK66,union(omega)) = sK140 )
| ~ sP6 ),
inference(superposition,[status(thm)],[c_140,c_154065]) ).
tcf(c_154505,plain,
( ( set_difference(sK110,union(omega)) = sK140 )
| ~ sP15 ),
inference(superposition,[status(thm)],[c_238,c_154065]) ).
tcf(c_154506,plain,
! [X0: $i] : set_difference(X0,union(set_union2(X0,unordered_pair(X0,X0)))) = sK140,
inference(superposition,[status(thm)],[c_256,c_154065]) ).
tcf(c_154507,plain,
! [X0: $i] : set_difference(X0,union(sK116(X0))) = sK140,
inference(superposition,[status(thm)],[c_272,c_154065]) ).
tcf(c_154508,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ( set_difference(X1,union(relation_dom(X0))) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_154065]) ).
tcf(c_154509,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( set_difference(apply(sK126(X1),X0),union(X0)) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2177,c_154065]) ).
tcf(c_154510,plain,
! [X0: $i] :
( ordinal(X0)
| ( set_difference(sK127(X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_367,c_154065]) ).
tcf(c_154511,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( set_difference(sK128(X0),union(X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_144620,c_154065]) ).
tcf(c_154512,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(sK130(X0,X1),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_400,c_154065]) ).
tcf(c_154513,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(sK130(X0,X1),union(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_401,c_154065]) ).
tcf(c_154514,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( set_difference(X2,union(subset_complement(X1,X0))) = sK140 )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5403,c_154065]) ).
tcf(c_154515,plain,
! [X0: $i] :
( relation(X0)
| ( set_difference(sK163(X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_561,c_154065]) ).
tcf(c_154516,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( set_difference(sK169(X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_579,c_154065]) ).
tcf(c_154517,plain,
! [X0: $i] :
( ( set_difference(sK173(X0),union(X0)) = sK140 )
| ~ sP20(X0) ),
inference(superposition,[status(thm)],[c_584,c_154065]) ).
tcf(c_154519,plain,
! [X0: $i] :
( ( set_difference(sK140,union(X0)) = sK140 )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151909,c_154065]) ).
tcf(c_154520,plain,
! [X0: $i] :
( ( X0 = omega )
| ( set_difference(sK140,union(sK263(X0))) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_154065]) ).
tcf(c_154521,plain,
! [X0: $i] :
( ( set_difference(sK268(X0),union(X0)) = sK140 )
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_864,c_154065]) ).
tcf(c_154522,plain,
! [X0: $i,X1: $i] : set_difference(X0,union(unordered_pair(X0,X1))) = sK140,
inference(superposition,[status(thm)],[c_939,c_154065]) ).
tcf(c_154523,plain,
! [X0: $i,X1: $i] : set_difference(X0,union(unordered_pair(X1,X0))) = sK140,
inference(superposition,[status(thm)],[c_940,c_154065]) ).
tcf(c_154524,plain,
! [X0: $i] : set_difference(X0,union(sK300(X0))) = sK140,
inference(superposition,[status(thm)],[c_965,c_154065]) ).
tcf(c_154525,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( set_difference(sK316(X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_1043,c_154065]) ).
tcf(c_154526,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( set_difference(sK320(X1,X0),union(X0)) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_154065]) ).
tcf(c_154527,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( set_difference(sK343(X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_1207,c_154065]) ).
tcf(c_154528,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( set_difference(sK344(X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_1208,c_154065]) ).
tcf(c_154529,plain,
set_difference(sK140,union(powerset(sK140))) = sK140,
inference(superposition,[status(thm)],[c_146165,c_154065]) ).
tcf(c_154530,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( set_difference(unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))),union(X0)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16344,c_154065]) ).
tcf(c_154531,plain,
( ( set_difference(sK119(sK64),union(sK64)) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_146098,c_154065]) ).
tcf(c_154532,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( set_difference(sK318(X0,X1),union(X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144619,c_154065]) ).
tcf(c_154533,plain,
( sP15
| ( set_difference(sK114(sK64),union(sK64)) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_145791,c_154065]) ).
tcf(c_154534,plain,
( ( set_difference(sK72(sK64),union(sK64)) = sK140 )
| ~ iPr_def_19
| ~ sP7 ),
inference(superposition,[status(thm)],[c_145863,c_154065]) ).
tcf(c_154535,plain,
( ( set_difference(sK67(sK64),union(sK64)) = sK140 )
| ~ sP6
| ~ sP7
| ~ in(sK140,sK66) ),
inference(superposition,[status(thm)],[c_146728,c_154065]) ).
tcf(c_154536,plain,
( ( set_difference(sK111(sK64),union(sK64)) = sK140 )
| ~ sP15
| ~ sP7
| ~ in(sK140,sK110) ),
inference(superposition,[status(thm)],[c_146738,c_154065]) ).
tcf(c_154537,plain,
( ( sK199(powerset(powerset(sK62))) = sK140 )
| ( set_difference(sK63(sK199(powerset(powerset(sK62)))),union(sK199(powerset(powerset(sK62))))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145355,c_154065]) ).
tcf(c_154538,plain,
! [X0: $i] :
( ( sK199(powerset(powerset(X0))) = sK140 )
| ( set_difference(sK119(sK199(powerset(powerset(X0)))),union(sK199(powerset(powerset(X0))))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145365,c_154065]) ).
tcf(c_154539,plain,
( ( sK199(powerset(powerset(sK261))) = sK140 )
| ( set_difference(sK262(sK199(powerset(powerset(sK261)))),union(sK199(powerset(powerset(sK261))))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145371,c_154065]) ).
tcf(c_154540,plain,
( ( powerset(sK62) = sK140 )
| ( set_difference(sK63(powerset(sK62)),union(powerset(sK62))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145625,c_154065]) ).
tcf(c_154541,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ( set_difference(sK72(powerset(X0)),union(powerset(X0))) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145633,c_154065]) ).
tcf(c_154542,plain,
! [X0: $i] :
( sP15
| ( powerset(X0) = sK140 )
| ( set_difference(sK114(powerset(X0)),union(powerset(X0))) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145634,c_154065]) ).
tcf(c_154543,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ( set_difference(sK119(powerset(X0)),union(powerset(X0))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145635,c_154065]) ).
tcf(c_154544,plain,
( ( powerset(sK261) = sK140 )
| ( set_difference(sK262(powerset(sK261)),union(powerset(sK261))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145641,c_154065]) ).
tcf(c_154545,plain,
( ( sK140 = omega )
| ( set_difference(sK128(omega),union(omega)) = sK140 )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146242,c_154065]) ).
tcf(c_154546,plain,
( ( sK140 = omega )
| ( set_difference(sK128(omega),union(omega)) = sK140 )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145922,c_154065]) ).
tcf(c_154547,plain,
( ( sK140 = omega )
| ( set_difference(sK128(omega),union(omega)) = sK140 )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145878,c_154065]) ).
tcf(c_154548,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X1,X2) = sK140 )
| ( set_difference(sK318(X0,set_difference(X1,X2)),union(set_difference(X1,X2))) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_146007,c_154065]) ).
tcf(c_154549,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = sK140 )
| ( set_difference(sK128(set_difference(X0,X1)),union(set_difference(X0,X1))) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_146008,c_154065]) ).
tcf(c_154550,plain,
set_difference(sK140,union(set_union2(sK140,powerset(sK140)))) = sK140,
inference(superposition,[status(thm)],[c_148508,c_154065]) ).
tcf(c_154551,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( set_difference(apply(sK126(X1),sK92(X0)),union(X0)) = sK140 )
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_151774,c_154065]) ).
tcf(c_154552,plain,
! [X0: $i] :
( ( sK92(X0) = sK140 )
| ( set_difference(sK169(sK92(X0)),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151778,c_154065]) ).
tcf(c_154553,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( set_difference(sK142(X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154138,c_154065]) ).
tcf(c_154554,plain,
set_difference(sK142(omega),union(omega)) = sK140,
inference(superposition,[status(thm)],[c_154124,c_154065]) ).
tcf(c_154614,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ( set_difference(sK119(powerset(X0)),X0) = sK140 )
| ~ finite(X0) ),
inference(light_normalisation,[status(thm)],[c_154543,c_516]) ).
tcf(c_154649,plain,
! [X0: $i] :
( sP15
| ( powerset(X0) = sK140 )
| ( set_difference(sK114(powerset(X0)),X0) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(light_normalisation,[status(thm)],[c_154542,c_516]) ).
tcf(c_154661,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ( set_difference(sK72(powerset(X0)),X0) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(light_normalisation,[status(thm)],[c_154541,c_516]) ).
tcf(c_154798,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ( set_difference(sK169(powerset(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_516,c_154516]) ).
tcf(c_154801,plain,
! [X0: $i] :
( disjoint(set_difference(sK169(X0),union(X0)),sK169(X0))
| ( X0 = sK140 ) ),
inference(superposition,[status(thm)],[c_154516,c_146330]) ).
tcf(c_154803,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( set_difference(sK140,sK169(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154516,c_146010]) ).
tcf(c_154804,plain,
! [X0: $i] :
( subset(sK140,sK169(X0))
| ( X0 = sK140 ) ),
inference(superposition,[status(thm)],[c_154516,c_383]) ).
tcf(c_154805,plain,
! [X0: $i] :
( disjoint(sK169(X0),union(X0))
| ( X0 = sK140 )
| ( set_difference(sK169(X0),sK140) != sK140 ) ),
inference(superposition,[status(thm)],[c_154516,c_625]) ).
tcf(c_154806,plain,
! [X0: $i] :
( subset(sK169(X0),union(X0))
| ( X0 = sK140 ) ),
inference(superposition,[status(thm)],[c_154516,c_387]) ).
tcf(c_154807,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,sK140),sK140)
| ( X1 = sK140 )
| ( set_difference(sK169(X1),union(X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,sK169(X1)) ),
inference(superposition,[status(thm)],[c_154516,c_146007]) ).
tcf(c_154817,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( set_difference(sK169(X1),union(X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,sK169(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_154807,c_580]) ).
tcf(c_154841,plain,
! [X0: $i] :
( subset(sK169(powerset(X0)),X0)
| ( powerset(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_516,c_154806]) ).
tcf(c_154842,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ~ proper_subset(union(X0),sK169(X0)) ),
inference(superposition,[status(thm)],[c_154806,c_472]) ).
tcf(c_154843,plain,
! [X0: $i] :
( in(sK140,sK169(X0))
| ( X0 = sK140 )
| ( union(X0) = sK140 )
| ( sK125(subset_complement(union(X0),sK169(X0))) = sK140 )
| ~ element(sK140,union(X0)) ),
inference(superposition,[status(thm)],[c_154806,c_145539]) ).
tcf(c_154844,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,sK169(X1))),sK169(X1))
| ( X1 = sK140 )
| ( sK169(X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_154806,c_1058]) ).
tcf(c_154845,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,sK169(X1)),sK169(X1))
| ( X1 = sK140 )
| ( sK169(X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,union(X1)) ),
inference(superposition,[status(thm)],[c_154806,c_1057]) ).
tcf(c_154846,plain,
! [X0: $i] :
( in(sK128(sK169(X0)),sK169(X0))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154806,c_369]) ).
tcf(c_154847,plain,
! [X0: $i] :
( ordinal(sK128(sK169(X0)))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154806,c_371]) ).
tcf(c_154849,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(sK169(X1)),X0)
| ( X1 = sK140 )
| ( sK169(X1) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(union(X1))
| ~ in(X0,sK169(X1)) ),
inference(superposition,[status(thm)],[c_154806,c_370]) ).
tcf(c_154890,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ( sK125(X1) = sK140 )
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_154131]) ).
tcf(c_154891,plain,
! [X0: $i] :
( sP3(X0)
| in(sK142(sK58(X0)),sK58(X0))
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_122,c_154131]) ).
tcf(c_154896,plain,
! [X0: $i] :
( in(sK142(X0),X0)
| ( sK125(set_union2(X0,unordered_pair(X0,X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_256,c_154131]) ).
tcf(c_154897,plain,
! [X0: $i] :
( in(sK142(X0),X0)
| ( sK125(sK116(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_272,c_154131]) ).
tcf(c_154898,plain,
! [X0: $i,X1: $i] :
( in(sK142(X1),X1)
| ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_154131]) ).
tcf(c_154899,plain,
! [X0: $i,X1: $i] :
( in(sK142(apply(sK126(X1),X0)),apply(sK126(X1),X0))
| ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2177,c_154131]) ).
tcf(c_154900,plain,
! [X0: $i] :
( ordinal(X0)
| in(sK142(sK127(X0)),sK127(X0))
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_367,c_154131]) ).
tcf(c_154901,plain,
! [X0: $i] :
( in(sK142(sK128(X0)),sK128(X0))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_144620,c_154131]) ).
tcf(c_154902,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK142(sK130(X0,X1)),sK130(X0,X1))
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_400,c_154131]) ).
tcf(c_154903,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| in(sK142(sK130(X1,X0)),sK130(X1,X0))
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_401,c_154131]) ).
tcf(c_154904,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(sK142(X2),X2)
| ( X1 = sK140 )
| ( sK125(subset_complement(X1,X0)) = sK140 )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5403,c_154131]) ).
tcf(c_154905,plain,
! [X0: $i] :
( relation(X0)
| in(sK142(sK163(X0)),sK163(X0))
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_561,c_154131]) ).
tcf(c_154906,plain,
! [X0: $i] :
( in(sK142(sK169(X0)),sK169(X0))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_579,c_154131]) ).
tcf(c_154907,plain,
! [X0: $i] :
( in(sK142(sK173(X0)),sK173(X0))
| ( sK125(X0) = sK140 )
| ~ sP20(X0) ),
inference(superposition,[status(thm)],[c_584,c_154131]) ).
tcf(c_154911,plain,
! [X0: $i] :
( in(sK142(sK268(X0)),sK268(X0))
| ( sK125(X0) = sK140 )
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_864,c_154131]) ).
tcf(c_154912,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ( sK125(unordered_pair(X0,X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_939,c_154131]) ).
tcf(c_154913,plain,
! [X0: $i,X1: $i] :
( in(sK142(X1),X1)
| ( sK125(unordered_pair(X0,X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_940,c_154131]) ).
tcf(c_154914,plain,
! [X0: $i] :
( in(sK142(X0),X0)
| ( sK125(sK300(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_965,c_154131]) ).
tcf(c_154915,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK142(sK316(X0)),sK316(X0))
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_1043,c_154131]) ).
tcf(c_154916,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK320(X1,X0)),sK320(X1,X0))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_154131]) ).
tcf(c_154917,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK142(sK343(X0)),sK343(X0))
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_1207,c_154131]) ).
tcf(c_154918,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK142(sK344(X0)),sK344(X0))
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_1208,c_154131]) ).
tcf(c_154920,plain,
! [X0: $i] :
( in(sK142(unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0)))),unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16344,c_154131]) ).
tcf(c_154921,plain,
( in(sK142(sK119(sK64)),sK119(sK64))
| ( sK125(sK64) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_146098,c_154131]) ).
tcf(c_154922,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK318(X0,X1)),sK318(X0,X1))
| ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144619,c_154131]) ).
tcf(c_154923,plain,
( sP15
| in(sK142(sK114(sK64)),sK114(sK64))
| ( sK125(sK64) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_145791,c_154131]) ).
tcf(c_154924,plain,
( in(sK142(sK72(sK64)),sK72(sK64))
| ( sK125(sK64) = sK140 )
| ~ iPr_def_19
| ~ sP7 ),
inference(superposition,[status(thm)],[c_145863,c_154131]) ).
tcf(c_154925,plain,
( in(sK142(sK67(sK64)),sK67(sK64))
| ( sK125(sK64) = sK140 )
| ~ sP6
| ~ sP7
| ~ in(sK140,sK66) ),
inference(superposition,[status(thm)],[c_146728,c_154131]) ).
tcf(c_154926,plain,
( in(sK142(sK111(sK64)),sK111(sK64))
| ( sK125(sK64) = sK140 )
| ~ sP15
| ~ sP7
| ~ in(sK140,sK110) ),
inference(superposition,[status(thm)],[c_146738,c_154131]) ).
tcf(c_154927,plain,
( in(sK142(sK63(sK199(powerset(powerset(sK62))))),sK63(sK199(powerset(powerset(sK62)))))
| ( sK199(powerset(powerset(sK62))) = sK140 )
| ( sK125(sK199(powerset(powerset(sK62)))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145355,c_154131]) ).
tcf(c_154928,plain,
! [X0: $i] :
( in(sK142(sK119(sK199(powerset(powerset(X0))))),sK119(sK199(powerset(powerset(X0)))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ( sK125(sK199(powerset(powerset(X0)))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145365,c_154131]) ).
tcf(c_154929,plain,
( in(sK142(sK262(sK199(powerset(powerset(sK261))))),sK262(sK199(powerset(powerset(sK261)))))
| ( sK199(powerset(powerset(sK261))) = sK140 )
| ( sK125(sK199(powerset(powerset(sK261)))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145371,c_154131]) ).
tcf(c_154930,plain,
( in(sK142(sK63(powerset(sK62))),sK63(powerset(sK62)))
| ( powerset(sK62) = sK140 )
| ( sK125(powerset(sK62)) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145625,c_154131]) ).
tcf(c_154931,plain,
! [X0: $i] :
( in(sK142(sK72(powerset(X0))),sK72(powerset(X0)))
| ( powerset(X0) = sK140 )
| ( sK125(powerset(X0)) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145633,c_154131]) ).
tcf(c_154932,plain,
! [X0: $i] :
( sP15
| in(sK142(sK114(powerset(X0))),sK114(powerset(X0)))
| ( powerset(X0) = sK140 )
| ( sK125(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145634,c_154131]) ).
tcf(c_154933,plain,
! [X0: $i] :
( in(sK142(sK119(powerset(X0))),sK119(powerset(X0)))
| ( powerset(X0) = sK140 )
| ( sK125(powerset(X0)) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145635,c_154131]) ).
tcf(c_154934,plain,
( in(sK142(sK262(powerset(sK261))),sK262(powerset(sK261)))
| ( powerset(sK261) = sK140 )
| ( sK125(powerset(sK261)) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145641,c_154131]) ).
tcf(c_154938,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK142(sK318(X0,set_difference(X1,X2))),sK318(X0,set_difference(X1,X2)))
| ( set_difference(X1,X2) = sK140 )
| ( sK125(set_difference(X1,X2)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_146007,c_154131]) ).
tcf(c_154939,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK128(set_difference(X0,X1))),sK128(set_difference(X0,X1)))
| ( set_difference(X0,X1) = sK140 )
| ( sK125(set_difference(X0,X1)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_146008,c_154131]) ).
tcf(c_154941,plain,
! [X0: $i,X1: $i] :
( in(sK142(apply(sK126(X1),sK92(X0))),apply(sK126(X1),sK92(X0)))
| ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_151774,c_154131]) ).
tcf(c_154942,plain,
! [X0: $i] :
( in(sK142(sK169(sK92(X0))),sK169(sK92(X0)))
| ( sK125(X0) = sK140 )
| ( sK92(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_151778,c_154131]) ).
tcf(c_154943,plain,
! [X0: $i] :
( in(sK142(sK142(X0)),sK142(X0))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_154138,c_154131]) ).
tcf(c_155163,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(X1))
| ( X1 = sK140 )
| ( set_difference(unordered_pair(X1,X1),set_difference(unordered_pair(X1,X1),X0)) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_151758,c_154064]) ).
tcf(c_155164,plain,
! [X0: $i] :
( sP3(X0)
| ordinal(sK128(sK58(X0)))
| ( sK58(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_122,c_154064]) ).
tcf(c_155166,plain,
( ordinal(sK128(sK66))
| ( sK140 = sK66 )
| ~ sP6
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_140,c_154064]) ).
tcf(c_155168,plain,
( ordinal(sK128(sK110))
| ( sK140 = sK110 )
| ~ sP15
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_238,c_154064]) ).
tcf(c_155169,plain,
! [X0: $i] :
( ordinal(sK128(X0))
| ( X0 = sK140 )
| ~ ordinal(union(set_union2(X0,unordered_pair(X0,X0)))) ),
inference(superposition,[status(thm)],[c_256,c_154064]) ).
tcf(c_155170,plain,
! [X0: $i] :
( ordinal(sK128(X0))
| ( X0 = sK140 )
| ~ ordinal(union(sK116(X0))) ),
inference(superposition,[status(thm)],[c_272,c_154064]) ).
tcf(c_155171,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(X1))
| ( X1 = sK140 )
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ ordinal(union(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_906,c_154064]) ).
tcf(c_155172,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(apply(sK126(X1),X0)))
| ( sK125(X1) = sK140 )
| ( apply(sK126(X1),X0) = sK140 )
| ~ ordinal(union(X0))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2177,c_154064]) ).
tcf(c_155173,plain,
! [X0: $i] :
( ordinal(X0)
| ordinal(sK128(sK127(X0)))
| ( sK127(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_367,c_154064]) ).
tcf(c_155174,plain,
! [X0: $i] :
( ordinal(sK128(sK128(X0)))
| ( X0 = sK140 )
| ( sK128(X0) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_144620,c_154064]) ).
tcf(c_155175,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ordinal(sK128(sK130(X0,X1)))
| ( sK130(X0,X1) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_400,c_154064]) ).
tcf(c_155176,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ordinal(sK128(sK130(X1,X0)))
| ( sK130(X1,X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_401,c_154064]) ).
tcf(c_155177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK128(X2))
| in(X2,X1)
| ( X2 = sK140 )
| ( X0 = sK140 )
| ~ element(X2,X0)
| ~ subset(X1,X0)
| ~ ordinal(union(subset_complement(X0,X1))) ),
inference(superposition,[status(thm)],[c_5403,c_154064]) ).
tcf(c_155178,plain,
! [X0: $i] :
( relation(X0)
| ordinal(sK128(sK163(X0)))
| ( sK163(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_561,c_154064]) ).
tcf(c_155180,plain,
! [X0: $i] :
( ordinal(sK128(sK173(X0)))
| ( sK173(X0) = sK140 )
| ~ sP20(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_584,c_154064]) ).
tcf(c_155184,plain,
! [X0: $i] :
( ordinal(sK128(sK268(X0)))
| ( sK268(X0) = sK140 )
| ~ sP34(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_864,c_154064]) ).
tcf(c_155185,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(X0))
| ( X0 = sK140 )
| ~ ordinal(union(unordered_pair(X0,X1))) ),
inference(superposition,[status(thm)],[c_939,c_154064]) ).
tcf(c_155186,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(X1))
| ( X1 = sK140 )
| ~ ordinal(union(unordered_pair(X0,X1))) ),
inference(superposition,[status(thm)],[c_940,c_154064]) ).
tcf(c_155187,plain,
! [X0: $i] :
( ordinal(sK128(X0))
| ( X0 = sK140 )
| ~ ordinal(union(sK300(X0))) ),
inference(superposition,[status(thm)],[c_965,c_154064]) ).
tcf(c_155188,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ordinal(sK128(sK316(X0)))
| ( sK316(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_1043,c_154064]) ).
tcf(c_155189,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(sK320(X1,X0)))
| ( X0 = sK140 )
| ( sK320(X1,X0) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ ordinal(union(X0))
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_154064]) ).
tcf(c_155190,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ordinal(sK128(sK343(X0)))
| ( sK343(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_1207,c_154064]) ).
tcf(c_155191,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ordinal(sK128(sK344(X0)))
| ( sK344(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_1208,c_154064]) ).
tcf(c_155193,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0)))))
| ( X0 = sK140 )
| ( unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))) = sK140 )
| ~ relation(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_16344,c_154064]) ).
tcf(c_155194,plain,
( ordinal(sK128(sK119(sK64)))
| ( sK119(sK64) = sK140 )
| ~ sP7
| ~ ordinal(union(sK64)) ),
inference(superposition,[status(thm)],[c_146098,c_154064]) ).
tcf(c_155195,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(sK318(X0,X1)))
| ( X1 = sK140 )
| ( sK318(X0,X1) = sK140 )
| ~ relation(X0)
| ~ ordinal(union(X1))
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144619,c_154064]) ).
tcf(c_155196,plain,
( sP15
| ordinal(sK128(sK114(sK64)))
| ( sK114(sK64) = sK140 )
| ~ sP7
| ~ ordinal(union(sK64)) ),
inference(superposition,[status(thm)],[c_145791,c_154064]) ).
tcf(c_155197,plain,
( ordinal(sK128(sK72(sK64)))
| ( sK72(sK64) = sK140 )
| ~ iPr_def_19
| ~ sP7
| ~ ordinal(union(sK64)) ),
inference(superposition,[status(thm)],[c_145863,c_154064]) ).
tcf(c_155198,plain,
( ordinal(sK128(sK67(sK64)))
| ( sK67(sK64) = sK140 )
| ~ sP6
| ~ sP7
| ~ ordinal(union(sK64))
| ~ in(sK140,sK66) ),
inference(superposition,[status(thm)],[c_146728,c_154064]) ).
tcf(c_155199,plain,
( ordinal(sK128(sK111(sK64)))
| ( sK111(sK64) = sK140 )
| ~ sP15
| ~ sP7
| ~ ordinal(union(sK64))
| ~ in(sK140,sK110) ),
inference(superposition,[status(thm)],[c_146738,c_154064]) ).
tcf(c_155200,plain,
( ordinal(sK128(sK63(sK199(powerset(powerset(sK62))))))
| ( sK199(powerset(powerset(sK62))) = sK140 )
| ( sK63(sK199(powerset(powerset(sK62)))) = sK140 )
| ~ iPr_def_21
| ~ ordinal(union(sK199(powerset(powerset(sK62))))) ),
inference(superposition,[status(thm)],[c_145355,c_154064]) ).
tcf(c_155201,plain,
! [X0: $i] :
( ordinal(sK128(sK119(sK199(powerset(powerset(X0))))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ( sK119(sK199(powerset(powerset(X0)))) = sK140 )
| ~ finite(X0)
| ~ ordinal(union(sK199(powerset(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_145365,c_154064]) ).
tcf(c_155202,plain,
( ordinal(sK128(sK262(sK199(powerset(powerset(sK261))))))
| ( sK199(powerset(powerset(sK261))) = sK140 )
| ( sK262(sK199(powerset(powerset(sK261)))) = sK140 )
| ~ iPr_def_15
| ~ ordinal(union(sK199(powerset(powerset(sK261))))) ),
inference(superposition,[status(thm)],[c_145371,c_154064]) ).
tcf(c_155203,plain,
( ordinal(sK128(sK63(powerset(sK62))))
| ( powerset(sK62) = sK140 )
| ( sK63(powerset(sK62)) = sK140 )
| ~ iPr_def_21
| ~ ordinal(union(powerset(sK62))) ),
inference(superposition,[status(thm)],[c_145625,c_154064]) ).
tcf(c_155204,plain,
! [X0: $i] :
( ordinal(sK128(sK72(powerset(X0))))
| ( powerset(X0) = sK140 )
| ( sK72(powerset(X0)) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ ordinal(union(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145633,c_154064]) ).
tcf(c_155205,plain,
! [X0: $i] :
( sP15
| ordinal(sK128(sK114(powerset(X0))))
| ( powerset(X0) = sK140 )
| ( sK114(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ ordinal(union(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145634,c_154064]) ).
tcf(c_155206,plain,
! [X0: $i] :
( ordinal(sK128(sK119(powerset(X0))))
| ( powerset(X0) = sK140 )
| ( sK119(powerset(X0)) = sK140 )
| ~ finite(X0)
| ~ ordinal(union(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145635,c_154064]) ).
tcf(c_155207,plain,
( ordinal(sK128(sK262(powerset(sK261))))
| ( powerset(sK261) = sK140 )
| ( sK262(powerset(sK261)) = sK140 )
| ~ iPr_def_15
| ~ ordinal(union(powerset(sK261))) ),
inference(superposition,[status(thm)],[c_145641,c_154064]) ).
tcf(c_155208,plain,
( ordinal(sK128(sK128(omega)))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(union(omega))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146242,c_154064]) ).
tcf(c_155209,plain,
( ordinal(sK128(sK128(omega)))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140))
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_145922,c_154064]) ).
tcf(c_155210,plain,
( ordinal(sK128(sK128(omega)))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140))
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_145878,c_154064]) ).
tcf(c_155211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK128(sK318(X2,set_difference(X0,X1))))
| ( set_difference(X0,X1) = sK140 )
| ( sK318(X2,set_difference(X0,X1)) = sK140 )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X0)
| ~ ordinal(union(set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_146007,c_154064]) ).
tcf(c_155212,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(sK128(set_difference(X0,X1))))
| ( set_difference(X0,X1) = sK140 )
| ( sK128(set_difference(X0,X1)) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(union(set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_146008,c_154064]) ).
tcf(c_155214,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(apply(sK126(X1),sK92(X0))))
| ( sK125(X1) = sK140 )
| ( apply(sK126(X1),sK92(X0)) = sK140 )
| ~ ordinal(union(X0))
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_151774,c_154064]) ).
tcf(c_155215,plain,
! [X0: $i] :
( ordinal(sK128(sK169(sK92(X0))))
| ( sK92(X0) = sK140 )
| ( sK169(sK92(X0)) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_151778,c_154064]) ).
tcf(c_155216,plain,
! [X0: $i] :
( ordinal(sK128(sK142(X0)))
| ( X0 = sK140 )
| ( sK142(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154138,c_154064]) ).
tcf(c_155217,plain,
( ordinal(sK128(sK142(omega)))
| ( sK142(omega) = sK140 )
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_154124,c_154064]) ).
tcf(c_155345,plain,
! [X0: $i] :
( ordinal(sK128(sK119(powerset(X0))))
| ( powerset(X0) = sK140 )
| ( sK119(powerset(X0)) = sK140 )
| ~ finite(X0)
| ~ ordinal(X0) ),
inference(light_normalisation,[status(thm)],[c_155206,c_516]) ).
tcf(c_155403,plain,
! [X0: $i] :
( sP15
| ordinal(sK128(sK114(powerset(X0))))
| ( powerset(X0) = sK140 )
| ( sK114(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(light_normalisation,[status(thm)],[c_155205,c_516]) ).
tcf(c_155410,plain,
! [X0: $i] :
( ordinal(sK128(sK72(powerset(X0))))
| ( powerset(X0) = sK140 )
| ( sK72(powerset(X0)) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(light_normalisation,[status(thm)],[c_155204,c_516]) ).
tcf(c_155513,plain,
( function(sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ~ empty(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_147195]) ).
tcf(c_155514,plain,
( finite(sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ~ empty(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_147193]) ).
tcf(c_155515,plain,
( epsilon_transitive(sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ~ empty(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_147192]) ).
tcf(c_155516,plain,
( epsilon_connected(sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ~ empty(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_147191]) ).
tcf(c_155517,plain,
( ordinal(sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ~ empty(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_147190]) ).
tcf(c_155518,plain,
( one_to_one(sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ~ empty(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_147189]) ).
tcf(c_155519,plain,
! [X0: $i] :
( ( sK125(sK198(sK242)) = sK140 )
| ( apply(sK126(sK198(sK242)),X0) = sK140 )
| ~ empty(sK198(sK242))
| ~ relation(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_150772]) ).
tcf(c_155520,plain,
! [X0: $i] :
( element(X0,sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ( apply(sK126(sK198(sK242)),X0) = sK140 )
| ~ function(sK126(sK198(sK242)))
| ~ relation(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_148552]) ).
tcf(c_155521,plain,
( relation(sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ~ empty(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_642]) ).
tcf(c_155522,plain,
( empty(sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ~ empty(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_641]) ).
tcf(c_155523,plain,
! [X0: $i] :
( in(X0,sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ( apply(sK126(sK198(sK242)),X0) = sK140 )
| ~ function(sK126(sK198(sK242)))
| ~ relation(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_906]) ).
tcf(c_155524,plain,
( ( sK125(sK198(sK242)) = sK140 )
| ( relation_rng(sK126(sK198(sK242))) = sK140 )
| ~ relation(sK126(sK198(sK242)))
| ( sK198(sK242) != sK140 ) ),
inference(superposition,[status(thm)],[c_147343,c_478]) ).
tcf(c_155525,plain,
( ( sK126(sK198(sK242)) = sK140 )
| ( sK125(sK198(sK242)) = sK140 )
| ~ relation(sK126(sK198(sK242)))
| ( sK198(sK242) != sK140 ) ),
inference(superposition,[status(thm)],[c_147343,c_475]) ).
tcf(c_155592,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X1,X1),set_difference(unordered_pair(X1,X1),X0)) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_151758,c_527]) ).
tcf(c_155593,plain,
! [X0: $i] :
( sP3(X0)
| ~ in(X0,sK58(X0)) ),
inference(superposition,[status(thm)],[c_122,c_527]) ).
tcf(c_155594,plain,
~ in(omega,sK140),
inference(superposition,[status(thm)],[c_847,c_527]) ).
tcf(c_155595,plain,
( ~ sP6
| ~ in(omega,sK66) ),
inference(superposition,[status(thm)],[c_140,c_527]) ).
tcf(c_155597,plain,
( ~ sP15
| ~ in(omega,sK110) ),
inference(superposition,[status(thm)],[c_238,c_527]) ).
tcf(c_155598,plain,
! [X0: $i] : ~ in(set_union2(X0,unordered_pair(X0,X0)),X0),
inference(superposition,[status(thm)],[c_256,c_527]) ).
tcf(c_155599,plain,
! [X0: $i] : ~ in(sK116(X0),X0),
inference(superposition,[status(thm)],[c_272,c_527]) ).
tcf(c_155600,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_906,c_527]) ).
tcf(c_155601,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ~ in(X0,X1)
| ~ in(X0,apply(sK126(X1),X0)) ),
inference(superposition,[status(thm)],[c_2177,c_527]) ).
tcf(c_155602,plain,
! [X0: $i] :
( ordinal(X0)
| ~ in(X0,sK127(X0)) ),
inference(superposition,[status(thm)],[c_367,c_527]) ).
tcf(c_155603,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ~ ordinal(X0)
| ~ in(X0,sK128(X0)) ),
inference(superposition,[status(thm)],[c_144620,c_527]) ).
tcf(c_155604,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ~ in(X0,sK130(X0,X1)) ),
inference(superposition,[status(thm)],[c_400,c_527]) ).
tcf(c_155605,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ in(X0,sK130(X1,X0)) ),
inference(superposition,[status(thm)],[c_401,c_527]) ).
tcf(c_155606,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ( X0 = sK140 )
| ~ element(X2,X0)
| ~ subset(X1,X0)
| ~ in(subset_complement(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_5403,c_527]) ).
tcf(c_155607,plain,
! [X0: $i] :
( relation(X0)
| ~ in(X0,sK163(X0)) ),
inference(superposition,[status(thm)],[c_561,c_527]) ).
tcf(c_155608,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ~ in(X0,sK169(X0)) ),
inference(superposition,[status(thm)],[c_579,c_527]) ).
tcf(c_155609,plain,
! [X0: $i] :
( ~ sP20(X0)
| ~ in(X0,sK173(X0)) ),
inference(superposition,[status(thm)],[c_584,c_527]) ).
tcf(c_155612,plain,
! [X0: $i] :
( ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0)
| ~ in(sK263(X0),sK140) ),
inference(superposition,[status(thm)],[c_844,c_527]) ).
tcf(c_155613,plain,
! [X0: $i] :
( ~ sP34(X0)
| ~ in(X0,sK268(X0)) ),
inference(superposition,[status(thm)],[c_864,c_527]) ).
tcf(c_155614,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,X1),X0),
inference(superposition,[status(thm)],[c_939,c_527]) ).
tcf(c_155615,plain,
! [X0: $i,X1: $i] : ~ in(unordered_pair(X0,X1),X1),
inference(superposition,[status(thm)],[c_940,c_527]) ).
tcf(c_155616,plain,
! [X0: $i] : ~ in(sK300(X0),X0),
inference(superposition,[status(thm)],[c_965,c_527]) ).
tcf(c_155617,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ in(X0,sK316(X0)) ),
inference(superposition,[status(thm)],[c_1043,c_527]) ).
tcf(c_155618,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1))
| ~ in(X0,sK320(X1,X0)) ),
inference(superposition,[status(thm)],[c_1062,c_527]) ).
tcf(c_155619,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(X0,sK343(X0)) ),
inference(superposition,[status(thm)],[c_1207,c_527]) ).
tcf(c_155620,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(X0,sK344(X0)) ),
inference(superposition,[status(thm)],[c_1208,c_527]) ).
tcf(c_155621,plain,
~ in(powerset(sK140),sK140),
inference(superposition,[status(thm)],[c_146165,c_527]) ).
tcf(c_155622,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ~ relation(X0)
| ~ in(X0,unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0)))) ),
inference(superposition,[status(thm)],[c_16344,c_527]) ).
tcf(c_155623,plain,
( ~ sP7
| ~ in(sK64,sK119(sK64)) ),
inference(superposition,[status(thm)],[c_146098,c_527]) ).
tcf(c_155624,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ~ relation(X1)
| ~ is_well_founded_in(X1,X0)
| ~ in(X0,sK318(X1,X0)) ),
inference(superposition,[status(thm)],[c_144619,c_527]) ).
tcf(c_155625,plain,
( sP15
| ~ sP7
| ~ in(sK64,sK114(sK64)) ),
inference(superposition,[status(thm)],[c_145791,c_527]) ).
tcf(c_155626,plain,
( ~ iPr_def_19
| ~ sP7
| ~ in(sK64,sK72(sK64)) ),
inference(superposition,[status(thm)],[c_145863,c_527]) ).
tcf(c_155627,plain,
( ~ sP6
| ~ sP7
| ~ in(sK140,sK66)
| ~ in(sK64,sK67(sK64)) ),
inference(superposition,[status(thm)],[c_146728,c_527]) ).
tcf(c_155628,plain,
( ~ sP15
| ~ sP7
| ~ in(sK140,sK110)
| ~ in(sK64,sK111(sK64)) ),
inference(superposition,[status(thm)],[c_146738,c_527]) ).
tcf(c_155629,plain,
( ( sK199(powerset(powerset(sK62))) = sK140 )
| ~ iPr_def_21
| ~ in(sK199(powerset(powerset(sK62))),sK63(sK199(powerset(powerset(sK62))))) ),
inference(superposition,[status(thm)],[c_145355,c_527]) ).
tcf(c_155630,plain,
! [X0: $i] :
( ( sK199(powerset(powerset(X0))) = sK140 )
| ~ finite(X0)
| ~ in(sK199(powerset(powerset(X0))),sK119(sK199(powerset(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_145365,c_527]) ).
tcf(c_155631,plain,
( ( sK199(powerset(powerset(sK261))) = sK140 )
| ~ iPr_def_15
| ~ in(sK199(powerset(powerset(sK261))),sK262(sK199(powerset(powerset(sK261))))) ),
inference(superposition,[status(thm)],[c_145371,c_527]) ).
tcf(c_155632,plain,
( ( powerset(sK62) = sK140 )
| ~ iPr_def_21
| ~ in(powerset(sK62),sK63(powerset(sK62))) ),
inference(superposition,[status(thm)],[c_145625,c_527]) ).
tcf(c_155633,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(powerset(X0),sK72(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145633,c_527]) ).
tcf(c_155634,plain,
! [X0: $i] :
( sP15
| ( powerset(X0) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ in(powerset(X0),sK114(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145634,c_527]) ).
tcf(c_155635,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ~ finite(X0)
| ~ in(powerset(X0),sK119(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145635,c_527]) ).
tcf(c_155636,plain,
( ( powerset(sK261) = sK140 )
| ~ iPr_def_15
| ~ in(powerset(sK261),sK262(powerset(sK261))) ),
inference(superposition,[status(thm)],[c_145641,c_527]) ).
tcf(c_155637,plain,
( ( sK140 = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140))
| ~ in(omega,sK128(omega)) ),
inference(superposition,[status(thm)],[c_146242,c_527]) ).
tcf(c_155638,plain,
( ( sK140 = omega )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140))
| ~ in(omega,sK128(omega)) ),
inference(superposition,[status(thm)],[c_145922,c_527]) ).
tcf(c_155639,plain,
( ( sK140 = omega )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140))
| ~ in(omega,sK128(omega)) ),
inference(superposition,[status(thm)],[c_145878,c_527]) ).
tcf(c_155640,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,X1) = sK140 )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X0)
| ~ in(set_difference(X0,X1),sK318(X2,set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_146007,c_527]) ).
tcf(c_155641,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ in(set_difference(X0,X1),sK128(set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_146008,c_527]) ).
tcf(c_155642,plain,
~ in(set_union2(sK140,powerset(sK140)),sK140),
inference(superposition,[status(thm)],[c_148508,c_527]) ).
tcf(c_155643,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ~ in(sK92(X0),X1)
| ~ in(X0,apply(sK126(X1),sK92(X0))) ),
inference(superposition,[status(thm)],[c_151774,c_527]) ).
tcf(c_155644,plain,
! [X0: $i] :
( ( sK92(X0) = sK140 )
| ~ in(X0,sK169(sK92(X0))) ),
inference(superposition,[status(thm)],[c_151778,c_527]) ).
tcf(c_155645,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ~ in(X0,sK142(X0)) ),
inference(superposition,[status(thm)],[c_154138,c_527]) ).
tcf(c_155646,plain,
~ in(omega,sK142(omega)),
inference(superposition,[status(thm)],[c_154124,c_527]) ).
tcf(c_155842,plain,
! [X0: $i] :
( reflexive(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_153290,c_570]) ).
tcf(c_155843,plain,
! [X0: $i] :
( reflexive(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_153265,c_570]) ).
tcf(c_155844,plain,
! [X0: $i] :
( reflexive(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_146155,c_570]) ).
tcf(c_155846,plain,
! [X0: $i,X1: $i] :
( reflexive(sK96(X0,X1))
| ~ sP12(X0,X1)
| ~ well_ordering(sK96(X0,X1)) ),
inference(superposition,[status(thm)],[c_208,c_570]) ).
tcf(c_155847,plain,
! [X0: $i] :
( sP13(X0)
| reflexive(sK108(X0))
| ~ well_ordering(sK108(X0)) ),
inference(superposition,[status(thm)],[c_230,c_570]) ).
tcf(c_155848,plain,
! [X0: $i] :
( reflexive(sK115(X0))
| ~ well_ordering(sK115(X0)) ),
inference(superposition,[status(thm)],[c_249,c_570]) ).
tcf(c_155849,plain,
! [X0: $i] :
( reflexive(sK124(X0))
| ~ well_ordering(sK124(X0)) ),
inference(superposition,[status(thm)],[c_346,c_570]) ).
tcf(c_155850,plain,
! [X0: $i] :
( empty(X0)
| reflexive(sK126(X0))
| ( sK125(X0) = sK140 )
| ~ well_ordering(sK126(X0)) ),
inference(superposition,[status(thm)],[c_355,c_570]) ).
tcf(c_155851,plain,
! [X0: $i] :
( reflexive(identity_relation(X0))
| ~ well_ordering(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1101,c_570]) ).
tcf(c_155852,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_773,c_570]) ).
tcf(c_155853,plain,
( reflexive(sK140)
| ~ well_ordering(sK140) ),
inference(superposition,[status(thm)],[c_577,c_570]) ).
tcf(c_155854,plain,
! [X0: $i] :
( reflexive(relation_dom(X0))
| ~ empty(X0)
| ~ well_ordering(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_642,c_570]) ).
tcf(c_155855,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_646,c_570]) ).
tcf(c_155856,plain,
( reflexive(sK240)
| ~ well_ordering(sK240) ),
inference(superposition,[status(thm)],[c_783,c_570]) ).
tcf(c_155857,plain,
( reflexive(sK242)
| ~ well_ordering(sK242) ),
inference(superposition,[status(thm)],[c_791,c_570]) ).
tcf(c_155858,plain,
! [X0: $i] :
( reflexive(sK264(X0))
| ~ finite(X0)
| ~ well_ordering(sK264(X0)) ),
inference(superposition,[status(thm)],[c_852,c_570]) ).
tcf(c_155859,plain,
! [X0: $i] :
( reflexive(relation_rng(X0))
| ~ empty(X0)
| ~ well_ordering(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_944,c_570]) ).
tcf(c_155860,plain,
! [X0: $i,X1: $i] :
( reflexive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_1013,c_570]) ).
tcf(c_155861,plain,
! [X0: $i,X1: $i] :
( reflexive(sK312(X0,X1))
| ~ well_ordering(sK312(X0,X1)) ),
inference(superposition,[status(thm)],[c_1019,c_570]) ).
tcf(c_155863,plain,
! [X0: $i] :
( reflexive(relation_inverse(X0))
| ~ relation(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1113,c_570]) ).
tcf(c_155864,plain,
! [X0: $i] :
( reflexive(relation_inverse(X0))
| ~ empty(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1112,c_570]) ).
tcf(c_155865,plain,
( reflexive(sK335)
| ~ well_ordering(sK335) ),
inference(superposition,[status(thm)],[c_1149,c_570]) ).
tcf(c_155866,plain,
! [X0: $i,X1: $i] :
( reflexive(sK347(X0,X1))
| ~ well_ordering(sK347(X0,X1)) ),
inference(superposition,[status(thm)],[c_1237,c_570]) ).
tcf(c_155978,plain,
! [X0: $i] :
( transitive(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_153290,c_571]) ).
tcf(c_155979,plain,
! [X0: $i] :
( transitive(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_153265,c_571]) ).
tcf(c_155980,plain,
! [X0: $i] :
( transitive(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_146155,c_571]) ).
tcf(c_155982,plain,
! [X0: $i,X1: $i] :
( transitive(sK96(X0,X1))
| ~ sP12(X0,X1)
| ~ well_ordering(sK96(X0,X1)) ),
inference(superposition,[status(thm)],[c_208,c_571]) ).
tcf(c_155983,plain,
! [X0: $i] :
( sP13(X0)
| transitive(sK108(X0))
| ~ well_ordering(sK108(X0)) ),
inference(superposition,[status(thm)],[c_230,c_571]) ).
tcf(c_155984,plain,
! [X0: $i] :
( transitive(sK115(X0))
| ~ well_ordering(sK115(X0)) ),
inference(superposition,[status(thm)],[c_249,c_571]) ).
tcf(c_155985,plain,
! [X0: $i] :
( transitive(sK124(X0))
| ~ well_ordering(sK124(X0)) ),
inference(superposition,[status(thm)],[c_346,c_571]) ).
tcf(c_155986,plain,
! [X0: $i] :
( empty(X0)
| transitive(sK126(X0))
| ( sK125(X0) = sK140 )
| ~ well_ordering(sK126(X0)) ),
inference(superposition,[status(thm)],[c_355,c_571]) ).
tcf(c_155987,plain,
! [X0: $i] :
( transitive(identity_relation(X0))
| ~ well_ordering(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1101,c_571]) ).
tcf(c_155988,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_773,c_571]) ).
tcf(c_155989,plain,
( transitive(sK140)
| ~ well_ordering(sK140) ),
inference(superposition,[status(thm)],[c_577,c_571]) ).
tcf(c_155990,plain,
! [X0: $i] :
( transitive(relation_dom(X0))
| ~ empty(X0)
| ~ well_ordering(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_642,c_571]) ).
tcf(c_155991,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_646,c_571]) ).
tcf(c_155992,plain,
( transitive(sK240)
| ~ well_ordering(sK240) ),
inference(superposition,[status(thm)],[c_783,c_571]) ).
tcf(c_155993,plain,
( transitive(sK242)
| ~ well_ordering(sK242) ),
inference(superposition,[status(thm)],[c_791,c_571]) ).
tcf(c_155994,plain,
! [X0: $i] :
( transitive(sK264(X0))
| ~ finite(X0)
| ~ well_ordering(sK264(X0)) ),
inference(superposition,[status(thm)],[c_852,c_571]) ).
tcf(c_155995,plain,
! [X0: $i] :
( transitive(relation_rng(X0))
| ~ empty(X0)
| ~ well_ordering(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_944,c_571]) ).
tcf(c_155996,plain,
! [X0: $i,X1: $i] :
( transitive(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_1013,c_571]) ).
tcf(c_155997,plain,
! [X0: $i,X1: $i] :
( transitive(sK312(X0,X1))
| ~ well_ordering(sK312(X0,X1)) ),
inference(superposition,[status(thm)],[c_1019,c_571]) ).
tcf(c_155999,plain,
! [X0: $i] :
( transitive(relation_inverse(X0))
| ~ relation(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1113,c_571]) ).
tcf(c_156000,plain,
! [X0: $i] :
( transitive(relation_inverse(X0))
| ~ empty(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1112,c_571]) ).
tcf(c_156001,plain,
( transitive(sK335)
| ~ well_ordering(sK335) ),
inference(superposition,[status(thm)],[c_1149,c_571]) ).
tcf(c_156002,plain,
! [X0: $i,X1: $i] :
( transitive(sK347(X0,X1))
| ~ well_ordering(sK347(X0,X1)) ),
inference(superposition,[status(thm)],[c_1237,c_571]) ).
tcf(c_156132,plain,
! [X0: $i] :
( antisymmetric(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_153290,c_572]) ).
tcf(c_156133,plain,
! [X0: $i] :
( antisymmetric(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_153265,c_572]) ).
tcf(c_156134,plain,
! [X0: $i] :
( antisymmetric(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_146155,c_572]) ).
tcf(c_156136,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK96(X0,X1))
| ~ sP12(X0,X1)
| ~ well_ordering(sK96(X0,X1)) ),
inference(superposition,[status(thm)],[c_208,c_572]) ).
tcf(c_156137,plain,
! [X0: $i] :
( sP13(X0)
| antisymmetric(sK108(X0))
| ~ well_ordering(sK108(X0)) ),
inference(superposition,[status(thm)],[c_230,c_572]) ).
tcf(c_156138,plain,
! [X0: $i] :
( antisymmetric(sK115(X0))
| ~ well_ordering(sK115(X0)) ),
inference(superposition,[status(thm)],[c_249,c_572]) ).
tcf(c_156139,plain,
! [X0: $i] :
( antisymmetric(sK124(X0))
| ~ well_ordering(sK124(X0)) ),
inference(superposition,[status(thm)],[c_346,c_572]) ).
tcf(c_156140,plain,
! [X0: $i] :
( empty(X0)
| antisymmetric(sK126(X0))
| ( sK125(X0) = sK140 )
| ~ well_ordering(sK126(X0)) ),
inference(superposition,[status(thm)],[c_355,c_572]) ).
tcf(c_156141,plain,
! [X0: $i] :
( antisymmetric(identity_relation(X0))
| ~ well_ordering(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1101,c_572]) ).
tcf(c_156142,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_773,c_572]) ).
tcf(c_156143,plain,
( antisymmetric(sK140)
| ~ well_ordering(sK140) ),
inference(superposition,[status(thm)],[c_577,c_572]) ).
tcf(c_156144,plain,
! [X0: $i] :
( antisymmetric(relation_dom(X0))
| ~ empty(X0)
| ~ well_ordering(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_642,c_572]) ).
tcf(c_156145,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_646,c_572]) ).
tcf(c_156146,plain,
( antisymmetric(sK240)
| ~ well_ordering(sK240) ),
inference(superposition,[status(thm)],[c_783,c_572]) ).
tcf(c_156147,plain,
( antisymmetric(sK242)
| ~ well_ordering(sK242) ),
inference(superposition,[status(thm)],[c_791,c_572]) ).
tcf(c_156148,plain,
! [X0: $i] :
( antisymmetric(sK264(X0))
| ~ finite(X0)
| ~ well_ordering(sK264(X0)) ),
inference(superposition,[status(thm)],[c_852,c_572]) ).
tcf(c_156149,plain,
! [X0: $i] :
( antisymmetric(relation_rng(X0))
| ~ empty(X0)
| ~ well_ordering(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_944,c_572]) ).
tcf(c_156150,plain,
! [X0: $i,X1: $i] :
( antisymmetric(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_1013,c_572]) ).
tcf(c_156151,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK312(X0,X1))
| ~ well_ordering(sK312(X0,X1)) ),
inference(superposition,[status(thm)],[c_1019,c_572]) ).
tcf(c_156153,plain,
! [X0: $i] :
( antisymmetric(relation_inverse(X0))
| ~ relation(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1113,c_572]) ).
tcf(c_156154,plain,
! [X0: $i] :
( antisymmetric(relation_inverse(X0))
| ~ empty(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1112,c_572]) ).
tcf(c_156155,plain,
( antisymmetric(sK335)
| ~ well_ordering(sK335) ),
inference(superposition,[status(thm)],[c_1149,c_572]) ).
tcf(c_156156,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK347(X0,X1))
| ~ well_ordering(sK347(X0,X1)) ),
inference(superposition,[status(thm)],[c_1237,c_572]) ).
tcf(c_156286,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),sK169(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_155608]) ).
tcf(c_156320,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ in(sK169(X0),sK142(sK169(X0))) ),
inference(superposition,[status(thm)],[c_154906,c_527]) ).
tcf(c_156321,plain,
! [X0: $i] :
( ordinal(sK128(sK142(sK169(X0))))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK142(sK169(X0)) = sK140 )
| ~ ordinal(union(sK169(X0))) ),
inference(superposition,[status(thm)],[c_154906,c_154064]) ).
tcf(c_156322,plain,
! [X0: $i] :
( in(sK142(sK142(sK169(X0))),sK142(sK169(X0)))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK169(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154906,c_154131]) ).
tcf(c_156323,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(sK142(sK169(X0)),union(sK169(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154906,c_154065]) ).
tcf(c_156325,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK169(X0)) = sK140 )
| ~ empty(sK142(sK169(X0))) ),
inference(superposition,[status(thm)],[c_154906,c_150230]) ).
tcf(c_156327,plain,
! [X0: $i] :
( element(sK142(sK169(X0)),sK169(X0))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_154906,c_526]) ).
tcf(c_156376,plain,
( function(sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ~ empty(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_147195]) ).
tcf(c_156377,plain,
( finite(sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ~ empty(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_147193]) ).
tcf(c_156378,plain,
( epsilon_transitive(sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ~ empty(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_147192]) ).
tcf(c_156379,plain,
( epsilon_connected(sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ~ empty(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_147191]) ).
tcf(c_156380,plain,
( ordinal(sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ~ empty(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_147190]) ).
tcf(c_156381,plain,
( one_to_one(sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ~ empty(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_147189]) ).
tcf(c_156382,plain,
! [X0: $i] :
( ( sK125(sK198(omega)) = sK140 )
| ( apply(sK126(sK198(omega)),X0) = sK140 )
| ~ empty(sK198(omega))
| ~ relation(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_150772]) ).
tcf(c_156383,plain,
! [X0: $i] :
( element(X0,sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ( apply(sK126(sK198(omega)),X0) = sK140 )
| ~ function(sK126(sK198(omega)))
| ~ relation(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_148552]) ).
tcf(c_156384,plain,
( relation(sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ~ empty(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_642]) ).
tcf(c_156385,plain,
( empty(sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ~ empty(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_641]) ).
tcf(c_156386,plain,
! [X0: $i] :
( in(X0,sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ( apply(sK126(sK198(omega)),X0) = sK140 )
| ~ function(sK126(sK198(omega)))
| ~ relation(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_906]) ).
tcf(c_156387,plain,
( ( sK125(sK198(omega)) = sK140 )
| ( relation_rng(sK126(sK198(omega))) = sK140 )
| ~ relation(sK126(sK198(omega)))
| ( sK198(omega) != sK140 ) ),
inference(superposition,[status(thm)],[c_147344,c_478]) ).
tcf(c_156388,plain,
( ( sK126(sK198(omega)) = sK140 )
| ( sK125(sK198(omega)) = sK140 )
| ~ relation(sK126(sK198(omega)))
| ( sK198(omega) != sK140 ) ),
inference(superposition,[status(thm)],[c_147344,c_475]) ).
tcf(c_156444,plain,
! [X0: $i] :
( connected(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_153290,c_573]) ).
tcf(c_156445,plain,
! [X0: $i] :
( connected(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_153265,c_573]) ).
tcf(c_156446,plain,
! [X0: $i] :
( connected(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_146155,c_573]) ).
tcf(c_156448,plain,
! [X0: $i,X1: $i] :
( connected(sK96(X0,X1))
| ~ sP12(X0,X1)
| ~ well_ordering(sK96(X0,X1)) ),
inference(superposition,[status(thm)],[c_208,c_573]) ).
tcf(c_156449,plain,
! [X0: $i] :
( sP13(X0)
| connected(sK108(X0))
| ~ well_ordering(sK108(X0)) ),
inference(superposition,[status(thm)],[c_230,c_573]) ).
tcf(c_156450,plain,
! [X0: $i] :
( connected(sK115(X0))
| ~ well_ordering(sK115(X0)) ),
inference(superposition,[status(thm)],[c_249,c_573]) ).
tcf(c_156451,plain,
! [X0: $i] :
( connected(sK124(X0))
| ~ well_ordering(sK124(X0)) ),
inference(superposition,[status(thm)],[c_346,c_573]) ).
tcf(c_156452,plain,
! [X0: $i] :
( empty(X0)
| connected(sK126(X0))
| ( sK125(X0) = sK140 )
| ~ well_ordering(sK126(X0)) ),
inference(superposition,[status(thm)],[c_355,c_573]) ).
tcf(c_156453,plain,
! [X0: $i] :
( connected(identity_relation(X0))
| ~ well_ordering(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1101,c_573]) ).
tcf(c_156454,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_773,c_573]) ).
tcf(c_156455,plain,
( connected(sK140)
| ~ well_ordering(sK140) ),
inference(superposition,[status(thm)],[c_577,c_573]) ).
tcf(c_156456,plain,
! [X0: $i] :
( connected(relation_dom(X0))
| ~ empty(X0)
| ~ well_ordering(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_642,c_573]) ).
tcf(c_156457,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_646,c_573]) ).
tcf(c_156458,plain,
( connected(sK240)
| ~ well_ordering(sK240) ),
inference(superposition,[status(thm)],[c_783,c_573]) ).
tcf(c_156459,plain,
( connected(sK242)
| ~ well_ordering(sK242) ),
inference(superposition,[status(thm)],[c_791,c_573]) ).
tcf(c_156460,plain,
! [X0: $i] :
( connected(sK264(X0))
| ~ finite(X0)
| ~ well_ordering(sK264(X0)) ),
inference(superposition,[status(thm)],[c_852,c_573]) ).
tcf(c_156461,plain,
! [X0: $i] :
( connected(relation_rng(X0))
| ~ empty(X0)
| ~ well_ordering(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_944,c_573]) ).
tcf(c_156462,plain,
! [X0: $i,X1: $i] :
( connected(relation_restriction(X0,X1))
| ~ relation(X0)
| ~ well_ordering(relation_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_1013,c_573]) ).
tcf(c_156463,plain,
! [X0: $i,X1: $i] :
( connected(sK312(X0,X1))
| ~ well_ordering(sK312(X0,X1)) ),
inference(superposition,[status(thm)],[c_1019,c_573]) ).
tcf(c_156464,plain,
! [X0: $i] :
( connected(inclusion_relation(X0))
| ~ well_ordering(inclusion_relation(X0)) ),
inference(superposition,[status(thm)],[c_1091,c_573]) ).
tcf(c_156465,plain,
! [X0: $i] :
( connected(relation_inverse(X0))
| ~ relation(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1113,c_573]) ).
tcf(c_156466,plain,
! [X0: $i] :
( connected(relation_inverse(X0))
| ~ empty(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1112,c_573]) ).
tcf(c_156467,plain,
( connected(sK335)
| ~ well_ordering(sK335) ),
inference(superposition,[status(thm)],[c_1149,c_573]) ).
tcf(c_156468,plain,
! [X0: $i,X1: $i] :
( connected(sK347(X0,X1))
| ~ well_ordering(sK347(X0,X1)) ),
inference(superposition,[status(thm)],[c_1237,c_573]) ).
tcf(c_156595,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_153290,c_574]) ).
tcf(c_156596,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_153265,c_574]) ).
tcf(c_156597,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ~ well_ordering(X0) ),
inference(superposition,[status(thm)],[c_146155,c_574]) ).
tcf(c_156599,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(sK96(X0,X1))
| ~ sP12(X0,X1)
| ~ well_ordering(sK96(X0,X1)) ),
inference(superposition,[status(thm)],[c_208,c_574]) ).
tcf(c_156600,plain,
! [X0: $i] :
( sP13(X0)
| well_founded_relation(sK108(X0))
| ~ well_ordering(sK108(X0)) ),
inference(superposition,[status(thm)],[c_230,c_574]) ).
tcf(c_156601,plain,
! [X0: $i] :
( well_founded_relation(sK115(X0))
| ~ well_ordering(sK115(X0)) ),
inference(superposition,[status(thm)],[c_249,c_574]) ).
tcf(c_156602,plain,
! [X0: $i] :
( well_founded_relation(sK124(X0))
| ~ well_ordering(sK124(X0)) ),
inference(superposition,[status(thm)],[c_346,c_574]) ).
tcf(c_156603,plain,
! [X0: $i] :
( empty(X0)
| well_founded_relation(sK126(X0))
| ( sK125(X0) = sK140 )
| ~ well_ordering(sK126(X0)) ),
inference(superposition,[status(thm)],[c_355,c_574]) ).
tcf(c_156604,plain,
! [X0: $i] :
( well_founded_relation(identity_relation(X0))
| ~ well_ordering(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1101,c_574]) ).
tcf(c_156605,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_773,c_574]) ).
tcf(c_156606,plain,
( well_founded_relation(sK140)
| ~ well_ordering(sK140) ),
inference(superposition,[status(thm)],[c_577,c_574]) ).
tcf(c_156607,plain,
! [X0: $i] :
( well_founded_relation(relation_dom(X0))
| ~ empty(X0)
| ~ well_ordering(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_642,c_574]) ).
tcf(c_156608,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_646,c_574]) ).
tcf(c_156609,plain,
( well_founded_relation(sK240)
| ~ well_ordering(sK240) ),
inference(superposition,[status(thm)],[c_783,c_574]) ).
tcf(c_156610,plain,
( well_founded_relation(sK242)
| ~ well_ordering(sK242) ),
inference(superposition,[status(thm)],[c_791,c_574]) ).
tcf(c_156611,plain,
! [X0: $i] :
( well_founded_relation(sK264(X0))
| ~ finite(X0)
| ~ well_ordering(sK264(X0)) ),
inference(superposition,[status(thm)],[c_852,c_574]) ).
tcf(c_156612,plain,
! [X0: $i] :
( well_founded_relation(relation_rng(X0))
| ~ empty(X0)
| ~ well_ordering(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_944,c_574]) ).
tcf(c_156613,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_1013,c_574]) ).
tcf(c_156614,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(sK312(X0,X1))
| ~ well_ordering(sK312(X0,X1)) ),
inference(superposition,[status(thm)],[c_1019,c_574]) ).
tcf(c_156615,plain,
! [X0: $i] :
( well_founded_relation(inclusion_relation(X0))
| ~ well_ordering(inclusion_relation(X0)) ),
inference(superposition,[status(thm)],[c_1091,c_574]) ).
tcf(c_156616,plain,
! [X0: $i] :
( well_founded_relation(relation_inverse(X0))
| ~ relation(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1113,c_574]) ).
tcf(c_156617,plain,
! [X0: $i] :
( well_founded_relation(relation_inverse(X0))
| ~ empty(X0)
| ~ well_ordering(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_1112,c_574]) ).
tcf(c_156618,plain,
( well_founded_relation(sK335)
| ~ well_ordering(sK335) ),
inference(superposition,[status(thm)],[c_1149,c_574]) ).
tcf(c_156619,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(sK347(X0,X1))
| ~ well_ordering(sK347(X0,X1)) ),
inference(superposition,[status(thm)],[c_1237,c_574]) ).
tcf(c_156739,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( sK125(set_union2(X1,X0)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_623,c_149522]) ).
tcf(c_156740,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(set_union2(X1,X0)) = sK140 )
| ( relation_dom(sK126(set_union2(X0,X1))) = set_union2(X0,X1) ) ),
inference(superposition,[status(thm)],[c_623,c_149417]) ).
tcf(c_156741,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(X1),X2)
| ( X1 = sK140 )
| ~ ordinal(X2)
| ~ in(X2,X1)
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_623,c_146043]) ).
tcf(c_156744,plain,
! [X0: $i,X1: $i] :
( in(sK128(X1),X1)
| ( X1 = sK140 )
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_623,c_146040]) ).
tcf(c_156745,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(X1))
| ( X1 = sK140 )
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_623,c_146041]) ).
tcf(c_156746,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_union2(X1,X0)) = sK140,
inference(superposition,[status(thm)],[c_623,c_146042]) ).
tcf(c_156747,plain,
! [X0: $i,X1: $i] : subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c_623,c_498]) ).
tcf(c_156748,plain,
! [X0: $i] : set_union2(sK140,X0) = X0,
inference(superposition,[status(thm)],[c_623,c_611]) ).
tcf(c_156749,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,X2)),X2)
| ( X2 = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_623,c_146038]) ).
tcf(c_156750,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,X2),X2)
| ( X2 = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,set_union2(X1,X2)) ),
inference(superposition,[status(thm)],[c_623,c_146039]) ).
tcf(c_156786,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK63(X0) = X1 )
| ~ iPr_def_20
| ~ in(X1,X0)
| ~ subset(X0,powerset(sK62))
| ~ subset(sK63(X0),X1) ),
inference(superposition,[status(thm)],[c_653,c_123600]) ).
tcf(c_156787,plain,
! [X0: $i] :
( in(sK63(X0),X0)
| ( X0 = sK140 )
| ~ iPr_def_21
| ~ subset(X0,powerset(sK62)) ),
inference(superposition,[status(thm)],[c_653,c_123602]) ).
tcf(c_156788,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sK140 )
| ( sK111(X0) = X1 )
| ~ sP15
| ~ ordinal(X2)
| ~ in(X2,sK110)
| ~ in(X2,omega)
| ~ in(X1,X0)
| ~ subset(X0,powerset(X2))
| ~ subset(sK111(X0),X1) ),
inference(superposition,[status(thm)],[c_653,c_240]) ).
tcf(c_156789,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sK140 )
| ( sK67(X0) = X1 )
| ~ sP6
| ~ ordinal(X2)
| ~ in(X2,sK66)
| ~ in(X2,omega)
| ~ in(X1,X0)
| ~ subset(X0,powerset(X2))
| ~ subset(sK67(X0),X1) ),
inference(superposition,[status(thm)],[c_653,c_143]) ).
tcf(c_156790,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sK140 )
| ( sK72(X0) = X1 )
| ~ iPr_def_18
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ in(X1,X0)
| ~ subset(X0,powerset(X2))
| ~ subset(sK72(X0),X1) ),
inference(superposition,[status(thm)],[c_653,c_123596]) ).
tcf(c_156791,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP15
| ( X0 = sK140 )
| ( sK114(X0) = X1 )
| ~ ordinal(X2)
| ~ in(X2,omega)
| ~ in(X1,X0)
| ~ subset(X0,powerset(X2))
| ~ subset(sK114(X0),X1) ),
inference(superposition,[status(thm)],[c_653,c_248]) ).
tcf(c_156792,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sK140 )
| ( sK119(X0) = X1 )
| ~ finite(X2)
| ~ in(X1,X0)
| ~ subset(X0,powerset(X2))
| ~ subset(sK119(X0),X1) ),
inference(superposition,[status(thm)],[c_653,c_308]) ).
tcf(c_156793,plain,
! [X0: $i,X1: $i] :
( in(sK111(X0),X0)
| ( X0 = sK140 )
| ~ sP15
| ~ ordinal(X1)
| ~ in(X1,sK110)
| ~ in(X1,omega)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_653,c_239]) ).
tcf(c_156794,plain,
! [X0: $i,X1: $i] :
( in(sK67(X0),X0)
| ( X0 = sK140 )
| ~ sP6
| ~ ordinal(X1)
| ~ in(X1,sK66)
| ~ in(X1,omega)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_653,c_142]) ).
tcf(c_156795,plain,
! [X0: $i,X1: $i] :
( in(sK72(X0),X0)
| ( X0 = sK140 )
| ~ iPr_def_19
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_653,c_123598]) ).
tcf(c_156796,plain,
! [X0: $i,X1: $i] :
( sP15
| in(sK114(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_653,c_247]) ).
tcf(c_156797,plain,
! [X0: $i,X1: $i] :
( in(sK119(X0),X0)
| ( X0 = sK140 )
| ~ finite(X1)
| ~ subset(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_653,c_307]) ).
tcf(c_156800,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = sK140 )
| ( sK255(X0) = X2 )
| ~ sP31(X3,X1)
| ~ in(X2,X0)
| ~ in(sK254(X1),omega)
| ~ subset(sK255(X0),X2)
| ~ subset(X0,powerset(sK254(X1))) ),
inference(superposition,[status(thm)],[c_653,c_826]) ).
tcf(c_156801,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK255(X0),X0)
| ( X0 = sK140 )
| ~ sP31(X2,X1)
| ~ in(sK254(X1),omega)
| ~ subset(X0,powerset(sK254(X1))) ),
inference(superposition,[status(thm)],[c_653,c_825]) ).
tcf(c_156802,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK262(X0) = X1 )
| ~ iPr_def_14
| ~ in(X1,X0)
| ~ subset(X0,powerset(sK261))
| ~ subset(sK262(X0),X1) ),
inference(superposition,[status(thm)],[c_653,c_123589]) ).
tcf(c_156803,plain,
! [X0: $i] :
( in(sK262(X0),X0)
| ( X0 = sK140 )
| ~ iPr_def_15
| ~ subset(X0,powerset(sK261)) ),
inference(superposition,[status(thm)],[c_653,c_123591]) ).
tcf(c_156954,plain,
! [X0: $i] : set_difference(unordered_pair(sK116(X0),sK116(X0)),set_difference(unordered_pair(sK116(X0),sK116(X0)),X0)) = sK140,
inference(superposition,[status(thm)],[c_151758,c_155599]) ).
tcf(c_156955,plain,
! [X0: $i] :
( ( apply(X0,sK116(relation_dom(X0))) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_155599]) ).
tcf(c_156956,plain,
! [X0: $i,X1: $i] :
( in(sK116(subset_complement(X0,X1)),X1)
| ( X0 = sK140 )
| ~ subset(X1,X0)
| ~ element(sK116(subset_complement(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_5403,c_155599]) ).
tcf(c_156989,plain,
! [X0: $i] : set_difference(unordered_pair(sK300(X0),sK300(X0)),set_difference(unordered_pair(sK300(X0),sK300(X0)),X0)) = sK140,
inference(superposition,[status(thm)],[c_151758,c_155616]) ).
tcf(c_156990,plain,
! [X0: $i] :
( ( apply(X0,sK300(relation_dom(X0))) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_155616]) ).
tcf(c_156991,plain,
! [X0: $i,X1: $i] :
( in(sK300(subset_complement(X0,X1)),X1)
| ( X0 = sK140 )
| ~ subset(X1,X0)
| ~ element(sK300(subset_complement(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_5403,c_155616]) ).
tcf(c_157001,plain,
set_difference(unordered_pair(omega,omega),set_difference(unordered_pair(omega,omega),sK142(omega))) = sK140,
inference(superposition,[status(thm)],[c_151758,c_155646]) ).
tcf(c_157016,plain,
~ empty(unordered_pair(sK140,sK140)),
inference(superposition,[status(thm)],[c_156748,c_892]) ).
tcf(c_157017,plain,
in(sK140,unordered_pair(sK140,sK140)),
inference(superposition,[status(thm)],[c_156748,c_256]) ).
tcf(c_157020,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( sK125(set_union2(sK140,X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_156748,c_149417]) ).
tcf(c_157057,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( apply(X0,sK116(relation_dom(X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_146146,c_156955]) ).
tcf(c_157058,plain,
! [X0: $i,X1: $i] :
( ( apply(sK96(X0,X1),sK116(relation_dom(sK96(X0,X1)))) = sK140 )
| ~ sP12(X0,X1)
| ~ relation(sK96(X0,X1)) ),
inference(superposition,[status(thm)],[c_209,c_156955]) ).
tcf(c_157059,plain,
! [X0: $i] :
( sP13(X0)
| ( apply(sK108(X0),sK116(relation_dom(sK108(X0)))) = sK140 )
| ~ relation(sK108(X0)) ),
inference(superposition,[status(thm)],[c_232,c_156955]) ).
tcf(c_157060,plain,
! [X0: $i] :
( ( apply(sK115(X0),sK116(relation_dom(sK115(X0)))) = sK140 )
| ~ relation(sK115(X0)) ),
inference(superposition,[status(thm)],[c_250,c_156955]) ).
tcf(c_157061,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),sK116(relation_dom(sK126(X0)))) = sK140 )
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_356,c_156955]) ).
tcf(c_157062,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK116(relation_dom(identity_relation(X0)))) = sK140 )
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1100,c_156955]) ).
tcf(c_157063,plain,
( ( apply(sK240,sK116(relation_dom(sK240))) = sK140 )
| ~ relation(sK240) ),
inference(superposition,[status(thm)],[c_784,c_156955]) ).
tcf(c_157064,plain,
! [X0: $i] :
( ( apply(sK264(X0),sK116(relation_dom(sK264(X0)))) = sK140 )
| ~ finite(X0)
| ~ relation(sK264(X0)) ),
inference(superposition,[status(thm)],[c_853,c_156955]) ).
tcf(c_157065,plain,
! [X0: $i,X1: $i] :
( ( apply(sK312(X0,X1),sK116(relation_dom(sK312(X0,X1)))) = sK140 )
| ~ relation(sK312(X0,X1)) ),
inference(superposition,[status(thm)],[c_1020,c_156955]) ).
tcf(c_157066,plain,
( ( apply(sK335,sK116(relation_dom(sK335))) = sK140 )
| ~ relation(sK335) ),
inference(superposition,[status(thm)],[c_1150,c_156955]) ).
tcf(c_157067,plain,
! [X0: $i,X1: $i] :
( ( apply(sK347(X0,X1),sK116(relation_dom(sK347(X0,X1)))) = sK140 )
| ~ relation(sK347(X0,X1)) ),
inference(superposition,[status(thm)],[c_1238,c_156955]) ).
tcf(c_157068,plain,
( ( apply(sK140,sK116(relation_dom(sK140))) = sK140 )
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_144215,c_156955]) ).
tcf(c_157069,plain,
! [X0: $i] :
( ( apply(relation_dom(X0),sK116(relation_dom(relation_dom(X0)))) = sK140 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_147195,c_156955]) ).
tcf(c_157070,plain,
( ( apply(sK140,sK116(sK140)) = sK140 )
| ~ relation(sK140) ),
inference(light_normalisation,[status(thm)],[c_157068,c_470]) ).
tcf(c_157071,plain,
apply(sK335,sK116(relation_dom(sK335))) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157066,c_1149]) ).
tcf(c_157072,plain,
apply(sK240,sK116(relation_dom(sK240))) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157063,c_783]) ).
tcf(c_157073,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK116(X0)) = sK140 )
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_157062,c_489]) ).
tcf(c_157074,plain,
! [X0: $i] : apply(identity_relation(X0),sK116(X0)) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157073,c_1101]) ).
tcf(c_157075,plain,
! [X0: $i] :
( ( apply(sK115(X0),sK116(X0)) = sK140 )
| ~ relation(sK115(X0)) ),
inference(light_normalisation,[status(thm)],[c_157060,c_251]) ).
tcf(c_157076,plain,
! [X0: $i] : apply(sK115(X0),sK116(X0)) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157075,c_249]) ).
tcf(c_157083,plain,
! [X0: $i,X1: $i] : apply(sK347(X0,X1),sK116(relation_dom(sK347(X0,X1)))) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157067,c_1237]) ).
tcf(c_157084,plain,
! [X0: $i,X1: $i] : apply(sK312(X0,X1),sK116(relation_dom(sK312(X0,X1)))) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157065,c_1019]) ).
tcf(c_157140,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( apply(X0,sK300(relation_dom(X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_146146,c_156990]) ).
tcf(c_157141,plain,
! [X0: $i,X1: $i] :
( ( apply(sK96(X0,X1),sK300(relation_dom(sK96(X0,X1)))) = sK140 )
| ~ sP12(X0,X1)
| ~ relation(sK96(X0,X1)) ),
inference(superposition,[status(thm)],[c_209,c_156990]) ).
tcf(c_157142,plain,
! [X0: $i] :
( sP13(X0)
| ( apply(sK108(X0),sK300(relation_dom(sK108(X0)))) = sK140 )
| ~ relation(sK108(X0)) ),
inference(superposition,[status(thm)],[c_232,c_156990]) ).
tcf(c_157143,plain,
! [X0: $i] :
( ( apply(sK115(X0),sK300(relation_dom(sK115(X0)))) = sK140 )
| ~ relation(sK115(X0)) ),
inference(superposition,[status(thm)],[c_250,c_156990]) ).
tcf(c_157144,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),sK300(relation_dom(sK126(X0)))) = sK140 )
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_356,c_156990]) ).
tcf(c_157145,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK300(relation_dom(identity_relation(X0)))) = sK140 )
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1100,c_156990]) ).
tcf(c_157146,plain,
( ( apply(sK240,sK300(relation_dom(sK240))) = sK140 )
| ~ relation(sK240) ),
inference(superposition,[status(thm)],[c_784,c_156990]) ).
tcf(c_157147,plain,
! [X0: $i] :
( ( apply(sK264(X0),sK300(relation_dom(sK264(X0)))) = sK140 )
| ~ finite(X0)
| ~ relation(sK264(X0)) ),
inference(superposition,[status(thm)],[c_853,c_156990]) ).
tcf(c_157148,plain,
! [X0: $i,X1: $i] :
( ( apply(sK312(X0,X1),sK300(relation_dom(sK312(X0,X1)))) = sK140 )
| ~ relation(sK312(X0,X1)) ),
inference(superposition,[status(thm)],[c_1020,c_156990]) ).
tcf(c_157149,plain,
( ( apply(sK335,sK300(relation_dom(sK335))) = sK140 )
| ~ relation(sK335) ),
inference(superposition,[status(thm)],[c_1150,c_156990]) ).
tcf(c_157150,plain,
! [X0: $i,X1: $i] :
( ( apply(sK347(X0,X1),sK300(relation_dom(sK347(X0,X1)))) = sK140 )
| ~ relation(sK347(X0,X1)) ),
inference(superposition,[status(thm)],[c_1238,c_156990]) ).
tcf(c_157151,plain,
( ( apply(sK140,sK300(relation_dom(sK140))) = sK140 )
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_144215,c_156990]) ).
tcf(c_157152,plain,
! [X0: $i] :
( ( apply(relation_dom(X0),sK300(relation_dom(relation_dom(X0)))) = sK140 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_147195,c_156990]) ).
tcf(c_157153,plain,
( ( apply(sK140,sK300(sK140)) = sK140 )
| ~ relation(sK140) ),
inference(light_normalisation,[status(thm)],[c_157151,c_470]) ).
tcf(c_157154,plain,
apply(sK335,sK300(relation_dom(sK335))) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157149,c_1149]) ).
tcf(c_157155,plain,
apply(sK240,sK300(relation_dom(sK240))) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157146,c_783]) ).
tcf(c_157156,plain,
! [X0: $i] :
( ( apply(identity_relation(X0),sK300(X0)) = sK140 )
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_157145,c_489]) ).
tcf(c_157157,plain,
! [X0: $i] : apply(identity_relation(X0),sK300(X0)) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157156,c_1101]) ).
tcf(c_157158,plain,
! [X0: $i] :
( ( apply(sK115(X0),sK300(X0)) = sK140 )
| ~ relation(sK115(X0)) ),
inference(light_normalisation,[status(thm)],[c_157143,c_251]) ).
tcf(c_157159,plain,
! [X0: $i] : apply(sK115(X0),sK300(X0)) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157158,c_249]) ).
tcf(c_157166,plain,
! [X0: $i,X1: $i] : apply(sK347(X0,X1),sK300(relation_dom(sK347(X0,X1)))) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157150,c_1237]) ).
tcf(c_157167,plain,
! [X0: $i,X1: $i] : apply(sK312(X0,X1),sK300(relation_dom(sK312(X0,X1)))) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157148,c_1019]) ).
tcf(c_157203,plain,
! [X0: $i] :
( in(sK63(relation_rng_restriction(X0,powerset(sK62))),relation_rng_restriction(X0,powerset(sK62)))
| ( relation_rng_restriction(X0,powerset(sK62)) = sK140 )
| ~ iPr_def_21
| ~ relation(powerset(sK62)) ),
inference(superposition,[status(thm)],[c_262,c_156787]) ).
tcf(c_157205,plain,
! [X0: $i] :
( in(sK63(set_difference(powerset(sK62),X0)),set_difference(powerset(sK62),X0))
| ( set_difference(powerset(sK62),X0) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_383,c_156787]) ).
tcf(c_157206,plain,
! [X0: $i] :
( in(sK63(relation_dom_restriction(powerset(sK62),X0)),relation_dom_restriction(powerset(sK62),X0))
| ( relation_dom_restriction(powerset(sK62),X0) = sK140 )
| ~ iPr_def_21
| ~ relation(powerset(sK62)) ),
inference(superposition,[status(thm)],[c_504,c_156787]) ).
tcf(c_157226,plain,
( ( sK125(sK198(unordered_pair(sK140,sK140))) = sK140 )
| ( relation_dom(sK126(sK198(powerset(sK140)))) = sK198(powerset(sK140)) ) ),
inference(superposition,[status(thm)],[c_314,c_147345]) ).
tcf(c_157227,plain,
! [X0: $i,X1: $i] :
( function(sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ~ empty(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_147195]) ).
tcf(c_157228,plain,
! [X0: $i,X1: $i] :
( finite(sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ~ empty(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_147193]) ).
tcf(c_157229,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ~ empty(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_147192]) ).
tcf(c_157230,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ~ empty(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_147191]) ).
tcf(c_157231,plain,
! [X0: $i,X1: $i] :
( ordinal(sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ~ empty(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_147190]) ).
tcf(c_157232,plain,
! [X0: $i,X1: $i] :
( one_to_one(sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ~ empty(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_147189]) ).
tcf(c_157233,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ( apply(sK126(sK198(unordered_pair(X0,X1))),X2) = sK140 )
| ~ empty(sK198(unordered_pair(X0,X1)))
| ~ relation(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_150772]) ).
tcf(c_157234,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ( apply(sK126(sK198(unordered_pair(X0,X1))),X2) = sK140 )
| ~ function(sK126(sK198(unordered_pair(X0,X1))))
| ~ relation(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_148552]) ).
tcf(c_157235,plain,
! [X0: $i,X1: $i] :
( relation(sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ~ empty(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_642]) ).
tcf(c_157236,plain,
! [X0: $i,X1: $i] :
( empty(sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ~ empty(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_641]) ).
tcf(c_157237,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ( apply(sK126(sK198(unordered_pair(X0,X1))),X2) = sK140 )
| ~ function(sK126(sK198(unordered_pair(X0,X1))))
| ~ relation(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_906]) ).
tcf(c_157238,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ( relation_rng(sK126(sK198(unordered_pair(X0,X1)))) = sK140 )
| ~ relation(sK126(sK198(unordered_pair(X0,X1))))
| ( sK198(unordered_pair(X0,X1)) != sK140 ) ),
inference(superposition,[status(thm)],[c_147345,c_478]) ).
tcf(c_157239,plain,
! [X0: $i,X1: $i] :
( ( sK126(sK198(unordered_pair(X0,X1))) = sK140 )
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ~ relation(sK126(sK198(unordered_pair(X0,X1))))
| ( sK198(unordered_pair(X0,X1)) != sK140 ) ),
inference(superposition,[status(thm)],[c_147345,c_475]) ).
tcf(c_157240,plain,
( ( sK125(sK198(powerset(sK140))) = sK140 )
| ( relation_dom(sK126(sK198(powerset(sK140)))) = sK198(powerset(sK140)) ) ),
inference(light_normalisation,[status(thm)],[c_157226,c_314]) ).
tcf(c_157332,plain,
( subset(sK64,powerset(sK140))
| ~ sP7 ),
inference(superposition,[status(thm)],[c_136,c_654]) ).
tcf(c_157333,plain,
! [X0: $i] :
( empty(X0)
| subset(sK198(X0),X0) ),
inference(superposition,[status(thm)],[c_693,c_654]) ).
tcf(c_157334,plain,
! [X0: $i] : subset(sK199(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_696,c_654]) ).
tcf(c_157335,plain,
! [X0: $i] :
( empty(X0)
| subset(sK302(X0),X0) ),
inference(superposition,[status(thm)],[c_972,c_654]) ).
tcf(c_157338,plain,
! [X0: $i,X1: $i] :
( subset(apply(sK126(X1),powerset(X0)),X0)
| ( sK125(X1) = sK140 )
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_148553,c_654]) ).
tcf(c_157340,plain,
! [X0: $i,X1: $i] :
( subset(sK320(X1,powerset(X0)),X0)
| ( powerset(X0) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(powerset(X0),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_148564,c_654]) ).
tcf(c_157362,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,sK193(X0,X1)) ),
inference(superposition,[status(thm)],[c_657,c_527]) ).
tcf(c_157363,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ordinal(sK128(sK193(X0,X1)))
| ( sK193(X0,X1) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_657,c_154064]) ).
tcf(c_157364,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK142(sK193(X0,X1)),sK193(X0,X1))
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_657,c_154131]) ).
tcf(c_157365,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(sK193(X0,X1),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_657,c_154065]) ).
tcf(c_157366,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK142(X0),X0) ),
inference(superposition,[status(thm)],[c_657,c_522]) ).
tcf(c_157367,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( sK125(X0) = sK140 )
| ~ empty(sK193(X0,X1)) ),
inference(superposition,[status(thm)],[c_657,c_150230]) ).
tcf(c_157368,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_657,c_787]) ).
tcf(c_157369,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| element(sK193(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_657,c_526]) ).
tcf(c_157370,plain,
! [X0: $i,X1: $i] :
( subset(sK92(X0),X1)
| in(sK193(sK92(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_657,c_198]) ).
tcf(c_157371,plain,
! [X0: $i,X1: $i] :
( subset(sK92(X0),X1)
| ordinal(sK193(sK92(X0),X1)) ),
inference(superposition,[status(thm)],[c_657,c_199]) ).
tcf(c_157372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(relation_inverse_image(X0,X3),X4)
| in(apply(X0,sK193(relation_inverse_image(X0,X3),X4)),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_657,c_425]) ).
tcf(c_157373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subset(relation_inverse_image(X0,X3),X4)
| in(sK193(relation_inverse_image(X0,X3),X4),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_657,c_424]) ).
tcf(c_157442,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ in(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_661,c_527]) ).
tcf(c_157443,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(X1))
| ( X1 = sK140 )
| ~ subset(X1,X0)
| ~ ordinal(union(powerset(X0))) ),
inference(superposition,[status(thm)],[c_661,c_154064]) ).
tcf(c_157445,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,union(powerset(X1))) = sK140 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_661,c_154065]) ).
tcf(c_157446,plain,
! [X0: $i,X1: $i] :
( in(sK142(powerset(X1)),powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_661,c_522]) ).
tcf(c_157448,plain,
! [X0: $i,X1: $i] :
( ~ empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_661,c_787]) ).
tcf(c_157450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X1,relation_inverse_image(X0,powerset(X2)))
| ( X4 = sK140 )
| ~ function(X0)
| ~ in(X1,X3)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ subset(apply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_661,c_423]) ).
tcf(c_157451,plain,
! [X0: $i] :
( ( powerset(X0) = omega )
| ( sK125(sK263(powerset(X0))) = sK140 )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0))
| ~ subset(sK140,X0) ),
inference(superposition,[status(thm)],[c_661,c_145540]) ).
tcf(c_157452,plain,
! [X0: $i] :
( ( sK125(powerset(X0)) = sK140 )
| ~ subset(sK140,X0) ),
inference(superposition,[status(thm)],[c_661,c_144395]) ).
tcf(c_157453,plain,
! [X0: $i] :
( ordinal(sK263(powerset(X0)))
| ( powerset(X0) = omega )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0))
| ~ subset(sK140,X0) ),
inference(superposition,[status(thm)],[c_661,c_846]) ).
tcf(c_157454,plain,
! [X0: $i] :
( being_limit_ordinal(sK263(powerset(X0)))
| ( powerset(X0) = omega )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0))
| ~ subset(sK140,X0) ),
inference(superposition,[status(thm)],[c_661,c_845]) ).
tcf(c_157455,plain,
! [X0: $i] :
( subset(omega,powerset(X0))
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0))
| ~ subset(sK140,X0) ),
inference(superposition,[status(thm)],[c_661,c_850]) ).
tcf(c_157456,plain,
! [X0: $i] : ~ subset(sK116(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_661,c_155599]) ).
tcf(c_157457,plain,
! [X0: $i] : ~ subset(sK300(powerset(X0)),X0),
inference(superposition,[status(thm)],[c_661,c_155616]) ).
tcf(c_157460,plain,
! [X0: $i] : sK125(powerset(X0)) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_157452,c_361]) ).
tcf(c_157465,plain,
! [X0: $i] :
( subset(omega,powerset(X0))
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_157455,c_361]) ).
tcf(c_157470,plain,
! [X0: $i] :
( being_limit_ordinal(sK263(powerset(X0)))
| ( powerset(X0) = omega )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_157454,c_361]) ).
tcf(c_157475,plain,
! [X0: $i] :
( ordinal(sK263(powerset(X0)))
| ( powerset(X0) = omega )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_157453,c_361]) ).
tcf(c_157480,plain,
! [X0: $i] :
( ( powerset(X0) = omega )
| ( sK125(sK263(powerset(X0))) = sK140 )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_157451,c_361]) ).
tcf(c_157500,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),powerset(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_662]) ).
tcf(c_157501,plain,
! [X0: $i] :
( sP3(powerset(X0))
| subset(sK58(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_122,c_662]) ).
tcf(c_157504,plain,
! [X0: $i] :
( ordinal(powerset(X0))
| subset(sK127(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_367,c_662]) ).
tcf(c_157505,plain,
! [X0: $i] :
( subset(sK128(powerset(X0)),X0)
| ( powerset(X0) = sK140 )
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_144620,c_662]) ).
tcf(c_157506,plain,
! [X0: $i,X1: $i] :
( disjoint(powerset(X0),X1)
| subset(sK130(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_400,c_662]) ).
tcf(c_157507,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,powerset(X1))
| subset(sK130(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_401,c_662]) ).
tcf(c_157508,plain,
! [X0: $i] :
( relation(powerset(X0))
| subset(sK163(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_561,c_662]) ).
tcf(c_157510,plain,
! [X0: $i] :
( subset(sK173(powerset(X0)),X0)
| ~ sP20(powerset(X0)) ),
inference(superposition,[status(thm)],[c_584,c_662]) ).
tcf(c_157512,plain,
! [X0: $i,X1: $i] :
( subset(powerset(X0),X1)
| subset(sK193(powerset(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_657,c_662]) ).
tcf(c_157515,plain,
! [X0: $i] :
( subset(sK268(powerset(X0)),X0)
| ~ sP34(powerset(X0)) ),
inference(superposition,[status(thm)],[c_864,c_662]) ).
tcf(c_157516,plain,
! [X0: $i] :
( epsilon_transitive(powerset(X0))
| subset(sK316(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_1043,c_662]) ).
tcf(c_157518,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| subset(sK343(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_1207,c_662]) ).
tcf(c_157519,plain,
! [X0: $i] :
( epsilon_connected(powerset(X0))
| subset(sK344(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_1208,c_662]) ).
tcf(c_157521,plain,
! [X0: $i] :
( subset(unordered_pair(unordered_pair(sK137(powerset(X0)),sK137(powerset(X0))),unordered_pair(sK137(powerset(X0)),sK138(powerset(X0)))),X0)
| ( powerset(X0) = sK140 )
| ~ relation(powerset(X0)) ),
inference(superposition,[status(thm)],[c_16344,c_662]) ).
tcf(c_157522,plain,
! [X0: $i,X1: $i] :
( subset(sK318(X0,powerset(X1)),X1)
| ( powerset(X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_144619,c_662]) ).
tcf(c_157523,plain,
( subset(sK63(powerset(sK62)),sK62)
| ( powerset(sK62) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145625,c_662]) ).
tcf(c_157524,plain,
! [X0: $i] :
( subset(sK72(powerset(X0)),X0)
| ( powerset(X0) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145633,c_662]) ).
tcf(c_157525,plain,
! [X0: $i] :
( sP15
| subset(sK114(powerset(X0)),X0)
| ( powerset(X0) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145634,c_662]) ).
tcf(c_157526,plain,
! [X0: $i] :
( subset(sK119(powerset(X0)),X0)
| ( powerset(X0) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145635,c_662]) ).
tcf(c_157527,plain,
( subset(sK262(powerset(sK261)),sK261)
| ( powerset(sK261) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145641,c_662]) ).
tcf(c_157528,plain,
! [X0: $i,X1: $i] :
( subset(apply(sK126(X1),sK92(powerset(X0))),X0)
| ( sK125(X1) = sK140 )
| ~ in(sK92(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_151774,c_662]) ).
tcf(c_157529,plain,
! [X0: $i] :
( subset(sK169(sK92(powerset(X0))),X0)
| ( sK92(powerset(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151778,c_662]) ).
tcf(c_157530,plain,
! [X0: $i] :
( subset(sK142(powerset(X0)),X0)
| ( powerset(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_154138,c_662]) ).
tcf(c_157673,plain,
( ~ sP7
| ~ proper_subset(powerset(sK140),sK64) ),
inference(superposition,[status(thm)],[c_157332,c_472]) ).
tcf(c_157674,plain,
( in(sK140,sK64)
| ( powerset(sK140) = sK140 )
| ( sK125(subset_complement(powerset(sK140),sK64)) = sK140 )
| ~ sP7
| ~ element(sK140,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157332,c_145539]) ).
tcf(c_157675,plain,
! [X0: $i] :
( disjoint(fiber(X0,sK318(X0,sK64)),sK64)
| ( sK140 = sK64 )
| ~ sP7
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157332,c_1058]) ).
tcf(c_157676,plain,
! [X0: $i] :
( in(sK318(X0,sK64),sK64)
| ( sK140 = sK64 )
| ~ sP7
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157332,c_1057]) ).
tcf(c_157677,plain,
( in(sK128(sK64),sK64)
| ( sK140 = sK64 )
| ~ sP7
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157332,c_369]) ).
tcf(c_157678,plain,
( ordinal(sK128(sK64))
| ( sK140 = sK64 )
| ~ sP7
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157332,c_371]) ).
tcf(c_157679,plain,
( ( set_difference(sK64,powerset(sK140)) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_157332,c_386]) ).
tcf(c_157680,plain,
! [X0: $i] :
( ordinal_subset(sK128(sK64),X0)
| ( sK140 = sK64 )
| ~ sP7
| ~ ordinal(X0)
| ~ ordinal(powerset(sK140))
| ~ in(X0,sK64) ),
inference(superposition,[status(thm)],[c_157332,c_370]) ).
tcf(c_157681,plain,
( ( sK140 = sK64 )
| ( powerset(sK140) = sK64 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_157332,c_144406]) ).
tcf(c_157713,plain,
( in(sK140,sK64)
| ( sK125(subset_complement(powerset(sK140),sK64)) = sK140 )
| ~ sP7 ),
inference(forward_subsumption_resolution,[status(thm)],[c_157674,c_144206,c_146123]) ).
tcf(c_157724,plain,
( iPr_def_20
| iPr_def_18
| sP6
| ( set_difference(sK64,powerset(sK140)) = sK140 )
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152819,c_157679]) ).
tcf(c_157725,plain,
( iPr_def_20
| iPr_def_19
| sP6
| ( set_difference(sK64,powerset(sK140)) = sK140 )
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152818,c_157679]) ).
tcf(c_157726,plain,
( iPr_def_21
| iPr_def_18
| sP6
| ( set_difference(sK64,powerset(sK140)) = sK140 )
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152763,c_157679]) ).
tcf(c_157727,plain,
( iPr_def_21
| iPr_def_19
| sP6
| ( set_difference(sK64,powerset(sK140)) = sK140 )
| ( set_difference(omega,set_difference(omega,unordered_pair(sK62,sK62))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152762,c_157679]) ).
tcf(c_157785,plain,
! [X0: $i] :
( ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0))
| ~ proper_subset(powerset(X0),omega) ),
inference(superposition,[status(thm)],[c_157465,c_472]) ).
tcf(c_157787,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,omega)),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(powerset(X1))
| ~ ordinal(powerset(X1))
| ~ is_well_founded_in(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_157465,c_1058]) ).
tcf(c_157788,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,omega),omega)
| ( sK140 = omega )
| ~ relation(X0)
| ~ being_limit_ordinal(powerset(X1))
| ~ ordinal(powerset(X1))
| ~ is_well_founded_in(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_157465,c_1057]) ).
tcf(c_157789,plain,
! [X0: $i] :
( in(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_157465,c_369]) ).
tcf(c_157790,plain,
! [X0: $i] :
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_157465,c_371]) ).
tcf(c_157791,plain,
! [X0: $i] :
( ( set_difference(omega,powerset(X0)) = sK140 )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_157465,c_386]) ).
tcf(c_157792,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(omega),X0)
| ( sK140 = omega )
| ~ ordinal(X0)
| ~ being_limit_ordinal(powerset(X1))
| ~ ordinal(powerset(X1))
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_157465,c_370]) ).
tcf(c_157793,plain,
( in(sK63(omega),omega)
| ( sK140 = omega )
| ~ iPr_def_21
| ~ being_limit_ordinal(powerset(sK62))
| ~ ordinal(powerset(sK62)) ),
inference(superposition,[status(thm)],[c_157465,c_156787]) ).
tcf(c_157832,plain,
( ordinal(sK128(sK64))
| ~ ordinal(powerset(sK140))
| ~ sP7 ),
inference(global_subsumption_just,[status(thm)],[c_157678,c_132,c_157678]) ).
tcf(c_157833,plain,
( ordinal(sK128(sK64))
| ~ sP7
| ~ ordinal(powerset(sK140)) ),
inference(renaming,[status(thm)],[c_157832]) ).
tcf(c_157840,plain,
( ordinal(sK128(sK64))
| ( sK125(powerset(sK140)) = sK140 )
| ( relation_dom(sK126(powerset(sK140))) = powerset(sK140) )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_146389,c_157833]) ).
tcf(c_157841,plain,
( in(sK128(sK64),sK64)
| ~ ordinal(powerset(sK140))
| ~ sP7 ),
inference(global_subsumption_just,[status(thm)],[c_157677,c_132,c_157677]) ).
tcf(c_157842,plain,
( in(sK128(sK64),sK64)
| ~ sP7
| ~ ordinal(powerset(sK140)) ),
inference(renaming,[status(thm)],[c_157841]) ).
tcf(c_157849,plain,
( ~ sP7
| ~ ordinal(powerset(sK140))
| ~ in(sK64,sK128(sK64)) ),
inference(superposition,[status(thm)],[c_157842,c_527]) ).
tcf(c_157850,plain,
( ordinal(sK128(sK128(sK64)))
| ( sK128(sK64) = sK140 )
| ~ sP7
| ~ ordinal(union(sK64))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157842,c_154064]) ).
tcf(c_157851,plain,
( in(sK142(sK128(sK64)),sK128(sK64))
| ( sK125(sK64) = sK140 )
| ~ sP7
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157842,c_154131]) ).
tcf(c_157852,plain,
( ( set_difference(sK128(sK64),union(sK64)) = sK140 )
| ~ sP7
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157842,c_154065]) ).
tcf(c_157854,plain,
( ( sK125(sK64) = sK140 )
| ~ sP7
| ~ ordinal(powerset(sK140))
| ~ empty(sK128(sK64)) ),
inference(superposition,[status(thm)],[c_157842,c_150230]) ).
tcf(c_157856,plain,
( element(sK128(sK64),sK64)
| ~ sP7
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157842,c_526]) ).
tcf(c_157887,plain,
! [X0: $i] :
( in(sK262(relation_rng_restriction(X0,powerset(sK261))),relation_rng_restriction(X0,powerset(sK261)))
| ( relation_rng_restriction(X0,powerset(sK261)) = sK140 )
| ~ iPr_def_15
| ~ relation(powerset(sK261)) ),
inference(superposition,[status(thm)],[c_262,c_156803]) ).
tcf(c_157889,plain,
! [X0: $i] :
( in(sK262(set_difference(powerset(sK261),X0)),set_difference(powerset(sK261),X0))
| ( set_difference(powerset(sK261),X0) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_383,c_156803]) ).
tcf(c_157890,plain,
! [X0: $i] :
( in(sK262(relation_dom_restriction(powerset(sK261),X0)),relation_dom_restriction(powerset(sK261),X0))
| ( relation_dom_restriction(powerset(sK261),X0) = sK140 )
| ~ iPr_def_15
| ~ relation(powerset(sK261)) ),
inference(superposition,[status(thm)],[c_504,c_156803]) ).
tcf(c_157892,plain,
( in(sK262(omega),omega)
| ( sK140 = omega )
| ~ iPr_def_15
| ~ being_limit_ordinal(powerset(sK261))
| ~ ordinal(powerset(sK261)) ),
inference(superposition,[status(thm)],[c_157465,c_156803]) ).
tcf(c_157924,plain,
( function(sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ~ empty(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_147195]) ).
tcf(c_157925,plain,
( finite(sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ~ empty(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_147193]) ).
tcf(c_157926,plain,
( epsilon_transitive(sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ~ empty(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_147192]) ).
tcf(c_157927,plain,
( epsilon_connected(sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ~ empty(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_147191]) ).
tcf(c_157928,plain,
( ordinal(sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ~ empty(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_147190]) ).
tcf(c_157929,plain,
( one_to_one(sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ~ empty(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_147189]) ).
tcf(c_157930,plain,
! [X0: $i] :
( ( sK125(sK198(sK303)) = sK140 )
| ( apply(sK126(sK198(sK303)),X0) = sK140 )
| ~ empty(sK198(sK303))
| ~ relation(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_150772]) ).
tcf(c_157931,plain,
! [X0: $i] :
( element(X0,sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ( apply(sK126(sK198(sK303)),X0) = sK140 )
| ~ function(sK126(sK198(sK303)))
| ~ relation(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_148552]) ).
tcf(c_157932,plain,
( relation(sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ~ empty(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_642]) ).
tcf(c_157933,plain,
( empty(sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ~ empty(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_641]) ).
tcf(c_157934,plain,
! [X0: $i] :
( in(X0,sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ( apply(sK126(sK198(sK303)),X0) = sK140 )
| ~ function(sK126(sK198(sK303)))
| ~ relation(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_906]) ).
tcf(c_157935,plain,
( ( sK125(sK198(sK303)) = sK140 )
| ( relation_rng(sK126(sK198(sK303))) = sK140 )
| ~ relation(sK126(sK198(sK303)))
| ( sK198(sK303) != sK140 ) ),
inference(superposition,[status(thm)],[c_147346,c_478]) ).
tcf(c_157936,plain,
( ( sK126(sK198(sK303)) = sK140 )
| ( sK125(sK198(sK303)) = sK140 )
| ~ relation(sK126(sK198(sK303)))
| ( sK198(sK303) != sK140 ) ),
inference(superposition,[status(thm)],[c_147346,c_475]) ).
tcf(c_158059,plain,
! [X0: $i] :
( being_limit_ordinal(powerset(X0))
| ( powerset(X0) != X0 ) ),
inference(superposition,[status(thm)],[c_516,c_713]) ).
tcf(c_158066,plain,
( ( union(sK66) = sK66 )
| ~ sP6 ),
inference(superposition,[status(thm)],[c_141,c_714]) ).
tcf(c_158067,plain,
union(omega) = omega,
inference(superposition,[status(thm)],[c_848,c_714]) ).
tcf(c_158068,plain,
union(sK281) = sK281,
inference(superposition,[status(thm)],[c_896,c_714]) ).
tcf(c_158069,plain,
( ( sK116(sK140) = omega )
| ( union(sK263(sK116(sK140))) = sK263(sK116(sK140)) )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145174,c_714]) ).
tcf(c_158070,plain,
( ( sK300(sK140) = omega )
| ( union(sK263(sK300(sK140))) = sK263(sK300(sK140)) )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145502,c_714]) ).
tcf(c_158071,plain,
! [X0: $i] :
( ( unordered_pair(sK140,X0) = omega )
| ( union(sK263(unordered_pair(sK140,X0))) = sK263(unordered_pair(sK140,X0)) )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146169,c_714]) ).
tcf(c_158072,plain,
( ( powerset(sK140) = omega )
| ( union(sK263(powerset(sK140))) = sK263(powerset(sK140)) )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146194,c_714]) ).
tcf(c_158073,plain,
! [X0: $i] :
( ( unordered_pair(X0,sK140) = omega )
| ( union(sK263(unordered_pair(X0,sK140))) = sK263(unordered_pair(X0,sK140)) )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146211,c_714]) ).
tcf(c_158103,plain,
! [X0: $i,X1: $i] :
( sP29
| ordinal(X0)
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),sK248(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_808]) ).
tcf(c_158104,plain,
! [X0: $i] :
( sP29
| sP3(sK248(X0))
| ordinal(sK58(sK248(X0))) ),
inference(superposition,[status(thm)],[c_122,c_808]) ).
tcf(c_158106,plain,
! [X0: $i,X1: $i] :
( sP29
| ordinal(apply(sK126(X1),sK248(X0)))
| ( sK125(X1) = sK140 )
| ~ in(sK248(X0),X1) ),
inference(superposition,[status(thm)],[c_2177,c_808]) ).
tcf(c_158107,plain,
! [X0: $i] :
( sP29
| ordinal(sK248(X0))
| ordinal(sK127(sK248(X0))) ),
inference(superposition,[status(thm)],[c_367,c_808]) ).
tcf(c_158108,plain,
! [X0: $i] :
( sP29
| ordinal(sK128(sK248(X0)))
| ( sK248(X0) = sK140 )
| ~ ordinal(sK248(X0)) ),
inference(superposition,[status(thm)],[c_144620,c_808]) ).
tcf(c_158109,plain,
! [X0: $i,X1: $i] :
( sP29
| disjoint(sK248(X0),X1)
| ordinal(sK130(sK248(X0),X1)) ),
inference(superposition,[status(thm)],[c_400,c_808]) ).
tcf(c_158110,plain,
! [X0: $i,X1: $i] :
( sP29
| disjoint(X0,sK248(X1))
| ordinal(sK130(X0,sK248(X1))) ),
inference(superposition,[status(thm)],[c_401,c_808]) ).
tcf(c_158111,plain,
! [X0: $i] :
( sP29
| relation(sK248(X0))
| ordinal(sK163(sK248(X0))) ),
inference(superposition,[status(thm)],[c_561,c_808]) ).
tcf(c_158112,plain,
! [X0: $i] :
( sP29
| ordinal(sK169(sK248(X0)))
| ( sK248(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_579,c_808]) ).
tcf(c_158113,plain,
! [X0: $i] :
( sP29
| ordinal(sK173(sK248(X0)))
| ~ sP20(sK248(X0)) ),
inference(superposition,[status(thm)],[c_584,c_808]) ).
tcf(c_158115,plain,
! [X0: $i,X1: $i] :
( sP29
| subset(sK248(X0),X1)
| ordinal(sK193(sK248(X0),X1)) ),
inference(superposition,[status(thm)],[c_657,c_808]) ).
tcf(c_158117,plain,
! [X0: $i] :
( sP29
| ordinal(sK268(sK248(X0)))
| ~ sP34(sK248(X0)) ),
inference(superposition,[status(thm)],[c_864,c_808]) ).
tcf(c_158118,plain,
! [X0: $i] :
( sP29
| epsilon_transitive(sK248(X0))
| ordinal(sK316(sK248(X0))) ),
inference(superposition,[status(thm)],[c_1043,c_808]) ).
tcf(c_158119,plain,
! [X0: $i,X1: $i] :
( sP29
| ordinal(sK320(X1,sK248(X0)))
| ( sK248(X0) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(sK248(X0),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_808]) ).
tcf(c_158120,plain,
! [X0: $i] :
( sP29
| epsilon_connected(sK248(X0))
| ordinal(sK343(sK248(X0))) ),
inference(superposition,[status(thm)],[c_1207,c_808]) ).
tcf(c_158121,plain,
! [X0: $i] :
( sP29
| epsilon_connected(sK248(X0))
| ordinal(sK344(sK248(X0))) ),
inference(superposition,[status(thm)],[c_1208,c_808]) ).
tcf(c_158122,plain,
! [X0: $i] :
( sP29
| ordinal(unordered_pair(unordered_pair(sK137(sK248(X0)),sK137(sK248(X0))),unordered_pair(sK137(sK248(X0)),sK138(sK248(X0)))))
| ( sK248(X0) = sK140 )
| ~ relation(sK248(X0)) ),
inference(superposition,[status(thm)],[c_16344,c_808]) ).
tcf(c_158123,plain,
! [X0: $i,X1: $i] :
( sP29
| ordinal(sK318(X0,sK248(X1)))
| ( sK248(X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,sK248(X1)) ),
inference(superposition,[status(thm)],[c_144619,c_808]) ).
tcf(c_158124,plain,
! [X0: $i,X1: $i] :
( sP29
| ordinal(apply(sK126(X1),sK92(sK248(X0))))
| ( sK125(X1) = sK140 )
| ~ in(sK92(sK248(X0)),X1) ),
inference(superposition,[status(thm)],[c_151774,c_808]) ).
tcf(c_158125,plain,
! [X0: $i] :
( sP29
| ordinal(sK169(sK92(sK248(X0))))
| ( sK92(sK248(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151778,c_808]) ).
tcf(c_158126,plain,
! [X0: $i] :
( sP29
| ordinal(sK142(sK248(X0)))
| ( sK248(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_154138,c_808]) ).
tcf(c_158232,plain,
! [X0: $i] :
( ~ finite(X0)
| ~ in(omega,relation_dom(sK264(X0))) ),
inference(superposition,[status(thm)],[c_855,c_527]) ).
tcf(c_158233,plain,
! [X0: $i] :
( ordinal(sK128(relation_dom(sK264(X0))))
| ( relation_dom(sK264(X0)) = sK140 )
| ~ finite(X0)
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_855,c_154064]) ).
tcf(c_158235,plain,
! [X0: $i] :
( ( set_difference(relation_dom(sK264(X0)),union(omega)) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_855,c_154065]) ).
tcf(c_158239,plain,
! [X0: $i] :
( element(relation_dom(sK264(X0)),omega)
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_855,c_526]) ).
tcf(c_158244,plain,
! [X0: $i] :
( ( set_difference(relation_dom(sK264(X0)),omega) = sK140 )
| ~ finite(X0) ),
inference(light_normalisation,[status(thm)],[c_158235,c_158067]) ).
tcf(c_158247,plain,
! [X0: $i] :
( ordinal(sK128(relation_dom(sK264(X0))))
| ( relation_dom(sK264(X0)) = sK140 )
| ~ ordinal(omega)
| ~ finite(X0) ),
inference(light_normalisation,[status(thm)],[c_158233,c_158067]) ).
tcf(c_158248,plain,
! [X0: $i] :
( ordinal(sK128(relation_dom(sK264(X0))))
| ( relation_dom(sK264(X0)) = sK140 )
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_158247,c_849]) ).
tcf(c_158278,plain,
! [X0: $i] :
( sP29
| ordinal(sK261)
| sP32(sK169(sK248(X0)))
| ( sK248(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_158112,c_833]) ).
tcf(c_158279,plain,
! [X0: $i] :
( sP29
| epsilon_connected(sK169(sK248(X0)))
| ( sK248(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_158112,c_1050]) ).
tcf(c_158280,plain,
! [X0: $i] :
( sP29
| epsilon_transitive(sK169(sK248(X0)))
| ( sK248(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_158112,c_1049]) ).
tcf(c_158314,plain,
! [X0: $i,X1: $i] :
( in(sK128(X1),X1)
| ( X1 = sK140 )
| ( set_difference(unordered_pair(X1,X1),set_difference(unordered_pair(X1,X1),X0)) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_151758,c_154063]) ).
tcf(c_158315,plain,
! [X0: $i] :
( sP3(X0)
| in(sK128(sK58(X0)),sK58(X0))
| ( sK58(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_122,c_154063]) ).
tcf(c_158317,plain,
( in(sK128(sK66),sK66)
| ( sK140 = sK66 )
| ~ sP6
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_140,c_154063]) ).
tcf(c_158319,plain,
( in(sK128(sK110),sK110)
| ( sK140 = sK110 )
| ~ sP15
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_238,c_154063]) ).
tcf(c_158320,plain,
! [X0: $i] :
( in(sK128(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(union(set_union2(X0,unordered_pair(X0,X0)))) ),
inference(superposition,[status(thm)],[c_256,c_154063]) ).
tcf(c_158321,plain,
! [X0: $i] :
( in(sK128(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(union(sK116(X0))) ),
inference(superposition,[status(thm)],[c_272,c_154063]) ).
tcf(c_158322,plain,
! [X0: $i,X1: $i] :
( in(sK128(X1),X1)
| ( X1 = sK140 )
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ ordinal(union(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_906,c_154063]) ).
tcf(c_158323,plain,
! [X0: $i,X1: $i] :
( in(sK128(apply(sK126(X1),X0)),apply(sK126(X1),X0))
| ( sK125(X1) = sK140 )
| ( apply(sK126(X1),X0) = sK140 )
| ~ ordinal(union(X0))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2177,c_154063]) ).
tcf(c_158324,plain,
! [X0: $i] :
( ordinal(X0)
| in(sK128(sK127(X0)),sK127(X0))
| ( sK127(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_367,c_154063]) ).
tcf(c_158325,plain,
! [X0: $i] :
( in(sK128(sK128(X0)),sK128(X0))
| ( X0 = sK140 )
| ( sK128(X0) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_144620,c_154063]) ).
tcf(c_158326,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK128(sK130(X0,X1)),sK130(X0,X1))
| ( sK130(X0,X1) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_400,c_154063]) ).
tcf(c_158327,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| in(sK128(sK130(X1,X0)),sK130(X1,X0))
| ( sK130(X1,X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_401,c_154063]) ).
tcf(c_158328,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| in(sK128(X2),X2)
| ( X2 = sK140 )
| ( X0 = sK140 )
| ~ element(X2,X0)
| ~ subset(X1,X0)
| ~ ordinal(union(subset_complement(X0,X1))) ),
inference(superposition,[status(thm)],[c_5403,c_154063]) ).
tcf(c_158329,plain,
! [X0: $i] :
( relation(X0)
| in(sK128(sK163(X0)),sK163(X0))
| ( sK163(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_561,c_154063]) ).
tcf(c_158331,plain,
! [X0: $i] :
( in(sK128(sK173(X0)),sK173(X0))
| ( sK173(X0) = sK140 )
| ~ sP20(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_584,c_154063]) ).
tcf(c_158333,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK128(sK193(X0,X1)),sK193(X0,X1))
| ( sK193(X0,X1) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_657,c_154063]) ).
tcf(c_158334,plain,
! [X0: $i,X1: $i] :
( in(sK128(X1),X1)
| ( X1 = sK140 )
| ~ subset(X1,X0)
| ~ ordinal(union(powerset(X0))) ),
inference(superposition,[status(thm)],[c_661,c_154063]) ).
tcf(c_158337,plain,
! [X0: $i] :
( in(sK128(relation_dom(sK264(X0))),relation_dom(sK264(X0)))
| ( relation_dom(sK264(X0)) = sK140 )
| ~ finite(X0)
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_855,c_154063]) ).
tcf(c_158338,plain,
! [X0: $i] :
( in(sK128(sK268(X0)),sK268(X0))
| ( sK268(X0) = sK140 )
| ~ sP34(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_864,c_154063]) ).
tcf(c_158339,plain,
! [X0: $i,X1: $i] :
( in(sK128(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(union(unordered_pair(X0,X1))) ),
inference(superposition,[status(thm)],[c_939,c_154063]) ).
tcf(c_158340,plain,
! [X0: $i,X1: $i] :
( in(sK128(X1),X1)
| ( X1 = sK140 )
| ~ ordinal(union(unordered_pair(X0,X1))) ),
inference(superposition,[status(thm)],[c_940,c_154063]) ).
tcf(c_158341,plain,
! [X0: $i] :
( in(sK128(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(union(sK300(X0))) ),
inference(superposition,[status(thm)],[c_965,c_154063]) ).
tcf(c_158342,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK128(sK316(X0)),sK316(X0))
| ( sK316(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_1043,c_154063]) ).
tcf(c_158343,plain,
! [X0: $i,X1: $i] :
( in(sK128(sK320(X1,X0)),sK320(X1,X0))
| ( X0 = sK140 )
| ( sK320(X1,X0) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ ordinal(union(X0))
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_154063]) ).
tcf(c_158344,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK128(sK343(X0)),sK343(X0))
| ( sK343(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_1207,c_154063]) ).
tcf(c_158345,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK128(sK344(X0)),sK344(X0))
| ( sK344(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_1208,c_154063]) ).
tcf(c_158347,plain,
! [X0: $i] :
( in(sK128(unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0)))),unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))))
| ( X0 = sK140 )
| ( unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))) = sK140 )
| ~ relation(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_16344,c_154063]) ).
tcf(c_158348,plain,
( in(sK128(sK119(sK64)),sK119(sK64))
| ( sK119(sK64) = sK140 )
| ~ sP7
| ~ ordinal(union(sK64)) ),
inference(superposition,[status(thm)],[c_146098,c_154063]) ).
tcf(c_158349,plain,
! [X0: $i,X1: $i] :
( in(sK128(sK318(X0,X1)),sK318(X0,X1))
| ( X1 = sK140 )
| ( sK318(X0,X1) = sK140 )
| ~ relation(X0)
| ~ ordinal(union(X1))
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144619,c_154063]) ).
tcf(c_158350,plain,
( sP15
| in(sK128(sK114(sK64)),sK114(sK64))
| ( sK114(sK64) = sK140 )
| ~ sP7
| ~ ordinal(union(sK64)) ),
inference(superposition,[status(thm)],[c_145791,c_154063]) ).
tcf(c_158351,plain,
( in(sK128(sK72(sK64)),sK72(sK64))
| ( sK72(sK64) = sK140 )
| ~ iPr_def_19
| ~ sP7
| ~ ordinal(union(sK64)) ),
inference(superposition,[status(thm)],[c_145863,c_154063]) ).
tcf(c_158352,plain,
( in(sK128(sK67(sK64)),sK67(sK64))
| ( sK67(sK64) = sK140 )
| ~ sP6
| ~ sP7
| ~ ordinal(union(sK64))
| ~ in(sK140,sK66) ),
inference(superposition,[status(thm)],[c_146728,c_154063]) ).
tcf(c_158353,plain,
( in(sK128(sK111(sK64)),sK111(sK64))
| ( sK111(sK64) = sK140 )
| ~ sP15
| ~ sP7
| ~ ordinal(union(sK64))
| ~ in(sK140,sK110) ),
inference(superposition,[status(thm)],[c_146738,c_154063]) ).
tcf(c_158354,plain,
( in(sK128(sK63(sK199(powerset(powerset(sK62))))),sK63(sK199(powerset(powerset(sK62)))))
| ( sK199(powerset(powerset(sK62))) = sK140 )
| ( sK63(sK199(powerset(powerset(sK62)))) = sK140 )
| ~ iPr_def_21
| ~ ordinal(union(sK199(powerset(powerset(sK62))))) ),
inference(superposition,[status(thm)],[c_145355,c_154063]) ).
tcf(c_158355,plain,
! [X0: $i] :
( in(sK128(sK119(sK199(powerset(powerset(X0))))),sK119(sK199(powerset(powerset(X0)))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ( sK119(sK199(powerset(powerset(X0)))) = sK140 )
| ~ finite(X0)
| ~ ordinal(union(sK199(powerset(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_145365,c_154063]) ).
tcf(c_158356,plain,
( in(sK128(sK262(sK199(powerset(powerset(sK261))))),sK262(sK199(powerset(powerset(sK261)))))
| ( sK199(powerset(powerset(sK261))) = sK140 )
| ( sK262(sK199(powerset(powerset(sK261)))) = sK140 )
| ~ iPr_def_15
| ~ ordinal(union(sK199(powerset(powerset(sK261))))) ),
inference(superposition,[status(thm)],[c_145371,c_154063]) ).
tcf(c_158357,plain,
( in(sK128(sK63(powerset(sK62))),sK63(powerset(sK62)))
| ( powerset(sK62) = sK140 )
| ( sK63(powerset(sK62)) = sK140 )
| ~ iPr_def_21
| ~ ordinal(union(powerset(sK62))) ),
inference(superposition,[status(thm)],[c_145625,c_154063]) ).
tcf(c_158358,plain,
! [X0: $i] :
( in(sK128(sK72(powerset(X0))),sK72(powerset(X0)))
| ( powerset(X0) = sK140 )
| ( sK72(powerset(X0)) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ ordinal(union(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145633,c_154063]) ).
tcf(c_158359,plain,
! [X0: $i] :
( sP15
| in(sK128(sK114(powerset(X0))),sK114(powerset(X0)))
| ( powerset(X0) = sK140 )
| ( sK114(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ ordinal(union(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145634,c_154063]) ).
tcf(c_158360,plain,
! [X0: $i] :
( in(sK128(sK119(powerset(X0))),sK119(powerset(X0)))
| ( powerset(X0) = sK140 )
| ( sK119(powerset(X0)) = sK140 )
| ~ finite(X0)
| ~ ordinal(union(powerset(X0))) ),
inference(superposition,[status(thm)],[c_145635,c_154063]) ).
tcf(c_158361,plain,
( in(sK128(sK262(powerset(sK261))),sK262(powerset(sK261)))
| ( powerset(sK261) = sK140 )
| ( sK262(powerset(sK261)) = sK140 )
| ~ iPr_def_15
| ~ ordinal(union(powerset(sK261))) ),
inference(superposition,[status(thm)],[c_145641,c_154063]) ).
tcf(c_158362,plain,
( in(sK128(sK128(omega)),sK128(omega))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(union(omega))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146242,c_154063]) ).
tcf(c_158363,plain,
( in(sK128(sK128(omega)),sK128(omega))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140))
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_145922,c_154063]) ).
tcf(c_158364,plain,
( in(sK128(sK128(omega)),sK128(omega))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140))
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_145878,c_154063]) ).
tcf(c_158365,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK128(sK318(X2,set_difference(X0,X1))),sK318(X2,set_difference(X0,X1)))
| ( set_difference(X0,X1) = sK140 )
| ( sK318(X2,set_difference(X0,X1)) = sK140 )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X0)
| ~ ordinal(union(set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_146007,c_154063]) ).
tcf(c_158366,plain,
! [X0: $i,X1: $i] :
( in(sK128(sK128(set_difference(X0,X1))),sK128(set_difference(X0,X1)))
| ( set_difference(X0,X1) = sK140 )
| ( sK128(set_difference(X0,X1)) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(union(set_difference(X0,X1))) ),
inference(superposition,[status(thm)],[c_146008,c_154063]) ).
tcf(c_158367,plain,
! [X0: $i,X1: $i] :
( in(sK128(apply(sK126(X1),sK92(X0))),apply(sK126(X1),sK92(X0)))
| ( sK125(X1) = sK140 )
| ( apply(sK126(X1),sK92(X0)) = sK140 )
| ~ ordinal(union(X0))
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_151774,c_154063]) ).
tcf(c_158368,plain,
! [X0: $i] :
( in(sK128(sK169(sK92(X0))),sK169(sK92(X0)))
| ( sK92(X0) = sK140 )
| ( sK169(sK92(X0)) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_151778,c_154063]) ).
tcf(c_158369,plain,
! [X0: $i] :
( in(sK128(sK142(X0)),sK142(X0))
| ( X0 = sK140 )
| ( sK142(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154138,c_154063]) ).
tcf(c_158370,plain,
( in(sK128(sK142(omega)),sK142(omega))
| ( sK142(omega) = sK140 )
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_154124,c_154063]) ).
tcf(c_158371,plain,
! [X0: $i] :
( in(sK128(sK142(sK169(X0))),sK142(sK169(X0)))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK142(sK169(X0)) = sK140 )
| ~ ordinal(union(sK169(X0))) ),
inference(superposition,[status(thm)],[c_154906,c_154063]) ).
tcf(c_158372,plain,
( in(sK128(sK128(sK64)),sK128(sK64))
| ( sK128(sK64) = sK140 )
| ~ sP7
| ~ ordinal(union(sK64))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157842,c_154063]) ).
tcf(c_158385,plain,
( in(sK128(sK110),sK110)
| ( sK140 = sK110 )
| ~ sP15
| ~ ordinal(omega) ),
inference(light_normalisation,[status(thm)],[c_158319,c_158067]) ).
tcf(c_158386,plain,
( in(sK128(sK110),sK110)
| ( sK140 = sK110 )
| ~ sP15 ),
inference(forward_subsumption_resolution,[status(thm)],[c_158385,c_849]) ).
tcf(c_158390,plain,
( in(sK128(sK66),sK66)
| ( sK140 = sK66 )
| ~ sP6
| ~ ordinal(omega) ),
inference(light_normalisation,[status(thm)],[c_158317,c_158067]) ).
tcf(c_158391,plain,
( in(sK128(sK66),sK66)
| ( sK140 = sK66 )
| ~ sP6 ),
inference(forward_subsumption_resolution,[status(thm)],[c_158390,c_849]) ).
tcf(c_158395,plain,
( in(sK128(sK142(omega)),sK142(omega))
| ( sK142(omega) = sK140 )
| ~ ordinal(omega) ),
inference(light_normalisation,[status(thm)],[c_158370,c_158067]) ).
tcf(c_158396,plain,
( in(sK128(sK142(omega)),sK142(omega))
| ( sK142(omega) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_158395,c_849]) ).
tcf(c_158466,plain,
! [X0: $i] :
( in(sK128(relation_dom(sK264(X0))),relation_dom(sK264(X0)))
| ( relation_dom(sK264(X0)) = sK140 )
| ~ ordinal(omega)
| ~ finite(X0) ),
inference(light_normalisation,[status(thm)],[c_158337,c_158067]) ).
tcf(c_158467,plain,
! [X0: $i] :
( in(sK128(relation_dom(sK264(X0))),relation_dom(sK264(X0)))
| ( relation_dom(sK264(X0)) = sK140 )
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_158466,c_849]) ).
tcf(c_158524,plain,
( in(sK128(sK128(omega)),sK128(omega))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ ordinal(omega)
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(light_normalisation,[status(thm)],[c_158364,c_158067]) ).
tcf(c_158525,plain,
( in(sK128(sK128(omega)),sK128(omega))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_158524,c_849]) ).
tcf(c_158531,plain,
( in(sK128(sK128(omega)),sK128(omega))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ ordinal(omega)
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(light_normalisation,[status(thm)],[c_158363,c_158067]) ).
tcf(c_158532,plain,
( in(sK128(sK128(omega)),sK128(omega))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_158531,c_849]) ).
tcf(c_158538,plain,
( in(sK128(sK128(omega)),sK128(omega))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ ordinal(omega)
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(light_normalisation,[status(thm)],[c_158362,c_158067]) ).
tcf(c_158539,plain,
( in(sK128(sK128(omega)),sK128(omega))
| ( sK140 = omega )
| ( sK128(omega) = sK140 )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_158538,c_849]) ).
tcf(c_158545,plain,
! [X0: $i] :
( in(sK128(sK119(powerset(X0))),sK119(powerset(X0)))
| ( powerset(X0) = sK140 )
| ( sK119(powerset(X0)) = sK140 )
| ~ finite(X0)
| ~ ordinal(X0) ),
inference(light_normalisation,[status(thm)],[c_158360,c_516]) ).
tcf(c_158579,plain,
! [X0: $i] :
( sP15
| in(sK128(sK114(powerset(X0))),sK114(powerset(X0)))
| ( powerset(X0) = sK140 )
| ( sK114(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(light_normalisation,[status(thm)],[c_158359,c_516]) ).
tcf(c_158586,plain,
! [X0: $i] :
( in(sK128(sK72(powerset(X0))),sK72(powerset(X0)))
| ( powerset(X0) = sK140 )
| ( sK72(powerset(X0)) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(light_normalisation,[status(thm)],[c_158358,c_516]) ).
tcf(c_158712,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),apply(sK126(X1),X0))) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_151758,c_155601]) ).
tcf(c_158713,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),apply(sK126(X0),sK140))) = sK140 )
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_151909,c_155601]) ).
tcf(c_158728,plain,
! [X0: $i,X1: $i] :
( in(sK119(relation_rng_restriction(X1,powerset(X0))),relation_rng_restriction(X1,powerset(X0)))
| ( relation_rng_restriction(X1,powerset(X0)) = sK140 )
| ~ finite(X0)
| ~ relation(powerset(X0)) ),
inference(superposition,[status(thm)],[c_262,c_156797]) ).
tcf(c_158730,plain,
! [X0: $i,X1: $i] :
( in(sK119(set_difference(powerset(X0),X1)),set_difference(powerset(X0),X1))
| ( set_difference(powerset(X0),X1) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_383,c_156797]) ).
tcf(c_158731,plain,
! [X0: $i,X1: $i] :
( in(sK119(relation_dom_restriction(powerset(X0),X1)),relation_dom_restriction(powerset(X0),X1))
| ( relation_dom_restriction(powerset(X0),X1) = sK140 )
| ~ finite(X0)
| ~ relation(powerset(X0)) ),
inference(superposition,[status(thm)],[c_504,c_156797]) ).
tcf(c_158734,plain,
! [X0: $i] :
( in(sK119(omega),omega)
| ( sK140 = omega )
| ~ finite(X0)
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_157465,c_156797]) ).
tcf(c_158769,plain,
! [X0: $i,X1: $i] :
( sP3(X1)
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_150222]) ).
tcf(c_158770,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X1) = sK140 )
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_148019]) ).
tcf(c_158771,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( relation_rng(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_147669]) ).
tcf(c_158772,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( relation_dom(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_147196]) ).
tcf(c_158773,plain,
! [X0: $i,X1: $i] :
( one_to_one(X1)
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_84200]) ).
tcf(c_158774,plain,
! [X0: $i,X1: $i] :
( ordinal(X1)
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_1047]) ).
tcf(c_158775,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X1)
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_1046]) ).
tcf(c_158776,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X1)
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_1045]) ).
tcf(c_158777,plain,
! [X0: $i,X1: $i] :
( finite(X1)
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_983]) ).
tcf(c_158778,plain,
! [X0: $i,X1: $i] :
( relation(X1)
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_799]) ).
tcf(c_158779,plain,
! [X0: $i,X1: $i] :
( function(X1)
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_785]) ).
tcf(c_158780,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK126(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_575]) ).
tcf(c_158781,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| ( sK125(set_union2(X1,X2)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(set_union2(X1,X2))),sK126(set_union2(X1,X2))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_615]) ).
tcf(c_158782,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X2)
| ( sK125(set_union2(X1,X2)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(set_union2(X1,X2))),sK126(set_union2(X1,X2))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_614]) ).
tcf(c_158783,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,X2) = sK140 )
| ( set_difference(relation_rng_restriction(X1,sK126(relation_dom(X0))),sK126(relation_dom(X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152610,c_150772]) ).
tcf(c_158784,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(sK198(X1)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK198(X1))),sK126(sK198(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_694]) ).
tcf(c_158785,plain,
! [X0: $i,X1: $i] :
( ( sK125(powerset(X1)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(powerset(X1))),sK126(powerset(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_695]) ).
tcf(c_158786,plain,
! [X0: $i] :
( ( sK125(sK241) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK241)),sK126(sK241)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_789]) ).
tcf(c_158787,plain,
! [X0: $i] :
( ( sK125(sK242) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK242)),sK126(sK242)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_790]) ).
tcf(c_158789,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(X1,unordered_pair(X1,X1))) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(set_union2(X1,unordered_pair(X1,X1)))),sK126(set_union2(X1,unordered_pair(X1,X1)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_892]) ).
tcf(c_158790,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(unordered_pair(X1,X2)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(unordered_pair(X1,X2))),sK126(unordered_pair(X1,X2))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_935]) ).
tcf(c_158791,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(sK302(X1)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK302(X1))),sK126(sK302(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_973]) ).
tcf(c_158792,plain,
! [X0: $i] :
( ( sK125(sK303) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK303)),sK126(sK303)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_975]) ).
tcf(c_158793,plain,
! [X0: $i] :
( ( sK125(sK313) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK313)),sK126(sK313)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_1025]) ).
tcf(c_158794,plain,
! [X0: $i] :
( ( sK125(sK346) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK346)),sK126(sK346)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_1223]) ).
tcf(c_158795,plain,
! [X0: $i] :
( ( sK125(sK358) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK358)),sK126(sK358)) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_1276]) ).
tcf(c_158796,plain,
! [X0: $i,X1: $i] :
( relation(X1)
| ( sK125(sK115(X1)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK115(X1))),sK126(sK115(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_147253]) ).
tcf(c_158797,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(sK115(X1)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK115(X1))),sK126(sK115(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_147177]) ).
tcf(c_158798,plain,
! [X0: $i,X1: $i] :
( relation(X1)
| ( sK125(identity_relation(X1)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(identity_relation(X1))),sK126(identity_relation(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_147255]) ).
tcf(c_158799,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(identity_relation(X1)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(identity_relation(X1))),sK126(identity_relation(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_147179]) ).
tcf(c_158800,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK116(X1)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK116(X1))),sK126(sK116(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_150228]) ).
tcf(c_158801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(subset_complement(X1,X0)) = sK140 )
| ( set_difference(relation_rng_restriction(X3,sK126(subset_complement(X1,X0))),sK126(subset_complement(X1,X0))) = sK140 )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_152610,c_150233]) ).
tcf(c_158802,plain,
! [X0: $i,X1: $i] :
( ( X0 = omega )
| ( sK125(sK263(X0)) = sK140 )
| ( set_difference(relation_rng_restriction(X1,sK126(sK263(X0))),sK126(sK263(X0))) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_152610,c_150238]) ).
tcf(c_158803,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK300(X1)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK300(X1))),sK126(sK300(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_150241]) ).
tcf(c_158804,plain,
! [X0: $i] :
( ( sK125(sK64) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK64)),sK126(sK64)) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_152610,c_150248]) ).
tcf(c_158805,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(apply(sK126(X1),X0)) = sK140 )
| ( set_difference(relation_rng_restriction(X2,sK126(apply(sK126(X1),X0))),sK126(apply(sK126(X1),X0))) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_152610,c_150503]) ).
tcf(c_158806,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( sK125(sK169(X1)) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(sK169(X1))),sK126(sK169(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_152610,c_150508]) ).
tcf(c_159003,plain,
! [X0: $i,X1: $i] :
( ordinal(sK261)
| sP32(sK128(relation_dom_restriction(X0,X1)))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_153992,c_833]) ).
tcf(c_159004,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(sK128(relation_dom_restriction(X0,X1)))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_153992,c_1050]) ).
tcf(c_159005,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(sK128(relation_dom_restriction(X0,X1)))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_153992,c_1049]) ).
tcf(c_159029,plain,
( function(sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ~ empty(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_147195]) ).
tcf(c_159030,plain,
( finite(sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ~ empty(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_147193]) ).
tcf(c_159031,plain,
( epsilon_transitive(sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ~ empty(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_147192]) ).
tcf(c_159032,plain,
( epsilon_connected(sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ~ empty(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_147191]) ).
tcf(c_159033,plain,
( ordinal(sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ~ empty(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_147190]) ).
tcf(c_159034,plain,
( one_to_one(sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ~ empty(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_147189]) ).
tcf(c_159035,plain,
! [X0: $i] :
( ( sK125(sK198(sK313)) = sK140 )
| ( apply(sK126(sK198(sK313)),X0) = sK140 )
| ~ empty(sK198(sK313))
| ~ relation(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_150772]) ).
tcf(c_159036,plain,
! [X0: $i] :
( element(X0,sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ( apply(sK126(sK198(sK313)),X0) = sK140 )
| ~ function(sK126(sK198(sK313)))
| ~ relation(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_148552]) ).
tcf(c_159037,plain,
( relation(sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ~ empty(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_642]) ).
tcf(c_159038,plain,
( empty(sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ~ empty(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_641]) ).
tcf(c_159039,plain,
! [X0: $i] :
( in(X0,sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ( apply(sK126(sK198(sK313)),X0) = sK140 )
| ~ function(sK126(sK198(sK313)))
| ~ relation(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_906]) ).
tcf(c_159040,plain,
( ( sK125(sK198(sK313)) = sK140 )
| ( relation_rng(sK126(sK198(sK313))) = sK140 )
| ~ relation(sK126(sK198(sK313)))
| ( sK198(sK313) != sK140 ) ),
inference(superposition,[status(thm)],[c_147347,c_478]) ).
tcf(c_159041,plain,
( ( sK126(sK198(sK313)) = sK140 )
| ( sK125(sK198(sK313)) = sK140 )
| ~ relation(sK126(sK198(sK313)))
| ( sK198(sK313) != sK140 ) ),
inference(superposition,[status(thm)],[c_147347,c_475]) ).
tcf(c_159112,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK198(unordered_pair(X1,X0))) = sK140 )
| ( relation_dom(sK126(sK198(unordered_pair(X0,X1)))) = sK198(unordered_pair(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_942,c_147345]) ).
tcf(c_159114,plain,
! [X0: $i,X1: $i] :
( ( sK125(unordered_pair(X1,X0)) = sK140 )
| ( relation_dom(sK126(unordered_pair(X0,X1))) = unordered_pair(X0,X1) ) ),
inference(superposition,[status(thm)],[c_942,c_146160]) ).
tcf(c_159119,plain,
! [X0: $i] :
( being_limit_ordinal(sK263(unordered_pair(X0,sK140)))
| ( unordered_pair(sK140,X0) = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_942,c_146169]) ).
tcf(c_159120,plain,
! [X0: $i] :
( ordinal(sK263(unordered_pair(X0,sK140)))
| ( unordered_pair(sK140,X0) = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_942,c_146168]) ).
tcf(c_159121,plain,
! [X0: $i] :
( ( set_difference(omega,unordered_pair(sK140,X0)) = sK140 )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_942,c_146512]) ).
tcf(c_159122,plain,
! [X0: $i] :
( in(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_942,c_146510]) ).
tcf(c_159123,plain,
! [X0: $i] :
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_942,c_146511]) ).
tcf(c_159125,plain,
! [X0: $i] :
( subset(omega,unordered_pair(X0,sK140))
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_942,c_146170]) ).
tcf(c_159126,plain,
! [X0: $i] :
( being_limit_ordinal(sK263(unordered_pair(sK140,X0)))
| ( unordered_pair(X0,sK140) = omega )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_942,c_146211]) ).
tcf(c_159127,plain,
! [X0: $i] :
( ordinal(sK263(unordered_pair(sK140,X0)))
| ( unordered_pair(X0,sK140) = omega )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_942,c_146210]) ).
tcf(c_159129,plain,
! [X0: $i] :
( ( set_difference(omega,unordered_pair(X0,sK140)) = sK140 )
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_942,c_146654]) ).
tcf(c_159130,plain,
! [X0: $i] :
( in(sK128(omega),omega)
| ( sK140 = omega )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_942,c_146652]) ).
tcf(c_159131,plain,
! [X0: $i] :
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_942,c_146653]) ).
tcf(c_159132,plain,
! [X0: $i] :
( subset(omega,unordered_pair(sK140,X0))
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_942,c_146212]) ).
tcf(c_159211,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( set_difference(unordered_pair(sK343(X0),sK343(X0)),set_difference(unordered_pair(sK343(X0),sK343(X0)),sK344(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_1209]) ).
tcf(c_159243,plain,
! [X0: $i,X1: $i] :
( sP3(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_150222]) ).
tcf(c_159244,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_148019]) ).
tcf(c_159245,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_147669]) ).
tcf(c_159246,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_147196]) ).
tcf(c_159247,plain,
! [X0: $i,X1: $i] :
( one_to_one(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_84200]) ).
tcf(c_159248,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_1047]) ).
tcf(c_159249,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_1046]) ).
tcf(c_159250,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_1045]) ).
tcf(c_159251,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_983]) ).
tcf(c_159252,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_799]) ).
tcf(c_159253,plain,
! [X0: $i,X1: $i] :
( function(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_785]) ).
tcf(c_159254,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_575]) ).
tcf(c_159255,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(set_union2(X0,X1)),X2),sK126(set_union2(X0,X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_615]) ).
tcf(c_159256,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(set_union2(X0,X1)),X2),sK126(set_union2(X0,X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_614]) ).
tcf(c_159257,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,X2) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(relation_dom(X0)),X1),sK126(relation_dom(X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_154400,c_150772]) ).
tcf(c_159258,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK198(X0)),X1),sK126(sK198(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_694]) ).
tcf(c_159260,plain,
! [X0: $i] :
( ( sK125(sK241) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK241),X0),sK126(sK241)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_789]) ).
tcf(c_159261,plain,
! [X0: $i] :
( ( sK125(sK242) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK242),X0),sK126(sK242)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_790]) ).
tcf(c_159263,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(X0,unordered_pair(X0,X0))) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(set_union2(X0,unordered_pair(X0,X0))),X1),sK126(set_union2(X0,unordered_pair(X0,X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_892]) ).
tcf(c_159264,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(unordered_pair(X0,X1)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(unordered_pair(X0,X1)),X2),sK126(unordered_pair(X0,X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_935]) ).
tcf(c_159265,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK302(X0)),X1),sK126(sK302(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_973]) ).
tcf(c_159266,plain,
! [X0: $i] :
( ( sK125(sK303) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK303),X0),sK126(sK303)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_975]) ).
tcf(c_159267,plain,
! [X0: $i] :
( ( sK125(sK313) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK313),X0),sK126(sK313)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_1025]) ).
tcf(c_159268,plain,
! [X0: $i] :
( ( sK125(sK346) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK346),X0),sK126(sK346)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_1223]) ).
tcf(c_159269,plain,
! [X0: $i] :
( ( sK125(sK358) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK358),X0),sK126(sK358)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_1276]) ).
tcf(c_159270,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK115(X0)),X1),sK126(sK115(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_147253]) ).
tcf(c_159271,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK115(X0)),X1),sK126(sK115(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_147177]) ).
tcf(c_159272,plain,
! [X0: $i,X1: $i] :
( relation(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(identity_relation(X0)),X1),sK126(identity_relation(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_147255]) ).
tcf(c_159273,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(identity_relation(X0)),X1),sK126(identity_relation(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_147179]) ).
tcf(c_159274,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK116(X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK116(X0)),X1),sK126(sK116(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_150228]) ).
tcf(c_159275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(subset_complement(X1,X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(subset_complement(X1,X0)),X3),sK126(subset_complement(X1,X0))) = sK140 )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_154400,c_150233]) ).
tcf(c_159276,plain,
! [X0: $i,X1: $i] :
( ( X0 = omega )
| ( sK125(sK263(X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK263(X0)),X1),sK126(sK263(X0))) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_154400,c_150238]) ).
tcf(c_159277,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK300(X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK300(X0)),X1),sK126(sK300(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_150241]) ).
tcf(c_159278,plain,
! [X0: $i] :
( ( sK125(sK64) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK64),X0),sK126(sK64)) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_154400,c_150248]) ).
tcf(c_159279,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(apply(sK126(X1),X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(apply(sK126(X1),X0)),X2),sK126(apply(sK126(X1),X0))) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_154400,c_150503]) ).
tcf(c_159280,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK169(X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(sK169(X0)),X1),sK126(sK169(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154400,c_150508]) ).
tcf(c_159457,plain,
! [X0: $i] :
( disjoint(sK169(X0),union(X0))
| ( X0 = sK140 )
| ( sK169(X0) != sK140 ) ),
inference(demodulation,[status(thm)],[c_154805,c_675]) ).
tcf(c_159475,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK128(sK169(X0)))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154847,c_833]) ).
tcf(c_159476,plain,
! [X0: $i] :
( epsilon_connected(sK128(sK169(X0)))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154847,c_1050]) ).
tcf(c_159477,plain,
! [X0: $i] :
( epsilon_transitive(sK128(sK169(X0)))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154847,c_1049]) ).
tcf(c_159538,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ( set_difference(unordered_pair(relation_dom(X0),relation_dom(X0)),set_difference(unordered_pair(relation_dom(X0),relation_dom(X0)),X1)) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_151758,c_155600]) ).
tcf(c_159539,plain,
! [X0: $i] :
( ( apply(X0,set_union2(relation_dom(X0),unordered_pair(relation_dom(X0),relation_dom(X0)))) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_256,c_155600]) ).
tcf(c_159541,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,relation_dom(X0)) = sK140 )
| ( apply(X0,relation_dom(X1)) = sK140 )
| ~ function(X1)
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_155600]) ).
tcf(c_159542,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(relation_dom(X0),X2)
| ( X1 = sK140 )
| ( apply(X0,subset_complement(X1,X2)) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(X2,X1)
| ~ element(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_5403,c_155600]) ).
tcf(c_159543,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,powerset(X1)) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ subset(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_661,c_155600]) ).
tcf(c_159544,plain,
! [X0: $i] :
( ( apply(sK264(X0),omega) = sK140 )
| ~ finite(X0)
| ~ function(sK264(X0))
| ~ relation(sK264(X0)) ),
inference(superposition,[status(thm)],[c_855,c_155600]) ).
tcf(c_159545,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,unordered_pair(relation_dom(X0),X1)) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_939,c_155600]) ).
tcf(c_159546,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,unordered_pair(X1,relation_dom(X0))) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_940,c_155600]) ).
tcf(c_159548,plain,
! [X0: $i,X1: $i] :
( ( apply(sK115(X0),X1) = sK140 )
| ~ function(sK115(X0))
| ~ relation(sK115(X0))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_251,c_155600]) ).
tcf(c_159549,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_148083,c_155600]) ).
tcf(c_159550,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_147734,c_155600]) ).
tcf(c_159551,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_147316,c_155600]) ).
tcf(c_159552,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_144306,c_155600]) ).
tcf(c_159553,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),X1) = sK140 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_489,c_155600]) ).
tcf(c_159555,plain,
! [X0: $i] :
( ( sK125(sK241) = sK140 )
| ( apply(sK126(sK241),X0) = sK140 )
| ~ function(sK126(sK241))
| ~ relation(sK126(sK241))
| ~ in(sK241,X0) ),
inference(superposition,[status(thm)],[c_144638,c_155600]) ).
tcf(c_159556,plain,
! [X0: $i] :
( ( sK125(sK242) = sK140 )
| ( apply(sK126(sK242),X0) = sK140 )
| ~ function(sK126(sK242))
| ~ relation(sK126(sK242))
| ~ in(sK242,X0) ),
inference(superposition,[status(thm)],[c_144641,c_155600]) ).
tcf(c_159557,plain,
! [X0: $i] :
( ( sK125(sK303) = sK140 )
| ( apply(sK126(sK303),X0) = sK140 )
| ~ function(sK126(sK303))
| ~ relation(sK126(sK303))
| ~ in(sK303,X0) ),
inference(superposition,[status(thm)],[c_144647,c_155600]) ).
tcf(c_159558,plain,
! [X0: $i] :
( ( sK125(sK313) = sK140 )
| ( apply(sK126(sK313),X0) = sK140 )
| ~ function(sK126(sK313))
| ~ relation(sK126(sK313))
| ~ in(sK313,X0) ),
inference(superposition,[status(thm)],[c_144797,c_155600]) ).
tcf(c_159559,plain,
! [X0: $i] :
( ( sK125(sK346) = sK140 )
| ( apply(sK126(sK346),X0) = sK140 )
| ~ function(sK126(sK346))
| ~ relation(sK126(sK346))
| ~ in(sK346,X0) ),
inference(superposition,[status(thm)],[c_144944,c_155600]) ).
tcf(c_159560,plain,
! [X0: $i] :
( ( sK125(sK358) = sK140 )
| ( apply(sK126(sK358),X0) = sK140 )
| ~ function(sK126(sK358))
| ~ relation(sK126(sK358))
| ~ in(sK358,X0) ),
inference(superposition,[status(thm)],[c_144947,c_155600]) ).
tcf(c_159561,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(unordered_pair(X0,X1)) = sK140 )
| ( apply(sK126(unordered_pair(X0,X1)),X2) = sK140 )
| ~ function(sK126(unordered_pair(X0,X1)))
| ~ relation(sK126(unordered_pair(X0,X1)))
| ~ in(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_146160,c_155600]) ).
tcf(c_159562,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( apply(sK126(set_union2(X0,X1)),X2) = sK140 )
| ~ function(sK126(set_union2(X0,X1)))
| ~ relation(sK126(set_union2(X0,X1)))
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_149522,c_155600]) ).
tcf(c_159563,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( apply(sK126(set_union2(X0,X1)),X2) = sK140 )
| ~ function(sK126(set_union2(X0,X1)))
| ~ relation(sK126(set_union2(X0,X1)))
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_149417,c_155600]) ).
tcf(c_159564,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0)))
| ~ in(sK198(X0),X1) ),
inference(superposition,[status(thm)],[c_147331,c_155600]) ).
tcf(c_159565,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0)))
| ~ in(sK198(X0),X1) ),
inference(superposition,[status(thm)],[c_147339,c_155600]) ).
tcf(c_159566,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK198(powerset(X0))) = sK140 )
| ( apply(sK126(sK198(powerset(X0))),X1) = sK140 )
| ~ function(sK126(sK198(powerset(X0))))
| ~ relation(sK126(sK198(powerset(X0))))
| ~ in(sK198(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_147341,c_155600]) ).
tcf(c_159567,plain,
! [X0: $i] :
( ( sK125(sK198(sK241)) = sK140 )
| ( apply(sK126(sK198(sK241)),X0) = sK140 )
| ~ function(sK126(sK198(sK241)))
| ~ relation(sK126(sK198(sK241)))
| ~ in(sK198(sK241),X0) ),
inference(superposition,[status(thm)],[c_147342,c_155600]) ).
tcf(c_159568,plain,
! [X0: $i] :
( ( sK125(sK198(sK242)) = sK140 )
| ( apply(sK126(sK198(sK242)),X0) = sK140 )
| ~ function(sK126(sK198(sK242)))
| ~ relation(sK126(sK198(sK242)))
| ~ in(sK198(sK242),X0) ),
inference(superposition,[status(thm)],[c_147343,c_155600]) ).
tcf(c_159569,plain,
! [X0: $i] :
( ( sK125(sK198(omega)) = sK140 )
| ( apply(sK126(sK198(omega)),X0) = sK140 )
| ~ function(sK126(sK198(omega)))
| ~ relation(sK126(sK198(omega)))
| ~ in(sK198(omega),X0) ),
inference(superposition,[status(thm)],[c_147344,c_155600]) ).
tcf(c_159570,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ( apply(sK126(sK198(unordered_pair(X0,X1))),X2) = sK140 )
| ~ function(sK126(sK198(unordered_pair(X0,X1))))
| ~ relation(sK126(sK198(unordered_pair(X0,X1))))
| ~ in(sK198(unordered_pair(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_147345,c_155600]) ).
tcf(c_159571,plain,
! [X0: $i] :
( ( sK125(sK198(sK303)) = sK140 )
| ( apply(sK126(sK198(sK303)),X0) = sK140 )
| ~ function(sK126(sK198(sK303)))
| ~ relation(sK126(sK198(sK303)))
| ~ in(sK198(sK303),X0) ),
inference(superposition,[status(thm)],[c_147346,c_155600]) ).
tcf(c_159572,plain,
! [X0: $i] :
( ( sK125(sK198(sK313)) = sK140 )
| ( apply(sK126(sK198(sK313)),X0) = sK140 )
| ~ function(sK126(sK198(sK313)))
| ~ relation(sK126(sK198(sK313)))
| ~ in(sK198(sK313),X0) ),
inference(superposition,[status(thm)],[c_147347,c_155600]) ).
tcf(c_159573,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0)))
| ~ in(sK302(X0),X1) ),
inference(superposition,[status(thm)],[c_147765,c_155600]) ).
tcf(c_159574,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK116(X0)) = sK140 )
| ( apply(sK126(sK116(X0)),X1) = sK140 )
| ~ function(sK126(sK116(X0)))
| ~ relation(sK126(sK116(X0)))
| ~ in(sK116(X0),X1) ),
inference(superposition,[status(thm)],[c_150446,c_155600]) ).
tcf(c_159575,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK300(X0)) = sK140 )
| ( apply(sK126(sK300(X0)),X1) = sK140 )
| ~ function(sK126(sK300(X0)))
| ~ relation(sK126(sK300(X0)))
| ~ in(sK300(X0),X1) ),
inference(superposition,[status(thm)],[c_150465,c_155600]) ).
tcf(c_159590,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),X1) = sK140 )
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_159553,c_1100,c_1101]) ).
tcf(c_159593,plain,
! [X0: $i,X1: $i] :
( ( apply(sK115(X0),X1) = sK140 )
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_159548,c_250,c_249]) ).
tcf(c_159807,plain,
! [X0: $i] :
( ( powerset(X0) = omega )
| ( union(sK263(powerset(X0))) = sK263(powerset(X0)) )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_157470,c_714]) ).
tcf(c_159820,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK263(powerset(X0)))
| ( powerset(X0) = omega )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_157475,c_833]) ).
tcf(c_159821,plain,
! [X0: $i] :
( epsilon_connected(sK263(powerset(X0)))
| ( powerset(X0) = omega )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_157475,c_1050]) ).
tcf(c_159822,plain,
! [X0: $i] :
( epsilon_transitive(sK263(powerset(X0)))
| ( powerset(X0) = omega )
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_157475,c_1049]) ).
tcf(c_159850,plain,
! [X0: $i,X1: $i] :
( sP29
| ordinal(sK261)
| sP32(apply(sK126(X1),sK248(X0)))
| ( sK125(X1) = sK140 )
| ~ in(sK248(X0),X1) ),
inference(superposition,[status(thm)],[c_158106,c_833]) ).
tcf(c_159851,plain,
! [X0: $i,X1: $i] :
( sP29
| epsilon_connected(apply(sK126(X1),sK248(X0)))
| ( sK125(X1) = sK140 )
| ~ in(sK248(X0),X1) ),
inference(superposition,[status(thm)],[c_158106,c_1050]) ).
tcf(c_159852,plain,
! [X0: $i,X1: $i] :
( sP29
| epsilon_transitive(apply(sK126(X1),sK248(X0)))
| ( sK125(X1) = sK140 )
| ~ in(sK248(X0),X1) ),
inference(superposition,[status(thm)],[c_158106,c_1049]) ).
tcf(c_159880,plain,
! [X0: $i] :
( ( sK125(sK198(sK346)) = sK140 )
| ( apply(sK126(sK198(sK346)),X0) = sK140 )
| ~ function(sK126(sK198(sK346)))
| ~ relation(sK126(sK198(sK346)))
| ~ in(sK198(sK346),X0) ),
inference(superposition,[status(thm)],[c_147348,c_155600]) ).
tcf(c_159881,plain,
( function(sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ~ empty(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_147195]) ).
tcf(c_159882,plain,
( finite(sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ~ empty(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_147193]) ).
tcf(c_159883,plain,
( epsilon_transitive(sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ~ empty(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_147192]) ).
tcf(c_159884,plain,
( epsilon_connected(sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ~ empty(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_147191]) ).
tcf(c_159885,plain,
( ordinal(sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ~ empty(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_147190]) ).
tcf(c_159886,plain,
( one_to_one(sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ~ empty(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_147189]) ).
tcf(c_159887,plain,
! [X0: $i] :
( ( sK125(sK198(sK346)) = sK140 )
| ( apply(sK126(sK198(sK346)),X0) = sK140 )
| ~ empty(sK198(sK346))
| ~ relation(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_150772]) ).
tcf(c_159888,plain,
! [X0: $i] :
( element(X0,sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ( apply(sK126(sK198(sK346)),X0) = sK140 )
| ~ function(sK126(sK198(sK346)))
| ~ relation(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_148552]) ).
tcf(c_159889,plain,
( relation(sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ~ empty(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_642]) ).
tcf(c_159890,plain,
( empty(sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ~ empty(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_641]) ).
tcf(c_159891,plain,
! [X0: $i] :
( in(X0,sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ( apply(sK126(sK198(sK346)),X0) = sK140 )
| ~ function(sK126(sK198(sK346)))
| ~ relation(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_906]) ).
tcf(c_159892,plain,
( ( sK125(sK198(sK346)) = sK140 )
| ( relation_rng(sK126(sK198(sK346))) = sK140 )
| ~ relation(sK126(sK198(sK346)))
| ( sK198(sK346) != sK140 ) ),
inference(superposition,[status(thm)],[c_147348,c_478]) ).
tcf(c_159893,plain,
( ( sK126(sK198(sK346)) = sK140 )
| ( sK125(sK198(sK346)) = sK140 )
| ~ relation(sK126(sK198(sK346)))
| ( sK198(sK346) != sK140 ) ),
inference(superposition,[status(thm)],[c_147348,c_475]) ).
tcf(c_159963,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( set_difference(unordered_pair(sK344(X0),sK344(X0)),set_difference(unordered_pair(sK344(X0),sK344(X0)),sK343(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_1211]) ).
tcf(c_160205,plain,
! [X0: $i,X1: $i] : ~ proper_subset(set_union2(X0,X1),X1),
inference(superposition,[status(thm)],[c_156747,c_472]) ).
tcf(c_160206,plain,
! [X0: $i,X1: $i] :
( in(sK140,X1)
| ( set_union2(X0,X1) = sK140 )
| ( sK125(subset_complement(set_union2(X0,X1),X1)) = sK140 )
| ~ element(sK140,set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_156747,c_145539]) ).
tcf(c_160213,plain,
! [X0: $i] :
( sP15
| ( set_union2(X0,sK114(sK64)) = sK114(sK64) )
| ~ sP7
| ~ in(set_union2(X0,sK114(sK64)),sK64) ),
inference(superposition,[status(thm)],[c_156747,c_150112]) ).
tcf(c_160214,plain,
! [X0: $i] :
( ( set_union2(X0,sK72(sK64)) = sK72(sK64) )
| ~ iPr_def_18
| ~ sP7
| ~ in(set_union2(X0,sK72(sK64)),sK64) ),
inference(superposition,[status(thm)],[c_156747,c_151580]) ).
tcf(c_160229,plain,
! [X0: $i] : ~ proper_subset(X0,sK199(powerset(X0))),
inference(superposition,[status(thm)],[c_157334,c_472]) ).
tcf(c_160230,plain,
! [X0: $i] :
( in(sK140,sK199(powerset(X0)))
| ( X0 = sK140 )
| ( sK125(subset_complement(X0,sK199(powerset(X0)))) = sK140 )
| ~ element(sK140,X0) ),
inference(superposition,[status(thm)],[c_157334,c_145539]) ).
tcf(c_160231,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,sK199(powerset(X1)))),sK199(powerset(X1)))
| ( sK199(powerset(X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_157334,c_1058]) ).
tcf(c_160232,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,sK199(powerset(X1))),sK199(powerset(X1)))
| ( sK199(powerset(X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_157334,c_1057]) ).
tcf(c_160233,plain,
! [X0: $i] :
( in(sK128(sK199(powerset(X0))),sK199(powerset(X0)))
| ( sK199(powerset(X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_157334,c_369]) ).
tcf(c_160234,plain,
! [X0: $i] :
( ordinal(sK128(sK199(powerset(X0))))
| ( sK199(powerset(X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_157334,c_371]) ).
tcf(c_160235,plain,
! [X0: $i] : set_difference(sK199(powerset(X0)),X0) = sK140,
inference(superposition,[status(thm)],[c_157334,c_386]) ).
tcf(c_160236,plain,
! [X0: $i] :
( ( sK199(powerset(unordered_pair(X0,X0))) = sK140 )
| ( sK199(powerset(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_157334,c_397]) ).
tcf(c_160237,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(sK199(powerset(X1))),X0)
| ( sK199(powerset(X1)) = sK140 )
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,sK199(powerset(X1))) ),
inference(superposition,[status(thm)],[c_157334,c_370]) ).
tcf(c_160238,plain,
sK199(powerset(sK140)) = sK140,
inference(superposition,[status(thm)],[c_157334,c_403]) ).
tcf(c_160242,plain,
( ( sK199(powerset(powerset(sK140))) = sK140 )
| ( sK199(powerset(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_157334,c_144406]) ).
tcf(c_160296,plain,
! [X0: $i] : disjoint(set_difference(sK199(powerset(X0)),X0),sK199(powerset(X0))),
inference(superposition,[status(thm)],[c_160235,c_146330]) ).
tcf(c_160298,plain,
! [X0: $i] : set_difference(sK140,sK199(powerset(X0))) = sK140,
inference(superposition,[status(thm)],[c_160235,c_146010]) ).
tcf(c_160299,plain,
! [X0: $i] : subset(sK140,sK199(powerset(X0))),
inference(superposition,[status(thm)],[c_160235,c_383]) ).
tcf(c_160300,plain,
! [X0: $i] :
( disjoint(sK199(powerset(X0)),X0)
| ( set_difference(sK199(powerset(X0)),sK140) != sK140 ) ),
inference(superposition,[status(thm)],[c_160235,c_625]) ).
tcf(c_160304,plain,
! [X0: $i] : disjoint(sK140,sK199(powerset(X0))),
inference(light_normalisation,[status(thm)],[c_160296,c_160235]) ).
tcf(c_160315,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK128(sK199(powerset(X0))))
| ( sK199(powerset(X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_160234,c_833]) ).
tcf(c_160316,plain,
! [X0: $i] :
( epsilon_connected(sK128(sK199(powerset(X0))))
| ( sK199(powerset(X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_160234,c_1050]) ).
tcf(c_160317,plain,
! [X0: $i] :
( epsilon_transitive(sK128(sK199(powerset(X0))))
| ( sK199(powerset(X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_160234,c_1049]) ).
tcf(c_160333,plain,
! [X0: $i] :
( disjoint(sK199(powerset(X0)),X0)
| ( sK199(powerset(X0)) != sK140 ) ),
inference(demodulation,[status(thm)],[c_160300,c_675]) ).
tcf(c_160340,plain,
disjoint(sK199(powerset(sK140)),sK140),
inference(superposition,[status(thm)],[c_160238,c_160333]) ).
tcf(c_160495,plain,
! [X0: $i] :
( in(sK128(sK128(sK199(powerset(X0)))),sK128(sK199(powerset(X0))))
| ( sK199(powerset(X0)) = sK140 )
| ( sK128(sK199(powerset(X0))) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(union(sK199(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_160233,c_154063]) ).
tcf(c_160496,plain,
! [X0: $i] :
( ( sK199(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(sK199(powerset(X0)),sK128(sK199(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_160233,c_527]) ).
tcf(c_160497,plain,
! [X0: $i] :
( ordinal(sK128(sK128(sK199(powerset(X0)))))
| ( sK199(powerset(X0)) = sK140 )
| ( sK128(sK199(powerset(X0))) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(union(sK199(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_160233,c_154064]) ).
tcf(c_160498,plain,
! [X0: $i] :
( in(sK142(sK128(sK199(powerset(X0)))),sK128(sK199(powerset(X0))))
| ( sK199(powerset(X0)) = sK140 )
| ( sK125(sK199(powerset(X0))) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_160233,c_154131]) ).
tcf(c_160499,plain,
! [X0: $i] :
( ( sK199(powerset(X0)) = sK140 )
| ( set_difference(sK128(sK199(powerset(X0))),union(sK199(powerset(X0)))) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_160233,c_154065]) ).
tcf(c_160500,plain,
! [X0: $i] :
( in(sK142(sK199(powerset(X0))),sK199(powerset(X0)))
| ( sK199(powerset(X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_160233,c_522]) ).
tcf(c_160501,plain,
! [X0: $i] :
( ( sK199(powerset(X0)) = sK140 )
| ( sK125(sK199(powerset(X0))) = sK140 )
| ~ ordinal(X0)
| ~ empty(sK128(sK199(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_160233,c_150230]) ).
tcf(c_160502,plain,
! [X0: $i] :
( ( sK199(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ empty(sK199(powerset(X0))) ),
inference(superposition,[status(thm)],[c_160233,c_787]) ).
tcf(c_160503,plain,
! [X0: $i] :
( element(sK128(sK199(powerset(X0))),sK199(powerset(X0)))
| ( sK199(powerset(X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_160233,c_526]) ).
tcf(c_160542,plain,
! [X0: $i] :
( ( sK125(sK198(sK358)) = sK140 )
| ( apply(sK126(sK198(sK358)),X0) = sK140 )
| ~ function(sK126(sK198(sK358)))
| ~ relation(sK126(sK198(sK358)))
| ~ in(sK198(sK358),X0) ),
inference(superposition,[status(thm)],[c_147349,c_155600]) ).
tcf(c_160543,plain,
( function(sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ~ empty(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_147195]) ).
tcf(c_160544,plain,
( finite(sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ~ empty(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_147193]) ).
tcf(c_160545,plain,
( epsilon_transitive(sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ~ empty(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_147192]) ).
tcf(c_160546,plain,
( epsilon_connected(sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ~ empty(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_147191]) ).
tcf(c_160547,plain,
( ordinal(sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ~ empty(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_147190]) ).
tcf(c_160548,plain,
( one_to_one(sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ~ empty(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_147189]) ).
tcf(c_160549,plain,
! [X0: $i] :
( ( sK125(sK198(sK358)) = sK140 )
| ( apply(sK126(sK198(sK358)),X0) = sK140 )
| ~ empty(sK198(sK358))
| ~ relation(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_150772]) ).
tcf(c_160550,plain,
! [X0: $i] :
( element(X0,sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ( apply(sK126(sK198(sK358)),X0) = sK140 )
| ~ function(sK126(sK198(sK358)))
| ~ relation(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_148552]) ).
tcf(c_160551,plain,
( relation(sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ~ empty(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_642]) ).
tcf(c_160552,plain,
( empty(sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ~ empty(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_641]) ).
tcf(c_160553,plain,
! [X0: $i] :
( in(X0,sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ( apply(sK126(sK198(sK358)),X0) = sK140 )
| ~ function(sK126(sK198(sK358)))
| ~ relation(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_906]) ).
tcf(c_160554,plain,
( ( sK125(sK198(sK358)) = sK140 )
| ( relation_rng(sK126(sK198(sK358))) = sK140 )
| ~ relation(sK126(sK198(sK358)))
| ( sK198(sK358) != sK140 ) ),
inference(superposition,[status(thm)],[c_147349,c_478]) ).
tcf(c_160555,plain,
( ( sK126(sK198(sK358)) = sK140 )
| ( sK125(sK198(sK358)) = sK140 )
| ~ relation(sK126(sK198(sK358)))
| ( sK198(sK358) != sK140 ) ),
inference(superposition,[status(thm)],[c_147349,c_475]) ).
tcf(c_160615,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(sK195(X0,X1))
| ~ are_equipotent(X0,X1)
| ~ well_ordering(sK195(X0,X1)) ),
inference(superposition,[status(thm)],[c_84692,c_574]) ).
tcf(c_160616,plain,
! [X0: $i,X1: $i] :
( connected(sK195(X0,X1))
| ~ are_equipotent(X0,X1)
| ~ well_ordering(sK195(X0,X1)) ),
inference(superposition,[status(thm)],[c_84692,c_573]) ).
tcf(c_160617,plain,
! [X0: $i,X1: $i] :
( antisymmetric(sK195(X0,X1))
| ~ are_equipotent(X0,X1)
| ~ well_ordering(sK195(X0,X1)) ),
inference(superposition,[status(thm)],[c_84692,c_572]) ).
tcf(c_160618,plain,
! [X0: $i,X1: $i] :
( transitive(sK195(X0,X1))
| ~ are_equipotent(X0,X1)
| ~ well_ordering(sK195(X0,X1)) ),
inference(superposition,[status(thm)],[c_84692,c_571]) ).
tcf(c_160619,plain,
! [X0: $i,X1: $i] :
( reflexive(sK195(X0,X1))
| ~ are_equipotent(X0,X1)
| ~ well_ordering(sK195(X0,X1)) ),
inference(superposition,[status(thm)],[c_84692,c_570]) ).
tcf(c_160620,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_dom_restriction(sK195(X0,X1),X2),sK195(X0,X1)) = sK140 )
| ~ are_equipotent(X0,X1) ),
inference(superposition,[status(thm)],[c_84692,c_153993]) ).
tcf(c_160621,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng_restriction(X2,sK195(X0,X1)),sK195(X0,X1)) = sK140 )
| ~ are_equipotent(X0,X1) ),
inference(superposition,[status(thm)],[c_84692,c_152219]) ).
tcf(c_160655,plain,
! [X0: $i,X1: $i] :
( ( apply(sK195(X0,X1),sK300(relation_dom(sK195(X0,X1)))) = sK140 )
| ~ are_equipotent(X0,X1)
| ~ relation(sK195(X0,X1)) ),
inference(superposition,[status(thm)],[c_84694,c_156990]) ).
tcf(c_160656,plain,
! [X0: $i,X1: $i] :
( ( apply(sK195(X0,X1),sK116(relation_dom(sK195(X0,X1)))) = sK140 )
| ~ are_equipotent(X0,X1)
| ~ relation(sK195(X0,X1)) ),
inference(superposition,[status(thm)],[c_84694,c_156955]) ).
tcf(c_160657,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(relation_dom(sK195(X0,X1))) = sK140 )
| ( apply(sK195(X0,X1),X2) = sK140 )
| ~ empty(X2)
| ~ are_equipotent(X0,X1)
| ~ relation(sK195(X0,X1)) ),
inference(superposition,[status(thm)],[c_84694,c_150502]) ).
tcf(c_160658,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(sK195(X0,X1))) = sK140 )
| ( apply(sK195(X0,X1),sK140) = sK140 )
| ~ are_equipotent(X0,X1)
| ~ relation(sK195(X0,X1)) ),
inference(superposition,[status(thm)],[c_84694,c_145538]) ).
tcf(c_160685,plain,
! [X0: $i,X1: $i] :
( in(sK128(sK49(X0,X1)),sK49(X0,X1))
| ( sK49(X0,X1) = sK140 )
| ~ ordinal(union(X0))
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_154063]) ).
tcf(c_160686,plain,
! [X0: $i,X1: $i] :
( ~ sP2(X0,X1)
| ~ in(X0,sK49(X0,X1)) ),
inference(superposition,[status(thm)],[c_98,c_527]) ).
tcf(c_160687,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(sK49(X0,X1)))
| ( sK49(X0,X1) = sK140 )
| ~ ordinal(union(X0))
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_154064]) ).
tcf(c_160688,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK49(X0,X1)),sK49(X0,X1))
| ( sK125(X0) = sK140 )
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_154131]) ).
tcf(c_160689,plain,
! [X0: $i,X1: $i] :
( ( set_difference(sK49(X0,X1),union(X0)) = sK140 )
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_154065]) ).
tcf(c_160690,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_522]) ).
tcf(c_160691,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ~ sP2(X0,X1)
| ~ empty(sK49(X0,X1)) ),
inference(superposition,[status(thm)],[c_98,c_150230]) ).
tcf(c_160692,plain,
! [X0: $i,X1: $i] :
( ~ empty(X0)
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_787]) ).
tcf(c_160693,plain,
! [X0: $i,X1: $i] :
( element(sK49(X0,X1),X0)
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_526]) ).
tcf(c_160694,plain,
! [X0: $i,X1: $i] :
( in(sK49(sK92(X0),X1),X0)
| ~ sP2(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_98,c_198]) ).
tcf(c_160695,plain,
! [X0: $i,X1: $i] :
( ordinal(sK49(sK92(X0),X1))
| ~ sP2(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_98,c_199]) ).
tcf(c_160696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK49(relation_inverse_image(X0,X1),X2)),X1)
| ( X4 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ sP2(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_98,c_425]) ).
tcf(c_160697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK49(relation_inverse_image(X0,X1),X2),X3)
| ( X4 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ sP2(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_98,c_424]) ).
tcf(c_160698,plain,
! [X0: $i] : ~ sP2(sK140,X0),
inference(superposition,[status(thm)],[c_98,c_580]) ).
tcf(c_160699,plain,
! [X0: $i,X1: $i] :
( subset(sK49(powerset(X0),X1),X0)
| ~ sP2(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_98,c_662]) ).
tcf(c_160700,plain,
! [X0: $i,X1: $i] :
( sP29
| ordinal(sK49(sK248(X0),X1))
| ~ sP2(sK248(X0),X1) ),
inference(superposition,[status(thm)],[c_98,c_808]) ).
tcf(c_160772,plain,
! [X0: $i] :
( subset(X0,omega)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_158067,c_513]) ).
tcf(c_160774,plain,
( subset(sK169(omega),omega)
| ( sK140 = omega ) ),
inference(superposition,[status(thm)],[c_158067,c_154806]) ).
tcf(c_160775,plain,
( ( sK140 = omega )
| ( set_difference(sK169(omega),omega) = sK140 ) ),
inference(superposition,[status(thm)],[c_158067,c_154516]) ).
tcf(c_160787,plain,
! [X0: $i] :
( subset(X0,sK281)
| ~ in(X0,sK281) ),
inference(superposition,[status(thm)],[c_158068,c_513]) ).
tcf(c_160789,plain,
( subset(sK169(sK281),sK281)
| ( sK140 = sK281 ) ),
inference(superposition,[status(thm)],[c_158068,c_154806]) ).
tcf(c_160790,plain,
( ( sK140 = sK281 )
| ( set_difference(sK169(sK281),sK281) = sK140 ) ),
inference(superposition,[status(thm)],[c_158068,c_154516]) ).
tcf(c_160830,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ( apply(sK126(sK115(X0)),X1) = sK140 )
| ~ function(sK126(sK115(X0)))
| ~ relation(sK126(sK115(X0)))
| ~ in(sK115(X0),X1) ),
inference(superposition,[status(thm)],[c_153342,c_155600]) ).
tcf(c_160832,plain,
! [X0: $i] :
( finite(sK115(X0))
| ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ~ empty(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_147193]) ).
tcf(c_160833,plain,
! [X0: $i] :
( epsilon_transitive(sK115(X0))
| ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ~ empty(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_147192]) ).
tcf(c_160834,plain,
! [X0: $i] :
( epsilon_connected(sK115(X0))
| ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ~ empty(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_147191]) ).
tcf(c_160835,plain,
! [X0: $i] :
( ordinal(sK115(X0))
| ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ~ empty(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_147190]) ).
tcf(c_160836,plain,
! [X0: $i] :
( one_to_one(sK115(X0))
| ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ~ empty(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_147189]) ).
tcf(c_160837,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ( apply(sK126(sK115(X0)),X1) = sK140 )
| ~ empty(sK115(X0))
| ~ relation(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_150772]) ).
tcf(c_160838,plain,
! [X0: $i,X1: $i] :
( element(X1,sK115(X0))
| ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ( apply(sK126(sK115(X0)),X1) = sK140 )
| ~ function(sK126(sK115(X0)))
| ~ relation(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_148552]) ).
tcf(c_160840,plain,
! [X0: $i] :
( empty(sK115(X0))
| ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ~ empty(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_641]) ).
tcf(c_160841,plain,
! [X0: $i,X1: $i] :
( in(X1,sK115(X0))
| ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ( apply(sK126(sK115(X0)),X1) = sK140 )
| ~ function(sK126(sK115(X0)))
| ~ relation(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_906]) ).
tcf(c_160842,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ( relation_rng(sK126(sK115(X0))) = sK140 )
| ~ relation(sK126(sK115(X0)))
| ( sK115(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_153342,c_478]) ).
tcf(c_160843,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK126(sK115(X0)) = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ~ relation(sK126(sK115(X0)))
| ( sK115(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_153342,c_475]) ).
tcf(c_160908,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ( apply(sK126(identity_relation(X0)),X1) = sK140 )
| ~ function(sK126(identity_relation(X0)))
| ~ relation(sK126(identity_relation(X0)))
| ~ in(identity_relation(X0),X1) ),
inference(superposition,[status(thm)],[c_153519,c_155600]) ).
tcf(c_160910,plain,
! [X0: $i] :
( finite(identity_relation(X0))
| ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ~ empty(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_147193]) ).
tcf(c_160911,plain,
! [X0: $i] :
( epsilon_transitive(identity_relation(X0))
| ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ~ empty(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_147192]) ).
tcf(c_160912,plain,
! [X0: $i] :
( epsilon_connected(identity_relation(X0))
| ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ~ empty(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_147191]) ).
tcf(c_160913,plain,
! [X0: $i] :
( ordinal(identity_relation(X0))
| ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ~ empty(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_147190]) ).
tcf(c_160914,plain,
! [X0: $i] :
( one_to_one(identity_relation(X0))
| ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ~ empty(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_147189]) ).
tcf(c_160915,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ( apply(sK126(identity_relation(X0)),X1) = sK140 )
| ~ empty(identity_relation(X0))
| ~ relation(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_150772]) ).
tcf(c_160916,plain,
! [X0: $i,X1: $i] :
( element(X1,identity_relation(X0))
| ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ( apply(sK126(identity_relation(X0)),X1) = sK140 )
| ~ function(sK126(identity_relation(X0)))
| ~ relation(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_148552]) ).
tcf(c_160918,plain,
! [X0: $i] :
( empty(identity_relation(X0))
| ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ~ empty(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_641]) ).
tcf(c_160919,plain,
! [X0: $i,X1: $i] :
( in(X1,identity_relation(X0))
| ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ( apply(sK126(identity_relation(X0)),X1) = sK140 )
| ~ function(sK126(identity_relation(X0)))
| ~ relation(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_906]) ).
tcf(c_160920,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_rng(sK126(identity_relation(X0))) = sK140 )
| ~ relation(sK126(identity_relation(X0)))
| ( identity_relation(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_153519,c_478]) ).
tcf(c_160921,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK126(identity_relation(X0)) = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ~ relation(sK126(identity_relation(X0)))
| ( identity_relation(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_153519,c_475]) ).
tcf(c_161019,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ( apply(sK115(X0),X1) = sK140 )
| ~ function(sK115(X0))
| ~ relation(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_154130]) ).
tcf(c_161020,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_154130]) ).
tcf(c_161021,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_154130]) ).
tcf(c_161022,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ~ function(sK126(X0))
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_154130]) ).
tcf(c_161024,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ( apply(identity_relation(X0),X1) = sK140 )
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_154130]) ).
tcf(c_161026,plain,
! [X0: $i] :
( in(sK142(sK241),sK241)
| ( sK125(sK241) = sK140 )
| ( apply(sK126(sK241),X0) = sK140 )
| ~ function(sK126(sK241))
| ~ relation(sK126(sK241)) ),
inference(superposition,[status(thm)],[c_144638,c_154130]) ).
tcf(c_161027,plain,
! [X0: $i] :
( in(sK142(sK242),sK242)
| ( sK125(sK242) = sK140 )
| ( apply(sK126(sK242),X0) = sK140 )
| ~ function(sK126(sK242))
| ~ relation(sK126(sK242)) ),
inference(superposition,[status(thm)],[c_144641,c_154130]) ).
tcf(c_161028,plain,
! [X0: $i] :
( in(sK142(sK303),sK303)
| ( sK125(sK303) = sK140 )
| ( apply(sK126(sK303),X0) = sK140 )
| ~ function(sK126(sK303))
| ~ relation(sK126(sK303)) ),
inference(superposition,[status(thm)],[c_144647,c_154130]) ).
tcf(c_161029,plain,
! [X0: $i] :
( in(sK142(sK313),sK313)
| ( sK125(sK313) = sK140 )
| ( apply(sK126(sK313),X0) = sK140 )
| ~ function(sK126(sK313))
| ~ relation(sK126(sK313)) ),
inference(superposition,[status(thm)],[c_144797,c_154130]) ).
tcf(c_161030,plain,
! [X0: $i] :
( in(sK142(sK346),sK346)
| ( sK125(sK346) = sK140 )
| ( apply(sK126(sK346),X0) = sK140 )
| ~ function(sK126(sK346))
| ~ relation(sK126(sK346)) ),
inference(superposition,[status(thm)],[c_144944,c_154130]) ).
tcf(c_161031,plain,
! [X0: $i] :
( in(sK142(sK358),sK358)
| ( sK125(sK358) = sK140 )
| ( apply(sK126(sK358),X0) = sK140 )
| ~ function(sK126(sK358))
| ~ relation(sK126(sK358)) ),
inference(superposition,[status(thm)],[c_144947,c_154130]) ).
tcf(c_161033,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK142(set_union2(X0,X1)),set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( apply(sK126(set_union2(X0,X1)),X2) = sK140 )
| ~ function(sK126(set_union2(X0,X1)))
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_154130]) ).
tcf(c_161034,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK142(set_union2(X0,X1)),set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( apply(sK126(set_union2(X0,X1)),X2) = sK140 )
| ~ function(sK126(set_union2(X0,X1)))
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_154130]) ).
tcf(c_161035,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK198(X0)),sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_154130]) ).
tcf(c_161036,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK198(X0)),sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_154130]) ).
tcf(c_161037,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK198(powerset(X0))),sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ( apply(sK126(sK198(powerset(X0))),X1) = sK140 )
| ~ function(sK126(sK198(powerset(X0))))
| ~ relation(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_154130]) ).
tcf(c_161038,plain,
! [X0: $i] :
( in(sK142(sK198(sK241)),sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ( apply(sK126(sK198(sK241)),X0) = sK140 )
| ~ function(sK126(sK198(sK241)))
| ~ relation(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_154130]) ).
tcf(c_161039,plain,
! [X0: $i] :
( in(sK142(sK198(sK242)),sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ( apply(sK126(sK198(sK242)),X0) = sK140 )
| ~ function(sK126(sK198(sK242)))
| ~ relation(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_154130]) ).
tcf(c_161040,plain,
! [X0: $i] :
( in(sK142(sK198(omega)),sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ( apply(sK126(sK198(omega)),X0) = sK140 )
| ~ function(sK126(sK198(omega)))
| ~ relation(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_154130]) ).
tcf(c_161041,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK142(sK198(unordered_pair(X0,X1))),sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ( apply(sK126(sK198(unordered_pair(X0,X1))),X2) = sK140 )
| ~ function(sK126(sK198(unordered_pair(X0,X1))))
| ~ relation(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_154130]) ).
tcf(c_161042,plain,
! [X0: $i] :
( in(sK142(sK198(sK303)),sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ( apply(sK126(sK198(sK303)),X0) = sK140 )
| ~ function(sK126(sK198(sK303)))
| ~ relation(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_154130]) ).
tcf(c_161043,plain,
! [X0: $i] :
( in(sK142(sK198(sK313)),sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ( apply(sK126(sK198(sK313)),X0) = sK140 )
| ~ function(sK126(sK198(sK313)))
| ~ relation(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_154130]) ).
tcf(c_161044,plain,
! [X0: $i] :
( in(sK142(sK198(sK346)),sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ( apply(sK126(sK198(sK346)),X0) = sK140 )
| ~ function(sK126(sK198(sK346)))
| ~ relation(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_154130]) ).
tcf(c_161045,plain,
! [X0: $i] :
( in(sK142(sK198(sK358)),sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ( apply(sK126(sK198(sK358)),X0) = sK140 )
| ~ function(sK126(sK198(sK358)))
| ~ relation(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_154130]) ).
tcf(c_161046,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK302(X0)),sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_154130]) ).
tcf(c_161049,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK115(X0)),sK115(X0))
| ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ( apply(sK126(sK115(X0)),X1) = sK140 )
| ~ function(sK126(sK115(X0)))
| ~ relation(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_154130]) ).
tcf(c_161050,plain,
! [X0: $i,X1: $i] :
( in(sK142(identity_relation(X0)),identity_relation(X0))
| ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ( apply(sK126(identity_relation(X0)),X1) = sK140 )
| ~ function(sK126(identity_relation(X0)))
| ~ relation(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_154130]) ).
tcf(c_161051,plain,
! [X0: $i,X1: $i] :
( in(sK128(sK142(relation_dom(X0))),sK142(relation_dom(X0)))
| ( sK142(relation_dom(X0)) = sK140 )
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ ordinal(union(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_154130,c_154063]) ).
tcf(c_161052,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),sK142(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_154130,c_527]) ).
tcf(c_161053,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(sK142(relation_dom(X0))))
| ( sK142(relation_dom(X0)) = sK140 )
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ ordinal(union(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_154130,c_154064]) ).
tcf(c_161054,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK142(relation_dom(X0))),sK142(relation_dom(X0)))
| ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_154130,c_154131]) ).
tcf(c_161055,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ( set_difference(sK142(relation_dom(X0)),union(relation_dom(X0))) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_154130,c_154065]) ).
tcf(c_161057,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(sK142(relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_154130,c_150230]) ).
tcf(c_161059,plain,
! [X0: $i,X1: $i] :
( element(sK142(relation_dom(X0)),relation_dom(X0))
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_154130,c_526]) ).
tcf(c_161068,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ( apply(identity_relation(X0),X1) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_161024,c_1100,c_1101]) ).
tcf(c_161071,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ( apply(sK115(X0),X1) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_161019,c_250,c_249]) ).
tcf(c_161371,plain,
( ( sK199(powerset(powerset(sK140))) = powerset(sK140) )
| ( sK199(powerset(unordered_pair(sK140,sK140))) = sK140 ) ),
inference(superposition,[status(thm)],[c_314,c_160236]) ).
tcf(c_161372,plain,
! [X0: $i] :
( element(unordered_pair(X0,X0),powerset(unordered_pair(X0,X0)))
| ( sK199(powerset(unordered_pair(X0,X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_160236,c_696]) ).
tcf(c_161373,plain,
! [X0: $i] :
( in(sK128(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ( sK199(powerset(unordered_pair(X0,X0))) = sK140 )
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_160236,c_160233]) ).
tcf(c_161375,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ( sK199(powerset(unordered_pair(X0,X0))) = sK140 )
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_160236,c_160234]) ).
tcf(c_161376,plain,
! [X0: $i] :
( ( sK199(powerset(unordered_pair(X0,X0))) = sK140 )
| ( set_difference(unordered_pair(X0,X0),unordered_pair(X0,X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_160236,c_160235]) ).
tcf(c_161377,plain,
! [X0: $i] :
( subset(unordered_pair(X0,X0),unordered_pair(X0,X0))
| ( sK199(powerset(unordered_pair(X0,X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_160236,c_157334]) ).
tcf(c_161395,plain,
! [X0: $i] :
( ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ proper_subset(X0,omega) ),
inference(superposition,[status(thm)],[c_151975,c_472]) ).
tcf(c_161397,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,omega)),omega)
| ( sK140 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X1)) = sK140 )
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_151975,c_1058]) ).
tcf(c_161398,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,omega),omega)
| ( sK140 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X1)) = sK140 )
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_151975,c_1057]) ).
tcf(c_161399,plain,
! [X0: $i] :
( in(sK128(omega),omega)
| ( sK140 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151975,c_369]) ).
tcf(c_161400,plain,
! [X0: $i] :
( ordinal(sK128(omega))
| ( sK140 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151975,c_371]) ).
tcf(c_161401,plain,
! [X0: $i] :
( ( set_difference(omega,X0) = sK140 )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151975,c_386]) ).
tcf(c_161402,plain,
! [X0: $i] :
( ( sK140 = omega )
| ( unordered_pair(X0,X0) = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),unordered_pair(X0,X0))) = sK140 )
| ~ being_limit_ordinal(unordered_pair(X0,X0))
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_151975,c_397]) ).
tcf(c_161403,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(omega),X0)
| ( sK140 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X1)) = sK140 )
| ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_151975,c_370]) ).
tcf(c_161404,plain,
( ( sK140 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),sK140)) = sK140 )
| ~ being_limit_ordinal(sK140)
| ~ ordinal(sK140) ),
inference(superposition,[status(thm)],[c_151975,c_403]) ).
tcf(c_161406,plain,
( in(sK63(omega),omega)
| ( sK140 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),powerset(sK62))) = sK140 )
| ~ iPr_def_21
| ~ being_limit_ordinal(powerset(sK62))
| ~ ordinal(powerset(sK62)) ),
inference(superposition,[status(thm)],[c_151975,c_156787]) ).
tcf(c_161407,plain,
! [X0: $i] :
( in(sK119(omega),omega)
| ( sK140 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),powerset(X0))) = sK140 )
| ~ finite(X0)
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_151975,c_156797]) ).
tcf(c_161408,plain,
( in(sK262(omega),omega)
| ( sK140 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),powerset(sK261))) = sK140 )
| ~ iPr_def_15
| ~ being_limit_ordinal(powerset(sK261))
| ~ ordinal(powerset(sK261)) ),
inference(superposition,[status(thm)],[c_151975,c_156803]) ).
tcf(c_161409,plain,
( ( sK140 = omega )
| ( powerset(sK140) = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),powerset(sK140))) = sK140 )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_151975,c_144406]) ).
tcf(c_161410,plain,
( ( sK140 = omega )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),sK140)) = sK140 )
| ~ being_limit_ordinal(sK140) ),
inference(forward_subsumption_resolution,[status(thm)],[c_161404,c_144282]) ).
tcf(c_161488,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( set_difference(apply(sK126(X1),X0),union(X0)) = sK140 )
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_154509]) ).
tcf(c_161489,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK49(X0,X1)),union(sK49(X0,X1))) = sK140 )
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_154509]) ).
tcf(c_161490,plain,
! [X0: $i] :
( sP3(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK58(X0)),union(sK58(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_122,c_154509]) ).
tcf(c_161495,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,unordered_pair(X0,X0))) = sK140 )
| ( set_difference(apply(sK126(set_union2(X0,unordered_pair(X0,X0))),X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_256,c_154509]) ).
tcf(c_161496,plain,
! [X0: $i] :
( ( sK125(sK116(X0)) = sK140 )
| ( set_difference(apply(sK126(sK116(X0)),X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_272,c_154509]) ).
tcf(c_161497,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,X1) = sK140 )
| ( set_difference(apply(sK126(relation_dom(X0)),X1),union(X1)) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_154509]) ).
tcf(c_161498,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),apply(sK126(X1),X0)),union(apply(sK126(X1),X0))) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2177,c_154509]) ).
tcf(c_161499,plain,
! [X0: $i] :
( ordinal(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK127(X0)),union(sK127(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_367,c_154509]) ).
tcf(c_161500,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK128(X0)),union(sK128(X0))) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_144620,c_154509]) ).
tcf(c_161501,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK130(X0,X1)),union(sK130(X0,X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_400,c_154509]) ).
tcf(c_161502,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK130(X1,X0)),union(sK130(X1,X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_401,c_154509]) ).
tcf(c_161503,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(subset_complement(X1,X0)) = sK140 )
| ( set_difference(apply(sK126(subset_complement(X1,X0)),X2),union(X2)) = sK140 )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5403,c_154509]) ).
tcf(c_161504,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK163(X0)),union(sK163(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_561,c_154509]) ).
tcf(c_161505,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK169(X0)),union(sK169(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_579,c_154509]) ).
tcf(c_161506,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK173(X0)),union(sK173(X0))) = sK140 )
| ~ sP20(X0) ),
inference(superposition,[status(thm)],[c_584,c_154509]) ).
tcf(c_161508,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK193(X0,X1)),union(sK193(X0,X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_657,c_154509]) ).
tcf(c_161509,plain,
! [X0: $i,X1: $i] :
( ( sK125(powerset(X1)) = sK140 )
| ( set_difference(apply(sK126(powerset(X1)),X0),union(X0)) = sK140 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_661,c_154509]) ).
tcf(c_161511,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK263(X0)) = sK140 )
| ( set_difference(apply(sK126(sK263(X0)),sK140),union(sK140)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_154509]) ).
tcf(c_161513,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK268(X0)),union(sK268(X0))) = sK140 )
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_864,c_154509]) ).
tcf(c_161514,plain,
! [X0: $i,X1: $i] :
( ( sK125(unordered_pair(X0,X1)) = sK140 )
| ( set_difference(apply(sK126(unordered_pair(X0,X1)),X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_939,c_154509]) ).
tcf(c_161515,plain,
! [X0: $i,X1: $i] :
( ( sK125(unordered_pair(X0,X1)) = sK140 )
| ( set_difference(apply(sK126(unordered_pair(X0,X1)),X1),union(X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_940,c_154509]) ).
tcf(c_161516,plain,
! [X0: $i] :
( ( sK125(sK300(X0)) = sK140 )
| ( set_difference(apply(sK126(sK300(X0)),X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_965,c_154509]) ).
tcf(c_161517,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK316(X0)),union(sK316(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_1043,c_154509]) ).
tcf(c_161518,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK320(X1,X0)),union(sK320(X1,X0))) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_154509]) ).
tcf(c_161519,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK343(X0)),union(sK343(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_1207,c_154509]) ).
tcf(c_161520,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK344(X0)),union(sK344(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_1208,c_154509]) ).
tcf(c_161521,plain,
( ( sK125(powerset(sK140)) = sK140 )
| ( set_difference(apply(sK126(powerset(sK140)),sK140),union(sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146165,c_154509]) ).
tcf(c_161522,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0)))),union(unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16344,c_154509]) ).
tcf(c_161523,plain,
( ( sK125(sK64) = sK140 )
| ( set_difference(apply(sK126(sK64),sK119(sK64)),union(sK119(sK64))) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_146098,c_154509]) ).
tcf(c_161524,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( set_difference(apply(sK126(X1),sK318(X0,X1)),union(sK318(X0,X1))) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144619,c_154509]) ).
tcf(c_161525,plain,
( sP15
| ( sK125(sK64) = sK140 )
| ( set_difference(apply(sK126(sK64),sK114(sK64)),union(sK114(sK64))) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_145791,c_154509]) ).
tcf(c_161526,plain,
( ( sK125(sK64) = sK140 )
| ( set_difference(apply(sK126(sK64),sK72(sK64)),union(sK72(sK64))) = sK140 )
| ~ iPr_def_19
| ~ sP7 ),
inference(superposition,[status(thm)],[c_145863,c_154509]) ).
tcf(c_161527,plain,
( ( sK125(sK64) = sK140 )
| ( set_difference(apply(sK126(sK64),sK67(sK64)),union(sK67(sK64))) = sK140 )
| ~ sP6
| ~ sP7
| ~ in(sK140,sK66) ),
inference(superposition,[status(thm)],[c_146728,c_154509]) ).
tcf(c_161528,plain,
( ( sK125(sK64) = sK140 )
| ( set_difference(apply(sK126(sK64),sK111(sK64)),union(sK111(sK64))) = sK140 )
| ~ sP15
| ~ sP7
| ~ in(sK140,sK110) ),
inference(superposition,[status(thm)],[c_146738,c_154509]) ).
tcf(c_161529,plain,
( ( sK199(powerset(powerset(sK62))) = sK140 )
| ( sK125(sK199(powerset(powerset(sK62)))) = sK140 )
| ( set_difference(apply(sK126(sK199(powerset(powerset(sK62)))),sK63(sK199(powerset(powerset(sK62))))),union(sK63(sK199(powerset(powerset(sK62)))))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145355,c_154509]) ).
tcf(c_161530,plain,
! [X0: $i] :
( ( sK199(powerset(powerset(X0))) = sK140 )
| ( sK125(sK199(powerset(powerset(X0)))) = sK140 )
| ( set_difference(apply(sK126(sK199(powerset(powerset(X0)))),sK119(sK199(powerset(powerset(X0))))),union(sK119(sK199(powerset(powerset(X0)))))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145365,c_154509]) ).
tcf(c_161531,plain,
( ( sK199(powerset(powerset(sK261))) = sK140 )
| ( sK125(sK199(powerset(powerset(sK261)))) = sK140 )
| ( set_difference(apply(sK126(sK199(powerset(powerset(sK261)))),sK262(sK199(powerset(powerset(sK261))))),union(sK262(sK199(powerset(powerset(sK261)))))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145371,c_154509]) ).
tcf(c_161532,plain,
( ( powerset(sK62) = sK140 )
| ( sK125(powerset(sK62)) = sK140 )
| ( set_difference(apply(sK126(powerset(sK62)),sK63(powerset(sK62))),union(sK63(powerset(sK62)))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145625,c_154509]) ).
tcf(c_161536,plain,
( ( powerset(sK261) = sK140 )
| ( sK125(powerset(sK261)) = sK140 )
| ( set_difference(apply(sK126(powerset(sK261)),sK262(powerset(sK261))),union(sK262(powerset(sK261)))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145641,c_154509]) ).
tcf(c_161539,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X1,X2) = sK140 )
| ( sK125(set_difference(X1,X2)) = sK140 )
| ( set_difference(apply(sK126(set_difference(X1,X2)),sK318(X0,set_difference(X1,X2))),union(sK318(X0,set_difference(X1,X2)))) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_146007,c_154509]) ).
tcf(c_161540,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = sK140 )
| ( sK125(set_difference(X0,X1)) = sK140 )
| ( set_difference(apply(sK126(set_difference(X0,X1)),sK128(set_difference(X0,X1))),union(sK128(set_difference(X0,X1)))) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_146008,c_154509]) ).
tcf(c_161541,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),apply(sK126(X1),sK92(X0))),union(apply(sK126(X1),sK92(X0)))) = sK140 )
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_151774,c_154509]) ).
tcf(c_161542,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( sK92(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK169(sK92(X0))),union(sK169(sK92(X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151778,c_154509]) ).
tcf(c_161544,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK142(X0)),union(sK142(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154138,c_154509]) ).
tcf(c_161546,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,X1) = sK140 )
| ( set_difference(apply(sK126(relation_dom(X0)),sK142(relation_dom(X0))),union(sK142(relation_dom(X0)))) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_154130,c_154509]) ).
tcf(c_161547,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK169(X0)) = sK140 )
| ( set_difference(apply(sK126(sK169(X0)),sK142(sK169(X0))),union(sK142(sK169(X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_154906,c_154509]) ).
tcf(c_161548,plain,
( ( sK125(sK64) = sK140 )
| ( set_difference(apply(sK126(sK64),sK128(sK64)),union(sK128(sK64))) = sK140 )
| ~ sP7
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157842,c_154509]) ).
tcf(c_161550,plain,
! [X0: $i] :
( ( sK199(powerset(X0)) = sK140 )
| ( sK125(sK199(powerset(X0))) = sK140 )
| ( set_difference(apply(sK126(sK199(powerset(X0))),sK128(sK199(powerset(X0)))),union(sK128(sK199(powerset(X0))))) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_160233,c_154509]) ).
tcf(c_161756,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ( sK125(sK169(X0)) = sK140 )
| ( set_difference(apply(sK126(sK169(X0)),sK128(sK169(X0))),union(sK128(sK169(X0)))) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154846,c_154509]) ).
tcf(c_161757,plain,
! [X0: $i] :
( in(sK128(sK128(sK169(X0))),sK128(sK169(X0)))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ( sK128(sK169(X0)) = sK140 )
| ~ ordinal(union(X0))
| ~ ordinal(union(sK169(X0))) ),
inference(superposition,[status(thm)],[c_154846,c_154063]) ).
tcf(c_161758,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ ordinal(union(X0))
| ~ in(sK169(X0),sK128(sK169(X0))) ),
inference(superposition,[status(thm)],[c_154846,c_527]) ).
tcf(c_161759,plain,
! [X0: $i] :
( ordinal(sK128(sK128(sK169(X0))))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ( sK128(sK169(X0)) = sK140 )
| ~ ordinal(union(X0))
| ~ ordinal(union(sK169(X0))) ),
inference(superposition,[status(thm)],[c_154846,c_154064]) ).
tcf(c_161760,plain,
! [X0: $i] :
( in(sK142(sK128(sK169(X0))),sK128(sK169(X0)))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ( sK125(sK169(X0)) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154846,c_154131]) ).
tcf(c_161761,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ( set_difference(sK128(sK169(X0)),union(sK169(X0))) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154846,c_154065]) ).
tcf(c_161762,plain,
! [X0: $i] :
( in(sK142(sK169(X0)),sK169(X0))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154846,c_522]) ).
tcf(c_161763,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ( sK125(sK169(X0)) = sK140 )
| ~ ordinal(union(X0))
| ~ empty(sK128(sK169(X0))) ),
inference(superposition,[status(thm)],[c_154846,c_150230]) ).
tcf(c_161764,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ ordinal(union(X0))
| ~ empty(sK169(X0)) ),
inference(superposition,[status(thm)],[c_154846,c_787]) ).
tcf(c_161765,plain,
! [X0: $i] :
( element(sK128(sK169(X0)),sK169(X0))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154846,c_526]) ).
tcf(c_161837,plain,
! [X0: $i] :
( in(sK318(X0,sK64),sK64)
| ~ is_well_founded_in(X0,powerset(sK140))
| ~ relation(X0)
| ~ sP7 ),
inference(global_subsumption_just,[status(thm)],[c_157676,c_132,c_157676]) ).
tcf(c_161838,plain,
! [X0: $i] :
( in(sK318(X0,sK64),sK64)
| ~ sP7
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(renaming,[status(thm)],[c_161837]) ).
tcf(c_161848,plain,
! [X0: $i] :
( ( sK125(sK64) = sK140 )
| ( set_difference(apply(sK126(sK64),sK318(X0,sK64)),union(sK318(X0,sK64))) = sK140 )
| ~ sP7
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_161838,c_154509]) ).
tcf(c_161849,plain,
! [X0: $i] :
( in(sK128(sK318(X0,sK64)),sK318(X0,sK64))
| ( sK318(X0,sK64) = sK140 )
| ~ sP7
| ~ relation(X0)
| ~ ordinal(union(sK64))
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_161838,c_154063]) ).
tcf(c_161850,plain,
! [X0: $i] :
( ~ sP7
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140))
| ~ in(sK64,sK318(X0,sK64)) ),
inference(superposition,[status(thm)],[c_161838,c_527]) ).
tcf(c_161851,plain,
! [X0: $i] :
( ordinal(sK128(sK318(X0,sK64)))
| ( sK318(X0,sK64) = sK140 )
| ~ sP7
| ~ relation(X0)
| ~ ordinal(union(sK64))
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_161838,c_154064]) ).
tcf(c_161852,plain,
! [X0: $i] :
( in(sK142(sK318(X0,sK64)),sK318(X0,sK64))
| ( sK125(sK64) = sK140 )
| ~ sP7
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_161838,c_154131]) ).
tcf(c_161853,plain,
! [X0: $i] :
( ( set_difference(sK318(X0,sK64),union(sK64)) = sK140 )
| ~ sP7
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_161838,c_154065]) ).
tcf(c_161855,plain,
! [X0: $i] :
( ( sK125(sK64) = sK140 )
| ~ sP7
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140))
| ~ empty(sK318(X0,sK64)) ),
inference(superposition,[status(thm)],[c_161838,c_150230]) ).
tcf(c_161857,plain,
! [X0: $i] :
( element(sK318(X0,sK64),sK64)
| ~ sP7
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_161838,c_526]) ).
tcf(c_161911,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK198(X0)),sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_154130]) ).
tcf(c_161912,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0)))
| ~ in(sK198(X0),X1) ),
inference(superposition,[status(thm)],[c_147733,c_155600]) ).
tcf(c_161913,plain,
! [X0: $i] :
( function(sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_147195]) ).
tcf(c_161914,plain,
! [X0: $i] :
( finite(sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_147193]) ).
tcf(c_161915,plain,
! [X0: $i] :
( epsilon_transitive(sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_147192]) ).
tcf(c_161916,plain,
! [X0: $i] :
( epsilon_connected(sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_147191]) ).
tcf(c_161917,plain,
! [X0: $i] :
( ordinal(sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_147190]) ).
tcf(c_161918,plain,
! [X0: $i] :
( one_to_one(sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_147189]) ).
tcf(c_161919,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ empty(sK198(X0))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_150772]) ).
tcf(c_161920,plain,
! [X0: $i,X1: $i] :
( element(X1,sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_148552]) ).
tcf(c_161921,plain,
! [X0: $i] :
( relation(sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_642]) ).
tcf(c_161922,plain,
! [X0: $i] :
( empty(sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_641]) ).
tcf(c_161923,plain,
! [X0: $i,X1: $i] :
( in(X1,sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( apply(sK126(sK198(X0)),X1) = sK140 )
| ~ function(sK126(sK198(X0)))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_906]) ).
tcf(c_161924,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ( relation_rng(sK126(sK198(X0))) = sK140 )
| ~ relation(sK126(sK198(X0)))
| ( sK198(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147733,c_478]) ).
tcf(c_161925,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK126(sK198(X0)) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ relation(sK126(sK198(X0)))
| ( sK198(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147733,c_475]) ).
tcf(c_162026,plain,
( in(sK128(set_union2(sK62,unordered_pair(sK62,sK62))),set_union2(sK62,unordered_pair(sK62,sK62)))
| ( set_union2(sK62,unordered_pair(sK62,sK62)) = sK140 )
| ~ sP8
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_128,c_154063]) ).
tcf(c_162027,plain,
( ~ sP8
| ~ in(omega,set_union2(sK62,unordered_pair(sK62,sK62))) ),
inference(superposition,[status(thm)],[c_128,c_527]) ).
tcf(c_162028,plain,
( ordinal(sK128(set_union2(sK62,unordered_pair(sK62,sK62))))
| ( set_union2(sK62,unordered_pair(sK62,sK62)) = sK140 )
| ~ sP8
| ~ ordinal(union(omega)) ),
inference(superposition,[status(thm)],[c_128,c_154064]) ).
tcf(c_162030,plain,
( ( set_difference(set_union2(sK62,unordered_pair(sK62,sK62)),union(omega)) = sK140 )
| ~ sP8 ),
inference(superposition,[status(thm)],[c_128,c_154065]) ).
tcf(c_162034,plain,
( element(set_union2(sK62,unordered_pair(sK62,sK62)),omega)
| ~ sP8 ),
inference(superposition,[status(thm)],[c_128,c_526]) ).
tcf(c_162039,plain,
( ( set_difference(set_union2(sK62,unordered_pair(sK62,sK62)),omega) = sK140 )
| ~ sP8 ),
inference(light_normalisation,[status(thm)],[c_162030,c_158067]) ).
tcf(c_162042,plain,
( ordinal(sK128(set_union2(sK62,unordered_pair(sK62,sK62))))
| ( set_union2(sK62,unordered_pair(sK62,sK62)) = sK140 )
| ~ sP8
| ~ ordinal(omega) ),
inference(light_normalisation,[status(thm)],[c_162028,c_158067]) ).
tcf(c_162043,plain,
( ordinal(sK128(set_union2(sK62,unordered_pair(sK62,sK62))))
| ( set_union2(sK62,unordered_pair(sK62,sK62)) = sK140 )
| ~ sP8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_162042,c_849]) ).
tcf(c_162047,plain,
( in(sK128(set_union2(sK62,unordered_pair(sK62,sK62))),set_union2(sK62,unordered_pair(sK62,sK62)))
| ( set_union2(sK62,unordered_pair(sK62,sK62)) = sK140 )
| ~ sP8
| ~ ordinal(omega) ),
inference(light_normalisation,[status(thm)],[c_162026,c_158067]) ).
tcf(c_162048,plain,
( in(sK128(set_union2(sK62,unordered_pair(sK62,sK62))),set_union2(sK62,unordered_pair(sK62,sK62)))
| ( set_union2(sK62,unordered_pair(sK62,sK62)) = sK140 )
| ~ sP8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_162047,c_849]) ).
tcf(c_162179,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(relation_rng_restriction(X1,sK126(X0)),sK126(X0)),relation_rng_restriction(X1,sK126(X0)))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_158780,c_146330]) ).
tcf(c_162181,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( set_difference(sK140,relation_rng_restriction(X0,sK126(X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_158780,c_146010]) ).
tcf(c_162182,plain,
! [X0: $i,X1: $i] :
( subset(sK140,relation_rng_restriction(X1,sK126(X0)))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_158780,c_383]) ).
tcf(c_162183,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_rng_restriction(X0,sK126(X1)),sK126(X1))
| ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng_restriction(X0,sK126(X1)),sK140) != sK140 ) ),
inference(superposition,[status(thm)],[c_158780,c_625]) ).
tcf(c_162184,plain,
! [X0: $i,X1: $i] :
( subset(relation_rng_restriction(X1,sK126(X0)),sK126(X0))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_158780,c_387]) ).
tcf(c_162185,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,sK140),sK140)
| ( X2 = sK140 )
| ( sK125(X2) = sK140 )
| ( set_difference(relation_rng_restriction(X1,sK126(X2)),sK126(X2)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_rng_restriction(X1,sK126(X2))) ),
inference(superposition,[status(thm)],[c_158780,c_146007]) ).
tcf(c_162196,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = sK140 )
| ( sK125(X2) = sK140 )
| ( set_difference(relation_rng_restriction(X1,sK126(X2)),sK126(X2)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_rng_restriction(X1,sK126(X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_162185,c_580]) ).
tcf(c_162229,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ proper_subset(sK126(X0),relation_rng_restriction(X1,sK126(X0))) ),
inference(superposition,[status(thm)],[c_162184,c_472]) ).
tcf(c_162230,plain,
! [X0: $i,X1: $i] :
( in(sK140,relation_rng_restriction(X1,sK126(X0)))
| ( X0 = sK140 )
| ( sK126(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(subset_complement(sK126(X0),relation_rng_restriction(X1,sK126(X0)))) = sK140 )
| ~ element(sK140,sK126(X0)) ),
inference(superposition,[status(thm)],[c_162184,c_145539]) ).
tcf(c_162231,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,relation_rng_restriction(X2,sK126(X1)))),relation_rng_restriction(X2,sK126(X1)))
| ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( relation_rng_restriction(X2,sK126(X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,sK126(X1)) ),
inference(superposition,[status(thm)],[c_162184,c_1058]) ).
tcf(c_162232,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,relation_rng_restriction(X2,sK126(X1))),relation_rng_restriction(X2,sK126(X1)))
| ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( relation_rng_restriction(X2,sK126(X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,sK126(X1)) ),
inference(superposition,[status(thm)],[c_162184,c_1057]) ).
tcf(c_162233,plain,
! [X0: $i,X1: $i] :
( in(sK128(relation_rng_restriction(X1,sK126(X0))),relation_rng_restriction(X1,sK126(X0)))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_rng_restriction(X1,sK126(X0)) = sK140 )
| ~ ordinal(sK126(X0)) ),
inference(superposition,[status(thm)],[c_162184,c_369]) ).
tcf(c_162234,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(relation_rng_restriction(X1,sK126(X0))))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_rng_restriction(X1,sK126(X0)) = sK140 )
| ~ ordinal(sK126(X0)) ),
inference(superposition,[status(thm)],[c_162184,c_371]) ).
tcf(c_162236,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(relation_rng_restriction(X1,sK126(X2))),X0)
| ( X2 = sK140 )
| ( sK125(X2) = sK140 )
| ( relation_rng_restriction(X1,sK126(X2)) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(sK126(X2))
| ~ in(X0,relation_rng_restriction(X1,sK126(X2))) ),
inference(superposition,[status(thm)],[c_162184,c_370]) ).
tcf(c_162283,plain,
! [X0: $i,X1: $i] :
( disjoint(set_difference(relation_dom_restriction(sK126(X0),X1),sK126(X0)),relation_dom_restriction(sK126(X0),X1))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_159254,c_146330]) ).
tcf(c_162285,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(sK140,relation_dom_restriction(sK126(X0),X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_159254,c_146010]) ).
tcf(c_162286,plain,
! [X0: $i,X1: $i] :
( subset(sK140,relation_dom_restriction(sK126(X0),X1))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_159254,c_383]) ).
tcf(c_162287,plain,
! [X0: $i,X1: $i] :
( disjoint(relation_dom_restriction(sK126(X0),X1),sK126(X0))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X0),X1),sK140) != sK140 ) ),
inference(superposition,[status(thm)],[c_159254,c_625]) ).
tcf(c_162288,plain,
! [X0: $i,X1: $i] :
( subset(relation_dom_restriction(sK126(X0),X1),sK126(X0))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_159254,c_387]) ).
tcf(c_162289,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,sK140),sK140)
| ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X1),X2),sK126(X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_dom_restriction(sK126(X1),X2)) ),
inference(superposition,[status(thm)],[c_159254,c_146007]) ).
tcf(c_162300,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(X1),X2),sK126(X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_dom_restriction(sK126(X1),X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_162289,c_580]) ).
tcf(c_162312,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ proper_subset(sK126(X0),relation_dom_restriction(sK126(X0),X1)) ),
inference(superposition,[status(thm)],[c_162288,c_472]) ).
tcf(c_162313,plain,
! [X0: $i,X1: $i] :
( in(sK140,relation_dom_restriction(sK126(X0),X1))
| ( X0 = sK140 )
| ( sK126(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(subset_complement(sK126(X0),relation_dom_restriction(sK126(X0),X1))) = sK140 )
| ~ element(sK140,sK126(X0)) ),
inference(superposition,[status(thm)],[c_162288,c_145539]) ).
tcf(c_162314,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,relation_dom_restriction(sK126(X1),X2))),relation_dom_restriction(sK126(X1),X2))
| ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( relation_dom_restriction(sK126(X1),X2) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,sK126(X1)) ),
inference(superposition,[status(thm)],[c_162288,c_1058]) ).
tcf(c_162315,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,relation_dom_restriction(sK126(X1),X2)),relation_dom_restriction(sK126(X1),X2))
| ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( relation_dom_restriction(sK126(X1),X2) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,sK126(X1)) ),
inference(superposition,[status(thm)],[c_162288,c_1057]) ).
tcf(c_162316,plain,
! [X0: $i,X1: $i] :
( in(sK128(relation_dom_restriction(sK126(X0),X1)),relation_dom_restriction(sK126(X0),X1))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_dom_restriction(sK126(X0),X1) = sK140 )
| ~ ordinal(sK126(X0)) ),
inference(superposition,[status(thm)],[c_162288,c_369]) ).
tcf(c_162317,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(relation_dom_restriction(sK126(X0),X1)))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_dom_restriction(sK126(X0),X1) = sK140 )
| ~ ordinal(sK126(X0)) ),
inference(superposition,[status(thm)],[c_162288,c_371]) ).
tcf(c_162319,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(relation_dom_restriction(sK126(X1),X2)),X0)
| ( X1 = sK140 )
| ( sK125(X1) = sK140 )
| ( relation_dom_restriction(sK126(X1),X2) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(sK126(X1))
| ~ in(X0,relation_dom_restriction(sK126(X1),X2)) ),
inference(superposition,[status(thm)],[c_162288,c_370]) ).
tcf(c_162388,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X1,X0) = sK140 )
| ( sK125(relation_rng_restriction(X1,X0)) = sK140 )
| ( set_difference(apply(sK126(relation_rng_restriction(X1,X0)),sK128(relation_rng_restriction(X1,X0))),union(sK128(relation_rng_restriction(X1,X0)))) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152217,c_154509]) ).
tcf(c_162389,plain,
! [X0: $i,X1: $i] :
( in(sK128(sK128(relation_rng_restriction(X0,X1))),sK128(relation_rng_restriction(X0,X1)))
| ( relation_rng_restriction(X0,X1) = sK140 )
| ( sK128(relation_rng_restriction(X0,X1)) = sK140 )
| ~ ordinal(X1)
| ~ relation(X1)
| ~ ordinal(union(relation_rng_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_152217,c_154063]) ).
tcf(c_162390,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X0,X1) = sK140 )
| ~ ordinal(X1)
| ~ relation(X1)
| ~ in(relation_rng_restriction(X0,X1),sK128(relation_rng_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_152217,c_527]) ).
tcf(c_162391,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(sK128(relation_rng_restriction(X0,X1))))
| ( relation_rng_restriction(X0,X1) = sK140 )
| ( sK128(relation_rng_restriction(X0,X1)) = sK140 )
| ~ ordinal(X1)
| ~ relation(X1)
| ~ ordinal(union(relation_rng_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_152217,c_154064]) ).
tcf(c_162392,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK128(relation_rng_restriction(X1,X0))),sK128(relation_rng_restriction(X1,X0)))
| ( relation_rng_restriction(X1,X0) = sK140 )
| ( sK125(relation_rng_restriction(X1,X0)) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152217,c_154131]) ).
tcf(c_162393,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X1,X0) = sK140 )
| ( set_difference(sK128(relation_rng_restriction(X1,X0)),union(relation_rng_restriction(X1,X0))) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152217,c_154065]) ).
tcf(c_162394,plain,
! [X0: $i,X1: $i] :
( in(sK142(relation_rng_restriction(X1,X0)),relation_rng_restriction(X1,X0))
| ( relation_rng_restriction(X1,X0) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152217,c_522]) ).
tcf(c_162395,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X0,X1) = sK140 )
| ( sK125(relation_rng_restriction(X0,X1)) = sK140 )
| ~ ordinal(X1)
| ~ relation(X1)
| ~ empty(sK128(relation_rng_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_152217,c_150230]) ).
tcf(c_162396,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X0,X1) = sK140 )
| ~ ordinal(X1)
| ~ relation(X1)
| ~ empty(relation_rng_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_152217,c_787]) ).
tcf(c_162397,plain,
! [X0: $i,X1: $i] :
( element(sK128(relation_rng_restriction(X1,X0)),relation_rng_restriction(X1,X0))
| ( relation_rng_restriction(X1,X0) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152217,c_526]) ).
tcf(c_162455,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(X0,X1) = sK140 )
| ( sK125(relation_dom_restriction(X0,X1)) = sK140 )
| ( set_difference(apply(sK126(relation_dom_restriction(X0,X1)),sK128(relation_dom_restriction(X0,X1))),union(sK128(relation_dom_restriction(X0,X1)))) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_153991,c_154509]) ).
tcf(c_162456,plain,
! [X0: $i,X1: $i] :
( in(sK128(sK128(relation_dom_restriction(X0,X1))),sK128(relation_dom_restriction(X0,X1)))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ( sK128(relation_dom_restriction(X0,X1)) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0)
| ~ ordinal(union(relation_dom_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_153991,c_154063]) ).
tcf(c_162457,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0)
| ~ in(relation_dom_restriction(X0,X1),sK128(relation_dom_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_153991,c_527]) ).
tcf(c_162458,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(sK128(relation_dom_restriction(X0,X1))))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ( sK128(relation_dom_restriction(X0,X1)) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0)
| ~ ordinal(union(relation_dom_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_153991,c_154064]) ).
tcf(c_162459,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK128(relation_dom_restriction(X0,X1))),sK128(relation_dom_restriction(X0,X1)))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ( sK125(relation_dom_restriction(X0,X1)) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_153991,c_154131]) ).
tcf(c_162460,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(X0,X1) = sK140 )
| ( set_difference(sK128(relation_dom_restriction(X0,X1)),union(relation_dom_restriction(X0,X1))) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_153991,c_154065]) ).
tcf(c_162461,plain,
! [X0: $i,X1: $i] :
( in(sK142(relation_dom_restriction(X0,X1)),relation_dom_restriction(X0,X1))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_153991,c_522]) ).
tcf(c_162462,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(X0,X1) = sK140 )
| ( sK125(relation_dom_restriction(X0,X1)) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0)
| ~ empty(sK128(relation_dom_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_153991,c_150230]) ).
tcf(c_162463,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0)
| ~ empty(relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_153991,c_787]) ).
tcf(c_162464,plain,
! [X0: $i,X1: $i] :
( element(sK128(relation_dom_restriction(X0,X1)),relation_dom_restriction(X0,X1))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_153991,c_526]) ).
tcf(c_162559,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK263(X0)) = sK140 )
| ( set_difference(apply(sK126(sK263(X0)),sK142(sK263(X0))),union(sK142(sK263(X0)))) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_154142,c_154509]) ).
tcf(c_162560,plain,
! [X0: $i] :
( in(sK128(sK142(sK263(X0))),sK142(sK263(X0)))
| ( X0 = omega )
| ( sK142(sK263(X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0)
| ~ ordinal(union(sK263(X0))) ),
inference(superposition,[status(thm)],[c_154142,c_154063]) ).
tcf(c_162561,plain,
! [X0: $i] :
( ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0)
| ~ in(sK263(X0),sK142(sK263(X0))) ),
inference(superposition,[status(thm)],[c_154142,c_527]) ).
tcf(c_162562,plain,
! [X0: $i] :
( ordinal(sK128(sK142(sK263(X0))))
| ( X0 = omega )
| ( sK142(sK263(X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0)
| ~ ordinal(union(sK263(X0))) ),
inference(superposition,[status(thm)],[c_154142,c_154064]) ).
tcf(c_162564,plain,
! [X0: $i] :
( ( X0 = omega )
| ( set_difference(sK142(sK263(X0)),union(sK263(X0))) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_154142,c_154065]) ).
tcf(c_162568,plain,
! [X0: $i] :
( element(sK142(sK263(X0)),sK263(X0))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_154142,c_526]) ).
tcf(c_162650,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( apply(X0,X1) = sK140 )
| ( set_difference(X1,union(relation_dom(X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_146146,c_154508]) ).
tcf(c_162651,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK96(X0,X1),X2) = sK140 )
| ( set_difference(X2,union(relation_dom(sK96(X0,X1)))) = sK140 )
| ~ sP12(X0,X1)
| ~ relation(sK96(X0,X1)) ),
inference(superposition,[status(thm)],[c_209,c_154508]) ).
tcf(c_162652,plain,
! [X0: $i,X1: $i] :
( sP13(X0)
| ( apply(sK108(X0),X1) = sK140 )
| ( set_difference(X1,union(relation_dom(sK108(X0)))) = sK140 )
| ~ relation(sK108(X0)) ),
inference(superposition,[status(thm)],[c_232,c_154508]) ).
tcf(c_162653,plain,
! [X0: $i,X1: $i] :
( ( apply(sK115(X0),X1) = sK140 )
| ( set_difference(X1,union(relation_dom(sK115(X0)))) = sK140 )
| ~ relation(sK115(X0)) ),
inference(superposition,[status(thm)],[c_250,c_154508]) ).
tcf(c_162654,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),X1) = sK140 )
| ( set_difference(X1,union(relation_dom(sK126(X0)))) = sK140 )
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_356,c_154508]) ).
tcf(c_162655,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),X1) = sK140 )
| ( set_difference(X1,union(relation_dom(identity_relation(X0)))) = sK140 )
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_1100,c_154508]) ).
tcf(c_162656,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK195(X0,X1),X2) = sK140 )
| ( set_difference(X2,union(relation_dom(sK195(X0,X1)))) = sK140 )
| ~ are_equipotent(X0,X1)
| ~ relation(sK195(X0,X1)) ),
inference(superposition,[status(thm)],[c_84694,c_154508]) ).
tcf(c_162657,plain,
! [X0: $i] :
( ( apply(sK240,X0) = sK140 )
| ( set_difference(X0,union(relation_dom(sK240))) = sK140 )
| ~ relation(sK240) ),
inference(superposition,[status(thm)],[c_784,c_154508]) ).
tcf(c_162658,plain,
! [X0: $i,X1: $i] :
( ( apply(sK264(X0),X1) = sK140 )
| ( set_difference(X1,union(relation_dom(sK264(X0)))) = sK140 )
| ~ finite(X0)
| ~ relation(sK264(X0)) ),
inference(superposition,[status(thm)],[c_853,c_154508]) ).
tcf(c_162659,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK312(X0,X1),X2) = sK140 )
| ( set_difference(X2,union(relation_dom(sK312(X0,X1)))) = sK140 )
| ~ relation(sK312(X0,X1)) ),
inference(superposition,[status(thm)],[c_1020,c_154508]) ).
tcf(c_162660,plain,
! [X0: $i] :
( ( apply(sK335,X0) = sK140 )
| ( set_difference(X0,union(relation_dom(sK335))) = sK140 )
| ~ relation(sK335) ),
inference(superposition,[status(thm)],[c_1150,c_154508]) ).
tcf(c_162661,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK347(X0,X1),X2) = sK140 )
| ( set_difference(X2,union(relation_dom(sK347(X0,X1)))) = sK140 )
| ~ relation(sK347(X0,X1)) ),
inference(superposition,[status(thm)],[c_1238,c_154508]) ).
tcf(c_162663,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_dom(X0),X1) = sK140 )
| ( set_difference(X1,union(relation_dom(relation_dom(X0)))) = sK140 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_147195,c_154508]) ).
tcf(c_162664,plain,
! [X0: $i] :
( ( apply(sK335,X0) = sK140 )
| ( set_difference(X0,union(relation_dom(sK335))) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_162660,c_1149]) ).
tcf(c_162667,plain,
! [X0: $i] :
( ( apply(sK240,X0) = sK140 )
| ( set_difference(X0,union(relation_dom(sK240))) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_162657,c_783]) ).
tcf(c_162670,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X0),X1) = sK140 )
| ( set_difference(X1,union(X0)) = sK140 )
| ~ relation(identity_relation(X0)) ),
inference(light_normalisation,[status(thm)],[c_162655,c_489]) ).
tcf(c_162671,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = sK140 )
| ( set_difference(X0,union(X1)) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_162670,c_1101]) ).
tcf(c_162674,plain,
! [X0: $i,X1: $i] :
( ( apply(sK115(X0),X1) = sK140 )
| ( set_difference(X1,union(X0)) = sK140 )
| ~ relation(sK115(X0)) ),
inference(light_normalisation,[status(thm)],[c_162653,c_251]) ).
tcf(c_162675,plain,
! [X0: $i,X1: $i] :
( ( apply(sK115(X1),X0) = sK140 )
| ( set_difference(X0,union(X1)) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_162674,c_249]) ).
tcf(c_162686,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK347(X1,X2),X0) = sK140 )
| ( set_difference(X0,union(relation_dom(sK347(X1,X2)))) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_162661,c_1237]) ).
tcf(c_162689,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(sK312(X1,X2),X0) = sK140 )
| ( set_difference(X0,union(relation_dom(sK312(X1,X2)))) = sK140 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_162659,c_1019]) ).
tcf(c_162736,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK302(X0)),sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_154130]) ).
tcf(c_162737,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0)))
| ~ in(sK302(X0),X1) ),
inference(superposition,[status(thm)],[c_147756,c_155600]) ).
tcf(c_162738,plain,
! [X0: $i] :
( function(sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_147195]) ).
tcf(c_162739,plain,
! [X0: $i] :
( finite(sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_147193]) ).
tcf(c_162740,plain,
! [X0: $i] :
( epsilon_transitive(sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_147192]) ).
tcf(c_162741,plain,
! [X0: $i] :
( epsilon_connected(sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_147191]) ).
tcf(c_162742,plain,
! [X0: $i] :
( ordinal(sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_147190]) ).
tcf(c_162743,plain,
! [X0: $i] :
( one_to_one(sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_147189]) ).
tcf(c_162744,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ empty(sK302(X0))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_150772]) ).
tcf(c_162745,plain,
! [X0: $i,X1: $i] :
( element(X1,sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_148552]) ).
tcf(c_162746,plain,
! [X0: $i] :
( relation(sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_642]) ).
tcf(c_162747,plain,
! [X0: $i] :
( empty(sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_641]) ).
tcf(c_162748,plain,
! [X0: $i,X1: $i] :
( in(X1,sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_906]) ).
tcf(c_162749,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( relation_rng(sK126(sK302(X0))) = sK140 )
| ~ relation(sK126(sK302(X0)))
| ( sK302(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147756,c_478]) ).
tcf(c_162750,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK140 )
| ( sK126(sK302(X0)) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ relation(sK126(sK302(X0)))
| ( sK302(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147756,c_475]) ).
tcf(c_162854,plain,
! [X0: $i] :
( subset(relation_rng(sK140),X0)
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_152224,c_261]) ).
tcf(c_162855,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ proper_subset(X0,relation_rng(relation_rng_restriction(X0,X1))) ),
inference(superposition,[status(thm)],[c_261,c_472]) ).
tcf(c_162856,plain,
! [X0: $i,X1: $i] :
( in(sK140,relation_rng(relation_rng_restriction(X0,X1)))
| ( X0 = sK140 )
| ( sK125(subset_complement(X0,relation_rng(relation_rng_restriction(X0,X1)))) = sK140 )
| ~ relation(X1)
| ~ element(sK140,X0) ),
inference(superposition,[status(thm)],[c_261,c_145539]) ).
tcf(c_162857,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,relation_rng(relation_rng_restriction(X1,X2)))),relation_rng(relation_rng_restriction(X1,X2)))
| ( relation_rng(relation_rng_restriction(X1,X2)) = sK140 )
| ~ relation(X2)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_261,c_1058]) ).
tcf(c_162858,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,relation_rng(relation_rng_restriction(X1,X2))),relation_rng(relation_rng_restriction(X1,X2)))
| ( relation_rng(relation_rng_restriction(X1,X2)) = sK140 )
| ~ relation(X2)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_261,c_1057]) ).
tcf(c_162859,plain,
! [X0: $i,X1: $i] :
( in(sK128(relation_rng(relation_rng_restriction(X1,X0))),relation_rng(relation_rng_restriction(X1,X0)))
| ( relation_rng(relation_rng_restriction(X1,X0)) = sK140 )
| ~ ordinal(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_261,c_369]) ).
tcf(c_162860,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(relation_rng(relation_rng_restriction(X1,X0))))
| ( relation_rng(relation_rng_restriction(X1,X0)) = sK140 )
| ~ ordinal(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_261,c_371]) ).
tcf(c_162861,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,X0)),X1) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_261,c_386]) ).
tcf(c_162862,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(unordered_pair(X1,X1),X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(unordered_pair(X1,X1),X0)) = unordered_pair(X1,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_261,c_397]) ).
tcf(c_162863,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(relation_rng(relation_rng_restriction(X1,X2))),X0)
| ( relation_rng(relation_rng_restriction(X1,X2)) = sK140 )
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(superposition,[status(thm)],[c_261,c_370]) ).
tcf(c_162864,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(sK140,X0)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_261,c_403]) ).
tcf(c_162865,plain,
! [X0: $i] :
( in(sK63(relation_rng(relation_rng_restriction(powerset(sK62),X0))),relation_rng(relation_rng_restriction(powerset(sK62),X0)))
| ( relation_rng(relation_rng_restriction(powerset(sK62),X0)) = sK140 )
| ~ iPr_def_21
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_261,c_156787]) ).
tcf(c_162866,plain,
! [X0: $i,X1: $i] :
( in(sK119(relation_rng(relation_rng_restriction(powerset(X1),X0))),relation_rng(relation_rng_restriction(powerset(X1),X0)))
| ( relation_rng(relation_rng_restriction(powerset(X1),X0)) = sK140 )
| ~ finite(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_261,c_156797]) ).
tcf(c_162867,plain,
! [X0: $i] :
( in(sK262(relation_rng(relation_rng_restriction(powerset(sK261),X0))),relation_rng(relation_rng_restriction(powerset(sK261),X0)))
| ( relation_rng(relation_rng_restriction(powerset(sK261),X0)) = sK140 )
| ~ iPr_def_15
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_261,c_156803]) ).
tcf(c_162868,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(powerset(sK140),X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(powerset(sK140),X0)) = powerset(sK140) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_261,c_144406]) ).
tcf(c_162869,plain,
! [X0: $i] :
( subset(sK140,X0)
| ~ relation(sK140) ),
inference(light_normalisation,[status(thm)],[c_162854,c_471]) ).
tcf(c_162942,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ finite(union(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_513,c_276]) ).
tcf(c_162943,plain,
! [X0: $i,X1: $i] :
( finite(relation_rng(relation_rng_restriction(X1,X0)))
| ~ finite(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_261,c_276]) ).
tcf(c_162944,plain,
! [X0: $i,X1: $i] :
( finite(relation_rng_restriction(X1,X0))
| ~ finite(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_262,c_276]) ).
tcf(c_162947,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ finite(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_498,c_276]) ).
tcf(c_162948,plain,
! [X0: $i,X1: $i] :
( finite(relation_dom_restriction(X0,X1))
| ~ finite(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_504,c_276]) ).
tcf(c_162950,plain,
! [X0: $i] :
( finite(omega)
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ finite(X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151975,c_276]) ).
tcf(c_162951,plain,
( finite(sK64)
| ~ sP7
| ~ finite(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157332,c_276]) ).
tcf(c_162952,plain,
( finite(omega)
| ~ finite(sK116(sK140))
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145175,c_276]) ).
tcf(c_162953,plain,
( finite(omega)
| ~ finite(sK300(sK140))
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145503,c_276]) ).
tcf(c_162954,plain,
! [X0: $i] :
( finite(omega)
| ~ finite(unordered_pair(sK140,X0))
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146170,c_276]) ).
tcf(c_162955,plain,
! [X0: $i] :
( finite(omega)
| ~ finite(unordered_pair(X0,sK140))
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146212,c_276]) ).
tcf(c_162956,plain,
! [X0: $i] :
( finite(sK169(X0))
| ( X0 = sK140 )
| ~ finite(union(X0)) ),
inference(superposition,[status(thm)],[c_154806,c_276]) ).
tcf(c_162957,plain,
! [X0: $i] :
( finite(omega)
| ~ finite(powerset(X0))
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_157465,c_276]) ).
tcf(c_162958,plain,
! [X0: $i,X1: $i] :
( finite(X1)
| ~ finite(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_156747,c_276]) ).
tcf(c_162959,plain,
! [X0: $i] :
( finite(sK199(powerset(X0)))
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_157334,c_276]) ).
tcf(c_162960,plain,
! [X0: $i,X1: $i] :
( finite(relation_rng_restriction(X1,sK126(X0)))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ finite(sK126(X0)) ),
inference(superposition,[status(thm)],[c_162184,c_276]) ).
tcf(c_162961,plain,
! [X0: $i,X1: $i] :
( finite(relation_dom_restriction(sK126(X0),X1))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ finite(sK126(X0)) ),
inference(superposition,[status(thm)],[c_162288,c_276]) ).
tcf(c_162968,plain,
( finite(sK64)
| ~ sP7 ),
inference(forward_subsumption_resolution,[status(thm)],[c_162951,c_145521]) ).
tcf(c_163058,plain,
! [X0: $i] :
( subset(relation_image(sK140,X0),sK140)
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_471,c_282]) ).
tcf(c_163059,plain,
! [X0: $i,X1: $i] :
( subset(relation_image(identity_relation(X0),X1),X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_490,c_282]) ).
tcf(c_163060,plain,
! [X0: $i,X1: $i] :
( finite(relation_image(X0,X1))
| ~ relation(X0)
| ~ finite(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_282,c_276]) ).
tcf(c_163061,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(relation_rng(X0),relation_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_282,c_472]) ).
tcf(c_163062,plain,
! [X0: $i,X1: $i] :
( in(sK140,relation_image(X0,X1))
| ( relation_rng(X0) = sK140 )
| ( sK125(subset_complement(relation_rng(X0),relation_image(X0,X1))) = sK140 )
| ~ relation(X0)
| ~ element(sK140,relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_282,c_145539]) ).
tcf(c_163063,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,relation_image(X1,X2))),relation_image(X1,X2))
| ( relation_image(X1,X2) = sK140 )
| ~ relation(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_282,c_1058]) ).
tcf(c_163064,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,relation_image(X1,X2)),relation_image(X1,X2))
| ( relation_image(X1,X2) = sK140 )
| ~ relation(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_282,c_1057]) ).
tcf(c_163065,plain,
! [X0: $i,X1: $i] :
( in(sK128(relation_image(X0,X1)),relation_image(X0,X1))
| ( relation_image(X0,X1) = sK140 )
| ~ relation(X0)
| ~ ordinal(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_282,c_369]) ).
tcf(c_163066,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(relation_image(X0,X1)))
| ( relation_image(X0,X1) = sK140 )
| ~ relation(X0)
| ~ ordinal(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_282,c_371]) ).
tcf(c_163067,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(X0,X1),relation_rng(X0)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_282,c_386]) ).
tcf(c_163068,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(relation_image(X1,X2)),X0)
| ( relation_image(X1,X2) = sK140 )
| ~ ordinal(X0)
| ~ relation(X1)
| ~ ordinal(relation_rng(X1))
| ~ in(X0,relation_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_282,c_370]) ).
tcf(c_163069,plain,
! [X0: $i] : subset(relation_image(sK140,X0),sK140),
inference(forward_subsumption_resolution,[status(thm)],[c_163058,c_577]) ).
tcf(c_163072,plain,
! [X0: $i,X1: $i] : subset(relation_image(identity_relation(X0),X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_163059,c_1101]) ).
tcf(c_163121,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK115(X0),X1),X0)
| ~ relation(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_296]) ).
tcf(c_163122,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(X0),X1),X0)
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_296]) ).
tcf(c_163123,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(X0),X1),X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147734,c_296]) ).
tcf(c_163124,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(X0),X1),X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_147316,c_296]) ).
tcf(c_163125,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(X0),X1),X0)
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_296]) ).
tcf(c_163126,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(identity_relation(X0),X1),X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_296]) ).
tcf(c_163127,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK140,X0),sK140)
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_470,c_296]) ).
tcf(c_163128,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK241),X0),sK241)
| ( sK125(sK241) = sK140 )
| ~ relation(sK126(sK241)) ),
inference(superposition,[status(thm)],[c_144638,c_296]) ).
tcf(c_163129,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK242),X0),sK242)
| ( sK125(sK242) = sK140 )
| ~ relation(sK126(sK242)) ),
inference(superposition,[status(thm)],[c_144641,c_296]) ).
tcf(c_163130,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK303),X0),sK303)
| ( sK125(sK303) = sK140 )
| ~ relation(sK126(sK303)) ),
inference(superposition,[status(thm)],[c_144647,c_296]) ).
tcf(c_163131,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK313),X0),sK313)
| ( sK125(sK313) = sK140 )
| ~ relation(sK126(sK313)) ),
inference(superposition,[status(thm)],[c_144797,c_296]) ).
tcf(c_163132,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK346),X0),sK346)
| ( sK125(sK346) = sK140 )
| ~ relation(sK126(sK346)) ),
inference(superposition,[status(thm)],[c_144944,c_296]) ).
tcf(c_163133,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK358),X0),sK358)
| ( sK125(sK358) = sK140 )
| ~ relation(sK126(sK358)) ),
inference(superposition,[status(thm)],[c_144947,c_296]) ).
tcf(c_163134,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(sK126(unordered_pair(X0,X1)),X2),unordered_pair(X0,X1))
| ( sK125(unordered_pair(X0,X1)) = sK140 )
| ~ relation(sK126(unordered_pair(X0,X1))) ),
inference(superposition,[status(thm)],[c_146160,c_296]) ).
tcf(c_163135,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(sK126(set_union2(X0,X1)),X2),set_union2(X0,X1))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_296]) ).
tcf(c_163136,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(sK126(set_union2(X0,X1)),X2),set_union2(X0,X1))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_296]) ).
tcf(c_163137,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(sK198(X0)),X1),sK198(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_296]) ).
tcf(c_163138,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(sK198(X0)),X1),sK198(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_296]) ).
tcf(c_163139,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(sK198(X0)),X1),sK198(X0))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_296]) ).
tcf(c_163140,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(sK198(powerset(X0))),X1),sK198(powerset(X0)))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ~ relation(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_296]) ).
tcf(c_163141,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK198(sK241)),X0),sK198(sK241))
| ( sK125(sK198(sK241)) = sK140 )
| ~ relation(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_296]) ).
tcf(c_163142,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK198(sK242)),X0),sK198(sK242))
| ( sK125(sK198(sK242)) = sK140 )
| ~ relation(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_296]) ).
tcf(c_163143,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK198(omega)),X0),sK198(omega))
| ( sK125(sK198(omega)) = sK140 )
| ~ relation(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_296]) ).
tcf(c_163144,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_inverse_image(sK126(sK198(unordered_pair(X0,X1))),X2),sK198(unordered_pair(X0,X1)))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ~ relation(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_296]) ).
tcf(c_163145,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK198(sK303)),X0),sK198(sK303))
| ( sK125(sK198(sK303)) = sK140 )
| ~ relation(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_296]) ).
tcf(c_163146,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK198(sK313)),X0),sK198(sK313))
| ( sK125(sK198(sK313)) = sK140 )
| ~ relation(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_296]) ).
tcf(c_163147,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK198(sK346)),X0),sK198(sK346))
| ( sK125(sK198(sK346)) = sK140 )
| ~ relation(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_296]) ).
tcf(c_163148,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK198(sK358)),X0),sK198(sK358))
| ( sK125(sK198(sK358)) = sK140 )
| ~ relation(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_296]) ).
tcf(c_163149,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(sK302(X0)),X1),sK302(X0))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_296]) ).
tcf(c_163150,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(sK302(X0)),X1),sK302(X0))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_296]) ).
tcf(c_163151,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(sK116(X0)),X1),sK116(X0))
| ( sK125(sK116(X0)) = sK140 )
| ~ relation(sK126(sK116(X0))) ),
inference(superposition,[status(thm)],[c_150446,c_296]) ).
tcf(c_163152,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(sK300(X0)),X1),sK300(X0))
| ( sK125(sK300(X0)) = sK140 )
| ~ relation(sK126(sK300(X0))) ),
inference(superposition,[status(thm)],[c_150465,c_296]) ).
tcf(c_163153,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(sK115(X0)),X1),sK115(X0))
| ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ~ relation(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_296]) ).
tcf(c_163154,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(identity_relation(X0)),X1),identity_relation(X0))
| ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ~ relation(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_296]) ).
tcf(c_163155,plain,
! [X0: $i,X1: $i] :
( finite(relation_inverse_image(X0,X1))
| ~ relation(X0)
| ~ finite(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_296,c_276]) ).
tcf(c_163156,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ proper_subset(relation_dom(X0),relation_inverse_image(X0,X1)) ),
inference(superposition,[status(thm)],[c_296,c_472]) ).
tcf(c_163157,plain,
! [X0: $i,X1: $i] :
( in(sK140,relation_inverse_image(X0,X1))
| ( relation_dom(X0) = sK140 )
| ( sK125(subset_complement(relation_dom(X0),relation_inverse_image(X0,X1))) = sK140 )
| ~ relation(X0)
| ~ element(sK140,relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_296,c_145539]) ).
tcf(c_163158,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,relation_inverse_image(X1,X2))),relation_inverse_image(X1,X2))
| ( relation_inverse_image(X1,X2) = sK140 )
| ~ relation(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_296,c_1058]) ).
tcf(c_163159,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,relation_inverse_image(X1,X2)),relation_inverse_image(X1,X2))
| ( relation_inverse_image(X1,X2) = sK140 )
| ~ relation(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_296,c_1057]) ).
tcf(c_163160,plain,
! [X0: $i,X1: $i] :
( in(sK128(relation_inverse_image(X0,X1)),relation_inverse_image(X0,X1))
| ( relation_inverse_image(X0,X1) = sK140 )
| ~ relation(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_296,c_369]) ).
tcf(c_163161,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(relation_inverse_image(X0,X1)))
| ( relation_inverse_image(X0,X1) = sK140 )
| ~ relation(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_296,c_371]) ).
tcf(c_163162,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(X0,X1),relation_dom(X0)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_296,c_386]) ).
tcf(c_163163,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(relation_inverse_image(X1,X2)),X0)
| ( relation_inverse_image(X1,X2) = sK140 )
| ~ ordinal(X0)
| ~ relation(X1)
| ~ ordinal(relation_dom(X1))
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(superposition,[status(thm)],[c_296,c_370]) ).
tcf(c_163164,plain,
! [X0: $i] : subset(relation_inverse_image(sK140,X0),sK140),
inference(forward_subsumption_resolution,[status(thm)],[c_163127,c_577]) ).
tcf(c_163167,plain,
! [X0: $i,X1: $i] : subset(relation_inverse_image(identity_relation(X0),X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_163126,c_1101]) ).
tcf(c_163168,plain,
! [X0: $i,X1: $i] : subset(relation_inverse_image(sK115(X0),X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_163121,c_249]) ).
tcf(c_163411,plain,
! [X0: $i] :
( finite(relation_image(sK140,X0))
| ~ finite(sK140) ),
inference(superposition,[status(thm)],[c_163069,c_276]) ).
tcf(c_163412,plain,
! [X0: $i] : ~ proper_subset(sK140,relation_image(sK140,X0)),
inference(superposition,[status(thm)],[c_163069,c_472]) ).
tcf(c_163418,plain,
! [X0: $i] : set_difference(relation_image(sK140,X0),sK140) = sK140,
inference(superposition,[status(thm)],[c_163069,c_386]) ).
tcf(c_163420,plain,
! [X0: $i] : relation_image(sK140,X0) = sK140,
inference(superposition,[status(thm)],[c_163069,c_403]) ).
tcf(c_163421,plain,
! [X0: $i] : finite(relation_image(sK140,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_163411,c_144943]) ).
tcf(c_163428,plain,
! [X0: $i] :
( finite(relation_inverse_image(sK140,X0))
| ~ finite(sK140) ),
inference(superposition,[status(thm)],[c_163164,c_276]) ).
tcf(c_163429,plain,
! [X0: $i] : ~ proper_subset(sK140,relation_inverse_image(sK140,X0)),
inference(superposition,[status(thm)],[c_163164,c_472]) ).
tcf(c_163435,plain,
! [X0: $i] : set_difference(relation_inverse_image(sK140,X0),sK140) = sK140,
inference(superposition,[status(thm)],[c_163164,c_386]) ).
tcf(c_163437,plain,
! [X0: $i] : relation_inverse_image(sK140,X0) = sK140,
inference(superposition,[status(thm)],[c_163164,c_403]) ).
tcf(c_163438,plain,
! [X0: $i] : finite(relation_inverse_image(sK140,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_163428,c_144943]) ).
tcf(c_163444,plain,
( subset(sK140,relation_rng(sK140))
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_163420,c_282]) ).
tcf(c_163446,plain,
( subset(sK140,relation_dom(sK140))
| ~ relation(sK140) ),
inference(superposition,[status(thm)],[c_163437,c_296]) ).
tcf(c_163447,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ~ relation(sK140)
| ~ subset(X0,relation_rng(sK140)) ),
inference(superposition,[status(thm)],[c_163437,c_301]) ).
tcf(c_163448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(sK140,X2),X3)
| ( X1 = sK140 )
| ~ function(sK140)
| ~ in(X2,sK140)
| ~ quasi_total(sK140,X0,X1)
| ~ relation_of2_as_subset(sK140,X0,X1) ),
inference(superposition,[status(thm)],[c_163437,c_425]) ).
tcf(c_163449,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ~ function(sK140)
| ~ in(X2,sK140)
| ~ quasi_total(sK140,X0,X1)
| ~ relation_of2_as_subset(sK140,X0,X1) ),
inference(superposition,[status(thm)],[c_163437,c_424]) ).
tcf(c_163451,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ~ relation(sK140)
| ~ subset(X0,sK140) ),
inference(light_normalisation,[status(thm)],[c_163447,c_471]) ).
tcf(c_163459,plain,
! [X0: $i] :
( ( sK125(identity_relation(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) ) ),
inference(superposition,[status(thm)],[c_153290,c_162864]) ).
tcf(c_163460,plain,
! [X0: $i] :
( ( sK125(sK115(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) ) ),
inference(superposition,[status(thm)],[c_153265,c_162864]) ).
tcf(c_163461,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( relation_rng(relation_rng_restriction(sK140,X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146155,c_162864]) ).
tcf(c_163463,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(sK140,sK96(X0,X1))) = sK140 )
| ~ sP12(X0,X1) ),
inference(superposition,[status(thm)],[c_208,c_162864]) ).
tcf(c_163464,plain,
! [X0: $i] :
( sP13(X0)
| ( relation_rng(relation_rng_restriction(sK140,sK108(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_230,c_162864]) ).
tcf(c_163465,plain,
! [X0: $i] : relation_rng(relation_rng_restriction(sK140,sK115(X0))) = sK140,
inference(superposition,[status(thm)],[c_249,c_162864]) ).
tcf(c_163466,plain,
! [X0: $i] : relation_rng(relation_rng_restriction(sK140,sK124(X0))) = sK140,
inference(superposition,[status(thm)],[c_346,c_162864]) ).
tcf(c_163467,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_355,c_162864]) ).
tcf(c_163468,plain,
! [X0: $i] : relation_rng(relation_rng_restriction(sK140,identity_relation(X0))) = sK140,
inference(superposition,[status(thm)],[c_1101,c_162864]) ).
tcf(c_163469,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(sK140,relation_dom_restriction(X0,X1))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_773,c_162864]) ).
tcf(c_163470,plain,
relation_rng(relation_rng_restriction(sK140,sK140)) = sK140,
inference(superposition,[status(thm)],[c_577,c_162864]) ).
tcf(c_163471,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(sK140,relation_dom(X0))) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_642,c_162864]) ).
tcf(c_163472,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(sK140,relation_rng_restriction(X1,X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_646,c_162864]) ).
tcf(c_163473,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(sK140,sK195(X0,X1))) = sK140 )
| ~ are_equipotent(X0,X1) ),
inference(superposition,[status(thm)],[c_84692,c_162864]) ).
tcf(c_163474,plain,
relation_rng(relation_rng_restriction(sK140,sK240)) = sK140,
inference(superposition,[status(thm)],[c_783,c_162864]) ).
tcf(c_163475,plain,
relation_rng(relation_rng_restriction(sK140,sK242)) = sK140,
inference(superposition,[status(thm)],[c_791,c_162864]) ).
tcf(c_163476,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(sK140,sK264(X0))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_852,c_162864]) ).
tcf(c_163477,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(sK140,relation_rng(X0))) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_944,c_162864]) ).
tcf(c_163478,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng_restriction(sK140,relation_restriction(X0,X1))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1013,c_162864]) ).
tcf(c_163479,plain,
! [X0: $i,X1: $i] : relation_rng(relation_rng_restriction(sK140,sK312(X0,X1))) = sK140,
inference(superposition,[status(thm)],[c_1019,c_162864]) ).
tcf(c_163480,plain,
! [X0: $i] : relation_rng(relation_rng_restriction(sK140,inclusion_relation(X0))) = sK140,
inference(superposition,[status(thm)],[c_1091,c_162864]) ).
tcf(c_163481,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(sK140,relation_inverse(X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1113,c_162864]) ).
tcf(c_163482,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(sK140,relation_inverse(X0))) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1112,c_162864]) ).
tcf(c_163483,plain,
relation_rng(relation_rng_restriction(sK140,sK335)) = sK140,
inference(superposition,[status(thm)],[c_1149,c_162864]) ).
tcf(c_163484,plain,
! [X0: $i,X1: $i] : relation_rng(relation_rng_restriction(sK140,sK347(X0,X1))) = sK140,
inference(superposition,[status(thm)],[c_1237,c_162864]) ).
tcf(c_163602,plain,
! [X0: $i,X1: $i] :
( ( sK125(identity_relation(X1)) = sK140 )
| ( relation_dom(sK126(identity_relation(X1))) = identity_relation(X1) )
| ( set_difference(relation_rng(relation_rng_restriction(X0,X1)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_153290,c_162861]) ).
tcf(c_163603,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK115(X1)) = sK140 )
| ( relation_dom(sK126(sK115(X1))) = sK115(X1) )
| ( set_difference(relation_rng(relation_rng_restriction(X0,X1)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_153265,c_162861]) ).
tcf(c_163604,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( relation_dom(sK126(X1)) = X1 )
| ( set_difference(relation_rng(relation_rng_restriction(X0,X1)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_146155,c_162861]) ).
tcf(c_163606,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X2,sK96(X0,X1))),X2) = sK140 )
| ~ sP12(X0,X1) ),
inference(superposition,[status(thm)],[c_208,c_162861]) ).
tcf(c_163607,plain,
! [X0: $i,X1: $i] :
( sP13(X1)
| ( set_difference(relation_rng(relation_rng_restriction(X0,sK108(X1))),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_230,c_162861]) ).
tcf(c_163608,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_rng_restriction(X0,sK115(X1))),X0) = sK140,
inference(superposition,[status(thm)],[c_249,c_162861]) ).
tcf(c_163609,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_rng_restriction(X0,sK124(X1))),X0) = sK140,
inference(superposition,[status(thm)],[c_346,c_162861]) ).
tcf(c_163610,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(X1) = sK140 )
| ( set_difference(relation_rng(relation_rng_restriction(X0,sK126(X1))),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_355,c_162861]) ).
tcf(c_163611,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_rng_restriction(X0,identity_relation(X1))),X0) = sK140,
inference(superposition,[status(thm)],[c_1101,c_162861]) ).
tcf(c_163612,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,relation_dom_restriction(X0,X2))),X1) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_773,c_162861]) ).
tcf(c_163613,plain,
! [X0: $i] : set_difference(relation_rng(relation_rng_restriction(X0,sK140)),X0) = sK140,
inference(superposition,[status(thm)],[c_577,c_162861]) ).
tcf(c_163614,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,relation_dom(X0))),X1) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_642,c_162861]) ).
tcf(c_163615,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,relation_rng_restriction(X2,X0))),X1) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_646,c_162861]) ).
tcf(c_163616,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X2,sK195(X0,X1))),X2) = sK140 )
| ~ are_equipotent(X0,X1) ),
inference(superposition,[status(thm)],[c_84692,c_162861]) ).
tcf(c_163617,plain,
! [X0: $i] : set_difference(relation_rng(relation_rng_restriction(X0,sK240)),X0) = sK140,
inference(superposition,[status(thm)],[c_783,c_162861]) ).
tcf(c_163618,plain,
! [X0: $i] : set_difference(relation_rng(relation_rng_restriction(X0,sK242)),X0) = sK140,
inference(superposition,[status(thm)],[c_791,c_162861]) ).
tcf(c_163619,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,sK264(X0))),X1) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_852,c_162861]) ).
tcf(c_163620,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,relation_rng(X0))),X1) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_944,c_162861]) ).
tcf(c_163621,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,relation_restriction(X0,X2))),X1) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1013,c_162861]) ).
tcf(c_163622,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_rng(relation_rng_restriction(X0,sK312(X1,X2))),X0) = sK140,
inference(superposition,[status(thm)],[c_1019,c_162861]) ).
tcf(c_163623,plain,
! [X0: $i,X1: $i] : set_difference(relation_rng(relation_rng_restriction(X0,inclusion_relation(X1))),X0) = sK140,
inference(superposition,[status(thm)],[c_1091,c_162861]) ).
tcf(c_163624,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,relation_inverse(X0))),X1) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1113,c_162861]) ).
tcf(c_163625,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,relation_inverse(X0))),X1) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1112,c_162861]) ).
tcf(c_163626,plain,
! [X0: $i] : set_difference(relation_rng(relation_rng_restriction(X0,sK335)),X0) = sK140,
inference(superposition,[status(thm)],[c_1149,c_162861]) ).
tcf(c_163627,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_rng(relation_rng_restriction(X0,sK347(X1,X2))),X0) = sK140,
inference(superposition,[status(thm)],[c_1237,c_162861]) ).
tcf(c_163693,plain,
! [X0: $i,X1: $i] :
( ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) )
| ( set_difference(relation_image(X0,X1),relation_rng(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_153290,c_163067]) ).
tcf(c_163694,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) )
| ( set_difference(relation_image(X0,X1),relation_rng(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_153265,c_163067]) ).
tcf(c_163695,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( set_difference(relation_image(X0,X1),relation_rng(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146155,c_163067]) ).
tcf(c_163697,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_image(sK96(X0,X1),X2),relation_rng(sK96(X0,X1))) = sK140 )
| ~ sP12(X0,X1) ),
inference(superposition,[status(thm)],[c_208,c_163067]) ).
tcf(c_163698,plain,
! [X0: $i,X1: $i] :
( sP13(X0)
| ( set_difference(relation_image(sK108(X0),X1),relation_rng(sK108(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_230,c_163067]) ).
tcf(c_163699,plain,
! [X0: $i,X1: $i] : set_difference(relation_image(sK115(X0),X1),relation_rng(sK115(X0))) = sK140,
inference(superposition,[status(thm)],[c_249,c_163067]) ).
tcf(c_163700,plain,
! [X0: $i,X1: $i] : set_difference(relation_image(sK124(X0),X1),relation_rng(sK124(X0))) = sK140,
inference(superposition,[status(thm)],[c_346,c_163067]) ).
tcf(c_163701,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_image(sK126(X0),X1),relation_rng(sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_355,c_163067]) ).
tcf(c_163702,plain,
! [X0: $i,X1: $i] : set_difference(relation_image(identity_relation(X0),X1),relation_rng(identity_relation(X0))) = sK140,
inference(superposition,[status(thm)],[c_1101,c_163067]) ).
tcf(c_163703,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_image(relation_dom_restriction(X0,X1),X2),relation_rng(relation_dom_restriction(X0,X1))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_773,c_163067]) ).
tcf(c_163704,plain,
! [X0: $i] : set_difference(relation_image(sK140,X0),relation_rng(sK140)) = sK140,
inference(superposition,[status(thm)],[c_577,c_163067]) ).
tcf(c_163705,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(relation_dom(X0),X1),relation_rng(relation_dom(X0))) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_642,c_163067]) ).
tcf(c_163706,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_image(relation_rng_restriction(X1,X0),X2),relation_rng(relation_rng_restriction(X1,X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_646,c_163067]) ).
tcf(c_163707,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_image(sK195(X0,X1),X2),relation_rng(sK195(X0,X1))) = sK140 )
| ~ are_equipotent(X0,X1) ),
inference(superposition,[status(thm)],[c_84692,c_163067]) ).
tcf(c_163708,plain,
! [X0: $i] : set_difference(relation_image(sK240,X0),relation_rng(sK240)) = sK140,
inference(superposition,[status(thm)],[c_783,c_163067]) ).
tcf(c_163709,plain,
! [X0: $i] : set_difference(relation_image(sK242,X0),relation_rng(sK242)) = sK140,
inference(superposition,[status(thm)],[c_791,c_163067]) ).
tcf(c_163710,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(sK264(X0),X1),relation_rng(sK264(X0))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_852,c_163067]) ).
tcf(c_163711,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(relation_rng(X0),X1),relation_rng(relation_rng(X0))) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_944,c_163067]) ).
tcf(c_163712,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_image(relation_restriction(X0,X1),X2),relation_rng(relation_restriction(X0,X1))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1013,c_163067]) ).
tcf(c_163713,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_image(sK312(X0,X1),X2),relation_rng(sK312(X0,X1))) = sK140,
inference(superposition,[status(thm)],[c_1019,c_163067]) ).
tcf(c_163714,plain,
! [X0: $i,X1: $i] : set_difference(relation_image(inclusion_relation(X0),X1),relation_rng(inclusion_relation(X0))) = sK140,
inference(superposition,[status(thm)],[c_1091,c_163067]) ).
tcf(c_163715,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(relation_inverse(X0),X1),relation_rng(relation_inverse(X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1113,c_163067]) ).
tcf(c_163716,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(relation_inverse(X0),X1),relation_rng(relation_inverse(X0))) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1112,c_163067]) ).
tcf(c_163717,plain,
! [X0: $i] : set_difference(relation_image(sK335,X0),relation_rng(sK335)) = sK140,
inference(superposition,[status(thm)],[c_1149,c_163067]) ).
tcf(c_163718,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_image(sK347(X0,X1),X2),relation_rng(sK347(X0,X1))) = sK140,
inference(superposition,[status(thm)],[c_1237,c_163067]) ).
tcf(c_163720,plain,
! [X0: $i,X1: $i] : set_difference(relation_image(identity_relation(X0),X1),X0) = sK140,
inference(light_normalisation,[status(thm)],[c_163702,c_490]) ).
tcf(c_163824,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(sK302(X0)),X1),sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_296]) ).
tcf(c_163825,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK302(X0)),sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_154130]) ).
tcf(c_163826,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0)))
| ~ in(sK302(X0),X1) ),
inference(superposition,[status(thm)],[c_147757,c_155600]) ).
tcf(c_163827,plain,
! [X0: $i] :
( function(sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_147195]) ).
tcf(c_163828,plain,
! [X0: $i] :
( finite(sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_147193]) ).
tcf(c_163829,plain,
! [X0: $i] :
( epsilon_transitive(sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_147192]) ).
tcf(c_163830,plain,
! [X0: $i] :
( epsilon_connected(sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_147191]) ).
tcf(c_163831,plain,
! [X0: $i] :
( ordinal(sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_147190]) ).
tcf(c_163832,plain,
! [X0: $i] :
( one_to_one(sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_147189]) ).
tcf(c_163833,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ empty(sK302(X0))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_150772]) ).
tcf(c_163834,plain,
! [X0: $i,X1: $i] :
( element(X1,sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_148552]) ).
tcf(c_163835,plain,
! [X0: $i] :
( relation(sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_642]) ).
tcf(c_163836,plain,
! [X0: $i] :
( empty(sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_641]) ).
tcf(c_163837,plain,
! [X0: $i,X1: $i] :
( in(X1,sK302(X0))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( apply(sK126(sK302(X0)),X1) = sK140 )
| ~ function(sK126(sK302(X0)))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_906]) ).
tcf(c_163838,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ( relation_rng(sK126(sK302(X0))) = sK140 )
| ~ relation(sK126(sK302(X0)))
| ( sK302(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147757,c_478]) ).
tcf(c_163839,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK140 )
| ( sK126(sK302(X0)) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ relation(sK126(sK302(X0)))
| ( sK302(X0) != sK140 ) ),
inference(superposition,[status(thm)],[c_147757,c_475]) ).
tcf(c_163919,plain,
! [X0: $i,X1: $i] :
( finite(relation_field(relation_restriction(X0,X1)))
| ~ finite(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_318,c_276]) ).
tcf(c_163920,plain,
! [X0: $i,X1: $i] :
( ~ relation(X1)
| ~ proper_subset(X0,relation_field(relation_restriction(X1,X0))) ),
inference(superposition,[status(thm)],[c_318,c_472]) ).
tcf(c_163921,plain,
! [X0: $i,X1: $i] :
( in(sK140,relation_field(relation_restriction(X1,X0)))
| ( X0 = sK140 )
| ( sK125(subset_complement(X0,relation_field(relation_restriction(X1,X0)))) = sK140 )
| ~ relation(X1)
| ~ element(sK140,X0) ),
inference(superposition,[status(thm)],[c_318,c_145539]) ).
tcf(c_163922,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X0,sK318(X0,relation_field(relation_restriction(X2,X1)))),relation_field(relation_restriction(X2,X1)))
| ( relation_field(relation_restriction(X2,X1)) = sK140 )
| ~ relation(X2)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_318,c_1058]) ).
tcf(c_163923,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,relation_field(relation_restriction(X2,X1))),relation_field(relation_restriction(X2,X1)))
| ( relation_field(relation_restriction(X2,X1)) = sK140 )
| ~ relation(X2)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_318,c_1057]) ).
tcf(c_163924,plain,
! [X0: $i,X1: $i] :
( in(sK128(relation_field(relation_restriction(X0,X1))),relation_field(relation_restriction(X0,X1)))
| ( relation_field(relation_restriction(X0,X1)) = sK140 )
| ~ ordinal(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_318,c_369]) ).
tcf(c_163925,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(relation_field(relation_restriction(X0,X1))))
| ( relation_field(relation_restriction(X0,X1)) = sK140 )
| ~ ordinal(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_318,c_371]) ).
tcf(c_163926,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_field(relation_restriction(X0,X1)),X1) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_318,c_386]) ).
tcf(c_163927,plain,
! [X0: $i,X1: $i] :
( ( relation_field(relation_restriction(X0,unordered_pair(X1,X1))) = sK140 )
| ( relation_field(relation_restriction(X0,unordered_pair(X1,X1))) = unordered_pair(X1,X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_318,c_397]) ).
tcf(c_163928,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(relation_field(relation_restriction(X1,X2))),X0)
| ( relation_field(relation_restriction(X1,X2)) = sK140 )
| ~ ordinal(X2)
| ~ ordinal(X0)
| ~ relation(X1)
| ~ in(X0,relation_field(relation_restriction(X1,X2))) ),
inference(superposition,[status(thm)],[c_318,c_370]) ).
tcf(c_163929,plain,
! [X0: $i] :
( ( relation_field(relation_restriction(X0,sK140)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_318,c_403]) ).
tcf(c_163930,plain,
! [X0: $i] :
( in(sK63(relation_field(relation_restriction(X0,powerset(sK62)))),relation_field(relation_restriction(X0,powerset(sK62))))
| ( relation_field(relation_restriction(X0,powerset(sK62))) = sK140 )
| ~ iPr_def_21
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_318,c_156787]) ).
tcf(c_163931,plain,
! [X0: $i,X1: $i] :
( in(sK119(relation_field(relation_restriction(X0,powerset(X1)))),relation_field(relation_restriction(X0,powerset(X1))))
| ( relation_field(relation_restriction(X0,powerset(X1))) = sK140 )
| ~ finite(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_318,c_156797]) ).
tcf(c_163932,plain,
! [X0: $i] :
( in(sK262(relation_field(relation_restriction(X0,powerset(sK261)))),relation_field(relation_restriction(X0,powerset(sK261))))
| ( relation_field(relation_restriction(X0,powerset(sK261))) = sK140 )
| ~ iPr_def_15
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_318,c_156803]) ).
tcf(c_163933,plain,
! [X0: $i] :
( ( relation_field(relation_restriction(X0,powerset(sK140))) = sK140 )
| ( relation_field(relation_restriction(X0,powerset(sK140))) = powerset(sK140) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_318,c_144406]) ).
tcf(c_164039,plain,
! [X0: $i,X1: $i] :
( ordinal(X1)
| ( set_difference(unordered_pair(X1,X1),set_difference(unordered_pair(X1,X1),X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151758,c_333]) ).
tcf(c_164040,plain,
! [X0: $i,X1: $i] :
( ordinal(sK49(X0,X1))
| ~ ordinal(X0)
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_333]) ).
tcf(c_164041,plain,
! [X0: $i] :
( sP3(X0)
| ordinal(sK58(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_122,c_333]) ).
tcf(c_164042,plain,
( ordinal(set_union2(sK62,unordered_pair(sK62,sK62)))
| ~ sP8
| ~ ordinal(omega) ),
inference(superposition,[status(thm)],[c_128,c_333]) ).
tcf(c_164048,plain,
! [X0: $i] :
( ordinal(X0)
| ~ ordinal(set_union2(X0,unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_256,c_333]) ).
tcf(c_164049,plain,
! [X0: $i] :
( ordinal(X0)
| ~ ordinal(sK116(X0)) ),
inference(superposition,[status(thm)],[c_272,c_333]) ).
tcf(c_164050,plain,
! [X0: $i,X1: $i] :
( ordinal(X1)
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_906,c_333]) ).
tcf(c_164051,plain,
! [X0: $i,X1: $i] :
( ordinal(apply(sK126(X1),X0))
| ( sK125(X1) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2177,c_333]) ).
tcf(c_164054,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ordinal(sK130(X0,X1))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_400,c_333]) ).
tcf(c_164055,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ordinal(sK130(X1,X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_401,c_333]) ).
tcf(c_164056,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(X2)
| in(X2,X1)
| ( X0 = sK140 )
| ~ element(X2,X0)
| ~ subset(X1,X0)
| ~ ordinal(subset_complement(X0,X1)) ),
inference(superposition,[status(thm)],[c_5403,c_333]) ).
tcf(c_164057,plain,
! [X0: $i] :
( relation(X0)
| ordinal(sK163(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_561,c_333]) ).
tcf(c_164058,plain,
! [X0: $i] :
( ordinal(sK169(X0))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_579,c_333]) ).
tcf(c_164059,plain,
! [X0: $i] :
( ordinal(sK173(X0))
| ~ sP20(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_584,c_333]) ).
tcf(c_164061,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ordinal(sK193(X0,X1))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_657,c_333]) ).
tcf(c_164062,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_661,c_333]) ).
tcf(c_164065,plain,
! [X0: $i] :
( ordinal(relation_dom(sK264(X0)))
| ~ ordinal(omega)
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_855,c_333]) ).
tcf(c_164067,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_939,c_333]) ).
tcf(c_164068,plain,
! [X0: $i,X1: $i] :
( ordinal(X1)
| ~ ordinal(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_940,c_333]) ).
tcf(c_164069,plain,
! [X0: $i] :
( ordinal(X0)
| ~ ordinal(sK300(X0)) ),
inference(superposition,[status(thm)],[c_965,c_333]) ).
tcf(c_164070,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ordinal(sK316(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_1043,c_333]) ).
tcf(c_164071,plain,
! [X0: $i,X1: $i] :
( ordinal(sK320(X1,X0))
| ( X0 = sK140 )
| ~ well_founded_relation(X1)
| ~ ordinal(X0)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_333]) ).
tcf(c_164072,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ordinal(sK343(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_1207,c_333]) ).
tcf(c_164073,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ordinal(sK344(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_1208,c_333]) ).
tcf(c_164075,plain,
! [X0: $i] :
( ordinal(unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))))
| ( X0 = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16344,c_333]) ).
tcf(c_164076,plain,
( ordinal(sK119(sK64))
| ~ sP7
| ~ ordinal(sK64) ),
inference(superposition,[status(thm)],[c_146098,c_333]) ).
tcf(c_164077,plain,
! [X0: $i,X1: $i] :
( ordinal(sK318(X0,X1))
| ( X1 = sK140 )
| ~ ordinal(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144619,c_333]) ).
tcf(c_164078,plain,
( sP15
| ordinal(sK114(sK64))
| ~ sP7
| ~ ordinal(sK64) ),
inference(superposition,[status(thm)],[c_145791,c_333]) ).
tcf(c_164079,plain,
( ordinal(sK72(sK64))
| ~ iPr_def_19
| ~ sP7
| ~ ordinal(sK64) ),
inference(superposition,[status(thm)],[c_145863,c_333]) ).
tcf(c_164080,plain,
( ordinal(sK67(sK64))
| ~ sP6
| ~ sP7
| ~ ordinal(sK64)
| ~ in(sK140,sK66) ),
inference(superposition,[status(thm)],[c_146728,c_333]) ).
tcf(c_164081,plain,
( ordinal(sK111(sK64))
| ~ sP15
| ~ sP7
| ~ ordinal(sK64)
| ~ in(sK140,sK110) ),
inference(superposition,[status(thm)],[c_146738,c_333]) ).
tcf(c_164082,plain,
( ordinal(sK63(sK199(powerset(powerset(sK62)))))
| ( sK199(powerset(powerset(sK62))) = sK140 )
| ~ iPr_def_21
| ~ ordinal(sK199(powerset(powerset(sK62)))) ),
inference(superposition,[status(thm)],[c_145355,c_333]) ).
tcf(c_164083,plain,
! [X0: $i] :
( ordinal(sK119(sK199(powerset(powerset(X0)))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ~ finite(X0)
| ~ ordinal(sK199(powerset(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_145365,c_333]) ).
tcf(c_164084,plain,
( ordinal(sK262(sK199(powerset(powerset(sK261)))))
| ( sK199(powerset(powerset(sK261))) = sK140 )
| ~ iPr_def_15
| ~ ordinal(sK199(powerset(powerset(sK261)))) ),
inference(superposition,[status(thm)],[c_145371,c_333]) ).
tcf(c_164085,plain,
( ordinal(sK63(powerset(sK62)))
| ( powerset(sK62) = sK140 )
| ~ iPr_def_21
| ~ ordinal(powerset(sK62)) ),
inference(superposition,[status(thm)],[c_145625,c_333]) ).
tcf(c_164086,plain,
! [X0: $i] :
( ordinal(sK72(powerset(X0)))
| ( powerset(X0) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ ordinal(powerset(X0))
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145633,c_333]) ).
tcf(c_164087,plain,
! [X0: $i] :
( sP15
| ordinal(sK114(powerset(X0)))
| ( powerset(X0) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(powerset(X0))
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145634,c_333]) ).
tcf(c_164088,plain,
! [X0: $i] :
( ordinal(sK119(powerset(X0)))
| ( powerset(X0) = sK140 )
| ~ finite(X0)
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_145635,c_333]) ).
tcf(c_164089,plain,
( ordinal(sK262(powerset(sK261)))
| ( powerset(sK261) = sK140 )
| ~ iPr_def_15
| ~ ordinal(powerset(sK261)) ),
inference(superposition,[status(thm)],[c_145641,c_333]) ).
tcf(c_164090,plain,
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ ordinal(omega)
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145922,c_333]) ).
tcf(c_164091,plain,
( ordinal(sK128(omega))
| ( sK140 = omega )
| ~ ordinal(omega)
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145878,c_333]) ).
tcf(c_164092,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK318(X2,set_difference(X0,X1)))
| ( set_difference(X0,X1) = sK140 )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X0)
| ~ ordinal(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_146007,c_333]) ).
tcf(c_164094,plain,
! [X0: $i,X1: $i] :
( ordinal(apply(sK126(X1),sK92(X0)))
| ( sK125(X1) = sK140 )
| ~ ordinal(X0)
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_151774,c_333]) ).
tcf(c_164096,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(relation_rng_restriction(X0,X1)))
| ( relation_rng_restriction(X0,X1) = sK140 )
| ~ ordinal(X1)
| ~ relation(X1)
| ~ ordinal(relation_rng_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_152217,c_333]) ).
tcf(c_164099,plain,
! [X0: $i] :
( ordinal(sK142(X0))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_154138,c_333]) ).
tcf(c_164101,plain,
! [X0: $i,X1: $i] :
( ordinal(sK142(relation_dom(X0)))
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_154130,c_333]) ).
tcf(c_164102,plain,
! [X0: $i] :
( ordinal(sK142(sK263(X0)))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ ordinal(sK263(X0))
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_154142,c_333]) ).
tcf(c_164103,plain,
! [X0: $i] :
( ordinal(sK128(sK169(X0)))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ ordinal(sK169(X0))
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154846,c_333]) ).
tcf(c_164104,plain,
! [X0: $i] :
( ordinal(sK142(sK169(X0)))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ ordinal(sK169(X0)) ),
inference(superposition,[status(thm)],[c_154906,c_333]) ).
tcf(c_164105,plain,
! [X0: $i] :
( ordinal(sK318(X0,sK64))
| ~ sP7
| ~ ordinal(sK64)
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_161838,c_333]) ).
tcf(c_164106,plain,
( ordinal(sK128(sK64))
| ~ sP7
| ~ ordinal(sK64)
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157842,c_333]) ).
tcf(c_164157,plain,
! [X0: $i] :
( ordinal(relation_dom(sK264(X0)))
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_164065,c_849]) ).
tcf(c_164178,plain,
( ordinal(set_union2(sK62,unordered_pair(sK62,sK62)))
| ~ sP8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_164042,c_849]) ).
tcf(c_164367,plain,
! [X0: $i] :
( empty(powerset(X0))
| relation(sK126(powerset(X0)))
| in(sK140,powerset(X0)) ),
inference(superposition,[status(thm)],[c_157460,c_351]) ).
tcf(c_164368,plain,
( empty(sK116(sK140))
| relation(sK126(sK116(sK140)))
| in(sK140,sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145537,c_351]) ).
tcf(c_164369,plain,
( empty(sK300(sK140))
| relation(sK126(sK300(sK140)))
| in(sK140,sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145541,c_351]) ).
tcf(c_164370,plain,
! [X0: $i] :
( empty(unordered_pair(sK140,X0))
| relation(sK126(unordered_pair(sK140,X0)))
| in(sK140,unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146167,c_351]) ).
tcf(c_164371,plain,
! [X0: $i] :
( empty(unordered_pair(X0,sK140))
| relation(sK126(unordered_pair(X0,sK140)))
| in(sK140,unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146209,c_351]) ).
tcf(c_164372,plain,
( empty(relation_dom(sK240))
| relation(sK126(relation_dom(sK240)))
| in(sK140,relation_dom(sK240))
| ( apply(sK240,sK140) = sK140 ) ),
inference(superposition,[status(thm)],[c_147099,c_351]) ).
tcf(c_164373,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom(sK312(X0,X1)))
| relation(sK126(relation_dom(sK312(X0,X1))))
| in(sK140,relation_dom(sK312(X0,X1)))
| ( apply(sK312(X0,X1),sK140) = sK140 ) ),
inference(superposition,[status(thm)],[c_147117,c_351]) ).
tcf(c_164374,plain,
( empty(relation_dom(sK335))
| relation(sK126(relation_dom(sK335)))
| in(sK140,relation_dom(sK335))
| ( apply(sK335,sK140) = sK140 ) ),
inference(superposition,[status(thm)],[c_147096,c_351]) ).
tcf(c_164375,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom(sK347(X0,X1)))
| relation(sK126(relation_dom(sK347(X0,X1))))
| in(sK140,relation_dom(sK347(X0,X1)))
| ( apply(sK347(X0,X1),sK140) = sK140 ) ),
inference(superposition,[status(thm)],[c_147114,c_351]) ).
tcf(c_164376,plain,
! [X0: $i] :
( empty(X0)
| ordinal(sK125(X0))
| relation(sK126(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_351,c_333]) ).
tcf(c_164378,plain,
! [X0: $i] :
( empty(X0)
| relation(sK126(X0))
| in(sK128(sK125(X0)),sK125(X0))
| ( sK125(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_351,c_154063]) ).
tcf(c_164379,plain,
! [X0: $i] :
( empty(X0)
| relation(sK126(X0))
| ~ in(X0,sK125(X0)) ),
inference(superposition,[status(thm)],[c_351,c_527]) ).
tcf(c_164380,plain,
! [X0: $i] :
( empty(X0)
| relation(sK126(X0))
| ordinal(sK128(sK125(X0)))
| ( sK125(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_351,c_154064]) ).
tcf(c_164381,plain,
! [X0: $i] :
( empty(X0)
| relation(sK126(X0))
| in(sK142(sK125(X0)),sK125(X0))
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_351,c_154131]) ).
tcf(c_164382,plain,
! [X0: $i] :
( empty(X0)
| relation(sK126(X0))
| ( set_difference(sK125(X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_351,c_154065]) ).
tcf(c_164383,plain,
! [X0: $i] :
( empty(X0)
| relation(sK126(X0))
| in(sK142(X0),X0) ),
inference(superposition,[status(thm)],[c_351,c_522]) ).
tcf(c_164386,plain,
! [X0: $i] :
( empty(X0)
| relation(sK126(X0))
| element(sK125(X0),X0) ),
inference(superposition,[status(thm)],[c_351,c_526]) ).
tcf(c_164387,plain,
! [X0: $i] :
( empty(sK92(X0))
| relation(sK126(sK92(X0)))
| in(sK125(sK92(X0)),X0) ),
inference(superposition,[status(thm)],[c_351,c_198]) ).
tcf(c_164388,plain,
! [X0: $i] :
( empty(sK92(X0))
| ordinal(sK125(sK92(X0)))
| relation(sK126(sK92(X0))) ),
inference(superposition,[status(thm)],[c_351,c_199]) ).
tcf(c_164389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(relation_inverse_image(X0,X3))
| relation(sK126(relation_inverse_image(X0,X3)))
| in(apply(X0,sK125(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_351,c_425]) ).
tcf(c_164390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(relation_inverse_image(X0,X3))
| relation(sK126(relation_inverse_image(X0,X3)))
| in(sK125(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_351,c_424]) ).
tcf(c_164392,plain,
! [X0: $i] :
( empty(powerset(X0))
| relation(sK126(powerset(X0)))
| subset(sK125(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_351,c_662]) ).
tcf(c_164393,plain,
! [X0: $i] :
( sP29
| empty(sK248(X0))
| ordinal(sK125(sK248(X0)))
| relation(sK126(sK248(X0))) ),
inference(superposition,[status(thm)],[c_351,c_808]) ).
tcf(c_164410,plain,
! [X0: $i] :
( relation(sK126(powerset(X0)))
| in(sK140,powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_164367,c_695]) ).
tcf(c_164417,plain,
! [X0: $i] :
( empty(powerset(X0))
| subset(sK140,X0)
| relation(sK126(powerset(X0))) ),
inference(light_normalisation,[status(thm)],[c_164392,c_157460]) ).
tcf(c_164497,plain,
! [X0: $i] :
( empty(powerset(X0))
| function(sK126(powerset(X0)))
| in(sK140,powerset(X0)) ),
inference(superposition,[status(thm)],[c_157460,c_352]) ).
tcf(c_164498,plain,
( empty(sK116(sK140))
| function(sK126(sK116(sK140)))
| in(sK140,sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145537,c_352]) ).
tcf(c_164499,plain,
( empty(sK300(sK140))
| function(sK126(sK300(sK140)))
| in(sK140,sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145541,c_352]) ).
tcf(c_164500,plain,
! [X0: $i] :
( empty(unordered_pair(sK140,X0))
| function(sK126(unordered_pair(sK140,X0)))
| in(sK140,unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146167,c_352]) ).
tcf(c_164501,plain,
! [X0: $i] :
( empty(unordered_pair(X0,sK140))
| function(sK126(unordered_pair(X0,sK140)))
| in(sK140,unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146209,c_352]) ).
tcf(c_164502,plain,
( empty(relation_dom(sK240))
| function(sK126(relation_dom(sK240)))
| in(sK140,relation_dom(sK240))
| ( apply(sK240,sK140) = sK140 ) ),
inference(superposition,[status(thm)],[c_147099,c_352]) ).
tcf(c_164503,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom(sK312(X0,X1)))
| function(sK126(relation_dom(sK312(X0,X1))))
| in(sK140,relation_dom(sK312(X0,X1)))
| ( apply(sK312(X0,X1),sK140) = sK140 ) ),
inference(superposition,[status(thm)],[c_147117,c_352]) ).
tcf(c_164504,plain,
( empty(relation_dom(sK335))
| function(sK126(relation_dom(sK335)))
| in(sK140,relation_dom(sK335))
| ( apply(sK335,sK140) = sK140 ) ),
inference(superposition,[status(thm)],[c_147096,c_352]) ).
tcf(c_164505,plain,
! [X0: $i,X1: $i] :
( empty(relation_dom(sK347(X0,X1)))
| function(sK126(relation_dom(sK347(X0,X1))))
| in(sK140,relation_dom(sK347(X0,X1)))
| ( apply(sK347(X0,X1),sK140) = sK140 ) ),
inference(superposition,[status(thm)],[c_147114,c_352]) ).
tcf(c_164506,plain,
! [X0: $i] :
( empty(X0)
| ordinal(sK125(X0))
| function(sK126(X0))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_352,c_333]) ).
tcf(c_164508,plain,
! [X0: $i] :
( empty(X0)
| function(sK126(X0))
| in(sK128(sK125(X0)),sK125(X0))
| ( sK125(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_352,c_154063]) ).
tcf(c_164509,plain,
! [X0: $i] :
( empty(X0)
| function(sK126(X0))
| ~ in(X0,sK125(X0)) ),
inference(superposition,[status(thm)],[c_352,c_527]) ).
tcf(c_164510,plain,
! [X0: $i] :
( empty(X0)
| function(sK126(X0))
| ordinal(sK128(sK125(X0)))
| ( sK125(X0) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_352,c_154064]) ).
tcf(c_164511,plain,
! [X0: $i] :
( empty(X0)
| function(sK126(X0))
| in(sK142(sK125(X0)),sK125(X0))
| ( sK125(X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_352,c_154131]) ).
tcf(c_164512,plain,
! [X0: $i] :
( empty(X0)
| function(sK126(X0))
| ( set_difference(sK125(X0),union(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_352,c_154065]) ).
tcf(c_164513,plain,
! [X0: $i] :
( empty(X0)
| function(sK126(X0))
| in(sK142(X0),X0) ),
inference(superposition,[status(thm)],[c_352,c_522]) ).
tcf(c_164516,plain,
! [X0: $i] :
( empty(X0)
| function(sK126(X0))
| element(sK125(X0),X0) ),
inference(superposition,[status(thm)],[c_352,c_526]) ).
tcf(c_164517,plain,
! [X0: $i] :
( empty(sK92(X0))
| function(sK126(sK92(X0)))
| in(sK125(sK92(X0)),X0) ),
inference(superposition,[status(thm)],[c_352,c_198]) ).
tcf(c_164518,plain,
! [X0: $i] :
( empty(sK92(X0))
| ordinal(sK125(sK92(X0)))
| function(sK126(sK92(X0))) ),
inference(superposition,[status(thm)],[c_352,c_199]) ).
tcf(c_164519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(relation_inverse_image(X0,X3))
| function(sK126(relation_inverse_image(X0,X3)))
| in(apply(X0,sK125(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_352,c_425]) ).
tcf(c_164520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( empty(relation_inverse_image(X0,X3))
| function(sK126(relation_inverse_image(X0,X3)))
| in(sK125(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_352,c_424]) ).
tcf(c_164522,plain,
! [X0: $i] :
( empty(powerset(X0))
| function(sK126(powerset(X0)))
| subset(sK125(powerset(X0)),X0) ),
inference(superposition,[status(thm)],[c_352,c_662]) ).
tcf(c_164523,plain,
! [X0: $i] :
( sP29
| empty(sK248(X0))
| ordinal(sK125(sK248(X0)))
| function(sK126(sK248(X0))) ),
inference(superposition,[status(thm)],[c_352,c_808]) ).
tcf(c_164540,plain,
! [X0: $i] :
( function(sK126(powerset(X0)))
| in(sK140,powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_164497,c_695]) ).
tcf(c_164547,plain,
! [X0: $i] :
( empty(powerset(X0))
| subset(sK140,X0)
| function(sK126(powerset(X0))) ),
inference(light_normalisation,[status(thm)],[c_164522,c_157460]) ).
tcf(c_164711,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_147663,c_833]) ).
tcf(c_164727,plain,
! [X0: $i] :
( ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) )
| ( relation_field(relation_restriction(X0,sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_153290,c_163929]) ).
tcf(c_164728,plain,
! [X0: $i] :
( ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) )
| ( relation_field(relation_restriction(X0,sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_153265,c_163929]) ).
tcf(c_164729,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( relation_field(relation_restriction(X0,sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146155,c_163929]) ).
tcf(c_164731,plain,
! [X0: $i,X1: $i] :
( ( relation_field(relation_restriction(sK96(X0,X1),sK140)) = sK140 )
| ~ sP12(X0,X1) ),
inference(superposition,[status(thm)],[c_208,c_163929]) ).
tcf(c_164732,plain,
! [X0: $i] :
( sP13(X0)
| ( relation_field(relation_restriction(sK108(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_230,c_163929]) ).
tcf(c_164733,plain,
! [X0: $i] : relation_field(relation_restriction(sK115(X0),sK140)) = sK140,
inference(superposition,[status(thm)],[c_249,c_163929]) ).
tcf(c_164734,plain,
! [X0: $i] : relation_field(relation_restriction(sK124(X0),sK140)) = sK140,
inference(superposition,[status(thm)],[c_346,c_163929]) ).
tcf(c_164735,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_355,c_163929]) ).
tcf(c_164736,plain,
! [X0: $i] : relation_field(relation_restriction(identity_relation(X0),sK140)) = sK140,
inference(superposition,[status(thm)],[c_1101,c_163929]) ).
tcf(c_164737,plain,
! [X0: $i,X1: $i] :
( ( relation_field(relation_restriction(relation_dom_restriction(X0,X1),sK140)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_773,c_163929]) ).
tcf(c_164738,plain,
relation_field(relation_restriction(sK140,sK140)) = sK140,
inference(superposition,[status(thm)],[c_577,c_163929]) ).
tcf(c_164739,plain,
! [X0: $i] :
( ( relation_field(relation_restriction(relation_dom(X0),sK140)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_642,c_163929]) ).
tcf(c_164740,plain,
! [X0: $i,X1: $i] :
( ( relation_field(relation_restriction(relation_rng_restriction(X1,X0),sK140)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_646,c_163929]) ).
tcf(c_164741,plain,
! [X0: $i,X1: $i] :
( ( relation_field(relation_restriction(sK195(X0,X1),sK140)) = sK140 )
| ~ are_equipotent(X0,X1) ),
inference(superposition,[status(thm)],[c_84692,c_163929]) ).
tcf(c_164742,plain,
relation_field(relation_restriction(sK240,sK140)) = sK140,
inference(superposition,[status(thm)],[c_783,c_163929]) ).
tcf(c_164743,plain,
relation_field(relation_restriction(sK242,sK140)) = sK140,
inference(superposition,[status(thm)],[c_791,c_163929]) ).
tcf(c_164744,plain,
! [X0: $i] :
( ( relation_field(relation_restriction(sK264(X0),sK140)) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_852,c_163929]) ).
tcf(c_164745,plain,
! [X0: $i] :
( ( relation_field(relation_restriction(relation_rng(X0),sK140)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_944,c_163929]) ).
tcf(c_164746,plain,
! [X0: $i,X1: $i] :
( ( relation_field(relation_restriction(relation_restriction(X0,X1),sK140)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1013,c_163929]) ).
tcf(c_164747,plain,
! [X0: $i,X1: $i] : relation_field(relation_restriction(sK312(X0,X1),sK140)) = sK140,
inference(superposition,[status(thm)],[c_1019,c_163929]) ).
tcf(c_164748,plain,
! [X0: $i] : relation_field(relation_restriction(inclusion_relation(X0),sK140)) = sK140,
inference(superposition,[status(thm)],[c_1091,c_163929]) ).
tcf(c_164749,plain,
! [X0: $i] :
( ( relation_field(relation_restriction(relation_inverse(X0),sK140)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1113,c_163929]) ).
tcf(c_164750,plain,
! [X0: $i] :
( ( relation_field(relation_restriction(relation_inverse(X0),sK140)) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1112,c_163929]) ).
tcf(c_164751,plain,
relation_field(relation_restriction(sK335,sK140)) = sK140,
inference(superposition,[status(thm)],[c_1149,c_163929]) ).
tcf(c_164752,plain,
! [X0: $i,X1: $i] : relation_field(relation_restriction(sK347(X0,X1),sK140)) = sK140,
inference(superposition,[status(thm)],[c_1237,c_163929]) ).
tcf(c_164857,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK169(X0))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_164058,c_833]) ).
tcf(c_164858,plain,
! [X0: $i] :
( epsilon_connected(sK169(X0))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_164058,c_1050]) ).
tcf(c_164859,plain,
! [X0: $i] :
( epsilon_transitive(sK169(X0))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_164058,c_1049]) ).
tcf(c_164879,plain,
! [X0: $i,X1: $i] :
( ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) )
| ( set_difference(relation_inverse_image(X0,X1),relation_dom(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_153290,c_163162]) ).
tcf(c_164880,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) )
| ( set_difference(relation_inverse_image(X0,X1),relation_dom(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_153265,c_163162]) ).
tcf(c_164881,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( set_difference(relation_inverse_image(X0,X1),relation_dom(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_146155,c_163162]) ).
tcf(c_164883,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_inverse_image(sK96(X0,X1),X2),relation_dom(sK96(X0,X1))) = sK140 )
| ~ sP12(X0,X1) ),
inference(superposition,[status(thm)],[c_208,c_163162]) ).
tcf(c_164884,plain,
! [X0: $i,X1: $i] :
( sP13(X0)
| ( set_difference(relation_inverse_image(sK108(X0),X1),relation_dom(sK108(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_230,c_163162]) ).
tcf(c_164885,plain,
! [X0: $i,X1: $i] : set_difference(relation_inverse_image(sK115(X0),X1),relation_dom(sK115(X0))) = sK140,
inference(superposition,[status(thm)],[c_249,c_163162]) ).
tcf(c_164886,plain,
! [X0: $i,X1: $i] : set_difference(relation_inverse_image(sK124(X0),X1),relation_dom(sK124(X0))) = sK140,
inference(superposition,[status(thm)],[c_346,c_163162]) ).
tcf(c_164887,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_inverse_image(sK126(X0),X1),relation_dom(sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_355,c_163162]) ).
tcf(c_164888,plain,
! [X0: $i,X1: $i] : set_difference(relation_inverse_image(identity_relation(X0),X1),relation_dom(identity_relation(X0))) = sK140,
inference(superposition,[status(thm)],[c_1101,c_163162]) ).
tcf(c_164889,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_inverse_image(relation_dom_restriction(X0,X1),X2),relation_dom(relation_dom_restriction(X0,X1))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_773,c_163162]) ).
tcf(c_164890,plain,
! [X0: $i] : set_difference(relation_inverse_image(sK140,X0),relation_dom(sK140)) = sK140,
inference(superposition,[status(thm)],[c_577,c_163162]) ).
tcf(c_164891,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(relation_dom(X0),X1),relation_dom(relation_dom(X0))) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_642,c_163162]) ).
tcf(c_164892,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_inverse_image(relation_rng_restriction(X1,X0),X2),relation_dom(relation_rng_restriction(X1,X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_646,c_163162]) ).
tcf(c_164893,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_inverse_image(sK195(X0,X1),X2),relation_dom(sK195(X0,X1))) = sK140 )
| ~ are_equipotent(X0,X1) ),
inference(superposition,[status(thm)],[c_84692,c_163162]) ).
tcf(c_164894,plain,
! [X0: $i] : set_difference(relation_inverse_image(sK240,X0),relation_dom(sK240)) = sK140,
inference(superposition,[status(thm)],[c_783,c_163162]) ).
tcf(c_164895,plain,
! [X0: $i] : set_difference(relation_inverse_image(sK242,X0),relation_dom(sK242)) = sK140,
inference(superposition,[status(thm)],[c_791,c_163162]) ).
tcf(c_164896,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(sK264(X0),X1),relation_dom(sK264(X0))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_852,c_163162]) ).
tcf(c_164897,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(relation_rng(X0),X1),relation_dom(relation_rng(X0))) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_944,c_163162]) ).
tcf(c_164898,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_inverse_image(relation_restriction(X0,X1),X2),relation_dom(relation_restriction(X0,X1))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1013,c_163162]) ).
tcf(c_164899,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_inverse_image(sK312(X0,X1),X2),relation_dom(sK312(X0,X1))) = sK140,
inference(superposition,[status(thm)],[c_1019,c_163162]) ).
tcf(c_164900,plain,
! [X0: $i,X1: $i] : set_difference(relation_inverse_image(inclusion_relation(X0),X1),relation_dom(inclusion_relation(X0))) = sK140,
inference(superposition,[status(thm)],[c_1091,c_163162]) ).
tcf(c_164901,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(relation_inverse(X0),X1),relation_dom(relation_inverse(X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1113,c_163162]) ).
tcf(c_164902,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(relation_inverse(X0),X1),relation_dom(relation_inverse(X0))) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1112,c_163162]) ).
tcf(c_164903,plain,
! [X0: $i] : set_difference(relation_inverse_image(sK335,X0),relation_dom(sK335)) = sK140,
inference(superposition,[status(thm)],[c_1149,c_163162]) ).
tcf(c_164904,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_inverse_image(sK347(X0,X1),X2),relation_dom(sK347(X0,X1))) = sK140,
inference(superposition,[status(thm)],[c_1237,c_163162]) ).
tcf(c_164906,plain,
! [X0: $i,X1: $i] : set_difference(relation_inverse_image(identity_relation(X0),X1),X0) = sK140,
inference(light_normalisation,[status(thm)],[c_164888,c_489]) ).
tcf(c_164907,plain,
! [X0: $i,X1: $i] : set_difference(relation_inverse_image(sK115(X0),X1),X0) = sK140,
inference(light_normalisation,[status(thm)],[c_164885,c_251]) ).
tcf(c_165080,plain,
! [X0: $i,X1: $i] :
( ( sK125(identity_relation(X0)) = sK140 )
| ( relation_dom(sK126(identity_relation(X0))) = identity_relation(X0) )
| ( set_difference(relation_field(relation_restriction(X0,X1)),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_153290,c_163926]) ).
tcf(c_165081,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK115(X0)) = sK140 )
| ( relation_dom(sK126(sK115(X0))) = sK115(X0) )
| ( set_difference(relation_field(relation_restriction(X0,X1)),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_153265,c_163926]) ).
tcf(c_165082,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ( set_difference(relation_field(relation_restriction(X0,X1)),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_146155,c_163926]) ).
tcf(c_165084,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_field(relation_restriction(sK96(X0,X1),X2)),X2) = sK140 )
| ~ sP12(X0,X1) ),
inference(superposition,[status(thm)],[c_208,c_163926]) ).
tcf(c_165085,plain,
! [X0: $i,X1: $i] :
( sP13(X0)
| ( set_difference(relation_field(relation_restriction(sK108(X0),X1)),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_230,c_163926]) ).
tcf(c_165086,plain,
! [X0: $i,X1: $i] : set_difference(relation_field(relation_restriction(sK115(X0),X1)),X1) = sK140,
inference(superposition,[status(thm)],[c_249,c_163926]) ).
tcf(c_165087,plain,
! [X0: $i,X1: $i] : set_difference(relation_field(relation_restriction(sK124(X0),X1)),X1) = sK140,
inference(superposition,[status(thm)],[c_346,c_163926]) ).
tcf(c_165088,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(relation_field(relation_restriction(sK126(X0),X1)),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_355,c_163926]) ).
tcf(c_165089,plain,
! [X0: $i,X1: $i] : set_difference(relation_field(relation_restriction(identity_relation(X0),X1)),X1) = sK140,
inference(superposition,[status(thm)],[c_1101,c_163926]) ).
tcf(c_165090,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_field(relation_restriction(relation_dom_restriction(X0,X1),X2)),X2) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_773,c_163926]) ).
tcf(c_165091,plain,
! [X0: $i] : set_difference(relation_field(relation_restriction(sK140,X0)),X0) = sK140,
inference(superposition,[status(thm)],[c_577,c_163926]) ).
tcf(c_165092,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_field(relation_restriction(relation_dom(X0),X1)),X1) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_642,c_163926]) ).
tcf(c_165093,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_field(relation_restriction(relation_rng_restriction(X1,X0),X2)),X2) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_646,c_163926]) ).
tcf(c_165094,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_field(relation_restriction(sK195(X0,X1),X2)),X2) = sK140 )
| ~ are_equipotent(X0,X1) ),
inference(superposition,[status(thm)],[c_84692,c_163926]) ).
tcf(c_165095,plain,
! [X0: $i] : set_difference(relation_field(relation_restriction(sK240,X0)),X0) = sK140,
inference(superposition,[status(thm)],[c_783,c_163926]) ).
tcf(c_165096,plain,
! [X0: $i] : set_difference(relation_field(relation_restriction(sK242,X0)),X0) = sK140,
inference(superposition,[status(thm)],[c_791,c_163926]) ).
tcf(c_165097,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_field(relation_restriction(sK264(X0),X1)),X1) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_852,c_163926]) ).
tcf(c_165098,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_field(relation_restriction(relation_rng(X0),X1)),X1) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_944,c_163926]) ).
tcf(c_165099,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(relation_field(relation_restriction(relation_restriction(X0,X1),X2)),X2) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1013,c_163926]) ).
tcf(c_165100,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_field(relation_restriction(sK312(X0,X1),X2)),X2) = sK140,
inference(superposition,[status(thm)],[c_1019,c_163926]) ).
tcf(c_165101,plain,
! [X0: $i,X1: $i] : set_difference(relation_field(relation_restriction(inclusion_relation(X0),X1)),X1) = sK140,
inference(superposition,[status(thm)],[c_1091,c_163926]) ).
tcf(c_165102,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_field(relation_restriction(relation_inverse(X0),X1)),X1) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_1113,c_163926]) ).
tcf(c_165103,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_field(relation_restriction(relation_inverse(X0),X1)),X1) = sK140 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_1112,c_163926]) ).
tcf(c_165104,plain,
! [X0: $i] : set_difference(relation_field(relation_restriction(sK335,X0)),X0) = sK140,
inference(superposition,[status(thm)],[c_1149,c_163926]) ).
tcf(c_165105,plain,
! [X0: $i,X1: $i,X2: $i] : set_difference(relation_field(relation_restriction(sK347(X0,X1),X2)),X2) = sK140,
inference(superposition,[status(thm)],[c_1237,c_163926]) ).
tcf(c_165168,plain,
! [X0: $i] : disjoint(set_difference(relation_field(relation_restriction(sK140,X0)),X0),relation_field(relation_restriction(sK140,X0))),
inference(superposition,[status(thm)],[c_165091,c_146330]) ).
tcf(c_165170,plain,
! [X0: $i] : set_difference(sK140,relation_field(relation_restriction(sK140,X0))) = sK140,
inference(superposition,[status(thm)],[c_165091,c_146010]) ).
tcf(c_165171,plain,
! [X0: $i] : subset(sK140,relation_field(relation_restriction(sK140,X0))),
inference(superposition,[status(thm)],[c_165091,c_383]) ).
tcf(c_165172,plain,
! [X0: $i] :
( disjoint(relation_field(relation_restriction(sK140,X0)),X0)
| ( set_difference(relation_field(relation_restriction(sK140,X0)),sK140) != sK140 ) ),
inference(superposition,[status(thm)],[c_165091,c_625]) ).
tcf(c_165173,plain,
! [X0: $i] : subset(relation_field(relation_restriction(sK140,X0)),X0),
inference(superposition,[status(thm)],[c_165091,c_387]) ).
tcf(c_165176,plain,
! [X0: $i] : disjoint(sK140,relation_field(relation_restriction(sK140,X0))),
inference(light_normalisation,[status(thm)],[c_165168,c_165091]) ).
tcf(c_165182,plain,
! [X0: $i] :
( finite(relation_field(relation_restriction(sK140,X0)))
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_165173,c_276]) ).
tcf(c_165183,plain,
! [X0: $i] : ~ proper_subset(X0,relation_field(relation_restriction(sK140,X0))),
inference(superposition,[status(thm)],[c_165173,c_472]) ).
tcf(c_165184,plain,
! [X0: $i] :
( in(sK140,relation_field(relation_restriction(sK140,X0)))
| ( X0 = sK140 )
| ( sK125(subset_complement(X0,relation_field(relation_restriction(sK140,X0)))) = sK140 )
| ~ element(sK140,X0) ),
inference(superposition,[status(thm)],[c_165173,c_145539]) ).
tcf(c_165185,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,relation_field(relation_restriction(sK140,X1)))),relation_field(relation_restriction(sK140,X1)))
| ( relation_field(relation_restriction(sK140,X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_165173,c_1058]) ).
tcf(c_165186,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,relation_field(relation_restriction(sK140,X1))),relation_field(relation_restriction(sK140,X1)))
| ( relation_field(relation_restriction(sK140,X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_165173,c_1057]) ).
tcf(c_165187,plain,
! [X0: $i] :
( in(sK128(relation_field(relation_restriction(sK140,X0))),relation_field(relation_restriction(sK140,X0)))
| ( relation_field(relation_restriction(sK140,X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_165173,c_369]) ).
tcf(c_165188,plain,
! [X0: $i] :
( ordinal(sK128(relation_field(relation_restriction(sK140,X0))))
| ( relation_field(relation_restriction(sK140,X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_165173,c_371]) ).
tcf(c_165190,plain,
! [X0: $i] :
( ( relation_field(relation_restriction(sK140,unordered_pair(X0,X0))) = sK140 )
| ( relation_field(relation_restriction(sK140,unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_165173,c_397]) ).
tcf(c_165191,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(relation_field(relation_restriction(sK140,X1))),X0)
| ( relation_field(relation_restriction(sK140,X1)) = sK140 )
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,relation_field(relation_restriction(sK140,X1))) ),
inference(superposition,[status(thm)],[c_165173,c_370]) ).
tcf(c_165193,plain,
( in(sK63(relation_field(relation_restriction(sK140,powerset(sK62)))),relation_field(relation_restriction(sK140,powerset(sK62))))
| ( relation_field(relation_restriction(sK140,powerset(sK62))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_165173,c_156787]) ).
tcf(c_165194,plain,
! [X0: $i] :
( in(sK119(relation_field(relation_restriction(sK140,powerset(X0)))),relation_field(relation_restriction(sK140,powerset(X0))))
| ( relation_field(relation_restriction(sK140,powerset(X0))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_165173,c_156797]) ).
tcf(c_165195,plain,
( in(sK262(relation_field(relation_restriction(sK140,powerset(sK261)))),relation_field(relation_restriction(sK140,powerset(sK261))))
| ( relation_field(relation_restriction(sK140,powerset(sK261))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_165173,c_156803]) ).
tcf(c_165196,plain,
( ( relation_field(relation_restriction(sK140,powerset(sK140))) = sK140 )
| ( relation_field(relation_restriction(sK140,powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_165173,c_144406]) ).
tcf(c_165245,plain,
! [X0: $i] :
( sP3(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_150222]) ).
tcf(c_165246,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_148019]) ).
tcf(c_165247,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_147669]) ).
tcf(c_165248,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_147196]) ).
tcf(c_165249,plain,
! [X0: $i] :
( one_to_one(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_84200]) ).
tcf(c_165250,plain,
! [X0: $i] :
( ordinal(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_1047]) ).
tcf(c_165251,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_1046]) ).
tcf(c_165252,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_1045]) ).
tcf(c_165253,plain,
! [X0: $i] :
( finite(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_983]) ).
tcf(c_165254,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_799]) ).
tcf(c_165255,plain,
! [X0: $i] :
( function(X0)
| ( sK125(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_785]) ).
tcf(c_165256,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_575]) ).
tcf(c_165257,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(set_union2(X0,X1)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_615]) ).
tcf(c_165258,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(set_union2(X0,X1)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_614]) ).
tcf(c_165259,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,X1) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(relation_dom(X0)))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_163467,c_150772]) ).
tcf(c_165260,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK198(X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_694]) ).
tcf(c_165262,plain,
( ( sK125(sK241) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK241))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_789]) ).
tcf(c_165263,plain,
( ( sK125(sK242) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK242))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_790]) ).
tcf(c_165265,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,unordered_pair(X0,X0))) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(set_union2(X0,unordered_pair(X0,X0))))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_892]) ).
tcf(c_165266,plain,
! [X0: $i,X1: $i] :
( ( sK125(unordered_pair(X0,X1)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(unordered_pair(X0,X1)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_935]) ).
tcf(c_165267,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK302(X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_973]) ).
tcf(c_165268,plain,
( ( sK125(sK303) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK303))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_975]) ).
tcf(c_165269,plain,
( ( sK125(sK313) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK313))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_1025]) ).
tcf(c_165270,plain,
( ( sK125(sK346) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK346))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_1223]) ).
tcf(c_165271,plain,
( ( sK125(sK358) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK358))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_1276]) ).
tcf(c_165272,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK115(X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_147253]) ).
tcf(c_165273,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK115(X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_147177]) ).
tcf(c_165274,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(identity_relation(X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_147255]) ).
tcf(c_165275,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(identity_relation(X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_147179]) ).
tcf(c_165276,plain,
! [X0: $i] :
( ( sK125(sK116(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK116(X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_150228]) ).
tcf(c_165277,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(subset_complement(X1,X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(subset_complement(X1,X0)))) = sK140 )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_163467,c_150233]) ).
tcf(c_165278,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK263(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK263(X0)))) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_163467,c_150238]) ).
tcf(c_165279,plain,
! [X0: $i] :
( ( sK125(sK300(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK300(X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_150241]) ).
tcf(c_165280,plain,
( ( sK125(sK64) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK64))) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_163467,c_150248]) ).
tcf(c_165281,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(apply(sK126(X1),X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(apply(sK126(X1),X0)))) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_163467,c_150503]) ).
tcf(c_165282,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK169(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(sK169(X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_163467,c_150508]) ).
tcf(c_165400,plain,
! [X0: $i,X1: $i] :
( subset(relation_inverse_image(sK126(sK302(powerset(X0))),X1),sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ~ relation(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_296]) ).
tcf(c_165401,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK302(powerset(X0))),sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ( apply(sK126(sK302(powerset(X0))),X1) = sK140 )
| ~ function(sK126(sK302(powerset(X0))))
| ~ relation(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_154130]) ).
tcf(c_165402,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK302(powerset(X0))) = sK140 )
| ( apply(sK126(sK302(powerset(X0))),X1) = sK140 )
| ~ function(sK126(sK302(powerset(X0))))
| ~ relation(sK126(sK302(powerset(X0))))
| ~ in(sK302(powerset(X0)),X1) ),
inference(superposition,[status(thm)],[c_147767,c_155600]) ).
tcf(c_165403,plain,
! [X0: $i] :
( function(sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ~ empty(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_147195]) ).
tcf(c_165404,plain,
! [X0: $i] :
( finite(sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ~ empty(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_147193]) ).
tcf(c_165405,plain,
! [X0: $i] :
( epsilon_transitive(sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ~ empty(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_147192]) ).
tcf(c_165406,plain,
! [X0: $i] :
( epsilon_connected(sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ~ empty(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_147191]) ).
tcf(c_165407,plain,
! [X0: $i] :
( ordinal(sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ~ empty(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_147190]) ).
tcf(c_165408,plain,
! [X0: $i] :
( one_to_one(sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ~ empty(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_147189]) ).
tcf(c_165409,plain,
! [X0: $i,X1: $i] :
( ( sK125(sK302(powerset(X0))) = sK140 )
| ( apply(sK126(sK302(powerset(X0))),X1) = sK140 )
| ~ empty(sK302(powerset(X0)))
| ~ relation(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_150772]) ).
tcf(c_165410,plain,
! [X0: $i,X1: $i] :
( element(X1,sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ( apply(sK126(sK302(powerset(X0))),X1) = sK140 )
| ~ function(sK126(sK302(powerset(X0))))
| ~ relation(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_148552]) ).
tcf(c_165411,plain,
! [X0: $i] :
( relation(sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ~ empty(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_642]) ).
tcf(c_165412,plain,
! [X0: $i] :
( empty(sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ~ empty(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_641]) ).
tcf(c_165413,plain,
! [X0: $i,X1: $i] :
( in(X1,sK302(powerset(X0)))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ( apply(sK126(sK302(powerset(X0))),X1) = sK140 )
| ~ function(sK126(sK302(powerset(X0))))
| ~ relation(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_906]) ).
tcf(c_165414,plain,
! [X0: $i] :
( ( sK125(sK302(powerset(X0))) = sK140 )
| ( relation_rng(sK126(sK302(powerset(X0)))) = sK140 )
| ~ relation(sK126(sK302(powerset(X0))))
| ( sK302(powerset(X0)) != sK140 ) ),
inference(superposition,[status(thm)],[c_147767,c_478]) ).
tcf(c_165415,plain,
! [X0: $i] :
( ( sK126(sK302(powerset(X0))) = sK140 )
| ( sK125(sK302(powerset(X0))) = sK140 )
| ~ relation(sK126(sK302(powerset(X0))))
| ( sK302(powerset(X0)) != sK140 ) ),
inference(superposition,[status(thm)],[c_147767,c_475]) ).
tcf(c_165524,plain,
! [X0: $i] :
( subset(powerset(sK140),X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_314,c_388]) ).
tcf(c_165526,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ proper_subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_388,c_472]) ).
tcf(c_165527,plain,
! [X0: $i,X1: $i] :
( in(sK140,unordered_pair(X0,X0))
| ( X1 = sK140 )
| ( sK125(subset_complement(X1,unordered_pair(X0,X0))) = sK140 )
| ~ element(sK140,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_388,c_145539]) ).
tcf(c_165528,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X2,sK318(X2,unordered_pair(X0,X0))),unordered_pair(X0,X0))
| ( unordered_pair(X0,X0) = sK140 )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_388,c_1058]) ).
tcf(c_165529,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X2,unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ( unordered_pair(X0,X0) = sK140 )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_388,c_1057]) ).
tcf(c_165530,plain,
! [X0: $i,X1: $i] :
( in(sK128(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ( unordered_pair(X0,X0) = sK140 )
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_388,c_369]) ).
tcf(c_165531,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ( unordered_pair(X0,X0) = sK140 )
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_388,c_371]) ).
tcf(c_165532,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),X1) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_388,c_386]) ).
tcf(c_165533,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = sK140 )
| ( unordered_pair(X0,X0) = unordered_pair(X1,X1) )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_388,c_397]) ).
tcf(c_165534,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(unordered_pair(X1,X1)),X0)
| ( unordered_pair(X1,X1) = sK140 )
| ~ ordinal(X2)
| ~ ordinal(X0)
| ~ in(X1,X2)
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_388,c_370]) ).
tcf(c_165536,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = omega )
| ~ being_limit_ordinal(unordered_pair(X0,X0))
| ~ ordinal(unordered_pair(X0,X0))
| ~ in(sK140,unordered_pair(X0,X0))
| ~ in(X0,sK263(unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_388,c_843]) ).
tcf(c_165537,plain,
! [X0: $i] :
( in(sK63(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ( unordered_pair(X0,X0) = sK140 )
| ~ iPr_def_21
| ~ in(X0,powerset(sK62)) ),
inference(superposition,[status(thm)],[c_388,c_156787]) ).
tcf(c_165538,plain,
! [X0: $i,X1: $i] :
( in(sK119(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ( unordered_pair(X0,X0) = sK140 )
| ~ finite(X1)
| ~ in(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_388,c_156797]) ).
tcf(c_165539,plain,
! [X0: $i] :
( in(sK262(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ( unordered_pair(X0,X0) = sK140 )
| ~ iPr_def_15
| ~ in(X0,powerset(sK261)) ),
inference(superposition,[status(thm)],[c_388,c_156803]) ).
tcf(c_165540,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = sK140 )
| ( unordered_pair(X0,X0) = powerset(sK140) )
| ~ in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_388,c_144406]) ).
tcf(c_165547,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = powerset(sK140) )
| ~ in(X0,powerset(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165540,c_52]) ).
tcf(c_165550,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165531,c_52]) ).
tcf(c_165554,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = unordered_pair(X1,X1) )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165533,c_52]) ).
tcf(c_165557,plain,
! [X0: $i] :
( in(sK262(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ~ iPr_def_15
| ~ in(X0,powerset(sK261)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165539,c_52]) ).
tcf(c_165561,plain,
! [X0: $i] :
( in(sK63(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ~ iPr_def_21
| ~ in(X0,powerset(sK62)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165537,c_52]) ).
tcf(c_165565,plain,
! [X0: $i,X1: $i] :
( in(sK128(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165530,c_52]) ).
tcf(c_165569,plain,
! [X0: $i,X1: $i] :
( in(sK119(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ~ finite(X1)
| ~ in(X0,powerset(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165538,c_52]) ).
tcf(c_165573,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X2,unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ~ relation(X2)
| ~ is_well_founded_in(X2,X1)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165529,c_52]) ).
tcf(c_165583,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal_subset(sK128(unordered_pair(X1,X1)),X0)
| ~ ordinal(X2)
| ~ ordinal(X0)
| ~ in(X1,X2)
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165534,c_52]) ).
tcf(c_165589,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(fiber(X2,sK318(X2,unordered_pair(X0,X0))),unordered_pair(X0,X0))
| ~ relation(X2)
| ~ is_well_founded_in(X2,X1)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165528,c_52]) ).
tcf(c_165640,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ in(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_513,c_391]) ).
tcf(c_165641,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(unordered_pair(X0,X1),X2)),
inference(superposition,[status(thm)],[c_498,c_391]) ).
tcf(c_165643,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(X1,unordered_pair(X0,X2))),
inference(superposition,[status(thm)],[c_156747,c_391]) ).
tcf(c_165646,plain,
! [X0: $i] :
( in(sK140,X0)
| ~ subset(powerset(sK140),X0) ),
inference(superposition,[status(thm)],[c_314,c_391]) ).
tcf(c_165658,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,union(X2))
| ~ in(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_513,c_392]) ).
tcf(c_165659,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(unordered_pair(X1,X0),X2)),
inference(superposition,[status(thm)],[c_498,c_392]) ).
tcf(c_165661,plain,
! [X0: $i,X1: $i,X2: $i] : in(X0,set_union2(X1,unordered_pair(X2,X0))),
inference(superposition,[status(thm)],[c_156747,c_392]) ).
tcf(c_165674,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK131(X0)),union(sK131(X0))) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_406,c_154509]) ).
tcf(c_165675,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| in(sK128(sK131(X0)),sK131(X0))
| ( sK131(X0) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_406,c_154063]) ).
tcf(c_165676,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(X0,sK131(X0)) ),
inference(superposition,[status(thm)],[c_406,c_527]) ).
tcf(c_165677,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ordinal(sK128(sK131(X0)))
| ( sK131(X0) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_406,c_154064]) ).
tcf(c_165678,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| in(sK142(sK131(X0)),sK131(X0))
| ( sK125(X0) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_406,c_154131]) ).
tcf(c_165679,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ( set_difference(sK131(X0),union(X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_406,c_154065]) ).
tcf(c_165680,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| in(sK142(X0),X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_406,c_522]) ).
tcf(c_165681,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ( sK125(X0) = sK140 )
| ~ ordinal(X0)
| ~ empty(sK131(X0)) ),
inference(superposition,[status(thm)],[c_406,c_150230]) ).
tcf(c_165682,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_406,c_787]) ).
tcf(c_165683,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| element(sK131(X0),X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_406,c_526]) ).
tcf(c_165684,plain,
! [X0: $i] :
( being_limit_ordinal(sK92(X0))
| in(sK131(sK92(X0)),X0)
| ~ ordinal(sK92(X0)) ),
inference(superposition,[status(thm)],[c_406,c_198]) ).
tcf(c_165685,plain,
! [X0: $i] :
( being_limit_ordinal(sK92(X0))
| ordinal(sK131(sK92(X0)))
| ~ ordinal(sK92(X0)) ),
inference(superposition,[status(thm)],[c_406,c_199]) ).
tcf(c_165686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( being_limit_ordinal(relation_inverse_image(X0,X3))
| in(apply(X0,sK131(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ ordinal(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_406,c_425]) ).
tcf(c_165687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( being_limit_ordinal(relation_inverse_image(X0,X3))
| in(sK131(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ ordinal(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_406,c_424]) ).
tcf(c_165688,plain,
( being_limit_ordinal(sK140)
| ~ ordinal(sK140) ),
inference(superposition,[status(thm)],[c_406,c_580]) ).
tcf(c_165689,plain,
! [X0: $i] :
( being_limit_ordinal(powerset(X0))
| subset(sK131(powerset(X0)),X0)
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_406,c_662]) ).
tcf(c_165690,plain,
! [X0: $i] :
( sP29
| being_limit_ordinal(sK248(X0))
| ordinal(sK131(sK248(X0)))
| ~ ordinal(sK248(X0)) ),
inference(superposition,[status(thm)],[c_406,c_808]) ).
tcf(c_165691,plain,
being_limit_ordinal(sK140),
inference(forward_subsumption_resolution,[status(thm)],[c_165688,c_144282]) ).
tcf(c_165804,plain,
union(sK140) = sK140,
inference(superposition,[status(thm)],[c_165691,c_714]) ).
tcf(c_165830,plain,
! [X0: $i] :
( ~ in(sK140,X0)
| ~ proper_subset(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_165524,c_472]) ).
tcf(c_165832,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,powerset(sK140))),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ relation(X0)
| ~ in(sK140,X1)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_165524,c_1058]) ).
tcf(c_165833,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,powerset(sK140)),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ relation(X0)
| ~ in(sK140,X1)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_165524,c_1057]) ).
tcf(c_165834,plain,
! [X0: $i] :
( in(sK128(powerset(sK140)),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_165524,c_369]) ).
tcf(c_165835,plain,
! [X0: $i] :
( ordinal(sK128(powerset(sK140)))
| ( powerset(sK140) = sK140 )
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_165524,c_371]) ).
tcf(c_165836,plain,
! [X0: $i] :
( ( set_difference(powerset(sK140),X0) = sK140 )
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_165524,c_386]) ).
tcf(c_165837,plain,
! [X0: $i] :
( ( powerset(sK140) = sK140 )
| ( unordered_pair(X0,X0) = powerset(sK140) )
| ~ in(sK140,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_165524,c_397]) ).
tcf(c_165838,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(powerset(sK140)),X0)
| ( powerset(sK140) = sK140 )
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(sK140,X1)
| ~ in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_165524,c_370]) ).
tcf(c_165839,plain,
( ( powerset(sK140) = sK140 )
| ~ in(sK140,sK140) ),
inference(superposition,[status(thm)],[c_165524,c_403]) ).
tcf(c_165840,plain,
( ( powerset(sK140) = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140))
| ~ in(sK140,powerset(sK140))
| ~ in(sK140,sK263(powerset(sK140))) ),
inference(superposition,[status(thm)],[c_165524,c_843]) ).
tcf(c_165841,plain,
( in(sK63(powerset(sK140)),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ iPr_def_21
| ~ in(sK140,powerset(sK62)) ),
inference(superposition,[status(thm)],[c_165524,c_156787]) ).
tcf(c_165842,plain,
! [X0: $i] :
( in(sK119(powerset(sK140)),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ finite(X0)
| ~ in(sK140,powerset(X0)) ),
inference(superposition,[status(thm)],[c_165524,c_156797]) ).
tcf(c_165843,plain,
( in(sK262(powerset(sK140)),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ iPr_def_15
| ~ in(sK140,powerset(sK261)) ),
inference(superposition,[status(thm)],[c_165524,c_156803]) ).
tcf(c_165849,plain,
! [X0: $i] :
( ordinal(sK128(powerset(sK140)))
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165835,c_144206]) ).
tcf(c_165853,plain,
( in(sK262(powerset(sK140)),powerset(sK140))
| ~ iPr_def_15
| ~ in(sK140,powerset(sK261)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165843,c_144206]) ).
tcf(c_165857,plain,
( in(sK63(powerset(sK140)),powerset(sK140))
| ~ iPr_def_21
| ~ in(sK140,powerset(sK62)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165841,c_144206]) ).
tcf(c_165861,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = powerset(sK140) )
| ~ in(sK140,unordered_pair(X0,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165837,c_144206]) ).
tcf(c_165864,plain,
! [X0: $i] :
( in(sK128(powerset(sK140)),powerset(sK140))
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165834,c_144206]) ).
tcf(c_165868,plain,
! [X0: $i] :
( in(sK119(powerset(sK140)),powerset(sK140))
| ~ finite(X0)
| ~ in(sK140,powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165842,c_144206]) ).
tcf(c_165872,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,powerset(sK140)),powerset(sK140))
| ~ relation(X0)
| ~ in(sK140,X1)
| ~ is_well_founded_in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165833,c_144206]) ).
tcf(c_165877,plain,
( ( powerset(sK140) = omega )
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140))
| ~ in(sK140,sK263(powerset(sK140))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165840,c_146165]) ).
tcf(c_165882,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(powerset(sK140)),X0)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(sK140,X1)
| ~ in(X0,powerset(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165838,c_144206]) ).
tcf(c_165888,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,powerset(sK140))),powerset(sK140))
| ~ relation(X0)
| ~ in(sK140,X1)
| ~ is_well_founded_in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_165832,c_144206]) ).
tcf(c_165898,plain,
! [X0: $i] :
( in(sK140,union(X0))
| ~ in(powerset(sK140),X0) ),
inference(superposition,[status(thm)],[c_513,c_165646]) ).
tcf(c_165899,plain,
! [X0: $i] : in(sK140,set_union2(powerset(sK140),X0)),
inference(superposition,[status(thm)],[c_498,c_165646]) ).
tcf(c_165902,plain,
! [X0: $i] : in(sK140,set_union2(X0,powerset(sK140))),
inference(superposition,[status(thm)],[c_156747,c_165646]) ).
tcf(c_165942,plain,
! [X0: $i] :
( ( set_difference(powerset(sK140),X0) = sK140 )
| ( set_difference(unordered_pair(sK140,sK140),set_difference(unordered_pair(sK140,sK140),X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_165836]) ).
tcf(c_165943,plain,
set_difference(powerset(sK140),omega) = sK140,
inference(superposition,[status(thm)],[c_847,c_165836]) ).
tcf(c_165944,plain,
set_difference(powerset(sK140),sK116(sK140)) = sK140,
inference(superposition,[status(thm)],[c_272,c_165836]) ).
tcf(c_165945,plain,
! [X0: $i] :
( ( apply(X0,sK140) = sK140 )
| ( set_difference(powerset(sK140),relation_dom(X0)) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_165836]) ).
tcf(c_165946,plain,
! [X0: $i,X1: $i] :
( in(sK140,X0)
| ( X1 = sK140 )
| ( set_difference(powerset(sK140),subset_complement(X1,X0)) = sK140 )
| ~ element(sK140,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5403,c_165836]) ).
tcf(c_165947,plain,
! [X0: $i] :
( ( set_difference(powerset(sK140),powerset(X0)) = sK140 )
| ~ subset(sK140,X0) ),
inference(superposition,[status(thm)],[c_661,c_165836]) ).
tcf(c_165948,plain,
! [X0: $i] :
( ( set_difference(powerset(sK140),X0) = sK140 )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151909,c_165836]) ).
tcf(c_165949,plain,
! [X0: $i] :
( ( X0 = omega )
| ( set_difference(powerset(sK140),sK263(X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_165836]) ).
tcf(c_165950,plain,
! [X0: $i] : set_difference(powerset(sK140),unordered_pair(sK140,X0)) = sK140,
inference(superposition,[status(thm)],[c_939,c_165836]) ).
tcf(c_165951,plain,
! [X0: $i] : set_difference(powerset(sK140),unordered_pair(X0,sK140)) = sK140,
inference(superposition,[status(thm)],[c_940,c_165836]) ).
tcf(c_165952,plain,
set_difference(powerset(sK140),sK300(sK140)) = sK140,
inference(superposition,[status(thm)],[c_965,c_165836]) ).
tcf(c_165953,plain,
set_difference(powerset(sK140),powerset(sK140)) = sK140,
inference(superposition,[status(thm)],[c_146165,c_165836]) ).
tcf(c_165954,plain,
! [X0: $i] : set_difference(powerset(sK140),powerset(X0)) = sK140,
inference(forward_subsumption_resolution,[status(thm)],[c_165947,c_361]) ).
tcf(c_165977,plain,
disjoint(set_difference(powerset(sK140),omega),powerset(sK140)),
inference(superposition,[status(thm)],[c_165943,c_146330]) ).
tcf(c_165979,plain,
set_difference(sK140,powerset(sK140)) = sK140,
inference(superposition,[status(thm)],[c_165943,c_146010]) ).
tcf(c_165980,plain,
subset(sK140,powerset(sK140)),
inference(superposition,[status(thm)],[c_165943,c_383]) ).
tcf(c_165981,plain,
( disjoint(powerset(sK140),omega)
| ( set_difference(powerset(sK140),sK140) != sK140 ) ),
inference(superposition,[status(thm)],[c_165943,c_625]) ).
tcf(c_165982,plain,
subset(powerset(sK140),omega),
inference(superposition,[status(thm)],[c_165943,c_387]) ).
tcf(c_165985,plain,
disjoint(sK140,powerset(sK140)),
inference(light_normalisation,[status(thm)],[c_165977,c_165943]) ).
tcf(c_166036,plain,
~ proper_subset(omega,powerset(sK140)),
inference(superposition,[status(thm)],[c_165982,c_472]) ).
tcf(c_166038,plain,
! [X0: $i] :
( disjoint(fiber(X0,sK318(X0,powerset(sK140))),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,omega) ),
inference(superposition,[status(thm)],[c_165982,c_1058]) ).
tcf(c_166039,plain,
! [X0: $i] :
( in(sK318(X0,powerset(sK140)),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,omega) ),
inference(superposition,[status(thm)],[c_165982,c_1057]) ).
tcf(c_166040,plain,
( in(sK128(powerset(sK140)),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ ordinal(omega) ),
inference(superposition,[status(thm)],[c_165982,c_369]) ).
tcf(c_166041,plain,
( ordinal(sK128(powerset(sK140)))
| ( powerset(sK140) = sK140 )
| ~ ordinal(omega) ),
inference(superposition,[status(thm)],[c_165982,c_371]) ).
tcf(c_166043,plain,
! [X0: $i] :
( ordinal_subset(sK128(powerset(sK140)),X0)
| ( powerset(sK140) = sK140 )
| ~ ordinal(omega)
| ~ ordinal(X0)
| ~ in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_165982,c_370]) ).
tcf(c_166045,plain,
ordinal(sK128(powerset(sK140))),
inference(forward_subsumption_resolution,[status(thm)],[c_166041,c_144206,c_849]) ).
tcf(c_166046,plain,
in(sK128(powerset(sK140)),powerset(sK140)),
inference(forward_subsumption_resolution,[status(thm)],[c_166040,c_144206,c_849]) ).
tcf(c_166047,plain,
! [X0: $i] :
( in(sK318(X0,powerset(sK140)),powerset(sK140))
| ~ relation(X0)
| ~ is_well_founded_in(X0,omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166039,c_144206]) ).
tcf(c_166051,plain,
! [X0: $i] :
( ordinal_subset(sK128(powerset(sK140)),X0)
| ~ ordinal(X0)
| ~ in(X0,powerset(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166043,c_144206,c_849]) ).
tcf(c_166055,plain,
! [X0: $i] :
( disjoint(fiber(X0,sK318(X0,powerset(sK140))),powerset(sK140))
| ~ relation(X0)
| ~ is_well_founded_in(X0,omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166038,c_144206]) ).
tcf(c_166065,plain,
! [X0: $i] : disjoint(set_difference(powerset(sK140),powerset(X0)),powerset(sK140)),
inference(superposition,[status(thm)],[c_165954,c_146330]) ).
tcf(c_166069,plain,
! [X0: $i] :
( disjoint(powerset(sK140),powerset(X0))
| ( set_difference(powerset(sK140),sK140) != sK140 ) ),
inference(superposition,[status(thm)],[c_165954,c_625]) ).
tcf(c_166070,plain,
! [X0: $i] : subset(powerset(sK140),powerset(X0)),
inference(superposition,[status(thm)],[c_165954,c_387]) ).
tcf(c_166079,plain,
! [X0: $i] : ~ proper_subset(powerset(X0),powerset(sK140)),
inference(superposition,[status(thm)],[c_166070,c_472]) ).
tcf(c_166081,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,powerset(sK140))),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_166070,c_1058]) ).
tcf(c_166082,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,powerset(sK140)),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(X1)) ),
inference(superposition,[status(thm)],[c_166070,c_1057]) ).
tcf(c_166086,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(powerset(sK140)),X0)
| ( powerset(sK140) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(powerset(X1))
| ~ in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_166070,c_370]) ).
tcf(c_166087,plain,
( in(sK63(powerset(sK140)),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_166070,c_156787]) ).
tcf(c_166088,plain,
! [X0: $i] :
( in(sK119(powerset(sK140)),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_166070,c_156797]) ).
tcf(c_166089,plain,
( in(sK262(powerset(sK140)),powerset(sK140))
| ( powerset(sK140) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_166070,c_156803]) ).
tcf(c_166091,plain,
! [X0: $i] : in(sK140,powerset(X0)),
inference(superposition,[status(thm)],[c_166070,c_165646]) ).
tcf(c_166092,plain,
( in(sK262(powerset(sK140)),powerset(sK140))
| ~ iPr_def_15 ),
inference(forward_subsumption_resolution,[status(thm)],[c_166089,c_144206]) ).
tcf(c_166095,plain,
( in(sK63(powerset(sK140)),powerset(sK140))
| ~ iPr_def_21 ),
inference(forward_subsumption_resolution,[status(thm)],[c_166087,c_144206]) ).
tcf(c_166098,plain,
! [X0: $i] :
( in(sK119(powerset(sK140)),powerset(sK140))
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166088,c_144206]) ).
tcf(c_166101,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,powerset(sK140)),powerset(sK140))
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166082,c_144206]) ).
tcf(c_166105,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(powerset(sK140)),X0)
| ~ ordinal(X0)
| ~ ordinal(powerset(X1))
| ~ in(X0,powerset(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166086,c_144206]) ).
tcf(c_166110,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,powerset(sK140))),powerset(sK140))
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166081,c_144206]) ).
tcf(c_166123,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),X1) = sK140 )
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_165532]) ).
tcf(c_166124,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(sK49(X0,X1),sK49(X0,X1)),X0) = sK140 )
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_165532]) ).
tcf(c_166125,plain,
! [X0: $i] :
( sP3(X0)
| ( set_difference(unordered_pair(sK58(X0),sK58(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_122,c_165532]) ).
tcf(c_166126,plain,
( ( set_difference(unordered_pair(set_union2(sK62,unordered_pair(sK62,sK62)),set_union2(sK62,unordered_pair(sK62,sK62))),omega) = sK140 )
| ~ sP8 ),
inference(superposition,[status(thm)],[c_128,c_165532]) ).
tcf(c_166127,plain,
set_difference(unordered_pair(sK140,sK140),omega) = sK140,
inference(superposition,[status(thm)],[c_847,c_165532]) ).
tcf(c_166128,plain,
( ( set_difference(unordered_pair(sK66,sK66),omega) = sK140 )
| ~ sP6 ),
inference(superposition,[status(thm)],[c_140,c_165532]) ).
tcf(c_166131,plain,
( ( set_difference(unordered_pair(sK110,sK110),omega) = sK140 )
| ~ sP15 ),
inference(superposition,[status(thm)],[c_238,c_165532]) ).
tcf(c_166132,plain,
! [X0: $i] : set_difference(unordered_pair(X0,X0),sK116(X0)) = sK140,
inference(superposition,[status(thm)],[c_272,c_165532]) ).
tcf(c_166133,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ( set_difference(unordered_pair(X1,X1),relation_dom(X0)) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_165532]) ).
tcf(c_166134,plain,
! [X0: $i] :
( empty(X0)
| function(sK126(X0))
| ( set_difference(unordered_pair(sK125(X0),sK125(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_352,c_165532]) ).
tcf(c_166135,plain,
! [X0: $i] :
( empty(X0)
| relation(sK126(X0))
| ( set_difference(unordered_pair(sK125(X0),sK125(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_351,c_165532]) ).
tcf(c_166136,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( set_difference(unordered_pair(apply(sK126(X1),X0),apply(sK126(X1),X0)),X0) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2177,c_165532]) ).
tcf(c_166137,plain,
! [X0: $i] :
( ordinal(X0)
| ( set_difference(unordered_pair(sK127(X0),sK127(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_367,c_165532]) ).
tcf(c_166138,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( set_difference(unordered_pair(sK128(X0),sK128(X0)),X0) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_144620,c_165532]) ).
tcf(c_166139,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(unordered_pair(sK130(X0,X1),sK130(X0,X1)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_400,c_165532]) ).
tcf(c_166140,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(unordered_pair(sK130(X0,X1),sK130(X0,X1)),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_401,c_165532]) ).
tcf(c_166141,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ( set_difference(unordered_pair(sK131(X0),sK131(X0)),X0) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_406,c_165532]) ).
tcf(c_166142,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( set_difference(unordered_pair(X2,X2),subset_complement(X1,X0)) = sK140 )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_5403,c_165532]) ).
tcf(c_166143,plain,
! [X0: $i] :
( relation(X0)
| ( set_difference(unordered_pair(sK163(X0),sK163(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_561,c_165532]) ).
tcf(c_166144,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( set_difference(unordered_pair(sK169(X0),sK169(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_579,c_165532]) ).
tcf(c_166145,plain,
! [X0: $i] :
( ( set_difference(unordered_pair(sK173(X0),sK173(X0)),X0) = sK140 )
| ~ sP20(X0) ),
inference(superposition,[status(thm)],[c_584,c_165532]) ).
tcf(c_166147,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(unordered_pair(sK193(X0,X1),sK193(X0,X1)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_657,c_165532]) ).
tcf(c_166148,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),powerset(X1)) = sK140 )
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_661,c_165532]) ).
tcf(c_166149,plain,
! [X0: $i] :
( ( set_difference(unordered_pair(sK140,sK140),X0) = sK140 )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151909,c_165532]) ).
tcf(c_166150,plain,
! [X0: $i] :
( ( X0 = omega )
| ( set_difference(unordered_pair(sK140,sK140),sK263(X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_165532]) ).
tcf(c_166151,plain,
! [X0: $i] :
( ( set_difference(unordered_pair(relation_dom(sK264(X0)),relation_dom(sK264(X0))),omega) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_855,c_165532]) ).
tcf(c_166152,plain,
! [X0: $i] :
( ( set_difference(unordered_pair(sK268(X0),sK268(X0)),X0) = sK140 )
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_864,c_165532]) ).
tcf(c_166153,plain,
! [X0: $i,X1: $i] : set_difference(unordered_pair(X0,X0),unordered_pair(X0,X1)) = sK140,
inference(superposition,[status(thm)],[c_939,c_165532]) ).
tcf(c_166154,plain,
! [X0: $i,X1: $i] : set_difference(unordered_pair(X0,X0),unordered_pair(X1,X0)) = sK140,
inference(superposition,[status(thm)],[c_940,c_165532]) ).
tcf(c_166155,plain,
! [X0: $i] : set_difference(unordered_pair(X0,X0),sK300(X0)) = sK140,
inference(superposition,[status(thm)],[c_965,c_165532]) ).
tcf(c_166156,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( set_difference(unordered_pair(sK316(X0),sK316(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_1043,c_165532]) ).
tcf(c_166157,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( set_difference(unordered_pair(sK320(X1,X0),sK320(X1,X0)),X0) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_165532]) ).
tcf(c_166158,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( set_difference(unordered_pair(sK343(X0),sK343(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_1207,c_165532]) ).
tcf(c_166159,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( set_difference(unordered_pair(sK344(X0),sK344(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_1208,c_165532]) ).
tcf(c_166160,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( set_difference(unordered_pair(unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))),unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0)))),X0) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16344,c_165532]) ).
tcf(c_166161,plain,
( ( set_difference(unordered_pair(sK119(sK64),sK119(sK64)),sK64) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_146098,c_165532]) ).
tcf(c_166162,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( set_difference(unordered_pair(sK318(X0,X1),sK318(X0,X1)),X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144619,c_165532]) ).
tcf(c_166163,plain,
( sP15
| ( set_difference(unordered_pair(sK114(sK64),sK114(sK64)),sK64) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_145791,c_165532]) ).
tcf(c_166164,plain,
( ( set_difference(unordered_pair(sK72(sK64),sK72(sK64)),sK64) = sK140 )
| ~ iPr_def_19
| ~ sP7 ),
inference(superposition,[status(thm)],[c_145863,c_165532]) ).
tcf(c_166165,plain,
( ( set_difference(unordered_pair(sK67(sK64),sK67(sK64)),sK64) = sK140 )
| ~ sP6
| ~ sP7
| ~ in(sK140,sK66) ),
inference(superposition,[status(thm)],[c_146728,c_165532]) ).
tcf(c_166166,plain,
( ( set_difference(unordered_pair(sK111(sK64),sK111(sK64)),sK64) = sK140 )
| ~ sP15
| ~ sP7
| ~ in(sK140,sK110) ),
inference(superposition,[status(thm)],[c_146738,c_165532]) ).
tcf(c_166167,plain,
( ( sK199(powerset(powerset(sK62))) = sK140 )
| ( set_difference(unordered_pair(sK63(sK199(powerset(powerset(sK62)))),sK63(sK199(powerset(powerset(sK62))))),sK199(powerset(powerset(sK62)))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145355,c_165532]) ).
tcf(c_166168,plain,
! [X0: $i] :
( ( sK199(powerset(powerset(X0))) = sK140 )
| ( set_difference(unordered_pair(sK119(sK199(powerset(powerset(X0)))),sK119(sK199(powerset(powerset(X0))))),sK199(powerset(powerset(X0)))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145365,c_165532]) ).
tcf(c_166169,plain,
( ( sK199(powerset(powerset(sK261))) = sK140 )
| ( set_difference(unordered_pair(sK262(sK199(powerset(powerset(sK261)))),sK262(sK199(powerset(powerset(sK261))))),sK199(powerset(powerset(sK261)))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145371,c_165532]) ).
tcf(c_166170,plain,
( ( powerset(sK62) = sK140 )
| ( set_difference(unordered_pair(sK63(powerset(sK62)),sK63(powerset(sK62))),powerset(sK62)) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_145625,c_165532]) ).
tcf(c_166171,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ( set_difference(unordered_pair(sK72(powerset(X0)),sK72(powerset(X0))),powerset(X0)) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145633,c_165532]) ).
tcf(c_166172,plain,
! [X0: $i] :
( sP15
| ( powerset(X0) = sK140 )
| ( set_difference(unordered_pair(sK114(powerset(X0)),sK114(powerset(X0))),powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145634,c_165532]) ).
tcf(c_166173,plain,
! [X0: $i] :
( ( powerset(X0) = sK140 )
| ( set_difference(unordered_pair(sK119(powerset(X0)),sK119(powerset(X0))),powerset(X0)) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_145635,c_165532]) ).
tcf(c_166174,plain,
( ( powerset(sK261) = sK140 )
| ( set_difference(unordered_pair(sK262(powerset(sK261)),sK262(powerset(sK261))),powerset(sK261)) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_145641,c_165532]) ).
tcf(c_166175,plain,
( ( sK140 = omega )
| ( set_difference(unordered_pair(sK128(omega),sK128(omega)),omega) = sK140 )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145922,c_165532]) ).
tcf(c_166176,plain,
( ( sK140 = omega )
| ( set_difference(unordered_pair(sK128(omega),sK128(omega)),omega) = sK140 )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145878,c_165532]) ).
tcf(c_166177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X1,X2) = sK140 )
| ( set_difference(unordered_pair(sK318(X0,set_difference(X1,X2)),sK318(X0,set_difference(X1,X2))),set_difference(X1,X2)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_146007,c_165532]) ).
tcf(c_166178,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = sK140 )
| ( set_difference(unordered_pair(sK128(set_difference(X0,X1)),sK128(set_difference(X0,X1))),set_difference(X0,X1)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_146008,c_165532]) ).
tcf(c_166179,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( set_difference(unordered_pair(apply(sK126(X1),sK92(X0)),apply(sK126(X1),sK92(X0))),X0) = sK140 )
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_151774,c_165532]) ).
tcf(c_166180,plain,
! [X0: $i] :
( ( sK92(X0) = sK140 )
| ( set_difference(unordered_pair(sK169(sK92(X0)),sK169(sK92(X0))),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_151778,c_165532]) ).
tcf(c_166181,plain,
! [X0: $i,X1: $i] :
( ( relation_rng_restriction(X1,X0) = sK140 )
| ( set_difference(unordered_pair(sK128(relation_rng_restriction(X1,X0)),sK128(relation_rng_restriction(X1,X0))),relation_rng_restriction(X1,X0)) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152217,c_165532]) ).
tcf(c_166183,plain,
! [X0: $i,X1: $i] :
( ( relation_dom_restriction(X0,X1) = sK140 )
| ( set_difference(unordered_pair(sK128(relation_dom_restriction(X0,X1)),sK128(relation_dom_restriction(X0,X1))),relation_dom_restriction(X0,X1)) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_153991,c_165532]) ).
tcf(c_166184,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( set_difference(unordered_pair(sK142(X0),sK142(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_154138,c_165532]) ).
tcf(c_166185,plain,
set_difference(unordered_pair(sK142(omega),sK142(omega)),omega) = sK140,
inference(superposition,[status(thm)],[c_154124,c_165532]) ).
tcf(c_166186,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = sK140 )
| ( set_difference(unordered_pair(sK142(relation_dom(X0)),sK142(relation_dom(X0))),relation_dom(X0)) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_154130,c_165532]) ).
tcf(c_166187,plain,
! [X0: $i] :
( ( X0 = omega )
| ( set_difference(unordered_pair(sK142(sK263(X0)),sK142(sK263(X0))),sK263(X0)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_154142,c_165532]) ).
tcf(c_166188,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ( set_difference(unordered_pair(sK128(sK169(X0)),sK128(sK169(X0))),sK169(X0)) = sK140 )
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154846,c_165532]) ).
tcf(c_166189,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( set_difference(unordered_pair(sK142(sK169(X0)),sK142(sK169(X0))),sK169(X0)) = sK140 ) ),
inference(superposition,[status(thm)],[c_154906,c_165532]) ).
tcf(c_166190,plain,
! [X0: $i] :
( ( set_difference(unordered_pair(sK318(X0,sK64),sK318(X0,sK64)),sK64) = sK140 )
| ~ sP7
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_161838,c_165532]) ).
tcf(c_166191,plain,
( ( set_difference(unordered_pair(sK128(sK64),sK128(sK64)),sK64) = sK140 )
| ~ sP7
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157842,c_165532]) ).
tcf(c_166193,plain,
! [X0: $i] :
( ( sK199(powerset(X0)) = sK140 )
| ( set_difference(unordered_pair(sK128(sK199(powerset(X0))),sK128(sK199(powerset(X0)))),sK199(powerset(X0))) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_160233,c_165532]) ).
tcf(c_166555,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK302(sK241)),X0),sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ~ relation(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_296]) ).
tcf(c_166556,plain,
! [X0: $i] :
( in(sK142(sK302(sK241)),sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ( apply(sK126(sK302(sK241)),X0) = sK140 )
| ~ function(sK126(sK302(sK241)))
| ~ relation(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_154130]) ).
tcf(c_166557,plain,
! [X0: $i] :
( ( sK125(sK302(sK241)) = sK140 )
| ( apply(sK126(sK302(sK241)),X0) = sK140 )
| ~ function(sK126(sK302(sK241)))
| ~ relation(sK126(sK302(sK241)))
| ~ in(sK302(sK241),X0) ),
inference(superposition,[status(thm)],[c_147768,c_155600]) ).
tcf(c_166558,plain,
( function(sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ~ empty(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_147195]) ).
tcf(c_166559,plain,
( finite(sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ~ empty(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_147193]) ).
tcf(c_166560,plain,
( epsilon_transitive(sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ~ empty(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_147192]) ).
tcf(c_166561,plain,
( epsilon_connected(sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ~ empty(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_147191]) ).
tcf(c_166562,plain,
( ordinal(sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ~ empty(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_147190]) ).
tcf(c_166563,plain,
( one_to_one(sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ~ empty(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_147189]) ).
tcf(c_166564,plain,
! [X0: $i] :
( ( sK125(sK302(sK241)) = sK140 )
| ( apply(sK126(sK302(sK241)),X0) = sK140 )
| ~ empty(sK302(sK241))
| ~ relation(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_150772]) ).
tcf(c_166565,plain,
! [X0: $i] :
( element(X0,sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ( apply(sK126(sK302(sK241)),X0) = sK140 )
| ~ function(sK126(sK302(sK241)))
| ~ relation(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_148552]) ).
tcf(c_166566,plain,
( relation(sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ~ empty(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_642]) ).
tcf(c_166567,plain,
( empty(sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ~ empty(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_641]) ).
tcf(c_166568,plain,
! [X0: $i] :
( in(X0,sK302(sK241))
| ( sK125(sK302(sK241)) = sK140 )
| ( apply(sK126(sK302(sK241)),X0) = sK140 )
| ~ function(sK126(sK302(sK241)))
| ~ relation(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_906]) ).
tcf(c_166569,plain,
( ( sK125(sK302(sK241)) = sK140 )
| ( relation_rng(sK126(sK302(sK241))) = sK140 )
| ~ relation(sK126(sK302(sK241)))
| ( sK302(sK241) != sK140 ) ),
inference(superposition,[status(thm)],[c_147768,c_478]) ).
tcf(c_166570,plain,
( ( sK126(sK302(sK241)) = sK140 )
| ( sK125(sK302(sK241)) = sK140 )
| ~ relation(sK126(sK302(sK241)))
| ( sK302(sK241) != sK140 ) ),
inference(superposition,[status(thm)],[c_147768,c_475]) ).
tcf(c_166699,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(sK144(X0,X1),sK144(X0,X1)),X0) = sK140 )
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_165532]) ).
tcf(c_166700,plain,
! [X0: $i,X1: $i] :
( ordinal(sK144(X0,X1))
| ~ ordinal(X0)
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_333]) ).
tcf(c_166701,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK144(X0,X1)),union(sK144(X0,X1))) = sK140 )
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_154509]) ).
tcf(c_166702,plain,
! [X0: $i,X1: $i] :
( in(sK128(sK144(X0,X1)),sK144(X0,X1))
| ( sK144(X0,X1) = sK140 )
| ~ ordinal(union(X0))
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_154063]) ).
tcf(c_166703,plain,
! [X0: $i,X1: $i] :
( ~ sP18(X0,X1)
| ~ in(X0,sK144(X0,X1)) ),
inference(superposition,[status(thm)],[c_533,c_527]) ).
tcf(c_166704,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(sK144(X0,X1)))
| ( sK144(X0,X1) = sK140 )
| ~ ordinal(union(X0))
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_154064]) ).
tcf(c_166705,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK144(X0,X1)),sK144(X0,X1))
| ( sK125(X0) = sK140 )
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_154131]) ).
tcf(c_166706,plain,
! [X0: $i,X1: $i] :
( ( set_difference(sK144(X0,X1),union(X0)) = sK140 )
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_154065]) ).
tcf(c_166707,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_522]) ).
tcf(c_166708,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ~ sP18(X0,X1)
| ~ empty(sK144(X0,X1)) ),
inference(superposition,[status(thm)],[c_533,c_150230]) ).
tcf(c_166709,plain,
! [X0: $i,X1: $i] :
( ~ empty(X0)
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_787]) ).
tcf(c_166710,plain,
! [X0: $i,X1: $i] :
( element(sK144(X0,X1),X0)
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_526]) ).
tcf(c_166711,plain,
! [X0: $i,X1: $i] :
( in(sK144(sK92(X0),X1),X0)
| ~ sP18(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_533,c_198]) ).
tcf(c_166712,plain,
! [X0: $i,X1: $i] :
( ordinal(sK144(sK92(X0),X1))
| ~ sP18(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_533,c_199]) ).
tcf(c_166713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK144(relation_inverse_image(X0,X1),X2)),X1)
| ( X4 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ sP18(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_533,c_425]) ).
tcf(c_166714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK144(relation_inverse_image(X0,X1),X2),X3)
| ( X4 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ sP18(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_533,c_424]) ).
tcf(c_166715,plain,
! [X0: $i] : ~ sP18(sK140,X0),
inference(superposition,[status(thm)],[c_533,c_580]) ).
tcf(c_166716,plain,
! [X0: $i,X1: $i] :
( subset(sK144(powerset(X0),X1),X0)
| ~ sP18(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_533,c_662]) ).
tcf(c_166717,plain,
! [X0: $i,X1: $i] :
( sP29
| ordinal(sK144(sK248(X0),X1))
| ~ sP18(sK248(X0),X1) ),
inference(superposition,[status(thm)],[c_533,c_808]) ).
tcf(c_166784,plain,
( ordinal(sK261)
| sP32(sK128(powerset(sK140))) ),
inference(superposition,[status(thm)],[c_166045,c_833]) ).
tcf(c_166785,plain,
epsilon_connected(sK128(powerset(sK140))),
inference(superposition,[status(thm)],[c_166045,c_1050]) ).
tcf(c_166786,plain,
epsilon_transitive(sK128(powerset(sK140))),
inference(superposition,[status(thm)],[c_166045,c_1049]) ).
tcf(c_166792,plain,
! [X0: $i] : set_difference(unordered_pair(sK140,sK140),powerset(X0)) = sK140,
inference(superposition,[status(thm)],[c_166091,c_165532]) ).
tcf(c_166796,plain,
! [X0: $i] : ~ in(powerset(X0),sK140),
inference(superposition,[status(thm)],[c_166091,c_527]) ).
tcf(c_166799,plain,
! [X0: $i] : set_difference(sK140,union(powerset(X0))) = sK140,
inference(superposition,[status(thm)],[c_166091,c_154065]) ).
tcf(c_166800,plain,
! [X0: $i] : in(sK142(powerset(X0)),powerset(X0)),
inference(superposition,[status(thm)],[c_166091,c_522]) ).
tcf(c_166817,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = powerset(sK140) )
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),powerset(sK140))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_165547]) ).
tcf(c_166818,plain,
! [X0: $i] :
( ( unordered_pair(sK49(powerset(sK140),X0),sK49(powerset(sK140),X0)) = powerset(sK140) )
| ~ sP2(powerset(sK140),X0) ),
inference(superposition,[status(thm)],[c_98,c_165547]) ).
tcf(c_166819,plain,
( sP3(powerset(sK140))
| ( unordered_pair(sK58(powerset(sK140)),sK58(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_122,c_165547]) ).
tcf(c_166822,plain,
( empty(powerset(sK140))
| function(sK126(powerset(sK140)))
| ( unordered_pair(sK125(powerset(sK140)),sK125(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_352,c_165547]) ).
tcf(c_166823,plain,
( empty(powerset(sK140))
| relation(sK126(powerset(sK140)))
| ( unordered_pair(sK125(powerset(sK140)),sK125(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_351,c_165547]) ).
tcf(c_166824,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( unordered_pair(apply(sK126(X0),powerset(sK140)),apply(sK126(X0),powerset(sK140))) = powerset(sK140) )
| ~ in(powerset(sK140),X0) ),
inference(superposition,[status(thm)],[c_2177,c_165547]) ).
tcf(c_166825,plain,
( ordinal(powerset(sK140))
| ( unordered_pair(sK127(powerset(sK140)),sK127(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_367,c_165547]) ).
tcf(c_166826,plain,
( ( powerset(sK140) = sK140 )
| ( unordered_pair(sK128(powerset(sK140)),sK128(powerset(sK140))) = powerset(sK140) )
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_144620,c_165547]) ).
tcf(c_166827,plain,
! [X0: $i] :
( disjoint(powerset(sK140),X0)
| ( unordered_pair(sK130(powerset(sK140),X0),sK130(powerset(sK140),X0)) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_400,c_165547]) ).
tcf(c_166828,plain,
! [X0: $i] :
( disjoint(X0,powerset(sK140))
| ( unordered_pair(sK130(X0,powerset(sK140)),sK130(X0,powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_401,c_165547]) ).
tcf(c_166829,plain,
( being_limit_ordinal(powerset(sK140))
| ( unordered_pair(sK131(powerset(sK140)),sK131(powerset(sK140))) = powerset(sK140) )
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_406,c_165547]) ).
tcf(c_166830,plain,
! [X0: $i] :
( ( unordered_pair(sK144(powerset(sK140),X0),sK144(powerset(sK140),X0)) = powerset(sK140) )
| ~ sP18(powerset(sK140),X0) ),
inference(superposition,[status(thm)],[c_533,c_165547]) ).
tcf(c_166831,plain,
( relation(powerset(sK140))
| ( unordered_pair(sK163(powerset(sK140)),sK163(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_561,c_165547]) ).
tcf(c_166832,plain,
( ( powerset(sK140) = sK140 )
| ( unordered_pair(sK169(powerset(sK140)),sK169(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_579,c_165547]) ).
tcf(c_166833,plain,
( ( unordered_pair(sK173(powerset(sK140)),sK173(powerset(sK140))) = powerset(sK140) )
| ~ sP20(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_584,c_165547]) ).
tcf(c_166835,plain,
! [X0: $i] :
( subset(powerset(sK140),X0)
| ( unordered_pair(sK193(powerset(sK140),X0),sK193(powerset(sK140),X0)) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_657,c_165547]) ).
tcf(c_166836,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = powerset(sK140) )
| ~ subset(X0,sK140) ),
inference(superposition,[status(thm)],[c_661,c_165547]) ).
tcf(c_166838,plain,
( ( unordered_pair(sK268(powerset(sK140)),sK268(powerset(sK140))) = powerset(sK140) )
| ~ sP34(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_864,c_165547]) ).
tcf(c_166839,plain,
( epsilon_transitive(powerset(sK140))
| ( unordered_pair(sK316(powerset(sK140)),sK316(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_1043,c_165547]) ).
tcf(c_166840,plain,
! [X0: $i] :
( ( powerset(sK140) = sK140 )
| ( unordered_pair(sK320(X0,powerset(sK140)),sK320(X0,powerset(sK140))) = powerset(sK140) )
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ subset(powerset(sK140),relation_field(X0)) ),
inference(superposition,[status(thm)],[c_1062,c_165547]) ).
tcf(c_166841,plain,
( epsilon_connected(powerset(sK140))
| ( unordered_pair(sK343(powerset(sK140)),sK343(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_1207,c_165547]) ).
tcf(c_166842,plain,
( epsilon_connected(powerset(sK140))
| ( unordered_pair(sK344(powerset(sK140)),sK344(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_1208,c_165547]) ).
tcf(c_166843,plain,
( ( powerset(sK140) = sK140 )
| ( unordered_pair(unordered_pair(unordered_pair(sK137(powerset(sK140)),sK137(powerset(sK140))),unordered_pair(sK137(powerset(sK140)),sK138(powerset(sK140)))),unordered_pair(unordered_pair(sK137(powerset(sK140)),sK137(powerset(sK140))),unordered_pair(sK137(powerset(sK140)),sK138(powerset(sK140))))) = powerset(sK140) )
| ~ relation(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_16344,c_165547]) ).
tcf(c_166844,plain,
! [X0: $i] :
( ( powerset(sK140) = sK140 )
| ( unordered_pair(sK318(X0,powerset(sK140)),sK318(X0,powerset(sK140))) = powerset(sK140) )
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_144619,c_165547]) ).
tcf(c_166845,plain,
( ( powerset(sK140) = sK140 )
| ( unordered_pair(sK72(powerset(sK140)),sK72(powerset(sK140))) = powerset(sK140) )
| ~ iPr_def_19
| ~ ordinal(sK140)
| ~ in(sK140,omega) ),
inference(superposition,[status(thm)],[c_145633,c_165547]) ).
tcf(c_166846,plain,
( sP15
| ( powerset(sK140) = sK140 )
| ( unordered_pair(sK114(powerset(sK140)),sK114(powerset(sK140))) = powerset(sK140) )
| ~ ordinal(sK140)
| ~ in(sK140,omega) ),
inference(superposition,[status(thm)],[c_145634,c_165547]) ).
tcf(c_166847,plain,
( ( powerset(sK140) = sK140 )
| ( unordered_pair(sK119(powerset(sK140)),sK119(powerset(sK140))) = powerset(sK140) )
| ~ finite(sK140) ),
inference(superposition,[status(thm)],[c_145635,c_165547]) ).
tcf(c_166848,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( unordered_pair(apply(sK126(X0),sK92(powerset(sK140))),apply(sK126(X0),sK92(powerset(sK140)))) = powerset(sK140) )
| ~ in(sK92(powerset(sK140)),X0) ),
inference(superposition,[status(thm)],[c_151774,c_165547]) ).
tcf(c_166849,plain,
( ( sK92(powerset(sK140)) = sK140 )
| ( unordered_pair(sK169(sK92(powerset(sK140))),sK169(sK92(powerset(sK140)))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_151778,c_165547]) ).
tcf(c_166850,plain,
( ( powerset(sK140) = sK140 )
| ( unordered_pair(sK142(powerset(sK140)),sK142(powerset(sK140))) = powerset(sK140) ) ),
inference(superposition,[status(thm)],[c_154138,c_165547]) ).
tcf(c_166874,plain,
unordered_pair(sK142(powerset(sK140)),sK142(powerset(sK140))) = powerset(sK140),
inference(forward_subsumption_resolution,[status(thm)],[c_166850,c_144206]) ).
tcf(c_166875,plain,
unordered_pair(sK169(powerset(sK140)),sK169(powerset(sK140))) = powerset(sK140),
inference(forward_subsumption_resolution,[status(thm)],[c_166832,c_144206]) ).
tcf(c_166887,plain,
( relation(sK126(powerset(sK140)))
| ( unordered_pair(sK125(powerset(sK140)),sK125(powerset(sK140))) = powerset(sK140) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166823,c_695]) ).
tcf(c_166890,plain,
( function(sK126(powerset(sK140)))
| ( unordered_pair(sK125(powerset(sK140)),sK125(powerset(sK140))) = powerset(sK140) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166822,c_695]) ).
tcf(c_166899,plain,
unordered_pair(sK119(powerset(sK140)),sK119(powerset(sK140))) = powerset(sK140),
inference(forward_subsumption_resolution,[status(thm)],[c_166847,c_144206,c_144943]) ).
tcf(c_166900,plain,
( ( unordered_pair(sK128(powerset(sK140)),sK128(powerset(sK140))) = powerset(sK140) )
| ~ ordinal(powerset(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166826,c_144206]) ).
tcf(c_166905,plain,
( sP15
| ( unordered_pair(sK114(powerset(sK140)),sK114(powerset(sK140))) = powerset(sK140) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166846,c_144206,c_144282,c_847]) ).
tcf(c_166908,plain,
( ( unordered_pair(sK72(powerset(sK140)),sK72(powerset(sK140))) = powerset(sK140) )
| ~ iPr_def_19 ),
inference(forward_subsumption_resolution,[status(thm)],[c_166845,c_144206,c_144282,c_847]) ).
tcf(c_166914,plain,
! [X0: $i] :
( ( unordered_pair(sK318(X0,powerset(sK140)),sK318(X0,powerset(sK140))) = powerset(sK140) )
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166844,c_144206]) ).
tcf(c_166921,plain,
! [X0: $i] :
( ( unordered_pair(sK320(X0,powerset(sK140)),sK320(X0,powerset(sK140))) = powerset(sK140) )
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ subset(powerset(sK140),relation_field(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166840,c_144206]) ).
tcf(c_166926,plain,
( ( unordered_pair(unordered_pair(unordered_pair(sK137(powerset(sK140)),sK137(powerset(sK140))),unordered_pair(sK137(powerset(sK140)),sK138(powerset(sK140)))),unordered_pair(unordered_pair(sK137(powerset(sK140)),sK137(powerset(sK140))),unordered_pair(sK137(powerset(sK140)),sK138(powerset(sK140))))) = powerset(sK140) )
| ~ relation(powerset(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166843,c_144206]) ).
tcf(c_167042,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(X1,X1)))
| ( set_difference(unordered_pair(X1,X1),set_difference(unordered_pair(X1,X1),X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151758,c_165550]) ).
tcf(c_167043,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(sK49(X0,X1),sK49(X0,X1))))
| ~ ordinal(X0)
| ~ sP2(X0,X1) ),
inference(superposition,[status(thm)],[c_98,c_165550]) ).
tcf(c_167044,plain,
! [X0: $i] :
( sP3(X0)
| ordinal(sK128(unordered_pair(sK58(X0),sK58(X0))))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_122,c_165550]) ).
tcf(c_167045,plain,
( ordinal(sK128(unordered_pair(set_union2(sK62,unordered_pair(sK62,sK62)),set_union2(sK62,unordered_pair(sK62,sK62)))))
| ~ sP8
| ~ ordinal(omega) ),
inference(superposition,[status(thm)],[c_128,c_165550]) ).
tcf(c_167046,plain,
( ordinal(sK128(unordered_pair(sK140,sK140)))
| ~ ordinal(omega) ),
inference(superposition,[status(thm)],[c_847,c_165550]) ).
tcf(c_167047,plain,
( ordinal(sK128(unordered_pair(sK66,sK66)))
| ~ sP6
| ~ ordinal(omega) ),
inference(superposition,[status(thm)],[c_140,c_165550]) ).
tcf(c_167050,plain,
( ordinal(sK128(unordered_pair(sK110,sK110)))
| ~ sP15
| ~ ordinal(omega) ),
inference(superposition,[status(thm)],[c_238,c_165550]) ).
tcf(c_167051,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ~ ordinal(sK116(X0)) ),
inference(superposition,[status(thm)],[c_272,c_165550]) ).
tcf(c_167052,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(X1,X1)))
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_906,c_165550]) ).
tcf(c_167053,plain,
! [X0: $i] :
( empty(X0)
| function(sK126(X0))
| ordinal(sK128(unordered_pair(sK125(X0),sK125(X0))))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_352,c_165550]) ).
tcf(c_167054,plain,
! [X0: $i] :
( empty(X0)
| relation(sK126(X0))
| ordinal(sK128(unordered_pair(sK125(X0),sK125(X0))))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_351,c_165550]) ).
tcf(c_167055,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(apply(sK126(X1),X0),apply(sK126(X1),X0))))
| ( sK125(X1) = sK140 )
| ~ ordinal(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_2177,c_165550]) ).
tcf(c_167057,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK128(X0),sK128(X0))))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_144620,c_165550]) ).
tcf(c_167058,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ordinal(sK128(unordered_pair(sK130(X0,X1),sK130(X0,X1))))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_400,c_165550]) ).
tcf(c_167059,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ordinal(sK128(unordered_pair(sK130(X1,X0),sK130(X1,X0))))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_401,c_165550]) ).
tcf(c_167060,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| ordinal(sK128(unordered_pair(sK131(X0),sK131(X0))))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_406,c_165550]) ).
tcf(c_167061,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ordinal(sK128(unordered_pair(X2,X2)))
| ( X0 = sK140 )
| ~ element(X2,X0)
| ~ subset(X1,X0)
| ~ ordinal(subset_complement(X0,X1)) ),
inference(superposition,[status(thm)],[c_5403,c_165550]) ).
tcf(c_167062,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(sK144(X0,X1),sK144(X0,X1))))
| ~ ordinal(X0)
| ~ sP18(X0,X1) ),
inference(superposition,[status(thm)],[c_533,c_165550]) ).
tcf(c_167063,plain,
! [X0: $i] :
( relation(X0)
| ordinal(sK128(unordered_pair(sK163(X0),sK163(X0))))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_561,c_165550]) ).
tcf(c_167064,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK169(X0),sK169(X0))))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_579,c_165550]) ).
tcf(c_167065,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK173(X0),sK173(X0))))
| ~ sP20(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_584,c_165550]) ).
tcf(c_167067,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ordinal(sK128(unordered_pair(sK193(X0,X1),sK193(X0,X1))))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_657,c_165550]) ).
tcf(c_167068,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ~ ordinal(powerset(X1))
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_661,c_165550]) ).
tcf(c_167069,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK140,sK140)))
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151909,c_165550]) ).
tcf(c_167070,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK140,sK140)))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ ordinal(sK263(X0))
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_844,c_165550]) ).
tcf(c_167071,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(relation_dom(sK264(X0)),relation_dom(sK264(X0)))))
| ~ ordinal(omega)
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_855,c_165550]) ).
tcf(c_167072,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK268(X0),sK268(X0))))
| ~ sP34(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_864,c_165550]) ).
tcf(c_167073,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ~ ordinal(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_939,c_165550]) ).
tcf(c_167074,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(X1,X1)))
| ~ ordinal(unordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_940,c_165550]) ).
tcf(c_167075,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ~ ordinal(sK300(X0)) ),
inference(superposition,[status(thm)],[c_965,c_165550]) ).
tcf(c_167076,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ordinal(sK128(unordered_pair(sK316(X0),sK316(X0))))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_1043,c_165550]) ).
tcf(c_167077,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(sK320(X1,X0),sK320(X1,X0))))
| ( X0 = sK140 )
| ~ well_founded_relation(X1)
| ~ ordinal(X0)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_165550]) ).
tcf(c_167078,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ordinal(sK128(unordered_pair(sK343(X0),sK343(X0))))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_1207,c_165550]) ).
tcf(c_167079,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ordinal(sK128(unordered_pair(sK344(X0),sK344(X0))))
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_1208,c_165550]) ).
tcf(c_167080,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))),unordered_pair(unordered_pair(sK137(X0),sK137(X0)),unordered_pair(sK137(X0),sK138(X0))))))
| ( X0 = sK140 )
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_16344,c_165550]) ).
tcf(c_167081,plain,
( ordinal(sK128(unordered_pair(sK119(sK64),sK119(sK64))))
| ~ sP7
| ~ ordinal(sK64) ),
inference(superposition,[status(thm)],[c_146098,c_165550]) ).
tcf(c_167082,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(sK318(X0,X1),sK318(X0,X1))))
| ( X1 = sK140 )
| ~ ordinal(X1)
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_144619,c_165550]) ).
tcf(c_167083,plain,
( sP15
| ordinal(sK128(unordered_pair(sK114(sK64),sK114(sK64))))
| ~ sP7
| ~ ordinal(sK64) ),
inference(superposition,[status(thm)],[c_145791,c_165550]) ).
tcf(c_167084,plain,
( ordinal(sK128(unordered_pair(sK72(sK64),sK72(sK64))))
| ~ iPr_def_19
| ~ sP7
| ~ ordinal(sK64) ),
inference(superposition,[status(thm)],[c_145863,c_165550]) ).
tcf(c_167085,plain,
( ordinal(sK128(unordered_pair(sK67(sK64),sK67(sK64))))
| ~ sP6
| ~ sP7
| ~ ordinal(sK64)
| ~ in(sK140,sK66) ),
inference(superposition,[status(thm)],[c_146728,c_165550]) ).
tcf(c_167086,plain,
( ordinal(sK128(unordered_pair(sK111(sK64),sK111(sK64))))
| ~ sP15
| ~ sP7
| ~ ordinal(sK64)
| ~ in(sK140,sK110) ),
inference(superposition,[status(thm)],[c_146738,c_165550]) ).
tcf(c_167087,plain,
( ordinal(sK128(unordered_pair(sK63(sK199(powerset(powerset(sK62)))),sK63(sK199(powerset(powerset(sK62)))))))
| ( sK199(powerset(powerset(sK62))) = sK140 )
| ~ iPr_def_21
| ~ ordinal(sK199(powerset(powerset(sK62)))) ),
inference(superposition,[status(thm)],[c_145355,c_165550]) ).
tcf(c_167088,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK119(sK199(powerset(powerset(X0)))),sK119(sK199(powerset(powerset(X0)))))))
| ( sK199(powerset(powerset(X0))) = sK140 )
| ~ finite(X0)
| ~ ordinal(sK199(powerset(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_145365,c_165550]) ).
tcf(c_167089,plain,
( ordinal(sK128(unordered_pair(sK262(sK199(powerset(powerset(sK261)))),sK262(sK199(powerset(powerset(sK261)))))))
| ( sK199(powerset(powerset(sK261))) = sK140 )
| ~ iPr_def_15
| ~ ordinal(sK199(powerset(powerset(sK261)))) ),
inference(superposition,[status(thm)],[c_145371,c_165550]) ).
tcf(c_167090,plain,
( ordinal(sK128(unordered_pair(sK63(powerset(sK62)),sK63(powerset(sK62)))))
| ( powerset(sK62) = sK140 )
| ~ iPr_def_21
| ~ ordinal(powerset(sK62)) ),
inference(superposition,[status(thm)],[c_145625,c_165550]) ).
tcf(c_167091,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK72(powerset(X0)),sK72(powerset(X0)))))
| ( powerset(X0) = sK140 )
| ~ iPr_def_19
| ~ ordinal(X0)
| ~ ordinal(powerset(X0))
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145633,c_165550]) ).
tcf(c_167092,plain,
! [X0: $i] :
( sP15
| ordinal(sK128(unordered_pair(sK114(powerset(X0)),sK114(powerset(X0)))))
| ( powerset(X0) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(powerset(X0))
| ~ in(X0,omega) ),
inference(superposition,[status(thm)],[c_145634,c_165550]) ).
tcf(c_167093,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK119(powerset(X0)),sK119(powerset(X0)))))
| ( powerset(X0) = sK140 )
| ~ finite(X0)
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_145635,c_165550]) ).
tcf(c_167094,plain,
( ordinal(sK128(unordered_pair(sK262(powerset(sK261)),sK262(powerset(sK261)))))
| ( powerset(sK261) = sK140 )
| ~ iPr_def_15
| ~ ordinal(powerset(sK261)) ),
inference(superposition,[status(thm)],[c_145641,c_165550]) ).
tcf(c_167095,plain,
( ordinal(sK128(unordered_pair(sK128(omega),sK128(omega))))
| ( sK140 = omega )
| ~ ordinal(omega)
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145922,c_165550]) ).
tcf(c_167096,plain,
( ordinal(sK128(unordered_pair(sK128(omega),sK128(omega))))
| ( sK140 = omega )
| ~ ordinal(omega)
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145878,c_165550]) ).
tcf(c_167097,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK128(unordered_pair(sK318(X2,set_difference(X0,X1)),sK318(X2,set_difference(X0,X1)))))
| ( set_difference(X0,X1) = sK140 )
| ~ relation(X2)
| ~ is_well_founded_in(X2,X0)
| ~ ordinal(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_146007,c_165550]) ).
tcf(c_167098,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(sK128(set_difference(X0,X1)),sK128(set_difference(X0,X1)))))
| ( set_difference(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_146008,c_165550]) ).
tcf(c_167099,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(apply(sK126(X1),sK92(X0)),apply(sK126(X1),sK92(X0)))))
| ( sK125(X1) = sK140 )
| ~ ordinal(X0)
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_151774,c_165550]) ).
tcf(c_167100,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK169(sK92(X0)),sK169(sK92(X0)))))
| ( sK92(X0) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_151778,c_165550]) ).
tcf(c_167101,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(sK128(relation_rng_restriction(X0,X1)),sK128(relation_rng_restriction(X0,X1)))))
| ( relation_rng_restriction(X0,X1) = sK140 )
| ~ ordinal(X1)
| ~ relation(X1)
| ~ ordinal(relation_rng_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_152217,c_165550]) ).
tcf(c_167103,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(sK128(relation_dom_restriction(X0,X1)),sK128(relation_dom_restriction(X0,X1)))))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ~ ordinal(X0)
| ~ relation(X0)
| ~ ordinal(relation_dom_restriction(X0,X1)) ),
inference(superposition,[status(thm)],[c_153991,c_165550]) ).
tcf(c_167104,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK142(X0),sK142(X0))))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_154138,c_165550]) ).
tcf(c_167105,plain,
( ordinal(sK128(unordered_pair(sK142(omega),sK142(omega))))
| ~ ordinal(omega) ),
inference(superposition,[status(thm)],[c_154124,c_165550]) ).
tcf(c_167106,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(sK142(relation_dom(X0)),sK142(relation_dom(X0)))))
| ( apply(X0,X1) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_154130,c_165550]) ).
tcf(c_167107,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK142(sK263(X0)),sK142(sK263(X0)))))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ ordinal(sK263(X0))
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_154142,c_165550]) ).
tcf(c_167108,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK128(sK169(X0)),sK128(sK169(X0)))))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ ordinal(sK169(X0))
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154846,c_165550]) ).
tcf(c_167109,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK142(sK169(X0)),sK142(sK169(X0)))))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ ordinal(sK169(X0)) ),
inference(superposition,[status(thm)],[c_154906,c_165550]) ).
tcf(c_167110,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK140,sK140)))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_166091,c_165550]) ).
tcf(c_167111,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK318(X0,sK64),sK318(X0,sK64))))
| ~ sP7
| ~ ordinal(sK64)
| ~ relation(X0)
| ~ is_well_founded_in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_161838,c_165550]) ).
tcf(c_167112,plain,
( ordinal(sK128(unordered_pair(sK128(sK64),sK128(sK64))))
| ~ sP7
| ~ ordinal(sK64)
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_157842,c_165550]) ).
tcf(c_167114,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK128(sK199(powerset(X0))),sK128(sK199(powerset(X0))))))
| ( sK199(powerset(X0)) = sK140 )
| ~ ordinal(X0)
| ~ ordinal(sK199(powerset(X0))) ),
inference(superposition,[status(thm)],[c_160233,c_165550]) ).
tcf(c_167115,plain,
( ordinal(sK128(powerset(sK140)))
| ~ ordinal(omega) ),
inference(light_normalisation,[status(thm)],[c_167046,c_314]) ).
tcf(c_167116,plain,
! [X0: $i] :
( ordinal(sK128(powerset(sK140)))
| ~ ordinal(powerset(X0)) ),
inference(light_normalisation,[status(thm)],[c_167110,c_314]) ).
tcf(c_167121,plain,
ordinal(sK128(unordered_pair(sK142(omega),sK142(omega)))),
inference(forward_subsumption_resolution,[status(thm)],[c_167105,c_849]) ).
tcf(c_167126,plain,
( ordinal(sK128(unordered_pair(sK110,sK110)))
| ~ sP15 ),
inference(forward_subsumption_resolution,[status(thm)],[c_167050,c_849]) ).
tcf(c_167129,plain,
( ordinal(sK128(unordered_pair(sK66,sK66)))
| ~ sP6 ),
inference(forward_subsumption_resolution,[status(thm)],[c_167047,c_849]) ).
tcf(c_167185,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(relation_dom(sK264(X0)),relation_dom(sK264(X0)))))
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_167071,c_849]) ).
tcf(c_167239,plain,
! [X0: $i] :
( ordinal(sK128(powerset(sK140)))
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),X0)) = sK140 )
| ~ ordinal(X0) ),
inference(light_normalisation,[status(thm)],[c_167069,c_314]) ).
tcf(c_167240,plain,
( ordinal(sK128(unordered_pair(set_union2(sK62,unordered_pair(sK62,sK62)),set_union2(sK62,unordered_pair(sK62,sK62)))))
| ~ sP8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_167045,c_849]) ).
tcf(c_167272,plain,
( ordinal(sK128(unordered_pair(sK128(omega),sK128(omega))))
| ( sK140 = omega )
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_167096,c_849]) ).
tcf(c_167277,plain,
( ordinal(sK128(unordered_pair(sK128(omega),sK128(omega))))
| ( sK140 = omega )
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_167095,c_849]) ).
tcf(c_167287,plain,
! [X0: $i] :
( ordinal(sK128(powerset(sK140)))
| ( X0 = omega )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ ordinal(sK263(X0))
| ~ in(sK140,X0) ),
inference(light_normalisation,[status(thm)],[c_167070,c_314]) ).
tcf(c_167417,plain,
( disjoint(powerset(sK140),omega)
| ( powerset(sK140) != sK140 ) ),
inference(demodulation,[status(thm)],[c_165981,c_675]) ).
tcf(c_167422,plain,
! [X0: $i] :
( disjoint(powerset(sK140),powerset(X0))
| ( powerset(sK140) != sK140 ) ),
inference(demodulation,[status(thm)],[c_166069,c_675]) ).
tcf(c_167431,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = unordered_pair(X1,X1) )
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),unordered_pair(X1,X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_165554]) ).
tcf(c_167432,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(sK49(unordered_pair(X0,X0),X1),sK49(unordered_pair(X0,X0),X1)) = unordered_pair(X0,X0) )
| ~ sP2(unordered_pair(X0,X0),X1) ),
inference(superposition,[status(thm)],[c_98,c_165554]) ).
tcf(c_167433,plain,
! [X0: $i] :
( sP3(unordered_pair(X0,X0))
| ( unordered_pair(sK58(unordered_pair(X0,X0)),sK58(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_122,c_165554]) ).
tcf(c_167436,plain,
! [X0: $i] :
( empty(unordered_pair(X0,X0))
| function(sK126(unordered_pair(X0,X0)))
| ( unordered_pair(sK125(unordered_pair(X0,X0)),sK125(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_352,c_165554]) ).
tcf(c_167437,plain,
! [X0: $i] :
( empty(unordered_pair(X0,X0))
| relation(sK126(unordered_pair(X0,X0)))
| ( unordered_pair(sK125(unordered_pair(X0,X0)),sK125(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_351,c_165554]) ).
tcf(c_167438,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( unordered_pair(apply(sK126(X1),unordered_pair(X0,X0)),apply(sK126(X1),unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ in(unordered_pair(X0,X0),X1) ),
inference(superposition,[status(thm)],[c_2177,c_165554]) ).
tcf(c_167439,plain,
! [X0: $i] :
( ordinal(unordered_pair(X0,X0))
| ( unordered_pair(sK127(unordered_pair(X0,X0)),sK127(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_367,c_165554]) ).
tcf(c_167440,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = sK140 )
| ( unordered_pair(sK128(unordered_pair(X0,X0)),sK128(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_144620,c_165554]) ).
tcf(c_167441,plain,
! [X0: $i,X1: $i] :
( disjoint(unordered_pair(X0,X0),X1)
| ( unordered_pair(sK130(unordered_pair(X0,X0),X1),sK130(unordered_pair(X0,X0),X1)) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_400,c_165554]) ).
tcf(c_167442,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,unordered_pair(X1,X1))
| ( unordered_pair(sK130(X0,unordered_pair(X1,X1)),sK130(X0,unordered_pair(X1,X1))) = unordered_pair(X1,X1) ) ),
inference(superposition,[status(thm)],[c_401,c_165554]) ).
tcf(c_167443,plain,
! [X0: $i] :
( being_limit_ordinal(unordered_pair(X0,X0))
| ( unordered_pair(sK131(unordered_pair(X0,X0)),sK131(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_406,c_165554]) ).
tcf(c_167444,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(sK144(unordered_pair(X0,X0),X1),sK144(unordered_pair(X0,X0),X1)) = unordered_pair(X0,X0) )
| ~ sP18(unordered_pair(X0,X0),X1) ),
inference(superposition,[status(thm)],[c_533,c_165554]) ).
tcf(c_167445,plain,
! [X0: $i] :
( relation(unordered_pair(X0,X0))
| ( unordered_pair(sK163(unordered_pair(X0,X0)),sK163(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_561,c_165554]) ).
tcf(c_167446,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = sK140 )
| ( unordered_pair(sK169(unordered_pair(X0,X0)),sK169(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_579,c_165554]) ).
tcf(c_167447,plain,
! [X0: $i] :
( ( unordered_pair(sK173(unordered_pair(X0,X0)),sK173(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ sP20(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_584,c_165554]) ).
tcf(c_167449,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ( unordered_pair(sK193(unordered_pair(X0,X0),X1),sK193(unordered_pair(X0,X0),X1)) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_657,c_165554]) ).
tcf(c_167450,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = unordered_pair(sK140,sK140) )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),unordered_pair(X0,X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151909,c_165554]) ).
tcf(c_167451,plain,
! [X0: $i] :
( ( unordered_pair(sK268(unordered_pair(X0,X0)),sK268(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ sP34(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_864,c_165554]) ).
tcf(c_167454,plain,
! [X0: $i] :
( epsilon_transitive(unordered_pair(X0,X0))
| ( unordered_pair(sK316(unordered_pair(X0,X0)),sK316(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_1043,c_165554]) ).
tcf(c_167455,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X0) = sK140 )
| ( unordered_pair(sK320(X1,unordered_pair(X0,X0)),sK320(X1,unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(unordered_pair(X0,X0),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_1062,c_165554]) ).
tcf(c_167456,plain,
! [X0: $i] :
( epsilon_connected(unordered_pair(X0,X0))
| ( unordered_pair(sK343(unordered_pair(X0,X0)),sK343(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_1207,c_165554]) ).
tcf(c_167457,plain,
! [X0: $i] :
( epsilon_connected(unordered_pair(X0,X0))
| ( unordered_pair(sK344(unordered_pair(X0,X0)),sK344(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_1208,c_165554]) ).
tcf(c_167458,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = sK140 )
| ( unordered_pair(unordered_pair(unordered_pair(sK137(unordered_pair(X0,X0)),sK137(unordered_pair(X0,X0))),unordered_pair(sK137(unordered_pair(X0,X0)),sK138(unordered_pair(X0,X0)))),unordered_pair(unordered_pair(sK137(unordered_pair(X0,X0)),sK137(unordered_pair(X0,X0))),unordered_pair(sK137(unordered_pair(X0,X0)),sK138(unordered_pair(X0,X0))))) = unordered_pair(X0,X0) )
| ~ relation(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_16344,c_165554]) ).
tcf(c_167459,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X1,X1) = sK140 )
| ( unordered_pair(sK318(X0,unordered_pair(X1,X1)),sK318(X0,unordered_pair(X1,X1))) = unordered_pair(X1,X1) )
| ~ relation(X0)
| ~ is_well_founded_in(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_144619,c_165554]) ).
tcf(c_167460,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( unordered_pair(apply(sK126(X1),sK92(unordered_pair(X0,X0))),apply(sK126(X1),sK92(unordered_pair(X0,X0)))) = unordered_pair(X0,X0) )
| ~ in(sK92(unordered_pair(X0,X0)),X1) ),
inference(superposition,[status(thm)],[c_151774,c_165554]) ).
tcf(c_167461,plain,
! [X0: $i] :
( ( sK92(unordered_pair(X0,X0)) = sK140 )
| ( unordered_pair(sK169(sK92(unordered_pair(X0,X0))),sK169(sK92(unordered_pair(X0,X0)))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_151778,c_165554]) ).
tcf(c_167462,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = sK140 )
| ( unordered_pair(sK142(unordered_pair(X0,X0)),sK142(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(superposition,[status(thm)],[c_154138,c_165554]) ).
tcf(c_167463,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = unordered_pair(sK140,sK140) )
| ~ in(X0,powerset(sK140)) ),
inference(superposition,[status(thm)],[c_314,c_165554]) ).
tcf(c_167485,plain,
! [X0: $i] : unordered_pair(sK142(unordered_pair(X0,X0)),sK142(unordered_pair(X0,X0))) = unordered_pair(X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_167462,c_52]) ).
tcf(c_167486,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = powerset(sK140) )
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),unordered_pair(X0,X0))) = sK140 ) ),
inference(light_normalisation,[status(thm)],[c_167450,c_314]) ).
tcf(c_167489,plain,
! [X0: $i] : unordered_pair(sK169(unordered_pair(X0,X0)),sK169(unordered_pair(X0,X0))) = unordered_pair(X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_167446,c_52]) ).
tcf(c_167509,plain,
! [X0: $i] :
( relation(sK126(unordered_pair(X0,X0)))
| ( unordered_pair(sK125(unordered_pair(X0,X0)),sK125(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_167437,c_935]) ).
tcf(c_167512,plain,
! [X0: $i] :
( function(sK126(unordered_pair(X0,X0)))
| ( unordered_pair(sK125(unordered_pair(X0,X0)),sK125(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_167436,c_935]) ).
tcf(c_167515,plain,
! [X0: $i] :
( ( unordered_pair(sK128(unordered_pair(X0,X0)),sK128(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_167440,c_52]) ).
tcf(c_167521,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(sK318(X0,unordered_pair(X1,X1)),sK318(X0,unordered_pair(X1,X1))) = unordered_pair(X1,X1) )
| ~ relation(X0)
| ~ is_well_founded_in(X0,unordered_pair(X1,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_167459,c_52]) ).
tcf(c_167528,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(sK320(X1,unordered_pair(X0,X0)),sK320(X1,unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(unordered_pair(X0,X0),relation_field(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_167455,c_52]) ).
tcf(c_167533,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(unordered_pair(sK137(unordered_pair(X0,X0)),sK137(unordered_pair(X0,X0))),unordered_pair(sK137(unordered_pair(X0,X0)),sK138(unordered_pair(X0,X0)))),unordered_pair(unordered_pair(sK137(unordered_pair(X0,X0)),sK137(unordered_pair(X0,X0))),unordered_pair(sK137(unordered_pair(X0,X0)),sK138(unordered_pair(X0,X0))))) = unordered_pair(X0,X0) )
| ~ relation(unordered_pair(X0,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_167458,c_52]) ).
tcf(c_167803,plain,
! [X0: $i] :
( disjoint(set_difference(unordered_pair(sK169(X0),sK169(X0)),X0),unordered_pair(sK169(X0),sK169(X0)))
| ( X0 = sK140 ) ),
inference(superposition,[status(thm)],[c_166144,c_146330]) ).
tcf(c_167805,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( set_difference(sK140,unordered_pair(sK169(X0),sK169(X0))) = sK140 ) ),
inference(superposition,[status(thm)],[c_166144,c_146010]) ).
tcf(c_167806,plain,
! [X0: $i] :
( subset(sK140,unordered_pair(sK169(X0),sK169(X0)))
| ( X0 = sK140 ) ),
inference(superposition,[status(thm)],[c_166144,c_383]) ).
tcf(c_167807,plain,
! [X0: $i] :
( disjoint(unordered_pair(sK169(X0),sK169(X0)),X0)
| ( X0 = sK140 )
| ( set_difference(unordered_pair(sK169(X0),sK169(X0)),sK140) != sK140 ) ),
inference(superposition,[status(thm)],[c_166144,c_625]) ).
tcf(c_167808,plain,
! [X0: $i] :
( subset(unordered_pair(sK169(X0),sK169(X0)),X0)
| ( X0 = sK140 ) ),
inference(superposition,[status(thm)],[c_166144,c_387]) ).
tcf(c_167809,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,sK140),sK140)
| ( X1 = sK140 )
| ( set_difference(unordered_pair(sK169(X1),sK169(X1)),X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,unordered_pair(sK169(X1),sK169(X1))) ),
inference(superposition,[status(thm)],[c_166144,c_146007]) ).
tcf(c_167811,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( unordered_pair(sK169(X0),sK169(X0)) = sK140 )
| ( set_difference(unordered_pair(sK169(X0),sK169(X0)),X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_166144,c_146011]) ).
tcf(c_167820,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK140 )
| ( set_difference(unordered_pair(sK169(X1),sK169(X1)),X1) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,unordered_pair(sK169(X1),sK169(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_167809,c_580]) ).
tcf(c_167940,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK302(sK242)),X0),sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ~ relation(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_296]) ).
tcf(c_167941,plain,
! [X0: $i] :
( in(sK142(sK302(sK242)),sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ( apply(sK126(sK302(sK242)),X0) = sK140 )
| ~ function(sK126(sK302(sK242)))
| ~ relation(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_154130]) ).
tcf(c_167942,plain,
! [X0: $i] :
( ( sK125(sK302(sK242)) = sK140 )
| ( apply(sK126(sK302(sK242)),X0) = sK140 )
| ~ function(sK126(sK302(sK242)))
| ~ relation(sK126(sK302(sK242)))
| ~ in(sK302(sK242),X0) ),
inference(superposition,[status(thm)],[c_147769,c_155600]) ).
tcf(c_167943,plain,
( function(sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ~ empty(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_147195]) ).
tcf(c_167944,plain,
( finite(sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ~ empty(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_147193]) ).
tcf(c_167945,plain,
( epsilon_transitive(sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ~ empty(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_147192]) ).
tcf(c_167946,plain,
( epsilon_connected(sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ~ empty(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_147191]) ).
tcf(c_167947,plain,
( ordinal(sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ~ empty(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_147190]) ).
tcf(c_167948,plain,
( one_to_one(sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ~ empty(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_147189]) ).
tcf(c_167949,plain,
! [X0: $i] :
( ( sK125(sK302(sK242)) = sK140 )
| ( apply(sK126(sK302(sK242)),X0) = sK140 )
| ~ empty(sK302(sK242))
| ~ relation(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_150772]) ).
tcf(c_167950,plain,
! [X0: $i] :
( element(X0,sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ( apply(sK126(sK302(sK242)),X0) = sK140 )
| ~ function(sK126(sK302(sK242)))
| ~ relation(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_148552]) ).
tcf(c_167951,plain,
( relation(sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ~ empty(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_642]) ).
tcf(c_167952,plain,
( empty(sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ~ empty(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_641]) ).
tcf(c_167953,plain,
! [X0: $i] :
( in(X0,sK302(sK242))
| ( sK125(sK302(sK242)) = sK140 )
| ( apply(sK126(sK302(sK242)),X0) = sK140 )
| ~ function(sK126(sK302(sK242)))
| ~ relation(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_906]) ).
tcf(c_167954,plain,
( ( sK125(sK302(sK242)) = sK140 )
| ( relation_rng(sK126(sK302(sK242))) = sK140 )
| ~ relation(sK126(sK302(sK242)))
| ( sK302(sK242) != sK140 ) ),
inference(superposition,[status(thm)],[c_147769,c_478]) ).
tcf(c_167955,plain,
( ( sK126(sK302(sK242)) = sK140 )
| ( sK125(sK302(sK242)) = sK140 )
| ~ relation(sK126(sK302(sK242)))
| ( sK302(sK242) != sK140 ) ),
inference(superposition,[status(thm)],[c_147769,c_475]) ).
tcf(c_168143,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK128(unordered_pair(X2,X2)))
| ~ in(X2,X0)
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_620,c_165550]) ).
tcf(c_168144,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(unordered_pair(X0,X0),set_union2(X1,X2)) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_620,c_165532]) ).
tcf(c_168145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(X2)
| ~ in(X2,X0)
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_620,c_333]) ).
tcf(c_168146,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(set_union2(X1,X2)) = sK140 )
| ( set_difference(apply(sK126(set_union2(X1,X2)),X0),union(X0)) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_620,c_154509]) ).
tcf(c_168147,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK128(X2),X2)
| ( X2 = sK140 )
| ~ in(X2,X0)
| ~ ordinal(union(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_620,c_154063]) ).
tcf(c_168148,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_620,c_527]) ).
tcf(c_168149,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK128(X2))
| ( X2 = sK140 )
| ~ in(X2,X0)
| ~ ordinal(union(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_620,c_154064]) ).
tcf(c_168150,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK142(X0),X0)
| ( sK125(set_union2(X1,X2)) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_620,c_154131]) ).
tcf(c_168151,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,union(set_union2(X1,X2))) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_620,c_154065]) ).
tcf(c_168152,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK142(set_union2(X1,X2)),set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_620,c_522]) ).
tcf(c_168153,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(set_union2(X1,X2)) = sK140 )
| ~ empty(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_620,c_150230]) ).
tcf(c_168154,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X0)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_620,c_787]) ).
tcf(c_168155,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_620,c_526]) ).
tcf(c_168156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X1,relation_inverse_image(X0,set_union2(X2,X5)))
| ( X4 = sK140 )
| ~ function(X0)
| ~ in(X1,X3)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ in(apply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_620,c_423]) ).
tcf(c_168157,plain,
! [X0: $i,X1: $i] :
( ( set_difference(powerset(sK140),set_union2(X0,X1)) = sK140 )
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_620,c_165836]) ).
tcf(c_168158,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = omega )
| ( sK125(sK263(set_union2(X0,X1))) = sK140 )
| ~ in(sK140,X0)
| ~ being_limit_ordinal(set_union2(X0,X1))
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_620,c_145540]) ).
tcf(c_168159,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(X0,X1)) = sK140 )
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_620,c_144395]) ).
tcf(c_168160,plain,
! [X0: $i,X1: $i] :
( ordinal(sK263(set_union2(X0,X1)))
| ( set_union2(X0,X1) = omega )
| ~ in(sK140,X0)
| ~ being_limit_ordinal(set_union2(X0,X1))
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_620,c_846]) ).
tcf(c_168161,plain,
! [X0: $i,X1: $i] :
( being_limit_ordinal(sK263(set_union2(X0,X1)))
| ( set_union2(X0,X1) = omega )
| ~ in(sK140,X0)
| ~ being_limit_ordinal(set_union2(X0,X1))
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_620,c_845]) ).
tcf(c_168162,plain,
! [X0: $i,X1: $i] :
( subset(omega,set_union2(X0,X1))
| ~ in(sK140,X0)
| ~ being_limit_ordinal(set_union2(X0,X1))
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_620,c_850]) ).
tcf(c_168163,plain,
! [X0: $i,X1: $i] : ~ in(sK116(set_union2(X0,X1)),X0),
inference(superposition,[status(thm)],[c_620,c_155599]) ).
tcf(c_168164,plain,
! [X0: $i,X1: $i] : ~ in(sK300(set_union2(X0,X1)),X0),
inference(superposition,[status(thm)],[c_620,c_155616]) ).
tcf(c_168165,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,set_union2(X1,X2)) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_620,c_155600]) ).
tcf(c_168283,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK128(unordered_pair(X2,X2)))
| ~ in(X2,X1)
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_621,c_165550]) ).
tcf(c_168284,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(unordered_pair(X0,X0),set_union2(X2,X1)) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_165532]) ).
tcf(c_168285,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(X2)
| ~ in(X2,X1)
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_621,c_333]) ).
tcf(c_168286,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(set_union2(X2,X1)) = sK140 )
| ( set_difference(apply(sK126(set_union2(X2,X1)),X0),union(X0)) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_154509]) ).
tcf(c_168287,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK128(X2),X2)
| ( X2 = sK140 )
| ~ in(X2,X1)
| ~ ordinal(union(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_621,c_154063]) ).
tcf(c_168288,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ in(set_union2(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_621,c_527]) ).
tcf(c_168289,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK128(X2))
| ( X2 = sK140 )
| ~ in(X2,X1)
| ~ ordinal(union(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_621,c_154064]) ).
tcf(c_168290,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK142(X0),X0)
| ( sK125(set_union2(X2,X1)) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_154131]) ).
tcf(c_168291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,union(set_union2(X2,X1))) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_154065]) ).
tcf(c_168292,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK142(set_union2(X2,X1)),set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_522]) ).
tcf(c_168293,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK125(set_union2(X2,X1)) = sK140 )
| ~ empty(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_150230]) ).
tcf(c_168294,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X2,X1)
| ~ empty(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_621,c_787]) ).
tcf(c_168295,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_621,c_526]) ).
tcf(c_168296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( in(X1,relation_inverse_image(X0,set_union2(X5,X2)))
| ( X4 = sK140 )
| ~ function(X0)
| ~ in(X1,X3)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ in(apply(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_621,c_423]) ).
tcf(c_168297,plain,
! [X0: $i,X1: $i] :
( ( set_difference(powerset(sK140),set_union2(X1,X0)) = sK140 )
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_621,c_165836]) ).
tcf(c_168298,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = omega )
| ( sK125(sK263(set_union2(X0,X1))) = sK140 )
| ~ in(sK140,X1)
| ~ being_limit_ordinal(set_union2(X0,X1))
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_621,c_145540]) ).
tcf(c_168299,plain,
! [X0: $i,X1: $i] :
( ( sK125(set_union2(X1,X0)) = sK140 )
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_621,c_144395]) ).
tcf(c_168300,plain,
! [X0: $i,X1: $i] :
( ordinal(sK263(set_union2(X0,X1)))
| ( set_union2(X0,X1) = omega )
| ~ in(sK140,X1)
| ~ being_limit_ordinal(set_union2(X0,X1))
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_621,c_846]) ).
tcf(c_168301,plain,
! [X0: $i,X1: $i] :
( being_limit_ordinal(sK263(set_union2(X0,X1)))
| ( set_union2(X0,X1) = omega )
| ~ in(sK140,X1)
| ~ being_limit_ordinal(set_union2(X0,X1))
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_621,c_845]) ).
tcf(c_168302,plain,
! [X0: $i,X1: $i] :
( subset(omega,set_union2(X0,X1))
| ~ in(sK140,X1)
| ~ being_limit_ordinal(set_union2(X0,X1))
| ~ ordinal(set_union2(X0,X1)) ),
inference(superposition,[status(thm)],[c_621,c_850]) ).
tcf(c_168303,plain,
! [X0: $i,X1: $i] : ~ in(sK116(set_union2(X0,X1)),X1),
inference(superposition,[status(thm)],[c_621,c_155599]) ).
tcf(c_168304,plain,
! [X0: $i,X1: $i] : ~ in(sK300(set_union2(X0,X1)),X1),
inference(superposition,[status(thm)],[c_621,c_155616]) ).
tcf(c_168305,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X0,set_union2(X2,X1)) = sK140 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_621,c_155600]) ).
tcf(c_168556,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(relation_dom(X0)) = sK140 )
| ( relation_rng(relation_rng_restriction(sK140,sK126(relation_dom(X0)))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_163467,c_643]) ).
tcf(c_168557,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(relation_dom(X0)) = sK140 )
| ( set_difference(relation_dom_restriction(sK126(relation_dom(X0)),X1),sK126(relation_dom(X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_154400,c_643]) ).
tcf(c_168558,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(identity_relation(relation_dom(X0))) = sK140 )
| ( relation_dom(sK126(identity_relation(relation_dom(X0)))) = identity_relation(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_151886,c_643]) ).
tcf(c_168559,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK115(relation_dom(X0))) = sK140 )
| ( relation_dom(sK126(sK115(relation_dom(X0)))) = sK115(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_151861,c_643]) ).
tcf(c_168560,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(set_union2(relation_dom(X0),X1)) = sK140 )
| ( relation_dom(sK126(set_union2(relation_dom(X0),X1))) = set_union2(relation_dom(X0),X1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_149359,c_643]) ).
tcf(c_168561,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK302(relation_dom(X0))) = sK140 )
| ( relation_dom(sK126(sK302(relation_dom(X0)))) = sK302(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_147722,c_643]) ).
tcf(c_168562,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK198(relation_dom(X0))) = sK140 )
| ( relation_dom(sK126(sK198(relation_dom(X0)))) = sK198(relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_147277,c_643]) ).
tcf(c_168563,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(relation_dom(X0)) = sK140 )
| ( relation_dom(sK126(relation_dom(X0))) = relation_dom(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_353,c_643]) ).
tcf(c_168564,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(relation_dom(X0)) = sK140 )
| ( set_difference(relation_rng_restriction(X1,sK126(relation_dom(X0))),sK126(relation_dom(X0))) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152610,c_643]) ).
tcf(c_168565,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(set_union2(X1,relation_dom(X0))) = sK140 )
| ( relation_dom(sK126(set_union2(X1,relation_dom(X0)))) = set_union2(X1,relation_dom(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_149341,c_643]) ).
tcf(c_168567,plain,
! [X0: $i] :
( empty(sK115(X0))
| ~ empty(X0)
| ~ relation(sK115(X0)) ),
inference(superposition,[status(thm)],[c_251,c_643]) ).
tcf(c_168568,plain,
! [X0: $i] :
( empty(sK126(X0))
| ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(X0)
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_148083,c_643]) ).
tcf(c_168571,plain,
! [X0: $i] :
( empty(sK126(X0))
| ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ~ empty(X0)
| ~ relation(sK126(X0)) ),
inference(superposition,[status(thm)],[c_144306,c_643]) ).
tcf(c_168572,plain,
! [X0: $i] :
( empty(identity_relation(X0))
| ~ empty(X0)
| ~ relation(identity_relation(X0)) ),
inference(superposition,[status(thm)],[c_489,c_643]) ).
tcf(c_168581,plain,
! [X0: $i,X1: $i] :
( empty(sK126(set_union2(X0,X1)))
| ( X0 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(set_union2(X0,X1))
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149522,c_643]) ).
tcf(c_168582,plain,
! [X0: $i,X1: $i] :
( empty(sK126(set_union2(X0,X1)))
| ( X1 = sK140 )
| ( sK125(set_union2(X0,X1)) = sK140 )
| ~ empty(set_union2(X0,X1))
| ~ relation(sK126(set_union2(X0,X1))) ),
inference(superposition,[status(thm)],[c_149417,c_643]) ).
tcf(c_168583,plain,
! [X0: $i] :
( empty(sK126(sK198(X0)))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK198(X0))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147733,c_643]) ).
tcf(c_168584,plain,
! [X0: $i] :
( empty(sK126(sK198(X0)))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK198(X0))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147331,c_643]) ).
tcf(c_168585,plain,
! [X0: $i] :
( empty(sK126(sK198(X0)))
| ( X0 = sK140 )
| ( sK125(sK198(X0)) = sK140 )
| ~ empty(sK198(X0))
| ~ relation(sK126(sK198(X0))) ),
inference(superposition,[status(thm)],[c_147339,c_643]) ).
tcf(c_168586,plain,
! [X0: $i] :
( empty(sK126(sK198(powerset(X0))))
| ( sK125(sK198(powerset(X0))) = sK140 )
| ~ empty(sK198(powerset(X0)))
| ~ relation(sK126(sK198(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147341,c_643]) ).
tcf(c_168587,plain,
( empty(sK126(sK198(sK241)))
| ( sK125(sK198(sK241)) = sK140 )
| ~ empty(sK198(sK241))
| ~ relation(sK126(sK198(sK241))) ),
inference(superposition,[status(thm)],[c_147342,c_643]) ).
tcf(c_168588,plain,
( empty(sK126(sK198(sK242)))
| ( sK125(sK198(sK242)) = sK140 )
| ~ empty(sK198(sK242))
| ~ relation(sK126(sK198(sK242))) ),
inference(superposition,[status(thm)],[c_147343,c_643]) ).
tcf(c_168589,plain,
( empty(sK126(sK198(omega)))
| ( sK125(sK198(omega)) = sK140 )
| ~ empty(sK198(omega))
| ~ relation(sK126(sK198(omega))) ),
inference(superposition,[status(thm)],[c_147344,c_643]) ).
tcf(c_168590,plain,
! [X0: $i,X1: $i] :
( empty(sK126(sK198(unordered_pair(X0,X1))))
| ( sK125(sK198(unordered_pair(X0,X1))) = sK140 )
| ~ empty(sK198(unordered_pair(X0,X1)))
| ~ relation(sK126(sK198(unordered_pair(X0,X1)))) ),
inference(superposition,[status(thm)],[c_147345,c_643]) ).
tcf(c_168591,plain,
( empty(sK126(sK198(sK303)))
| ( sK125(sK198(sK303)) = sK140 )
| ~ empty(sK198(sK303))
| ~ relation(sK126(sK198(sK303))) ),
inference(superposition,[status(thm)],[c_147346,c_643]) ).
tcf(c_168592,plain,
( empty(sK126(sK198(sK313)))
| ( sK125(sK198(sK313)) = sK140 )
| ~ empty(sK198(sK313))
| ~ relation(sK126(sK198(sK313))) ),
inference(superposition,[status(thm)],[c_147347,c_643]) ).
tcf(c_168593,plain,
( empty(sK126(sK198(sK346)))
| ( sK125(sK198(sK346)) = sK140 )
| ~ empty(sK198(sK346))
| ~ relation(sK126(sK198(sK346))) ),
inference(superposition,[status(thm)],[c_147348,c_643]) ).
tcf(c_168594,plain,
( empty(sK126(sK198(sK358)))
| ( sK125(sK198(sK358)) = sK140 )
| ~ empty(sK198(sK358))
| ~ relation(sK126(sK198(sK358))) ),
inference(superposition,[status(thm)],[c_147349,c_643]) ).
tcf(c_168595,plain,
! [X0: $i] :
( empty(sK126(sK302(X0)))
| ( relation_dom(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK302(X0))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147757,c_643]) ).
tcf(c_168596,plain,
! [X0: $i] :
( empty(sK126(sK302(X0)))
| ( relation_rng(X0) = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK302(X0))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147756,c_643]) ).
tcf(c_168597,plain,
! [X0: $i] :
( empty(sK126(sK302(X0)))
| ( X0 = sK140 )
| ( sK125(sK302(X0)) = sK140 )
| ~ empty(sK302(X0))
| ~ relation(sK126(sK302(X0))) ),
inference(superposition,[status(thm)],[c_147765,c_643]) ).
tcf(c_168598,plain,
! [X0: $i] :
( empty(sK126(sK302(powerset(X0))))
| ( sK125(sK302(powerset(X0))) = sK140 )
| ~ empty(sK302(powerset(X0)))
| ~ relation(sK126(sK302(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_147767,c_643]) ).
tcf(c_168599,plain,
( empty(sK126(sK302(sK241)))
| ( sK125(sK302(sK241)) = sK140 )
| ~ empty(sK302(sK241))
| ~ relation(sK126(sK302(sK241))) ),
inference(superposition,[status(thm)],[c_147768,c_643]) ).
tcf(c_168600,plain,
( empty(sK126(sK302(sK242)))
| ( sK125(sK302(sK242)) = sK140 )
| ~ empty(sK302(sK242))
| ~ relation(sK126(sK302(sK242))) ),
inference(superposition,[status(thm)],[c_147769,c_643]) ).
tcf(c_168603,plain,
! [X0: $i] :
( empty(sK126(sK115(X0)))
| ( X0 = sK140 )
| ( sK125(sK115(X0)) = sK140 )
| ~ empty(sK115(X0))
| ~ relation(sK126(sK115(X0))) ),
inference(superposition,[status(thm)],[c_153342,c_643]) ).
tcf(c_168604,plain,
! [X0: $i] :
( empty(sK126(identity_relation(X0)))
| ( X0 = sK140 )
| ( sK125(identity_relation(X0)) = sK140 )
| ~ empty(identity_relation(X0))
| ~ relation(sK126(identity_relation(X0))) ),
inference(superposition,[status(thm)],[c_153519,c_643]) ).
tcf(c_168605,plain,
! [X0: $i] :
( empty(identity_relation(X0))
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_168572,c_1101]) ).
tcf(c_168608,plain,
! [X0: $i] :
( empty(sK115(X0))
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_168567,c_249]) ).
tcf(c_169044,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_rng(X0),X1) = sK140 )
| ( set_difference(X1,union(relation_dom(relation_rng(X0)))) = sK140 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_147668,c_154508]) ).
tcf(c_169045,plain,
! [X0: $i] :
( ( apply(relation_rng(X0),sK300(relation_dom(relation_rng(X0)))) = sK140 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_147668,c_156990]) ).
tcf(c_169046,plain,
! [X0: $i] :
( ( apply(relation_rng(X0),sK116(relation_dom(relation_rng(X0)))) = sK140 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_147668,c_156955]) ).
tcf(c_169047,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(relation_rng(X0))) = sK140 )
| ( apply(relation_rng(X0),X1) = sK140 )
| ~ empty(X1)
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_147668,c_150502]) ).
tcf(c_169048,plain,
! [X0: $i] :
( ( sK125(relation_dom(relation_rng(X0))) = sK140 )
| ( apply(relation_rng(X0),sK140) = sK140 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_147668,c_145538]) ).
tcf(c_169076,plain,
! [X0: $i] :
( finite(unordered_pair(sK169(X0),sK169(X0)))
| ( X0 = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_167808,c_276]) ).
tcf(c_169077,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ~ proper_subset(X0,unordered_pair(sK169(X0),sK169(X0))) ),
inference(superposition,[status(thm)],[c_167808,c_472]) ).
tcf(c_169078,plain,
! [X0: $i] :
( in(sK140,unordered_pair(sK169(X0),sK169(X0)))
| ( X0 = sK140 )
| ( sK125(subset_complement(X0,unordered_pair(sK169(X0),sK169(X0)))) = sK140 )
| ~ element(sK140,X0) ),
inference(superposition,[status(thm)],[c_167808,c_145539]) ).
tcf(c_169079,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,unordered_pair(sK169(X1),sK169(X1)))),unordered_pair(sK169(X1),sK169(X1)))
| ( X1 = sK140 )
| ( unordered_pair(sK169(X1),sK169(X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_167808,c_1058]) ).
tcf(c_169080,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,unordered_pair(sK169(X1),sK169(X1))),unordered_pair(sK169(X1),sK169(X1)))
| ( X1 = sK140 )
| ( unordered_pair(sK169(X1),sK169(X1)) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_167808,c_1057]) ).
tcf(c_169081,plain,
! [X0: $i] :
( in(sK128(unordered_pair(sK169(X0),sK169(X0))),unordered_pair(sK169(X0),sK169(X0)))
| ( X0 = sK140 )
| ( unordered_pair(sK169(X0),sK169(X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_167808,c_369]) ).
tcf(c_169082,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK169(X0),sK169(X0))))
| ( X0 = sK140 )
| ( unordered_pair(sK169(X0),sK169(X0)) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_167808,c_371]) ).
tcf(c_169085,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(unordered_pair(sK169(X1),sK169(X1))),X0)
| ( X1 = sK140 )
| ( unordered_pair(sK169(X1),sK169(X1)) = sK140 )
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,unordered_pair(sK169(X1),sK169(X1))) ),
inference(superposition,[status(thm)],[c_167808,c_370]) ).
tcf(c_169089,plain,
( in(sK63(unordered_pair(sK169(powerset(sK62)),sK169(powerset(sK62)))),unordered_pair(sK169(powerset(sK62)),sK169(powerset(sK62))))
| ( powerset(sK62) = sK140 )
| ( unordered_pair(sK169(powerset(sK62)),sK169(powerset(sK62))) = sK140 )
| ~ iPr_def_21 ),
inference(superposition,[status(thm)],[c_167808,c_156787]) ).
tcf(c_169090,plain,
! [X0: $i] :
( in(sK119(unordered_pair(sK169(powerset(X0)),sK169(powerset(X0)))),unordered_pair(sK169(powerset(X0)),sK169(powerset(X0))))
| ( powerset(X0) = sK140 )
| ( unordered_pair(sK169(powerset(X0)),sK169(powerset(X0))) = sK140 )
| ~ finite(X0) ),
inference(superposition,[status(thm)],[c_167808,c_156797]) ).
tcf(c_169091,plain,
( in(sK262(unordered_pair(sK169(powerset(sK261)),sK169(powerset(sK261)))),unordered_pair(sK169(powerset(sK261)),sK169(powerset(sK261))))
| ( powerset(sK261) = sK140 )
| ( unordered_pair(sK169(powerset(sK261)),sK169(powerset(sK261))) = sK140 )
| ~ iPr_def_15 ),
inference(superposition,[status(thm)],[c_167808,c_156803]) ).
tcf(c_169100,plain,
! [X0: $i] :
( in(sK128(unordered_pair(sK169(X0),sK169(X0))),unordered_pair(sK169(X0),sK169(X0)))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_169081,c_52]) ).
tcf(c_169104,plain,
! [X0: $i,X1: $i] :
( in(sK318(X0,unordered_pair(sK169(X1),sK169(X1))),unordered_pair(sK169(X1),sK169(X1)))
| ( X1 = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_169080,c_52]) ).
tcf(c_169109,plain,
( in(sK262(unordered_pair(sK169(powerset(sK261)),sK169(powerset(sK261)))),unordered_pair(sK169(powerset(sK261)),sK169(powerset(sK261))))
| ( powerset(sK261) = sK140 )
| ~ iPr_def_15 ),
inference(forward_subsumption_resolution,[status(thm)],[c_169091,c_52]) ).
tcf(c_169113,plain,
( in(sK63(unordered_pair(sK169(powerset(sK62)),sK169(powerset(sK62)))),unordered_pair(sK169(powerset(sK62)),sK169(powerset(sK62))))
| ( powerset(sK62) = sK140 )
| ~ iPr_def_21 ),
inference(forward_subsumption_resolution,[status(thm)],[c_169089,c_52]) ).
tcf(c_169117,plain,
! [X0: $i] :
( in(sK119(unordered_pair(sK169(powerset(X0)),sK169(powerset(X0)))),unordered_pair(sK169(powerset(X0)),sK169(powerset(X0))))
| ( powerset(X0) = sK140 )
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_169090,c_52]) ).
tcf(c_169121,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(sK128(unordered_pair(sK169(X1),sK169(X1))),X0)
| ( X1 = sK140 )
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ in(X0,unordered_pair(sK169(X1),sK169(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_169085,c_52]) ).
tcf(c_169127,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X0,sK318(X0,unordered_pair(sK169(X1),sK169(X1)))),unordered_pair(sK169(X1),sK169(X1)))
| ( X1 = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_169079,c_52]) ).
tcf(c_169347,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK128(unordered_pair(sK169(X0),sK169(X0))))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_167064,c_833]) ).
tcf(c_169348,plain,
! [X0: $i] :
( epsilon_connected(sK128(unordered_pair(sK169(X0),sK169(X0))))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_167064,c_1050]) ).
tcf(c_169349,plain,
! [X0: $i] :
( epsilon_transitive(sK128(unordered_pair(sK169(X0),sK169(X0))))
| ( X0 = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_167064,c_1049]) ).
tcf(c_169404,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(sK142(unordered_pair(X1,X1)),sK142(unordered_pair(X1,X1))) = unordered_pair(X0,X0) )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_167485,c_165554]) ).
tcf(c_169405,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( unordered_pair(sK142(unordered_pair(X1,X1)),sK142(unordered_pair(X1,X1))) = X0 )
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_167485,c_397]) ).
tcf(c_169406,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(sK142(unordered_pair(X0,X0)),X1) ),
inference(superposition,[status(thm)],[c_167485,c_388]) ).
tcf(c_169407,plain,
! [X0: $i] :
( ( sK199(powerset(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ( sK199(powerset(unordered_pair(sK142(unordered_pair(X0,X0)),sK142(unordered_pair(X0,X0))))) = sK140 ) ),
inference(superposition,[status(thm)],[c_167485,c_160236]) ).
tcf(c_169408,plain,
! [X0: $i,X1: $i] :
( disjoint(unordered_pair(X0,X0),X1)
| in(sK142(unordered_pair(X0,X0)),X1) ),
inference(superposition,[status(thm)],[c_167485,c_55]) ).
tcf(c_169409,plain,
! [X0: $i] : ~ empty(set_union2(sK142(unordered_pair(X0,X0)),unordered_pair(X0,X0))),
inference(superposition,[status(thm)],[c_167485,c_892]) ).
tcf(c_169410,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),X1) = unordered_pair(X0,X0) )
| ( set_difference(unordered_pair(sK142(unordered_pair(X0,X0)),sK142(unordered_pair(X0,X0))),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_167485,c_146011]) ).
tcf(c_169413,plain,
! [X0: $i,X1: $i] :
( in(sK142(unordered_pair(X0,X0)),X1)
| ~ subset(unordered_pair(X0,X0),X1) ),
inference(superposition,[status(thm)],[c_167485,c_392]) ).
tcf(c_169415,plain,
! [X0: $i] :
( ( relation_dom(sK126(sK198(unordered_pair(X0,X0)))) = sK198(unordered_pair(X0,X0)) )
| ( sK125(sK198(unordered_pair(sK142(unordered_pair(X0,X0)),sK142(unordered_pair(X0,X0))))) = sK140 ) ),
inference(superposition,[status(thm)],[c_167485,c_147345]) ).
tcf(c_169417,plain,
! [X0: $i] :
( ( relation_dom(sK126(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ( sK125(unordered_pair(sK142(unordered_pair(X0,X0)),sK142(unordered_pair(X0,X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_167485,c_146160]) ).
tcf(c_169419,plain,
! [X0: $i] : ~ empty(unordered_pair(X0,X0)),
inference(superposition,[status(thm)],[c_167485,c_935]) ).
tcf(c_169420,plain,
! [X0: $i] : element(sK142(unordered_pair(X0,X0)),unordered_pair(X0,X0)),
inference(superposition,[status(thm)],[c_167485,c_148561]) ).
tcf(c_169421,plain,
! [X0: $i] : in(sK142(unordered_pair(X0,X0)),unordered_pair(X0,X0)),
inference(superposition,[status(thm)],[c_167485,c_940]) ).
tcf(c_169433,plain,
! [X0: $i] :
( ( sK125(unordered_pair(X0,X0)) = sK140 )
| ( relation_dom(sK126(unordered_pair(X0,X0))) = unordered_pair(X0,X0) ) ),
inference(light_normalisation,[status(thm)],[c_169417,c_167485]) ).
tcf(c_169438,plain,
! [X0: $i] :
( ( sK125(sK198(unordered_pair(X0,X0))) = sK140 )
| ( relation_dom(sK126(sK198(unordered_pair(X0,X0)))) = sK198(unordered_pair(X0,X0)) ) ),
inference(light_normalisation,[status(thm)],[c_169415,c_167485]) ).
tcf(c_169571,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(sK169(unordered_pair(X1,X1)),sK169(unordered_pair(X1,X1))) = unordered_pair(X0,X0) )
| ~ in(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_167489,c_165554]) ).
tcf(c_169572,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK140 )
| ( unordered_pair(sK169(unordered_pair(X1,X1)),sK169(unordered_pair(X1,X1))) = X0 )
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_167489,c_397]) ).
tcf(c_169574,plain,
! [X0: $i,X1: $i] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(sK169(unordered_pair(X0,X0)),X1) ),
inference(superposition,[status(thm)],[c_167489,c_388]) ).
tcf(c_169575,plain,
! [X0: $i] :
( ( sK199(powerset(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ( sK199(powerset(unordered_pair(sK169(unordered_pair(X0,X0)),sK169(unordered_pair(X0,X0))))) = sK140 ) ),
inference(superposition,[status(thm)],[c_167489,c_160236]) ).
tcf(c_169576,plain,
! [X0: $i,X1: $i] :
( disjoint(unordered_pair(X0,X0),X1)
| in(sK169(unordered_pair(X0,X0)),X1) ),
inference(superposition,[status(thm)],[c_167489,c_55]) ).
tcf(c_169577,plain,
! [X0: $i] : ~ empty(set_union2(sK169(unordered_pair(X0,X0)),unordered_pair(X0,X0))),
inference(superposition,[status(thm)],[c_167489,c_892]) ).
tcf(c_169578,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(X0,X0),X1) = unordered_pair(X0,X0) )
| ( set_difference(unordered_pair(sK169(unordered_pair(X0,X0)),sK169(unordered_pair(X0,X0))),X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_167489,c_146011]) ).
tcf(c_169581,plain,
! [X0: $i,X1: $i] :
( in(sK169(unordered_pair(X0,X0)),X1)
| ~ subset(unordered_pair(X0,X0),X1) ),
inference(superposition,[status(thm)],[c_167489,c_392]) ).
tcf(c_169583,plain,
! [X0: $i] :
( ( relation_dom(sK126(sK198(unordered_pair(X0,X0)))) = sK198(unordered_pair(X0,X0)) )
| ( sK125(sK198(unordered_pair(sK169(unordered_pair(X0,X0)),sK169(unordered_pair(X0,X0))))) = sK140 ) ),
inference(superposition,[status(thm)],[c_167489,c_147345]) ).
tcf(c_169585,plain,
! [X0: $i] :
( ( relation_dom(sK126(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ( sK125(unordered_pair(sK169(unordered_pair(X0,X0)),sK169(unordered_pair(X0,X0)))) = sK140 ) ),
inference(superposition,[status(thm)],[c_167489,c_146160]) ).
tcf(c_169588,plain,
! [X0: $i] : element(sK169(unordered_pair(X0,X0)),unordered_pair(X0,X0)),
inference(superposition,[status(thm)],[c_167489,c_148561]) ).
tcf(c_169589,plain,
! [X0: $i] : in(sK169(unordered_pair(X0,X0)),unordered_pair(X0,X0)),
inference(superposition,[status(thm)],[c_167489,c_940]) ).
tcf(c_169590,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ( unordered_pair(X0,X0) = sK140 )
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_167489,c_167064]) ).
tcf(c_169591,plain,
! [X0: $i] :
( subset(unordered_pair(X0,X0),unordered_pair(X0,X0))
| ( unordered_pair(X0,X0) = sK140 ) ),
inference(superposition,[status(thm)],[c_167489,c_167808]) ).
tcf(c_169599,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_169590,c_52]) ).
tcf(c_169622,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ~ ordinal(unordered_pair(sK169(unordered_pair(X0,X0)),sK169(unordered_pair(X0,X0)))) ),
inference(superposition,[status(thm)],[c_167489,c_169599]) ).
tcf(c_169623,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(X0,X0)))
| ~ ordinal(unordered_pair(sK142(unordered_pair(X0,X0)),sK142(unordered_pair(X0,X0)))) ),
inference(superposition,[status(thm)],[c_167485,c_169599]) ).
tcf(c_169624,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK128(unordered_pair(X0,X0)))
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_169599,c_833]) ).
tcf(c_169625,plain,
! [X0: $i] :
( epsilon_connected(sK128(unordered_pair(X0,X0)))
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_169599,c_1050]) ).
tcf(c_169626,plain,
! [X0: $i] :
( epsilon_transitive(sK128(unordered_pair(X0,X0)))
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_169599,c_1049]) ).
tcf(c_169694,plain,
! [X0: $i] :
( sP3(X0)
| ( sK125(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_150222]) ).
tcf(c_169695,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_148019]) ).
tcf(c_169696,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_rng(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_147669]) ).
tcf(c_169697,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( relation_dom(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_147196]) ).
tcf(c_169698,plain,
! [X0: $i] :
( one_to_one(X0)
| ( sK125(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_84200]) ).
tcf(c_169699,plain,
! [X0: $i] :
( ordinal(X0)
| ( sK125(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_1047]) ).
tcf(c_169700,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK125(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_1046]) ).
tcf(c_169701,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ( sK125(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_1045]) ).
tcf(c_169702,plain,
! [X0: $i] :
( finite(X0)
| ( sK125(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_983]) ).
tcf(c_169703,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_799]) ).
tcf(c_169704,plain,
! [X0: $i] :
( function(X0)
| ( sK125(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_785]) ).
tcf(c_169705,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( relation_field(relation_restriction(sK126(X0),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_575]) ).
tcf(c_169706,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_field(relation_restriction(sK126(set_union2(X0,X1)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_615]) ).
tcf(c_169707,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| ( sK125(set_union2(X0,X1)) = sK140 )
| ( relation_field(relation_restriction(sK126(set_union2(X0,X1)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_614]) ).
tcf(c_169708,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(relation_dom(X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(relation_dom(X0)),sK140)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_164735,c_643]) ).
tcf(c_169709,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(X0)) = sK140 )
| ( apply(X0,X1) = sK140 )
| ( relation_field(relation_restriction(sK126(relation_dom(X0)),sK140)) = sK140 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_164735,c_150772]) ).
tcf(c_169710,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK198(X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(sK198(X0)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_694]) ).
tcf(c_169712,plain,
( ( sK125(sK241) = sK140 )
| ( relation_field(relation_restriction(sK126(sK241),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_789]) ).
tcf(c_169713,plain,
( ( sK125(sK242) = sK140 )
| ( relation_field(relation_restriction(sK126(sK242),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_790]) ).
tcf(c_169715,plain,
! [X0: $i] :
( ( sK125(set_union2(X0,unordered_pair(X0,X0))) = sK140 )
| ( relation_field(relation_restriction(sK126(set_union2(X0,unordered_pair(X0,X0))),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_892]) ).
tcf(c_169716,plain,
! [X0: $i,X1: $i] :
( ( sK125(unordered_pair(X0,X1)) = sK140 )
| ( relation_field(relation_restriction(sK126(unordered_pair(X0,X1)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_935]) ).
tcf(c_169717,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK302(X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(sK302(X0)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_973]) ).
tcf(c_169718,plain,
( ( sK125(sK303) = sK140 )
| ( relation_field(relation_restriction(sK126(sK303),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_975]) ).
tcf(c_169719,plain,
( ( sK125(sK313) = sK140 )
| ( relation_field(relation_restriction(sK126(sK313),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_1025]) ).
tcf(c_169720,plain,
( ( sK125(sK346) = sK140 )
| ( relation_field(relation_restriction(sK126(sK346),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_1223]) ).
tcf(c_169721,plain,
( ( sK125(sK358) = sK140 )
| ( relation_field(relation_restriction(sK126(sK358),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_1276]) ).
tcf(c_169722,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(sK115(X0)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_147253]) ).
tcf(c_169723,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(sK115(X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(sK115(X0)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_147177]) ).
tcf(c_169724,plain,
! [X0: $i] :
( relation(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(identity_relation(X0)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_147255]) ).
tcf(c_169725,plain,
! [X0: $i] :
( empty(X0)
| ( sK125(identity_relation(X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(identity_relation(X0)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_147179]) ).
tcf(c_169726,plain,
! [X0: $i] :
( ( sK125(sK116(X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(sK116(X0)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_150228]) ).
tcf(c_169727,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| ( X1 = sK140 )
| ( sK125(subset_complement(X1,X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(subset_complement(X1,X0)),sK140)) = sK140 )
| ~ element(X2,X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_164735,c_150233]) ).
tcf(c_169728,plain,
! [X0: $i] :
( ( X0 = omega )
| ( sK125(sK263(X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(sK263(X0)),sK140)) = sK140 )
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0)
| ~ in(sK140,X0) ),
inference(superposition,[status(thm)],[c_164735,c_150238]) ).
tcf(c_169729,plain,
! [X0: $i] :
( ( sK125(sK300(X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(sK300(X0)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_150241]) ).
tcf(c_169730,plain,
( ( sK125(sK64) = sK140 )
| ( relation_field(relation_restriction(sK126(sK64),sK140)) = sK140 )
| ~ sP7 ),
inference(superposition,[status(thm)],[c_164735,c_150248]) ).
tcf(c_169731,plain,
! [X0: $i,X1: $i] :
( ( sK125(X1) = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(apply(sK126(X1),X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(apply(sK126(X1),X0)),sK140)) = sK140 )
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_164735,c_150503]) ).
tcf(c_169732,plain,
! [X0: $i] :
( ( X0 = sK140 )
| ( sK125(X0) = sK140 )
| ( sK125(sK169(X0)) = sK140 )
| ( relation_field(relation_restriction(sK126(sK169(X0)),sK140)) = sK140 ) ),
inference(superposition,[status(thm)],[c_164735,c_150508]) ).
tcf(c_170102,plain,
! [X0: $i] :
( in(sK262(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ~ iPr_def_15
| ~ in(sK169(unordered_pair(X0,X0)),powerset(sK261)) ),
inference(superposition,[status(thm)],[c_167489,c_165557]) ).
tcf(c_170103,plain,
! [X0: $i] :
( in(sK262(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ~ iPr_def_15
| ~ in(sK142(unordered_pair(X0,X0)),powerset(sK261)) ),
inference(superposition,[status(thm)],[c_167485,c_165557]) ).
tcf(c_170104,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK262(unordered_pair(X0,X0)),sK262(unordered_pair(X0,X0)))))
| ~ iPr_def_15
| ~ in(X0,powerset(sK261))
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_165557,c_165550]) ).
tcf(c_170105,plain,
! [X0: $i] :
( ( set_difference(unordered_pair(sK262(unordered_pair(X0,X0)),sK262(unordered_pair(X0,X0))),unordered_pair(X0,X0)) = sK140 )
| ~ iPr_def_15
| ~ in(X0,powerset(sK261)) ),
inference(superposition,[status(thm)],[c_165557,c_165532]) ).
tcf(c_170106,plain,
! [X0: $i] :
( ordinal(sK262(unordered_pair(X0,X0)))
| ~ iPr_def_15
| ~ in(X0,powerset(sK261))
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_165557,c_333]) ).
tcf(c_170107,plain,
! [X0: $i] :
( ( sK125(unordered_pair(X0,X0)) = sK140 )
| ( set_difference(apply(sK126(unordered_pair(X0,X0)),sK262(unordered_pair(X0,X0))),union(sK262(unordered_pair(X0,X0)))) = sK140 )
| ~ iPr_def_15
| ~ in(X0,powerset(sK261)) ),
inference(superposition,[status(thm)],[c_165557,c_154509]) ).
tcf(c_170108,plain,
! [X0: $i] :
( in(sK128(sK262(unordered_pair(X0,X0))),sK262(unordered_pair(X0,X0)))
| ( sK262(unordered_pair(X0,X0)) = sK140 )
| ~ iPr_def_15
| ~ in(X0,powerset(sK261))
| ~ ordinal(union(unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_165557,c_154063]) ).
tcf(c_170109,plain,
! [X0: $i] :
( ~ iPr_def_15
| ~ in(X0,powerset(sK261))
| ~ in(unordered_pair(X0,X0),sK262(unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_165557,c_527]) ).
tcf(c_170110,plain,
! [X0: $i] :
( ordinal(sK128(sK262(unordered_pair(X0,X0))))
| ( sK262(unordered_pair(X0,X0)) = sK140 )
| ~ iPr_def_15
| ~ in(X0,powerset(sK261))
| ~ ordinal(union(unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_165557,c_154064]) ).
tcf(c_170111,plain,
! [X0: $i] :
( in(sK142(sK262(unordered_pair(X0,X0))),sK262(unordered_pair(X0,X0)))
| ( sK125(unordered_pair(X0,X0)) = sK140 )
| ~ iPr_def_15
| ~ in(X0,powerset(sK261)) ),
inference(superposition,[status(thm)],[c_165557,c_154131]) ).
tcf(c_170112,plain,
! [X0: $i] :
( ( set_difference(sK262(unordered_pair(X0,X0)),union(unordered_pair(X0,X0))) = sK140 )
| ~ iPr_def_15
| ~ in(X0,powerset(sK261)) ),
inference(superposition,[status(thm)],[c_165557,c_154065]) ).
tcf(c_170114,plain,
! [X0: $i] :
( ( sK125(unordered_pair(X0,X0)) = sK140 )
| ~ iPr_def_15
| ~ in(X0,powerset(sK261))
| ~ empty(sK262(unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_165557,c_150230]) ).
tcf(c_170115,plain,
! [X0: $i] :
( ~ iPr_def_15
| ~ in(X0,powerset(sK261))
| ~ empty(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_165557,c_787]) ).
tcf(c_170116,plain,
! [X0: $i] :
( element(sK262(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ~ iPr_def_15
| ~ in(X0,powerset(sK261)) ),
inference(superposition,[status(thm)],[c_165557,c_526]) ).
tcf(c_170117,plain,
! [X0: $i] :
( ( unordered_pair(sK262(unordered_pair(X0,X0)),sK262(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ iPr_def_15
| ~ in(X0,powerset(sK261)) ),
inference(superposition,[status(thm)],[c_165557,c_165554]) ).
tcf(c_170238,plain,
! [X0: $i] :
( in(sK63(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ~ iPr_def_21
| ~ in(sK169(unordered_pair(X0,X0)),powerset(sK62)) ),
inference(superposition,[status(thm)],[c_167489,c_165561]) ).
tcf(c_170239,plain,
! [X0: $i] :
( in(sK63(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ~ iPr_def_21
| ~ in(sK142(unordered_pair(X0,X0)),powerset(sK62)) ),
inference(superposition,[status(thm)],[c_167485,c_165561]) ).
tcf(c_170240,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK63(unordered_pair(X0,X0)),sK63(unordered_pair(X0,X0)))))
| ~ iPr_def_21
| ~ in(X0,powerset(sK62))
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_165561,c_165550]) ).
tcf(c_170241,plain,
! [X0: $i] :
( ( set_difference(unordered_pair(sK63(unordered_pair(X0,X0)),sK63(unordered_pair(X0,X0))),unordered_pair(X0,X0)) = sK140 )
| ~ iPr_def_21
| ~ in(X0,powerset(sK62)) ),
inference(superposition,[status(thm)],[c_165561,c_165532]) ).
tcf(c_170242,plain,
! [X0: $i] :
( ordinal(sK63(unordered_pair(X0,X0)))
| ~ iPr_def_21
| ~ in(X0,powerset(sK62))
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_165561,c_333]) ).
tcf(c_170243,plain,
! [X0: $i] :
( ( sK125(unordered_pair(X0,X0)) = sK140 )
| ( set_difference(apply(sK126(unordered_pair(X0,X0)),sK63(unordered_pair(X0,X0))),union(sK63(unordered_pair(X0,X0)))) = sK140 )
| ~ iPr_def_21
| ~ in(X0,powerset(sK62)) ),
inference(superposition,[status(thm)],[c_165561,c_154509]) ).
tcf(c_170244,plain,
! [X0: $i] :
( in(sK128(sK63(unordered_pair(X0,X0))),sK63(unordered_pair(X0,X0)))
| ( sK63(unordered_pair(X0,X0)) = sK140 )
| ~ iPr_def_21
| ~ in(X0,powerset(sK62))
| ~ ordinal(union(unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_165561,c_154063]) ).
tcf(c_170245,plain,
! [X0: $i] :
( ~ iPr_def_21
| ~ in(X0,powerset(sK62))
| ~ in(unordered_pair(X0,X0),sK63(unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_165561,c_527]) ).
tcf(c_170246,plain,
! [X0: $i] :
( ordinal(sK128(sK63(unordered_pair(X0,X0))))
| ( sK63(unordered_pair(X0,X0)) = sK140 )
| ~ iPr_def_21
| ~ in(X0,powerset(sK62))
| ~ ordinal(union(unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_165561,c_154064]) ).
tcf(c_170247,plain,
! [X0: $i] :
( in(sK142(sK63(unordered_pair(X0,X0))),sK63(unordered_pair(X0,X0)))
| ( sK125(unordered_pair(X0,X0)) = sK140 )
| ~ iPr_def_21
| ~ in(X0,powerset(sK62)) ),
inference(superposition,[status(thm)],[c_165561,c_154131]) ).
tcf(c_170248,plain,
! [X0: $i] :
( ( set_difference(sK63(unordered_pair(X0,X0)),union(unordered_pair(X0,X0))) = sK140 )
| ~ iPr_def_21
| ~ in(X0,powerset(sK62)) ),
inference(superposition,[status(thm)],[c_165561,c_154065]) ).
tcf(c_170250,plain,
! [X0: $i] :
( ( sK125(unordered_pair(X0,X0)) = sK140 )
| ~ iPr_def_21
| ~ in(X0,powerset(sK62))
| ~ empty(sK63(unordered_pair(X0,X0))) ),
inference(superposition,[status(thm)],[c_165561,c_150230]) ).
tcf(c_170251,plain,
! [X0: $i] :
( ~ iPr_def_21
| ~ in(X0,powerset(sK62))
| ~ empty(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_165561,c_787]) ).
tcf(c_170252,plain,
! [X0: $i] :
( element(sK63(unordered_pair(X0,X0)),unordered_pair(X0,X0))
| ~ iPr_def_21
| ~ in(X0,powerset(sK62)) ),
inference(superposition,[status(thm)],[c_165561,c_526]) ).
tcf(c_170253,plain,
! [X0: $i] :
( ( unordered_pair(sK63(unordered_pair(X0,X0)),sK63(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ iPr_def_21
| ~ in(X0,powerset(sK62)) ),
inference(superposition,[status(thm)],[c_165561,c_165554]) ).
tcf(c_170326,plain,
( empty(sK126(sK302(omega)))
| ( sK125(sK302(omega)) = sK140 )
| ~ empty(sK302(omega))
| ~ relation(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_643]) ).
tcf(c_170327,plain,
! [X0: $i] :
( subset(relation_inverse_image(sK126(sK302(omega)),X0),sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ~ relation(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_296]) ).
tcf(c_170328,plain,
! [X0: $i] :
( in(sK142(sK302(omega)),sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ( apply(sK126(sK302(omega)),X0) = sK140 )
| ~ function(sK126(sK302(omega)))
| ~ relation(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_154130]) ).
tcf(c_170329,plain,
! [X0: $i] :
( ( sK125(sK302(omega)) = sK140 )
| ( apply(sK126(sK302(omega)),X0) = sK140 )
| ~ function(sK126(sK302(omega)))
| ~ relation(sK126(sK302(omega)))
| ~ in(sK302(omega),X0) ),
inference(superposition,[status(thm)],[c_147770,c_155600]) ).
tcf(c_170330,plain,
( function(sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ~ empty(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_147195]) ).
tcf(c_170331,plain,
( finite(sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ~ empty(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_147193]) ).
tcf(c_170332,plain,
( epsilon_transitive(sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ~ empty(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_147192]) ).
tcf(c_170333,plain,
( epsilon_connected(sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ~ empty(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_147191]) ).
tcf(c_170334,plain,
( ordinal(sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ~ empty(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_147190]) ).
tcf(c_170335,plain,
( one_to_one(sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ~ empty(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_147189]) ).
tcf(c_170336,plain,
! [X0: $i] :
( ( sK125(sK302(omega)) = sK140 )
| ( apply(sK126(sK302(omega)),X0) = sK140 )
| ~ empty(sK302(omega))
| ~ relation(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_150772]) ).
tcf(c_170337,plain,
! [X0: $i] :
( element(X0,sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ( apply(sK126(sK302(omega)),X0) = sK140 )
| ~ function(sK126(sK302(omega)))
| ~ relation(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_148552]) ).
tcf(c_170338,plain,
( relation(sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ~ empty(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_642]) ).
tcf(c_170339,plain,
( empty(sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ~ empty(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_641]) ).
tcf(c_170340,plain,
! [X0: $i] :
( in(X0,sK302(omega))
| ( sK125(sK302(omega)) = sK140 )
| ( apply(sK126(sK302(omega)),X0) = sK140 )
| ~ function(sK126(sK302(omega)))
| ~ relation(sK126(sK302(omega))) ),
inference(superposition,[status(thm)],[c_147770,c_906]) ).
tcf(c_170341,plain,
( ( sK125(sK302(omega)) = sK140 )
| ( relation_rng(sK126(sK302(omega))) = sK140 )
| ~ relation(sK126(sK302(omega)))
| ( sK302(omega) != sK140 ) ),
inference(superposition,[status(thm)],[c_147770,c_478]) ).
tcf(c_170342,plain,
( ( sK126(sK302(omega)) = sK140 )
| ( sK125(sK302(omega)) = sK140 )
| ~ relation(sK126(sK302(omega)))
| ( sK302(omega) != sK140 ) ),
inference(superposition,[status(thm)],[c_147770,c_475]) ).
tcf(c_170566,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(unordered_pair(sK193(X0,X1),sK193(X0,X1)),set_difference(unordered_pair(sK193(X0,X1),sK193(X0,X1)),X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_656]) ).
tcf(c_170567,plain,
! [X0: $i,X1: $i] :
( subset(X1,relation_dom(X0))
| ( apply(X0,sK193(X1,relation_dom(X0))) = sK140 )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_906,c_656]) ).
tcf(c_170568,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,subset_complement(X1,X2))
| in(sK193(X0,subset_complement(X1,X2)),X2)
| ( X1 = sK140 )
| ~ subset(X2,X1)
| ~ element(sK193(X0,subset_complement(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_5403,c_656]) ).
tcf(c_170569,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_union2(X1,X2))
| ~ in(sK193(X0,set_union2(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_620,c_656]) ).
tcf(c_170570,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_union2(X1,X2))
| ~ in(sK193(X0,set_union2(X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_621,c_656]) ).
tcf(c_170572,plain,
! [X0: $i,X1: $i] :
( subset(X0,powerset(X1))
| ~ subset(sK193(X0,powerset(X1)),X1) ),
inference(superposition,[status(thm)],[c_661,c_656]) ).
tcf(c_170624,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ( set_difference(unordered_pair(X0,X0),set_difference(unordered_pair(X0,X0),set_difference(X1,X2))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_687]) ).
tcf(c_170625,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK49(set_difference(X0,X1),X2),X0)
| ~ sP2(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_98,c_687]) ).
tcf(c_170626,plain,
! [X0: $i,X1: $i] :
( sP3(set_difference(X0,X1))
| in(sK58(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_122,c_687]) ).
tcf(c_170629,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X0,X1))
| function(sK126(set_difference(X0,X1)))
| in(sK125(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_352,c_687]) ).
tcf(c_170630,plain,
! [X0: $i,X1: $i] :
( empty(set_difference(X0,X1))
| relation(sK126(set_difference(X0,X1)))
| in(sK125(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_351,c_687]) ).
tcf(c_170631,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK126(X2),set_difference(X0,X1)),X0)
| ( sK125(X2) = sK140 )
| ~ in(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_2177,c_687]) ).
tcf(c_170632,plain,
! [X0: $i,X1: $i] :
( ordinal(set_difference(X0,X1))
| in(sK127(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_367,c_687]) ).
tcf(c_170633,plain,
! [X0: $i,X1: $i] :
( in(sK128(set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = sK140 )
| ~ ordinal(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_144620,c_687]) ).
tcf(c_170634,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(set_difference(X0,X1),X2)
| in(sK130(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_400,c_687]) ).
tcf(c_170635,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,set_difference(X1,X2))
| in(sK130(X0,set_difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_401,c_687]) ).
tcf(c_170636,plain,
! [X0: $i,X1: $i] :
( being_limit_ordinal(set_difference(X0,X1))
| in(sK131(set_difference(X0,X1)),X0)
| ~ ordinal(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_406,c_687]) ).
tcf(c_170637,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK144(set_difference(X0,X1),X2),X0)
| ~ sP18(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_533,c_687]) ).
tcf(c_170638,plain,
! [X0: $i,X1: $i] :
( relation(set_difference(X0,X1))
| in(sK163(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_561,c_687]) ).
tcf(c_170639,plain,
! [X0: $i,X1: $i] :
( in(sK169(set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_579,c_687]) ).
tcf(c_170640,plain,
! [X0: $i,X1: $i] :
( in(sK173(set_difference(X0,X1)),X0)
| ~ sP20(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_584,c_687]) ).
tcf(c_170642,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(set_difference(X0,X1),X2)
| in(sK193(set_difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_657,c_687]) ).
tcf(c_170643,plain,
! [X0: $i,X1: $i] :
( in(sK140,X0)
| ( set_difference(powerset(sK140),set_difference(powerset(sK140),set_difference(X0,X1))) = sK140 ) ),
inference(superposition,[status(thm)],[c_151909,c_687]) ).
tcf(c_170644,plain,
! [X0: $i,X1: $i] :
( in(sK268(set_difference(X0,X1)),X0)
| ~ sP34(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_864,c_687]) ).
tcf(c_170645,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(set_difference(X0,X1))
| in(sK316(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_1043,c_687]) ).
tcf(c_170646,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK320(X2,set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = sK140 )
| ~ well_founded_relation(X2)
| ~ relation(X2)
| ~ subset(set_difference(X0,X1),relation_field(X2)) ),
inference(superposition,[status(thm)],[c_1062,c_687]) ).
tcf(c_170647,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_difference(X0,X1))
| in(sK343(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_1207,c_687]) ).
tcf(c_170648,plain,
! [X0: $i,X1: $i] :
( epsilon_connected(set_difference(X0,X1))
| in(sK344(set_difference(X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_1208,c_687]) ).
tcf(c_170649,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK137(set_difference(X0,X1)),sK137(set_difference(X0,X1))),unordered_pair(sK137(set_difference(X0,X1)),sK138(set_difference(X0,X1)))),X0)
| ( set_difference(X0,X1) = sK140 )
| ~ relation(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_16344,c_687]) ).
tcf(c_170650,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,set_difference(X1,X2)),X1)
| ( set_difference(X1,X2) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,set_difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_144619,c_687]) ).
tcf(c_170651,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK318(X0,set_difference(X1,X2)),X1)
| ( set_difference(X1,X2) = sK140 )
| ~ relation(X0)
| ~ is_well_founded_in(X0,X1) ),
inference(superposition,[status(thm)],[c_146007,c_687]) ).
tcf(c_170652,plain,
! [X0: $i,X1: $i] :
( in(sK128(set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = sK140 )
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_146008,c_687]) ).
tcf(c_170653,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(sK126(X2),sK92(set_difference(X0,X1))),X0)
| ( sK125(X2) = sK140 )
| ~ in(sK92(set_difference(X0,X1)),X2) ),
inference(superposition,[status(thm)],[c_151774,c_687]) ).
tcf(c_170654,plain,
! [X0: $i,X1: $i] :
( in(sK169(sK92(set_difference(X0,X1))),X0)
| ( sK92(set_difference(X0,X1)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151778,c_687]) ).
tcf(c_170655,plain,
! [X0: $i,X1: $i] :
( in(sK142(set_difference(X0,X1)),X0)
| ( set_difference(X0,X1) = sK140 ) ),
inference(superposition,[status(thm)],[c_154138,c_687]) ).
fof(f1099,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(f1100,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(f1101,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(f1102,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| sP2(X0,X1)
| ? [X9] :
( sP1(X0,X1,X9)
& function(X9)
& relation(X9) ) ),
inference(definition_folding,[],[f622,f1101,f1100,f1099]) ).
fof(f1103,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(f1104,plain,
! [X0] :
( ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 )
| sP3(X0) ),
inference(definition_folding,[],[f624,f1103]) ).
fof(f1105,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(f1106,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(f1107,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(f1108,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(f1109,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(f1110,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,[],[f628,f1109,f1108,f1107,f1106,f1105]) ).
fof(f1111,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(f1112,definition,
! [X0] :
( ~ sP10(X0)
| ? [X1] :
! [X2] :
( in(X2,X1)
<=> sP9(X0,X2) ) ),
introduced(definition,[new_symbols(definition,[sP10])],[predicate_definition_introduction]) ).
fof(f1113,plain,
! [X0] :
( ~ ordinal(X0)
| sP10(X0) ),
inference(definition_folding,[],[f634,f1112,f1111]) ).
fof(f1114,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(f1115,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(f1116,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,[],[f643,f1115,f1114]) ).
fof(f1117,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(f1118,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,[],[f645,f1117]) ).
fof(f1119,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(f1120,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(f1121,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,[],[f647,f1120,f1119]) ).
fof(f1122,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(f1123,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,[],[f801,f1122]) ).
fof(f1124,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(f1125,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(f1126,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,[],[f855,f1125,f1124]) ).
fof(f1127,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(f1128,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(f1129,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,[],[f867,f1128,f1127]) ).
fof(f1130,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(f1131,plain,
! [X0] :
( sP21(X0)
| ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( singleton(X6) = X5
& in(X6,X0)
& in(X6,X0) ) ) ),
inference(definition_folding,[],[f869,f1130]) ).
fof(f1132,definition,
! [X0,X1,X2] :
( sP22(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,[sP22])],[predicate_definition_introduction]) ).
fof(f1133,definition,
! [X2,X1,X0] :
( ~ sP23(X2,X1,X0)
| ( X2 = topstr_closure(X0,X1)
<=> sP22(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sP23])],[predicate_definition_introduction]) ).
fof(f1134,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X0)))
| sP23(X2,X1,X0) ) ) ),
inference(definition_folding,[],[f878,f1133,f1132]) ).
fof(f1135,definition,
! [X1,X2] :
( ~ sP24(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,[sP24])],[predicate_definition_introduction]) ).
fof(f1136,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| sP24(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,[],[f909,f1135]) ).
fof(f1137,definition,
! [X5,X0,X1] :
( ~ sP25(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,[sP25])],[predicate_definition_introduction]) ).
fof(f1138,definition,
! [X4,X0,X1] :
( ~ sP26(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,[sP26])],[predicate_definition_introduction]) ).
fof(f1139,definition,
! [X2,X0,X15,X1] :
( sP27(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,[sP27])],[predicate_definition_introduction]) ).
fof(f1140,definition,
! [X1,X0,X2] :
( ~ sP28(X1,X0,X2)
| ? [X14] :
! [X15] :
( in(X15,X14)
<=> sP27(X2,X0,X15,X1) ) ),
introduced(definition,[new_symbols(definition,[sP28])],[predicate_definition_introduction]) ).
fof(f1141,plain,
! [X0,X1] :
( ~ relation(X1)
| empty(X0)
| ! [X2] :
( ? [X3,X4,X5] :
( sP25(X5,X0,X1)
& X3 = X5
& sP26(X4,X0,X1)
& X3 = X4
& X4 != X5 )
| sP28(X1,X0,X2) ) ),
inference(definition_folding,[],[f911,f1140,f1139,f1138,f1137]) ).
fof(f1142,definition,
( ~ sP29
| ? [X1,X2,X3] :
( ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2
& X2 != X3 ) ),
introduced(definition,[new_symbols(definition,[sP29])],[predicate_definition_introduction]) ).
fof(f1143,plain,
! [X0] :
( sP29
| ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( ordinal(X5)
& X5 = X6
& in(X6,X0) ) ) ),
inference(definition_folding,[],[f929,f1142]) ).
fof(f1144,definition,
! [X3] :
( ~ sP30(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,[sP30])],[predicate_definition_introduction]) ).
fof(f1145,definition,
! [X0,X13] :
( sP31(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,[sP31])],[predicate_definition_introduction]) ).
fof(f1146,definition,
! [X0] :
( ~ sP32(X0)
| ? [X12] :
! [X13] :
( in(X13,X12)
<=> sP31(X0,X13) ) ),
introduced(definition,[new_symbols(definition,[sP32])],[predicate_definition_introduction]) ).
fof(f1147,plain,
! [X0] :
( ~ ordinal(X0)
| ? [X1,X2,X3] :
( sP30(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 )
| sP32(X0) ),
inference(definition_folding,[],[f937,f1146,f1145,f1144]) ).
fof(f1148,definition,
! [X4,X0] :
( ~ sP33(X4,X0)
| ? [X6] :
( in(X6,X0)
& X4 = X6
& ordinal(X6) ) ),
introduced(definition,[new_symbols(definition,[sP33])],[predicate_definition_introduction]) ).
fof(f1149,definition,
! [X0] :
( ~ sP34(X0)
| ? [X2,X3,X4] :
( sP33(X4,X0)
& X2 = X4
& ? [X5] :
( in(X5,X0)
& X3 = X5
& ordinal(X5) )
& X2 = X3
& X3 != X4 ) ),
introduced(definition,[new_symbols(definition,[sP34])],[predicate_definition_introduction]) ).
fof(f1150,plain,
! [X0,X1] :
( ~ ordinal(X1)
| sP34(X0)
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( in(X10,X0)
& X8 = X10
& ordinal(X10) )
& X8 = X9
& in(X9,succ(X1)) ) ) ),
inference(definition_folding,[],[f942,f1149,f1148]) ).
fof(f1151,definition,
! [X1,X0] :
( ~ sP35(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,[sP35])],[predicate_definition_introduction]) ).
fof(f1152,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(succ(X0))))
| ~ ordinal(X0)
| sP35(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,[],[f944,f1151]) ).
fof(f1153,definition,
! [X1,X2] :
( ~ sP36(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,[sP36])],[predicate_definition_introduction]) ).
fof(f1154,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| sP36(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,[],[f955,f1153]) ).
fof(f1155,definition,
! [X2,X0,X1] :
( sP37(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,[sP37])],[predicate_definition_introduction]) ).
fof(f1156,definition,
! [X1,X0,X2] :
( ~ sP38(X1,X0,X2)
| ( relation_isomorphism(X0,X1,X2)
<=> sP37(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP38])],[predicate_definition_introduction]) ).
fof(f1157,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| sP38(X1,X0,X2) ) ) ),
inference(definition_folding,[],[f1052,f1156,f1155]) ).
fof(f1187,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,[],[f1099]) ).
fof(f1188,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,[],[f1187]) ).
fof(f1189,plain,
! [X0,X1,X2] :
( ~ sP0(X0,X1,X2)
| ( ! [X4] :
( ~ in(X4,sK55(X0,X1,X2))
| in(ordered_pair(X1,X4),X2) )
& in(X1,sK55(X0,X1,X2))
& sK55(X0,X1,X2) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(X3,sK55(X0,X1,X2))],[f1188]) ).
fof(f1192,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,[],[f1103]) ).
fof(f1193,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,[],[f1192]) ).
fof(f1194,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,[],[f1193]) ).
fof(f1195,plain,
! [X0] :
( ~ sP3(X0)
| ( ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),sK57(X0))
| ( singleton(X2) = X3
& in(X2,X0)
& in(X2,X0) ) )
& ( singleton(X2) != X3
| ~ in(X2,X0)
| ~ in(X2,X0)
| in(ordered_pair(X2,X3),sK57(X0)) ) )
& function(sK57(X0))
& relation(sK57(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(X1,sK57(X0))],[f1194]) ).
fof(f1210,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,[],[f1105]) ).
fof(f1211,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,[],[f1210]) ).
fof(f1212,plain,
! [X0] :
( ~ sP4(X0)
| ( element(sK70(X0),powerset(powerset(X0)))
& ! [X2] :
( ( subset(X2,sK71(X0,X2))
& in(sK71(X0,X2),sK70(X0))
& sK71(X0,X2) != X2 )
| ~ in(X2,sK70(X0)) )
& empty_set != sK70(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70,sK71]),skolemize(X1,sK70(X0)),skolemize(X3,sK71(X0,X2))],[f1211]) ).
fof(f1228,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,[],[f1111]) ).
fof(f1229,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,[],[f1228]) ).
fof(f1230,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,[],[f1229]) ).
fof(f1231,plain,
! [X0,X1] :
( ( ~ sP9(X0,X1)
| ( ( ~ in(sK85(X1),omega)
| ! [X7] :
( ~ element(X7,powerset(powerset(sK85(X1))))
| ( ! [X9] :
( ~ subset(sK86(X7),X9)
| ~ in(X9,X7)
| sK86(X7) = X9 )
& in(sK86(X7),X7) )
| empty_set = X7 ) )
& sK85(X1) = X1
& ordinal(sK85(X1))
& in(X1,succ(X0)) ) )
& ( ! [X2] :
( ( in(X2,omega)
& element(sK83(X2),powerset(powerset(X2)))
& ! [X4] :
( ( subset(X4,sK84(X2,X4))
& in(sK84(X2,X4),sK83(X2))
& sK84(X2,X4) != X4 )
| ~ in(X4,sK83(X2)) )
& empty_set != sK83(X2) )
| X1 != X2
| ~ ordinal(X2) )
| ~ in(X1,succ(X0))
| sP9(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83,sK84,sK85,sK86]),skolemize(X3,sK83(X2)),skolemize(X5,sK84(X2,X4)),skolemize(X6,sK85(X1)),skolemize(X8,sK86(X7))],[f1230]) ).
fof(f1253,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,[],[f1114]) ).
fof(f1254,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| ( ! [X8] :
( ~ in(X8,sK102(X0,X1))
| in(ordered_pair(sK100(X0,X1),X8),X1) )
& in(sK100(X0,X1),sK102(X0,X1))
& sK98(X0,X1) = sK102(X0,X1)
& ! [X6] :
( ~ in(X6,sK101(X0,X1))
| in(ordered_pair(sK99(X0,X1),X6),X1) )
& in(sK99(X0,X1),sK101(X0,X1))
& sK98(X0,X1) = sK101(X0,X1)
& in(sK98(X0,X1),X0)
& sK99(X0,X1) != sK100(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98,sK99,sK100,sK101,sK102]),skolemize(X2,sK98(X0,X1)),skolemize(X3,sK99(X0,X1)),skolemize(X4,sK100(X0,X1)),skolemize(X5,sK101(X0,X1)),skolemize(X7,sK102(X0,X1))],[f1253]) ).
fof(f1257,plain,
! [X0] :
( ~ sP13(X0)
| ? [X1,X2,X3] :
( X3 = singleton(X1)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 ) ),
inference(nnf_transformation,[],[f1117]) ).
fof(f1258,plain,
! [X0] :
( ~ sP13(X0)
| ( sK107(X0) = singleton(sK105(X0))
& sK106(X0) = singleton(sK105(X0))
& in(sK105(X0),X0)
& sK106(X0) != sK107(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105,sK106,sK107]),skolemize(X1,sK105(X0)),skolemize(X2,sK106(X0)),skolemize(X3,sK107(X0))],[f1257]) ).
fof(f1263,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,[],[f1119]) ).
fof(f1264,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,[],[f1263]) ).
fof(f1265,plain,
! [X0] :
( ~ sP14(X0)
| ( element(sK112(X0),powerset(powerset(X0)))
& ! [X2] :
( ( subset(X2,sK113(X0,X2))
& in(sK113(X0,X2),sK112(X0))
& sK113(X0,X2) != X2 )
| ~ in(X2,sK112(X0)) )
& empty_set != sK112(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112,sK113]),skolemize(X1,sK112(X0)),skolemize(X3,sK113(X0,X2))],[f1264]) ).
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(nnf_transformation,[],[f1122]) ).
fof(f1321,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,[],[f1320]) ).
fof(f1322,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,[],[f1321]) ).
fof(f1349,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,[],[f1124]) ).
fof(f1350,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,[],[f1349]) ).
fof(f1351,plain,
! [X0,X1,X2] :
( ~ sP17(X0,X1,X2)
| ( ! [X4] :
( ~ in(X4,sK148(X0,X1,X2))
| in(ordered_pair(X1,X4),X2) )
& in(X1,sK148(X0,X1,X2))
& sK148(X0,X1,X2) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(X3,sK148(X0,X1,X2))],[f1350]) ).
fof(f1381,plain,
! [X4,X0] :
( ~ sP19(X4,X0)
| ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 ) ),
inference(nnf_transformation,[],[f1127]) ).
fof(f1382,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| ? [X2,X3] :
( singleton(X2) = X3
& in(X2,X1)
& ordered_pair(X2,X3) = X0 ) ),
inference(rectify,[],[f1381]) ).
fof(f1383,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| ( sK176(X0,X1) = singleton(sK175(X0,X1))
& in(sK175(X0,X1),X1)
& ordered_pair(sK175(X0,X1),sK176(X0,X1)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175,sK176]),skolemize(X2,sK175(X0,X1)),skolemize(X3,sK176(X0,X1))],[f1382]) ).
fof(f1387,plain,
! [X0] :
( ~ sP21(X0)
| ? [X1,X2,X3] :
( X3 = singleton(X1)
& in(X1,X0)
& X2 = singleton(X1)
& in(X1,X0)
& X2 != X3 ) ),
inference(nnf_transformation,[],[f1130]) ).
fof(f1388,plain,
! [X0] :
( ~ sP21(X0)
| ( sK183(X0) = singleton(sK181(X0))
& in(sK181(X0),X0)
& sK182(X0) = singleton(sK181(X0))
& in(sK181(X0),X0)
& sK182(X0) != sK183(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK181,sK182,sK183]),skolemize(X1,sK181(X0)),skolemize(X2,sK182(X0)),skolemize(X3,sK183(X0))],[f1387]) ).
fof(f1402,plain,
! [X0,X1,X2] :
( ( ~ sP22(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) ) ) )
| sP22(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f1132]) ).
fof(f1403,plain,
! [X0,X1,X2] :
( ( ~ sP22(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) ) ) )
| sP22(X0,X1,X2) ) ),
inference(flattening,[],[f1402]) ).
fof(f1404,plain,
! [X0,X1,X2] :
( ( ~ sP22(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) ) ) )
| sP22(X0,X1,X2) ) ),
inference(rectify,[],[f1403]) ).
fof(f1405,plain,
! [X0,X1,X2] :
( ( ~ sP22(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(sK190(X0,X1,X6),powerset(the_carrier(X0)))
& disjoint(X1,sK190(X0,X1,X6))
& in(X6,sK190(X0,X1,X6))
& open_subset(sK190(X0,X1,X6),X0) )
| in(X6,X2) ) ) ) )
& ( ( in(sK188(X0,X1,X2),the_carrier(X0))
& ( in(sK188(X0,X1,X2),X2)
| ! [X5] :
( ~ element(X5,powerset(the_carrier(X0)))
| ~ disjoint(X1,X5)
| ~ in(sK188(X0,X1,X2),X5)
| ~ open_subset(X5,X0) ) )
& ( ~ in(sK188(X0,X1,X2),X2)
| ( element(sK189(X0,X1,X2),powerset(the_carrier(X0)))
& disjoint(X1,sK189(X0,X1,X2))
& in(sK188(X0,X1,X2),sK189(X0,X1,X2))
& open_subset(sK189(X0,X1,X2),X0) ) ) )
| sP22(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK188,sK189,sK190]),skolemize(X3,sK188(X0,X1,X2)),skolemize(X4,sK189(X0,X1,X2)),skolemize(X7,sK190(X0,X1,X6))],[f1404]) ).
fof(f1437,plain,
! [X1,X2] :
( ~ sP24(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,[],[f1135]) ).
fof(f1438,plain,
! [X0,X1] :
( ~ sP24(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,[],[f1437]) ).
fof(f1439,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| ( in(ordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK212(X0,X1))),X0)
& sK208(X0,X1) = ordered_pair(sK211(X0,X1),sK212(X0,X1))
& sK206(X0,X1) = sK208(X0,X1)
& in(ordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK210(X0,X1))),X0)
& sK207(X0,X1) = ordered_pair(sK209(X0,X1),sK210(X0,X1))
& sK206(X0,X1) = sK207(X0,X1)
& sK207(X0,X1) != sK208(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK206,sK207,sK208,sK209,sK210,sK211,sK212]),skolemize(X2,sK206(X0,X1)),skolemize(X3,sK207(X0,X1)),skolemize(X4,sK208(X0,X1)),skolemize(X5,sK209(X0,X1)),skolemize(X6,sK210(X0,X1)),skolemize(X7,sK211(X0,X1)),skolemize(X8,sK212(X0,X1))],[f1438]) ).
fof(f1452,plain,
! [X5,X0,X1] :
( ~ sP25(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,[],[f1137]) ).
fof(f1453,plain,
! [X0,X1,X2] :
( ~ sP25(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,[],[f1452]) ).
fof(f1454,plain,
! [X0,X1,X2] :
( ~ sP25(X0,X1,X2)
| ( ! [X6] :
( ~ in(X6,sK228(X0,X1,X2))
| in(ordered_pair(sK227(X0,X1,X2),X6),X2) )
& in(sK227(X0,X1,X2),sK228(X0,X1,X2))
& sK226(X0,X1,X2) = sK228(X0,X1,X2)
& in(sK226(X0,X1,X2),X1)
& ordered_pair(sK226(X0,X1,X2),sK227(X0,X1,X2)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK226,sK227,sK228]),skolemize(X3,sK226(X0,X1,X2)),skolemize(X4,sK227(X0,X1,X2)),skolemize(X5,sK228(X0,X1,X2))],[f1453]) ).
fof(f1470,plain,
( ~ sP29
| ? [X1,X2,X3] :
( ordinal(X3)
& X1 = X3
& ordinal(X2)
& X1 = X2
& X2 != X3 ) ),
inference(nnf_transformation,[],[f1142]) ).
fof(f1471,plain,
( ~ sP29
| ? [X0,X1,X2] :
( ordinal(X2)
& X0 = X2
& ordinal(X1)
& X0 = X1
& X1 != X2 ) ),
inference(rectify,[],[f1470]) ).
fof(f1472,plain,
( ~ sP29
| ( ordinal(sK247)
& sK245 = sK247
& ordinal(sK246)
& sK245 = sK246
& sK246 != sK247 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK245,sK246,sK247]),skolemize(X0,sK245),skolemize(X1,sK246),skolemize(X2,sK247)],[f1471]) ).
fof(f1483,plain,
! [X3] :
( ~ sP30(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,[],[f1144]) ).
fof(f1484,plain,
! [X0] :
( ~ sP30(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,[],[f1483]) ).
fof(f1485,plain,
! [X0] :
( ~ sP30(X0)
| ( ( ~ in(sK256(X0),omega)
| ! [X2] :
( ~ element(X2,powerset(powerset(sK256(X0))))
| ( ! [X4] :
( ~ subset(sK257(X2),X4)
| ~ in(X4,X2)
| sK257(X2) = X4 )
& in(sK257(X2),X2) )
| empty_set = X2 ) )
& sK256(X0) = X0
& ordinal(sK256(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK256,sK257]),skolemize(X1,sK256(X0)),skolemize(X3,sK257(X2))],[f1484]) ).
fof(f1497,plain,
! [X4,X0] :
( ~ sP33(X4,X0)
| ? [X6] :
( in(X6,X0)
& X4 = X6
& ordinal(X6) ) ),
inference(nnf_transformation,[],[f1148]) ).
fof(f1498,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| ? [X2] :
( in(X2,X1)
& X0 = X2
& ordinal(X2) ) ),
inference(rectify,[],[f1497]) ).
fof(f1499,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| ( in(sK269(X0,X1),X1)
& sK269(X0,X1) = X0
& ordinal(sK269(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(X2,sK269(X0,X1))],[f1498]) ).
fof(f1503,plain,
! [X1,X0] :
( ~ sP35(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,[],[f1151]) ).
fof(f1504,plain,
! [X0,X1] :
( ~ sP35(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,[],[f1503]) ).
fof(f1505,plain,
! [X0,X1] :
( ~ sP35(X0,X1)
| ( sK275(X0,X1) = set_difference(sK277(X0,X1),singleton(X1))
& in(sK277(X0,X1),X0)
& sK273(X0,X1) = sK275(X0,X1)
& sK274(X0,X1) = set_difference(sK276(X0,X1),singleton(X1))
& in(sK276(X0,X1),X0)
& sK273(X0,X1) = sK274(X0,X1)
& sK274(X0,X1) != sK275(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK273,sK274,sK275,sK276,sK277]),skolemize(X2,sK273(X0,X1)),skolemize(X3,sK274(X0,X1)),skolemize(X4,sK275(X0,X1)),skolemize(X5,sK276(X0,X1)),skolemize(X6,sK277(X0,X1))],[f1504]) ).
fof(f1515,plain,
! [X1,X2] :
( ~ sP36(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,[],[f1153]) ).
fof(f1516,plain,
! [X0,X1] :
( ~ sP36(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,[],[f1515]) ).
fof(f1517,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| ( in(relation_image(X1,sK288(X0,X1)),X0)
& sK286(X0,X1) = sK288(X0,X1)
& in(relation_image(X1,sK287(X0,X1)),X0)
& sK286(X0,X1) = sK287(X0,X1)
& sK287(X0,X1) != sK288(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK286,sK287,sK288]),skolemize(X2,sK286(X0,X1)),skolemize(X3,sK287(X0,X1)),skolemize(X4,sK288(X0,X1))],[f1516]) ).
fof(f1595,plain,
! [X2,X0,X1] :
( ( ~ sP37(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)
| sP37(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1155]) ).
fof(f1596,plain,
! [X2,X0,X1] :
( ( ~ sP37(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)
| sP37(X2,X0,X1) ) ),
inference(flattening,[],[f1595]) ).
fof(f1597,plain,
! [X0,X1,X2] :
( ( ~ sP37(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)
| sP37(X0,X1,X2) ) ),
inference(rectify,[],[f1596]) ).
fof(f1598,plain,
! [X0,X1,X2] :
( ( ~ sP37(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(sK333(X0,X1,X2),sK334(X0,X1,X2)),X1)
| ( in(ordered_pair(apply(X0,sK333(X0,X1,X2)),apply(X0,sK334(X0,X1,X2))),X2)
& in(sK334(X0,X1,X2),relation_field(X1))
& in(sK333(X0,X1,X2),relation_field(X1)) ) )
& ( ~ in(ordered_pair(sK333(X0,X1,X2),sK334(X0,X1,X2)),X1)
| ~ in(ordered_pair(apply(X0,sK333(X0,X1,X2)),apply(X0,sK334(X0,X1,X2))),X2)
| ~ in(sK334(X0,X1,X2),relation_field(X1))
| ~ in(sK333(X0,X1,X2),relation_field(X1)) ) )
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP37(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK333,sK334]),skolemize(X3,sK333(X0,X1,X2)),skolemize(X4,sK334(X0,X1,X2))],[f1597]) ).
fof(f1697,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,sK55(X0,X1,X2))
| in(ordered_pair(X1,X4),X2) ),
inference(cnf_transformation,[],[f1189]) ).
fof(f1698,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| in(X1,sK55(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1189]) ).
fof(f1699,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| sK55(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f1189]) ).
fof(f1703,plain,
! [X2,X3,X0] :
( ~ sP3(X0)
| ~ in(ordered_pair(X2,X3),sK57(X0))
| singleton(X2) = X3 ),
inference(cnf_transformation,[],[f1195]) ).
fof(f1704,plain,
! [X2,X3,X0] :
( ~ sP3(X0)
| ~ in(ordered_pair(X2,X3),sK57(X0))
| in(X2,X0) ),
inference(cnf_transformation,[],[f1195]) ).
fof(f1707,plain,
! [X0] :
( ~ sP3(X0)
| function(sK57(X0)) ),
inference(cnf_transformation,[],[f1195]) ).
fof(f1708,plain,
! [X0] :
( ~ sP3(X0)
| relation(sK57(X0)) ),
inference(cnf_transformation,[],[f1195]) ).
fof(f1740,plain,
! [X0] :
( ~ sP4(X0)
| element(sK70(X0),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1212]) ).
fof(f1741,plain,
! [X2,X0] :
( ~ sP4(X0)
| subset(X2,sK71(X0,X2))
| ~ in(X2,sK70(X0)) ),
inference(cnf_transformation,[],[f1212]) ).
fof(f1742,plain,
! [X2,X0] :
( ~ sP4(X0)
| in(sK71(X0,X2),sK70(X0))
| ~ in(X2,sK70(X0)) ),
inference(cnf_transformation,[],[f1212]) ).
fof(f1743,plain,
! [X2,X0] :
( ~ sP4(X0)
| sK71(X0,X2) != X2
| ~ in(X2,sK70(X0)) ),
inference(cnf_transformation,[],[f1212]) ).
fof(f1744,plain,
! [X0] :
( ~ sP4(X0)
| empty_set != sK70(X0) ),
inference(cnf_transformation,[],[f1212]) ).
fof(f1767,plain,
! [X0,X1,X9,X7] :
( ~ sP9(X0,X1)
| ~ in(sK85(X1),omega)
| ~ element(X7,powerset(powerset(sK85(X1))))
| ~ subset(sK86(X7),X9)
| ~ in(X9,X7)
| sK86(X7) = X9
| empty_set = X7 ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1768,plain,
! [X0,X1,X7] :
( ~ sP9(X0,X1)
| ~ in(sK85(X1),omega)
| ~ element(X7,powerset(powerset(sK85(X1))))
| in(sK86(X7),X7)
| empty_set = X7 ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1769,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| sK85(X1) = X1 ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1770,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| ordinal(sK85(X1)) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1771,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| in(X1,succ(X0)) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1772,plain,
! [X2,X0,X1] :
( in(X2,omega)
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1773,plain,
! [X2,X0,X1] :
( element(sK83(X2),powerset(powerset(X2)))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1774,plain,
! [X2,X0,X1,X4] :
( subset(X4,sK84(X2,X4))
| ~ in(X4,sK83(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1775,plain,
! [X2,X0,X1,X4] :
( in(sK84(X2,X4),sK83(X2))
| ~ in(X4,sK83(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1776,plain,
! [X2,X0,X1,X4] :
( sK84(X2,X4) != X4
| ~ in(X4,sK83(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1777,plain,
! [X2,X0,X1] :
( empty_set != sK83(X2)
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,succ(X0))
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1804,plain,
! [X0,X1,X8] :
( ~ sP11(X0,X1)
| ~ in(X8,sK102(X0,X1))
| in(ordered_pair(sK100(X0,X1),X8),X1) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1805,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| in(sK100(X0,X1),sK102(X0,X1)) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1806,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| sK98(X0,X1) = sK102(X0,X1) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1807,plain,
! [X0,X1,X6] :
( ~ sP11(X0,X1)
| ~ in(X6,sK101(X0,X1))
| in(ordered_pair(sK99(X0,X1),X6),X1) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1808,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| in(sK99(X0,X1),sK101(X0,X1)) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1809,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| sK98(X0,X1) = sK101(X0,X1) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1810,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| in(sK98(X0,X1),X0) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1811,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| sK99(X0,X1) != sK100(X0,X1) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f1815,plain,
! [X0] :
( ~ sP13(X0)
| sK107(X0) = singleton(sK105(X0)) ),
inference(cnf_transformation,[],[f1258]) ).
fof(f1816,plain,
! [X0] :
( ~ sP13(X0)
| sK106(X0) = singleton(sK105(X0)) ),
inference(cnf_transformation,[],[f1258]) ).
fof(f1817,plain,
! [X0] :
( ~ sP13(X0)
| in(sK105(X0),X0) ),
inference(cnf_transformation,[],[f1258]) ).
fof(f1818,plain,
! [X0] :
( ~ sP13(X0)
| sK106(X0) != sK107(X0) ),
inference(cnf_transformation,[],[f1258]) ).
fof(f1832,plain,
! [X0] :
( ~ sP14(X0)
| element(sK112(X0),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f1265]) ).
fof(f1833,plain,
! [X2,X0] :
( ~ sP14(X0)
| subset(X2,sK113(X0,X2))
| ~ in(X2,sK112(X0)) ),
inference(cnf_transformation,[],[f1265]) ).
fof(f1834,plain,
! [X2,X0] :
( ~ sP14(X0)
| in(sK113(X0,X2),sK112(X0))
| ~ in(X2,sK112(X0)) ),
inference(cnf_transformation,[],[f1265]) ).
fof(f1835,plain,
! [X2,X0] :
( ~ sP14(X0)
| sK113(X0,X2) != X2
| ~ in(X2,sK112(X0)) ),
inference(cnf_transformation,[],[f1265]) ).
fof(f1836,plain,
! [X0] :
( ~ sP14(X0)
| empty_set != sK112(X0) ),
inference(cnf_transformation,[],[f1265]) ).
fof(f2035,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,[],[f1322]) ).
fof(f2036,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,[],[f1322]) ).
fof(f2037,plain,
! [X2,X3,X0,X1] :
( apply(X0,X2) = X1
| sP16(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1322]) ).
fof(f2038,plain,
! [X2,X3,X0,X1] :
( in(X2,relation_dom(X0))
| sP16(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1322]) ).
fof(f2039,plain,
! [X2,X3,X0,X1] :
( apply(X3,X1) != X2
| ~ in(X1,relation_rng(X0))
| sP16(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1322]) ).
fof(f2130,plain,
! [X2,X0,X1,X4] :
( ~ sP17(X0,X1,X2)
| ~ in(X4,sK148(X0,X1,X2))
| in(ordered_pair(X1,X4),X2) ),
inference(cnf_transformation,[],[f1351]) ).
fof(f2131,plain,
! [X2,X0,X1] :
( ~ sP17(X0,X1,X2)
| in(X1,sK148(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1351]) ).
fof(f2132,plain,
! [X2,X0,X1] :
( ~ sP17(X0,X1,X2)
| sK148(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f1351]) ).
fof(f2183,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| sK176(X0,X1) = singleton(sK175(X0,X1)) ),
inference(cnf_transformation,[],[f1383]) ).
fof(f2184,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| in(sK175(X0,X1),X1) ),
inference(cnf_transformation,[],[f1383]) ).
fof(f2185,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| ordered_pair(sK175(X0,X1),sK176(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f1383]) ).
fof(f2192,plain,
! [X0] :
( ~ sP21(X0)
| sK183(X0) = singleton(sK181(X0)) ),
inference(cnf_transformation,[],[f1388]) ).
fof(f2193,plain,
! [X0] :
( ~ sP21(X0)
| in(sK181(X0),X0) ),
inference(cnf_transformation,[],[f1388]) ).
fof(f2194,plain,
! [X0] :
( ~ sP21(X0)
| sK182(X0) = singleton(sK181(X0)) ),
inference(cnf_transformation,[],[f1388]) ).
fof(f2196,plain,
! [X0] :
( ~ sP21(X0)
| sK182(X0) != sK183(X0) ),
inference(cnf_transformation,[],[f1388]) ).
fof(f2225,plain,
! [X2,X0,X1,X8,X6] :
( ~ sP22(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,[],[f1405]) ).
fof(f2226,plain,
! [X2,X0,X1,X6] :
( ~ sP22(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| element(sK190(X0,X1,X6),powerset(the_carrier(X0)))
| in(X6,X2) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2227,plain,
! [X2,X0,X1,X6] :
( ~ sP22(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| disjoint(X1,sK190(X0,X1,X6))
| in(X6,X2) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2228,plain,
! [X2,X0,X1,X6] :
( ~ sP22(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| in(X6,sK190(X0,X1,X6))
| in(X6,X2) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2229,plain,
! [X2,X0,X1,X6] :
( ~ sP22(X0,X1,X2)
| ~ in(X6,the_carrier(X0))
| open_subset(sK190(X0,X1,X6),X0)
| in(X6,X2) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2230,plain,
! [X2,X0,X1] :
( in(sK188(X0,X1,X2),the_carrier(X0))
| sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2231,plain,
! [X2,X0,X1,X5] :
( in(sK188(X0,X1,X2),X2)
| ~ element(X5,powerset(the_carrier(X0)))
| ~ disjoint(X1,X5)
| ~ in(sK188(X0,X1,X2),X5)
| ~ open_subset(X5,X0)
| sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2232,plain,
! [X2,X0,X1] :
( ~ in(sK188(X0,X1,X2),X2)
| element(sK189(X0,X1,X2),powerset(the_carrier(X0)))
| sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2233,plain,
! [X2,X0,X1] :
( ~ in(sK188(X0,X1,X2),X2)
| disjoint(X1,sK189(X0,X1,X2))
| sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2234,plain,
! [X2,X0,X1] :
( ~ in(sK188(X0,X1,X2),X2)
| in(sK188(X0,X1,X2),sK189(X0,X1,X2))
| sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2235,plain,
! [X2,X0,X1] :
( ~ in(sK188(X0,X1,X2),X2)
| open_subset(sK189(X0,X1,X2),X0)
| sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1405]) ).
fof(f2317,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| in(ordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK212(X0,X1))),X0) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2318,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| sK208(X0,X1) = ordered_pair(sK211(X0,X1),sK212(X0,X1)) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2319,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| sK206(X0,X1) = sK208(X0,X1) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2320,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| in(ordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK210(X0,X1))),X0) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2321,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| sK207(X0,X1) = ordered_pair(sK209(X0,X1),sK210(X0,X1)) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2322,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| sK206(X0,X1) = sK207(X0,X1) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2323,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| sK207(X0,X1) != sK208(X0,X1) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2345,plain,
! [X2,X0,X1,X6] :
( ~ sP25(X0,X1,X2)
| ~ in(X6,sK228(X0,X1,X2))
| in(ordered_pair(sK227(X0,X1,X2),X6),X2) ),
inference(cnf_transformation,[],[f1454]) ).
fof(f2346,plain,
! [X2,X0,X1] :
( ~ sP25(X0,X1,X2)
| in(sK227(X0,X1,X2),sK228(X0,X1,X2)) ),
inference(cnf_transformation,[],[f1454]) ).
fof(f2347,plain,
! [X2,X0,X1] :
( ~ sP25(X0,X1,X2)
| sK226(X0,X1,X2) = sK228(X0,X1,X2) ),
inference(cnf_transformation,[],[f1454]) ).
fof(f2348,plain,
! [X2,X0,X1] :
( ~ sP25(X0,X1,X2)
| in(sK226(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f1454]) ).
fof(f2349,plain,
! [X2,X0,X1] :
( ~ sP25(X0,X1,X2)
| ordered_pair(sK226(X0,X1,X2),sK227(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f1454]) ).
fof(f2396,plain,
( ~ sP29
| ordinal(sK247) ),
inference(cnf_transformation,[],[f1472]) ).
fof(f2397,plain,
( ~ sP29
| sK245 = sK247 ),
inference(cnf_transformation,[],[f1472]) ).
fof(f2398,plain,
( ~ sP29
| ordinal(sK246) ),
inference(cnf_transformation,[],[f1472]) ).
fof(f2399,plain,
( ~ sP29
| sK245 = sK246 ),
inference(cnf_transformation,[],[f1472]) ).
fof(f2400,plain,
( ~ sP29
| sK246 != sK247 ),
inference(cnf_transformation,[],[f1472]) ).
fof(f2423,plain,
! [X2,X0,X4] :
( ~ sP30(X0)
| ~ in(sK256(X0),omega)
| ~ element(X2,powerset(powerset(sK256(X0))))
| ~ subset(sK257(X2),X4)
| ~ in(X4,X2)
| sK257(X2) = X4
| empty_set = X2 ),
inference(cnf_transformation,[],[f1485]) ).
fof(f2424,plain,
! [X2,X0] :
( ~ sP30(X0)
| ~ in(sK256(X0),omega)
| ~ element(X2,powerset(powerset(sK256(X0))))
| in(sK257(X2),X2)
| empty_set = X2 ),
inference(cnf_transformation,[],[f1485]) ).
fof(f2425,plain,
! [X0] :
( ~ sP30(X0)
| sK256(X0) = X0 ),
inference(cnf_transformation,[],[f1485]) ).
fof(f2426,plain,
! [X0] :
( ~ sP30(X0)
| ordinal(sK256(X0)) ),
inference(cnf_transformation,[],[f1485]) ).
fof(f2463,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| in(sK269(X0,X1),X1) ),
inference(cnf_transformation,[],[f1499]) ).
fof(f2464,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| sK269(X0,X1) = X0 ),
inference(cnf_transformation,[],[f1499]) ).
fof(f2465,plain,
! [X0,X1] :
( ~ sP33(X0,X1)
| ordinal(sK269(X0,X1)) ),
inference(cnf_transformation,[],[f1499]) ).
fof(f2472,plain,
! [X0,X1] :
( ~ sP35(X0,X1)
| sK275(X0,X1) = set_difference(sK277(X0,X1),singleton(X1)) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2473,plain,
! [X0,X1] :
( ~ sP35(X0,X1)
| in(sK277(X0,X1),X0) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2474,plain,
! [X0,X1] :
( ~ sP35(X0,X1)
| sK273(X0,X1) = sK275(X0,X1) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2475,plain,
! [X0,X1] :
( ~ sP35(X0,X1)
| sK274(X0,X1) = set_difference(sK276(X0,X1),singleton(X1)) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2476,plain,
! [X0,X1] :
( ~ sP35(X0,X1)
| in(sK276(X0,X1),X0) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2477,plain,
! [X0,X1] :
( ~ sP35(X0,X1)
| sK273(X0,X1) = sK274(X0,X1) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2478,plain,
! [X0,X1] :
( ~ sP35(X0,X1)
| sK274(X0,X1) != sK275(X0,X1) ),
inference(cnf_transformation,[],[f1505]) ).
fof(f2507,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| in(relation_image(X1,sK288(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1517]) ).
fof(f2508,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| sK286(X0,X1) = sK288(X0,X1) ),
inference(cnf_transformation,[],[f1517]) ).
fof(f2509,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| in(relation_image(X1,sK287(X0,X1)),X0) ),
inference(cnf_transformation,[],[f1517]) ).
fof(f2510,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| sK286(X0,X1) = sK287(X0,X1) ),
inference(cnf_transformation,[],[f1517]) ).
fof(f2511,plain,
! [X0,X1] :
( ~ sP36(X0,X1)
| sK287(X0,X1) != sK288(X0,X1) ),
inference(cnf_transformation,[],[f1517]) ).
fof(f2734,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP37(X0,X1,X2)
| ~ in(ordered_pair(X5,X6),X1)
| in(ordered_pair(apply(X0,X5),apply(X0,X6)),X2) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2735,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP37(X0,X1,X2)
| ~ in(ordered_pair(X5,X6),X1)
| in(X6,relation_field(X1)) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2736,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP37(X0,X1,X2)
| ~ in(ordered_pair(X5,X6),X1)
| in(X5,relation_field(X1)) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2737,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP37(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,[],[f1598]) ).
fof(f2738,plain,
! [X2,X0,X1] :
( ~ sP37(X0,X1,X2)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2739,plain,
! [X2,X0,X1] :
( ~ sP37(X0,X1,X2)
| relation_rng(X0) = relation_field(X2) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2740,plain,
! [X2,X0,X1] :
( ~ sP37(X0,X1,X2)
| relation_dom(X0) = relation_field(X1) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2741,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK333(X0,X1,X2),sK334(X0,X1,X2)),X1)
| in(ordered_pair(apply(X0,sK333(X0,X1,X2)),apply(X0,sK334(X0,X1,X2))),X2)
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2742,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK333(X0,X1,X2),sK334(X0,X1,X2)),X1)
| in(sK334(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2743,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK333(X0,X1,X2),sK334(X0,X1,X2)),X1)
| in(sK333(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2744,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(sK333(X0,X1,X2),sK334(X0,X1,X2)),X1)
| ~ in(ordered_pair(apply(X0,sK333(X0,X1,X2)),apply(X0,sK334(X0,X1,X2))),X2)
| ~ in(sK334(X0,X1,X2),relation_field(X1))
| ~ in(sK333(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f1598]) ).
fof(f2951,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,sK55(X0,X1,X2))
| in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),X2) ),
inference(definition_unfolding,[],[f1697,f2915]) ).
fof(f2954,plain,
! [X2,X3,X0] :
( ~ sP3(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),sK57(X0))
| in(X2,X0) ),
inference(definition_unfolding,[],[f1704,f2915]) ).
fof(f2955,plain,
! [X2,X3,X0] :
( ~ sP3(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),sK57(X0))
| unordered_pair(X2,X2) = X3 ),
inference(definition_unfolding,[],[f1703,f2077,f2915]) ).
fof(f2969,plain,
! [X0] :
( ~ sP4(X0)
| sK70(X0) != sK140 ),
inference(definition_unfolding,[],[f1744,f2057]) ).
fof(f2983,plain,
! [X2,X0,X1] :
( sK83(X2) != sK140
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X1) ),
inference(definition_unfolding,[],[f1777,f2914,f2057]) ).
fof(f2984,plain,
! [X2,X0,X1,X4] :
( sK84(X2,X4) != X4
| ~ in(X4,sK83(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X1) ),
inference(definition_unfolding,[],[f1776,f2914]) ).
fof(f2985,plain,
! [X2,X0,X1,X4] :
( in(sK84(X2,X4),sK83(X2))
| ~ in(X4,sK83(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X1) ),
inference(definition_unfolding,[],[f1775,f2914]) ).
fof(f2986,plain,
! [X2,X0,X1,X4] :
( subset(X4,sK84(X2,X4))
| ~ in(X4,sK83(X2))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X1) ),
inference(definition_unfolding,[],[f1774,f2914]) ).
fof(f2987,plain,
! [X2,X0,X1] :
( element(sK83(X2),powerset(powerset(X2)))
| X1 != X2
| ~ ordinal(X2)
| ~ in(X1,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X1) ),
inference(definition_unfolding,[],[f1773,f2914]) ).
fof(f2988,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,[],[f1772,f2914]) ).
fof(f2989,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| in(X1,set_union2(X0,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f1771,f2914]) ).
fof(f2990,plain,
! [X0,X1,X7] :
( ~ sP9(X0,X1)
| ~ in(sK85(X1),omega)
| ~ element(X7,powerset(powerset(sK85(X1))))
| in(sK86(X7),X7)
| sK140 = X7 ),
inference(definition_unfolding,[],[f1768,f2057]) ).
fof(f2991,plain,
! [X0,X1,X9,X7] :
( ~ sP9(X0,X1)
| ~ in(sK85(X1),omega)
| ~ element(X7,powerset(powerset(sK85(X1))))
| ~ subset(sK86(X7),X9)
| ~ in(X9,X7)
| sK86(X7) = X9
| sK140 = X7 ),
inference(definition_unfolding,[],[f1767,f2057]) ).
fof(f3002,plain,
! [X0,X1,X6] :
( ~ sP11(X0,X1)
| ~ in(X6,sK101(X0,X1))
| in(unordered_pair(unordered_pair(sK99(X0,X1),X6),unordered_pair(sK99(X0,X1),sK99(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1807,f2915]) ).
fof(f3003,plain,
! [X0,X1,X8] :
( ~ sP11(X0,X1)
| ~ in(X8,sK102(X0,X1))
| in(unordered_pair(unordered_pair(sK100(X0,X1),X8),unordered_pair(sK100(X0,X1),sK100(X0,X1))),X1) ),
inference(definition_unfolding,[],[f1804,f2915]) ).
fof(f3005,plain,
! [X0] :
( ~ sP13(X0)
| sK106(X0) = unordered_pair(sK105(X0),sK105(X0)) ),
inference(definition_unfolding,[],[f1816,f2077]) ).
fof(f3006,plain,
! [X0] :
( ~ sP13(X0)
| sK107(X0) = unordered_pair(sK105(X0),sK105(X0)) ),
inference(definition_unfolding,[],[f1815,f2077]) ).
fof(f3014,plain,
! [X0] :
( ~ sP14(X0)
| sK112(X0) != sK140 ),
inference(definition_unfolding,[],[f1836,f2057]) ).
fof(f3112,plain,
! [X2,X0,X1,X4] :
( ~ sP17(X0,X1,X2)
| ~ in(X4,sK148(X0,X1,X2))
| in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),X2) ),
inference(definition_unfolding,[],[f2130,f2915]) ).
fof(f3144,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| unordered_pair(unordered_pair(sK175(X0,X1),sK176(X0,X1)),unordered_pair(sK175(X0,X1),sK175(X0,X1))) = X0 ),
inference(definition_unfolding,[],[f2185,f2915]) ).
fof(f3145,plain,
! [X0,X1] :
( ~ sP19(X0,X1)
| sK176(X0,X1) = unordered_pair(sK175(X0,X1),sK175(X0,X1)) ),
inference(definition_unfolding,[],[f2183,f2077]) ).
fof(f3149,plain,
! [X0] :
( ~ sP21(X0)
| sK182(X0) = unordered_pair(sK181(X0),sK181(X0)) ),
inference(definition_unfolding,[],[f2194,f2077]) ).
fof(f3150,plain,
! [X0] :
( ~ sP21(X0)
| sK183(X0) = unordered_pair(sK181(X0),sK181(X0)) ),
inference(definition_unfolding,[],[f2192,f2077]) ).
fof(f3169,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| sK207(X0,X1) = unordered_pair(unordered_pair(sK209(X0,X1),sK210(X0,X1)),unordered_pair(sK209(X0,X1),sK209(X0,X1))) ),
inference(definition_unfolding,[],[f2321,f2915]) ).
fof(f3170,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| in(unordered_pair(unordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK210(X0,X1))),unordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK209(X0,X1)))),X0) ),
inference(definition_unfolding,[],[f2320,f2915]) ).
fof(f3171,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| sK208(X0,X1) = unordered_pair(unordered_pair(sK211(X0,X1),sK212(X0,X1)),unordered_pair(sK211(X0,X1),sK211(X0,X1))) ),
inference(definition_unfolding,[],[f2318,f2915]) ).
fof(f3172,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| in(unordered_pair(unordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK212(X0,X1))),unordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK211(X0,X1)))),X0) ),
inference(definition_unfolding,[],[f2317,f2915]) ).
fof(f3182,plain,
! [X2,X0,X1] :
( ~ sP25(X0,X1,X2)
| unordered_pair(unordered_pair(sK226(X0,X1,X2),sK227(X0,X1,X2)),unordered_pair(sK226(X0,X1,X2),sK226(X0,X1,X2))) = X0 ),
inference(definition_unfolding,[],[f2349,f2915]) ).
fof(f3183,plain,
! [X2,X0,X1,X6] :
( ~ sP25(X0,X1,X2)
| ~ in(X6,sK228(X0,X1,X2))
| in(unordered_pair(unordered_pair(sK227(X0,X1,X2),X6),unordered_pair(sK227(X0,X1,X2),sK227(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f2345,f2915]) ).
fof(f3204,plain,
! [X2,X0] :
( ~ sP30(X0)
| ~ in(sK256(X0),omega)
| ~ element(X2,powerset(powerset(sK256(X0))))
| in(sK257(X2),X2)
| sK140 = X2 ),
inference(definition_unfolding,[],[f2424,f2057]) ).
fof(f3205,plain,
! [X2,X0,X4] :
( ~ sP30(X0)
| ~ in(sK256(X0),omega)
| ~ element(X2,powerset(powerset(sK256(X0))))
| ~ subset(sK257(X2),X4)
| ~ in(X4,X2)
| sK257(X2) = X4
| sK140 = X2 ),
inference(definition_unfolding,[],[f2423,f2057]) ).
fof(f3216,plain,
! [X0,X1] :
( ~ sP35(X0,X1)
| sK274(X0,X1) = set_difference(sK276(X0,X1),unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f2475,f2077]) ).
fof(f3217,plain,
! [X0,X1] :
( ~ sP35(X0,X1)
| sK275(X0,X1) = set_difference(sK277(X0,X1),unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f2472,f2077]) ).
fof(f3297,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK333(X0,X1,X2),sK334(X0,X1,X2)),unordered_pair(sK333(X0,X1,X2),sK333(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(apply(X0,sK333(X0,X1,X2)),apply(X0,sK334(X0,X1,X2))),unordered_pair(apply(X0,sK333(X0,X1,X2)),apply(X0,sK333(X0,X1,X2)))),X2)
| ~ in(sK334(X0,X1,X2),relation_field(X1))
| ~ in(sK333(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP37(X0,X1,X2) ),
inference(definition_unfolding,[],[f2744,f2915,f2915]) ).
fof(f3298,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK333(X0,X1,X2),sK334(X0,X1,X2)),unordered_pair(sK333(X0,X1,X2),sK333(X0,X1,X2))),X1)
| in(sK333(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP37(X0,X1,X2) ),
inference(definition_unfolding,[],[f2743,f2915]) ).
fof(f3299,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK333(X0,X1,X2),sK334(X0,X1,X2)),unordered_pair(sK333(X0,X1,X2),sK333(X0,X1,X2))),X1)
| in(sK334(X0,X1,X2),relation_field(X1))
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP37(X0,X1,X2) ),
inference(definition_unfolding,[],[f2742,f2915]) ).
fof(f3300,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK333(X0,X1,X2),sK334(X0,X1,X2)),unordered_pair(sK333(X0,X1,X2),sK333(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(apply(X0,sK333(X0,X1,X2)),apply(X0,sK334(X0,X1,X2))),unordered_pair(apply(X0,sK333(X0,X1,X2)),apply(X0,sK333(X0,X1,X2)))),X2)
| ~ one_to_one(X0)
| relation_rng(X0) != relation_field(X2)
| relation_dom(X0) != relation_field(X1)
| sP37(X0,X1,X2) ),
inference(definition_unfolding,[],[f2741,f2915,f2915]) ).
fof(f3301,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP37(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,[],[f2737,f2915,f2915]) ).
fof(f3302,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP37(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| in(X5,relation_field(X1)) ),
inference(definition_unfolding,[],[f2736,f2915]) ).
fof(f3303,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP37(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X1)
| in(X6,relation_field(X1)) ),
inference(definition_unfolding,[],[f2735,f2915]) ).
fof(f3304,plain,
! [X2,X0,X1,X6,X5] :
( ~ sP37(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,[],[f2734,f2915,f2915]) ).
fof(f3369,plain,
! [X2,X0] :
( sK83(X2) != sK140
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f2983]) ).
fof(f3370,plain,
! [X2,X0,X4] :
( sK84(X2,X4) != X4
| ~ in(X4,sK83(X2))
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f2984]) ).
fof(f3371,plain,
! [X2,X0,X4] :
( in(sK84(X2,X4),sK83(X2))
| ~ in(X4,sK83(X2))
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f2985]) ).
fof(f3372,plain,
! [X2,X0,X4] :
( subset(X4,sK84(X2,X4))
| ~ in(X4,sK83(X2))
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f2986]) ).
fof(f3373,plain,
! [X2,X0] :
( element(sK83(X2),powerset(powerset(X2)))
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f2987]) ).
fof(f3374,plain,
! [X2,X0] :
( in(X2,omega)
| ~ ordinal(X2)
| ~ in(X2,set_union2(X0,unordered_pair(X0,X0)))
| sP9(X0,X2) ),
inference(equality_resolution,[],[f2988]) ).
fof(f3391,plain,
! [X3,X0,X1] :
( ~ in(X1,relation_rng(X0))
| sP16(X0,X1,apply(X3,X1),X3) ),
inference(equality_resolution,[],[f2039]) ).
fof(f3392,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,[],[f2036]) ).
fof(f3393,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,[],[f2035]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK55(X0,X1,X2) = X0 )
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f1699]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK55(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f1698]) ).
tcf(c_109,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,sK55(X1,X2,X3)) ),
inference(cnf_transformation,[],[f2951]) ).
tcf(c_113,plain,
! [X0: $i] :
( relation(sK57(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f1708]) ).
tcf(c_114,plain,
! [X0: $i] :
( function(sK57(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f1707]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ sP3(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK57(X2)) ),
inference(cnf_transformation,[],[f2954]) ).
tcf(c_118,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)),sK57(X2)) ),
inference(cnf_transformation,[],[f2955]) ).
tcf(c_150,negated_conjecture,
! [X0: $i] :
( ~ sP4(X0)
| ( sK70(X0) != sK140 ) ),
inference(cnf_transformation,[],[f2969]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( ~ sP4(X0)
| ~ in(X1,sK70(X0))
| ( sK71(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f1743]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( in(sK71(X1,X0),sK70(X1))
| ~ sP4(X1)
| ~ in(X0,sK70(X1)) ),
inference(cnf_transformation,[],[f1742]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK71(X1,X0))
| ~ sP4(X1)
| ~ in(X0,sK70(X1)) ),
inference(cnf_transformation,[],[f1741]) ).
tcf(c_154,plain,
! [X0: $i] :
( element(sK70(X0),powerset(powerset(X0)))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f1740]) ).
tcf(c_177,negated_conjecture,
! [X0: $i,X1: $i] :
( sP9(X1,X0)
| ~ ordinal(X0)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1)))
| ( sK83(X0) != sK140 ) ),
inference(cnf_transformation,[],[f3369]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP9(X2,X0)
| ~ ordinal(X0)
| ~ in(X1,sK83(X0))
| ~ in(X0,set_union2(X2,unordered_pair(X2,X2)))
| ( sK84(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f3370]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP9(X1,X0)
| in(sK84(X0,X2),sK83(X0))
| ~ ordinal(X0)
| ~ in(X2,sK83(X0))
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3371]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP9(X1,X0)
| subset(X2,sK84(X0,X2))
| ~ ordinal(X0)
| ~ in(X2,sK83(X0))
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3372]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i] :
( sP9(X1,X0)
| element(sK83(X0),powerset(powerset(X0)))
| ~ ordinal(X0)
| ~ in(X0,set_union2(X1,unordered_pair(X1,X1))) ),
inference(cnf_transformation,[],[f3373]) ).
tcf(c_182,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,[],[f3374]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( in(X1,set_union2(X0,unordered_pair(X0,X0)))
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f2989]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( ordinal(sK85(X1))
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f1770]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] :
( ( sK85(X1) = X1 )
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f1769]) ).
tcf(c_186,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( in(sK86(X0),X0)
| ( X0 = sK140 )
| ~ sP9(X2,X1)
| ~ in(sK85(X1),omega)
| ~ element(X0,powerset(powerset(sK85(X1)))) ),
inference(cnf_transformation,[],[f2990]) ).
tcf(c_187,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = sK140 )
| ( sK86(X0) = X2 )
| ~ sP9(X3,X1)
| ~ in(X2,X0)
| ~ in(sK85(X1),omega)
| ~ subset(sK86(X0),X2)
| ~ element(X0,powerset(powerset(sK85(X1)))) ),
inference(cnf_transformation,[],[f2991]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i] :
( ~ sP11(X0,X1)
| ( sK99(X0,X1) != sK100(X0,X1) ) ),
inference(cnf_transformation,[],[f1811]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] :
( in(sK98(X0,X1),X0)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1810]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i] :
( ( sK98(X0,X1) = sK101(X0,X1) )
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1809]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] :
( in(sK99(X0,X1),sK101(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1808]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK99(X1,X2),X0),unordered_pair(sK99(X1,X2),sK99(X1,X2))),X2)
| ~ sP11(X1,X2)
| ~ in(X0,sK101(X1,X2)) ),
inference(cnf_transformation,[],[f3002]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i] :
( ( sK98(X0,X1) = sK102(X0,X1) )
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1806]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i] :
( in(sK100(X0,X1),sK102(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1805]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(sK100(X1,X2),X0),unordered_pair(sK100(X1,X2),sK100(X1,X2))),X2)
| ~ sP11(X1,X2)
| ~ in(X0,sK102(X1,X2)) ),
inference(cnf_transformation,[],[f3003]) ).
tcf(c_225,plain,
! [X0: $i] :
( ~ sP13(X0)
| ( sK106(X0) != sK107(X0) ) ),
inference(cnf_transformation,[],[f1818]) ).
tcf(c_226,plain,
! [X0: $i] :
( in(sK105(X0),X0)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f1817]) ).
tcf(c_227,plain,
! [X0: $i] :
( ( unordered_pair(sK105(X0),sK105(X0)) = sK106(X0) )
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f3005]) ).
tcf(c_228,plain,
! [X0: $i] :
( ( unordered_pair(sK105(X0),sK105(X0)) = sK107(X0) )
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f3006]) ).
tcf(c_242,negated_conjecture,
! [X0: $i] :
( ~ sP14(X0)
| ( sK112(X0) != sK140 ) ),
inference(cnf_transformation,[],[f3014]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] :
( ~ sP14(X0)
| ~ in(X1,sK112(X0))
| ( sK113(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f1835]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i] :
( in(sK113(X1,X0),sK112(X1))
| ~ sP14(X1)
| ~ in(X0,sK112(X1)) ),
inference(cnf_transformation,[],[f1834]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] :
( subset(X0,sK113(X1,X0))
| ~ sP14(X1)
| ~ in(X0,sK112(X1)) ),
inference(cnf_transformation,[],[f1833]) ).
tcf(c_246,plain,
! [X0: $i] :
( element(sK112(X0),powerset(powerset(X0)))
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f1832]) ).
tcf(c_444,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP16(X1,X0,apply(X2,X0),X2)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f3391]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,relation_dom(X0))
| sP16(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f2038]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP16(X0,X2,X1,X3)
| ( apply(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f2037]) ).
tcf(c_447,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,[],[f3392]) ).
tcf(c_448,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,[],[f3393]) ).
tcf(c_535,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK148(X0,X1,X2) = X0 )
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f2132]) ).
tcf(c_536,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK148(X0,X1,X2))
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f2131]) ).
tcf(c_537,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,sK148(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3112]) ).
tcf(c_588,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK175(X0,X1),sK176(X0,X1)),unordered_pair(sK175(X0,X1),sK175(X0,X1))) = X0 )
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f3144]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i] :
( in(sK175(X0,X1),X1)
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f2184]) ).
tcf(c_590,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(sK175(X0,X1),sK175(X0,X1)) = sK176(X0,X1) )
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f3145]) ).
tcf(c_597,plain,
! [X0: $i] :
( ~ sP21(X0)
| ( sK182(X0) != sK183(X0) ) ),
inference(cnf_transformation,[],[f2196]) ).
tcf(c_599,plain,
! [X0: $i] :
( ( unordered_pair(sK181(X0),sK181(X0)) = sK182(X0) )
| ~ sP21(X0) ),
inference(cnf_transformation,[],[f3149]) ).
tcf(c_600,plain,
! [X0: $i] :
( in(sK181(X0),X0)
| ~ sP21(X0) ),
inference(cnf_transformation,[],[f2193]) ).
tcf(c_601,plain,
! [X0: $i] :
( ( unordered_pair(sK181(X0),sK181(X0)) = sK183(X0) )
| ~ sP21(X0) ),
inference(cnf_transformation,[],[f3150]) ).
tcf(c_629,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP22(X0,X1,X2)
| open_subset(sK189(X0,X1,X2),X0)
| ~ in(sK188(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2235]) ).
tcf(c_630,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP22(X0,X1,X2)
| in(sK188(X0,X1,X2),sK189(X0,X1,X2))
| ~ in(sK188(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2234]) ).
tcf(c_631,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP22(X0,X1,X2)
| disjoint(X1,sK189(X0,X1,X2))
| ~ in(sK188(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2233]) ).
tcf(c_632,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP22(X0,X1,X2)
| element(sK189(X0,X1,X2),powerset(the_carrier(X0)))
| ~ in(sK188(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f2232]) ).
tcf(c_633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP22(X0,X1,X2)
| in(sK188(X0,X1,X2),X2)
| ~ open_subset(X3,X0)
| ~ disjoint(X1,X3)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(sK188(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f2231]) ).
tcf(c_634,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP22(X0,X1,X2)
| in(sK188(X0,X1,X2),the_carrier(X0)) ),
inference(cnf_transformation,[],[f2230]) ).
tcf(c_635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| open_subset(sK190(X0,X1,X3),X0)
| ~ in(X3,the_carrier(X0))
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f2229]) ).
tcf(c_636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| in(X3,sK190(X0,X1,X3))
| ~ in(X3,the_carrier(X0))
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f2228]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| disjoint(X1,sK190(X0,X1,X3))
| ~ in(X3,the_carrier(X0))
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f2227]) ).
tcf(c_638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X2)
| element(sK190(X0,X1,X3),powerset(the_carrier(X0)))
| ~ in(X3,the_carrier(X0))
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f2226]) ).
tcf(c_639,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))
| ~ sP22(X1,X2,X3)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f2225]) ).
tcf(c_721,plain,
! [X0: $i,X1: $i] :
( ~ sP24(X0,X1)
| ( sK207(X0,X1) != sK208(X0,X1) ) ),
inference(cnf_transformation,[],[f2323]) ).
tcf(c_722,plain,
! [X0: $i,X1: $i] :
( ( sK207(X0,X1) = sK206(X0,X1) )
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f2322]) ).
tcf(c_723,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK209(X0,X1),sK210(X0,X1)),unordered_pair(sK209(X0,X1),sK209(X0,X1))) = sK207(X0,X1) )
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f3169]) ).
tcf(c_724,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK210(X0,X1))),unordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK209(X0,X1)))),X0)
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f3170]) ).
tcf(c_725,plain,
! [X0: $i,X1: $i] :
( ( sK208(X0,X1) = sK206(X0,X1) )
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f2319]) ).
tcf(c_726,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK211(X0,X1),sK212(X0,X1)),unordered_pair(sK211(X0,X1),sK211(X0,X1))) = sK208(X0,X1) )
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f3171]) ).
tcf(c_727,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK212(X0,X1))),unordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK211(X0,X1)))),X0)
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f3172]) ).
tcf(c_749,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK226(X0,X1,X2),sK227(X0,X1,X2)),unordered_pair(sK226(X0,X1,X2),sK226(X0,X1,X2))) = X0 )
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f3182]) ).
tcf(c_750,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK226(X0,X1,X2),X1)
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f2348]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK226(X0,X1,X2) = sK228(X0,X1,X2) )
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f2347]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK227(X0,X1,X2),sK228(X0,X1,X2))
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f2346]) ).
tcf(c_753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(sK227(X1,X2,X3),X0),unordered_pair(sK227(X1,X2,X3),sK227(X1,X2,X3))),X3)
| ~ sP25(X1,X2,X3)
| ~ in(X0,sK228(X1,X2,X3)) ),
inference(cnf_transformation,[],[f3183]) ).
tcf(c_800,plain,
( ~ sP29
| ( sK246 != sK247 ) ),
inference(cnf_transformation,[],[f2400]) ).
tcf(c_801,plain,
( ( sK246 = sK245 )
| ~ sP29 ),
inference(cnf_transformation,[],[f2399]) ).
tcf(c_802,plain,
( ordinal(sK246)
| ~ sP29 ),
inference(cnf_transformation,[],[f2398]) ).
tcf(c_803,plain,
( ( sK247 = sK245 )
| ~ sP29 ),
inference(cnf_transformation,[],[f2397]) ).
tcf(c_804,plain,
( ordinal(sK247)
| ~ sP29 ),
inference(cnf_transformation,[],[f2396]) ).
tcf(c_827,plain,
! [X0: $i] :
( ordinal(sK256(X0))
| ~ sP30(X0) ),
inference(cnf_transformation,[],[f2426]) ).
tcf(c_828,plain,
! [X0: $i] :
( ( sK256(X0) = X0 )
| ~ sP30(X0) ),
inference(cnf_transformation,[],[f2425]) ).
tcf(c_829,negated_conjecture,
! [X0: $i,X1: $i] :
( in(sK257(X0),X0)
| ( X0 = sK140 )
| ~ sP30(X1)
| ~ in(sK256(X1),omega)
| ~ element(X0,powerset(powerset(sK256(X1)))) ),
inference(cnf_transformation,[],[f3204]) ).
tcf(c_830,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sK140 )
| ( sK257(X0) = X2 )
| ~ sP30(X1)
| ~ in(X2,X0)
| ~ in(sK256(X1),omega)
| ~ subset(sK257(X0),X2)
| ~ element(X0,powerset(powerset(sK256(X1)))) ),
inference(cnf_transformation,[],[f3205]) ).
tcf(c_867,plain,
! [X0: $i,X1: $i] :
( ordinal(sK269(X0,X1))
| ~ sP33(X0,X1) ),
inference(cnf_transformation,[],[f2465]) ).
tcf(c_868,plain,
! [X0: $i,X1: $i] :
( ( sK269(X0,X1) = X0 )
| ~ sP33(X0,X1) ),
inference(cnf_transformation,[],[f2464]) ).
tcf(c_869,plain,
! [X0: $i,X1: $i] :
( in(sK269(X0,X1),X1)
| ~ sP33(X0,X1) ),
inference(cnf_transformation,[],[f2463]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i] :
( ~ sP35(X0,X1)
| ( sK274(X0,X1) != sK275(X0,X1) ) ),
inference(cnf_transformation,[],[f2478]) ).
tcf(c_877,plain,
! [X0: $i,X1: $i] :
( ( sK274(X0,X1) = sK273(X0,X1) )
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f2477]) ).
tcf(c_878,plain,
! [X0: $i,X1: $i] :
( in(sK276(X0,X1),X0)
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f2476]) ).
tcf(c_879,plain,
! [X0: $i,X1: $i] :
( ( set_difference(sK276(X0,X1),unordered_pair(X1,X1)) = sK274(X0,X1) )
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f3216]) ).
tcf(c_880,plain,
! [X0: $i,X1: $i] :
( ( sK275(X0,X1) = sK273(X0,X1) )
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f2474]) ).
tcf(c_881,plain,
! [X0: $i,X1: $i] :
( in(sK277(X0,X1),X0)
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f2473]) ).
tcf(c_882,plain,
! [X0: $i,X1: $i] :
( ( set_difference(sK277(X0,X1),unordered_pair(X1,X1)) = sK275(X0,X1) )
| ~ sP35(X0,X1) ),
inference(cnf_transformation,[],[f3217]) ).
tcf(c_911,plain,
! [X0: $i,X1: $i] :
( ~ sP36(X0,X1)
| ( sK287(X0,X1) != sK288(X0,X1) ) ),
inference(cnf_transformation,[],[f2511]) ).
tcf(c_912,plain,
! [X0: $i,X1: $i] :
( ( sK287(X0,X1) = sK286(X0,X1) )
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f2510]) ).
tcf(c_913,plain,
! [X0: $i,X1: $i] :
( in(relation_image(X1,sK287(X0,X1)),X0)
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f2509]) ).
tcf(c_914,plain,
! [X0: $i,X1: $i] :
( ( sK288(X0,X1) = sK286(X0,X1) )
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f2508]) ).
tcf(c_915,plain,
! [X0: $i,X1: $i] :
( in(relation_image(X1,sK288(X0,X1)),X0)
| ~ sP36(X0,X1) ),
inference(cnf_transformation,[],[f2507]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP37(X1,X0,X2)
| ~ one_to_one(X1)
| ~ in(sK334(X1,X0,X2),relation_field(X0))
| ~ in(sK333(X1,X0,X2),relation_field(X0))
| ~ in(unordered_pair(unordered_pair(sK333(X1,X0,X2),sK334(X1,X0,X2)),unordered_pair(sK333(X1,X0,X2),sK333(X1,X0,X2))),X0)
| ~ in(unordered_pair(unordered_pair(apply(X1,sK333(X1,X0,X2)),apply(X1,sK334(X1,X0,X2))),unordered_pair(apply(X1,sK333(X1,X0,X2)),apply(X1,sK333(X1,X0,X2)))),X2)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(cnf_transformation,[],[f3297]) ).
tcf(c_1138,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP37(X1,X0,X2)
| in(sK333(X1,X0,X2),relation_field(X0))
| in(unordered_pair(unordered_pair(sK333(X1,X0,X2),sK334(X1,X0,X2)),unordered_pair(sK333(X1,X0,X2),sK333(X1,X0,X2))),X0)
| ~ one_to_one(X1)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(cnf_transformation,[],[f3298]) ).
tcf(c_1139,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP37(X1,X0,X2)
| in(sK334(X1,X0,X2),relation_field(X0))
| in(unordered_pair(unordered_pair(sK333(X1,X0,X2),sK334(X1,X0,X2)),unordered_pair(sK333(X1,X0,X2),sK333(X1,X0,X2))),X0)
| ~ one_to_one(X1)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(cnf_transformation,[],[f3299]) ).
tcf(c_1140,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP37(X1,X0,X2)
| in(unordered_pair(unordered_pair(sK333(X1,X0,X2),sK334(X1,X0,X2)),unordered_pair(sK333(X1,X0,X2),sK333(X1,X0,X2))),X0)
| in(unordered_pair(unordered_pair(apply(X1,sK333(X1,X0,X2)),apply(X1,sK334(X1,X0,X2))),unordered_pair(apply(X1,sK333(X1,X0,X2)),apply(X1,sK333(X1,X0,X2)))),X2)
| ~ one_to_one(X1)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(cnf_transformation,[],[f3300]) ).
tcf(c_1141,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_field(X1) = relation_dom(X0) )
| ~ sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f2740]) ).
tcf(c_1142,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_field(X2) = relation_rng(X0) )
| ~ sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f2739]) ).
tcf(c_1143,plain,
! [X0: $i,X1: $i,X2: $i] :
( one_to_one(X0)
| ~ sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f2738]) ).
tcf(c_1144,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))
| ~ sP37(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,[],[f3301]) ).
tcf(c_1145,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X0,relation_field(X2))
| ~ sP37(X3,X2,X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3302]) ).
tcf(c_1146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X1,relation_field(X2))
| ~ sP37(X3,X2,X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3303]) ).
tcf(c_1147,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)
| ~ sP37(X3,X2,X4)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f3304]) ).
tcf(c_2570,plain,
! [X0: $i] :
( ~ sP4(X0)
| ( sK70(X0) != sK140 ) ),
inference(prop_impl_just,[status(thm)],[c_150]) ).
tcf(c_2574,plain,
! [X0: $i] :
( element(sK70(X0),powerset(powerset(X0)))
| ~ sP4(X0) ),
inference(prop_impl_just,[status(thm)],[c_154]) ).
tcf(c_2654,plain,
! [X0: $i] :
( ~ sP14(X0)
| ( sK112(X0) != sK140 ) ),
inference(prop_impl_just,[status(thm)],[c_242]) ).
tcf(c_2658,plain,
! [X0: $i] :
( element(sK112(X0),powerset(powerset(X0)))
| ~ sP14(X0) ),
inference(prop_impl_just,[status(thm)],[c_246]) ).
tcf(c_2790,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK175(X0,X1),sK176(X0,X1)),unordered_pair(sK175(X0,X1),sK175(X0,X1))) = X0 )
| ~ sP19(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_588]) ).
tcf(c_2792,plain,
! [X0: $i,X1: $i] :
( in(sK175(X0,X1),X1)
| ~ sP19(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_589]) ).
tcf(c_2794,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(sK175(X0,X1),sK175(X0,X1)) = sK176(X0,X1) )
| ~ sP19(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_590]) ).
tcf(c_2892,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK209(X0,X1),sK210(X0,X1)),unordered_pair(sK209(X0,X1),sK209(X0,X1))) = sK207(X0,X1) )
| ~ sP24(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_723]) ).
tcf(c_2894,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK210(X0,X1))),unordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK209(X0,X1)))),X0)
| ~ sP24(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_724]) ).
tcf(c_2898,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK211(X0,X1),sK212(X0,X1)),unordered_pair(sK211(X0,X1),sK211(X0,X1))) = sK208(X0,X1) )
| ~ sP24(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_726]) ).
tcf(c_2900,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK212(X0,X1))),unordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK211(X0,X1)))),X0)
| ~ sP24(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_727]) ).
tcf(c_2922,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK226(X0,X1,X2),sK227(X0,X1,X2)),unordered_pair(sK226(X0,X1,X2),sK226(X0,X1,X2))) = X0 )
| ~ sP25(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_749]) ).
tcf(c_2958,plain,
! [X0: $i] :
( ordinal(sK256(X0))
| ~ sP30(X0) ),
inference(prop_impl_just,[status(thm)],[c_827]) ).
tcf(c_2960,plain,
! [X0: $i] :
( ( sK256(X0) = X0 )
| ~ sP30(X0) ),
inference(prop_impl_just,[status(thm)],[c_828]) ).
tcf(c_2986,plain,
! [X0: $i,X1: $i] :
( ordinal(sK269(X0,X1))
| ~ sP33(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_867]) ).
tcf(c_2988,plain,
! [X0: $i,X1: $i] :
( ( sK269(X0,X1) = X0 )
| ~ sP33(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_868]) ).
tcf(c_2990,plain,
! [X0: $i,X1: $i] :
( in(sK269(X0,X1),X1)
| ~ sP33(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_869]) ).
tcf(c_16780,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK175(X0,X1),sK175(X0,X1)),unordered_pair(sK175(X0,X1),sK176(X0,X1))) = X0 )
| ~ sP19(X0,X1) ),
inference(demodulation,[status(thm)],[c_2790,c_942]) ).
tcf(c_17216,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK211(X0,X1),sK211(X0,X1)),unordered_pair(sK211(X0,X1),sK212(X0,X1))) = sK208(X0,X1) )
| ~ sP24(X0,X1) ),
inference(demodulation,[status(thm)],[c_2898,c_942]) ).
tcf(c_17223,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK209(X0,X1),sK209(X0,X1)),unordered_pair(sK209(X0,X1),sK210(X0,X1))) = sK207(X0,X1) )
| ~ sP24(X0,X1) ),
inference(demodulation,[status(thm)],[c_2892,c_942]) ).
tcf(c_17699,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK226(X0,X1,X2),sK226(X0,X1,X2)),unordered_pair(sK226(X0,X1,X2),sK227(X0,X1,X2))) = X0 )
| ~ sP25(X0,X1,X2) ),
inference(demodulation,[status(thm)],[c_2922,c_942]) ).
tcf(c_17985,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK211(X0,X1))),unordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK212(X0,X1)))),X0)
| ~ sP24(X0,X1) ),
inference(demodulation,[status(thm)],[c_2900,c_942]) ).
tcf(c_17992,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK209(X0,X1))),unordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK210(X0,X1)))),X0)
| ~ sP24(X0,X1) ),
inference(demodulation,[status(thm)],[c_2894,c_942]) ).
tcf(c_19175,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP37(X1,X0,X2)
| in(sK334(X1,X0,X2),relation_field(X0))
| in(unordered_pair(unordered_pair(sK333(X1,X0,X2),sK333(X1,X0,X2)),unordered_pair(sK333(X1,X0,X2),sK334(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_1139,c_942]) ).
tcf(c_19194,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP37(X1,X0,X2)
| in(sK333(X1,X0,X2),relation_field(X0))
| in(unordered_pair(unordered_pair(sK333(X1,X0,X2),sK333(X1,X0,X2)),unordered_pair(sK333(X1,X0,X2),sK334(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_1138,c_942]) ).
tcf(c_19405,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP37(X1,X0,X2)
| in(unordered_pair(unordered_pair(sK333(X1,X0,X2),sK333(X1,X0,X2)),unordered_pair(sK333(X1,X0,X2),sK334(X1,X0,X2))),X0)
| in(unordered_pair(unordered_pair(apply(X1,sK333(X1,X0,X2)),apply(X1,sK333(X1,X0,X2))),unordered_pair(apply(X1,sK333(X1,X0,X2)),apply(X1,sK334(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_1140,c_942]) ).
tcf(c_19424,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP37(X1,X0,X2)
| ~ one_to_one(X1)
| ~ in(sK334(X1,X0,X2),relation_field(X0))
| ~ in(sK333(X1,X0,X2),relation_field(X0))
| ~ in(unordered_pair(unordered_pair(sK333(X1,X0,X2),sK333(X1,X0,X2)),unordered_pair(sK333(X1,X0,X2),sK334(X1,X0,X2))),X0)
| ~ in(unordered_pair(unordered_pair(apply(X1,sK333(X1,X0,X2)),apply(X1,sK333(X1,X0,X2))),unordered_pair(apply(X1,sK333(X1,X0,X2)),apply(X1,sK334(X1,X0,X2)))),X2)
| ( relation_field(X2) != relation_rng(X1) )
| ( relation_field(X0) != relation_dom(X1) ) ),
inference(demodulation,[status(thm)],[c_1137,c_942]) ).
tcf(c_19662,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK175(X1,X2),sK175(X1,X2)),unordered_pair(sK175(X1,X2),sK176(X1,X2))) = X1 )
| ~ sP20(X0)
| ( X0 != X2 )
| ( sK172(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2788,c_16780]) ).
tcf(c_19663,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK175(sK172(X0),X0),sK175(sK172(X0),X0)),unordered_pair(sK175(sK172(X0),X0),sK176(sK172(X0),X0))) = sK172(X0) )
| ~ sP20(X0) ),
inference(unflattening,[status(thm)],[c_19662]) ).
tcf(c_19671,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(sK175(X1,X2),sK175(X1,X2)) = sK176(X1,X2) )
| ~ sP20(X0)
| ( X0 != X2 )
| ( sK172(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2788,c_2794]) ).
tcf(c_19672,plain,
! [X0: $i] :
( ( unordered_pair(sK175(sK172(X0),X0),sK175(sK172(X0),X0)) = sK176(sK172(X0),X0) )
| ~ sP20(X0) ),
inference(unflattening,[status(thm)],[c_19671]) ).
tcf(c_19680,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK175(X1,X2),X2)
| ~ sP20(X0)
| ( X0 != X2 )
| ( sK172(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2788,c_2792]) ).
tcf(c_19681,plain,
! [X0: $i] :
( in(sK175(sK172(X0),X0),X0)
| ~ sP20(X0) ),
inference(unflattening,[status(thm)],[c_19680]) ).
tcf(c_19695,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK269(X1,X2),X2)
| ~ sP34(X0)
| ( X0 != X2 )
| ( sK267(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2984,c_2990]) ).
tcf(c_19696,plain,
! [X0: $i] :
( in(sK269(sK267(X0),X0),X0)
| ~ sP34(X0) ),
inference(unflattening,[status(thm)],[c_19695]) ).
tcf(c_19704,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK269(X1,X2) = X1 )
| ~ sP34(X0)
| ( X0 != X2 )
| ( sK267(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2984,c_2988]) ).
tcf(c_19705,plain,
! [X0: $i] :
( ( sK269(sK267(X0),X0) = sK267(X0) )
| ~ sP34(X0) ),
inference(unflattening,[status(thm)],[c_19704]) ).
tcf(c_19713,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordinal(sK269(X1,X2))
| ~ sP34(X0)
| ( X0 != X2 )
| ( sK267(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2984,c_2986]) ).
tcf(c_19714,plain,
! [X0: $i] :
( ordinal(sK269(sK267(X0),X0))
| ~ sP34(X0) ),
inference(unflattening,[status(thm)],[c_19713]) ).
tcf(c_20092,plain,
! [X0: $i] :
( element(sK70(X0),powerset(powerset(X0)))
| ~ sP6
| ( X0 != sK66 ) ),
inference(resolution_lifted,[status(thm)],[c_2544,c_2574]) ).
tcf(c_20093,plain,
( element(sK70(sK66),powerset(powerset(sK66)))
| ~ sP6 ),
inference(unflattening,[status(thm)],[c_20092]) ).
tcf(c_20100,plain,
! [X0: $i,X1: $i] :
( ~ sP6
| ~ in(X1,sK70(X0))
| ( X0 != sK66 )
| ( sK71(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2544,c_151]) ).
tcf(c_20101,plain,
! [X0: $i] :
( ~ sP6
| ~ in(X0,sK70(sK66))
| ( sK71(sK66,X0) != X0 ) ),
inference(unflattening,[status(thm)],[c_20100]) ).
tcf(c_20112,plain,
! [X0: $i] :
( ~ sP6
| ( X0 != sK66 )
| ( sK70(X0) != sK140 ) ),
inference(resolution_lifted,[status(thm)],[c_2544,c_2570]) ).
tcf(c_20113,plain,
( ~ sP6
| ( sK70(sK66) != sK140 ) ),
inference(unflattening,[status(thm)],[c_20112]) ).
tcf(c_20120,plain,
! [X0: $i,X1: $i] :
( subset(X1,sK71(X0,X1))
| ~ sP6
| ~ in(X1,sK70(X0))
| ( X0 != sK66 ) ),
inference(resolution_lifted,[status(thm)],[c_2544,c_153]) ).
tcf(c_20121,plain,
! [X0: $i] :
( subset(X0,sK71(sK66,X0))
| ~ sP6
| ~ in(X0,sK70(sK66)) ),
inference(unflattening,[status(thm)],[c_20120]) ).
tcf(c_20132,plain,
! [X0: $i,X1: $i] :
( in(sK71(X0,X1),sK70(X0))
| ~ sP6
| ~ in(X1,sK70(X0))
| ( X0 != sK66 ) ),
inference(resolution_lifted,[status(thm)],[c_2544,c_152]) ).
tcf(c_20133,plain,
! [X0: $i] :
( in(sK71(sK66,X0),sK70(sK66))
| ~ sP6
| ~ in(X0,sK70(sK66)) ),
inference(unflattening,[status(thm)],[c_20132]) ).
tcf(c_20157,plain,
! [X0: $i] :
( element(sK112(X0),powerset(powerset(X0)))
| ~ sP15
| ( X0 != sK110 ) ),
inference(resolution_lifted,[status(thm)],[c_2648,c_2658]) ).
tcf(c_20158,plain,
( element(sK112(sK110),powerset(powerset(sK110)))
| ~ sP15 ),
inference(unflattening,[status(thm)],[c_20157]) ).
tcf(c_20165,plain,
! [X0: $i,X1: $i] :
( ~ sP15
| ~ in(X1,sK112(X0))
| ( X0 != sK110 )
| ( sK113(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_2648,c_243]) ).
tcf(c_20166,plain,
! [X0: $i] :
( ~ sP15
| ~ in(X0,sK112(sK110))
| ( sK113(sK110,X0) != X0 ) ),
inference(unflattening,[status(thm)],[c_20165]) ).
tcf(c_20177,plain,
! [X0: $i] :
( ~ sP15
| ( X0 != sK110 )
| ( sK112(X0) != sK140 ) ),
inference(resolution_lifted,[status(thm)],[c_2648,c_2654]) ).
tcf(c_20178,plain,
( ~ sP15
| ( sK112(sK110) != sK140 ) ),
inference(unflattening,[status(thm)],[c_20177]) ).
tcf(c_20185,plain,
! [X0: $i,X1: $i] :
( subset(X1,sK113(X0,X1))
| ~ sP15
| ~ in(X1,sK112(X0))
| ( X0 != sK110 ) ),
inference(resolution_lifted,[status(thm)],[c_2648,c_245]) ).
tcf(c_20186,plain,
! [X0: $i] :
( subset(X0,sK113(sK110,X0))
| ~ sP15
| ~ in(X0,sK112(sK110)) ),
inference(unflattening,[status(thm)],[c_20185]) ).
tcf(c_20197,plain,
! [X0: $i,X1: $i] :
( in(sK113(X0,X1),sK112(X0))
| ~ sP15
| ~ in(X1,sK112(X0))
| ( X0 != sK110 ) ),
inference(resolution_lifted,[status(thm)],[c_2648,c_244]) ).
tcf(c_20198,plain,
! [X0: $i] :
( in(sK113(sK110,X0),sK112(sK110))
| ~ sP15
| ~ in(X0,sK112(sK110)) ),
inference(unflattening,[status(thm)],[c_20197]) ).
tcf(c_20459,plain,
! [X0: $i,X1: $i] :
( sP32(X1)
| ( sK256(X0) = X0 )
| ~ ordinal(X1)
| ( X0 != sK260 ) ),
inference(resolution_lifted,[status(thm)],[c_2960,c_838]) ).
tcf(c_20460,plain,
! [X0: $i] :
( sP32(X0)
| ( sK256(sK260) = sK260 )
| ~ ordinal(X0) ),
inference(unflattening,[status(thm)],[c_20459]) ).
tcf(c_20471,plain,
! [X0: $i,X1: $i] :
( sP32(X1)
| ordinal(sK256(X0))
| ~ ordinal(X1)
| ( X0 != sK260 ) ),
inference(resolution_lifted,[status(thm)],[c_2958,c_838]) ).
tcf(c_20472,plain,
! [X0: $i] :
( sP32(X0)
| ordinal(sK256(sK260))
| ~ ordinal(X0) ),
inference(unflattening,[status(thm)],[c_20471]) ).
tcf(c_20483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP32(X3)
| ( X1 = sK140 )
| ( sK257(X1) = X2 )
| ~ ordinal(X3)
| ~ in(X2,X1)
| ~ in(sK256(X0),omega)
| ~ subset(sK257(X1),X2)
| ~ element(X1,powerset(powerset(sK256(X0))))
| ( X0 != sK260 ) ),
inference(resolution_lifted,[status(thm)],[c_830,c_838]) ).
tcf(c_20484,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP32(X2)
| ( X0 = sK140 )
| ( sK257(X0) = X1 )
| ~ ordinal(X2)
| ~ in(X1,X0)
| ~ in(sK256(sK260),omega)
| ~ subset(sK257(X0),X1)
| ~ element(X0,powerset(powerset(sK256(sK260)))) ),
inference(unflattening,[status(thm)],[c_20483]) ).
tcf(c_20509,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP32(X2)
| in(sK257(X1),X1)
| ( X1 = sK140 )
| ~ ordinal(X2)
| ~ in(sK256(X0),omega)
| ~ element(X1,powerset(powerset(sK256(X0))))
| ( X0 != sK260 ) ),
inference(resolution_lifted,[status(thm)],[c_829,c_838]) ).
tcf(c_20510,plain,
! [X0: $i,X1: $i] :
( sP32(X1)
| in(sK257(X0),X0)
| ( X0 = sK140 )
| ~ ordinal(X1)
| ~ in(sK256(sK260),omega)
| ~ element(X0,powerset(powerset(sK256(sK260)))) ),
inference(unflattening,[status(thm)],[c_20509]) ).
tcf(c_84286,plain,
( element(sK70(sK66),powerset(powerset(sK66)))
| ~ sP6 ),
inference(prop_impl_just,[status(thm)],[c_20093]) ).
tcf(c_84288,plain,
( ( sK70(sK66) != sK140 )
| ~ sP6 ),
inference(prop_impl_just,[status(thm)],[c_20113]) ).
tcf(c_84289,plain,
( ~ sP6
| ( sK70(sK66) != sK140 ) ),
inference(renaming,[status(thm)],[c_84288]) ).
tcf(c_84376,plain,
( element(sK112(sK110),powerset(powerset(sK110)))
| ~ sP15 ),
inference(prop_impl_just,[status(thm)],[c_20158]) ).
tcf(c_84378,plain,
( ( sK112(sK110) != sK140 )
| ~ sP15 ),
inference(prop_impl_just,[status(thm)],[c_20178]) ).
tcf(c_84379,plain,
( ~ sP15
| ( sK112(sK110) != sK140 ) ),
inference(renaming,[status(thm)],[c_84378]) ).
tcf(c_84502,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(sK175(sK172(X0),X0),sK175(sK172(X0),X0)),unordered_pair(sK175(sK172(X0),X0),sK176(sK172(X0),X0))) = sK172(X0) )
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_19663]) ).
tcf(c_84504,plain,
! [X0: $i] :
( ( unordered_pair(sK175(sK172(X0),X0),sK175(sK172(X0),X0)) = sK176(sK172(X0),X0) )
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_19672]) ).
tcf(c_84506,plain,
! [X0: $i] :
( in(sK175(sK172(X0),X0),X0)
| ~ sP20(X0) ),
inference(prop_impl_just,[status(thm)],[c_19681]) ).
tcf(c_84552,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK211(X0,X1),sK211(X0,X1)),unordered_pair(sK211(X0,X1),sK212(X0,X1))) = sK208(X0,X1) )
| ~ sP24(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_17216]) ).
tcf(c_84554,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(unordered_pair(sK209(X0,X1),sK209(X0,X1)),unordered_pair(sK209(X0,X1),sK210(X0,X1))) = sK207(X0,X1) )
| ~ sP24(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_17223]) ).
tcf(c_84556,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK211(X0,X1))),unordered_pair(apply(X1,sK211(X0,X1)),apply(X1,sK212(X0,X1)))),X0)
| ~ sP24(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_17985]) ).
tcf(c_84558,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK209(X0,X1))),unordered_pair(apply(X1,sK209(X0,X1)),apply(X1,sK210(X0,X1)))),X0)
| ~ sP24(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_17992]) ).
tcf(c_84586,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK226(X0,X1,X2),sK226(X0,X1,X2)),unordered_pair(sK226(X0,X1,X2),sK227(X0,X1,X2))) = X0 )
| ~ sP25(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_17699]) ).
tcf(c_84636,plain,
! [X0: $i] :
( in(sK269(sK267(X0),X0),X0)
| ~ sP34(X0) ),
inference(prop_impl_just,[status(thm)],[c_19696]) ).
tcf(c_84638,plain,
! [X0: $i] :
( ( sK269(sK267(X0),X0) = sK267(X0) )
| ~ sP34(X0) ),
inference(prop_impl_just,[status(thm)],[c_19705]) ).
tcf(c_84640,plain,
! [X0: $i] :
( ordinal(sK269(sK267(X0),X0))
| ~ sP34(X0) ),
inference(prop_impl_just,[status(thm)],[c_19714]) ).
tcf(c_123582,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ ordinal(X0)
| sP32(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_20510]) ).
tcf(c_123583,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( X0 = sK140 )
| in(sK257(X0),X0)
| ~ element(X0,powerset(powerset(sK256(sK260)))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_20510]) ).
tcf(c_123584,plain,
( iPr_def_11
| iPr_def_10
| ~ in(sK256(sK260),omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_20510]) ).
tcf(c_123585,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_12
| ( sK257(X0) = X1 )
| ( X0 = sK140 )
| ~ in(X1,X0)
| ~ subset(sK257(X0),X1)
| ~ element(X0,powerset(powerset(sK256(sK260)))) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_20484]) ).
tcf(c_123586,plain,
( iPr_def_12
| iPr_def_10
| ~ in(sK256(sK260),omega) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_20484]) ).
tcf(c_145291,plain,
( sP32(sK62)
| ~ iPr_def_10
| ~ sP8 ),
inference(superposition,[status(thm)],[c_131,c_123582]) ).
tcf(c_145292,plain,
( sP32(sK66)
| ~ iPr_def_10
| ~ sP6 ),
inference(superposition,[status(thm)],[c_144,c_123582]) ).
tcf(c_145293,plain,
( sP32(sK110)
| ~ iPr_def_10
| ~ sP15 ),
inference(superposition,[status(thm)],[c_241,c_123582]) ).
tcf(c_145294,plain,
( sP32(omega)
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_849,c_123582]) ).
tcf(c_145295,plain,
( sP32(sK281)
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_895,c_123582]) ).
tcf(c_145296,plain,
( sP32(sK313)
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_1028,c_123582]) ).
tcf(c_145297,plain,
( sP32(sK315)
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_1038,c_123582]) ).
tcf(c_145298,plain,
( sP32(sK346)
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_1226,c_123582]) ).
tcf(c_145299,plain,
( sP32(sK140)
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_144282,c_123582]) ).
tcf(c_145366,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK199(powerset(powerset(sK85(X0)))) = sK140 )
| ( sK86(sK199(powerset(powerset(sK85(X0))))) = X1 )
| ~ sP9(X2,X0)
| ~ in(sK85(X0),omega)
| ~ in(X1,sK199(powerset(powerset(sK85(X0)))))
| ~ subset(sK86(sK199(powerset(powerset(sK85(X0))))),X1) ),
inference(superposition,[status(thm)],[c_696,c_187]) ).
tcf(c_145367,plain,
! [X0: $i,X1: $i] :
( in(sK86(sK199(powerset(powerset(sK85(X0))))),sK199(powerset(powerset(sK85(X0)))))
| ( sK199(powerset(powerset(sK85(X0)))) = sK140 )
| ~ sP9(X1,X0)
| ~ in(sK85(X0),omega) ),
inference(superposition,[status(thm)],[c_696,c_186]) ).
tcf(c_145488,plain,
( sP32(sK246)
| ~ iPr_def_10
| ~ sP29 ),
inference(superposition,[status(thm)],[c_802,c_123582]) ).
tcf(c_145496,plain,
( sP32(sK247)
| ~ iPr_def_10
| ~ sP29 ),
inference(superposition,[status(thm)],[c_804,c_123582]) ).
tcf(c_145573,plain,
! [X0: $i] :
( sP32(sK128(X0))
| ( X0 = sK140 )
| ~ iPr_def_10
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_144621,c_123582]) ).
tcf(c_145636,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(sK85(X0)) = sK140 )
| ( sK86(powerset(sK85(X0))) = X1 )
| ~ sP9(X2,X0)
| ~ in(sK85(X0),omega)
| ~ in(X1,powerset(sK85(X0)))
| ~ subset(sK86(powerset(sK85(X0))),X1) ),
inference(superposition,[status(thm)],[c_12479,c_187]) ).
tcf(c_145637,plain,
! [X0: $i,X1: $i] :
( in(sK86(powerset(sK85(X0))),powerset(sK85(X0)))
| ( powerset(sK85(X0)) = sK140 )
| ~ sP9(X1,X0)
| ~ in(sK85(X0),omega) ),
inference(superposition,[status(thm)],[c_12479,c_186]) ).
tcf(c_146324,plain,
! [X0: $i,X1: $i] :
( sP32(sK128(set_difference(X0,X1)))
| ( set_difference(X0,X1) = sK140 )
| ~ iPr_def_10
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_146009,c_123582]) ).
tcf(c_146403,plain,
( epsilon_transitive(sK246)
| ~ sP29 ),
inference(superposition,[status(thm)],[c_802,c_1049]) ).
tcf(c_146404,plain,
( epsilon_transitive(sK247)
| ~ sP29 ),
inference(superposition,[status(thm)],[c_804,c_1049]) ).
tcf(c_146465,plain,
! [X0: $i] :
( sP32(X0)
| ( sK125(X0) = sK140 )
| ( relation_dom(sK126(X0)) = X0 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_146389,c_123582]) ).
tcf(c_146586,plain,
( epsilon_connected(sK246)
| ~ sP29 ),
inference(superposition,[status(thm)],[c_802,c_1050]) ).
tcf(c_146587,plain,
( epsilon_connected(sK247)
| ~ sP29 ),
inference(superposition,[status(thm)],[c_804,c_1050]) ).
tcf(c_146855,plain,
( in(sK257(sK199(powerset(powerset(sK256(sK260))))),sK199(powerset(powerset(sK256(sK260)))))
| ( sK199(powerset(powerset(sK256(sK260)))) = sK140 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_696,c_123583]) ).
tcf(c_146856,plain,
( in(sK257(powerset(sK256(sK260))),powerset(sK256(sK260)))
| ( powerset(sK256(sK260)) = sK140 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_12479,c_123583]) ).
tcf(c_146874,plain,
( sP32(sK263(sK116(sK140)))
| ( sK116(sK140) = omega )
| ~ iPr_def_10
| ~ being_limit_ordinal(sK116(sK140))
| ~ ordinal(sK116(sK140)) ),
inference(superposition,[status(thm)],[c_145173,c_123582]) ).
tcf(c_146906,plain,
( sP32(sK263(sK300(sK140)))
| ( sK300(sK140) = omega )
| ~ iPr_def_10
| ~ being_limit_ordinal(sK300(sK140))
| ~ ordinal(sK300(sK140)) ),
inference(superposition,[status(thm)],[c_145501,c_123582]) ).
tcf(c_147010,plain,
( sP32(sK263(powerset(sK140)))
| ( powerset(sK140) = omega )
| ~ iPr_def_10
| ~ being_limit_ordinal(powerset(sK140))
| ~ ordinal(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_146193,c_123582]) ).
tcf(c_147084,plain,
! [X0: $i] :
( ( sK125(relation_dom(sK57(X0))) = sK140 )
| ( apply(sK57(X0),sK140) = sK140 )
| ~ sP3(X0)
| ~ relation(sK57(X0)) ),
inference(superposition,[status(thm)],[c_114,c_145538]) ).
tcf(c_147304,plain,
! [X0: $i] :
( sP32(union(X0))
| ~ iPr_def_10
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_712,c_123582]) ).
tcf(c_147644,plain,
! [X0: $i] :
( sP32(sK268(X0))
| ~ iPr_def_10
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_862,c_123582]) ).
tcf(c_147701,plain,
( sP32(sK199(omega))
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_147637,c_123582]) ).
tcf(c_148489,plain,
! [X0: $i] :
( ordinal(sK105(sK92(X0)))
| ~ sP13(sK92(X0)) ),
inference(superposition,[status(thm)],[c_226,c_199]) ).
tcf(c_148490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK105(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ sP13(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_226,c_425]) ).
tcf(c_148491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK105(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ sP13(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_226,c_424]) ).
tcf(c_148492,plain,
~ sP13(sK140),
inference(superposition,[status(thm)],[c_226,c_580]) ).
tcf(c_148548,plain,
! [X0: $i] :
( element(sK105(X0),X0)
| ~ sP13(X0) ),
inference(superposition,[status(thm)],[c_226,c_526]) ).
tcf(c_148735,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( powerset(powerset(sK85(X0))) = sK140 )
| ( sK169(powerset(powerset(sK85(X0)))) = sK140 )
| ( sK86(sK169(powerset(powerset(sK85(X0))))) = X1 )
| ~ sP9(X2,X0)
| ~ in(sK85(X0),omega)
| ~ in(X1,sK169(powerset(powerset(sK85(X0)))))
| ~ subset(sK86(sK169(powerset(powerset(sK85(X0))))),X1) ),
inference(superposition,[status(thm)],[c_148558,c_187]) ).
tcf(c_148736,plain,
! [X0: $i,X1: $i] :
( in(sK86(sK169(powerset(powerset(sK85(X0))))),sK169(powerset(powerset(sK85(X0)))))
| ( powerset(powerset(sK85(X0))) = sK140 )
| ( sK169(powerset(powerset(sK85(X0)))) = sK140 )
| ~ sP9(X1,X0)
| ~ in(sK85(X0),omega) ),
inference(superposition,[status(thm)],[c_148558,c_186]) ).
tcf(c_148744,plain,
( in(sK257(sK169(powerset(powerset(sK256(sK260))))),sK169(powerset(powerset(sK256(sK260)))))
| ( powerset(powerset(sK256(sK260))) = sK140 )
| ( sK169(powerset(powerset(sK256(sK260)))) = sK140 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_148558,c_123583]) ).
tcf(c_148891,plain,
! [X0: $i] :
( sP32(sK169(sK92(X0)))
| ( sK92(X0) = sK140 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_148434,c_123582]) ).
tcf(c_148920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(sK85(X1)))) = sK140 )
| ( sK86(apply(sK126(X0),powerset(powerset(sK85(X1))))) = X2 )
| ~ sP9(X3,X1)
| ~ in(sK85(X1),omega)
| ~ in(powerset(powerset(sK85(X1))),X0)
| ~ in(X2,apply(sK126(X0),powerset(powerset(sK85(X1)))))
| ~ subset(sK86(apply(sK126(X0),powerset(powerset(sK85(X1))))),X2) ),
inference(superposition,[status(thm)],[c_148553,c_187]) ).
tcf(c_148921,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK86(apply(sK126(X1),powerset(powerset(sK85(X0))))),apply(sK126(X1),powerset(powerset(sK85(X0)))))
| ( sK125(X1) = sK140 )
| ( apply(sK126(X1),powerset(powerset(sK85(X0)))) = sK140 )
| ~ sP9(X2,X0)
| ~ in(sK85(X0),omega)
| ~ in(powerset(powerset(sK85(X0))),X1) ),
inference(superposition,[status(thm)],[c_148553,c_186]) ).
tcf(c_148929,plain,
! [X0: $i] :
( in(sK257(apply(sK126(X0),powerset(powerset(sK256(sK260))))),apply(sK126(X0),powerset(powerset(sK256(sK260)))))
| ( sK125(X0) = sK140 )
| ( apply(sK126(X0),powerset(powerset(sK256(sK260)))) = sK140 )
| ~ iPr_def_11
| ~ in(powerset(powerset(sK256(sK260))),X0) ),
inference(superposition,[status(thm)],[c_148553,c_123583]) ).
tcf(c_149106,plain,
! [X0: $i,X1: $i] :
( sP32(apply(sK126(X1),sK92(X0)))
| ( sK125(X1) = sK140 )
| ~ iPr_def_10
| ~ in(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_148430,c_123582]) ).
tcf(c_149313,plain,
! [X0: $i] :
( element(sK181(X0),X0)
| ~ sP21(X0) ),
inference(superposition,[status(thm)],[c_600,c_526]) ).
tcf(c_149314,plain,
! [X0: $i] :
( ordinal(sK181(sK92(X0)))
| ~ sP21(sK92(X0)) ),
inference(superposition,[status(thm)],[c_600,c_199]) ).
tcf(c_149315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(apply(X0,sK181(relation_inverse_image(X0,X3))),X3)
| ( X2 = sK140 )
| ~ function(X0)
| ~ sP21(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_600,c_425]) ).
tcf(c_149316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK181(relation_inverse_image(X0,X3)),X1)
| ( X2 = sK140 )
| ~ function(X0)
| ~ sP21(relation_inverse_image(X0,X3))
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_600,c_424]) ).
tcf(c_149317,plain,
~ sP21(sK140),
inference(superposition,[status(thm)],[c_600,c_580]) ).
tcf(c_149688,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(sK85(X0)))
| ( sK198(powerset(sK85(X0))) = sK140 )
| ( sK86(sK198(powerset(sK85(X0)))) = X1 )
| ~ sP9(X2,X0)
| ~ in(sK85(X0),omega)
| ~ in(X1,sK198(powerset(sK85(X0))))
| ~ subset(sK86(sK198(powerset(sK85(X0)))),X1) ),
inference(superposition,[status(thm)],[c_693,c_187]) ).
tcf(c_149689,plain,
! [X0: $i,X1: $i] :
( empty(powerset(sK85(X0)))
| in(sK86(sK198(powerset(sK85(X0)))),sK198(powerset(sK85(X0))))
| ( sK198(powerset(sK85(X0))) = sK140 )
| ~ sP9(X1,X0)
| ~ in(sK85(X0),omega) ),
inference(superposition,[status(thm)],[c_693,c_186]) ).
tcf(c_149694,plain,
( empty(powerset(sK256(sK260)))
| in(sK257(sK198(powerset(sK256(sK260)))),sK198(powerset(sK256(sK260))))
| ( sK198(powerset(sK256(sK260))) = sK140 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_693,c_123583]) ).
tcf(c_149707,plain,
( in(sK257(sK198(powerset(sK256(sK260)))),sK198(powerset(sK256(sK260))))
| ( sK198(powerset(sK256(sK260))) = sK140 )
| ~ iPr_def_11 ),
inference(forward_subsumption_resolution,[status(thm)],[c_149694,c_695]) ).
tcf(c_149728,plain,
! [X0: $i,X1: $i] :
( in(sK86(sK198(powerset(sK85(X0)))),sK198(powerset(sK85(X0))))
| ( sK198(powerset(sK85(X0))) = sK140 )
| ~ sP9(X1,X0)
| ~ in(sK85(X0),omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149689,c_695]) ).
tcf(c_149806,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK198(powerset(sK85(X0))) = sK140 )
| ( sK86(sK198(powerset(sK85(X0)))) = X1 )
| ~ sP9(X2,X0)
| ~ in(sK85(X0),omega)
| ~ in(X1,sK198(powerset(sK85(X0))))
| ~ subset(sK86(sK198(powerset(sK85(X0)))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_149688,c_695]) ).
tcf(c_149880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( powerset(powerset(sK85(X1))) = sK140 )
| ( sK320(X0,powerset(powerset(sK85(X1)))) = sK140 )
| ( sK86(sK320(X0,powerset(powerset(sK85(X1))))) = X2 )
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ sP9(X3,X1)
| ~ in(sK85(X1),omega)
| ~ subset(powerset(powerset(sK85(X1))),relation_field(X0))
| ~ in(X2,sK320(X0,powerset(powerset(sK85(X1)))))
| ~ subset(sK86(sK320(X0,powerset(powerset(sK85(X1))))),X2) ),
inference(superposition,[status(thm)],[c_148564,c_187]) ).
tcf(c_149881,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK86(sK320(X1,powerset(powerset(sK85(X0))))),sK320(X1,powerset(powerset(sK85(X0)))))
| ( powerset(powerset(sK85(X0))) = sK140 )
| ( sK320(X1,powerset(powerset(sK85(X0)))) = sK140 )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ sP9(X2,X0)
| ~ in(sK85(X0),omega)
| ~ subset(powerset(powerset(sK85(X0))),relation_field(X1)) ),
inference(superposition,[status(thm)],[c_148564,c_186]) ).
tcf(c_149889,plain,
! [X0: $i] :
( in(sK257(sK320(X0,powerset(powerset(sK256(sK260))))),sK320(X0,powerset(powerset(sK256(sK260)))))
| ( powerset(powerset(sK256(sK260))) = sK140 )
| ( sK320(X0,powerset(powerset(sK256(sK260)))) = sK140 )
| ~ iPr_def_11
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ subset(powerset(powerset(sK256(sK260))),relation_field(X0)) ),
inference(superposition,[status(thm)],[c_148564,c_123583]) ).
tcf(c_150142,plain,
! [X0: $i] :
( sP32(sK263(unordered_pair(sK140,X0)))
| ( unordered_pair(sK140,X0) = omega )
| ~ iPr_def_10
| ~ being_limit_ordinal(unordered_pair(sK140,X0))
| ~ ordinal(unordered_pair(sK140,X0)) ),
inference(superposition,[status(thm)],[c_146168,c_123582]) ).
tcf(c_150181,plain,
! [X0: $i] :
( sP32(sK263(unordered_pair(X0,sK140)))
| ( unordered_pair(X0,sK140) = omega )
| ~ iPr_def_10
| ~ being_limit_ordinal(unordered_pair(X0,sK140))
| ~ ordinal(unordered_pair(X0,sK140)) ),
inference(superposition,[status(thm)],[c_146210,c_123582]) ).
tcf(c_150225,plain,
! [X0: $i] :
( ~ sP13(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_226,c_787]) ).
tcf(c_150237,plain,
! [X0: $i] :
( ~ sP21(X0)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_600,c_787]) ).
tcf(c_150341,plain,
( sP32(sK246)
| ordinal(sK261)
| ~ sP29 ),
inference(superposition,[status(thm)],[c_802,c_833]) ).
tcf(c_150342,plain,
( sP32(sK247)
| ordinal(sK261)
| ~ sP29 ),
inference(superposition,[status(thm)],[c_804,c_833]) ).
tcf(c_150498,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ~ sP13(X0)
| ~ empty(sK105(X0)) ),
inference(superposition,[status(thm)],[c_226,c_150230]) ).
tcf(c_150510,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ~ sP21(X0)
| ~ empty(sK181(X0)) ),
inference(superposition,[status(thm)],[c_600,c_150230]) ).
tcf(c_151210,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(powerset(sK85(X0)))
| ( sK302(powerset(sK85(X0))) = sK140 )
| ( sK86(sK302(powerset(sK85(X0)))) = X1 )
| ~ sP9(X2,X0)
| ~ in(sK85(X0),omega)
| ~ in(X1,sK302(powerset(sK85(X0))))
| ~ subset(sK86(sK302(powerset(sK85(X0)))),X1) ),
inference(superposition,[status(thm)],[c_972,c_187]) ).
tcf(c_151211,plain,
! [X0: $i,X1: $i] :
( empty(powerset(sK85(X0)))
| in(sK86(sK302(powerset(sK85(X0)))),sK302(powerset(sK85(X0))))
| ( sK302(powerset(sK85(X0))) = sK140 )
| ~ sP9(X1,X0)
| ~ in(sK85(X0),omega) ),
inference(superposition,[status(thm)],[c_972,c_186]) ).
tcf(c_151216,plain,
( empty(powerset(sK256(sK260)))
| in(sK257(sK302(powerset(sK256(sK260)))),sK302(powerset(sK256(sK260))))
| ( sK302(powerset(sK256(sK260))) = sK140 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_972,c_123583]) ).
tcf(c_151229,plain,
( in(sK257(sK302(powerset(sK256(sK260)))),sK302(powerset(sK256(sK260))))
| ( sK302(powerset(sK256(sK260))) = sK140 )
| ~ iPr_def_11 ),
inference(forward_subsumption_resolution,[status(thm)],[c_151216,c_695]) ).
tcf(c_151250,plain,
! [X0: $i,X1: $i] :
( in(sK86(sK302(powerset(sK85(X0)))),sK302(powerset(sK85(X0))))
| ( sK302(powerset(sK85(X0))) = sK140 )
| ~ sP9(X1,X0)
| ~ in(sK85(X0),omega) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151211,c_695]) ).
tcf(c_151328,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK302(powerset(sK85(X0))) = sK140 )
| ( sK86(sK302(powerset(sK85(X0)))) = X1 )
| ~ sP9(X2,X0)
| ~ in(sK85(X0),omega)
| ~ in(X1,sK302(powerset(sK85(X0))))
| ~ subset(sK86(sK302(powerset(sK85(X0)))),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_151210,c_695]) ).
tcf(c_151514,plain,
! [X0: $i,X1: $i] :
( ( sK125(relation_dom(sK57(X0))) = sK140 )
| ( apply(sK57(X0),X1) = sK140 )
| ~ sP3(X0)
| ~ empty(X1)
| ~ relation(sK57(X0)) ),
inference(superposition,[status(thm)],[c_114,c_150502]) ).
tcf(c_151773,plain,
! [X0: $i] :
( in(sK105(sK92(X0)),X0)
| ~ sP13(sK92(X0)) ),
inference(superposition,[status(thm)],[c_226,c_198]) ).
tcf(c_151780,plain,
! [X0: $i] :
( in(sK181(sK92(X0)),X0)
| ~ sP21(sK92(X0)) ),
inference(superposition,[status(thm)],[c_600,c_198]) ).
tcf(c_152043,plain,
( iPr_def_12
| iPr_def_10
| ( set_difference(unordered_pair(sK256(sK260),sK256(sK260)),set_difference(unordered_pair(sK256(sK260),sK256(sK260)),omega)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_123586]) ).
tcf(c_152044,plain,
( iPr_def_11
| iPr_def_10
| ( set_difference(unordered_pair(sK256(sK260),sK256(sK260)),set_difference(unordered_pair(sK256(sK260),sK256(sK260)),omega)) = sK140 ) ),
inference(superposition,[status(thm)],[c_151758,c_123584]) ).
tcf(c_152207,plain,
relation_dom(sK108(sK140)) = sK140,
inference(superposition,[status(thm)],[c_234,c_148492]) ).
tcf(c_152383,plain,
! [X0: $i] :
( sP32(relation_dom(X0))
| ~ iPr_def_10
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_147190,c_123582]) ).
tcf(c_152605,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng_restriction(X1,sK57(X0)),sK57(X0)) = sK140 )
| ~ sP3(X0) ),
inference(superposition,[status(thm)],[c_113,c_152219]) ).
tcf(c_152996,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| sP32(sK131(X0))
| ~ iPr_def_10
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_407,c_123582]) ).
tcf(c_153024,plain,
! [X0: $i] :
( being_limit_ordinal(X0)
| sP32(sK132(X0))
| ~ iPr_def_10
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_410,c_123582]) ).
tcf(c_153816,plain,
! [X0: $i,X1: $i] :
( sP32(sK128(relation_rng_restriction(X1,X0)))
| ( relation_rng_restriction(X1,X0) = sK140 )
| ~ iPr_def_10
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_152218,c_123582]) ).
tcf(c_154126,plain,
! [X0: $i] :
( in(sK142(X0),X0)
| ~ sP13(X0) ),
inference(superposition,[status(thm)],[c_226,c_522]) ).
tcf(c_154140,plain,
! [X0: $i] :
( in(sK142(X0),X0)
| ~ sP21(X0) ),
inference(superposition,[status(thm)],[c_600,c_522]) ).
tcf(c_154347,plain,
( sP32(sK142(omega))
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_154341,c_123582]) ).
tcf(c_154395,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_dom_restriction(sK57(X0),X1),sK57(X0)) = sK140 )
| ~ sP3(X0) ),
inference(superposition,[status(thm)],[c_113,c_153993]) ).
tcf(c_154504,plain,
! [X0: $i] :
( ( set_difference(sK105(X0),union(X0)) = sK140 )
| ~ sP13(X0) ),
inference(superposition,[status(thm)],[c_226,c_154065]) ).
tcf(c_154518,plain,
! [X0: $i] :
( ( set_difference(sK181(X0),union(X0)) = sK140 )
| ~ sP21(X0) ),
inference(superposition,[status(thm)],[c_600,c_154065]) ).
tcf(c_154894,plain,
! [X0: $i] :
( in(sK142(sK105(X0)),sK105(X0))
| ( sK125(X0) = sK140 )
| ~ sP13(X0) ),
inference(superposition,[status(thm)],[c_226,c_154131]) ).
tcf(c_154908,plain,
! [X0: $i] :
( in(sK142(sK181(X0)),sK181(X0))
| ( sK125(X0) = sK140 )
| ~ sP21(X0) ),
inference(superposition,[status(thm)],[c_600,c_154131]) ).
tcf(c_155167,plain,
! [X0: $i] :
( ordinal(sK128(sK105(X0)))
| ( sK105(X0) = sK140 )
| ~ sP13(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_226,c_154064]) ).
tcf(c_155181,plain,
! [X0: $i] :
( ordinal(sK128(sK181(X0)))
| ( sK181(X0) = sK140 )
| ~ sP21(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_600,c_154064]) ).
tcf(c_155596,plain,
! [X0: $i] :
( ~ sP13(X0)
| ~ in(X0,sK105(X0)) ),
inference(superposition,[status(thm)],[c_226,c_527]) ).
tcf(c_155610,plain,
! [X0: $i] :
( ~ sP21(X0)
| ~ in(X0,sK181(X0)) ),
inference(superposition,[status(thm)],[c_600,c_527]) ).
tcf(c_155845,plain,
! [X0: $i] :
( reflexive(sK57(X0))
| ~ sP3(X0)
| ~ well_ordering(sK57(X0)) ),
inference(superposition,[status(thm)],[c_113,c_570]) ).
tcf(c_155981,plain,
! [X0: $i] :
( transitive(sK57(X0))
| ~ sP3(X0)
| ~ well_ordering(sK57(X0)) ),
inference(superposition,[status(thm)],[c_113,c_571]) ).
tcf(c_156135,plain,
! [X0: $i] :
( antisymmetric(sK57(X0))
| ~ sP3(X0)
| ~ well_ordering(sK57(X0)) ),
inference(superposition,[status(thm)],[c_113,c_572]) ).
tcf(c_156447,plain,
! [X0: $i] :
( connected(sK57(X0))
| ~ sP3(X0)
| ~ well_ordering(sK57(X0)) ),
inference(superposition,[status(thm)],[c_113,c_573]) ).
tcf(c_156598,plain,
! [X0: $i] :
( well_founded_relation(sK57(X0))
| ~ sP3(X0)
| ~ well_ordering(sK57(X0)) ),
inference(superposition,[status(thm)],[c_113,c_574]) ).
tcf(c_156798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = sK140 )
| ( sK86(X0) = X2 )
| ~ sP9(X3,X1)
| ~ in(X2,X0)
| ~ in(sK85(X1),omega)
| ~ subset(sK86(X0),X2)
| ~ subset(X0,powerset(sK85(X1))) ),
inference(superposition,[status(thm)],[c_653,c_187]) ).
tcf(c_156799,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK86(X0),X0)
| ( X0 = sK140 )
| ~ sP9(X2,X1)
| ~ in(sK85(X1),omega)
| ~ subset(X0,powerset(sK85(X1))) ),
inference(superposition,[status(thm)],[c_653,c_186]) ).
tcf(c_156804,plain,
! [X0: $i] :
( in(sK257(X0),X0)
| ( X0 = sK140 )
| ~ iPr_def_11
| ~ subset(X0,powerset(sK256(sK260))) ),
inference(superposition,[status(thm)],[c_653,c_123583]) ).
tcf(c_157056,plain,
! [X0: $i] :
( ( apply(sK57(X0),sK116(relation_dom(sK57(X0)))) = sK140 )
| ~ sP3(X0)
| ~ relation(sK57(X0)) ),
inference(superposition,[status(thm)],[c_114,c_156955]) ).
tcf(c_157139,plain,
! [X0: $i] :
( ( apply(sK57(X0),sK300(relation_dom(sK57(X0)))) = sK140 )
| ~ sP3(X0)
| ~ relation(sK57(X0)) ),
inference(superposition,[status(thm)],[c_114,c_156990]) ).
tcf(c_157502,plain,
! [X0: $i] :
( subset(sK105(powerset(X0)),X0)
| ~ sP13(powerset(X0)) ),
inference(superposition,[status(thm)],[c_226,c_662]) ).
tcf(c_157511,plain,
! [X0: $i] :
( subset(sK181(powerset(X0)),X0)
| ~ sP21(powerset(X0)) ),
inference(superposition,[status(thm)],[c_600,c_662]) ).
tcf(c_158105,plain,
! [X0: $i] :
( sP29
| ordinal(sK105(sK248(X0)))
| ~ sP13(sK248(X0)) ),
inference(superposition,[status(thm)],[c_226,c_808]) ).
tcf(c_158114,plain,
! [X0: $i] :
( sP29
| ordinal(sK181(sK248(X0)))
| ~ sP21(sK248(X0)) ),
inference(superposition,[status(thm)],[c_600,c_808]) ).
tcf(c_158281,plain,
! [X0: $i] :
( sP29
| sP32(sK169(sK248(X0)))
| ( sK248(X0) = sK140 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_158112,c_123582]) ).
tcf(c_158318,plain,
! [X0: $i] :
( in(sK128(sK105(X0)),sK105(X0))
| ( sK105(X0) = sK140 )
| ~ sP13(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_226,c_154063]) ).
tcf(c_158332,plain,
! [X0: $i] :
( in(sK128(sK181(X0)),sK181(X0))
| ( sK181(X0) = sK140 )
| ~ sP21(X0)
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_600,c_154063]) ).
tcf(c_159006,plain,
! [X0: $i,X1: $i] :
( sP32(sK128(relation_dom_restriction(X0,X1)))
| ( relation_dom_restriction(X0,X1) = sK140 )
| ~ iPr_def_10
| ~ ordinal(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_153992,c_123582]) ).
tcf(c_159478,plain,
! [X0: $i] :
( sP32(sK128(sK169(X0)))
| ( X0 = sK140 )
| ( sK169(X0) = sK140 )
| ~ iPr_def_10
| ~ ordinal(union(X0)) ),
inference(superposition,[status(thm)],[c_154847,c_123582]) ).
tcf(c_159823,plain,
! [X0: $i] :
( sP32(sK263(powerset(X0)))
| ( powerset(X0) = omega )
| ~ iPr_def_10
| ~ being_limit_ordinal(powerset(X0))
| ~ ordinal(powerset(X0)) ),
inference(superposition,[status(thm)],[c_157475,c_123582]) ).
tcf(c_159853,plain,
! [X0: $i,X1: $i] :
( sP29
| sP32(apply(sK126(X1),sK248(X0)))
| ( sK125(X1) = sK140 )
| ~ iPr_def_10
| ~ in(sK248(X0),X1) ),
inference(superposition,[status(thm)],[c_158106,c_123582]) ).
tcf(c_159971,plain,
( subset(sK70(sK66),powerset(sK66))
| ~ sP6 ),
inference(superposition,[status(thm)],[c_84286,c_654]) ).
tcf(c_159972,plain,
! [X0: $i] :
( ( sK70(sK66) = sK140 )
| ( sK111(sK70(sK66)) = X0 )
| ~ sP15
| ~ sP6
| ~ ordinal(sK66)
| ~ in(sK66,sK110)
| ~ in(sK66,omega)
| ~ in(X0,sK70(sK66))
| ~ subset(sK111(sK70(sK66)),X0) ),
inference(superposition,[status(thm)],[c_84286,c_240]) ).
tcf(c_159973,plain,
! [X0: $i] :
( ( sK70(sK66) = sK140 )
| ( sK67(sK70(sK66)) = X0 )
| ~ sP6
| ~ ordinal(sK66)
| ~ in(sK66,sK66)
| ~ in(sK66,omega)
| ~ in(X0,sK70(sK66))
| ~ subset(sK67(sK70(sK66)),X0) ),
inference(superposition,[status(thm)],[c_84286,c_143]) ).
tcf(c_159974,plain,
! [X0: $i] :
( ( sK70(sK66) = sK140 )
| ( sK72(sK70(sK66)) = X0 )
| ~ iPr_def_18
| ~ sP6
| ~ ordinal(sK66)
| ~ in(sK66,omega)
| ~ in(X0,sK70(sK66))
| ~ subset(sK72(sK70(sK66)),X0) ),
inference(superposition,[status(thm)],[c_84286,c_123596]) ).
tcf(c_159975,plain,
! [X0: $i] :
( sP15
| ( sK70(sK66) = sK140 )
| ( sK114(sK70(sK66)) = X0 )
| ~ sP6
| ~ ordinal(sK66)
| ~ in(sK66,omega)
| ~ in(X0,sK70(sK66))
| ~ subset(sK114(sK70(sK66)),X0) ),
inference(superposition,[status(thm)],[c_84286,c_248]) ).
tcf(c_159976,plain,
! [X0: $i] :
( ( sK70(sK66) = sK140 )
| ( sK119(sK70(sK66)) = X0 )
| ~ sP6
| ~ finite(sK66)
| ~ in(X0,sK70(sK66))
| ~ subset(sK119(sK70(sK66)),X0) ),
inference(superposition,[status(thm)],[c_84286,c_308]) ).
tcf(c_159977,plain,
( in(sK111(sK70(sK66)),sK70(sK66))
| ( sK70(sK66) = sK140 )
| ~ sP15
| ~ sP6
| ~ ordinal(sK66)
| ~ in(sK66,sK110)
| ~ in(sK66,omega) ),
inference(superposition,[status(thm)],[c_84286,c_239]) ).
tcf(c_159978,plain,
( in(sK67(sK70(sK66)),sK70(sK66))
| ( sK70(sK66) = sK140 )
| ~ sP6
| ~ ordinal(sK66)
| ~ in(sK66,sK66)
| ~ in(sK66,omega) ),
inference(superposition,[status(thm)],[c_84286,c_142]) ).
tcf(c_159979,plain,
( in(sK72(sK70(sK66)),sK70(sK66))
| ( sK70(sK66) = sK140 )
| ~ iPr_def_19
| ~ sP6
| ~ ordinal(sK66)
| ~ in(sK66,omega) ),
inference(superposition,[status(thm)],[c_84286,c_123598]) ).
tcf(c_159980,plain,
( sP15
| in(sK114(sK70(sK66)),sK70(sK66))
| ( sK70(sK66) = sK140 )
| ~ sP6
| ~ ordinal(sK66)
| ~ in(sK66,omega) ),
inference(superposition,[status(thm)],[c_84286,c_247]) ).
tcf(c_159981,plain,
( in(sK119(sK70(sK66)),sK70(sK66))
| ( sK70(sK66) = sK140 )
| ~ sP6
| ~ finite(sK66) ),
inference(superposition,[status(thm)],[c_84286,c_307]) ).
tcf(c_160083,plain,
( subset(sK112(sK110),powerset(sK110))
| ~ sP15 ),
inference(superposition,[status(thm)],[c_84376,c_654]) ).
tcf(c_160084,plain,
! [X0: $i] :
( ( sK112(sK110) = sK140 )
| ( sK111(sK112(sK110)) = X0 )
| ~ sP15
| ~ ordinal(sK110)
| ~ in(sK110,sK110)
| ~ in(sK110,omega)
| ~ in(X0,sK112(sK110))
| ~ subset(sK111(sK112(sK110)),X0) ),
inference(superposition,[status(thm)],[c_84376,c_240]) ).
tcf(c_160085,plain,
! [X0: $i] :
( ( sK112(sK110) = sK140 )
| ( sK67(sK112(sK110)) = X0 )
| ~ sP15
| ~ sP6
| ~ ordinal(sK110)
| ~ in(sK110,sK66)
| ~ in(sK110,omega)
| ~ in(X0,sK112(sK110))
| ~ subset(sK67(sK112(sK110)),X0) ),
inference(superposition,[status(thm)],[c_84376,c_143]) ).
tcf(c_160086,plain,
! [X0: $i] :
( ( sK112(sK110) = sK140 )
| ( sK72(sK112(sK110)) = X0 )
| ~ iPr_def_18
| ~ sP15
| ~ ordinal(sK110)
| ~ in(sK110,omega)
| ~ in(X0,sK112(sK110))
| ~ subset(sK72(sK112(sK110)),X0) ),
inference(superposition,[status(thm)],[c_84376,c_123596]) ).
tcf(c_160088,plain,
! [X0: $i] :
( ( sK112(sK110) = sK140 )
| ( sK119(sK112(sK110)) = X0 )
| ~ sP15
| ~ finite(sK110)
| ~ in(X0,sK112(sK110))
| ~ subset(sK119(sK112(sK110)),X0) ),
inference(superposition,[status(thm)],[c_84376,c_308]) ).
tcf(c_160089,plain,
( in(sK111(sK112(sK110)),sK112(sK110))
| ( sK112(sK110) = sK140 )
| ~ sP15
| ~ ordinal(sK110)
| ~ in(sK110,sK110)
| ~ in(sK110,omega) ),
inference(superposition,[status(thm)],[c_84376,c_239]) ).
tcf(c_160090,plain,
( in(sK67(sK112(sK110)),sK112(sK110))
| ( sK112(sK110) = sK140 )
| ~ sP15
| ~ sP6
| ~ ordinal(sK110)
| ~ in(sK110,sK66)
| ~ in(sK110,omega) ),
inference(superposition,[status(thm)],[c_84376,c_142]) ).
tcf(c_160091,plain,
( in(sK72(sK112(sK110)),sK112(sK110))
| ( sK112(sK110) = sK140 )
| ~ iPr_def_19
| ~ sP15
| ~ ordinal(sK110)
| ~ in(sK110,omega) ),
inference(superposition,[status(thm)],[c_84376,c_123598]) ).
tcf(c_160093,plain,
( in(sK119(sK112(sK110)),sK112(sK110))
| ( sK112(sK110) = sK140 )
| ~ sP15
| ~ finite(sK110) ),
inference(superposition,[status(thm)],[c_84376,c_307]) ).
tcf(c_160178,plain,
! [X0: $i] :
( ordinal(sK261)
| sP32(sK269(sK267(X0),X0))
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_84640,c_833]) ).
tcf(c_160179,plain,
! [X0: $i] :
( epsilon_connected(sK269(sK267(X0),X0))
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_84640,c_1050]) ).
tcf(c_160180,plain,
! [X0: $i] :
( epsilon_transitive(sK269(sK267(X0),X0))
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_84640,c_1049]) ).
tcf(c_160181,plain,
! [X0: $i] :
( sP32(sK269(sK267(X0),X0))
| ~ iPr_def_10
| ~ sP34(X0) ),
inference(superposition,[status(thm)],[c_84640,c_123582]) ).
tcf(c_160318,plain,
! [X0: $i] :
( sP32(sK128(sK199(powerset(X0))))
| ( sK199(powerset(X0)) = sK140 )
| ~ iPr_def_10
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_160234,c_123582]) ).
tcf(c_160342,plain,
( in(sK119(sK70(sK66)),sK70(sK66))
| ~ finite(sK66)
| ~ sP6 ),
inference(global_subsumption_just,[status(thm)],[c_159981,c_20113,c_159981]) ).
tcf(c_160343,plain,
( in(sK119(sK70(sK66)),sK70(sK66))
| ~ sP6
| ~ finite(sK66) ),
inference(renaming,[status(thm)],[c_160342]) ).
tcf(c_160350,plain,
( in(sK128(sK119(sK70(sK66))),sK119(sK70(sK66)))
| ( sK119(sK70(sK66)) = sK140 )
| ~ sP6
| ~ finite(sK66)
| ~ ordinal(union(sK70(sK66))) ),
inference(superposition,[status(thm)],[c_160343,c_154063]) ).
tcf(c_160351,plain,
( ~ sP6
| ~ finite(sK66)
| ~ in(sK70(sK66),sK119(sK70(sK66))) ),
inference(superposition,[status(thm)],[c_160343,c_527]) ).
tcf(c_160352,plain,
( ordinal(sK128(sK119(sK70(sK66))))
| ( sK119(sK70(sK66)) = sK140 )
| ~ sP6
| ~ finite(sK66)
| ~ ordinal(union(sK70(sK66))) ),
inference(superposition,[status(thm)],[c_160343,c_154064]) ).
tcf(c_160353,plain,
( in(sK142(sK119(sK70(sK66))),sK119(sK70(sK66)))
| ( sK125(sK70(sK66)) = sK140 )
| ~ sP6
| ~ finite(sK66) ),
inference(superposition,[status(thm)],[c_160343,c_154131]) ).
tcf(c_160354,plain,
( ( set_difference(sK119(sK70(sK66)),union(sK70(sK66))) = sK140 )
| ~ sP6
| ~ finite(sK66) ),
inference(superposition,[status(thm)],[c_160343,c_154065]) ).
tcf(c_160355,plain,
( in(sK142(sK70(sK66)),sK70(sK66))
| ~ sP6
| ~ finite(sK66) ),
inference(superposition,[status(thm)],[c_160343,c_522]) ).
tcf(c_160356,plain,
( ( sK125(sK70(sK66)) = sK140 )
| ~ sP6
| ~ finite(sK66)
| ~ empty(sK119(sK70(sK66))) ),
inference(superposition,[status(thm)],[c_160343,c_150230]) ).
tcf(c_160357,plain,
( ~ sP6
| ~ finite(sK66)
| ~ empty(sK70(sK66)) ),
inference(superposition,[status(thm)],[c_160343,c_787]) ).
tcf(c_160358,plain,
( element(sK119(sK70(sK66)),sK70(sK66))
| ~ sP6
| ~ finite(sK66) ),
inference(superposition,[status(thm)],[c_160343,c_526]) ).
tcf(c_160392,plain,
( in(sK119(sK112(sK110)),sK112(sK110))
| ~ finite(sK110)
| ~ sP15 ),
inference(global_subsumption_just,[status(thm)],[c_160093,c_20178,c_160093]) ).
tcf(c_160393,plain,
( in(sK119(sK112(sK110)),sK112(sK110))
| ~ sP15
| ~ finite(sK110) ),
inference(renaming,[status(thm)],[c_160392]) ).
tcf(c_160400,plain,
( in(sK128(sK119(sK112(sK110))),sK119(sK112(sK110)))
| ( sK119(sK112(sK110)) = sK140 )
| ~ sP15
| ~ finite(sK110)
| ~ ordinal(union(sK112(sK110))) ),
inference(superposition,[status(thm)],[c_160393,c_154063]) ).
tcf(c_160401,plain,
( ~ sP15
| ~ finite(sK110)
| ~ in(sK112(sK110),sK119(sK112(sK110))) ),
inference(superposition,[status(thm)],[c_160393,c_527]) ).
tcf(c_160402,plain,
( ordinal(sK128(sK119(sK112(sK110))))
| ( sK119(sK112(sK110)) = sK140 )
| ~ sP15
| ~ finite(sK110)
| ~ ordinal(union(sK112(sK110))) ),
inference(superposition,[status(thm)],[c_160393,c_154064]) ).
tcf(c_160403,plain,
( in(sK142(sK119(sK112(sK110))),sK119(sK112(sK110)))
| ( sK125(sK112(sK110)) = sK140 )
| ~ sP15
| ~ finite(sK110) ),
inference(superposition,[status(thm)],[c_160393,c_154131]) ).
tcf(c_160404,plain,
( ( set_difference(sK119(sK112(sK110)),union(sK112(sK110))) = sK140 )
| ~ sP15
| ~ finite(sK110) ),
inference(superposition,[status(thm)],[c_160393,c_154065]) ).
tcf(c_160405,plain,
( in(sK142(sK112(sK110)),sK112(sK110))
| ~ sP15
| ~ finite(sK110) ),
inference(superposition,[status(thm)],[c_160393,c_522]) ).
tcf(c_160406,plain,
( ( sK125(sK112(sK110)) = sK140 )
| ~ sP15
| ~ finite(sK110)
| ~ empty(sK119(sK112(sK110))) ),
inference(superposition,[status(thm)],[c_160393,c_150230]) ).
tcf(c_160407,plain,
( ~ sP15
| ~ finite(sK110)
| ~ empty(sK112(sK110)) ),
inference(superposition,[status(thm)],[c_160393,c_787]) ).
tcf(c_160408,plain,
( element(sK119(sK112(sK110)),sK112(sK110))
| ~ sP15
| ~ finite(sK110) ),
inference(superposition,[status(thm)],[c_160393,c_526]) ).
tcf(c_161493,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK105(X0)),union(sK105(X0))) = sK140 )
| ~ sP13(X0) ),
inference(superposition,[status(thm)],[c_226,c_154509]) ).
tcf(c_161507,plain,
! [X0: $i] :
( ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK181(X0)),union(sK181(X0))) = sK140 )
| ~ sP21(X0) ),
inference(superposition,[status(thm)],[c_600,c_154509]) ).
tcf(c_161543,plain,
( ( sK125(sK112(sK110)) = sK140 )
| ( set_difference(apply(sK126(sK112(sK110)),sK119(sK112(sK110))),union(sK119(sK112(sK110)))) = sK140 )
| ~ sP15
| ~ finite(sK110) ),
inference(superposition,[status(thm)],[c_160393,c_154509]) ).
tcf(c_161549,plain,
( ( sK125(sK70(sK66)) = sK140 )
| ( set_difference(apply(sK126(sK70(sK66)),sK119(sK70(sK66))),union(sK119(sK70(sK66)))) = sK140 )
| ~ sP6
| ~ finite(sK66) ),
inference(superposition,[status(thm)],[c_160343,c_154509]) ).
tcf(c_162066,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ( set_difference(apply(sK126(X0),sK98(X0,X1)),union(sK98(X0,X1))) = sK140 )
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_154509]) ).
tcf(c_162067,plain,
! [X0: $i,X1: $i] :
( in(sK128(sK98(X0,X1)),sK98(X0,X1))
| ( sK98(X0,X1) = sK140 )
| ~ ordinal(union(X0))
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_154063]) ).
tcf(c_162068,plain,
! [X0: $i,X1: $i] :
( ~ sP11(X0,X1)
| ~ in(X0,sK98(X0,X1)) ),
inference(superposition,[status(thm)],[c_215,c_527]) ).
tcf(c_162069,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(sK98(X0,X1)))
| ( sK98(X0,X1) = sK140 )
| ~ ordinal(union(X0))
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_154064]) ).
tcf(c_162070,plain,
! [X0: $i,X1: $i] :
( in(sK142(sK98(X0,X1)),sK98(X0,X1))
| ( sK125(X0) = sK140 )
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_154131]) ).
tcf(c_162071,plain,
! [X0: $i,X1: $i] :
( ( set_difference(sK98(X0,X1),union(X0)) = sK140 )
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_154065]) ).
tcf(c_162072,plain,
! [X0: $i,X1: $i] :
( in(sK142(X0),X0)
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_522]) ).
tcf(c_162073,plain,
! [X0: $i,X1: $i] :
( ( sK125(X0) = sK140 )
| ~ sP11(X0,X1)
| ~ empty(sK98(X0,X1)) ),
inference(superposition,[status(thm)],[c_215,c_150230]) ).
tcf(c_162074,plain,
! [X0: $i,X1: $i] :
( ~ empty(X0)
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_787]) ).
tcf(c_162075,plain,
! [X0: $i,X1: $i] :
( element(sK98(X0,X1),X0)
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_526]) ).
tcf(c_162076,plain,
! [X0: $i,X1: $i] :
( in(sK98(sK92(X0),X1),X0)
| ~ sP11(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_215,c_198]) ).
tcf(c_162077,plain,
! [X0: $i,X1: $i] :
( ordinal(sK98(sK92(X0),X1))
| ~ sP11(sK92(X0),X1) ),
inference(superposition,[status(thm)],[c_215,c_199]) ).
tcf(c_162078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(apply(X0,sK98(relation_inverse_image(X0,X1),X2)),X1)
| ( X4 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ sP11(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_215,c_425]) ).
tcf(c_162079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(sK98(relation_inverse_image(X0,X1),X2),X3)
| ( X4 = sK140 )
| ~ function(X0)
| ~ quasi_total(X0,X3,X4)
| ~ relation_of2_as_subset(X0,X3,X4)
| ~ sP11(relation_inverse_image(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_215,c_424]) ).
tcf(c_162080,plain,
! [X0: $i] : ~ sP11(sK140,X0),
inference(superposition,[status(thm)],[c_215,c_580]) ).
tcf(c_162081,plain,
! [X0: $i,X1: $i] :
( subset(sK98(powerset(X0),X1),X0)
| ~ sP11(powerset(X0),X1) ),
inference(superposition,[status(thm)],[c_215,c_662]) ).
tcf(c_162082,plain,
! [X0: $i,X1: $i] :
( sP29
| ordinal(sK98(sK248(X0),X1))
| ~ sP11(sK248(X0),X1) ),
inference(superposition,[status(thm)],[c_215,c_808]) ).
tcf(c_162649,plain,
! [X0: $i,X1: $i] :
( ( apply(sK57(X0),X1) = sK140 )
| ( set_difference(X1,union(relation_dom(sK57(X0)))) = sK140 )
| ~ sP3(X0)
| ~ relation(sK57(X0)) ),
inference(superposition,[status(thm)],[c_114,c_154508]) ).
tcf(c_163462,plain,
! [X0: $i] :
( ( relation_rng(relation_rng_restriction(sK140,sK57(X0))) = sK140 )
| ~ sP3(X0) ),
inference(superposition,[status(thm)],[c_113,c_162864]) ).
tcf(c_163605,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_rng(relation_rng_restriction(X1,sK57(X0))),X1) = sK140 )
| ~ sP3(X0) ),
inference(superposition,[status(thm)],[c_113,c_162861]) ).
tcf(c_163696,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_image(sK57(X0),X1),relation_rng(sK57(X0))) = sK140 )
| ~ sP3(X0) ),
inference(superposition,[status(thm)],[c_113,c_163067]) ).
tcf(c_164045,plain,
! [X0: $i,X1: $i] :
( ordinal(sK98(X0,X1))
| ~ ordinal(X0)
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_333]) ).
tcf(c_164046,plain,
! [X0: $i] :
( ordinal(sK105(X0))
| ~ sP13(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_226,c_333]) ).
tcf(c_164060,plain,
! [X0: $i] :
( ordinal(sK181(X0))
| ~ sP21(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_600,c_333]) ).
tcf(c_164097,plain,
( ordinal(sK119(sK112(sK110)))
| ~ sP15
| ~ finite(sK110)
| ~ ordinal(sK112(sK110)) ),
inference(superposition,[status(thm)],[c_160393,c_333]) ).
tcf(c_164107,plain,
( ordinal(sK119(sK70(sK66)))
| ~ sP6
| ~ finite(sK66)
| ~ ordinal(sK70(sK66)) ),
inference(superposition,[status(thm)],[c_160343,c_333]) ).
tcf(c_164714,plain,
! [X0: $i] :
( sP32(relation_rng(X0))
| ~ iPr_def_10
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_147663,c_123582]) ).
tcf(c_164730,plain,
! [X0: $i] :
( ( relation_field(relation_restriction(sK57(X0),sK140)) = sK140 )
| ~ sP3(X0) ),
inference(superposition,[status(thm)],[c_113,c_163929]) ).
tcf(c_164860,plain,
! [X0: $i] :
( sP32(sK169(X0))
| ( X0 = sK140 )
| ~ iPr_def_10
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_164058,c_123582]) ).
tcf(c_164882,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_inverse_image(sK57(X0),X1),relation_dom(sK57(X0))) = sK140 )
| ~ sP3(X0) ),
inference(superposition,[status(thm)],[c_113,c_163162]) ).
tcf(c_165083,plain,
! [X0: $i,X1: $i] :
( ( set_difference(relation_field(relation_restriction(sK57(X0),X1)),X1) = sK140 )
| ~ sP3(X0) ),
inference(superposition,[status(thm)],[c_113,c_163926]) ).
tcf(c_166129,plain,
! [X0: $i,X1: $i] :
( ( set_difference(unordered_pair(sK98(X0,X1),sK98(X0,X1)),X0) = sK140 )
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_165532]) ).
tcf(c_166130,plain,
! [X0: $i] :
( ( set_difference(unordered_pair(sK105(X0),sK105(X0)),X0) = sK140 )
| ~ sP13(X0) ),
inference(superposition,[status(thm)],[c_226,c_165532]) ).
tcf(c_166146,plain,
! [X0: $i] :
( ( set_difference(unordered_pair(sK181(X0),sK181(X0)),X0) = sK140 )
| ~ sP21(X0) ),
inference(superposition,[status(thm)],[c_600,c_165532]) ).
tcf(c_166182,plain,
( ( set_difference(unordered_pair(sK119(sK112(sK110)),sK119(sK112(sK110))),sK112(sK110)) = sK140 )
| ~ sP15
| ~ finite(sK110) ),
inference(superposition,[status(thm)],[c_160393,c_165532]) ).
tcf(c_166192,plain,
( ( set_difference(unordered_pair(sK119(sK70(sK66)),sK119(sK70(sK66))),sK70(sK66)) = sK140 )
| ~ sP6
| ~ finite(sK66) ),
inference(superposition,[status(thm)],[c_160343,c_165532]) ).
tcf(c_166787,plain,
( sP32(sK128(powerset(sK140)))
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_166045,c_123582]) ).
tcf(c_166820,plain,
! [X0: $i] :
( ( unordered_pair(sK98(powerset(sK140),X0),sK98(powerset(sK140),X0)) = powerset(sK140) )
| ~ sP11(powerset(sK140),X0) ),
inference(superposition,[status(thm)],[c_215,c_165547]) ).
tcf(c_166821,plain,
( ( unordered_pair(sK105(powerset(sK140)),sK105(powerset(sK140))) = powerset(sK140) )
| ~ sP13(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_226,c_165547]) ).
tcf(c_166834,plain,
( ( unordered_pair(sK181(powerset(sK140)),sK181(powerset(sK140))) = powerset(sK140) )
| ~ sP21(powerset(sK140)) ),
inference(superposition,[status(thm)],[c_600,c_165547]) ).
tcf(c_167048,plain,
! [X0: $i,X1: $i] :
( ordinal(sK128(unordered_pair(sK98(X0,X1),sK98(X0,X1))))
| ~ ordinal(X0)
| ~ sP11(X0,X1) ),
inference(superposition,[status(thm)],[c_215,c_165550]) ).
tcf(c_167049,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK105(X0),sK105(X0))))
| ~ sP13(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_226,c_165550]) ).
tcf(c_167066,plain,
! [X0: $i] :
( ordinal(sK128(unordered_pair(sK181(X0),sK181(X0))))
| ~ sP21(X0)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_600,c_165550]) ).
tcf(c_167102,plain,
( ordinal(sK128(unordered_pair(sK119(sK112(sK110)),sK119(sK112(sK110)))))
| ~ sP15
| ~ finite(sK110)
| ~ ordinal(sK112(sK110)) ),
inference(superposition,[status(thm)],[c_160393,c_165550]) ).
tcf(c_167113,plain,
( ordinal(sK128(unordered_pair(sK119(sK70(sK66)),sK119(sK70(sK66)))))
| ~ sP6
| ~ finite(sK66)
| ~ ordinal(sK70(sK66)) ),
inference(superposition,[status(thm)],[c_160343,c_165550]) ).
tcf(c_167434,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(sK98(unordered_pair(X0,X0),X1),sK98(unordered_pair(X0,X0),X1)) = unordered_pair(X0,X0) )
| ~ sP11(unordered_pair(X0,X0),X1) ),
inference(superposition,[status(thm)],[c_215,c_165554]) ).
tcf(c_167435,plain,
! [X0: $i] :
( ( unordered_pair(sK105(unordered_pair(X0,X0)),sK105(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ sP13(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_226,c_165554]) ).
tcf(c_167448,plain,
! [X0: $i] :
( ( unordered_pair(sK181(unordered_pair(X0,X0)),sK181(unordered_pair(X0,X0))) = unordered_pair(X0,X0) )
| ~ sP21(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_600,c_165554]) ).
tcf(c_169350,plain,
! [X0: $i] :
( sP32(sK128(unordered_pair(sK169(X0),sK169(X0))))
| ( X0 = sK140 )
| ~ iPr_def_10
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_167064,c_123582]) ).
tcf(c_169627,plain,
! [X0: $i] :
( sP32(sK128(unordered_pair(X0,X0)))
| ~ iPr_def_10
| ~ ordinal(unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_169599,c_123582]) ).
tcf(c_170627,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK98(set_difference(X0,X1),X2),X0)
| ~ sP11(set_difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_215,c_687]) ).
tcf(c_170628,plain,
! [X0: $i,X1: $i] :
( in(sK105(set_difference(X0,X1)),X0)
| ~ sP13(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_226,c_687]) ).
tcf(c_170641,plain,
! [X0: $i,X1: $i] :
( in(sK181(set_difference(X0,X1)),X0)
| ~ sP21(set_difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_600,c_687]) ).
tcf(c_170863,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_170655,c_170654,c_170653,c_170652,c_170651,c_170650,c_170649,c_170648,c_170647,c_170646,c_170645,c_170644,c_170643,c_170642,c_170641,c_170640,c_170639,c_170638,c_170637,c_170636,c_170635,c_170634,c_170633,c_170632,c_170631,c_170630,c_170629,c_170628,c_170627,c_170626,c_170625,c_170624,c_170572,c_170570,c_170569,c_170568,c_170567,c_170566,c_170342,c_170341,c_170340,c_170339,c_170338,c_170337,c_170336,c_170335,c_170334,c_170333,c_170332,c_170331,c_170330,c_170329,c_170328,c_170327,c_170326,c_170253,c_170252,c_170251,c_170250,c_170248,c_170247,c_170246,c_170245,c_170244,c_170243,c_170242,c_170241,c_170240,c_170239,c_170238,c_170117,c_170116,c_170115,c_170114,c_170112,c_170111,c_170110,c_170109,c_170108,c_170107,c_170106,c_170105,c_170104,c_170103,c_170102,c_169732,c_169731,c_169730,c_169729,c_169728,c_169727,c_169726,c_169725,c_169724,c_169723,c_169722,c_169721,c_169720,c_169719,c_169718,c_169717,c_169716,c_169715,c_169713,c_169712,c_169710,c_169709,c_169708,c_169707,c_169706,c_169705,c_169704,c_169703,c_169702,c_169701,c_169700,c_169699,c_169698,c_169697,c_169696,c_169695,c_169694,c_169627,c_169626,c_169625,c_169624,c_169623,c_169622,c_169599,c_169591,c_169590,c_169589,c_169585,c_169588,c_169583,c_169581,c_169578,c_169577,c_169576,c_169575,c_169574,c_169572,c_169571,c_169438,c_169433,c_169421,c_169417,c_169420,c_169415,c_169413,c_169410,c_169409,c_169408,c_169407,c_169406,c_169405,c_169404,c_169350,c_169349,c_169348,c_169347,c_169127,c_169121,c_169117,c_169113,c_169109,c_169104,c_169100,c_169091,c_169090,c_169089,c_169085,c_169082,c_169081,c_169080,c_169079,c_169078,c_169077,c_169076,c_169048,c_169047,c_169046,c_169045,c_169044,c_168608,c_168605,c_168604,c_168603,c_168600,c_168599,c_168598,c_168597,c_168596,c_168595,c_168594,c_168593,c_168592,c_168591,c_168590,c_168589,c_168588,c_168587,c_168586,c_168585,c_168584,c_168583,c_168582,c_168581,c_168572,c_168571,c_168568,c_168567,c_168565,c_168564,c_168563,c_168562,c_168561,c_168560,c_168559,c_168558,c_168557,c_168556,c_168305,c_168304,c_168303,c_168302,c_168301,c_168300,c_168299,c_168298,c_168297,c_168296,c_168295,c_168294,c_168293,c_168292,c_168291,c_168290,c_168289,c_168288,c_168287,c_168286,c_168285,c_168284,c_168283,c_168165,c_168164,c_168163,c_168162,c_168161,c_168160,c_168159,c_168158,c_168157,c_168156,c_168155,c_168154,c_168153,c_168152,c_168151,c_168150,c_168149,c_168148,c_168147,c_168146,c_168145,c_168144,c_168143,c_167955,c_167954,c_167953,c_167952,c_167951,c_167950,c_167949,c_167948,c_167947,c_167946,c_167945,c_167944,c_167943,c_167942,c_167941,c_167940,c_167820,c_167809,c_167808,c_167807,c_167806,c_167805,c_167803,c_167811,c_167533,c_167528,c_167521,c_167515,c_167512,c_167509,c_167489,c_167486,c_167485,c_167463,c_167462,c_167461,c_167460,c_167459,c_167458,c_167457,c_167456,c_167455,c_167454,c_167451,c_167450,c_167449,c_167448,c_167447,c_167446,c_167445,c_167444,c_167443,c_167442,c_167441,c_167440,c_167439,c_167438,c_167437,c_167436,c_167435,c_167434,c_167433,c_167432,c_167431,c_167422,c_167417,c_167287,c_167277,c_167272,c_167240,c_167239,c_167185,c_167129,c_167126,c_167121,c_167116,c_167115,c_167114,c_167113,c_167112,c_167111,c_167110,c_167109,c_167108,c_167107,c_167106,c_167105,c_167104,c_167103,c_167102,c_167101,c_167100,c_167099,c_167098,c_167097,c_167096,c_167095,c_167094,c_167093,c_167092,c_167091,c_167090,c_167089,c_167088,c_167087,c_167086,c_167085,c_167084,c_167083,c_167082,c_167081,c_167080,c_167079,c_167078,c_167077,c_167076,c_167075,c_167074,c_167073,c_167072,c_167071,c_167070,c_167069,c_167068,c_167067,c_167066,c_167065,c_167064,c_167063,c_167062,c_167061,c_167060,c_167059,c_167058,c_167057,c_167055,c_167054,c_167053,c_167052,c_167051,c_167050,c_167049,c_167048,c_167047,c_167046,c_167045,c_167044,c_167043,c_167042,c_166926,c_166921,c_166914,c_166908,c_166905,c_166900,c_166899,c_166890,c_166887,c_166875,c_166874,c_166850,c_166849,c_166848,c_166847,c_166846,c_166845,c_166844,c_166843,c_166842,c_166841,c_166840,c_166839,c_166838,c_166836,c_166835,c_166834,c_166833,c_166832,c_166831,c_166830,c_166829,c_166828,c_166827,c_166826,c_166825,c_166824,c_166823,c_166822,c_166821,c_166820,c_166819,c_166818,c_166817,c_166800,c_166799,c_166796,c_166792,c_166787,c_166786,c_166785,c_166784,c_166717,c_166716,c_166715,c_166714,c_166713,c_166712,c_166711,c_166710,c_166709,c_166708,c_166707,c_166706,c_166705,c_166704,c_166703,c_166702,c_166701,c_166700,c_166699,c_166570,c_166569,c_166568,c_166567,c_166566,c_166565,c_166564,c_166563,c_166562,c_166561,c_166560,c_166559,c_166558,c_166557,c_166556,c_166555,c_166193,c_166192,c_166191,c_166190,c_166189,c_166188,c_166187,c_166186,c_166185,c_166184,c_166183,c_166182,c_166181,c_166180,c_166179,c_166178,c_166177,c_166176,c_166175,c_166174,c_166173,c_166172,c_166171,c_166170,c_166169,c_166168,c_166167,c_166166,c_166165,c_166164,c_166163,c_166162,c_166161,c_166160,c_166159,c_166158,c_166157,c_166156,c_166155,c_166154,c_166153,c_166152,c_166151,c_166150,c_166149,c_166148,c_166147,c_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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU325+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.40 % Computer : n015.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.16/5.40 % CPULimit : 300
% 0.16/5.40 % WCLimit : 300
% 0.16/5.40 % DateTime : Thu Sep 24 13:46:02 UTC 2026
% 0.16/5.40 % CPUTime :
% 0.16/5.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.44 Running first-order theorem proving
% 0.16/5.44 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
% 0.16/5.45
% 0.16/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.45
% 0.16/5.45 % Detected problem language: tptp
% 0.16/5.46 % Proving...
% 88.78/18.45 % SZS status Started for theBenchmark.p
% 88.78/18.45 % SZS status Theorem for theBenchmark.p
% 88.78/18.45
% 88.78/18.45 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 88.78/18.45
% 88.78/18.45 % ------ iProver source info
% 88.78/18.45
% 88.78/18.45 % git: date: 2026-07-19 20:42:38 +0200
% 88.78/18.45 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 88.78/18.45 % git: non_committed_changes: false
% 88.78/18.45
% 88.78/18.45 % ------ Parsing...
% 88.78/18.45 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 88.78/18.45
% 88.78/18.45 % ------ 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_e sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe_e %
% 88.78/18.45
% 88.78/18.45 % ------ Preprocessing... gs_s sp: 15 0s gs_e snvd_s sp: 0 0s snvd_e %
% 88.78/18.45
% 88.78/18.45 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 88.78/18.45 % ------ Proving...
% 88.78/18.45 % ------ Problem Properties
% 88.78/18.45
% 88.78/18.45 %
% 88.78/18.45 % clauses 1086
% 88.78/18.45 % conjectures 92
% 88.78/18.45 % EPR 172
% 88.78/18.45 % Horn 800
% 88.78/18.45 % unary 132
% 88.78/18.45 % binary 329
% 88.78/18.45 % lits 3267
% 88.78/18.45 % lits eq 453
% 88.78/18.45 % fd_pure 0
% 88.78/18.45 % fd_pseudo 0
% 88.78/18.45 % fd_cond 41
% 88.78/18.45 % fd_pseudo_cond 109
% 88.78/18.45 % AC symbols 0
% 88.78/18.45
% 88.78/18.45 % ------ Schedule dynamic 5 is on
% 88.78/18.45
% 88.78/18.45 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 88.78/18.45
% 88.78/18.45
% 88.78/18.45 % ------
% 88.78/18.45 % Current options:
% 88.78/18.45 % ------
% 88.78/18.45
% 88.78/18.45
% 88.78/18.45 %
% 88.78/18.45
% 88.78/18.45 % ------ Proving...
% 88.78/18.45 %
% 88.78/18.45
% 88.78/18.45 % SZS status Theorem for theBenchmark.p
% 88.78/18.45
% 88.78/18.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 89.23/18.65
% 89.23/18.65
%------------------------------------------------------------------------------