%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU382+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Wed Oct 7 10:44:13 AM UTC 2026
% Result : Theorem 13.45s 2.51s
% Output : CNFRefutation 13.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 98
% Syntax : Number of formulae : 899 ( 501 unt; 0 typ; 0 def)
% Number of atoms : 4910 (1628 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 9679 (1933 ~;1169 |; 117 &;6265 @)
% ( 18 <=>; 177 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 240 ( 237 usr; 5 con; 0-6 aty)
% Number of variables : 1736 ( 0 ^;1715 !; 21 ?;1736 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_1_0_filter_1,type,
a_1_0_filter_1: $i > $i ).
thf(tp_a_2_2_lattice3,type,
a_2_2_lattice3: $i > $i > $i ).
thf(tp_a_2_3_lattice3,type,
a_2_3_lattice3: $i > $i > $i ).
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_apply_as_element,type,
apply_as_element: $i > $i > $i > $i > $i ).
thf(tp_apply_binary,type,
apply_binary: $i > $i > $i > $i ).
thf(tp_apply_binary_as_element,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_apply_netmap,type,
apply_netmap: $i > $i > $i > $i ).
thf(tp_apply_on_set_and_struct,type,
apply_on_set_and_struct: $i > $i > $i > $i > $i ).
thf(tp_apply_on_structs,type,
apply_on_structs: $i > $i > $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
thf(tp_below,type,
below: $i > $i > $i > $o ).
thf(tp_below_refl,type,
below_refl: $i > $i > $i > $o ).
thf(tp_bijective,type,
bijective: $i > $i > $i > $o ).
thf(tp_boole_POSet,type,
boole_POSet: $i > $i ).
thf(tp_boole_lattice,type,
boole_lattice: $i > $i ).
thf(tp_boolean_lattstr,type,
boolean_lattstr: $i > $o ).
thf(tp_boolean_relstr,type,
boolean_relstr: $i > $o ).
thf(tp_bottom_of_relstr,type,
bottom_of_relstr: $i > $i ).
thf(tp_bottom_of_semilattstr,type,
bottom_of_semilattstr: $i > $i ).
thf(tp_bounded_lattstr,type,
bounded_lattstr: $i > $o ).
thf(tp_bounded_relstr,type,
bounded_relstr: $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
thf(tp_cast_to_el_of_LattPOSet,type,
cast_to_el_of_LattPOSet: $i > $i > $i ).
thf(tp_cast_to_el_of_lattice,type,
cast_to_el_of_lattice: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_centered,type,
centered: $i > $o ).
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_closed_subsets,type,
closed_subsets: $i > $i > $o ).
thf(tp_compact_top_space,type,
compact_top_space: $i > $o ).
thf(tp_complemented_lattstr,type,
complemented_lattstr: $i > $o ).
thf(tp_complemented_relstr,type,
complemented_relstr: $i > $o ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_complete_latt_str,type,
complete_latt_str: $i > $o ).
thf(tp_complete_relstr,type,
complete_relstr: $i > $o ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_connected_relstr,type,
connected_relstr: $i > $o ).
thf(tp_cup_closed,type,
cup_closed: $i > $o ).
thf(tp_diff_closed,type,
diff_closed: $i > $o ).
thf(tp_directed_relstr,type,
directed_relstr: $i > $o ).
thf(tp_directed_subset,type,
directed_subset: $i > $i > $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_distributive_lattstr,type,
distributive_lattstr: $i > $o ).
thf(tp_distributive_relstr,type,
distributive_relstr: $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_carrier,type,
empty_carrier: $i > $o ).
thf(tp_empty_carrier_subset,type,
empty_carrier_subset: $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_equipotent,type,
equipotent: $i > $i > $o ).
thf(tp_ex_inf_of_relstr_set,type,
ex_inf_of_relstr_set: $i > $i > $o ).
thf(tp_ex_sup_of_relstr_set,type,
ex_sup_of_relstr_set: $i > $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_filtered_subset,type,
filtered_subset: $i > $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_full_subnetstr,type,
full_subnetstr: $i > $i > $i > $o ).
thf(tp_full_subrelstr,type,
full_subrelstr: $i > $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_function_invverse_img_as_carrier_subset,type,
function_invverse_img_as_carrier_subset: $i > $i > $i > $i > $i ).
thf(tp_function_of_composition,type,
function_of_composition: $i > $i > $i > $i > $i > $i ).
thf(tp_heyting_relstr,type,
heyting_relstr: $i > $o ).
thf(tp_identity_as_relation_of,type,
identity_as_relation_of: $i > $i ).
thf(tp_identity_on_carrier,type,
identity_on_carrier: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_incl_POSet,type,
incl_POSet: $i > $i ).
thf(tp_inclusion_order,type,
inclusion_order: $i > $i ).
thf(tp_inclusion_relation,type,
inclusion_relation: $i > $i ).
thf(tp_interior,type,
interior: $i > $i > $i ).
thf(tp_is_a_cover_of_carrier,type,
is_a_cover_of_carrier: $i > $i > $o ).
thf(tp_is_antisymmetric_in,type,
is_antisymmetric_in: $i > $i > $o ).
thf(tp_is_connected_in,type,
is_connected_in: $i > $i > $o ).
thf(tp_is_eventually_in,type,
is_eventually_in: $i > $i > $i > $o ).
thf(tp_is_often_in,type,
is_often_in: $i > $i > $i > $o ).
thf(tp_is_reflexive_in,type,
is_reflexive_in: $i > $i > $o ).
thf(tp_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_is_well_founded_in,type,
is_well_founded_in: $i > $i > $o ).
thf(tp_join,type,
join: $i > $i > $i > $i ).
thf(tp_join_absorbing,type,
join_absorbing: $i > $o ).
thf(tp_join_associative,type,
join_associative: $i > $o ).
thf(tp_join_commut,type,
join_commut: $i > $i > $i > $i ).
thf(tp_join_commutative,type,
join_commutative: $i > $o ).
thf(tp_join_complete_relstr,type,
join_complete_relstr: $i > $o ).
thf(tp_join_of_latt_set,type,
join_of_latt_set: $i > $i > $i ).
thf(tp_join_on_relstr,type,
join_on_relstr: $i > $i > $i ).
thf(tp_join_semilatt_str,type,
join_semilatt_str: $i > $o ).
thf(tp_k10_filter_1,type,
k10_filter_1: $i > $i > $i > $i > $i ).
thf(tp_k1_pcomps_1,type,
k1_pcomps_1: $i > $i ).
thf(tp_k2_lattice3,type,
k2_lattice3: $i > $i ).
thf(tp_k8_filter_1,type,
k8_filter_1: $i > $i > $i ).
thf(tp_latt_element_smaller,type,
latt_element_smaller: $i > $i > $i > $o ).
thf(tp_latt_set_smaller,type,
latt_set_smaller: $i > $i > $i > $o ).
thf(tp_latt_str,type,
latt_str: $i > $o ).
thf(tp_latt_str_of,type,
latt_str_of: $i > $i > $i > $i ).
thf(tp_lattice,type,
lattice: $i > $o ).
thf(tp_lim_points_of_net,type,
lim_points_of_net: $i > $i > $i ).
thf(tp_lower_bounded_relstr,type,
lower_bounded_relstr: $i > $o ).
thf(tp_lower_bounded_semilattstr,type,
lower_bounded_semilattstr: $i > $o ).
thf(tp_meet,type,
meet: $i > $i > $i > $i ).
thf(tp_meet_absorbing,type,
meet_absorbing: $i > $o ).
thf(tp_meet_associative,type,
meet_associative: $i > $o ).
thf(tp_meet_commut,type,
meet_commut: $i > $i > $i > $i ).
thf(tp_meet_commutative,type,
meet_commutative: $i > $o ).
thf(tp_meet_of_latt_set,type,
meet_of_latt_set: $i > $i > $i ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_meet_on_relstr,type,
meet_on_relstr: $i > $i > $i ).
thf(tp_meet_semilatt_str,type,
meet_semilatt_str: $i > $o ).
thf(tp_modular_lattstr,type,
modular_lattstr: $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_net_str,type,
net_str: $i > $i > $o ).
thf(tp_net_str_of,type,
net_str_of: $i > $i > $i > $i > $i ).
thf(tp_omega,type,
omega: $i ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_onto,type,
onto: $i > $i > $i > $o ).
thf(tp_open_subset,type,
open_subset: $i > $i > $o ).
thf(tp_open_subsets,type,
open_subsets: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_ordered_pair_as_product_element,type,
ordered_pair_as_product_element: $i > $i > $i > $i > $i ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_ordinal_subset,type,
ordinal_subset: $i > $i > $o ).
thf(tp_pair_first,type,
pair_first: $i > $i ).
thf(tp_pair_second,type,
pair_second: $i > $i ).
thf(tp_point_neighbourhood,type,
point_neighbourhood: $i > $i > $i > $o ).
thf(tp_poset_of_lattice,type,
poset_of_lattice: $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_preboolean,type,
preboolean: $i > $o ).
thf(tp_preimage_subnetstr,type,
preimage_subnetstr: $i > $i > $i > $i ).
thf(tp_proper_element,type,
proper_element: $i > $i > $o ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_quasi_total,type,
quasi_total: $i > $i > $i > $o ).
thf(tp_reflexive,type,
reflexive: $i > $o ).
thf(tp_reflexive_relstr,type,
reflexive_relstr: $i > $o ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_rel_str_of,type,
rel_str_of: $i > $i > $i ).
thf(tp_related,type,
related: $i > $i > $i > $o ).
thf(tp_related_reflexive,type,
related_reflexive: $i > $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_as_subset,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(tp_relation_dom_restr_as_relation_of,type,
relation_dom_restr_as_relation_of: $i > $i > $i > $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_isomorphism,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_of_lattice,type,
relation_of_lattice: $i > $i ).
thf(tp_relation_restriction,type,
relation_restriction: $i > $i > $i ).
thf(tp_relation_restriction_as_relation_of,type,
relation_restriction_as_relation_of: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_as_subset,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_relstr_element_smaller,type,
relstr_element_smaller: $i > $i > $i > $o ).
thf(tp_relstr_set_smaller,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(tp_sK10_SY228,type,
sK10_SY228: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY158,type,
sK2_SY158: $i > $i ).
thf(tp_sK3_SY163,type,
sK3_SY163: $i > $i ).
thf(tp_sK4_SY167,type,
sK4_SY167: $i > $i ).
thf(tp_sK5_SY197,type,
sK5_SY197: $i > $i ).
thf(tp_sK6_SY230,type,
sK6_SY230: $i > $i > $i ).
thf(tp_sK7_SY157,type,
sK7_SY157: $i > $i ).
thf(tp_sK8_SY196,type,
sK8_SY196: $i > $i ).
thf(tp_sK9_SY204,type,
sK9_SY204: $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_strict_latt_str,type,
strict_latt_str: $i > $o ).
thf(tp_strict_net_str,type,
strict_net_str: $i > $i > $o ).
thf(tp_strict_rel_str,type,
strict_rel_str: $i > $o ).
thf(tp_subnet,type,
subnet: $i > $i > $i > $o ).
thf(tp_subnetstr,type,
subnetstr: $i > $i > $i > $o ).
thf(tp_subrelstr,type,
subrelstr: $i > $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_subset_intersection2,type,
subset_intersection2: $i > $i > $i > $i ).
thf(tp_subset_union2,type,
subset_union2: $i > $i > $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_symmetric,type,
symmetric: $i > $o ).
thf(tp_the_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_L_join,type,
the_L_join: $i > $i ).
thf(tp_the_L_meet,type,
the_L_meet: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_the_mapping,type,
the_mapping: $i > $i > $i ).
thf(tp_the_topology,type,
the_topology: $i > $i ).
thf(tp_top_str,type,
top_str: $i > $o ).
thf(tp_topological_space,type,
topological_space: $i > $o ).
thf(tp_topstr_closure,type,
topstr_closure: $i > $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_transitive_relstr,type,
transitive_relstr: $i > $o ).
thf(tp_trivial_carrier,type,
trivial_carrier: $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(tp_unordered_pair_as_carrier_subset,type,
unordered_pair_as_carrier_subset: $i > $i > $i > $i ).
thf(tp_unordered_triple,type,
unordered_triple: $i > $i > $i > $i ).
thf(tp_up_complete_relstr,type,
up_complete_relstr: $i > $o ).
thf(tp_upper_bounded_relstr,type,
upper_bounded_relstr: $i > $o ).
thf(tp_upper_bounded_semilattstr,type,
upper_bounded_semilattstr: $i > $o ).
thf(tp_upper_relstr_subset,type,
upper_relstr_subset: $i > $i > $o ).
thf(tp_v1_binop_1,type,
v1_binop_1: $i > $i > $o ).
thf(tp_v1_int_1,type,
v1_int_1: $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $i > $o ).
thf(tp_v1_partfun1,type,
v1_partfun1: $i > $i > $i > $o ).
thf(tp_v1_rat_1,type,
v1_rat_1: $i > $o ).
thf(tp_v1_waybel_2,type,
v1_waybel_2: $i > $o ).
thf(tp_v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
thf(tp_v1_xreal_0,type,
v1_xreal_0: $i > $o ).
thf(tp_v1_yellow_3,type,
v1_yellow_3: $i > $o ).
thf(tp_v2_binop_1,type,
v2_binop_1: $i > $i > $o ).
thf(tp_v2_membered,type,
v2_membered: $i > $o ).
thf(tp_v2_waybel_2,type,
v2_waybel_2: $i > $o ).
thf(tp_v2_waybel_3,type,
v2_waybel_3: $i > $o ).
thf(tp_v3_membered,type,
v3_membered: $i > $o ).
thf(tp_v3_waybel_3,type,
v3_waybel_3: $i > $o ).
thf(tp_v4_membered,type,
v4_membered: $i > $o ).
thf(tp_v5_membered,type,
v5_membered: $i > $o ).
thf(tp_well_founded_relation,type,
well_founded_relation: $i > $o ).
thf(tp_well_ordering,type,
well_ordering: $i > $o ).
thf(tp_well_orders,type,
well_orders: $i > $i > $o ).
thf(tp_with_infima_relstr,type,
with_infima_relstr: $i > $o ).
thf(tp_with_suprema_relstr,type,
with_suprema_relstr: $i > $o ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(66,axiom,
! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
thf(80,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(88,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(91,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(95,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_2) ).
thf(96,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(113,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(219,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(220,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(259,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(260,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( element @ ( the_topology @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
thf(261,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(267,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(268,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(273,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(277,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(298,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(301,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(302,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_union2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(309,axiom,
! [A: $i] :
( ( strict_rel_str @ ( boole_POSet @ A ) )
& ( rel_str @ ( boole_POSet @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
thf(310,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
thf(311,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(313,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(314,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(315,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(318,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(320,axiom,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( meet_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_0) ).
thf(321,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(323,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(324,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(326,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(327,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(328,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(333,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
thf(336,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(338,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(342,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(343,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(344,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(345,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pre_topc) ).
thf(346,axiom,
! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).
thf(347,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(348,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(351,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(352,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(354,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(358,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(415,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(421,axiom,
! [A: $i] :
( ( boole_POSet @ A )
= ( poset_of_lattice @ ( boole_lattice @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_yellow_1) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(448,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier @ A )
<=> ( empty @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
thf(486,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_grcat_1) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( subset_union2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(539,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(561,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_membered) ).
thf(562,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
thf(582,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(623,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(637,axiom,
! [A: $i] :
( ( boole_POSet @ A )
= ( incl_POSet @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_yellow_1) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ( ( related_reflexive @ ( boole_POSet @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_yellow_1) ).
thf(736,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(737,axiom,
! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow_1) ).
thf(744,axiom,
! [A: $i] :
( ( bottom_of_relstr @ ( boole_POSet @ A ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_yellow_1) ).
thf(776,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(780,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tops_2) ).
thf(824,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
thf(843,conjecture,
! [A: $i] :
( ( the_carrier @ ( boole_POSet @ A ) )
= ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_waybel_7) ).
thf(844,negated_conjecture,
( ( ! [A: $i] :
( ( the_carrier @ ( boole_POSet @ A ) )
= ( powerset @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[843]) ).
thf(845,plain,
( ( ! [A: $i] :
( ( the_carrier @ ( boole_POSet @ A ) )
= ( powerset @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[844]) ).
thf(846,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(847,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(848,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(849,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(850,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(851,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(852,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(853,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(854,plain,
( ( ! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(855,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(856,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(857,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(858,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(859,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(860,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(861,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(862,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(863,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(864,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(865,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(866,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(867,plain,
$true = $true,
inference(unfold_def,[status(thm)],[259]) ).
thf(868,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( element @ ( the_topology @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(869,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(870,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(871,plain,
$true = $true,
inference(unfold_def,[status(thm)],[267]) ).
thf(872,plain,
$true = $true,
inference(unfold_def,[status(thm)],[268]) ).
thf(873,plain,
$true = $true,
inference(unfold_def,[status(thm)],[273]) ).
thf(874,plain,
$true = $true,
inference(unfold_def,[status(thm)],[277]) ).
thf(875,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(876,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(877,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(878,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(879,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(880,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(881,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(882,plain,
$true = $true,
inference(unfold_def,[status(thm)],[298]) ).
thf(883,plain,
$true = $true,
inference(unfold_def,[status(thm)],[301]) ).
thf(884,plain,
$true = $true,
inference(unfold_def,[status(thm)],[302]) ).
thf(885,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_union2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(886,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(887,plain,
( ( ! [A: $i] :
( ( strict_rel_str @ ( boole_POSet @ A ) )
& ( rel_str @ ( boole_POSet @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(888,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(889,plain,
$true = $true,
inference(unfold_def,[status(thm)],[311]) ).
thf(890,plain,
$true = $true,
inference(unfold_def,[status(thm)],[313]) ).
thf(891,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(892,plain,
$true = $true,
inference(unfold_def,[status(thm)],[315]) ).
thf(893,plain,
$true = $true,
inference(unfold_def,[status(thm)],[318]) ).
thf(894,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( meet_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(895,plain,
$true = $true,
inference(unfold_def,[status(thm)],[321]) ).
thf(896,plain,
$true = $true,
inference(unfold_def,[status(thm)],[323]) ).
thf(897,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(898,plain,
$true = $true,
inference(unfold_def,[status(thm)],[326]) ).
thf(899,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(900,plain,
$true = $true,
inference(unfold_def,[status(thm)],[328]) ).
thf(901,plain,
$true = $true,
inference(unfold_def,[status(thm)],[333]) ).
thf(902,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(903,plain,
$true = $true,
inference(unfold_def,[status(thm)],[336]) ).
thf(904,plain,
$true = $true,
inference(unfold_def,[status(thm)],[338]) ).
thf(905,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(906,plain,
$true = $true,
inference(unfold_def,[status(thm)],[342]) ).
thf(907,plain,
$true = $true,
inference(unfold_def,[status(thm)],[343]) ).
thf(908,plain,
$true = $true,
inference(unfold_def,[status(thm)],[344]) ).
thf(909,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(910,plain,
( ( ! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(911,plain,
$true = $true,
inference(unfold_def,[status(thm)],[347]) ).
thf(912,plain,
$true = $true,
inference(unfold_def,[status(thm)],[348]) ).
thf(913,plain,
$true = $true,
inference(unfold_def,[status(thm)],[351]) ).
thf(914,plain,
$true = $true,
inference(unfold_def,[status(thm)],[352]) ).
thf(915,plain,
$true = $true,
inference(unfold_def,[status(thm)],[354]) ).
thf(916,plain,
$true = $true,
inference(unfold_def,[status(thm)],[358]) ).
thf(917,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(918,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(919,plain,
( ( ! [A: $i] :
( ( boole_POSet @ A )
= ( poset_of_lattice @ ( boole_lattice @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(920,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(921,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier @ A )
<=> ( empty @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(922,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(923,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(924,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( subset_union2 @ A @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(925,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(926,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(927,plain,
( ( ! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(928,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(929,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(930,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(931,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(932,plain,
( ( ! [A: $i] :
( ( boole_POSet @ A )
= ( incl_POSet @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(933,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(934,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ( ( related_reflexive @ ( boole_POSet @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(935,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[736]) ).
thf(936,plain,
( ( ! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[737]) ).
thf(937,plain,
( ( ! [A: $i] :
( ( bottom_of_relstr @ ( boole_POSet @ A ) )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[744]) ).
thf(938,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[776]) ).
thf(939,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[780]) ).
thf(940,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[791]) ).
thf(941,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[824]) ).
thf(942,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[832]) ).
thf(943,plain,
( ( ( the_carrier @ ( boole_POSet @ sK1_A ) )
= ( powerset @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[845]) ).
thf(944,plain,
( ( ( the_carrier @ ( boole_POSet @ sK1_A ) )
!= ( powerset @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[943]) ).
thf(945,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(946,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(947,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(948,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(949,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(950,plain,
( ( ! [A: $i] :
( ( bottom_of_relstr @ ( boole_POSet @ A ) )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[937]) ).
thf(951,plain,
( ( ! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(952,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(953,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_POSet @ A ) ) )
=> ( ( related_reflexive @ ( boole_POSet @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[934]) ).
thf(954,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(955,plain,
( ( ! [A: $i] :
( ( boole_POSet @ A )
= ( incl_POSet @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(956,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(957,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(958,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(959,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(960,plain,
( ( ! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(961,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(962,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(963,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( subset_union2 @ A @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(964,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(965,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(966,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier @ A )
<=> ( empty @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(967,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(968,plain,
( ( ! [A: $i] :
( ( boole_POSet @ A )
= ( poset_of_lattice @ ( boole_lattice @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(969,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(970,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[917]) ).
thf(971,plain,
$true = $true,
inference(copy,[status(thm)],[916]) ).
thf(972,plain,
$true = $true,
inference(copy,[status(thm)],[915]) ).
thf(973,plain,
$true = $true,
inference(copy,[status(thm)],[914]) ).
thf(974,plain,
$true = $true,
inference(copy,[status(thm)],[913]) ).
thf(975,plain,
$true = $true,
inference(copy,[status(thm)],[912]) ).
thf(976,plain,
$true = $true,
inference(copy,[status(thm)],[911]) ).
thf(977,plain,
( ( ! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(978,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(979,plain,
$true = $true,
inference(copy,[status(thm)],[908]) ).
thf(980,plain,
$true = $true,
inference(copy,[status(thm)],[907]) ).
thf(981,plain,
$true = $true,
inference(copy,[status(thm)],[906]) ).
thf(982,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(983,plain,
$true = $true,
inference(copy,[status(thm)],[904]) ).
thf(984,plain,
$true = $true,
inference(copy,[status(thm)],[903]) ).
thf(985,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(986,plain,
$true = $true,
inference(copy,[status(thm)],[901]) ).
thf(987,plain,
$true = $true,
inference(copy,[status(thm)],[900]) ).
thf(988,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(989,plain,
$true = $true,
inference(copy,[status(thm)],[898]) ).
thf(990,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(991,plain,
$true = $true,
inference(copy,[status(thm)],[896]) ).
thf(992,plain,
$true = $true,
inference(copy,[status(thm)],[895]) ).
thf(993,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( meet_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(994,plain,
$true = $true,
inference(copy,[status(thm)],[893]) ).
thf(995,plain,
$true = $true,
inference(copy,[status(thm)],[892]) ).
thf(996,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[891]) ).
thf(997,plain,
$true = $true,
inference(copy,[status(thm)],[890]) ).
thf(998,plain,
$true = $true,
inference(copy,[status(thm)],[889]) ).
thf(999,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(1000,plain,
( ( ! [A: $i] :
( ( strict_rel_str @ ( boole_POSet @ A ) )
& ( rel_str @ ( boole_POSet @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(1001,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(1002,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_union2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(1003,plain,
$true = $true,
inference(copy,[status(thm)],[884]) ).
thf(1004,plain,
$true = $true,
inference(copy,[status(thm)],[883]) ).
thf(1005,plain,
$true = $true,
inference(copy,[status(thm)],[882]) ).
thf(1006,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(1007,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(1008,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(1009,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(1010,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(1011,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(1012,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(1013,plain,
$true = $true,
inference(copy,[status(thm)],[874]) ).
thf(1014,plain,
$true = $true,
inference(copy,[status(thm)],[873]) ).
thf(1015,plain,
$true = $true,
inference(copy,[status(thm)],[872]) ).
thf(1016,plain,
$true = $true,
inference(copy,[status(thm)],[871]) ).
thf(1017,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(1018,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(1019,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( element @ ( the_topology @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(1020,plain,
$true = $true,
inference(copy,[status(thm)],[867]) ).
thf(1021,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(1022,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(1023,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(1024,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(1025,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(1026,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(1027,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(1028,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(1029,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1030,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ~ ( empty @ B )
& ( finite @ B ) ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(1031,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(1032,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(1033,plain,
( ( ! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(1034,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(1035,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(1036,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(1037,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(1038,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(1039,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(1040,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(1041,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(1042,plain,
( ( ( the_carrier @ ( boole_POSet @ sK1_A ) )
!= ( powerset @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(1043,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ~ ( ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) )
| ( SX1 != SX0 ) )
| ~ ( ~ ( ( SX1 != SX0 ) )
| ( proper_element @ SX1 @ ( powerset @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[957]) ).
thf(1044,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ( relation @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[961]) ).
thf(1045,plain,
( ( ! [SX0: $i] :
~ ( ~ ( strict_rel_str @ ( boole_POSet @ SX0 ) )
| ~ ( rel_str @ ( boole_POSet @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1000]) ).
thf(1046,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( element @ SX2 @ ( powerset @ ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1017]) ).
thf(1047,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1040]) ).
thf(1048,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( element @ ( subset_intersection2 @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1008]) ).
thf(1049,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( element @ ( subset_union2 @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1002]) ).
thf(1050,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( element @ ( subset_complement @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[996]) ).
thf(1051,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ~ ~ ( ~ ( ( SX1 != empty_set ) )
| ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) )
| ( SX1 != empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[947]) ).
thf(1052,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_union2 @ SX0 @ SX1 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1023]) ).
thf(1053,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1031]) ).
thf(1054,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( powerset @ SX2 ) @ SX1 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SX1 )
| ~ ~ ( are_equipotent @ SX2 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[949]) ).
thf(1055,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ( element @ ( the_topology @ SX0 ) @ ( powerset @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1019]) ).
thf(1056,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( identity_on_carrier @ SX0 )
= ( identity_as_relation_of @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[965]) ).
thf(1057,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1029]) ).
thf(1058,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_difference @ SX0 @ SX1 @ SX2 )
= ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1038]) ).
thf(1059,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( element @ ( bottom_of_relstr @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[999]) ).
thf(1060,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ ( subset_complement @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1025]) ).
thf(1061,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1028]) ).
thf(1062,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( meet_of_subsets @ SX0 @ SX1 )
= ( set_meet @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1037]) ).
thf(1063,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_intersection2 @ SX0 @ SX1 @ SX2 )
= ( subset_intersection2 @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[964]) ).
thf(1064,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( cast_as_carrier_subset @ SX0 )
= ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[969]) ).
thf(1065,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_union2 @ SX0 @ SX1 @ SX2 )
= ( subset_union2 @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[963]) ).
thf(1066,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_union2 @ SX0 @ SX1 @ SX2 )
= ( set_union2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1034]) ).
thf(1067,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ( empty @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1021]) ).
thf(1068,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ~ ( ~ ( in @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[956]) ).
thf(1069,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( powerset @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[967]) ).
thf(1070,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( meet_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1010]) ).
thf(1071,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( top_str @ SX0 )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ( element @ ( topstr_closure @ SX0 @ SX1 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1009]) ).
thf(1072,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ SX1 )
= ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[970]) ).
thf(1073,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( union_of_subsets @ SX0 @ SX1 )
= ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1035]) ).
thf(1074,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_str @ SX0 )
| ( element @ ( join_on_relstr @ SX0 @ SX1 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[985]) ).
thf(1075,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[959]) ).
thf(1076,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[945]) ).
thf(1077,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( complements_of_subsets @ SX0 @ ( complements_of_subsets @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1026]) ).
thf(1078,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[946]) ).
thf(1079,plain,
( ( ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ~ ( v1_membered @ SX1 )
| ~ ( v2_membered @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[960]) ).
thf(1080,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_intersection2 @ SX0 @ SX1 @ SX2 )
= ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1036]) ).
thf(1081,plain,
( ( ! [SX0: $i] :
~ ( ( ( the_carrier @ ( incl_POSet @ SX0 ) )
!= SX0 )
| ( ( the_InternalRel @ ( incl_POSet @ SX0 ) )
!= ( inclusion_order @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[951]) ).
thf(1082,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( element @ ( empty_carrier_subset @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[978]) ).
thf(1083,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( element @ ( relation_rng_as_subset @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1006]) ).
thf(1084,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1032]) ).
thf(1085,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1030]) ).
thf(1086,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( complements_of_subsets @ SX0 @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1012]) ).
thf(1087,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( element @ ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1001]) ).
thf(1088,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1041]) ).
thf(1089,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( top_str @ SX0 )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ( element @ ( interior @ SX0 @ SX1 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[982]) ).
thf(1090,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1027]) ).
thf(1091,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[962]) ).
thf(1092,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1 != empty_set ) )
| ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[954]) ).
thf(1093,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ ( boole_POSet @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ ( boole_POSet @ SX0 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SX0 ) @ SX1 @ SX2 )
| ( subset @ SX1 @ SX2 ) )
| ~ ( ~ ( subset @ SX1 @ SX2 )
| ( related_reflexive @ ( boole_POSet @ SX0 ) @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[953]) ).
thf(1094,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( element @ ( subset_difference @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1011]) ).
thf(1095,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_intersection2 @ SX0 @ SX1 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1024]) ).
thf(1096,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ( ~ ( empty_carrier @ SX0 )
| ( empty @ ( the_carrier @ SX0 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SX0 ) )
| ( empty_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[966]) ).
thf(1097,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( union_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1007]) ).
thf(1098,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( cast_as_carrier_subset @ SX0 )
= ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[948]) ).
thf(1099,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1039]) ).
thf(1100,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_str @ SX0 )
| ( element @ ( meet_on_relstr @ SX0 @ SX1 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[993]) ).
thf(1101,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1018]) ).
thf(1102,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( element @ ( cast_as_carrier_subset @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[988]) ).
thf(1103,plain,
! [SV1: $i] :
( ( ( bottom_of_relstr @ ( boole_POSet @ SV1 ) )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1104,plain,
! [SV2: $i] :
( ( ( boole_POSet @ SV2 )
= ( incl_POSet @ ( powerset @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1105,plain,
! [SV3: $i] :
( ( ( union @ ( powerset @ SV3 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1106,plain,
! [SV4: $i] :
( ( ( boole_POSet @ SV4 )
= ( poset_of_lattice @ ( boole_lattice @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1107,plain,
! [SV5: $i] :
( ( element @ ( k1_pcomps_1 @ SV5 ) @ ( powerset @ ( powerset @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1108,plain,
! [SV6: $i] :
( ( element @ ( cast_to_subset @ SV6 ) @ ( powerset @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1109,plain,
! [SV7: $i] :
( ( ~ ( empty @ ( powerset @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1110,plain,
! [SV8: $i] :
( ( ( k1_pcomps_1 @ SV8 )
= ( powerset @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1111,plain,
( ( ( the_carrier @ ( boole_POSet @ sK1_A ) )
= ( powerset @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1112,plain,
! [SV9: $i] :
( ( ! [SY142: $i] :
( ~ ( element @ SY142 @ ( powerset @ SV9 ) )
| ~ ( ~ ( ~ ( proper_element @ SY142 @ ( powerset @ SV9 ) )
| ( SY142 != SV9 ) )
| ~ ( ~ ( ( SY142 != SV9 ) )
| ( proper_element @ SY142 @ ( powerset @ SV9 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1113,plain,
! [SV10: $i] :
( ( ! [SY143: $i,SY144: $i] :
( ~ ( element @ SY144 @ ( powerset @ ( cartesian_product2 @ SV10 @ SY143 ) ) )
| ( relation @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1114,plain,
! [SV11: $i] :
( ( ~ ( ~ ( strict_rel_str @ ( boole_POSet @ SV11 ) )
| ~ ( rel_str @ ( boole_POSet @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1115,plain,
! [SV12: $i] :
( ( ! [SY145: $i,SY146: $i] :
( ~ ( relation_of2_as_subset @ SY146 @ SV12 @ SY145 )
| ( element @ SY146 @ ( powerset @ ( cartesian_product2 @ SV12 @ SY145 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1116,plain,
! [SV13: $i] :
( ( ! [SY147: $i,SY148: $i] :
( ~ ~ ( ~ ( in @ SV13 @ SY147 )
| ~ ( element @ SY147 @ ( powerset @ SY148 ) ) )
| ( element @ SV13 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1117,plain,
! [SV14: $i] :
( ( ! [SY149: $i,SY150: $i] :
( ~ ~ ( ~ ( element @ SY149 @ ( powerset @ SV14 ) )
| ~ ( element @ SY150 @ ( powerset @ SV14 ) ) )
| ( element @ ( subset_intersection2 @ SV14 @ SY149 @ SY150 ) @ ( powerset @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1118,plain,
! [SV15: $i] :
( ( ! [SY151: $i,SY152: $i] :
( ~ ~ ( ~ ( element @ SY151 @ ( powerset @ SV15 ) )
| ~ ( element @ SY152 @ ( powerset @ SV15 ) ) )
| ( element @ ( subset_union2 @ SV15 @ SY151 @ SY152 ) @ ( powerset @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1119,plain,
! [SV16: $i] :
( ( ! [SY153: $i] :
( ~ ( element @ SY153 @ ( powerset @ SV16 ) )
| ( element @ ( subset_complement @ SV16 @ SY153 ) @ ( powerset @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1120,plain,
! [SV17: $i] :
( ( ! [SY154: $i] :
( ~ ( element @ SY154 @ ( powerset @ ( powerset @ SV17 ) ) )
| ~ ( ~ ~ ~ ( ~ ( ( SY154 != empty_set ) )
| ( ( complements_of_subsets @ SV17 @ SY154 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV17 @ SY154 )
!= empty_set ) )
| ( SY154 != empty_set ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1121,plain,
! [SV18: $i] :
( ( ! [SY155: $i,SY156: $i] :
( ~ ~ ( ~ ( element @ SY155 @ ( powerset @ SV18 ) )
| ~ ( element @ SY156 @ ( powerset @ SV18 ) ) )
| ( ( subset_union2 @ SV18 @ SY155 @ SY155 )
= SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1122,plain,
! [SV19: $i] :
( ( ~ ~ ( empty @ SV19 )
| ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY157 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY157 ) )
| ~ ( finite @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1123,plain,
! [SV20: $i] :
( ( ~ ! [SY158: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV20 @ SY158 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY158 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY158 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY158 )
| ( in @ ( powerset @ SX2 ) @ SY158 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY158 )
| ~ ~ ( are_equipotent @ SX2 @ SY158 ) )
| ~ ~ ( in @ SX2 @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1124,plain,
! [SV21: $i] :
( ( ~ ( top_str @ SV21 )
| ( element @ ( the_topology @ SV21 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1125,plain,
! [SV22: $i] :
( ( ~ ( one_sorted_str @ SV22 )
| ( ( identity_on_carrier @ SV22 )
= ( identity_as_relation_of @ ( the_carrier @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1126,plain,
! [SV23: $i] :
( ( ~ ! [SY163: $i] :
~ ~ ( ~ ( element @ SY163 @ ( powerset @ SV23 ) )
| ~ ~ ( proper_element @ SY163 @ ( powerset @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1127,plain,
! [SV24: $i] :
( ( ! [SY164: $i,SY165: $i] :
( ~ ~ ( ~ ( element @ SY164 @ ( powerset @ SV24 ) )
| ~ ( element @ SY165 @ ( powerset @ SV24 ) ) )
| ( ( subset_difference @ SV24 @ SY164 @ SY165 )
= ( set_difference @ SY164 @ SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1128,plain,
! [SV25: $i] :
( ( ~ ( rel_str @ SV25 )
| ( element @ ( bottom_of_relstr @ SV25 ) @ ( the_carrier @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1129,plain,
! [SV26: $i] :
( ( ! [SY166: $i] :
( ~ ( element @ SY166 @ ( powerset @ SV26 ) )
| ( ( subset_complement @ SV26 @ ( subset_complement @ SV26 @ SY166 ) )
= SY166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1130,plain,
! [SV27: $i] :
( ( ~ ! [SY167: $i] :
~ ~ ( ~ ( element @ SY167 @ ( powerset @ SV27 ) )
| ~ ( empty @ SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1131,plain,
! [SV28: $i] :
( ( ! [SY168: $i] :
( ~ ( element @ SY168 @ ( powerset @ ( powerset @ SV28 ) ) )
| ( ( meet_of_subsets @ SV28 @ SY168 )
= ( set_meet @ SY168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1132,plain,
! [SV29: $i] :
( ( ! [SY169: $i,SY170: $i] :
( ~ ~ ( ~ ( element @ SY169 @ ( powerset @ SV29 ) )
| ~ ( element @ SY170 @ ( powerset @ SV29 ) ) )
| ( ( subset_intersection2 @ SV29 @ SY169 @ SY170 )
= ( subset_intersection2 @ SV29 @ SY170 @ SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1133,plain,
! [SV30: $i] :
( ( ~ ( one_sorted_str @ SV30 )
| ( ( cast_as_carrier_subset @ SV30 )
= ( the_carrier @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1134,plain,
! [SV31: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ~ ~ ( ~ ( element @ SY171 @ ( powerset @ SV31 ) )
| ~ ( element @ SY172 @ ( powerset @ SV31 ) ) )
| ( ( subset_union2 @ SV31 @ SY171 @ SY172 )
= ( subset_union2 @ SV31 @ SY172 @ SY171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1135,plain,
! [SV32: $i] :
( ( ! [SY173: $i,SY174: $i] :
( ~ ~ ( ~ ( element @ SY173 @ ( powerset @ SV32 ) )
| ~ ( element @ SY174 @ ( powerset @ SV32 ) ) )
| ( ( subset_union2 @ SV32 @ SY173 @ SY174 )
= ( set_union2 @ SY173 @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1136,plain,
! [SV33: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV33 )
| ~ ( one_sorted_str @ SV33 ) )
| ~ ( empty @ ( the_carrier @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1137,plain,
! [SV34: $i] :
( ( ! [SY175: $i,SY176: $i] :
( ~ ( element @ SY176 @ ( powerset @ SV34 ) )
| ~ ~ ( ~ ( in @ SY175 @ ( subset_complement @ SV34 @ SY176 ) )
| ~ ( in @ SY175 @ SY176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1138,plain,
! [SV35: $i] :
( ( ! [SY177: $i] :
~ ( ~ ( ( SY177
!= ( powerset @ SV35 ) )
| ! [SY178: $i] :
~ ( ~ ( ~ ( in @ SY178 @ SY177 )
| ( subset @ SY178 @ SV35 ) )
| ~ ( ~ ( subset @ SY178 @ SV35 )
| ( in @ SY178 @ SY177 ) ) ) )
| ~ ( ~ ! [SY179: $i] :
~ ( ~ ( ~ ( in @ SY179 @ SY177 )
| ( subset @ SY179 @ SV35 ) )
| ~ ( ~ ( subset @ SY179 @ SV35 )
| ( in @ SY179 @ SY177 ) ) )
| ( SY177
= ( powerset @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1139,plain,
! [SV36: $i] :
( ( ! [SY180: $i] :
( ~ ( element @ SY180 @ ( powerset @ ( powerset @ SV36 ) ) )
| ( element @ ( meet_of_subsets @ SV36 @ SY180 ) @ ( powerset @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1140,plain,
! [SV37: $i] :
( ( ! [SY181: $i] :
( ~ ~ ( ~ ( top_str @ SV37 )
| ~ ( element @ SY181 @ ( powerset @ ( the_carrier @ SV37 ) ) ) )
| ( element @ ( topstr_closure @ SV37 @ SY181 ) @ ( powerset @ ( the_carrier @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1141,plain,
! [SV38: $i] :
( ( ! [SY182: $i] :
( ~ ( element @ SY182 @ ( powerset @ SV38 ) )
| ( ( subset_complement @ SV38 @ SY182 )
= ( set_difference @ SV38 @ SY182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1142,plain,
! [SV39: $i] :
( ( ! [SY183: $i] :
( ~ ( element @ SY183 @ ( powerset @ ( powerset @ SV39 ) ) )
| ( ( union_of_subsets @ SV39 @ SY183 )
= ( union @ SY183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1143,plain,
! [SV40: $i] :
( ( ! [SY184: $i] :
( ~ ( rel_str @ SV40 )
| ( element @ ( join_on_relstr @ SV40 @ SY184 ) @ ( the_carrier @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1144,plain,
! [SV41: $i] :
( ( ~ ( v1_membered @ SV41 )
| ! [SY185: $i] :
( ~ ( element @ SY185 @ ( powerset @ SV41 ) )
| ( v1_membered @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1145,plain,
! [SV42: $i] :
( ( ! [SY186: $i] :
( ~ ( element @ SY186 @ ( powerset @ SV42 ) )
| ! [SY187: $i] :
( ~ ( in @ SY187 @ SY186 )
| ( in @ SY187 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1146,plain,
! [SV43: $i] :
( ( ! [SY188: $i] :
( ~ ( element @ SY188 @ ( powerset @ ( powerset @ SV43 ) ) )
| ( ( complements_of_subsets @ SV43 @ ( complements_of_subsets @ SV43 @ SY188 ) )
= SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1147,plain,
! [SV44: $i] :
( ( ! [SY189: $i] :
( ~ ! [SY190: $i] :
( ~ ( in @ SY190 @ SV44 )
| ( in @ SY190 @ SY189 ) )
| ( element @ SV44 @ ( powerset @ SY189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1148,plain,
! [SV45: $i] :
( ( ~ ( v2_membered @ SV45 )
| ! [SY191: $i] :
( ~ ( element @ SY191 @ ( powerset @ SV45 ) )
| ~ ( ~ ( v1_membered @ SY191 )
| ~ ( v2_membered @ SY191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1149,plain,
! [SV46: $i] :
( ( ! [SY192: $i,SY193: $i] :
( ~ ~ ( ~ ( element @ SY192 @ ( powerset @ SV46 ) )
| ~ ( element @ SY193 @ ( powerset @ SV46 ) ) )
| ( ( subset_intersection2 @ SV46 @ SY192 @ SY193 )
= ( set_intersection2 @ SY192 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1150,plain,
! [SV47: $i] :
( ( ~ ( ( ( the_carrier @ ( incl_POSet @ SV47 ) )
!= SV47 )
| ( ( the_InternalRel @ ( incl_POSet @ SV47 ) )
!= ( inclusion_order @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1151,plain,
! [SV48: $i] :
( ( ~ ( one_sorted_str @ SV48 )
| ( element @ ( empty_carrier_subset @ SV48 ) @ ( powerset @ ( the_carrier @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1152,plain,
! [SV49: $i] :
( ( ! [SY194: $i,SY195: $i] :
( ~ ( relation_of2 @ SY195 @ SV49 @ SY194 )
| ( element @ ( relation_rng_as_subset @ SV49 @ SY194 @ SY195 ) @ ( powerset @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1153,plain,
! [SV50: $i] :
( ( ~ ~ ( empty @ SV50 )
| ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY196 @ ( powerset @ SV50 ) )
| ~ ~ ( empty @ SY196 ) )
| ~ ( finite @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1154,plain,
! [SV51: $i] :
( ( ~ ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY197 @ ( powerset @ ( powerset @ SV51 ) ) )
| ~ ~ ( empty @ SY197 ) )
| ~ ( finite @ SY197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1155,plain,
! [SV52: $i] :
( ( ! [SY198: $i] :
( ~ ( element @ SY198 @ ( powerset @ ( powerset @ SV52 ) ) )
| ( element @ ( complements_of_subsets @ SV52 @ SY198 ) @ ( powerset @ ( powerset @ SV52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1156,plain,
! [SV53: $i] :
( ( ! [SY199: $i,SY200: $i] :
( ~ ( relation_of2 @ SY200 @ SV53 @ SY199 )
| ( element @ ( relation_dom_as_subset @ SV53 @ SY199 @ SY200 ) @ ( powerset @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1157,plain,
! [SV54: $i] :
( ( ! [SY201: $i,SY202: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV54 @ SY201 )
| ~ ( element @ SY201 @ ( powerset @ SY202 ) ) )
| ~ ( empty @ SY202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1158,plain,
! [SV55: $i] :
( ( ! [SY203: $i] :
( ~ ~ ( ~ ( top_str @ SV55 )
| ~ ( element @ SY203 @ ( powerset @ ( the_carrier @ SV55 ) ) ) )
| ( element @ ( interior @ SV55 @ SY203 ) @ ( powerset @ ( the_carrier @ SV55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1159,plain,
! [SV56: $i] :
( ( ~ ~ ( empty @ SV56 )
| ~ ! [SY204: $i] :
~ ~ ( ~ ( element @ SY204 @ ( powerset @ SV56 ) )
| ~ ~ ( empty @ SY204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1160,plain,
! [SV57: $i] :
( ( ~ ( finite @ SV57 )
| ! [SY205: $i] :
( ~ ( element @ SY205 @ ( powerset @ SV57 ) )
| ( finite @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1161,plain,
! [SV58: $i] :
( ( ! [SY206: $i] :
( ~ ( element @ SY206 @ ( powerset @ ( powerset @ SV58 ) ) )
| ~ ~ ( ~ ( ( SY206 != empty_set ) )
| ( ( complements_of_subsets @ SV58 @ SY206 )
!= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1162,plain,
! [SV59: $i] :
( ( ! [SY207: $i] :
( ~ ( element @ SY207 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
| ! [SY208: $i] :
( ~ ( element @ SY208 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV59 ) @ SY207 @ SY208 )
| ( subset @ SY207 @ SY208 ) )
| ~ ( ~ ( subset @ SY207 @ SY208 )
| ( related_reflexive @ ( boole_POSet @ SV59 ) @ SY207 @ SY208 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1163,plain,
! [SV60: $i] :
( ( ! [SY209: $i,SY210: $i] :
( ~ ~ ( ~ ( element @ SY209 @ ( powerset @ SV60 ) )
| ~ ( element @ SY210 @ ( powerset @ SV60 ) ) )
| ( element @ ( subset_difference @ SV60 @ SY209 @ SY210 ) @ ( powerset @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1164,plain,
! [SV61: $i] :
( ( ! [SY211: $i,SY212: $i] :
( ~ ~ ( ~ ( element @ SY211 @ ( powerset @ SV61 ) )
| ~ ( element @ SY212 @ ( powerset @ SV61 ) ) )
| ( ( subset_intersection2 @ SV61 @ SY211 @ SY211 )
= SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1165,plain,
! [SV62: $i] :
( ( ~ ( one_sorted_str @ SV62 )
| ~ ( ~ ( ~ ( empty_carrier @ SV62 )
| ( empty @ ( the_carrier @ SV62 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV62 ) )
| ( empty_carrier @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1166,plain,
! [SV63: $i] :
( ( ! [SY213: $i] :
( ~ ( element @ SY213 @ ( powerset @ ( powerset @ SV63 ) ) )
| ( element @ ( union_of_subsets @ SV63 @ SY213 ) @ ( powerset @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1167,plain,
! [SV64: $i] :
( ( ~ ( one_sorted_str @ SV64 )
| ( ( cast_as_carrier_subset @ SV64 )
= ( the_carrier @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1168,plain,
! [SV65: $i] :
( ( ! [SY214: $i] :
~ ( ~ ( ~ ( element @ SV65 @ ( powerset @ SY214 ) )
| ( subset @ SV65 @ SY214 ) )
| ~ ( ~ ( subset @ SV65 @ SY214 )
| ( element @ SV65 @ ( powerset @ SY214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1169,plain,
! [SV66: $i] :
( ( ! [SY215: $i] :
( ~ ( rel_str @ SV66 )
| ( element @ ( meet_on_relstr @ SV66 @ SY215 ) @ ( the_carrier @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1170,plain,
! [SV67: $i] :
( ( ~ ( rel_str @ SV67 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SV67 ) @ ( the_carrier @ SV67 ) @ ( the_carrier @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1171,plain,
! [SV68: $i] :
( ( ~ ( one_sorted_str @ SV68 )
| ( element @ ( cast_as_carrier_subset @ SV68 ) @ ( powerset @ ( the_carrier @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1172,plain,
! [SV7: $i] :
( ( empty @ ( powerset @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1173,plain,
! [SV9: $i,SV69: $i] :
( ( ~ ( element @ SV69 @ ( powerset @ SV9 ) )
| ~ ( ~ ( ~ ( proper_element @ SV69 @ ( powerset @ SV9 ) )
| ( SV69 != SV9 ) )
| ~ ( ~ ( ( SV69 != SV9 ) )
| ( proper_element @ SV69 @ ( powerset @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1174,plain,
! [SV70: $i,SV10: $i] :
( ( ! [SY216: $i] :
( ~ ( element @ SY216 @ ( powerset @ ( cartesian_product2 @ SV10 @ SV70 ) ) )
| ( relation @ SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1175,plain,
! [SV11: $i] :
( ( ~ ( strict_rel_str @ ( boole_POSet @ SV11 ) )
| ~ ( rel_str @ ( boole_POSet @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1176,plain,
! [SV71: $i,SV12: $i] :
( ( ! [SY217: $i] :
( ~ ( relation_of2_as_subset @ SY217 @ SV12 @ SV71 )
| ( element @ SY217 @ ( powerset @ ( cartesian_product2 @ SV12 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1177,plain,
! [SV72: $i,SV13: $i] :
( ( ! [SY218: $i] :
( ~ ~ ( ~ ( in @ SV13 @ SV72 )
| ~ ( element @ SV72 @ ( powerset @ SY218 ) ) )
| ( element @ SV13 @ SY218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1178,plain,
! [SV14: $i,SV73: $i] :
( ( ! [SY219: $i] :
( ~ ~ ( ~ ( element @ SV73 @ ( powerset @ SV14 ) )
| ~ ( element @ SY219 @ ( powerset @ SV14 ) ) )
| ( element @ ( subset_intersection2 @ SV14 @ SV73 @ SY219 ) @ ( powerset @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1179,plain,
! [SV15: $i,SV74: $i] :
( ( ! [SY220: $i] :
( ~ ~ ( ~ ( element @ SV74 @ ( powerset @ SV15 ) )
| ~ ( element @ SY220 @ ( powerset @ SV15 ) ) )
| ( element @ ( subset_union2 @ SV15 @ SV74 @ SY220 ) @ ( powerset @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1180,plain,
! [SV16: $i,SV75: $i] :
( ( ~ ( element @ SV75 @ ( powerset @ SV16 ) )
| ( element @ ( subset_complement @ SV16 @ SV75 ) @ ( powerset @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1181,plain,
! [SV17: $i,SV76: $i] :
( ( ~ ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
| ~ ( ~ ~ ~ ( ~ ( ( SV76 != empty_set ) )
| ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ( SV76 != empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1182,plain,
! [SV18: $i,SV77: $i] :
( ( ! [SY221: $i] :
( ~ ~ ( ~ ( element @ SV77 @ ( powerset @ SV18 ) )
| ~ ( element @ SY221 @ ( powerset @ SV18 ) ) )
| ( ( subset_union2 @ SV18 @ SV77 @ SV77 )
= SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1183,plain,
! [SV19: $i] :
( ( ( ~ ~ ( empty @ SV19 ) )
= $true )
| ( ( ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY157 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY157 ) )
| ~ ( finite @ SY157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1184,plain,
! [SV20: $i] :
( ( ! [SY158: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV20 @ SY158 )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY158 )
| ~ ( subset @ SX3 @ SX2 ) )
| ( in @ SX3 @ SY158 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY158 )
| ( in @ ( powerset @ SX2 ) @ SY158 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SX2 @ SY158 )
| ~ ~ ( are_equipotent @ SX2 @ SY158 ) )
| ~ ~ ( in @ SX2 @ SY158 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1185,plain,
! [SV21: $i] :
( ( ( ~ ( top_str @ SV21 ) )
= $true )
| ( ( element @ ( the_topology @ SV21 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1186,plain,
! [SV22: $i] :
( ( ( ~ ( one_sorted_str @ SV22 ) )
= $true )
| ( ( ( identity_on_carrier @ SV22 )
= ( identity_as_relation_of @ ( the_carrier @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1187,plain,
! [SV23: $i] :
( ( ! [SY163: $i] :
~ ~ ( ~ ( element @ SY163 @ ( powerset @ SV23 ) )
| ~ ~ ( proper_element @ SY163 @ ( powerset @ SV23 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1188,plain,
! [SV24: $i,SV78: $i] :
( ( ! [SY222: $i] :
( ~ ~ ( ~ ( element @ SV78 @ ( powerset @ SV24 ) )
| ~ ( element @ SY222 @ ( powerset @ SV24 ) ) )
| ( ( subset_difference @ SV24 @ SV78 @ SY222 )
= ( set_difference @ SV78 @ SY222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1189,plain,
! [SV25: $i] :
( ( ( ~ ( rel_str @ SV25 ) )
= $true )
| ( ( element @ ( bottom_of_relstr @ SV25 ) @ ( the_carrier @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1190,plain,
! [SV26: $i,SV79: $i] :
( ( ~ ( element @ SV79 @ ( powerset @ SV26 ) )
| ( ( subset_complement @ SV26 @ ( subset_complement @ SV26 @ SV79 ) )
= SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1191,plain,
! [SV27: $i] :
( ( ! [SY167: $i] :
~ ~ ( ~ ( element @ SY167 @ ( powerset @ SV27 ) )
| ~ ( empty @ SY167 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1192,plain,
! [SV28: $i,SV80: $i] :
( ( ~ ( element @ SV80 @ ( powerset @ ( powerset @ SV28 ) ) )
| ( ( meet_of_subsets @ SV28 @ SV80 )
= ( set_meet @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1193,plain,
! [SV29: $i,SV81: $i] :
( ( ! [SY223: $i] :
( ~ ~ ( ~ ( element @ SV81 @ ( powerset @ SV29 ) )
| ~ ( element @ SY223 @ ( powerset @ SV29 ) ) )
| ( ( subset_intersection2 @ SV29 @ SV81 @ SY223 )
= ( subset_intersection2 @ SV29 @ SY223 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1194,plain,
! [SV30: $i] :
( ( ( ~ ( one_sorted_str @ SV30 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV30 )
= ( the_carrier @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1195,plain,
! [SV31: $i,SV82: $i] :
( ( ! [SY224: $i] :
( ~ ~ ( ~ ( element @ SV82 @ ( powerset @ SV31 ) )
| ~ ( element @ SY224 @ ( powerset @ SV31 ) ) )
| ( ( subset_union2 @ SV31 @ SV82 @ SY224 )
= ( subset_union2 @ SV31 @ SY224 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1196,plain,
! [SV32: $i,SV83: $i] :
( ( ! [SY225: $i] :
( ~ ~ ( ~ ( element @ SV83 @ ( powerset @ SV32 ) )
| ~ ( element @ SY225 @ ( powerset @ SV32 ) ) )
| ( ( subset_union2 @ SV32 @ SV83 @ SY225 )
= ( set_union2 @ SV83 @ SY225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1197,plain,
! [SV33: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV33 )
| ~ ( one_sorted_str @ SV33 ) ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1198,plain,
! [SV84: $i,SV34: $i] :
( ( ! [SY226: $i] :
( ~ ( element @ SY226 @ ( powerset @ SV34 ) )
| ~ ~ ( ~ ( in @ SV84 @ ( subset_complement @ SV34 @ SY226 ) )
| ~ ( in @ SV84 @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1199,plain,
! [SV35: $i,SV85: $i] :
( ( ~ ( ~ ( ( SV85
!= ( powerset @ SV35 ) )
| ! [SY227: $i] :
~ ( ~ ( ~ ( in @ SY227 @ SV85 )
| ( subset @ SY227 @ SV35 ) )
| ~ ( ~ ( subset @ SY227 @ SV35 )
| ( in @ SY227 @ SV85 ) ) ) )
| ~ ( ~ ! [SY228: $i] :
~ ( ~ ( ~ ( in @ SY228 @ SV85 )
| ( subset @ SY228 @ SV35 ) )
| ~ ( ~ ( subset @ SY228 @ SV35 )
| ( in @ SY228 @ SV85 ) ) )
| ( SV85
= ( powerset @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1200,plain,
! [SV36: $i,SV86: $i] :
( ( ~ ( element @ SV86 @ ( powerset @ ( powerset @ SV36 ) ) )
| ( element @ ( meet_of_subsets @ SV36 @ SV86 ) @ ( powerset @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1201,plain,
! [SV87: $i,SV37: $i] :
( ( ~ ~ ( ~ ( top_str @ SV37 )
| ~ ( element @ SV87 @ ( powerset @ ( the_carrier @ SV37 ) ) ) )
| ( element @ ( topstr_closure @ SV37 @ SV87 ) @ ( powerset @ ( the_carrier @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1202,plain,
! [SV38: $i,SV88: $i] :
( ( ~ ( element @ SV88 @ ( powerset @ SV38 ) )
| ( ( subset_complement @ SV38 @ SV88 )
= ( set_difference @ SV38 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1203,plain,
! [SV39: $i,SV89: $i] :
( ( ~ ( element @ SV89 @ ( powerset @ ( powerset @ SV39 ) ) )
| ( ( union_of_subsets @ SV39 @ SV89 )
= ( union @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1204,plain,
! [SV90: $i,SV40: $i] :
( ( ~ ( rel_str @ SV40 )
| ( element @ ( join_on_relstr @ SV40 @ SV90 ) @ ( the_carrier @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1205,plain,
! [SV41: $i] :
( ( ( ~ ( v1_membered @ SV41 ) )
= $true )
| ( ( ! [SY185: $i] :
( ~ ( element @ SY185 @ ( powerset @ SV41 ) )
| ( v1_membered @ SY185 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1206,plain,
! [SV42: $i,SV91: $i] :
( ( ~ ( element @ SV91 @ ( powerset @ SV42 ) )
| ! [SY229: $i] :
( ~ ( in @ SY229 @ SV91 )
| ( in @ SY229 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1207,plain,
! [SV43: $i,SV92: $i] :
( ( ~ ( element @ SV92 @ ( powerset @ ( powerset @ SV43 ) ) )
| ( ( complements_of_subsets @ SV43 @ ( complements_of_subsets @ SV43 @ SV92 ) )
= SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1208,plain,
! [SV93: $i,SV44: $i] :
( ( ~ ! [SY230: $i] :
( ~ ( in @ SY230 @ SV44 )
| ( in @ SY230 @ SV93 ) )
| ( element @ SV44 @ ( powerset @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1209,plain,
! [SV45: $i] :
( ( ( ~ ( v2_membered @ SV45 ) )
= $true )
| ( ( ! [SY191: $i] :
( ~ ( element @ SY191 @ ( powerset @ SV45 ) )
| ~ ( ~ ( v1_membered @ SY191 )
| ~ ( v2_membered @ SY191 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1210,plain,
! [SV46: $i,SV94: $i] :
( ( ! [SY231: $i] :
( ~ ~ ( ~ ( element @ SV94 @ ( powerset @ SV46 ) )
| ~ ( element @ SY231 @ ( powerset @ SV46 ) ) )
| ( ( subset_intersection2 @ SV46 @ SV94 @ SY231 )
= ( set_intersection2 @ SV94 @ SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1211,plain,
! [SV47: $i] :
( ( ( ( the_carrier @ ( incl_POSet @ SV47 ) )
!= SV47 )
| ( ( the_InternalRel @ ( incl_POSet @ SV47 ) )
!= ( inclusion_order @ SV47 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1212,plain,
! [SV48: $i] :
( ( ( ~ ( one_sorted_str @ SV48 ) )
= $true )
| ( ( element @ ( empty_carrier_subset @ SV48 ) @ ( powerset @ ( the_carrier @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1213,plain,
! [SV95: $i,SV49: $i] :
( ( ! [SY232: $i] :
( ~ ( relation_of2 @ SY232 @ SV49 @ SV95 )
| ( element @ ( relation_rng_as_subset @ SV49 @ SV95 @ SY232 ) @ ( powerset @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1214,plain,
! [SV50: $i] :
( ( ( ~ ~ ( empty @ SV50 ) )
= $true )
| ( ( ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY196 @ ( powerset @ SV50 ) )
| ~ ~ ( empty @ SY196 ) )
| ~ ( finite @ SY196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1215,plain,
! [SV51: $i] :
( ( ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY197 @ ( powerset @ ( powerset @ SV51 ) ) )
| ~ ~ ( empty @ SY197 ) )
| ~ ( finite @ SY197 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1216,plain,
! [SV52: $i,SV96: $i] :
( ( ~ ( element @ SV96 @ ( powerset @ ( powerset @ SV52 ) ) )
| ( element @ ( complements_of_subsets @ SV52 @ SV96 ) @ ( powerset @ ( powerset @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1217,plain,
! [SV97: $i,SV53: $i] :
( ( ! [SY233: $i] :
( ~ ( relation_of2 @ SY233 @ SV53 @ SV97 )
| ( element @ ( relation_dom_as_subset @ SV53 @ SV97 @ SY233 ) @ ( powerset @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1218,plain,
! [SV98: $i,SV54: $i] :
( ( ! [SY234: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV54 @ SV98 )
| ~ ( element @ SV98 @ ( powerset @ SY234 ) ) )
| ~ ( empty @ SY234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1219,plain,
! [SV99: $i,SV55: $i] :
( ( ~ ~ ( ~ ( top_str @ SV55 )
| ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ SV55 ) ) ) )
| ( element @ ( interior @ SV55 @ SV99 ) @ ( powerset @ ( the_carrier @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1220,plain,
! [SV56: $i] :
( ( ( ~ ~ ( empty @ SV56 ) )
= $true )
| ( ( ~ ! [SY204: $i] :
~ ~ ( ~ ( element @ SY204 @ ( powerset @ SV56 ) )
| ~ ~ ( empty @ SY204 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1221,plain,
! [SV57: $i] :
( ( ( ~ ( finite @ SV57 ) )
= $true )
| ( ( ! [SY205: $i] :
( ~ ( element @ SY205 @ ( powerset @ SV57 ) )
| ( finite @ SY205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1222,plain,
! [SV58: $i,SV100: $i] :
( ( ~ ( element @ SV100 @ ( powerset @ ( powerset @ SV58 ) ) )
| ~ ~ ( ~ ( ( SV100 != empty_set ) )
| ( ( complements_of_subsets @ SV58 @ SV100 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1223,plain,
! [SV59: $i,SV101: $i] :
( ( ~ ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
| ! [SY235: $i] :
( ~ ( element @ SY235 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SY235 )
| ( subset @ SV101 @ SY235 ) )
| ~ ( ~ ( subset @ SV101 @ SY235 )
| ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SY235 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1224,plain,
! [SV60: $i,SV102: $i] :
( ( ! [SY236: $i] :
( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV60 ) )
| ~ ( element @ SY236 @ ( powerset @ SV60 ) ) )
| ( element @ ( subset_difference @ SV60 @ SV102 @ SY236 ) @ ( powerset @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1225,plain,
! [SV61: $i,SV103: $i] :
( ( ! [SY237: $i] :
( ~ ~ ( ~ ( element @ SV103 @ ( powerset @ SV61 ) )
| ~ ( element @ SY237 @ ( powerset @ SV61 ) ) )
| ( ( subset_intersection2 @ SV61 @ SV103 @ SV103 )
= SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1226,plain,
! [SV62: $i] :
( ( ( ~ ( one_sorted_str @ SV62 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( empty_carrier @ SV62 )
| ( empty @ ( the_carrier @ SV62 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV62 ) )
| ( empty_carrier @ SV62 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1227,plain,
! [SV63: $i,SV104: $i] :
( ( ~ ( element @ SV104 @ ( powerset @ ( powerset @ SV63 ) ) )
| ( element @ ( union_of_subsets @ SV63 @ SV104 ) @ ( powerset @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1228,plain,
! [SV64: $i] :
( ( ( ~ ( one_sorted_str @ SV64 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV64 )
= ( the_carrier @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1229,plain,
! [SV105: $i,SV65: $i] :
( ( ~ ( ~ ( ~ ( element @ SV65 @ ( powerset @ SV105 ) )
| ( subset @ SV65 @ SV105 ) )
| ~ ( ~ ( subset @ SV65 @ SV105 )
| ( element @ SV65 @ ( powerset @ SV105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1230,plain,
! [SV106: $i,SV66: $i] :
( ( ~ ( rel_str @ SV66 )
| ( element @ ( meet_on_relstr @ SV66 @ SV106 ) @ ( the_carrier @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1231,plain,
! [SV67: $i] :
( ( ( ~ ( rel_str @ SV67 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV67 ) @ ( the_carrier @ SV67 ) @ ( the_carrier @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1232,plain,
! [SV68: $i] :
( ( ( ~ ( one_sorted_str @ SV68 ) )
= $true )
| ( ( element @ ( cast_as_carrier_subset @ SV68 ) @ ( powerset @ ( the_carrier @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1233,plain,
! [SV9: $i,SV69: $i] :
( ( ( ~ ( element @ SV69 @ ( powerset @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV69 @ ( powerset @ SV9 ) )
| ( SV69 != SV9 ) )
| ~ ( ~ ( ( SV69 != SV9 ) )
| ( proper_element @ SV69 @ ( powerset @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1234,plain,
! [SV70: $i,SV10: $i,SV107: $i] :
( ( ~ ( element @ SV107 @ ( powerset @ ( cartesian_product2 @ SV10 @ SV70 ) ) )
| ( relation @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1235,plain,
! [SV11: $i] :
( ( ~ ( strict_rel_str @ ( boole_POSet @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1236,plain,
! [SV11: $i] :
( ( ~ ( rel_str @ ( boole_POSet @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1237,plain,
! [SV71: $i,SV12: $i,SV108: $i] :
( ( ~ ( relation_of2_as_subset @ SV108 @ SV12 @ SV71 )
| ( element @ SV108 @ ( powerset @ ( cartesian_product2 @ SV12 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1238,plain,
! [SV109: $i,SV72: $i,SV13: $i] :
( ( ~ ~ ( ~ ( in @ SV13 @ SV72 )
| ~ ( element @ SV72 @ ( powerset @ SV109 ) ) )
| ( element @ SV13 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1239,plain,
! [SV110: $i,SV14: $i,SV73: $i] :
( ( ~ ~ ( ~ ( element @ SV73 @ ( powerset @ SV14 ) )
| ~ ( element @ SV110 @ ( powerset @ SV14 ) ) )
| ( element @ ( subset_intersection2 @ SV14 @ SV73 @ SV110 ) @ ( powerset @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1240,plain,
! [SV111: $i,SV15: $i,SV74: $i] :
( ( ~ ~ ( ~ ( element @ SV74 @ ( powerset @ SV15 ) )
| ~ ( element @ SV111 @ ( powerset @ SV15 ) ) )
| ( element @ ( subset_union2 @ SV15 @ SV74 @ SV111 ) @ ( powerset @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1241,plain,
! [SV16: $i,SV75: $i] :
( ( ( ~ ( element @ SV75 @ ( powerset @ SV16 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV16 @ SV75 ) @ ( powerset @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1242,plain,
! [SV17: $i,SV76: $i] :
( ( ( ~ ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ~ ( ~ ( ( SV76 != empty_set ) )
| ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ( SV76 != empty_set ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1243,plain,
! [SV112: $i,SV18: $i,SV77: $i] :
( ( ~ ~ ( ~ ( element @ SV77 @ ( powerset @ SV18 ) )
| ~ ( element @ SV112 @ ( powerset @ SV18 ) ) )
| ( ( subset_union2 @ SV18 @ SV77 @ SV77 )
= SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1244,plain,
! [SV19: $i] :
( ( ( ~ ( empty @ SV19 ) )
= $false )
| ( ( ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY157 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY157 ) )
| ~ ( finite @ SY157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1245,plain,
! [SV20: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV20 @ ( sK2_SY158 @ SV20 ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( in @ SY238 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY239 @ SY238 ) )
| ( in @ SY239 @ ( sK2_SY158 @ SV20 ) ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY158 @ SV20 ) )
| ( in @ ( powerset @ SY240 ) @ ( sK2_SY158 @ SV20 ) ) ) )
| ~ ! [SY241: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY241 @ ( sK2_SY158 @ SV20 ) )
| ~ ~ ( are_equipotent @ SY241 @ ( sK2_SY158 @ SV20 ) ) )
| ~ ~ ( in @ SY241 @ ( sK2_SY158 @ SV20 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1184]) ).
thf(1246,plain,
! [SV21: $i] :
( ( ( top_str @ SV21 )
= $false )
| ( ( element @ ( the_topology @ SV21 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1247,plain,
! [SV22: $i] :
( ( ( one_sorted_str @ SV22 )
= $false )
| ( ( ( identity_on_carrier @ SV22 )
= ( identity_as_relation_of @ ( the_carrier @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1248,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ( element @ ( sK3_SY163 @ SV23 ) @ ( powerset @ SV23 ) )
| ~ ~ ( proper_element @ ( sK3_SY163 @ SV23 ) @ ( powerset @ SV23 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1187]) ).
thf(1249,plain,
! [SV113: $i,SV24: $i,SV78: $i] :
( ( ~ ~ ( ~ ( element @ SV78 @ ( powerset @ SV24 ) )
| ~ ( element @ SV113 @ ( powerset @ SV24 ) ) )
| ( ( subset_difference @ SV24 @ SV78 @ SV113 )
= ( set_difference @ SV78 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1250,plain,
! [SV25: $i] :
( ( ( rel_str @ SV25 )
= $false )
| ( ( element @ ( bottom_of_relstr @ SV25 ) @ ( the_carrier @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1251,plain,
! [SV26: $i,SV79: $i] :
( ( ( ~ ( element @ SV79 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( ( subset_complement @ SV26 @ ( subset_complement @ SV26 @ SV79 ) )
= SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1252,plain,
! [SV27: $i] :
( ( ~ ~ ( ~ ( element @ ( sK4_SY167 @ SV27 ) @ ( powerset @ SV27 ) )
| ~ ( empty @ ( sK4_SY167 @ SV27 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1191]) ).
thf(1253,plain,
! [SV28: $i,SV80: $i] :
( ( ( ~ ( element @ SV80 @ ( powerset @ ( powerset @ SV28 ) ) ) )
= $true )
| ( ( ( meet_of_subsets @ SV28 @ SV80 )
= ( set_meet @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1254,plain,
! [SV114: $i,SV29: $i,SV81: $i] :
( ( ~ ~ ( ~ ( element @ SV81 @ ( powerset @ SV29 ) )
| ~ ( element @ SV114 @ ( powerset @ SV29 ) ) )
| ( ( subset_intersection2 @ SV29 @ SV81 @ SV114 )
= ( subset_intersection2 @ SV29 @ SV114 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1255,plain,
! [SV30: $i] :
( ( ( one_sorted_str @ SV30 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV30 )
= ( the_carrier @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1256,plain,
! [SV115: $i,SV31: $i,SV82: $i] :
( ( ~ ~ ( ~ ( element @ SV82 @ ( powerset @ SV31 ) )
| ~ ( element @ SV115 @ ( powerset @ SV31 ) ) )
| ( ( subset_union2 @ SV31 @ SV82 @ SV115 )
= ( subset_union2 @ SV31 @ SV115 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1257,plain,
! [SV116: $i,SV32: $i,SV83: $i] :
( ( ~ ~ ( ~ ( element @ SV83 @ ( powerset @ SV32 ) )
| ~ ( element @ SV116 @ ( powerset @ SV32 ) ) )
| ( ( subset_union2 @ SV32 @ SV83 @ SV116 )
= ( set_union2 @ SV83 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1258,plain,
! [SV33: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV33 )
| ~ ( one_sorted_str @ SV33 ) ) )
= $false )
| ( ( ~ ( empty @ ( the_carrier @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1259,plain,
! [SV84: $i,SV34: $i,SV117: $i] :
( ( ~ ( element @ SV117 @ ( powerset @ SV34 ) )
| ~ ~ ( ~ ( in @ SV84 @ ( subset_complement @ SV34 @ SV117 ) )
| ~ ( in @ SV84 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1260,plain,
! [SV35: $i,SV85: $i] :
( ( ~ ( ( SV85
!= ( powerset @ SV35 ) )
| ! [SY227: $i] :
~ ( ~ ( ~ ( in @ SY227 @ SV85 )
| ( subset @ SY227 @ SV35 ) )
| ~ ( ~ ( subset @ SY227 @ SV35 )
| ( in @ SY227 @ SV85 ) ) ) )
| ~ ( ~ ! [SY228: $i] :
~ ( ~ ( ~ ( in @ SY228 @ SV85 )
| ( subset @ SY228 @ SV35 ) )
| ~ ( ~ ( subset @ SY228 @ SV35 )
| ( in @ SY228 @ SV85 ) ) )
| ( SV85
= ( powerset @ SV35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1261,plain,
! [SV36: $i,SV86: $i] :
( ( ( ~ ( element @ SV86 @ ( powerset @ ( powerset @ SV36 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV36 @ SV86 ) @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1262,plain,
! [SV87: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ( top_str @ SV37 )
| ~ ( element @ SV87 @ ( powerset @ ( the_carrier @ SV37 ) ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV37 @ SV87 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1263,plain,
! [SV38: $i,SV88: $i] :
( ( ( ~ ( element @ SV88 @ ( powerset @ SV38 ) ) )
= $true )
| ( ( ( subset_complement @ SV38 @ SV88 )
= ( set_difference @ SV38 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1264,plain,
! [SV39: $i,SV89: $i] :
( ( ( ~ ( element @ SV89 @ ( powerset @ ( powerset @ SV39 ) ) ) )
= $true )
| ( ( ( union_of_subsets @ SV39 @ SV89 )
= ( union @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1265,plain,
! [SV90: $i,SV40: $i] :
( ( ( ~ ( rel_str @ SV40 ) )
= $true )
| ( ( element @ ( join_on_relstr @ SV40 @ SV90 ) @ ( the_carrier @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1266,plain,
! [SV41: $i] :
( ( ( v1_membered @ SV41 )
= $false )
| ( ( ! [SY185: $i] :
( ~ ( element @ SY185 @ ( powerset @ SV41 ) )
| ( v1_membered @ SY185 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1267,plain,
! [SV42: $i,SV91: $i] :
( ( ( ~ ( element @ SV91 @ ( powerset @ SV42 ) ) )
= $true )
| ( ( ! [SY229: $i] :
( ~ ( in @ SY229 @ SV91 )
| ( in @ SY229 @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1268,plain,
! [SV43: $i,SV92: $i] :
( ( ( ~ ( element @ SV92 @ ( powerset @ ( powerset @ SV43 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV43 @ ( complements_of_subsets @ SV43 @ SV92 ) )
= SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1269,plain,
! [SV93: $i,SV44: $i] :
( ( ( ~ ! [SY230: $i] :
( ~ ( in @ SY230 @ SV44 )
| ( in @ SY230 @ SV93 ) ) )
= $true )
| ( ( element @ SV44 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1270,plain,
! [SV45: $i] :
( ( ( v2_membered @ SV45 )
= $false )
| ( ( ! [SY191: $i] :
( ~ ( element @ SY191 @ ( powerset @ SV45 ) )
| ~ ( ~ ( v1_membered @ SY191 )
| ~ ( v2_membered @ SY191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1271,plain,
! [SV118: $i,SV46: $i,SV94: $i] :
( ( ~ ~ ( ~ ( element @ SV94 @ ( powerset @ SV46 ) )
| ~ ( element @ SV118 @ ( powerset @ SV46 ) ) )
| ( ( subset_intersection2 @ SV46 @ SV94 @ SV118 )
= ( set_intersection2 @ SV94 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1272,plain,
! [SV47: $i] :
( ( ( the_carrier @ ( incl_POSet @ SV47 ) )
!= SV47 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1211]) ).
thf(1273,plain,
! [SV47: $i] :
( ( ( the_InternalRel @ ( incl_POSet @ SV47 ) )
!= ( inclusion_order @ SV47 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1211]) ).
thf(1274,plain,
! [SV48: $i] :
( ( ( one_sorted_str @ SV48 )
= $false )
| ( ( element @ ( empty_carrier_subset @ SV48 ) @ ( powerset @ ( the_carrier @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1275,plain,
! [SV95: $i,SV49: $i,SV119: $i] :
( ( ~ ( relation_of2 @ SV119 @ SV49 @ SV95 )
| ( element @ ( relation_rng_as_subset @ SV49 @ SV95 @ SV119 ) @ ( powerset @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1276,plain,
! [SV50: $i] :
( ( ( ~ ( empty @ SV50 ) )
= $false )
| ( ( ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY196 @ ( powerset @ SV50 ) )
| ~ ~ ( empty @ SY196 ) )
| ~ ( finite @ SY196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1277,plain,
! [SV51: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK5_SY197 @ SV51 ) @ ( powerset @ ( powerset @ SV51 ) ) )
| ~ ~ ( empty @ ( sK5_SY197 @ SV51 ) ) )
| ~ ( finite @ ( sK5_SY197 @ SV51 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1215]) ).
thf(1278,plain,
! [SV52: $i,SV96: $i] :
( ( ( ~ ( element @ SV96 @ ( powerset @ ( powerset @ SV52 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV52 @ SV96 ) @ ( powerset @ ( powerset @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1279,plain,
! [SV97: $i,SV53: $i,SV120: $i] :
( ( ~ ( relation_of2 @ SV120 @ SV53 @ SV97 )
| ( element @ ( relation_dom_as_subset @ SV53 @ SV97 @ SV120 ) @ ( powerset @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1280,plain,
! [SV121: $i,SV98: $i,SV54: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV54 @ SV98 )
| ~ ( element @ SV98 @ ( powerset @ SV121 ) ) )
| ~ ( empty @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1281,plain,
! [SV99: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( top_str @ SV55 )
| ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ SV55 ) ) ) ) )
= $true )
| ( ( element @ ( interior @ SV55 @ SV99 ) @ ( powerset @ ( the_carrier @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1282,plain,
! [SV56: $i] :
( ( ( ~ ( empty @ SV56 ) )
= $false )
| ( ( ~ ! [SY204: $i] :
~ ~ ( ~ ( element @ SY204 @ ( powerset @ SV56 ) )
| ~ ~ ( empty @ SY204 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1283,plain,
! [SV57: $i] :
( ( ( finite @ SV57 )
= $false )
| ( ( ! [SY205: $i] :
( ~ ( element @ SY205 @ ( powerset @ SV57 ) )
| ( finite @ SY205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1284,plain,
! [SV58: $i,SV100: $i] :
( ( ( ~ ( element @ SV100 @ ( powerset @ ( powerset @ SV58 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV100 != empty_set ) )
| ( ( complements_of_subsets @ SV58 @ SV100 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1285,plain,
! [SV59: $i,SV101: $i] :
( ( ( ~ ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) ) )
= $true )
| ( ( ! [SY235: $i] :
( ~ ( element @ SY235 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SY235 )
| ( subset @ SV101 @ SY235 ) )
| ~ ( ~ ( subset @ SV101 @ SY235 )
| ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SY235 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1286,plain,
! [SV122: $i,SV60: $i,SV102: $i] :
( ( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV60 ) )
| ~ ( element @ SV122 @ ( powerset @ SV60 ) ) )
| ( element @ ( subset_difference @ SV60 @ SV102 @ SV122 ) @ ( powerset @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1287,plain,
! [SV123: $i,SV61: $i,SV103: $i] :
( ( ~ ~ ( ~ ( element @ SV103 @ ( powerset @ SV61 ) )
| ~ ( element @ SV123 @ ( powerset @ SV61 ) ) )
| ( ( subset_intersection2 @ SV61 @ SV103 @ SV103 )
= SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1288,plain,
! [SV62: $i] :
( ( ( one_sorted_str @ SV62 )
= $false )
| ( ( ~ ( ~ ( ~ ( empty_carrier @ SV62 )
| ( empty @ ( the_carrier @ SV62 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV62 ) )
| ( empty_carrier @ SV62 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1289,plain,
! [SV63: $i,SV104: $i] :
( ( ( ~ ( element @ SV104 @ ( powerset @ ( powerset @ SV63 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV63 @ SV104 ) @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1290,plain,
! [SV64: $i] :
( ( ( one_sorted_str @ SV64 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV64 )
= ( the_carrier @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1291,plain,
! [SV105: $i,SV65: $i] :
( ( ~ ( ~ ( element @ SV65 @ ( powerset @ SV105 ) )
| ( subset @ SV65 @ SV105 ) )
| ~ ( ~ ( subset @ SV65 @ SV105 )
| ( element @ SV65 @ ( powerset @ SV105 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1292,plain,
! [SV106: $i,SV66: $i] :
( ( ( ~ ( rel_str @ SV66 ) )
= $true )
| ( ( element @ ( meet_on_relstr @ SV66 @ SV106 ) @ ( the_carrier @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1293,plain,
! [SV67: $i] :
( ( ( rel_str @ SV67 )
= $false )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV67 ) @ ( the_carrier @ SV67 ) @ ( the_carrier @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1294,plain,
! [SV68: $i] :
( ( ( one_sorted_str @ SV68 )
= $false )
| ( ( element @ ( cast_as_carrier_subset @ SV68 ) @ ( powerset @ ( the_carrier @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1295,plain,
! [SV9: $i,SV69: $i] :
( ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV69 @ ( powerset @ SV9 ) )
| ( SV69 != SV9 ) )
| ~ ( ~ ( ( SV69 != SV9 ) )
| ( proper_element @ SV69 @ ( powerset @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1296,plain,
! [SV70: $i,SV10: $i,SV107: $i] :
( ( ( ~ ( element @ SV107 @ ( powerset @ ( cartesian_product2 @ SV10 @ SV70 ) ) ) )
= $true )
| ( ( relation @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1297,plain,
! [SV11: $i] :
( ( strict_rel_str @ ( boole_POSet @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1298,plain,
! [SV11: $i] :
( ( rel_str @ ( boole_POSet @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1299,plain,
! [SV71: $i,SV12: $i,SV108: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV108 @ SV12 @ SV71 ) )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( cartesian_product2 @ SV12 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1300,plain,
! [SV109: $i,SV72: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ SV13 @ SV72 )
| ~ ( element @ SV72 @ ( powerset @ SV109 ) ) ) )
= $true )
| ( ( element @ SV13 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1301,plain,
! [SV110: $i,SV14: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ( element @ SV73 @ ( powerset @ SV14 ) )
| ~ ( element @ SV110 @ ( powerset @ SV14 ) ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV14 @ SV73 @ SV110 ) @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1302,plain,
! [SV111: $i,SV15: $i,SV74: $i] :
( ( ( ~ ~ ( ~ ( element @ SV74 @ ( powerset @ SV15 ) )
| ~ ( element @ SV111 @ ( powerset @ SV15 ) ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV15 @ SV74 @ SV111 ) @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1303,plain,
! [SV16: $i,SV75: $i] :
( ( ( element @ SV75 @ ( powerset @ SV16 ) )
= $false )
| ( ( element @ ( subset_complement @ SV16 @ SV75 ) @ ( powerset @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1304,plain,
! [SV17: $i,SV76: $i] :
( ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ( ( SV76 != empty_set ) )
| ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ( SV76 != empty_set ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1305,plain,
! [SV112: $i,SV18: $i,SV77: $i] :
( ( ( ~ ~ ( ~ ( element @ SV77 @ ( powerset @ SV18 ) )
| ~ ( element @ SV112 @ ( powerset @ SV18 ) ) ) )
= $true )
| ( ( ( subset_union2 @ SV18 @ SV77 @ SV77 )
= SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1306,plain,
! [SV19: $i] :
( ( ( empty @ SV19 )
= $true )
| ( ( ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY157 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY157 ) )
| ~ ( finite @ SY157 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1307,plain,
! [SV20: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SV20 @ ( sK2_SY158 @ SV20 ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( in @ SY238 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY239 @ SY238 ) )
| ( in @ SY239 @ ( sK2_SY158 @ SV20 ) ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY158 @ SV20 ) )
| ( in @ ( powerset @ SY240 ) @ ( sK2_SY158 @ SV20 ) ) ) )
| ~ ! [SY241: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY241 @ ( sK2_SY158 @ SV20 ) )
| ~ ~ ( are_equipotent @ SY241 @ ( sK2_SY158 @ SV20 ) ) )
| ~ ~ ( in @ SY241 @ ( sK2_SY158 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1308,plain,
! [SV23: $i] :
( ( ~ ( ~ ( element @ ( sK3_SY163 @ SV23 ) @ ( powerset @ SV23 ) )
| ~ ~ ( proper_element @ ( sK3_SY163 @ SV23 ) @ ( powerset @ SV23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1248]) ).
thf(1309,plain,
! [SV113: $i,SV24: $i,SV78: $i] :
( ( ( ~ ~ ( ~ ( element @ SV78 @ ( powerset @ SV24 ) )
| ~ ( element @ SV113 @ ( powerset @ SV24 ) ) ) )
= $true )
| ( ( ( subset_difference @ SV24 @ SV78 @ SV113 )
= ( set_difference @ SV78 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1310,plain,
! [SV26: $i,SV79: $i] :
( ( ( element @ SV79 @ ( powerset @ SV26 ) )
= $false )
| ( ( ( subset_complement @ SV26 @ ( subset_complement @ SV26 @ SV79 ) )
= SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1311,plain,
! [SV27: $i] :
( ( ~ ( ~ ( element @ ( sK4_SY167 @ SV27 ) @ ( powerset @ SV27 ) )
| ~ ( empty @ ( sK4_SY167 @ SV27 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1252]) ).
thf(1312,plain,
! [SV28: $i,SV80: $i] :
( ( ( element @ SV80 @ ( powerset @ ( powerset @ SV28 ) ) )
= $false )
| ( ( ( meet_of_subsets @ SV28 @ SV80 )
= ( set_meet @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1313,plain,
! [SV114: $i,SV29: $i,SV81: $i] :
( ( ( ~ ~ ( ~ ( element @ SV81 @ ( powerset @ SV29 ) )
| ~ ( element @ SV114 @ ( powerset @ SV29 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV29 @ SV81 @ SV114 )
= ( subset_intersection2 @ SV29 @ SV114 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1314,plain,
! [SV115: $i,SV31: $i,SV82: $i] :
( ( ( ~ ~ ( ~ ( element @ SV82 @ ( powerset @ SV31 ) )
| ~ ( element @ SV115 @ ( powerset @ SV31 ) ) ) )
= $true )
| ( ( ( subset_union2 @ SV31 @ SV82 @ SV115 )
= ( subset_union2 @ SV31 @ SV115 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1315,plain,
! [SV116: $i,SV32: $i,SV83: $i] :
( ( ( ~ ~ ( ~ ( element @ SV83 @ ( powerset @ SV32 ) )
| ~ ( element @ SV116 @ ( powerset @ SV32 ) ) ) )
= $true )
| ( ( ( subset_union2 @ SV32 @ SV83 @ SV116 )
= ( set_union2 @ SV83 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1316,plain,
! [SV33: $i] :
( ( ( ~ ~ ( empty_carrier @ SV33 )
| ~ ( one_sorted_str @ SV33 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1258]) ).
thf(1317,plain,
! [SV84: $i,SV34: $i,SV117: $i] :
( ( ( ~ ( element @ SV117 @ ( powerset @ SV34 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( in @ SV84 @ ( subset_complement @ SV34 @ SV117 ) )
| ~ ( in @ SV84 @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1318,plain,
! [SV35: $i,SV85: $i] :
( ( ~ ( ( SV85
!= ( powerset @ SV35 ) )
| ! [SY227: $i] :
~ ( ~ ( ~ ( in @ SY227 @ SV85 )
| ( subset @ SY227 @ SV35 ) )
| ~ ( ~ ( subset @ SY227 @ SV35 )
| ( in @ SY227 @ SV85 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1319,plain,
! [SV35: $i,SV85: $i] :
( ( ~ ( ~ ! [SY228: $i] :
~ ( ~ ( ~ ( in @ SY228 @ SV85 )
| ( subset @ SY228 @ SV35 ) )
| ~ ( ~ ( subset @ SY228 @ SV35 )
| ( in @ SY228 @ SV85 ) ) )
| ( SV85
= ( powerset @ SV35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1320,plain,
! [SV36: $i,SV86: $i] :
( ( ( element @ SV86 @ ( powerset @ ( powerset @ SV36 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV36 @ SV86 ) @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1321,plain,
! [SV87: $i,SV37: $i] :
( ( ( ~ ( ~ ( top_str @ SV37 )
| ~ ( element @ SV87 @ ( powerset @ ( the_carrier @ SV37 ) ) ) ) )
= $false )
| ( ( element @ ( topstr_closure @ SV37 @ SV87 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1322,plain,
! [SV38: $i,SV88: $i] :
( ( ( element @ SV88 @ ( powerset @ SV38 ) )
= $false )
| ( ( ( subset_complement @ SV38 @ SV88 )
= ( set_difference @ SV38 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1323,plain,
! [SV39: $i,SV89: $i] :
( ( ( element @ SV89 @ ( powerset @ ( powerset @ SV39 ) ) )
= $false )
| ( ( ( union_of_subsets @ SV39 @ SV89 )
= ( union @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1324,plain,
! [SV90: $i,SV40: $i] :
( ( ( rel_str @ SV40 )
= $false )
| ( ( element @ ( join_on_relstr @ SV40 @ SV90 ) @ ( the_carrier @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1325,plain,
! [SV41: $i,SV124: $i] :
( ( ( ~ ( element @ SV124 @ ( powerset @ SV41 ) )
| ( v1_membered @ SV124 ) )
= $true )
| ( ( v1_membered @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1326,plain,
! [SV42: $i,SV91: $i] :
( ( ( element @ SV91 @ ( powerset @ SV42 ) )
= $false )
| ( ( ! [SY229: $i] :
( ~ ( in @ SY229 @ SV91 )
| ( in @ SY229 @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1327,plain,
! [SV43: $i,SV92: $i] :
( ( ( element @ SV92 @ ( powerset @ ( powerset @ SV43 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV43 @ ( complements_of_subsets @ SV43 @ SV92 ) )
= SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1328,plain,
! [SV93: $i,SV44: $i] :
( ( ( ! [SY230: $i] :
( ~ ( in @ SY230 @ SV44 )
| ( in @ SY230 @ SV93 ) ) )
= $false )
| ( ( element @ SV44 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1329,plain,
! [SV45: $i,SV125: $i] :
( ( ( ~ ( element @ SV125 @ ( powerset @ SV45 ) )
| ~ ( ~ ( v1_membered @ SV125 )
| ~ ( v2_membered @ SV125 ) ) )
= $true )
| ( ( v2_membered @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1330,plain,
! [SV118: $i,SV46: $i,SV94: $i] :
( ( ( ~ ~ ( ~ ( element @ SV94 @ ( powerset @ SV46 ) )
| ~ ( element @ SV118 @ ( powerset @ SV46 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV46 @ SV94 @ SV118 )
= ( set_intersection2 @ SV94 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1331,plain,
! [SV47: $i] :
( ( ( the_carrier @ ( incl_POSet @ SV47 ) )
= SV47 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1272]) ).
thf(1332,plain,
! [SV47: $i] :
( ( ( the_InternalRel @ ( incl_POSet @ SV47 ) )
= ( inclusion_order @ SV47 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1333,plain,
! [SV95: $i,SV49: $i,SV119: $i] :
( ( ( ~ ( relation_of2 @ SV119 @ SV49 @ SV95 ) )
= $true )
| ( ( element @ ( relation_rng_as_subset @ SV49 @ SV95 @ SV119 ) @ ( powerset @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1334,plain,
! [SV50: $i] :
( ( ( empty @ SV50 )
= $true )
| ( ( ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY196 @ ( powerset @ SV50 ) )
| ~ ~ ( empty @ SY196 ) )
| ~ ( finite @ SY196 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1276]) ).
thf(1335,plain,
! [SV51: $i] :
( ( ~ ( ~ ~ ( ~ ( element @ ( sK5_SY197 @ SV51 ) @ ( powerset @ ( powerset @ SV51 ) ) )
| ~ ~ ( empty @ ( sK5_SY197 @ SV51 ) ) )
| ~ ( finite @ ( sK5_SY197 @ SV51 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1277]) ).
thf(1336,plain,
! [SV52: $i,SV96: $i] :
( ( ( element @ SV96 @ ( powerset @ ( powerset @ SV52 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV52 @ SV96 ) @ ( powerset @ ( powerset @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1337,plain,
! [SV97: $i,SV53: $i,SV120: $i] :
( ( ( ~ ( relation_of2 @ SV120 @ SV53 @ SV97 ) )
= $true )
| ( ( element @ ( relation_dom_as_subset @ SV53 @ SV97 @ SV120 ) @ ( powerset @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1279]) ).
thf(1338,plain,
! [SV121: $i,SV98: $i,SV54: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV54 @ SV98 )
| ~ ( element @ SV98 @ ( powerset @ SV121 ) ) )
| ~ ( empty @ SV121 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1339,plain,
! [SV99: $i,SV55: $i] :
( ( ( ~ ( ~ ( top_str @ SV55 )
| ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ SV55 ) ) ) ) )
= $false )
| ( ( element @ ( interior @ SV55 @ SV99 ) @ ( powerset @ ( the_carrier @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1340,plain,
! [SV56: $i] :
( ( ( empty @ SV56 )
= $true )
| ( ( ~ ! [SY204: $i] :
~ ~ ( ~ ( element @ SY204 @ ( powerset @ SV56 ) )
| ~ ~ ( empty @ SY204 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1282]) ).
thf(1341,plain,
! [SV57: $i,SV126: $i] :
( ( ( ~ ( element @ SV126 @ ( powerset @ SV57 ) )
| ( finite @ SV126 ) )
= $true )
| ( ( finite @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1342,plain,
! [SV58: $i,SV100: $i] :
( ( ( element @ SV100 @ ( powerset @ ( powerset @ SV58 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV100 != empty_set ) )
| ( ( complements_of_subsets @ SV58 @ SV100 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1343,plain,
! [SV59: $i,SV101: $i] :
( ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false )
| ( ( ! [SY235: $i] :
( ~ ( element @ SY235 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SY235 )
| ( subset @ SV101 @ SY235 ) )
| ~ ( ~ ( subset @ SV101 @ SY235 )
| ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SY235 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1344,plain,
! [SV122: $i,SV60: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV60 ) )
| ~ ( element @ SV122 @ ( powerset @ SV60 ) ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV60 @ SV102 @ SV122 ) @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1345,plain,
! [SV123: $i,SV61: $i,SV103: $i] :
( ( ( ~ ~ ( ~ ( element @ SV103 @ ( powerset @ SV61 ) )
| ~ ( element @ SV123 @ ( powerset @ SV61 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV61 @ SV103 @ SV103 )
= SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1346,plain,
! [SV62: $i] :
( ( ( ~ ( ~ ( empty_carrier @ SV62 )
| ( empty @ ( the_carrier @ SV62 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV62 ) )
| ( empty_carrier @ SV62 ) ) )
= $false )
| ( ( one_sorted_str @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1347,plain,
! [SV63: $i,SV104: $i] :
( ( ( element @ SV104 @ ( powerset @ ( powerset @ SV63 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV63 @ SV104 ) @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1348,plain,
! [SV105: $i,SV65: $i] :
( ( ~ ( ~ ( element @ SV65 @ ( powerset @ SV105 ) )
| ( subset @ SV65 @ SV105 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1349,plain,
! [SV105: $i,SV65: $i] :
( ( ~ ( ~ ( subset @ SV65 @ SV105 )
| ( element @ SV65 @ ( powerset @ SV105 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1350,plain,
! [SV106: $i,SV66: $i] :
( ( ( rel_str @ SV66 )
= $false )
| ( ( element @ ( meet_on_relstr @ SV66 @ SV106 ) @ ( the_carrier @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1351,plain,
! [SV9: $i,SV69: $i] :
( ( ( ~ ( ~ ( proper_element @ SV69 @ ( powerset @ SV9 ) )
| ( SV69 != SV9 ) )
| ~ ( ~ ( ( SV69 != SV9 ) )
| ( proper_element @ SV69 @ ( powerset @ SV9 ) ) ) )
= $false )
| ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1352,plain,
! [SV70: $i,SV10: $i,SV107: $i] :
( ( ( element @ SV107 @ ( powerset @ ( cartesian_product2 @ SV10 @ SV70 ) ) )
= $false )
| ( ( relation @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1353,plain,
! [SV71: $i,SV12: $i,SV108: $i] :
( ( ( relation_of2_as_subset @ SV108 @ SV12 @ SV71 )
= $false )
| ( ( element @ SV108 @ ( powerset @ ( cartesian_product2 @ SV12 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1354,plain,
! [SV109: $i,SV72: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ SV13 @ SV72 )
| ~ ( element @ SV72 @ ( powerset @ SV109 ) ) ) )
= $false )
| ( ( element @ SV13 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1355,plain,
! [SV110: $i,SV14: $i,SV73: $i] :
( ( ( ~ ( ~ ( element @ SV73 @ ( powerset @ SV14 ) )
| ~ ( element @ SV110 @ ( powerset @ SV14 ) ) ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV14 @ SV73 @ SV110 ) @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1356,plain,
! [SV111: $i,SV15: $i,SV74: $i] :
( ( ( ~ ( ~ ( element @ SV74 @ ( powerset @ SV15 ) )
| ~ ( element @ SV111 @ ( powerset @ SV15 ) ) ) )
= $false )
| ( ( element @ ( subset_union2 @ SV15 @ SV74 @ SV111 ) @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1357,plain,
! [SV17: $i,SV76: $i] :
( ( ( ~ ~ ~ ( ~ ( ( SV76 != empty_set ) )
| ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ( SV76 != empty_set ) ) )
= $false )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1358,plain,
! [SV112: $i,SV18: $i,SV77: $i] :
( ( ( ~ ( ~ ( element @ SV77 @ ( powerset @ SV18 ) )
| ~ ( element @ SV112 @ ( powerset @ SV18 ) ) ) )
= $false )
| ( ( ( subset_union2 @ SV18 @ SV77 @ SV77 )
= SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1359,plain,
! [SV19: $i] :
( ( ( ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY157 @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ SY157 ) )
| ~ ( finite @ SY157 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1360,plain,
! [SV20: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV20 @ ( sK2_SY158 @ SV20 ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( in @ SY238 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY239 @ SY238 ) )
| ( in @ SY239 @ ( sK2_SY158 @ SV20 ) ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY158 @ SV20 ) )
| ( in @ ( powerset @ SY240 ) @ ( sK2_SY158 @ SV20 ) ) ) )
| ~ ! [SY241: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY241 @ ( sK2_SY158 @ SV20 ) )
| ~ ~ ( are_equipotent @ SY241 @ ( sK2_SY158 @ SV20 ) ) )
| ~ ~ ( in @ SY241 @ ( sK2_SY158 @ SV20 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1361,plain,
! [SV23: $i] :
( ( ~ ( element @ ( sK3_SY163 @ SV23 ) @ ( powerset @ SV23 ) )
| ~ ~ ( proper_element @ ( sK3_SY163 @ SV23 ) @ ( powerset @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1362,plain,
! [SV113: $i,SV24: $i,SV78: $i] :
( ( ( ~ ( ~ ( element @ SV78 @ ( powerset @ SV24 ) )
| ~ ( element @ SV113 @ ( powerset @ SV24 ) ) ) )
= $false )
| ( ( ( subset_difference @ SV24 @ SV78 @ SV113 )
= ( set_difference @ SV78 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1363,plain,
! [SV27: $i] :
( ( ~ ( element @ ( sK4_SY167 @ SV27 ) @ ( powerset @ SV27 ) )
| ~ ( empty @ ( sK4_SY167 @ SV27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1364,plain,
! [SV114: $i,SV29: $i,SV81: $i] :
( ( ( ~ ( ~ ( element @ SV81 @ ( powerset @ SV29 ) )
| ~ ( element @ SV114 @ ( powerset @ SV29 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV29 @ SV81 @ SV114 )
= ( subset_intersection2 @ SV29 @ SV114 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1365,plain,
! [SV115: $i,SV31: $i,SV82: $i] :
( ( ( ~ ( ~ ( element @ SV82 @ ( powerset @ SV31 ) )
| ~ ( element @ SV115 @ ( powerset @ SV31 ) ) ) )
= $false )
| ( ( ( subset_union2 @ SV31 @ SV82 @ SV115 )
= ( subset_union2 @ SV31 @ SV115 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1366,plain,
! [SV116: $i,SV32: $i,SV83: $i] :
( ( ( ~ ( ~ ( element @ SV83 @ ( powerset @ SV32 ) )
| ~ ( element @ SV116 @ ( powerset @ SV32 ) ) ) )
= $false )
| ( ( ( subset_union2 @ SV32 @ SV83 @ SV116 )
= ( set_union2 @ SV83 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1367,plain,
! [SV33: $i] :
( ( ( ~ ~ ( empty_carrier @ SV33 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV33 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1368,plain,
! [SV84: $i,SV34: $i,SV117: $i] :
( ( ( element @ SV117 @ ( powerset @ SV34 ) )
= $false )
| ( ( ~ ~ ( ~ ( in @ SV84 @ ( subset_complement @ SV34 @ SV117 ) )
| ~ ( in @ SV84 @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1369,plain,
! [SV35: $i,SV85: $i] :
( ( ( SV85
!= ( powerset @ SV35 ) )
| ! [SY227: $i] :
~ ( ~ ( ~ ( in @ SY227 @ SV85 )
| ( subset @ SY227 @ SV35 ) )
| ~ ( ~ ( subset @ SY227 @ SV35 )
| ( in @ SY227 @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1318]) ).
thf(1370,plain,
! [SV35: $i,SV85: $i] :
( ( ~ ! [SY228: $i] :
~ ( ~ ( ~ ( in @ SY228 @ SV85 )
| ( subset @ SY228 @ SV35 ) )
| ~ ( ~ ( subset @ SY228 @ SV35 )
| ( in @ SY228 @ SV85 ) ) )
| ( SV85
= ( powerset @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1319]) ).
thf(1371,plain,
! [SV87: $i,SV37: $i] :
( ( ( ~ ( top_str @ SV37 )
| ~ ( element @ SV87 @ ( powerset @ ( the_carrier @ SV37 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV37 @ SV87 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1321]) ).
thf(1372,plain,
! [SV41: $i,SV124: $i] :
( ( ( ~ ( element @ SV124 @ ( powerset @ SV41 ) ) )
= $true )
| ( ( v1_membered @ SV124 )
= $true )
| ( ( v1_membered @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1373,plain,
! [SV42: $i,SV91: $i,SV127: $i] :
( ( ( ~ ( in @ SV127 @ SV91 )
| ( in @ SV127 @ SV42 ) )
= $true )
| ( ( element @ SV91 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1374,plain,
! [SV44: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK6_SY230 @ SV93 @ SV44 ) @ SV44 )
| ( in @ ( sK6_SY230 @ SV93 @ SV44 ) @ SV93 ) )
= $false )
| ( ( element @ SV44 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1328]) ).
thf(1375,plain,
! [SV45: $i,SV125: $i] :
( ( ( ~ ( element @ SV125 @ ( powerset @ SV45 ) ) )
= $true )
| ( ( ~ ( ~ ( v1_membered @ SV125 )
| ~ ( v2_membered @ SV125 ) ) )
= $true )
| ( ( v2_membered @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1376,plain,
! [SV118: $i,SV46: $i,SV94: $i] :
( ( ( ~ ( ~ ( element @ SV94 @ ( powerset @ SV46 ) )
| ~ ( element @ SV118 @ ( powerset @ SV46 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV46 @ SV94 @ SV118 )
= ( set_intersection2 @ SV94 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1377,plain,
! [SV95: $i,SV49: $i,SV119: $i] :
( ( ( relation_of2 @ SV119 @ SV49 @ SV95 )
= $false )
| ( ( element @ ( relation_rng_as_subset @ SV49 @ SV95 @ SV119 ) @ ( powerset @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1378,plain,
! [SV50: $i] :
( ( ( ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY196 @ ( powerset @ SV50 ) )
| ~ ~ ( empty @ SY196 ) )
| ~ ( finite @ SY196 ) ) )
= $false )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1334]) ).
thf(1379,plain,
! [SV51: $i] :
( ( ~ ~ ( ~ ( element @ ( sK5_SY197 @ SV51 ) @ ( powerset @ ( powerset @ SV51 ) ) )
| ~ ~ ( empty @ ( sK5_SY197 @ SV51 ) ) )
| ~ ( finite @ ( sK5_SY197 @ SV51 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1380,plain,
! [SV97: $i,SV53: $i,SV120: $i] :
( ( ( relation_of2 @ SV120 @ SV53 @ SV97 )
= $false )
| ( ( element @ ( relation_dom_as_subset @ SV53 @ SV97 @ SV120 ) @ ( powerset @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1381,plain,
! [SV121: $i,SV98: $i,SV54: $i] :
( ( ~ ~ ( ~ ( in @ SV54 @ SV98 )
| ~ ( element @ SV98 @ ( powerset @ SV121 ) ) )
| ~ ( empty @ SV121 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1338]) ).
thf(1382,plain,
! [SV99: $i,SV55: $i] :
( ( ( ~ ( top_str @ SV55 )
| ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ SV55 ) ) ) )
= $true )
| ( ( element @ ( interior @ SV55 @ SV99 ) @ ( powerset @ ( the_carrier @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1339]) ).
thf(1383,plain,
! [SV56: $i] :
( ( ( ! [SY204: $i] :
~ ~ ( ~ ( element @ SY204 @ ( powerset @ SV56 ) )
| ~ ~ ( empty @ SY204 ) ) )
= $false )
| ( ( empty @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1384,plain,
! [SV57: $i,SV126: $i] :
( ( ( ~ ( element @ SV126 @ ( powerset @ SV57 ) ) )
= $true )
| ( ( finite @ SV126 )
= $true )
| ( ( finite @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1385,plain,
! [SV58: $i,SV100: $i] :
( ( ( ~ ( ~ ( ( SV100 != empty_set ) )
| ( ( complements_of_subsets @ SV58 @ SV100 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV100 @ ( powerset @ ( powerset @ SV58 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1386,plain,
! [SV101: $i,SV59: $i,SV128: $i] :
( ( ( ~ ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
| ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 )
| ( subset @ SV101 @ SV128 ) )
| ~ ( ~ ( subset @ SV101 @ SV128 )
| ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 ) ) ) )
= $true )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1387,plain,
! [SV122: $i,SV60: $i,SV102: $i] :
( ( ( ~ ( ~ ( element @ SV102 @ ( powerset @ SV60 ) )
| ~ ( element @ SV122 @ ( powerset @ SV60 ) ) ) )
= $false )
| ( ( element @ ( subset_difference @ SV60 @ SV102 @ SV122 ) @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1388,plain,
! [SV123: $i,SV61: $i,SV103: $i] :
( ( ( ~ ( ~ ( element @ SV103 @ ( powerset @ SV61 ) )
| ~ ( element @ SV123 @ ( powerset @ SV61 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV61 @ SV103 @ SV103 )
= SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1389,plain,
! [SV62: $i] :
( ( ( ~ ( ~ ( empty_carrier @ SV62 )
| ( empty @ ( the_carrier @ SV62 ) ) ) )
= $false )
| ( ( one_sorted_str @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1390,plain,
! [SV62: $i] :
( ( ( ~ ( ~ ( empty @ ( the_carrier @ SV62 ) )
| ( empty_carrier @ SV62 ) ) )
= $false )
| ( ( one_sorted_str @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1391,plain,
! [SV105: $i,SV65: $i] :
( ( ~ ( element @ SV65 @ ( powerset @ SV105 ) )
| ( subset @ SV65 @ SV105 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1392,plain,
! [SV105: $i,SV65: $i] :
( ( ~ ( subset @ SV65 @ SV105 )
| ( element @ SV65 @ ( powerset @ SV105 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1349]) ).
thf(1393,plain,
! [SV9: $i,SV69: $i] :
( ( ( ~ ( ~ ( proper_element @ SV69 @ ( powerset @ SV9 ) )
| ( SV69 != SV9 ) ) )
= $false )
| ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1394,plain,
! [SV9: $i,SV69: $i] :
( ( ( ~ ( ~ ( ( SV69 != SV9 ) )
| ( proper_element @ SV69 @ ( powerset @ SV9 ) ) ) )
= $false )
| ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1395,plain,
! [SV109: $i,SV72: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV72 )
| ~ ( element @ SV72 @ ( powerset @ SV109 ) ) )
= $true )
| ( ( element @ SV13 @ SV109 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1354]) ).
thf(1396,plain,
! [SV110: $i,SV14: $i,SV73: $i] :
( ( ( ~ ( element @ SV73 @ ( powerset @ SV14 ) )
| ~ ( element @ SV110 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV14 @ SV73 @ SV110 ) @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1397,plain,
! [SV111: $i,SV15: $i,SV74: $i] :
( ( ( ~ ( element @ SV74 @ ( powerset @ SV15 ) )
| ~ ( element @ SV111 @ ( powerset @ SV15 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV15 @ SV74 @ SV111 ) @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1356]) ).
thf(1398,plain,
! [SV17: $i,SV76: $i] :
( ( ( ~ ~ ~ ( ~ ( ( SV76 != empty_set ) )
| ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1399,plain,
! [SV76: $i,SV17: $i] :
( ( ( ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ( SV76 != empty_set ) ) )
= $false )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1400,plain,
! [SV112: $i,SV18: $i,SV77: $i] :
( ( ( ~ ( element @ SV77 @ ( powerset @ SV18 ) )
| ~ ( element @ SV112 @ ( powerset @ SV18 ) ) )
= $true )
| ( ( ( subset_union2 @ SV18 @ SV77 @ SV77 )
= SV77 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1401,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK7_SY157 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK7_SY157 @ SV19 ) ) )
| ~ ( finite @ ( sK7_SY157 @ SV19 ) ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1359]) ).
thf(1402,plain,
! [SV20: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV20 @ ( sK2_SY158 @ SV20 ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( in @ SY238 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY239 @ SY238 ) )
| ( in @ SY239 @ ( sK2_SY158 @ SV20 ) ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY158 @ SV20 ) )
| ( in @ ( powerset @ SY240 ) @ ( sK2_SY158 @ SV20 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1403,plain,
! [SV20: $i] :
( ( ~ ! [SY241: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY241 @ ( sK2_SY158 @ SV20 ) )
| ~ ~ ( are_equipotent @ SY241 @ ( sK2_SY158 @ SV20 ) ) )
| ~ ~ ( in @ SY241 @ ( sK2_SY158 @ SV20 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1404,plain,
! [SV23: $i] :
( ( ~ ( element @ ( sK3_SY163 @ SV23 ) @ ( powerset @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1405,plain,
! [SV23: $i] :
( ( ~ ~ ( proper_element @ ( sK3_SY163 @ SV23 ) @ ( powerset @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1406,plain,
! [SV113: $i,SV24: $i,SV78: $i] :
( ( ( ~ ( element @ SV78 @ ( powerset @ SV24 ) )
| ~ ( element @ SV113 @ ( powerset @ SV24 ) ) )
= $true )
| ( ( ( subset_difference @ SV24 @ SV78 @ SV113 )
= ( set_difference @ SV78 @ SV113 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1407,plain,
! [SV27: $i] :
( ( ~ ( element @ ( sK4_SY167 @ SV27 ) @ ( powerset @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1408,plain,
! [SV27: $i] :
( ( ~ ( empty @ ( sK4_SY167 @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1409,plain,
! [SV114: $i,SV29: $i,SV81: $i] :
( ( ( ~ ( element @ SV81 @ ( powerset @ SV29 ) )
| ~ ( element @ SV114 @ ( powerset @ SV29 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV29 @ SV81 @ SV114 )
= ( subset_intersection2 @ SV29 @ SV114 @ SV81 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1364]) ).
thf(1410,plain,
! [SV115: $i,SV31: $i,SV82: $i] :
( ( ( ~ ( element @ SV82 @ ( powerset @ SV31 ) )
| ~ ( element @ SV115 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ( subset_union2 @ SV31 @ SV82 @ SV115 )
= ( subset_union2 @ SV31 @ SV115 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1365]) ).
thf(1411,plain,
! [SV116: $i,SV32: $i,SV83: $i] :
( ( ( ~ ( element @ SV83 @ ( powerset @ SV32 ) )
| ~ ( element @ SV116 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( ( subset_union2 @ SV32 @ SV83 @ SV116 )
= ( set_union2 @ SV83 @ SV116 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1412,plain,
! [SV33: $i] :
( ( ( ~ ( empty_carrier @ SV33 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV33 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1413,plain,
! [SV117: $i,SV34: $i,SV84: $i] :
( ( ( ~ ( ~ ( in @ SV84 @ ( subset_complement @ SV34 @ SV117 ) )
| ~ ( in @ SV84 @ SV117 ) ) )
= $false )
| ( ( element @ SV117 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1414,plain,
! [SV35: $i,SV85: $i] :
( ( ( SV85
!= ( powerset @ SV35 ) )
= $true )
| ( ( ! [SY227: $i] :
~ ( ~ ( ~ ( in @ SY227 @ SV85 )
| ( subset @ SY227 @ SV35 ) )
| ~ ( ~ ( subset @ SY227 @ SV35 )
| ( in @ SY227 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1415,plain,
! [SV35: $i,SV85: $i] :
( ( ( ~ ! [SY228: $i] :
~ ( ~ ( ~ ( in @ SY228 @ SV85 )
| ( subset @ SY228 @ SV35 ) )
| ~ ( ~ ( subset @ SY228 @ SV35 )
| ( in @ SY228 @ SV85 ) ) ) )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1370]) ).
thf(1416,plain,
! [SV87: $i,SV37: $i] :
( ( ( ~ ( top_str @ SV37 ) )
= $true )
| ( ( ~ ( element @ SV87 @ ( powerset @ ( the_carrier @ SV37 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV37 @ SV87 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1417,plain,
! [SV41: $i,SV124: $i] :
( ( ( element @ SV124 @ ( powerset @ SV41 ) )
= $false )
| ( ( v1_membered @ SV124 )
= $true )
| ( ( v1_membered @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1418,plain,
! [SV42: $i,SV91: $i,SV127: $i] :
( ( ( ~ ( in @ SV127 @ SV91 ) )
= $true )
| ( ( in @ SV127 @ SV42 )
= $true )
| ( ( element @ SV91 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1419,plain,
! [SV44: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK6_SY230 @ SV93 @ SV44 ) @ SV44 ) )
= $false )
| ( ( element @ SV44 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1420,plain,
! [SV44: $i,SV93: $i] :
( ( ( in @ ( sK6_SY230 @ SV93 @ SV44 ) @ SV93 )
= $false )
| ( ( element @ SV44 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1421,plain,
! [SV45: $i,SV125: $i] :
( ( ( element @ SV125 @ ( powerset @ SV45 ) )
= $false )
| ( ( ~ ( ~ ( v1_membered @ SV125 )
| ~ ( v2_membered @ SV125 ) ) )
= $true )
| ( ( v2_membered @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1422,plain,
! [SV118: $i,SV46: $i,SV94: $i] :
( ( ( ~ ( element @ SV94 @ ( powerset @ SV46 ) )
| ~ ( element @ SV118 @ ( powerset @ SV46 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV46 @ SV94 @ SV118 )
= ( set_intersection2 @ SV94 @ SV118 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1376]) ).
thf(1423,plain,
! [SV50: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK8_SY196 @ SV50 ) @ ( powerset @ SV50 ) )
| ~ ~ ( empty @ ( sK8_SY196 @ SV50 ) ) )
| ~ ( finite @ ( sK8_SY196 @ SV50 ) ) ) )
= $false )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1378]) ).
thf(1424,plain,
! [SV51: $i] :
( ( ~ ~ ( ~ ( element @ ( sK5_SY197 @ SV51 ) @ ( powerset @ ( powerset @ SV51 ) ) )
| ~ ~ ( empty @ ( sK5_SY197 @ SV51 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1425,plain,
! [SV51: $i] :
( ( ~ ( finite @ ( sK5_SY197 @ SV51 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1426,plain,
! [SV121: $i,SV98: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ( in @ SV54 @ SV98 )
| ~ ( element @ SV98 @ ( powerset @ SV121 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1427,plain,
! [SV99: $i,SV55: $i] :
( ( ( ~ ( top_str @ SV55 ) )
= $true )
| ( ( ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ SV55 ) ) ) )
= $true )
| ( ( element @ ( interior @ SV55 @ SV99 ) @ ( powerset @ ( the_carrier @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1428,plain,
! [SV56: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_SY204 @ SV56 ) @ ( powerset @ SV56 ) )
| ~ ~ ( empty @ ( sK9_SY204 @ SV56 ) ) ) )
= $false )
| ( ( empty @ SV56 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1383]) ).
thf(1429,plain,
! [SV57: $i,SV126: $i] :
( ( ( element @ SV126 @ ( powerset @ SV57 ) )
= $false )
| ( ( finite @ SV126 )
= $true )
| ( ( finite @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1430,plain,
! [SV58: $i,SV100: $i] :
( ( ( ~ ( ( SV100 != empty_set ) )
| ( ( complements_of_subsets @ SV58 @ SV100 )
!= empty_set ) )
= $true )
| ( ( element @ SV100 @ ( powerset @ ( powerset @ SV58 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1385]) ).
thf(1431,plain,
! [SV101: $i,SV59: $i,SV128: $i] :
( ( ( ~ ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 )
| ( subset @ SV101 @ SV128 ) )
| ~ ( ~ ( subset @ SV101 @ SV128 )
| ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 ) ) ) )
= $true )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1432,plain,
! [SV122: $i,SV60: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV60 ) )
| ~ ( element @ SV122 @ ( powerset @ SV60 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV60 @ SV102 @ SV122 ) @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1387]) ).
thf(1433,plain,
! [SV123: $i,SV61: $i,SV103: $i] :
( ( ( ~ ( element @ SV103 @ ( powerset @ SV61 ) )
| ~ ( element @ SV123 @ ( powerset @ SV61 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV61 @ SV103 @ SV103 )
= SV103 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1388]) ).
thf(1434,plain,
! [SV62: $i] :
( ( ( ~ ( empty_carrier @ SV62 )
| ( empty @ ( the_carrier @ SV62 ) ) )
= $true )
| ( ( one_sorted_str @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1389]) ).
thf(1435,plain,
! [SV62: $i] :
( ( ( ~ ( empty @ ( the_carrier @ SV62 ) )
| ( empty_carrier @ SV62 ) )
= $true )
| ( ( one_sorted_str @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1390]) ).
thf(1436,plain,
! [SV105: $i,SV65: $i] :
( ( ( ~ ( element @ SV65 @ ( powerset @ SV105 ) ) )
= $true )
| ( ( subset @ SV65 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1437,plain,
! [SV105: $i,SV65: $i] :
( ( ( ~ ( subset @ SV65 @ SV105 ) )
= $true )
| ( ( element @ SV65 @ ( powerset @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1438,plain,
! [SV9: $i,SV69: $i] :
( ( ( ~ ( proper_element @ SV69 @ ( powerset @ SV9 ) )
| ( SV69 != SV9 ) )
= $true )
| ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1393]) ).
thf(1439,plain,
! [SV9: $i,SV69: $i] :
( ( ( ~ ( ( SV69 != SV9 ) )
| ( proper_element @ SV69 @ ( powerset @ SV9 ) ) )
= $true )
| ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1394]) ).
thf(1440,plain,
! [SV109: $i,SV72: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV72 ) )
= $true )
| ( ( ~ ( element @ SV72 @ ( powerset @ SV109 ) ) )
= $true )
| ( ( element @ SV13 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1441,plain,
! [SV110: $i,SV14: $i,SV73: $i] :
( ( ( ~ ( element @ SV73 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( ~ ( element @ SV110 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV14 @ SV73 @ SV110 ) @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1442,plain,
! [SV111: $i,SV15: $i,SV74: $i] :
( ( ( ~ ( element @ SV74 @ ( powerset @ SV15 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ SV15 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV15 @ SV74 @ SV111 ) @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1443,plain,
! [SV17: $i,SV76: $i] :
( ( ( ~ ~ ( ~ ( ( SV76 != empty_set ) )
| ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) ) )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1398]) ).
thf(1444,plain,
! [SV76: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ( SV76 != empty_set ) ) )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1399]) ).
thf(1445,plain,
! [SV112: $i,SV18: $i,SV77: $i] :
( ( ( ~ ( element @ SV77 @ ( powerset @ SV18 ) ) )
= $true )
| ( ( ~ ( element @ SV112 @ ( powerset @ SV18 ) ) )
= $true )
| ( ( ( subset_union2 @ SV18 @ SV77 @ SV77 )
= SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1446,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK7_SY157 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK7_SY157 @ SV19 ) ) )
| ~ ( finite @ ( sK7_SY157 @ SV19 ) ) ) )
= $true )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1447,plain,
! [SV20: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV20 @ ( sK2_SY158 @ SV20 ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( in @ SY238 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY239 @ SY238 ) )
| ( in @ SY239 @ ( sK2_SY158 @ SV20 ) ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY158 @ SV20 ) )
| ( in @ ( powerset @ SY240 ) @ ( sK2_SY158 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1448,plain,
! [SV20: $i] :
( ( ! [SY241: $i] :
~ ~ ( ~ ~ ( ~ ( subset @ SY241 @ ( sK2_SY158 @ SV20 ) )
| ~ ~ ( are_equipotent @ SY241 @ ( sK2_SY158 @ SV20 ) ) )
| ~ ~ ( in @ SY241 @ ( sK2_SY158 @ SV20 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1403]) ).
thf(1449,plain,
! [SV23: $i] :
( ( element @ ( sK3_SY163 @ SV23 ) @ ( powerset @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1450,plain,
! [SV23: $i] :
( ( ~ ( proper_element @ ( sK3_SY163 @ SV23 ) @ ( powerset @ SV23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1451,plain,
! [SV113: $i,SV24: $i,SV78: $i] :
( ( ( ~ ( element @ SV78 @ ( powerset @ SV24 ) ) )
= $true )
| ( ( ~ ( element @ SV113 @ ( powerset @ SV24 ) ) )
= $true )
| ( ( ( subset_difference @ SV24 @ SV78 @ SV113 )
= ( set_difference @ SV78 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1452,plain,
! [SV27: $i] :
( ( element @ ( sK4_SY167 @ SV27 ) @ ( powerset @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1407]) ).
thf(1453,plain,
! [SV27: $i] :
( ( empty @ ( sK4_SY167 @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1408]) ).
thf(1454,plain,
! [SV114: $i,SV29: $i,SV81: $i] :
( ( ( ~ ( element @ SV81 @ ( powerset @ SV29 ) ) )
= $true )
| ( ( ~ ( element @ SV114 @ ( powerset @ SV29 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV29 @ SV81 @ SV114 )
= ( subset_intersection2 @ SV29 @ SV114 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1455,plain,
! [SV115: $i,SV31: $i,SV82: $i] :
( ( ( ~ ( element @ SV82 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ~ ( element @ SV115 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ( subset_union2 @ SV31 @ SV82 @ SV115 )
= ( subset_union2 @ SV31 @ SV115 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1456,plain,
! [SV116: $i,SV32: $i,SV83: $i] :
( ( ( ~ ( element @ SV83 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( ~ ( element @ SV116 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( ( subset_union2 @ SV32 @ SV83 @ SV116 )
= ( set_union2 @ SV83 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1457,plain,
! [SV33: $i] :
( ( ( empty_carrier @ SV33 )
= $true )
| ( ( ~ ( one_sorted_str @ SV33 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1412]) ).
thf(1458,plain,
! [SV117: $i,SV34: $i,SV84: $i] :
( ( ( ~ ( in @ SV84 @ ( subset_complement @ SV34 @ SV117 ) )
| ~ ( in @ SV84 @ SV117 ) )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1459,plain,
! [SV35: $i,SV85: $i] :
( ( ( SV85
= ( powerset @ SV35 ) )
= $false )
| ( ( ! [SY227: $i] :
~ ( ~ ( ~ ( in @ SY227 @ SV85 )
| ( subset @ SY227 @ SV35 ) )
| ~ ( ~ ( subset @ SY227 @ SV35 )
| ( in @ SY227 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1460,plain,
! [SV35: $i,SV85: $i] :
( ( ( ! [SY228: $i] :
~ ( ~ ( ~ ( in @ SY228 @ SV85 )
| ( subset @ SY228 @ SV35 ) )
| ~ ( ~ ( subset @ SY228 @ SV35 )
| ( in @ SY228 @ SV85 ) ) ) )
= $false )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1461,plain,
! [SV87: $i,SV37: $i] :
( ( ( top_str @ SV37 )
= $false )
| ( ( ~ ( element @ SV87 @ ( powerset @ ( the_carrier @ SV37 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV37 @ SV87 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1462,plain,
! [SV42: $i,SV91: $i,SV127: $i] :
( ( ( in @ SV127 @ SV91 )
= $false )
| ( ( in @ SV127 @ SV42 )
= $true )
| ( ( element @ SV91 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1418]) ).
thf(1463,plain,
! [SV44: $i,SV93: $i] :
( ( ( in @ ( sK6_SY230 @ SV93 @ SV44 ) @ SV44 )
= $true )
| ( ( element @ SV44 @ ( powerset @ SV93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1419]) ).
thf(1464,plain,
! [SV45: $i,SV125: $i] :
( ( ( ~ ( v1_membered @ SV125 )
| ~ ( v2_membered @ SV125 ) )
= $false )
| ( ( element @ SV125 @ ( powerset @ SV45 ) )
= $false )
| ( ( v2_membered @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1465,plain,
! [SV118: $i,SV46: $i,SV94: $i] :
( ( ( ~ ( element @ SV94 @ ( powerset @ SV46 ) ) )
= $true )
| ( ( ~ ( element @ SV118 @ ( powerset @ SV46 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV46 @ SV94 @ SV118 )
= ( set_intersection2 @ SV94 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1466,plain,
! [SV50: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK8_SY196 @ SV50 ) @ ( powerset @ SV50 ) )
| ~ ~ ( empty @ ( sK8_SY196 @ SV50 ) ) )
| ~ ( finite @ ( sK8_SY196 @ SV50 ) ) ) )
= $true )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1423]) ).
thf(1467,plain,
! [SV51: $i] :
( ( ~ ( ~ ( element @ ( sK5_SY197 @ SV51 ) @ ( powerset @ ( powerset @ SV51 ) ) )
| ~ ~ ( empty @ ( sK5_SY197 @ SV51 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1424]) ).
thf(1468,plain,
! [SV51: $i] :
( ( finite @ ( sK5_SY197 @ SV51 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1425]) ).
thf(1469,plain,
! [SV121: $i,SV98: $i,SV54: $i] :
( ( ( ~ ( ~ ( in @ SV54 @ SV98 )
| ~ ( element @ SV98 @ ( powerset @ SV121 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1470,plain,
! [SV99: $i,SV55: $i] :
( ( ( top_str @ SV55 )
= $false )
| ( ( ~ ( element @ SV99 @ ( powerset @ ( the_carrier @ SV55 ) ) ) )
= $true )
| ( ( element @ ( interior @ SV55 @ SV99 ) @ ( powerset @ ( the_carrier @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1471,plain,
! [SV56: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_SY204 @ SV56 ) @ ( powerset @ SV56 ) )
| ~ ~ ( empty @ ( sK9_SY204 @ SV56 ) ) ) )
= $true )
| ( ( empty @ SV56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1428]) ).
thf(1472,plain,
! [SV58: $i,SV100: $i] :
( ( ( ~ ( ( SV100 != empty_set ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV58 @ SV100 )
!= empty_set )
= $true )
| ( ( element @ SV100 @ ( powerset @ ( powerset @ SV58 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1473,plain,
! [SV101: $i,SV59: $i,SV128: $i] :
( ( ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 )
| ( subset @ SV101 @ SV128 ) )
| ~ ( ~ ( subset @ SV101 @ SV128 )
| ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 ) ) ) )
= $true )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1474,plain,
! [SV122: $i,SV60: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV60 ) ) )
= $true )
| ( ( ~ ( element @ SV122 @ ( powerset @ SV60 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV60 @ SV102 @ SV122 ) @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1475,plain,
! [SV123: $i,SV61: $i,SV103: $i] :
( ( ( ~ ( element @ SV103 @ ( powerset @ SV61 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( powerset @ SV61 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV61 @ SV103 @ SV103 )
= SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1476,plain,
! [SV62: $i] :
( ( ( ~ ( empty_carrier @ SV62 ) )
= $true )
| ( ( empty @ ( the_carrier @ SV62 ) )
= $true )
| ( ( one_sorted_str @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1477,plain,
! [SV62: $i] :
( ( ( ~ ( empty @ ( the_carrier @ SV62 ) ) )
= $true )
| ( ( empty_carrier @ SV62 )
= $true )
| ( ( one_sorted_str @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1478,plain,
! [SV105: $i,SV65: $i] :
( ( ( element @ SV65 @ ( powerset @ SV105 ) )
= $false )
| ( ( subset @ SV65 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1479,plain,
! [SV105: $i,SV65: $i] :
( ( ( subset @ SV65 @ SV105 )
= $false )
| ( ( element @ SV65 @ ( powerset @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1480,plain,
! [SV9: $i,SV69: $i] :
( ( ( ~ ( proper_element @ SV69 @ ( powerset @ SV9 ) ) )
= $true )
| ( ( SV69 != SV9 )
= $true )
| ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1481,plain,
! [SV9: $i,SV69: $i] :
( ( ( ~ ( ( SV69 != SV9 ) ) )
= $true )
| ( ( proper_element @ SV69 @ ( powerset @ SV9 ) )
= $true )
| ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1482,plain,
! [SV109: $i,SV72: $i,SV13: $i] :
( ( ( in @ SV13 @ SV72 )
= $false )
| ( ( ~ ( element @ SV72 @ ( powerset @ SV109 ) ) )
= $true )
| ( ( element @ SV13 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1483,plain,
! [SV110: $i,SV14: $i,SV73: $i] :
( ( ( element @ SV73 @ ( powerset @ SV14 ) )
= $false )
| ( ( ~ ( element @ SV110 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV14 @ SV73 @ SV110 ) @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1484,plain,
! [SV111: $i,SV15: $i,SV74: $i] :
( ( ( element @ SV74 @ ( powerset @ SV15 ) )
= $false )
| ( ( ~ ( element @ SV111 @ ( powerset @ SV15 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV15 @ SV74 @ SV111 ) @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1485,plain,
! [SV17: $i,SV76: $i] :
( ( ( ~ ( ~ ( ( SV76 != empty_set ) )
| ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1486,plain,
! [SV76: $i,SV17: $i] :
( ( ( ~ ( ~ ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ( SV76 != empty_set ) ) )
= $false )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1487,plain,
! [SV112: $i,SV18: $i,SV77: $i] :
( ( ( element @ SV77 @ ( powerset @ SV18 ) )
= $false )
| ( ( ~ ( element @ SV112 @ ( powerset @ SV18 ) ) )
= $true )
| ( ( ( subset_union2 @ SV18 @ SV77 @ SV77 )
= SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1488,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY157 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK7_SY157 @ SV19 ) ) )
| ~ ( finite @ ( sK7_SY157 @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1489,plain,
! [SV20: $i] :
( ( ~ ~ ( ~ ( in @ SV20 @ ( sK2_SY158 @ SV20 ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( in @ SY238 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY239 @ SY238 ) )
| ( in @ SY239 @ ( sK2_SY158 @ SV20 ) ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY158 @ SV20 ) )
| ( in @ ( powerset @ SY240 ) @ ( sK2_SY158 @ SV20 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1490,plain,
! [SV20: $i,SV129: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) )
| ~ ~ ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
| ~ ~ ( in @ SV129 @ ( sK2_SY158 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1491,plain,
! [SV23: $i] :
( ( proper_element @ ( sK3_SY163 @ SV23 ) @ ( powerset @ SV23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1492,plain,
! [SV113: $i,SV24: $i,SV78: $i] :
( ( ( element @ SV78 @ ( powerset @ SV24 ) )
= $false )
| ( ( ~ ( element @ SV113 @ ( powerset @ SV24 ) ) )
= $true )
| ( ( ( subset_difference @ SV24 @ SV78 @ SV113 )
= ( set_difference @ SV78 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1493,plain,
! [SV114: $i,SV29: $i,SV81: $i] :
( ( ( element @ SV81 @ ( powerset @ SV29 ) )
= $false )
| ( ( ~ ( element @ SV114 @ ( powerset @ SV29 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV29 @ SV81 @ SV114 )
= ( subset_intersection2 @ SV29 @ SV114 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1454]) ).
thf(1494,plain,
! [SV115: $i,SV31: $i,SV82: $i] :
( ( ( element @ SV82 @ ( powerset @ SV31 ) )
= $false )
| ( ( ~ ( element @ SV115 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ( subset_union2 @ SV31 @ SV82 @ SV115 )
= ( subset_union2 @ SV31 @ SV115 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1495,plain,
! [SV116: $i,SV32: $i,SV83: $i] :
( ( ( element @ SV83 @ ( powerset @ SV32 ) )
= $false )
| ( ( ~ ( element @ SV116 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( ( subset_union2 @ SV32 @ SV83 @ SV116 )
= ( set_union2 @ SV83 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1496,plain,
! [SV33: $i] :
( ( ( one_sorted_str @ SV33 )
= $false )
| ( ( empty_carrier @ SV33 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1497,plain,
! [SV117: $i,SV34: $i,SV84: $i] :
( ( ( ~ ( in @ SV84 @ ( subset_complement @ SV34 @ SV117 ) ) )
= $true )
| ( ( ~ ( in @ SV84 @ SV117 ) )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1498,plain,
! [SV35: $i,SV85: $i,SV130: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV130 @ SV85 )
| ( subset @ SV130 @ SV35 ) )
| ~ ( ~ ( subset @ SV130 @ SV35 )
| ( in @ SV130 @ SV85 ) ) ) )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1499,plain,
! [SV85: $i,SV35: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 )
| ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 ) )
| ~ ( ~ ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
| ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 ) ) ) )
= $false )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1460]) ).
thf(1500,plain,
! [SV37: $i,SV87: $i] :
( ( ( element @ SV87 @ ( powerset @ ( the_carrier @ SV37 ) ) )
= $false )
| ( ( top_str @ SV37 )
= $false )
| ( ( element @ ( topstr_closure @ SV37 @ SV87 ) @ ( powerset @ ( the_carrier @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1501,plain,
! [SV45: $i,SV125: $i] :
( ( ( ~ ( v1_membered @ SV125 ) )
= $false )
| ( ( element @ SV125 @ ( powerset @ SV45 ) )
= $false )
| ( ( v2_membered @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1464]) ).
thf(1502,plain,
! [SV45: $i,SV125: $i] :
( ( ( ~ ( v2_membered @ SV125 ) )
= $false )
| ( ( element @ SV125 @ ( powerset @ SV45 ) )
= $false )
| ( ( v2_membered @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1464]) ).
thf(1503,plain,
! [SV118: $i,SV46: $i,SV94: $i] :
( ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false )
| ( ( ~ ( element @ SV118 @ ( powerset @ SV46 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV46 @ SV94 @ SV118 )
= ( set_intersection2 @ SV94 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1504,plain,
! [SV50: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK8_SY196 @ SV50 ) @ ( powerset @ SV50 ) )
| ~ ~ ( empty @ ( sK8_SY196 @ SV50 ) ) )
| ~ ( finite @ ( sK8_SY196 @ SV50 ) ) )
= $false )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1505,plain,
! [SV51: $i] :
( ( ~ ( element @ ( sK5_SY197 @ SV51 ) @ ( powerset @ ( powerset @ SV51 ) ) )
| ~ ~ ( empty @ ( sK5_SY197 @ SV51 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1506,plain,
! [SV121: $i,SV98: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV98 )
| ~ ( element @ SV98 @ ( powerset @ SV121 ) ) )
= $true )
| ( ( ~ ( empty @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1507,plain,
! [SV55: $i,SV99: $i] :
( ( ( element @ SV99 @ ( powerset @ ( the_carrier @ SV55 ) ) )
= $false )
| ( ( top_str @ SV55 )
= $false )
| ( ( element @ ( interior @ SV55 @ SV99 ) @ ( powerset @ ( the_carrier @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1508,plain,
! [SV56: $i] :
( ( ( ~ ( element @ ( sK9_SY204 @ SV56 ) @ ( powerset @ SV56 ) )
| ~ ~ ( empty @ ( sK9_SY204 @ SV56 ) ) )
= $false )
| ( ( empty @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1509,plain,
! [SV58: $i,SV100: $i] :
( ( ( SV100 != empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV58 @ SV100 )
!= empty_set )
= $true )
| ( ( element @ SV100 @ ( powerset @ ( powerset @ SV58 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1510,plain,
! [SV128: $i,SV101: $i,SV59: $i] :
( ( ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 )
| ( subset @ SV101 @ SV128 ) )
| ~ ( ~ ( subset @ SV101 @ SV128 )
| ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 ) ) )
= $false )
| ( ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1511,plain,
! [SV122: $i,SV60: $i,SV102: $i] :
( ( ( element @ SV102 @ ( powerset @ SV60 ) )
= $false )
| ( ( ~ ( element @ SV122 @ ( powerset @ SV60 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV60 @ SV102 @ SV122 ) @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1512,plain,
! [SV123: $i,SV61: $i,SV103: $i] :
( ( ( element @ SV103 @ ( powerset @ SV61 ) )
= $false )
| ( ( ~ ( element @ SV123 @ ( powerset @ SV61 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV61 @ SV103 @ SV103 )
= SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1513,plain,
! [SV62: $i] :
( ( ( empty_carrier @ SV62 )
= $false )
| ( ( empty @ ( the_carrier @ SV62 ) )
= $true )
| ( ( one_sorted_str @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1514,plain,
! [SV62: $i] :
( ( ( empty @ ( the_carrier @ SV62 ) )
= $false )
| ( ( empty_carrier @ SV62 )
= $true )
| ( ( one_sorted_str @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1515,plain,
! [SV9: $i,SV69: $i] :
( ( ( proper_element @ SV69 @ ( powerset @ SV9 ) )
= $false )
| ( ( SV69 != SV9 )
= $true )
| ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1516,plain,
! [SV9: $i,SV69: $i] :
( ( ( SV69 != SV9 )
= $false )
| ( ( proper_element @ SV69 @ ( powerset @ SV9 ) )
= $true )
| ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1517,plain,
! [SV13: $i,SV109: $i,SV72: $i] :
( ( ( element @ SV72 @ ( powerset @ SV109 ) )
= $false )
| ( ( in @ SV13 @ SV72 )
= $false )
| ( ( element @ SV13 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1518,plain,
! [SV73: $i,SV14: $i,SV110: $i] :
( ( ( element @ SV110 @ ( powerset @ SV14 ) )
= $false )
| ( ( element @ SV73 @ ( powerset @ SV14 ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV14 @ SV73 @ SV110 ) @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1519,plain,
! [SV74: $i,SV15: $i,SV111: $i] :
( ( ( element @ SV111 @ ( powerset @ SV15 ) )
= $false )
| ( ( element @ SV74 @ ( powerset @ SV15 ) )
= $false )
| ( ( element @ ( subset_union2 @ SV15 @ SV74 @ SV111 ) @ ( powerset @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1520,plain,
! [SV17: $i,SV76: $i] :
( ( ( ~ ( ( SV76 != empty_set ) )
| ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1521,plain,
! [SV76: $i,SV17: $i] :
( ( ( ~ ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) )
| ( SV76 != empty_set ) )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1522,plain,
! [SV77: $i,SV18: $i,SV112: $i] :
( ( ( element @ SV112 @ ( powerset @ SV18 ) )
= $false )
| ( ( element @ SV77 @ ( powerset @ SV18 ) )
= $false )
| ( ( ( subset_union2 @ SV18 @ SV77 @ SV77 )
= SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1523,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY157 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK7_SY157 @ SV19 ) ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1488]) ).
thf(1524,plain,
! [SV19: $i] :
( ( ( ~ ( finite @ ( sK7_SY157 @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1488]) ).
thf(1525,plain,
! [SV20: $i] :
( ( ~ ~ ( ~ ( in @ SV20 @ ( sK2_SY158 @ SV20 ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( in @ SY238 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY239 @ SY238 ) )
| ( in @ SY239 @ ( sK2_SY158 @ SV20 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1489]) ).
thf(1526,plain,
! [SV20: $i] :
( ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY158 @ SV20 ) )
| ( in @ ( powerset @ SY240 ) @ ( sK2_SY158 @ SV20 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1489]) ).
thf(1527,plain,
! [SV20: $i,SV129: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) )
| ~ ~ ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
| ~ ~ ( in @ SV129 @ ( sK2_SY158 @ SV20 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1528,plain,
! [SV78: $i,SV24: $i,SV113: $i] :
( ( ( element @ SV113 @ ( powerset @ SV24 ) )
= $false )
| ( ( element @ SV78 @ ( powerset @ SV24 ) )
= $false )
| ( ( ( subset_difference @ SV24 @ SV78 @ SV113 )
= ( set_difference @ SV78 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1529,plain,
! [SV81: $i,SV29: $i,SV114: $i] :
( ( ( element @ SV114 @ ( powerset @ SV29 ) )
= $false )
| ( ( element @ SV81 @ ( powerset @ SV29 ) )
= $false )
| ( ( ( subset_intersection2 @ SV29 @ SV81 @ SV114 )
= ( subset_intersection2 @ SV29 @ SV114 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1530,plain,
! [SV82: $i,SV31: $i,SV115: $i] :
( ( ( element @ SV115 @ ( powerset @ SV31 ) )
= $false )
| ( ( element @ SV82 @ ( powerset @ SV31 ) )
= $false )
| ( ( ( subset_union2 @ SV31 @ SV82 @ SV115 )
= ( subset_union2 @ SV31 @ SV115 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1531,plain,
! [SV83: $i,SV32: $i,SV116: $i] :
( ( ( element @ SV116 @ ( powerset @ SV32 ) )
= $false )
| ( ( element @ SV83 @ ( powerset @ SV32 ) )
= $false )
| ( ( ( subset_union2 @ SV32 @ SV83 @ SV116 )
= ( set_union2 @ SV83 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1532,plain,
! [SV33: $i] :
( ( ( empty @ ( the_carrier @ SV33 ) )
= $false )
| ( ( empty_carrier @ SV33 )
= $true )
| ( ( one_sorted_str @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1533,plain,
! [SV117: $i,SV34: $i,SV84: $i] :
( ( ( in @ SV84 @ ( subset_complement @ SV34 @ SV117 ) )
= $false )
| ( ( ~ ( in @ SV84 @ SV117 ) )
= $true )
| ( ( element @ SV117 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1534,plain,
! [SV35: $i,SV85: $i,SV130: $i] :
( ( ( ~ ( ~ ( in @ SV130 @ SV85 )
| ( subset @ SV130 @ SV35 ) )
| ~ ( ~ ( subset @ SV130 @ SV35 )
| ( in @ SV130 @ SV85 ) ) )
= $false )
| ( ( SV85
= ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1535,plain,
! [SV85: $i,SV35: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 )
| ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 ) )
| ~ ( ~ ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
| ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1499]) ).
thf(1536,plain,
! [SV45: $i,SV125: $i] :
( ( ( v1_membered @ SV125 )
= $true )
| ( ( element @ SV125 @ ( powerset @ SV45 ) )
= $false )
| ( ( v2_membered @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1501]) ).
thf(1537,plain,
! [SV45: $i,SV125: $i] :
( ( ( v2_membered @ SV125 )
= $true )
| ( ( element @ SV125 @ ( powerset @ SV45 ) )
= $false )
| ( ( v2_membered @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1502]) ).
thf(1538,plain,
! [SV94: $i,SV46: $i,SV118: $i] :
( ( ( element @ SV118 @ ( powerset @ SV46 ) )
= $false )
| ( ( element @ SV94 @ ( powerset @ SV46 ) )
= $false )
| ( ( ( subset_intersection2 @ SV46 @ SV94 @ SV118 )
= ( set_intersection2 @ SV94 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1539,plain,
! [SV50: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK8_SY196 @ SV50 ) @ ( powerset @ SV50 ) )
| ~ ~ ( empty @ ( sK8_SY196 @ SV50 ) ) ) )
= $false )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1504]) ).
thf(1540,plain,
! [SV50: $i] :
( ( ( ~ ( finite @ ( sK8_SY196 @ SV50 ) ) )
= $false )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1504]) ).
thf(1541,plain,
! [SV51: $i] :
( ( ~ ( element @ ( sK5_SY197 @ SV51 ) @ ( powerset @ ( powerset @ SV51 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1505]) ).
thf(1542,plain,
! [SV51: $i] :
( ( ~ ~ ( empty @ ( sK5_SY197 @ SV51 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1505]) ).
thf(1543,plain,
! [SV121: $i,SV98: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV98 ) )
= $true )
| ( ( ~ ( element @ SV98 @ ( powerset @ SV121 ) ) )
= $true )
| ( ( ~ ( empty @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1506]) ).
thf(1544,plain,
! [SV56: $i] :
( ( ( ~ ( element @ ( sK9_SY204 @ SV56 ) @ ( powerset @ SV56 ) ) )
= $false )
| ( ( empty @ SV56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1508]) ).
thf(1545,plain,
! [SV56: $i] :
( ( ( ~ ~ ( empty @ ( sK9_SY204 @ SV56 ) ) )
= $false )
| ( ( empty @ SV56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1508]) ).
thf(1546,plain,
! [SV58: $i,SV100: $i] :
( ( ( SV100 = empty_set )
= $true )
| ( ( ( complements_of_subsets @ SV58 @ SV100 )
!= empty_set )
= $true )
| ( ( element @ SV100 @ ( powerset @ ( powerset @ SV58 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1509]) ).
thf(1547,plain,
! [SV128: $i,SV101: $i,SV59: $i] :
( ( ( ~ ( ~ ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 )
| ( subset @ SV101 @ SV128 ) ) )
= $false )
| ( ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1548,plain,
! [SV59: $i,SV128: $i,SV101: $i] :
( ( ( ~ ( ~ ( subset @ SV101 @ SV128 )
| ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 ) ) )
= $false )
| ( ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1549,plain,
! [SV102: $i,SV60: $i,SV122: $i] :
( ( ( element @ SV122 @ ( powerset @ SV60 ) )
= $false )
| ( ( element @ SV102 @ ( powerset @ SV60 ) )
= $false )
| ( ( element @ ( subset_difference @ SV60 @ SV102 @ SV122 ) @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1550,plain,
! [SV103: $i,SV61: $i,SV123: $i] :
( ( ( element @ SV123 @ ( powerset @ SV61 ) )
= $false )
| ( ( element @ SV103 @ ( powerset @ SV61 ) )
= $false )
| ( ( ( subset_intersection2 @ SV61 @ SV103 @ SV103 )
= SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1551,plain,
! [SV9: $i,SV69: $i] :
( ( ( SV69 = SV9 )
= $false )
| ( ( proper_element @ SV69 @ ( powerset @ SV9 ) )
= $false )
| ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1552,plain,
! [SV9: $i,SV69: $i] :
( ( ( SV69 = SV9 )
= $true )
| ( ( proper_element @ SV69 @ ( powerset @ SV9 ) )
= $true )
| ( ( element @ SV69 @ ( powerset @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1516]) ).
thf(1553,plain,
! [SV17: $i,SV76: $i] :
( ( ( ~ ( ( SV76 != empty_set ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1554,plain,
! [SV76: $i,SV17: $i] :
( ( ( ~ ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set ) ) )
= $true )
| ( ( SV76 != empty_set )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1555,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_SY157 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK7_SY157 @ SV19 ) ) ) )
= $true )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1523]) ).
thf(1556,plain,
! [SV19: $i] :
( ( ( finite @ ( sK7_SY157 @ SV19 ) )
= $true )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1524]) ).
thf(1557,plain,
! [SV20: $i] :
( ( ~ ( ~ ( in @ SV20 @ ( sK2_SY158 @ SV20 ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( in @ SY238 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY239 @ SY238 ) )
| ( in @ SY239 @ ( sK2_SY158 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1558,plain,
! [SV20: $i] :
( ( ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK2_SY158 @ SV20 ) )
| ( in @ ( powerset @ SY240 ) @ ( sK2_SY158 @ SV20 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1559,plain,
! [SV20: $i,SV129: $i] :
( ( ~ ~ ( ~ ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) )
| ~ ~ ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
| ~ ~ ( in @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1527]) ).
thf(1560,plain,
! [SV34: $i,SV117: $i,SV84: $i] :
( ( ( in @ SV84 @ SV117 )
= $false )
| ( ( in @ SV84 @ ( subset_complement @ SV34 @ SV117 ) )
= $false )
| ( ( element @ SV117 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1561,plain,
! [SV35: $i,SV85: $i,SV130: $i] :
( ( ( ~ ( ~ ( in @ SV130 @ SV85 )
| ( subset @ SV130 @ SV35 ) ) )
= $false )
| ( ( SV85
= ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1534]) ).
thf(1562,plain,
! [SV85: $i,SV35: $i,SV130: $i] :
( ( ( ~ ( ~ ( subset @ SV130 @ SV35 )
| ( in @ SV130 @ SV85 ) ) )
= $false )
| ( ( SV85
= ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1534]) ).
thf(1563,plain,
! [SV85: $i,SV35: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 )
| ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 ) ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
| ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1564,plain,
! [SV50: $i] :
( ( ( ~ ( ~ ( element @ ( sK8_SY196 @ SV50 ) @ ( powerset @ SV50 ) )
| ~ ~ ( empty @ ( sK8_SY196 @ SV50 ) ) ) )
= $true )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1565,plain,
! [SV50: $i] :
( ( ( finite @ ( sK8_SY196 @ SV50 ) )
= $true )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1540]) ).
thf(1566,plain,
! [SV51: $i] :
( ( element @ ( sK5_SY197 @ SV51 ) @ ( powerset @ ( powerset @ SV51 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1567,plain,
! [SV51: $i] :
( ( ~ ( empty @ ( sK5_SY197 @ SV51 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1542]) ).
thf(1568,plain,
! [SV121: $i,SV98: $i,SV54: $i] :
( ( ( in @ SV54 @ SV98 )
= $false )
| ( ( ~ ( element @ SV98 @ ( powerset @ SV121 ) ) )
= $true )
| ( ( ~ ( empty @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1569,plain,
! [SV56: $i] :
( ( ( element @ ( sK9_SY204 @ SV56 ) @ ( powerset @ SV56 ) )
= $true )
| ( ( empty @ SV56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1544]) ).
thf(1570,plain,
! [SV56: $i] :
( ( ( ~ ( empty @ ( sK9_SY204 @ SV56 ) ) )
= $true )
| ( ( empty @ SV56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1571,plain,
! [SV100: $i,SV58: $i] :
( ( ( ( complements_of_subsets @ SV58 @ SV100 )
= empty_set )
= $false )
| ( ( SV100 = empty_set )
= $true )
| ( ( element @ SV100 @ ( powerset @ ( powerset @ SV58 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1572,plain,
! [SV128: $i,SV101: $i,SV59: $i] :
( ( ( ~ ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 )
| ( subset @ SV101 @ SV128 ) )
= $true )
| ( ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1573,plain,
! [SV59: $i,SV128: $i,SV101: $i] :
( ( ( ~ ( subset @ SV101 @ SV128 )
| ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 ) )
= $true )
| ( ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1548]) ).
thf(1574,plain,
! [SV17: $i,SV76: $i] :
( ( ( SV76 != empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1575,plain,
! [SV76: $i,SV17: $i] :
( ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set )
= $false )
| ( ( SV76 != empty_set )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1576,plain,
! [SV19: $i] :
( ( ( ~ ( element @ ( sK7_SY157 @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ~ ( empty @ ( sK7_SY157 @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1577,plain,
! [SV20: $i] :
( ( ~ ( in @ SV20 @ ( sK2_SY158 @ SV20 ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( in @ SY238 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY239 @ SY238 ) )
| ( in @ SY239 @ ( sK2_SY158 @ SV20 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1578,plain,
! [SV20: $i,SV131: $i] :
( ( ~ ( in @ SV131 @ ( sK2_SY158 @ SV20 ) )
| ( in @ ( powerset @ SV131 ) @ ( sK2_SY158 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1579,plain,
! [SV20: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) )
| ~ ~ ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) ) ) )
= $true )
| ( ( ~ ~ ( in @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1580,plain,
! [SV35: $i,SV85: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV85 )
| ( subset @ SV130 @ SV35 ) )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1581,plain,
! [SV85: $i,SV35: $i,SV130: $i] :
( ( ( ~ ( subset @ SV130 @ SV35 )
| ( in @ SV130 @ SV85 ) )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1582,plain,
! [SV85: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 )
| ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
| ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1583,plain,
! [SV50: $i] :
( ( ( ~ ( element @ ( sK8_SY196 @ SV50 ) @ ( powerset @ SV50 ) )
| ~ ~ ( empty @ ( sK8_SY196 @ SV50 ) ) )
= $false )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1584,plain,
! [SV51: $i] :
( ( empty @ ( sK5_SY197 @ SV51 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1585,plain,
! [SV54: $i,SV121: $i,SV98: $i] :
( ( ( element @ SV98 @ ( powerset @ SV121 ) )
= $false )
| ( ( in @ SV54 @ SV98 )
= $false )
| ( ( ~ ( empty @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1586,plain,
! [SV56: $i] :
( ( ( empty @ ( sK9_SY204 @ SV56 ) )
= $false )
| ( ( empty @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1587,plain,
! [SV128: $i,SV101: $i,SV59: $i] :
( ( ( ~ ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 ) )
= $true )
| ( ( subset @ SV101 @ SV128 )
= $true )
| ( ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1588,plain,
! [SV59: $i,SV128: $i,SV101: $i] :
( ( ( ~ ( subset @ SV101 @ SV128 ) )
= $true )
| ( ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 )
= $true )
| ( ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1573]) ).
thf(1589,plain,
! [SV17: $i,SV76: $i] :
( ( ( SV76 = empty_set )
= $true )
| ( ( ( complements_of_subsets @ SV17 @ SV76 )
!= empty_set )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1590,plain,
! [SV76: $i,SV17: $i] :
( ( ( ( complements_of_subsets @ SV17 @ SV76 )
= empty_set )
= $true )
| ( ( SV76 != empty_set )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1591,plain,
! [SV19: $i] :
( ( ( ~ ( element @ ( sK7_SY157 @ SV19 ) @ ( powerset @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1576]) ).
thf(1592,plain,
! [SV19: $i] :
( ( ( ~ ~ ( empty @ ( sK7_SY157 @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1576]) ).
thf(1593,plain,
! [SV20: $i] :
( ( ~ ( in @ SV20 @ ( sK2_SY158 @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1594,plain,
! [SV20: $i] :
( ( ~ ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( in @ SY238 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY239 @ SY238 ) )
| ( in @ SY239 @ ( sK2_SY158 @ SV20 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1595,plain,
! [SV20: $i,SV131: $i] :
( ( ( ~ ( in @ SV131 @ ( sK2_SY158 @ SV20 ) ) )
= $true )
| ( ( in @ ( powerset @ SV131 ) @ ( sK2_SY158 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1578]) ).
thf(1596,plain,
! [SV20: $i,SV129: $i] :
( ( ( ~ ( ~ ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) )
| ~ ~ ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) ) ) )
= $false )
| ( ( ~ ~ ( in @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1597,plain,
! [SV35: $i,SV85: $i,SV130: $i] :
( ( ( ~ ( in @ SV130 @ SV85 ) )
= $true )
| ( ( subset @ SV130 @ SV35 )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1580]) ).
thf(1598,plain,
! [SV85: $i,SV35: $i,SV130: $i] :
( ( ( ~ ( subset @ SV130 @ SV35 ) )
= $true )
| ( ( in @ SV130 @ SV85 )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1599,plain,
! [SV85: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 ) )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
| ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1582]) ).
thf(1600,plain,
! [SV85: $i,SV35: $i] :
( ( ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
= $false )
| ( ( ~ ( ~ ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
| ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1582]) ).
thf(1601,plain,
! [SV50: $i] :
( ( ( ~ ( element @ ( sK8_SY196 @ SV50 ) @ ( powerset @ SV50 ) ) )
= $false )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1602,plain,
! [SV50: $i] :
( ( ( ~ ~ ( empty @ ( sK8_SY196 @ SV50 ) ) )
= $false )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1603,plain,
! [SV98: $i,SV54: $i,SV121: $i] :
( ( ( empty @ SV121 )
= $false )
| ( ( in @ SV54 @ SV98 )
= $false )
| ( ( element @ SV98 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1604,plain,
! [SV128: $i,SV101: $i,SV59: $i] :
( ( ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 )
= $false )
| ( ( subset @ SV101 @ SV128 )
= $true )
| ( ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1605,plain,
! [SV59: $i,SV128: $i,SV101: $i] :
( ( ( subset @ SV101 @ SV128 )
= $false )
| ( ( related_reflexive @ ( boole_POSet @ SV59 ) @ SV101 @ SV128 )
= $true )
| ( ( element @ SV128 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false )
| ( ( element @ SV101 @ ( the_carrier @ ( boole_POSet @ SV59 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1606,plain,
! [SV76: $i,SV17: $i] :
( ( ( ( complements_of_subsets @ SV17 @ SV76 )
= empty_set )
= $false )
| ( ( SV76 = empty_set )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1607,plain,
! [SV17: $i,SV76: $i] :
( ( ( SV76 = empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV17 @ SV76 )
= empty_set )
= $true )
| ( ( element @ SV76 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1608,plain,
! [SV19: $i] :
( ( ( element @ ( sK7_SY157 @ SV19 ) @ ( powerset @ SV19 ) )
= $true )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1609,plain,
! [SV19: $i] :
( ( ( ~ ( empty @ ( sK7_SY157 @ SV19 ) ) )
= $true )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1610,plain,
! [SV20: $i] :
( ( in @ SV20 @ ( sK2_SY158 @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1593]) ).
thf(1611,plain,
! [SV20: $i] :
( ( ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( in @ SY238 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY239 @ SY238 ) )
| ( in @ SY239 @ ( sK2_SY158 @ SV20 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1594]) ).
thf(1612,plain,
! [SV20: $i,SV131: $i] :
( ( ( in @ SV131 @ ( sK2_SY158 @ SV20 ) )
= $false )
| ( ( in @ ( powerset @ SV131 ) @ ( sK2_SY158 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1613,plain,
! [SV20: $i,SV129: $i] :
( ( ( ~ ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) )
| ~ ~ ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1596]) ).
thf(1614,plain,
! [SV35: $i,SV85: $i,SV130: $i] :
( ( ( in @ SV130 @ SV85 )
= $false )
| ( ( subset @ SV130 @ SV35 )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1615,plain,
! [SV85: $i,SV35: $i,SV130: $i] :
( ( ( subset @ SV130 @ SV35 )
= $false )
| ( ( in @ SV130 @ SV85 )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1616,plain,
! [SV85: $i,SV35: $i] :
( ( ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 )
= $true )
| ( ( ~ ( ~ ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
| ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1599]) ).
thf(1617,plain,
! [SV85: $i,SV35: $i] :
( ( ( ~ ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
| ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 ) )
= $false )
| ( ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
= $false )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1618,plain,
! [SV50: $i] :
( ( ( element @ ( sK8_SY196 @ SV50 ) @ ( powerset @ SV50 ) )
= $true )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1601]) ).
thf(1619,plain,
! [SV50: $i] :
( ( ( ~ ( empty @ ( sK8_SY196 @ SV50 ) ) )
= $true )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1602]) ).
thf(1620,plain,
! [SV19: $i] :
( ( ( empty @ ( sK7_SY157 @ SV19 ) )
= $false )
| ( ( empty @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1621,plain,
! [SV20: $i,SV132: $i] :
( ( ! [SY242: $i] :
( ~ ~ ( ~ ( in @ SV132 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SY242 @ SV132 ) )
| ( in @ SY242 @ ( sK2_SY158 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1622,plain,
! [SV20: $i,SV129: $i] :
( ( ( ~ ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true )
| ( ( ~ ~ ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1613]) ).
thf(1623,plain,
! [SV85: $i,SV35: $i] :
( ( ( ~ ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
| ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 ) )
= $false )
| ( ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1624,plain,
! [SV85: $i,SV35: $i] :
( ( ( ~ ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 ) )
= $false )
| ( ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
= $false )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1617]) ).
thf(1625,plain,
! [SV85: $i,SV35: $i] :
( ( ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 )
= $false )
| ( ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
= $false )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1617]) ).
thf(1626,plain,
! [SV50: $i] :
( ( ( empty @ ( sK8_SY196 @ SV50 ) )
= $false )
| ( ( empty @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1627,plain,
! [SV133: $i,SV20: $i,SV132: $i] :
( ( ~ ~ ( ~ ( in @ SV132 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SV133 @ SV132 ) )
| ( in @ SV133 @ ( sK2_SY158 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1628,plain,
! [SV20: $i,SV129: $i] :
( ( ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) )
= $false )
| ( ( ~ ~ ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1629,plain,
! [SV85: $i,SV35: $i] :
( ( ( ~ ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 ) )
= $false )
| ( ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1623]) ).
thf(1630,plain,
! [SV85: $i,SV35: $i] :
( ( ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 )
= $false )
| ( ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1623]) ).
thf(1631,plain,
! [SV85: $i,SV35: $i] :
( ( ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
= $true )
| ( ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
= $false )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1632,plain,
! [SV133: $i,SV20: $i,SV132: $i] :
( ( ( ~ ~ ( ~ ( in @ SV132 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SV133 @ SV132 ) ) )
= $true )
| ( ( in @ SV133 @ ( sK2_SY158 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1633,plain,
! [SV20: $i,SV129: $i] :
( ( ( ~ ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $false )
| ( ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) )
= $false )
| ( ( ~ ~ ( in @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1634,plain,
! [SV85: $i,SV35: $i] :
( ( ( subset @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV35 )
= $true )
| ( ( in @ ( sK10_SY228 @ SV35 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1635,plain,
! [SV133: $i,SV20: $i,SV132: $i] :
( ( ( ~ ( ~ ( in @ SV132 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SV133 @ SV132 ) ) )
= $false )
| ( ( in @ SV133 @ ( sK2_SY158 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1636,plain,
! [SV20: $i,SV129: $i] :
( ( ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) )
= $true )
| ( ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) )
= $false )
| ( ( ~ ~ ( in @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1637,plain,
! [SV133: $i,SV20: $i,SV132: $i] :
( ( ( ~ ( in @ SV132 @ ( sK2_SY158 @ SV20 ) )
| ~ ( subset @ SV133 @ SV132 ) )
= $true )
| ( ( in @ SV133 @ ( sK2_SY158 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1638,plain,
! [SV20: $i,SV129: $i] :
( ( ( ~ ( in @ SV129 @ ( sK2_SY158 @ SV20 ) ) )
= $false )
| ( ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) )
= $false )
| ( ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1639,plain,
! [SV133: $i,SV20: $i,SV132: $i] :
( ( ( ~ ( in @ SV132 @ ( sK2_SY158 @ SV20 ) ) )
= $true )
| ( ( ~ ( subset @ SV133 @ SV132 ) )
= $true )
| ( ( in @ SV133 @ ( sK2_SY158 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1640,plain,
! [SV20: $i,SV129: $i] :
( ( ( in @ SV129 @ ( sK2_SY158 @ SV20 ) )
= $true )
| ( ( subset @ SV129 @ ( sK2_SY158 @ SV20 ) )
= $false )
| ( ( are_equipotent @ SV129 @ ( sK2_SY158 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1641,plain,
! [SV133: $i,SV20: $i,SV132: $i] :
( ( ( in @ SV132 @ ( sK2_SY158 @ SV20 ) )
= $false )
| ( ( ~ ( subset @ SV133 @ SV132 ) )
= $true )
| ( ( in @ SV133 @ ( sK2_SY158 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1642,plain,
! [SV20: $i,SV132: $i,SV133: $i] :
( ( ( subset @ SV133 @ SV132 )
= $false )
| ( ( in @ SV132 @ ( sK2_SY158 @ SV20 ) )
= $false )
| ( ( in @ SV133 @ ( sK2_SY158 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1643,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[952,1642,1640,1634,1631,1630,1626,1625,1620,1618,1615,1614,1612,1610,1608,1607,1606,1605,1604,1603,1586,1584,1571,1569,1566,1565,1560,1556,1552,1551,1550,1549,1538,1537,1536,1532,1531,1530,1529,1528,1522,1519,1518,1517,1514,1513,1507,1500,1491,1479,1478,1468,1463,1462,1453,1452,1449,1429,1420,1417,1380,1377,1353,1352,1350,1347,1336,1332,1331,1327,1324,1323,1322,1320,1312,1310,1303,1298,1297,1294,1293,1290,1274,1255,1250,1247,1246,1172,1111,1110,1108,1107,1106,1105,1104,1103,1020,1016,1015,1014,1013,1005,1004,1003,998,997,995,994,992,991,989,987,986,984,983,981,980,979,976,975,974,973,972,971]) ).
thf(1644,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1643]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU382+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:21:28 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.45/2.51 .......
% 13.45/2.51
% 13.45/2.51 No.of.Axioms: 97
% 13.45/2.51
% 13.45/2.51 Length.of.Defs: 0
% 13.45/2.51
% 13.45/2.51 Contains.Choice.Funs: false
% 13.45/2.51 .................................
% 13.45/2.51
% 13.45/2.51 ********************************
% 13.45/2.51 * All subproblems solved! *
% 13.45/2.51 ********************************
% 13.45/2.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:97,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1643,loop_count:0,foatp_calls:1,translation:fof_full)
% 13.45/2.51
% 13.45/2.51 %**** Beginning of derivation protocol ****
% 13.45/2.51 % SZS output start CNFRefutation
% See solution above
% 13.45/2.51
% 13.45/2.51 %**** End of derivation protocol ****
% 13.45/2.51 %**** no. of clauses in derivation: 899 ****
% 13.45/2.51 %**** clause counter: 1643 ****
% 13.45/2.51
% 13.45/2.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:97,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1643,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------