%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU354+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 : n013.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 10:44:05 AM UTC 2026
% Result : Theorem 6.65s 1.34s
% Output : CNFRefutation 6.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 59
% Syntax : Number of formulae : 702 ( 453 unt; 0 typ; 0 def)
% Number of atoms : 3457 (1143 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 6239 (1057 ~; 710 |; 44 &;4303 @)
% ( 14 <=>; 111 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 184 ( 181 usr; 6 con; 0-6 aty)
% Number of variables : 1271 ( 0 ^;1255 !; 16 ?;1271 :)
% 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_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_lattice,type,
boole_lattice: $i > $i ).
thf(tp_bottom_of_semilattstr,type,
bottom_of_semilattstr: $i > $i ).
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_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_complete_latt_str,type,
complete_latt_str: $i > $o ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_cup_closed,type,
cup_closed: $i > $o ).
thf(tp_diff_closed,type,
diff_closed: $i > $o ).
thf(tp_disjoint,type,
disjoint: $i > $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_fiber,type,
fiber: $i > $i > $i ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
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_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_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_of_latt_set,type,
join_of_latt_set: $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_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_semilatt_str,type,
meet_semilatt_str: $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
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_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_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_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_SY135,type,
sK10_SY135: $i > $i ).
thf(tp_sK11_SY154,type,
sK11_SY154: $i > $i > $i ).
thf(tp_sK12_SY130,type,
sK12_SY130: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY67,type,
sK2_SY67: $i ).
thf(tp_sK3_SY81,type,
sK3_SY81: $i > $i ).
thf(tp_sK4_SY93,type,
sK4_SY93: $i > $i ).
thf(tp_sK5_SY99,type,
sK5_SY99: $i > $i ).
thf(tp_sK6_SY109,type,
sK6_SY109: $i > $i > $i ).
thf(tp_sK7_SY94,type,
sK7_SY94: $i > $i ).
thf(tp_sK8_SY113,type,
sK8_SY113: $i > $i ).
thf(tp_sK9_SY119,type,
sK9_SY119: $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_rel_str,type,
strict_rel_str: $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_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_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_triple,type,
unordered_triple: $i > $i > $i > $i ).
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_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
thf(tp_v1_xreal_0,type,
v1_xreal_0: $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_v3_membered,type,
v3_membered: $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(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(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(57,axiom,
! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
thf(76,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(77,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(87,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(99,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(101,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(102,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(103,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(167,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(187,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(197,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(202,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(203,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(207,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(211,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(216,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(219,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(220,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(224,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(225,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(228,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(231,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(232,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(233,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(238,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(239,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(240,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(241,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(244,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(245,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(247,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(248,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(249,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(251,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(256,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(257,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(259,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(261,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(262,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(263,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(265,axiom,
! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).
thf(266,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(267,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(270,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(271,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(273,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(276,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_2) ).
thf(386,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(387,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(407,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(424,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(437,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(651,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(659,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(670,conjecture,
! [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(671,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[670]) ).
thf(672,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[671]) ).
thf(673,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(674,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(675,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(676,plain,
( ( ! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(677,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(678,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(679,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(680,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)],[99]) ).
thf(681,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(682,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)],[102]) ).
thf(683,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)],[103]) ).
thf(684,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(685,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(686,plain,
$true = $true,
inference(unfold_def,[status(thm)],[197]) ).
thf(687,plain,
$true = $true,
inference(unfold_def,[status(thm)],[202]) ).
thf(688,plain,
$true = $true,
inference(unfold_def,[status(thm)],[203]) ).
thf(689,plain,
$true = $true,
inference(unfold_def,[status(thm)],[207]) ).
thf(690,plain,
$true = $true,
inference(unfold_def,[status(thm)],[211]) ).
thf(691,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)],[216]) ).
thf(692,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)],[219]) ).
thf(693,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(694,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)],[224]) ).
thf(695,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(696,plain,
$true = $true,
inference(unfold_def,[status(thm)],[228]) ).
thf(697,plain,
$true = $true,
inference(unfold_def,[status(thm)],[231]) ).
thf(698,plain,
$true = $true,
inference(unfold_def,[status(thm)],[232]) ).
thf(699,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)],[233]) ).
thf(700,plain,
$true = $true,
inference(unfold_def,[status(thm)],[238]) ).
thf(701,plain,
$true = $true,
inference(unfold_def,[status(thm)],[239]) ).
thf(702,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(703,plain,
$true = $true,
inference(unfold_def,[status(thm)],[241]) ).
thf(704,plain,
$true = $true,
inference(unfold_def,[status(thm)],[244]) ).
thf(705,plain,
$true = $true,
inference(unfold_def,[status(thm)],[245]) ).
thf(706,plain,
$true = $true,
inference(unfold_def,[status(thm)],[247]) ).
thf(707,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(708,plain,
$true = $true,
inference(unfold_def,[status(thm)],[249]) ).
thf(709,plain,
$true = $true,
inference(unfold_def,[status(thm)],[251]) ).
thf(710,plain,
$true = $true,
inference(unfold_def,[status(thm)],[256]) ).
thf(711,plain,
$true = $true,
inference(unfold_def,[status(thm)],[257]) ).
thf(712,plain,
$true = $true,
inference(unfold_def,[status(thm)],[259]) ).
thf(713,plain,
$true = $true,
inference(unfold_def,[status(thm)],[261]) ).
thf(714,plain,
$true = $true,
inference(unfold_def,[status(thm)],[262]) ).
thf(715,plain,
$true = $true,
inference(unfold_def,[status(thm)],[263]) ).
thf(716,plain,
( ( ! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(717,plain,
$true = $true,
inference(unfold_def,[status(thm)],[266]) ).
thf(718,plain,
$true = $true,
inference(unfold_def,[status(thm)],[267]) ).
thf(719,plain,
$true = $true,
inference(unfold_def,[status(thm)],[270]) ).
thf(720,plain,
$true = $true,
inference(unfold_def,[status(thm)],[271]) ).
thf(721,plain,
$true = $true,
inference(unfold_def,[status(thm)],[273]) ).
thf(722,plain,
$true = $true,
inference(unfold_def,[status(thm)],[276]) ).
thf(723,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(724,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)],[386]) ).
thf(725,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)],[387]) ).
thf(726,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(727,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(728,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(729,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(730,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(731,plain,
( ( ! [SY67: $i] :
( ( element @ SY67 @ ( powerset @ sK1_A ) )
=> ( ( proper_element @ SY67 @ ( powerset @ sK1_A ) )
<=> ( SY67 != sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[672]) ).
thf(732,plain,
( ( ( element @ sK2_SY67 @ ( powerset @ sK1_A ) )
=> ( ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) )
<=> ( sK2_SY67 != sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[731]) ).
thf(733,plain,
( ( element @ sK2_SY67 @ ( powerset @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[732]) ).
thf(734,plain,
( ( ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) )
<=> ( sK2_SY67 != sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[732]) ).
thf(735,plain,
( ( ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) )
=> ( sK2_SY67 != sK1_A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[734]) ).
thf(736,plain,
( ( ( sK2_SY67 != sK1_A )
=> ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[734]) ).
thf(737,plain,
( ( ~ ( ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) )
=> ( sK2_SY67 != sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[735]) ).
thf(738,plain,
( ( ~ ( ( sK2_SY67 != sK1_A )
=> ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[736]) ).
thf(739,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(740,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(741,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(742,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(743,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(744,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)],[725]) ).
thf(745,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)],[724]) ).
thf(746,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(747,plain,
$true = $true,
inference(copy,[status(thm)],[722]) ).
thf(748,plain,
$true = $true,
inference(copy,[status(thm)],[721]) ).
thf(749,plain,
$true = $true,
inference(copy,[status(thm)],[720]) ).
thf(750,plain,
$true = $true,
inference(copy,[status(thm)],[719]) ).
thf(751,plain,
$true = $true,
inference(copy,[status(thm)],[718]) ).
thf(752,plain,
$true = $true,
inference(copy,[status(thm)],[717]) ).
thf(753,plain,
( ( ! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(754,plain,
$true = $true,
inference(copy,[status(thm)],[715]) ).
thf(755,plain,
$true = $true,
inference(copy,[status(thm)],[714]) ).
thf(756,plain,
$true = $true,
inference(copy,[status(thm)],[713]) ).
thf(757,plain,
$true = $true,
inference(copy,[status(thm)],[712]) ).
thf(758,plain,
$true = $true,
inference(copy,[status(thm)],[711]) ).
thf(759,plain,
$true = $true,
inference(copy,[status(thm)],[710]) ).
thf(760,plain,
$true = $true,
inference(copy,[status(thm)],[709]) ).
thf(761,plain,
$true = $true,
inference(copy,[status(thm)],[708]) ).
thf(762,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(763,plain,
$true = $true,
inference(copy,[status(thm)],[706]) ).
thf(764,plain,
$true = $true,
inference(copy,[status(thm)],[705]) ).
thf(765,plain,
$true = $true,
inference(copy,[status(thm)],[704]) ).
thf(766,plain,
$true = $true,
inference(copy,[status(thm)],[703]) ).
thf(767,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(768,plain,
$true = $true,
inference(copy,[status(thm)],[701]) ).
thf(769,plain,
$true = $true,
inference(copy,[status(thm)],[700]) ).
thf(770,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)],[699]) ).
thf(771,plain,
$true = $true,
inference(copy,[status(thm)],[698]) ).
thf(772,plain,
$true = $true,
inference(copy,[status(thm)],[697]) ).
thf(773,plain,
$true = $true,
inference(copy,[status(thm)],[696]) ).
thf(774,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(775,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)],[694]) ).
thf(776,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(777,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)],[692]) ).
thf(778,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(779,plain,
$true = $true,
inference(copy,[status(thm)],[690]) ).
thf(780,plain,
$true = $true,
inference(copy,[status(thm)],[689]) ).
thf(781,plain,
$true = $true,
inference(copy,[status(thm)],[688]) ).
thf(782,plain,
$true = $true,
inference(copy,[status(thm)],[687]) ).
thf(783,plain,
$true = $true,
inference(copy,[status(thm)],[686]) ).
thf(784,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(785,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(786,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)],[683]) ).
thf(787,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)],[682]) ).
thf(788,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(789,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)],[680]) ).
thf(790,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(791,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(792,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(793,plain,
( ( ! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(794,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(795,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(796,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(797,plain,
( ( element @ sK2_SY67 @ ( powerset @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(798,plain,
( ( ~ ( ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) )
=> ( sK2_SY67 != sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(799,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[739]) ).
thf(800,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)],[775]) ).
thf(801,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)],[770]) ).
thf(802,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[796]) ).
thf(803,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ ( subset_complement @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[788]) ).
thf(804,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[743]) ).
thf(805,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)],[795]) ).
thf(806,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)],[745]) ).
thf(807,plain,
( ( ~ ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) )
| ( sK2_SY67 != sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[798]) ).
thf(808,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[792]) ).
thf(809,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)],[786]) ).
thf(810,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[740]) ).
thf(811,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)],[789]) ).
thf(812,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)],[777]) ).
thf(813,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)],[778]) ).
thf(814,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[742]) ).
thf(815,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[794]) ).
thf(816,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( union_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[774]) ).
thf(817,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[784]) ).
thf(818,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[790]) ).
thf(819,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)],[787]) ).
thf(820,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( meet_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[776]) ).
thf(821,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( element @ ( subset_complement @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[767]) ).
thf(822,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[791]) ).
thf(823,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ~ ( ~ ( ~ ( proper_element @ SX1 @ SX0 )
| ( SX1
!= ( union @ SX0 ) ) )
| ~ ( ~ ( ( SX1
!= ( union @ SX0 ) ) )
| ( proper_element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[746]) ).
thf(824,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)],[744]) ).
thf(825,plain,
! [SV1: $i] :
( ( ( union @ ( powerset @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(826,plain,
! [SV2: $i] :
( ( element @ ( k1_pcomps_1 @ SV2 ) @ ( powerset @ ( powerset @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(827,plain,
! [SV3: $i] :
( ( element @ ( cast_to_subset @ SV3 ) @ ( powerset @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(828,plain,
! [SV4: $i] :
( ( ~ ( empty @ ( powerset @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(829,plain,
! [SV5: $i] :
( ( ( k1_pcomps_1 @ SV5 )
= ( powerset @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(830,plain,
! [SV6: $i] :
( ( ! [SY68: $i] :
( ~ ( element @ SY68 @ ( powerset @ SV6 ) )
| ! [SY69: $i] :
( ~ ( in @ SY69 @ SY68 )
| ( in @ SY69 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(831,plain,
! [SV7: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ~ ~ ( ~ ( element @ SY70 @ ( powerset @ SV7 ) )
| ~ ( element @ SY71 @ ( powerset @ SV7 ) ) )
| ( element @ ( subset_intersection2 @ SV7 @ SY70 @ SY71 ) @ ( powerset @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(832,plain,
! [SV8: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ~ ~ ( ~ ( element @ SY72 @ ( powerset @ SV8 ) )
| ~ ( element @ SY73 @ ( powerset @ SV8 ) ) )
| ( element @ ( subset_union2 @ SV8 @ SY72 @ SY73 ) @ ( powerset @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(833,plain,
! [SV9: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ~ ~ ( ~ ( in @ SV9 @ SY74 )
| ~ ( element @ SY74 @ ( powerset @ SY75 ) ) )
| ( element @ SV9 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(834,plain,
! [SV10: $i] :
( ( ! [SY76: $i] :
( ~ ( element @ SY76 @ ( powerset @ SV10 ) )
| ( ( subset_complement @ SV10 @ ( subset_complement @ SV10 @ SY76 ) )
= SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(835,plain,
! [SV11: $i] :
( ( ~ ( finite @ SV11 )
| ! [SY77: $i] :
( ~ ( element @ SY77 @ ( powerset @ SV11 ) )
| ( finite @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(836,plain,
! [SV12: $i] :
( ( ! [SY78: $i] :
~ ( ~ ( ~ ( element @ SV12 @ ( powerset @ SY78 ) )
| ( subset @ SV12 @ SY78 ) )
| ~ ( ~ ( subset @ SV12 @ SY78 )
| ( element @ SV12 @ ( powerset @ SY78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(837,plain,
! [SV13: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ~ ~ ( ~ ( element @ SY79 @ ( powerset @ SV13 ) )
| ~ ( element @ SY80 @ ( powerset @ SV13 ) ) )
| ( ( subset_intersection2 @ SV13 @ SY79 @ SY80 )
= ( subset_intersection2 @ SV13 @ SY80 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(838,plain,
( ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) )
| ( sK2_SY67 != sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(839,plain,
! [SV14: $i] :
( ( ~ ! [SY81: $i] :
~ ~ ( ~ ( element @ SY81 @ ( powerset @ SV14 ) )
| ~ ~ ( proper_element @ SY81 @ ( powerset @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(840,plain,
! [SV15: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ~ ~ ( ~ ( element @ SY82 @ ( powerset @ SV15 ) )
| ~ ( element @ SY83 @ ( powerset @ SV15 ) ) )
| ( ( subset_union2 @ SV15 @ SY82 @ SY82 )
= SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(841,plain,
! [SV16: $i] :
( ( ! [SY84: $i] :
( ~ ! [SY85: $i] :
( ~ ( in @ SY85 @ SV16 )
| ( in @ SY85 @ SY84 ) )
| ( element @ SV16 @ ( powerset @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(842,plain,
! [SV17: $i] :
( ( ! [SY86: $i] :
( ~ ( element @ SY86 @ ( powerset @ ( powerset @ SV17 ) ) )
| ( ( complements_of_subsets @ SV17 @ ( complements_of_subsets @ SV17 @ SY86 ) )
= SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(843,plain,
! [SV18: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ~ ~ ( ~ ( element @ SY87 @ ( powerset @ SV18 ) )
| ~ ( element @ SY88 @ ( powerset @ SV18 ) ) )
| ( element @ ( subset_difference @ SV18 @ SY87 @ SY88 ) @ ( powerset @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(844,plain,
! [SV19: $i] :
( ( ! [SY89: $i] :
( ~ ( element @ SY89 @ ( powerset @ ( powerset @ SV19 ) ) )
| ( element @ ( complements_of_subsets @ SV19 @ SY89 ) @ ( powerset @ ( powerset @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(845,plain,
! [SV20: $i] :
( ( ~ ( v1_membered @ SV20 )
| ! [SY90: $i] :
( ~ ( element @ SY90 @ ( powerset @ SV20 ) )
| ( v1_membered @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(846,plain,
! [SV21: $i] :
( ( ! [SY91: $i] :
( ~ ( in @ SV21 @ SY91 )
| ( element @ SV21 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(847,plain,
! [SV22: $i] :
( ( ! [SY92: $i] :
( ~ ( element @ SY92 @ ( powerset @ ( powerset @ SV22 ) ) )
| ( element @ ( union_of_subsets @ SV22 @ SY92 ) @ ( powerset @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(848,plain,
! [SV23: $i] :
( ( ~ ! [SY93: $i] :
~ ( element @ SY93 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(849,plain,
! [SV24: $i] :
( ( ~ ~ ( empty @ SV24 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ( element @ SY94 @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(850,plain,
! [SV25: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ~ ~ ( ~ ( element @ SY95 @ ( powerset @ SV25 ) )
| ~ ( element @ SY96 @ ( powerset @ SV25 ) ) )
| ( ( subset_intersection2 @ SV25 @ SY95 @ SY95 )
= SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(851,plain,
! [SV26: $i] :
( ( ! [SY97: $i] :
( ~ ( element @ SY97 @ ( powerset @ ( powerset @ SV26 ) ) )
| ( element @ ( meet_of_subsets @ SV26 @ SY97 ) @ ( powerset @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(852,plain,
! [SV27: $i] :
( ( ! [SY98: $i] :
( ~ ( element @ SY98 @ ( powerset @ SV27 ) )
| ( element @ ( subset_complement @ SV27 @ SY98 ) @ ( powerset @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(853,plain,
! [SV28: $i] :
( ( ~ ! [SY99: $i] :
~ ~ ( ~ ( element @ SY99 @ ( powerset @ SV28 ) )
| ~ ( empty @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(854,plain,
! [SV29: $i] :
( ( ! [SY100: $i] :
( ~ ( element @ SY100 @ SV29 )
| ~ ( ~ ( ~ ( proper_element @ SY100 @ SV29 )
| ( SY100
!= ( union @ SV29 ) ) )
| ~ ( ~ ( ( SY100
!= ( union @ SV29 ) ) )
| ( proper_element @ SY100 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(855,plain,
! [SV30: $i] :
( ( ! [SY101: $i,SY102: $i] :
( ~ ~ ( ~ ( element @ SY101 @ ( powerset @ SV30 ) )
| ~ ( element @ SY102 @ ( powerset @ SV30 ) ) )
| ( ( subset_union2 @ SV30 @ SY101 @ SY102 )
= ( subset_union2 @ SV30 @ SY102 @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(856,plain,
! [SV4: $i] :
( ( empty @ ( powerset @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(857,plain,
! [SV6: $i,SV31: $i] :
( ( ~ ( element @ SV31 @ ( powerset @ SV6 ) )
| ! [SY103: $i] :
( ~ ( in @ SY103 @ SV31 )
| ( in @ SY103 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(858,plain,
! [SV7: $i,SV32: $i] :
( ( ! [SY104: $i] :
( ~ ~ ( ~ ( element @ SV32 @ ( powerset @ SV7 ) )
| ~ ( element @ SY104 @ ( powerset @ SV7 ) ) )
| ( element @ ( subset_intersection2 @ SV7 @ SV32 @ SY104 ) @ ( powerset @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(859,plain,
! [SV8: $i,SV33: $i] :
( ( ! [SY105: $i] :
( ~ ~ ( ~ ( element @ SV33 @ ( powerset @ SV8 ) )
| ~ ( element @ SY105 @ ( powerset @ SV8 ) ) )
| ( element @ ( subset_union2 @ SV8 @ SV33 @ SY105 ) @ ( powerset @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(860,plain,
! [SV34: $i,SV9: $i] :
( ( ! [SY106: $i] :
( ~ ~ ( ~ ( in @ SV9 @ SV34 )
| ~ ( element @ SV34 @ ( powerset @ SY106 ) ) )
| ( element @ SV9 @ SY106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(861,plain,
! [SV10: $i,SV35: $i] :
( ( ~ ( element @ SV35 @ ( powerset @ SV10 ) )
| ( ( subset_complement @ SV10 @ ( subset_complement @ SV10 @ SV35 ) )
= SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(862,plain,
! [SV11: $i] :
( ( ( ~ ( finite @ SV11 ) )
= $true )
| ( ( ! [SY77: $i] :
( ~ ( element @ SY77 @ ( powerset @ SV11 ) )
| ( finite @ SY77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(863,plain,
! [SV36: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( element @ SV12 @ ( powerset @ SV36 ) )
| ( subset @ SV12 @ SV36 ) )
| ~ ( ~ ( subset @ SV12 @ SV36 )
| ( element @ SV12 @ ( powerset @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(864,plain,
! [SV13: $i,SV37: $i] :
( ( ! [SY107: $i] :
( ~ ~ ( ~ ( element @ SV37 @ ( powerset @ SV13 ) )
| ~ ( element @ SY107 @ ( powerset @ SV13 ) ) )
| ( ( subset_intersection2 @ SV13 @ SV37 @ SY107 )
= ( subset_intersection2 @ SV13 @ SY107 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(865,plain,
( ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(866,plain,
( ( sK2_SY67 != sK1_A )
= $false ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(867,plain,
! [SV14: $i] :
( ( ! [SY81: $i] :
~ ~ ( ~ ( element @ SY81 @ ( powerset @ SV14 ) )
| ~ ~ ( proper_element @ SY81 @ ( powerset @ SV14 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(868,plain,
! [SV15: $i,SV38: $i] :
( ( ! [SY108: $i] :
( ~ ~ ( ~ ( element @ SV38 @ ( powerset @ SV15 ) )
| ~ ( element @ SY108 @ ( powerset @ SV15 ) ) )
| ( ( subset_union2 @ SV15 @ SV38 @ SV38 )
= SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(869,plain,
! [SV39: $i,SV16: $i] :
( ( ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ SV16 )
| ( in @ SY109 @ SV39 ) )
| ( element @ SV16 @ ( powerset @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(870,plain,
! [SV17: $i,SV40: $i] :
( ( ~ ( element @ SV40 @ ( powerset @ ( powerset @ SV17 ) ) )
| ( ( complements_of_subsets @ SV17 @ ( complements_of_subsets @ SV17 @ SV40 ) )
= SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(871,plain,
! [SV18: $i,SV41: $i] :
( ( ! [SY110: $i] :
( ~ ~ ( ~ ( element @ SV41 @ ( powerset @ SV18 ) )
| ~ ( element @ SY110 @ ( powerset @ SV18 ) ) )
| ( element @ ( subset_difference @ SV18 @ SV41 @ SY110 ) @ ( powerset @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(872,plain,
! [SV19: $i,SV42: $i] :
( ( ~ ( element @ SV42 @ ( powerset @ ( powerset @ SV19 ) ) )
| ( element @ ( complements_of_subsets @ SV19 @ SV42 ) @ ( powerset @ ( powerset @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(873,plain,
! [SV20: $i] :
( ( ( ~ ( v1_membered @ SV20 ) )
= $true )
| ( ( ! [SY90: $i] :
( ~ ( element @ SY90 @ ( powerset @ SV20 ) )
| ( v1_membered @ SY90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(874,plain,
! [SV43: $i,SV21: $i] :
( ( ~ ( in @ SV21 @ SV43 )
| ( element @ SV21 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(875,plain,
! [SV22: $i,SV44: $i] :
( ( ~ ( element @ SV44 @ ( powerset @ ( powerset @ SV22 ) ) )
| ( element @ ( union_of_subsets @ SV22 @ SV44 ) @ ( powerset @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(876,plain,
! [SV23: $i] :
( ( ! [SY93: $i] :
~ ( element @ SY93 @ SV23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(877,plain,
! [SV24: $i] :
( ( ( ~ ~ ( empty @ SV24 ) )
= $true )
| ( ( ~ ! [SY94: $i] :
~ ~ ( ~ ( element @ SY94 @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ SY94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(878,plain,
! [SV25: $i,SV45: $i] :
( ( ! [SY111: $i] :
( ~ ~ ( ~ ( element @ SV45 @ ( powerset @ SV25 ) )
| ~ ( element @ SY111 @ ( powerset @ SV25 ) ) )
| ( ( subset_intersection2 @ SV25 @ SV45 @ SV45 )
= SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(879,plain,
! [SV26: $i,SV46: $i] :
( ( ~ ( element @ SV46 @ ( powerset @ ( powerset @ SV26 ) ) )
| ( element @ ( meet_of_subsets @ SV26 @ SV46 ) @ ( powerset @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(880,plain,
! [SV27: $i,SV47: $i] :
( ( ~ ( element @ SV47 @ ( powerset @ SV27 ) )
| ( element @ ( subset_complement @ SV27 @ SV47 ) @ ( powerset @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(881,plain,
! [SV28: $i] :
( ( ! [SY99: $i] :
~ ~ ( ~ ( element @ SY99 @ ( powerset @ SV28 ) )
| ~ ( empty @ SY99 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(882,plain,
! [SV29: $i,SV48: $i] :
( ( ~ ( element @ SV48 @ SV29 )
| ~ ( ~ ( ~ ( proper_element @ SV48 @ SV29 )
| ( SV48
!= ( union @ SV29 ) ) )
| ~ ( ~ ( ( SV48
!= ( union @ SV29 ) ) )
| ( proper_element @ SV48 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(883,plain,
! [SV30: $i,SV49: $i] :
( ( ! [SY112: $i] :
( ~ ~ ( ~ ( element @ SV49 @ ( powerset @ SV30 ) )
| ~ ( element @ SY112 @ ( powerset @ SV30 ) ) )
| ( ( subset_union2 @ SV30 @ SV49 @ SY112 )
= ( subset_union2 @ SV30 @ SY112 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(884,plain,
! [SV6: $i,SV31: $i] :
( ( ( ~ ( element @ SV31 @ ( powerset @ SV6 ) ) )
= $true )
| ( ( ! [SY103: $i] :
( ~ ( in @ SY103 @ SV31 )
| ( in @ SY103 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(885,plain,
! [SV50: $i,SV7: $i,SV32: $i] :
( ( ~ ~ ( ~ ( element @ SV32 @ ( powerset @ SV7 ) )
| ~ ( element @ SV50 @ ( powerset @ SV7 ) ) )
| ( element @ ( subset_intersection2 @ SV7 @ SV32 @ SV50 ) @ ( powerset @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(886,plain,
! [SV51: $i,SV8: $i,SV33: $i] :
( ( ~ ~ ( ~ ( element @ SV33 @ ( powerset @ SV8 ) )
| ~ ( element @ SV51 @ ( powerset @ SV8 ) ) )
| ( element @ ( subset_union2 @ SV8 @ SV33 @ SV51 ) @ ( powerset @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(887,plain,
! [SV52: $i,SV34: $i,SV9: $i] :
( ( ~ ~ ( ~ ( in @ SV9 @ SV34 )
| ~ ( element @ SV34 @ ( powerset @ SV52 ) ) )
| ( element @ SV9 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(888,plain,
! [SV10: $i,SV35: $i] :
( ( ( ~ ( element @ SV35 @ ( powerset @ SV10 ) ) )
= $true )
| ( ( ( subset_complement @ SV10 @ ( subset_complement @ SV10 @ SV35 ) )
= SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(889,plain,
! [SV11: $i] :
( ( ( finite @ SV11 )
= $false )
| ( ( ! [SY77: $i] :
( ~ ( element @ SY77 @ ( powerset @ SV11 ) )
| ( finite @ SY77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(890,plain,
! [SV36: $i,SV12: $i] :
( ( ~ ( ~ ( element @ SV12 @ ( powerset @ SV36 ) )
| ( subset @ SV12 @ SV36 ) )
| ~ ( ~ ( subset @ SV12 @ SV36 )
| ( element @ SV12 @ ( powerset @ SV36 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(891,plain,
! [SV53: $i,SV13: $i,SV37: $i] :
( ( ~ ~ ( ~ ( element @ SV37 @ ( powerset @ SV13 ) )
| ~ ( element @ SV53 @ ( powerset @ SV13 ) ) )
| ( ( subset_intersection2 @ SV13 @ SV37 @ SV53 )
= ( subset_intersection2 @ SV13 @ SV53 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(892,plain,
( ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[865]) ).
thf(893,plain,
( ( sK2_SY67 = sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(894,plain,
! [SV14: $i] :
( ( ~ ~ ( ~ ( element @ ( sK3_SY81 @ SV14 ) @ ( powerset @ SV14 ) )
| ~ ~ ( proper_element @ ( sK3_SY81 @ SV14 ) @ ( powerset @ SV14 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[867]) ).
thf(895,plain,
! [SV54: $i,SV15: $i,SV38: $i] :
( ( ~ ~ ( ~ ( element @ SV38 @ ( powerset @ SV15 ) )
| ~ ( element @ SV54 @ ( powerset @ SV15 ) ) )
| ( ( subset_union2 @ SV15 @ SV38 @ SV38 )
= SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(896,plain,
! [SV39: $i,SV16: $i] :
( ( ( ~ ! [SY109: $i] :
( ~ ( in @ SY109 @ SV16 )
| ( in @ SY109 @ SV39 ) ) )
= $true )
| ( ( element @ SV16 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(897,plain,
! [SV17: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( powerset @ ( powerset @ SV17 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV17 @ ( complements_of_subsets @ SV17 @ SV40 ) )
= SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(898,plain,
! [SV55: $i,SV18: $i,SV41: $i] :
( ( ~ ~ ( ~ ( element @ SV41 @ ( powerset @ SV18 ) )
| ~ ( element @ SV55 @ ( powerset @ SV18 ) ) )
| ( element @ ( subset_difference @ SV18 @ SV41 @ SV55 ) @ ( powerset @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(899,plain,
! [SV19: $i,SV42: $i] :
( ( ( ~ ( element @ SV42 @ ( powerset @ ( powerset @ SV19 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV19 @ SV42 ) @ ( powerset @ ( powerset @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(900,plain,
! [SV20: $i] :
( ( ( v1_membered @ SV20 )
= $false )
| ( ( ! [SY90: $i] :
( ~ ( element @ SY90 @ ( powerset @ SV20 ) )
| ( v1_membered @ SY90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(901,plain,
! [SV43: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV43 ) )
= $true )
| ( ( element @ SV21 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(902,plain,
! [SV22: $i,SV44: $i] :
( ( ( ~ ( element @ SV44 @ ( powerset @ ( powerset @ SV22 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV22 @ SV44 ) @ ( powerset @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(903,plain,
! [SV23: $i] :
( ( ~ ( element @ ( sK4_SY93 @ SV23 ) @ SV23 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[876]) ).
thf(904,plain,
! [SV24: $i] :
( ( ( ~ ( empty @ SV24 ) )
= $false )
| ( ( ~ ! [SY94: $i] :
~ ~ ( ~ ( element @ SY94 @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ SY94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(905,plain,
! [SV56: $i,SV25: $i,SV45: $i] :
( ( ~ ~ ( ~ ( element @ SV45 @ ( powerset @ SV25 ) )
| ~ ( element @ SV56 @ ( powerset @ SV25 ) ) )
| ( ( subset_intersection2 @ SV25 @ SV45 @ SV45 )
= SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(906,plain,
! [SV26: $i,SV46: $i] :
( ( ( ~ ( element @ SV46 @ ( powerset @ ( powerset @ SV26 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV26 @ SV46 ) @ ( powerset @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(907,plain,
! [SV27: $i,SV47: $i] :
( ( ( ~ ( element @ SV47 @ ( powerset @ SV27 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV27 @ SV47 ) @ ( powerset @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(908,plain,
! [SV28: $i] :
( ( ~ ~ ( ~ ( element @ ( sK5_SY99 @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ( empty @ ( sK5_SY99 @ SV28 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[881]) ).
thf(909,plain,
! [SV29: $i,SV48: $i] :
( ( ( ~ ( element @ SV48 @ SV29 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV48 @ SV29 )
| ( SV48
!= ( union @ SV29 ) ) )
| ~ ( ~ ( ( SV48
!= ( union @ SV29 ) ) )
| ( proper_element @ SV48 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(910,plain,
! [SV57: $i,SV30: $i,SV49: $i] :
( ( ~ ~ ( ~ ( element @ SV49 @ ( powerset @ SV30 ) )
| ~ ( element @ SV57 @ ( powerset @ SV30 ) ) )
| ( ( subset_union2 @ SV30 @ SV49 @ SV57 )
= ( subset_union2 @ SV30 @ SV57 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(911,plain,
! [SV6: $i,SV31: $i] :
( ( ( element @ SV31 @ ( powerset @ SV6 ) )
= $false )
| ( ( ! [SY103: $i] :
( ~ ( in @ SY103 @ SV31 )
| ( in @ SY103 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(912,plain,
! [SV50: $i,SV7: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( element @ SV32 @ ( powerset @ SV7 ) )
| ~ ( element @ SV50 @ ( powerset @ SV7 ) ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV7 @ SV32 @ SV50 ) @ ( powerset @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(913,plain,
! [SV51: $i,SV8: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( element @ SV33 @ ( powerset @ SV8 ) )
| ~ ( element @ SV51 @ ( powerset @ SV8 ) ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV8 @ SV33 @ SV51 ) @ ( powerset @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(914,plain,
! [SV52: $i,SV34: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( in @ SV9 @ SV34 )
| ~ ( element @ SV34 @ ( powerset @ SV52 ) ) ) )
= $true )
| ( ( element @ SV9 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(915,plain,
! [SV10: $i,SV35: $i] :
( ( ( element @ SV35 @ ( powerset @ SV10 ) )
= $false )
| ( ( ( subset_complement @ SV10 @ ( subset_complement @ SV10 @ SV35 ) )
= SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(916,plain,
! [SV11: $i,SV58: $i] :
( ( ( ~ ( element @ SV58 @ ( powerset @ SV11 ) )
| ( finite @ SV58 ) )
= $true )
| ( ( finite @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(917,plain,
! [SV36: $i,SV12: $i] :
( ( ~ ( ~ ( element @ SV12 @ ( powerset @ SV36 ) )
| ( subset @ SV12 @ SV36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(918,plain,
! [SV36: $i,SV12: $i] :
( ( ~ ( ~ ( subset @ SV12 @ SV36 )
| ( element @ SV12 @ ( powerset @ SV36 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(919,plain,
! [SV53: $i,SV13: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ( element @ SV37 @ ( powerset @ SV13 ) )
| ~ ( element @ SV53 @ ( powerset @ SV13 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV13 @ SV37 @ SV53 )
= ( subset_intersection2 @ SV13 @ SV53 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(920,plain,
! [SV14: $i] :
( ( ~ ( ~ ( element @ ( sK3_SY81 @ SV14 ) @ ( powerset @ SV14 ) )
| ~ ~ ( proper_element @ ( sK3_SY81 @ SV14 ) @ ( powerset @ SV14 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(921,plain,
! [SV54: $i,SV15: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( element @ SV38 @ ( powerset @ SV15 ) )
| ~ ( element @ SV54 @ ( powerset @ SV15 ) ) ) )
= $true )
| ( ( ( subset_union2 @ SV15 @ SV38 @ SV38 )
= SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(922,plain,
! [SV39: $i,SV16: $i] :
( ( ( ! [SY109: $i] :
( ~ ( in @ SY109 @ SV16 )
| ( in @ SY109 @ SV39 ) ) )
= $false )
| ( ( element @ SV16 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(923,plain,
! [SV17: $i,SV40: $i] :
( ( ( element @ SV40 @ ( powerset @ ( powerset @ SV17 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV17 @ ( complements_of_subsets @ SV17 @ SV40 ) )
= SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(924,plain,
! [SV55: $i,SV18: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ( element @ SV41 @ ( powerset @ SV18 ) )
| ~ ( element @ SV55 @ ( powerset @ SV18 ) ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV18 @ SV41 @ SV55 ) @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(925,plain,
! [SV19: $i,SV42: $i] :
( ( ( element @ SV42 @ ( powerset @ ( powerset @ SV19 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV19 @ SV42 ) @ ( powerset @ ( powerset @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(926,plain,
! [SV20: $i,SV59: $i] :
( ( ( ~ ( element @ SV59 @ ( powerset @ SV20 ) )
| ( v1_membered @ SV59 ) )
= $true )
| ( ( v1_membered @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(927,plain,
! [SV43: $i,SV21: $i] :
( ( ( in @ SV21 @ SV43 )
= $false )
| ( ( element @ SV21 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(928,plain,
! [SV22: $i,SV44: $i] :
( ( ( element @ SV44 @ ( powerset @ ( powerset @ SV22 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV22 @ SV44 ) @ ( powerset @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(929,plain,
! [SV23: $i] :
( ( element @ ( sK4_SY93 @ SV23 ) @ SV23 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(930,plain,
! [SV24: $i] :
( ( ( empty @ SV24 )
= $true )
| ( ( ~ ! [SY94: $i] :
~ ~ ( ~ ( element @ SY94 @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ SY94 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(931,plain,
! [SV56: $i,SV25: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ( element @ SV45 @ ( powerset @ SV25 ) )
| ~ ( element @ SV56 @ ( powerset @ SV25 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV25 @ SV45 @ SV45 )
= SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(932,plain,
! [SV26: $i,SV46: $i] :
( ( ( element @ SV46 @ ( powerset @ ( powerset @ SV26 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV26 @ SV46 ) @ ( powerset @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(933,plain,
! [SV27: $i,SV47: $i] :
( ( ( element @ SV47 @ ( powerset @ SV27 ) )
= $false )
| ( ( element @ ( subset_complement @ SV27 @ SV47 ) @ ( powerset @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(934,plain,
! [SV28: $i] :
( ( ~ ( ~ ( element @ ( sK5_SY99 @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ( empty @ ( sK5_SY99 @ SV28 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[908]) ).
thf(935,plain,
! [SV29: $i,SV48: $i] :
( ( ( element @ SV48 @ SV29 )
= $false )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV48 @ SV29 )
| ( SV48
!= ( union @ SV29 ) ) )
| ~ ( ~ ( ( SV48
!= ( union @ SV29 ) ) )
| ( proper_element @ SV48 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(936,plain,
! [SV57: $i,SV30: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( element @ SV49 @ ( powerset @ SV30 ) )
| ~ ( element @ SV57 @ ( powerset @ SV30 ) ) ) )
= $true )
| ( ( ( subset_union2 @ SV30 @ SV49 @ SV57 )
= ( subset_union2 @ SV30 @ SV57 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(937,plain,
! [SV6: $i,SV31: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ SV31 )
| ( in @ SV60 @ SV6 ) )
= $true )
| ( ( element @ SV31 @ ( powerset @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(938,plain,
! [SV50: $i,SV7: $i,SV32: $i] :
( ( ( ~ ( ~ ( element @ SV32 @ ( powerset @ SV7 ) )
| ~ ( element @ SV50 @ ( powerset @ SV7 ) ) ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV7 @ SV32 @ SV50 ) @ ( powerset @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(939,plain,
! [SV51: $i,SV8: $i,SV33: $i] :
( ( ( ~ ( ~ ( element @ SV33 @ ( powerset @ SV8 ) )
| ~ ( element @ SV51 @ ( powerset @ SV8 ) ) ) )
= $false )
| ( ( element @ ( subset_union2 @ SV8 @ SV33 @ SV51 ) @ ( powerset @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(940,plain,
! [SV52: $i,SV34: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ SV9 @ SV34 )
| ~ ( element @ SV34 @ ( powerset @ SV52 ) ) ) )
= $false )
| ( ( element @ SV9 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(941,plain,
! [SV11: $i,SV58: $i] :
( ( ( ~ ( element @ SV58 @ ( powerset @ SV11 ) ) )
= $true )
| ( ( finite @ SV58 )
= $true )
| ( ( finite @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(942,plain,
! [SV36: $i,SV12: $i] :
( ( ~ ( element @ SV12 @ ( powerset @ SV36 ) )
| ( subset @ SV12 @ SV36 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(943,plain,
! [SV36: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV36 )
| ( element @ SV12 @ ( powerset @ SV36 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(944,plain,
! [SV53: $i,SV13: $i,SV37: $i] :
( ( ( ~ ( ~ ( element @ SV37 @ ( powerset @ SV13 ) )
| ~ ( element @ SV53 @ ( powerset @ SV13 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV13 @ SV37 @ SV53 )
= ( subset_intersection2 @ SV13 @ SV53 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(945,plain,
! [SV14: $i] :
( ( ~ ( element @ ( sK3_SY81 @ SV14 ) @ ( powerset @ SV14 ) )
| ~ ~ ( proper_element @ ( sK3_SY81 @ SV14 ) @ ( powerset @ SV14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(946,plain,
! [SV54: $i,SV15: $i,SV38: $i] :
( ( ( ~ ( ~ ( element @ SV38 @ ( powerset @ SV15 ) )
| ~ ( element @ SV54 @ ( powerset @ SV15 ) ) ) )
= $false )
| ( ( ( subset_union2 @ SV15 @ SV38 @ SV38 )
= SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(947,plain,
! [SV16: $i,SV39: $i] :
( ( ( ~ ( in @ ( sK6_SY109 @ SV39 @ SV16 ) @ SV16 )
| ( in @ ( sK6_SY109 @ SV39 @ SV16 ) @ SV39 ) )
= $false )
| ( ( element @ SV16 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[922]) ).
thf(948,plain,
! [SV55: $i,SV18: $i,SV41: $i] :
( ( ( ~ ( ~ ( element @ SV41 @ ( powerset @ SV18 ) )
| ~ ( element @ SV55 @ ( powerset @ SV18 ) ) ) )
= $false )
| ( ( element @ ( subset_difference @ SV18 @ SV41 @ SV55 ) @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(949,plain,
! [SV20: $i,SV59: $i] :
( ( ( ~ ( element @ SV59 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( v1_membered @ SV59 )
= $true )
| ( ( v1_membered @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(950,plain,
! [SV24: $i] :
( ( ( ! [SY94: $i] :
~ ~ ( ~ ( element @ SY94 @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ SY94 ) ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(951,plain,
! [SV56: $i,SV25: $i,SV45: $i] :
( ( ( ~ ( ~ ( element @ SV45 @ ( powerset @ SV25 ) )
| ~ ( element @ SV56 @ ( powerset @ SV25 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV25 @ SV45 @ SV45 )
= SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(952,plain,
! [SV28: $i] :
( ( ~ ( element @ ( sK5_SY99 @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ( empty @ ( sK5_SY99 @ SV28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(953,plain,
! [SV29: $i,SV48: $i] :
( ( ( ~ ( ~ ( proper_element @ SV48 @ SV29 )
| ( SV48
!= ( union @ SV29 ) ) )
| ~ ( ~ ( ( SV48
!= ( union @ SV29 ) ) )
| ( proper_element @ SV48 @ SV29 ) ) )
= $false )
| ( ( element @ SV48 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(954,plain,
! [SV57: $i,SV30: $i,SV49: $i] :
( ( ( ~ ( ~ ( element @ SV49 @ ( powerset @ SV30 ) )
| ~ ( element @ SV57 @ ( powerset @ SV30 ) ) ) )
= $false )
| ( ( ( subset_union2 @ SV30 @ SV49 @ SV57 )
= ( subset_union2 @ SV30 @ SV57 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(955,plain,
! [SV6: $i,SV31: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ SV31 ) )
= $true )
| ( ( in @ SV60 @ SV6 )
= $true )
| ( ( element @ SV31 @ ( powerset @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(956,plain,
! [SV50: $i,SV7: $i,SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( powerset @ SV7 ) )
| ~ ( element @ SV50 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV7 @ SV32 @ SV50 ) @ ( powerset @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(957,plain,
! [SV51: $i,SV8: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( powerset @ SV8 ) )
| ~ ( element @ SV51 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV8 @ SV33 @ SV51 ) @ ( powerset @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[939]) ).
thf(958,plain,
! [SV52: $i,SV34: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV34 )
| ~ ( element @ SV34 @ ( powerset @ SV52 ) ) )
= $true )
| ( ( element @ SV9 @ SV52 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[940]) ).
thf(959,plain,
! [SV11: $i,SV58: $i] :
( ( ( element @ SV58 @ ( powerset @ SV11 ) )
= $false )
| ( ( finite @ SV58 )
= $true )
| ( ( finite @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(960,plain,
! [SV36: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( powerset @ SV36 ) ) )
= $true )
| ( ( subset @ SV12 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(961,plain,
! [SV36: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV36 ) )
= $true )
| ( ( element @ SV12 @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(962,plain,
! [SV53: $i,SV13: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( powerset @ SV13 ) )
| ~ ( element @ SV53 @ ( powerset @ SV13 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV13 @ SV37 @ SV53 )
= ( subset_intersection2 @ SV13 @ SV53 @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(963,plain,
! [SV14: $i] :
( ( ~ ( element @ ( sK3_SY81 @ SV14 ) @ ( powerset @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(964,plain,
! [SV14: $i] :
( ( ~ ~ ( proper_element @ ( sK3_SY81 @ SV14 ) @ ( powerset @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(965,plain,
! [SV54: $i,SV15: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( powerset @ SV15 ) )
| ~ ( element @ SV54 @ ( powerset @ SV15 ) ) )
= $true )
| ( ( ( subset_union2 @ SV15 @ SV38 @ SV38 )
= SV38 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[946]) ).
thf(966,plain,
! [SV16: $i,SV39: $i] :
( ( ( ~ ( in @ ( sK6_SY109 @ SV39 @ SV16 ) @ SV16 ) )
= $false )
| ( ( element @ SV16 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(967,plain,
! [SV16: $i,SV39: $i] :
( ( ( in @ ( sK6_SY109 @ SV39 @ SV16 ) @ SV39 )
= $false )
| ( ( element @ SV16 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(968,plain,
! [SV55: $i,SV18: $i,SV41: $i] :
( ( ( ~ ( element @ SV41 @ ( powerset @ SV18 ) )
| ~ ( element @ SV55 @ ( powerset @ SV18 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV18 @ SV41 @ SV55 ) @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(969,plain,
! [SV20: $i,SV59: $i] :
( ( ( element @ SV59 @ ( powerset @ SV20 ) )
= $false )
| ( ( v1_membered @ SV59 )
= $true )
| ( ( v1_membered @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(970,plain,
! [SV24: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY94 @ SV24 ) @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ ( sK7_SY94 @ SV24 ) ) ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[950]) ).
thf(971,plain,
! [SV56: $i,SV25: $i,SV45: $i] :
( ( ( ~ ( element @ SV45 @ ( powerset @ SV25 ) )
| ~ ( element @ SV56 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV25 @ SV45 @ SV45 )
= SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(972,plain,
! [SV28: $i] :
( ( ~ ( element @ ( sK5_SY99 @ SV28 ) @ ( powerset @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(973,plain,
! [SV28: $i] :
( ( ~ ( empty @ ( sK5_SY99 @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(974,plain,
! [SV29: $i,SV48: $i] :
( ( ( ~ ( ~ ( proper_element @ SV48 @ SV29 )
| ( SV48
!= ( union @ SV29 ) ) ) )
= $false )
| ( ( element @ SV48 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(975,plain,
! [SV29: $i,SV48: $i] :
( ( ( ~ ( ~ ( ( SV48
!= ( union @ SV29 ) ) )
| ( proper_element @ SV48 @ SV29 ) ) )
= $false )
| ( ( element @ SV48 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(976,plain,
! [SV57: $i,SV30: $i,SV49: $i] :
( ( ( ~ ( element @ SV49 @ ( powerset @ SV30 ) )
| ~ ( element @ SV57 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( ( subset_union2 @ SV30 @ SV49 @ SV57 )
= ( subset_union2 @ SV30 @ SV57 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(977,plain,
! [SV6: $i,SV31: $i,SV60: $i] :
( ( ( in @ SV60 @ SV31 )
= $false )
| ( ( in @ SV60 @ SV6 )
= $true )
| ( ( element @ SV31 @ ( powerset @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(978,plain,
! [SV50: $i,SV7: $i,SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( ~ ( element @ SV50 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV7 @ SV32 @ SV50 ) @ ( powerset @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(979,plain,
! [SV51: $i,SV8: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV51 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV8 @ SV33 @ SV51 ) @ ( powerset @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(980,plain,
! [SV52: $i,SV34: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV34 ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( powerset @ SV52 ) ) )
= $true )
| ( ( element @ SV9 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(981,plain,
! [SV36: $i,SV12: $i] :
( ( ( element @ SV12 @ ( powerset @ SV36 ) )
= $false )
| ( ( subset @ SV12 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(982,plain,
! [SV36: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV36 )
= $false )
| ( ( element @ SV12 @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(983,plain,
! [SV53: $i,SV13: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( powerset @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV53 @ ( powerset @ SV13 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV13 @ SV37 @ SV53 )
= ( subset_intersection2 @ SV13 @ SV53 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(984,plain,
! [SV14: $i] :
( ( element @ ( sK3_SY81 @ SV14 ) @ ( powerset @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(985,plain,
! [SV14: $i] :
( ( ~ ( proper_element @ ( sK3_SY81 @ SV14 ) @ ( powerset @ SV14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[964]) ).
thf(986,plain,
! [SV54: $i,SV15: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( powerset @ SV15 ) ) )
= $true )
| ( ( ~ ( element @ SV54 @ ( powerset @ SV15 ) ) )
= $true )
| ( ( ( subset_union2 @ SV15 @ SV38 @ SV38 )
= SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(987,plain,
! [SV16: $i,SV39: $i] :
( ( ( in @ ( sK6_SY109 @ SV39 @ SV16 ) @ SV16 )
= $true )
| ( ( element @ SV16 @ ( powerset @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(988,plain,
! [SV55: $i,SV18: $i,SV41: $i] :
( ( ( ~ ( element @ SV41 @ ( powerset @ SV18 ) ) )
= $true )
| ( ( ~ ( element @ SV55 @ ( powerset @ SV18 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV18 @ SV41 @ SV55 ) @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(989,plain,
! [SV24: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_SY94 @ SV24 ) @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ ( sK7_SY94 @ SV24 ) ) ) )
= $true )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(990,plain,
! [SV56: $i,SV25: $i,SV45: $i] :
( ( ( ~ ( element @ SV45 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( ~ ( element @ SV56 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV25 @ SV45 @ SV45 )
= SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(991,plain,
! [SV28: $i] :
( ( element @ ( sK5_SY99 @ SV28 ) @ ( powerset @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(992,plain,
! [SV28: $i] :
( ( empty @ ( sK5_SY99 @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(993,plain,
! [SV29: $i,SV48: $i] :
( ( ( ~ ( proper_element @ SV48 @ SV29 )
| ( SV48
!= ( union @ SV29 ) ) )
= $true )
| ( ( element @ SV48 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(994,plain,
! [SV29: $i,SV48: $i] :
( ( ( ~ ( ( SV48
!= ( union @ SV29 ) ) )
| ( proper_element @ SV48 @ SV29 ) )
= $true )
| ( ( element @ SV48 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(995,plain,
! [SV57: $i,SV30: $i,SV49: $i] :
( ( ( ~ ( element @ SV49 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( ~ ( element @ SV57 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( ( subset_union2 @ SV30 @ SV49 @ SV57 )
= ( subset_union2 @ SV30 @ SV57 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(996,plain,
! [SV50: $i,SV7: $i,SV32: $i] :
( ( ( element @ SV32 @ ( powerset @ SV7 ) )
= $false )
| ( ( ~ ( element @ SV50 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV7 @ SV32 @ SV50 ) @ ( powerset @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(997,plain,
! [SV51: $i,SV8: $i,SV33: $i] :
( ( ( element @ SV33 @ ( powerset @ SV8 ) )
= $false )
| ( ( ~ ( element @ SV51 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV8 @ SV33 @ SV51 ) @ ( powerset @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(998,plain,
! [SV52: $i,SV34: $i,SV9: $i] :
( ( ( in @ SV9 @ SV34 )
= $false )
| ( ( ~ ( element @ SV34 @ ( powerset @ SV52 ) ) )
= $true )
| ( ( element @ SV9 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(999,plain,
! [SV53: $i,SV13: $i,SV37: $i] :
( ( ( element @ SV37 @ ( powerset @ SV13 ) )
= $false )
| ( ( ~ ( element @ SV53 @ ( powerset @ SV13 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV13 @ SV37 @ SV53 )
= ( subset_intersection2 @ SV13 @ SV53 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1000,plain,
! [SV14: $i] :
( ( proper_element @ ( sK3_SY81 @ SV14 ) @ ( powerset @ SV14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1001,plain,
! [SV54: $i,SV15: $i,SV38: $i] :
( ( ( element @ SV38 @ ( powerset @ SV15 ) )
= $false )
| ( ( ~ ( element @ SV54 @ ( powerset @ SV15 ) ) )
= $true )
| ( ( ( subset_union2 @ SV15 @ SV38 @ SV38 )
= SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1002,plain,
! [SV55: $i,SV18: $i,SV41: $i] :
( ( ( element @ SV41 @ ( powerset @ SV18 ) )
= $false )
| ( ( ~ ( element @ SV55 @ ( powerset @ SV18 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV18 @ SV41 @ SV55 ) @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1003,plain,
! [SV24: $i] :
( ( ( ~ ( element @ ( sK7_SY94 @ SV24 ) @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ ( sK7_SY94 @ SV24 ) ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1004,plain,
! [SV56: $i,SV25: $i,SV45: $i] :
( ( ( element @ SV45 @ ( powerset @ SV25 ) )
= $false )
| ( ( ~ ( element @ SV56 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV25 @ SV45 @ SV45 )
= SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1005,plain,
! [SV29: $i,SV48: $i] :
( ( ( ~ ( proper_element @ SV48 @ SV29 ) )
= $true )
| ( ( SV48
!= ( union @ SV29 ) )
= $true )
| ( ( element @ SV48 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1006,plain,
! [SV29: $i,SV48: $i] :
( ( ( ~ ( ( SV48
!= ( union @ SV29 ) ) ) )
= $true )
| ( ( proper_element @ SV48 @ SV29 )
= $true )
| ( ( element @ SV48 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1007,plain,
! [SV57: $i,SV30: $i,SV49: $i] :
( ( ( element @ SV49 @ ( powerset @ SV30 ) )
= $false )
| ( ( ~ ( element @ SV57 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( ( subset_union2 @ SV30 @ SV49 @ SV57 )
= ( subset_union2 @ SV30 @ SV57 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1008,plain,
! [SV32: $i,SV7: $i,SV50: $i] :
( ( ( element @ SV50 @ ( powerset @ SV7 ) )
= $false )
| ( ( element @ SV32 @ ( powerset @ SV7 ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV7 @ SV32 @ SV50 ) @ ( powerset @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1009,plain,
! [SV33: $i,SV8: $i,SV51: $i] :
( ( ( element @ SV51 @ ( powerset @ SV8 ) )
= $false )
| ( ( element @ SV33 @ ( powerset @ SV8 ) )
= $false )
| ( ( element @ ( subset_union2 @ SV8 @ SV33 @ SV51 ) @ ( powerset @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1010,plain,
! [SV9: $i,SV52: $i,SV34: $i] :
( ( ( element @ SV34 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV9 @ SV34 )
= $false )
| ( ( element @ SV9 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1011,plain,
! [SV37: $i,SV13: $i,SV53: $i] :
( ( ( element @ SV53 @ ( powerset @ SV13 ) )
= $false )
| ( ( element @ SV37 @ ( powerset @ SV13 ) )
= $false )
| ( ( ( subset_intersection2 @ SV13 @ SV37 @ SV53 )
= ( subset_intersection2 @ SV13 @ SV53 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1012,plain,
! [SV38: $i,SV15: $i,SV54: $i] :
( ( ( element @ SV54 @ ( powerset @ SV15 ) )
= $false )
| ( ( element @ SV38 @ ( powerset @ SV15 ) )
= $false )
| ( ( ( subset_union2 @ SV15 @ SV38 @ SV38 )
= SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1013,plain,
! [SV41: $i,SV18: $i,SV55: $i] :
( ( ( element @ SV55 @ ( powerset @ SV18 ) )
= $false )
| ( ( element @ SV41 @ ( powerset @ SV18 ) )
= $false )
| ( ( element @ ( subset_difference @ SV18 @ SV41 @ SV55 ) @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1014,plain,
! [SV24: $i] :
( ( ( ~ ( element @ ( sK7_SY94 @ SV24 ) @ ( powerset @ SV24 ) ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1003]) ).
thf(1015,plain,
! [SV24: $i] :
( ( ( ~ ~ ( empty @ ( sK7_SY94 @ SV24 ) ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1003]) ).
thf(1016,plain,
! [SV45: $i,SV25: $i,SV56: $i] :
( ( ( element @ SV56 @ ( powerset @ SV25 ) )
= $false )
| ( ( element @ SV45 @ ( powerset @ SV25 ) )
= $false )
| ( ( ( subset_intersection2 @ SV25 @ SV45 @ SV45 )
= SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1017,plain,
! [SV29: $i,SV48: $i] :
( ( ( proper_element @ SV48 @ SV29 )
= $false )
| ( ( SV48
!= ( union @ SV29 ) )
= $true )
| ( ( element @ SV48 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1018,plain,
! [SV29: $i,SV48: $i] :
( ( ( SV48
!= ( union @ SV29 ) )
= $false )
| ( ( proper_element @ SV48 @ SV29 )
= $true )
| ( ( element @ SV48 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1019,plain,
! [SV49: $i,SV30: $i,SV57: $i] :
( ( ( element @ SV57 @ ( powerset @ SV30 ) )
= $false )
| ( ( element @ SV49 @ ( powerset @ SV30 ) )
= $false )
| ( ( ( subset_union2 @ SV30 @ SV49 @ SV57 )
= ( subset_union2 @ SV30 @ SV57 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1020,plain,
! [SV24: $i] :
( ( ( element @ ( sK7_SY94 @ SV24 ) @ ( powerset @ SV24 ) )
= $true )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1021,plain,
! [SV24: $i] :
( ( ( ~ ( empty @ ( sK7_SY94 @ SV24 ) ) )
= $true )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1015]) ).
thf(1022,plain,
! [SV29: $i,SV48: $i] :
( ( ( SV48
= ( union @ SV29 ) )
= $false )
| ( ( proper_element @ SV48 @ SV29 )
= $false )
| ( ( element @ SV48 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1023,plain,
! [SV29: $i,SV48: $i] :
( ( ( SV48
= ( union @ SV29 ) )
= $true )
| ( ( proper_element @ SV48 @ SV29 )
= $true )
| ( ( element @ SV48 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1024,plain,
! [SV24: $i] :
( ( ( empty @ ( sK7_SY94 @ SV24 ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1025,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[747,1024,1023,1022,1020,1019,1016,1013,1012,1011,1010,1009,1008,1000,992,991,987,984,982,981,977,969,967,959,933,932,929,928,927,925,923,915,893,892,856,829,827,826,825,797,783,782,781,780,779,773,772,771,769,768,766,765,764,763,761,760,759,758,757,756,755,754,752,751,750,749,748]) ).
thf(1026,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(1027,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(1028,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(1029,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(1030,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(1031,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)],[725]) ).
thf(1032,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)],[724]) ).
thf(1033,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(1034,plain,
$true = $true,
inference(copy,[status(thm)],[722]) ).
thf(1035,plain,
$true = $true,
inference(copy,[status(thm)],[721]) ).
thf(1036,plain,
$true = $true,
inference(copy,[status(thm)],[720]) ).
thf(1037,plain,
$true = $true,
inference(copy,[status(thm)],[719]) ).
thf(1038,plain,
$true = $true,
inference(copy,[status(thm)],[718]) ).
thf(1039,plain,
$true = $true,
inference(copy,[status(thm)],[717]) ).
thf(1040,plain,
( ( ! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(1041,plain,
$true = $true,
inference(copy,[status(thm)],[715]) ).
thf(1042,plain,
$true = $true,
inference(copy,[status(thm)],[714]) ).
thf(1043,plain,
$true = $true,
inference(copy,[status(thm)],[713]) ).
thf(1044,plain,
$true = $true,
inference(copy,[status(thm)],[712]) ).
thf(1045,plain,
$true = $true,
inference(copy,[status(thm)],[711]) ).
thf(1046,plain,
$true = $true,
inference(copy,[status(thm)],[710]) ).
thf(1047,plain,
$true = $true,
inference(copy,[status(thm)],[709]) ).
thf(1048,plain,
$true = $true,
inference(copy,[status(thm)],[708]) ).
thf(1049,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(1050,plain,
$true = $true,
inference(copy,[status(thm)],[706]) ).
thf(1051,plain,
$true = $true,
inference(copy,[status(thm)],[705]) ).
thf(1052,plain,
$true = $true,
inference(copy,[status(thm)],[704]) ).
thf(1053,plain,
$true = $true,
inference(copy,[status(thm)],[703]) ).
thf(1054,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(1055,plain,
$true = $true,
inference(copy,[status(thm)],[701]) ).
thf(1056,plain,
$true = $true,
inference(copy,[status(thm)],[700]) ).
thf(1057,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)],[699]) ).
thf(1058,plain,
$true = $true,
inference(copy,[status(thm)],[698]) ).
thf(1059,plain,
$true = $true,
inference(copy,[status(thm)],[697]) ).
thf(1060,plain,
$true = $true,
inference(copy,[status(thm)],[696]) ).
thf(1061,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(1062,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)],[694]) ).
thf(1063,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(1064,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)],[692]) ).
thf(1065,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(1066,plain,
$true = $true,
inference(copy,[status(thm)],[690]) ).
thf(1067,plain,
$true = $true,
inference(copy,[status(thm)],[689]) ).
thf(1068,plain,
$true = $true,
inference(copy,[status(thm)],[688]) ).
thf(1069,plain,
$true = $true,
inference(copy,[status(thm)],[687]) ).
thf(1070,plain,
$true = $true,
inference(copy,[status(thm)],[686]) ).
thf(1071,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(1072,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(1073,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)],[683]) ).
thf(1074,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)],[682]) ).
thf(1075,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(1076,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)],[680]) ).
thf(1077,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(1078,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(1079,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(1080,plain,
( ( ! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(1081,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(1082,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(1083,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(1084,plain,
( ( element @ sK2_SY67 @ ( powerset @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(1085,plain,
( ( ~ ( ( sK2_SY67 != sK1_A )
=> ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(1086,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1078]) ).
thf(1087,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ~ ( ~ ( ~ ( proper_element @ SX1 @ SX0 )
| ( SX1
!= ( union @ SX0 ) ) )
| ~ ( ~ ( ( SX1
!= ( union @ SX0 ) ) )
| ( proper_element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1033]) ).
thf(1088,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)],[1073]) ).
thf(1089,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)],[1031]) ).
thf(1090,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1079]) ).
thf(1091,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1029]) ).
thf(1092,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)],[1065]) ).
thf(1093,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( union_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1061]) ).
thf(1094,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( meet_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1063]) ).
thf(1095,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1081]) ).
thf(1096,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1026]) ).
thf(1097,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)],[1074]) ).
thf(1098,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)],[1082]) ).
thf(1099,plain,
( ( ~ ( ~ ( ( sK2_SY67 != sK1_A ) )
| ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1085]) ).
thf(1100,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1077]) ).
thf(1101,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1083]) ).
thf(1102,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)],[1032]) ).
thf(1103,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[1071]) ).
thf(1104,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1030]) ).
thf(1105,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1027]) ).
thf(1106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( element @ ( subset_complement @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1054]) ).
thf(1107,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)],[1057]) ).
thf(1108,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)],[1062]) ).
thf(1109,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ ( subset_complement @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1075]) ).
thf(1110,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)],[1076]) ).
thf(1111,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)],[1064]) ).
thf(1112,plain,
! [SV61: $i] :
( ( ( union @ ( powerset @ SV61 ) )
= SV61 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1113,plain,
! [SV62: $i] :
( ( element @ ( k1_pcomps_1 @ SV62 ) @ ( powerset @ ( powerset @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1114,plain,
! [SV63: $i] :
( ( element @ ( cast_to_subset @ SV63 ) @ ( powerset @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1115,plain,
! [SV64: $i] :
( ( ~ ( empty @ ( powerset @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1116,plain,
! [SV65: $i] :
( ( ( k1_pcomps_1 @ SV65 )
= ( powerset @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1117,plain,
! [SV66: $i] :
( ( ~ ! [SY113: $i] :
~ ~ ( ~ ( element @ SY113 @ ( powerset @ SV66 ) )
| ~ ( empty @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1118,plain,
! [SV67: $i] :
( ( ! [SY114: $i] :
( ~ ( element @ SY114 @ SV67 )
| ~ ( ~ ( ~ ( proper_element @ SY114 @ SV67 )
| ( SY114
!= ( union @ SV67 ) ) )
| ~ ( ~ ( ( SY114
!= ( union @ SV67 ) ) )
| ( proper_element @ SY114 @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1119,plain,
! [SV68: $i] :
( ( ! [SY115: $i,SY116: $i] :
( ~ ~ ( ~ ( element @ SY115 @ ( powerset @ SV68 ) )
| ~ ( element @ SY116 @ ( powerset @ SV68 ) ) )
| ( ( subset_union2 @ SV68 @ SY115 @ SY115 )
= SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1120,plain,
! [SV69: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ~ ~ ( ~ ( element @ SY117 @ ( powerset @ SV69 ) )
| ~ ( element @ SY118 @ ( powerset @ SV69 ) ) )
| ( ( subset_union2 @ SV69 @ SY117 @ SY118 )
= ( subset_union2 @ SV69 @ SY118 @ SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1121,plain,
! [SV70: $i] :
( ( ~ ! [SY119: $i] :
~ ~ ( ~ ( element @ SY119 @ ( powerset @ SV70 ) )
| ~ ~ ( proper_element @ SY119 @ ( powerset @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1122,plain,
! [SV71: $i] :
( ( ~ ( v1_membered @ SV71 )
| ! [SY120: $i] :
( ~ ( element @ SY120 @ ( powerset @ SV71 ) )
| ( v1_membered @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1123,plain,
! [SV72: $i] :
( ( ! [SY121: $i] :
( ~ ( element @ SY121 @ ( powerset @ ( powerset @ SV72 ) ) )
| ( element @ ( complements_of_subsets @ SV72 @ SY121 ) @ ( powerset @ ( powerset @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1124,plain,
! [SV73: $i] :
( ( ! [SY122: $i] :
( ~ ( element @ SY122 @ ( powerset @ ( powerset @ SV73 ) ) )
| ( element @ ( union_of_subsets @ SV73 @ SY122 ) @ ( powerset @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1125,plain,
! [SV74: $i] :
( ( ! [SY123: $i] :
( ~ ( element @ SY123 @ ( powerset @ ( powerset @ SV74 ) ) )
| ( element @ ( meet_of_subsets @ SV74 @ SY123 ) @ ( powerset @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1126,plain,
! [SV75: $i] :
( ( ! [SY124: $i] :
( ~ ( in @ SV75 @ SY124 )
| ( element @ SV75 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1127,plain,
! [SV76: $i] :
( ( ! [SY125: $i] :
( ~ ( element @ SY125 @ ( powerset @ SV76 ) )
| ! [SY126: $i] :
( ~ ( in @ SY126 @ SY125 )
| ( in @ SY126 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1128,plain,
! [SV77: $i] :
( ( ! [SY127: $i,SY128: $i] :
( ~ ~ ( ~ ( element @ SY127 @ ( powerset @ SV77 ) )
| ~ ( element @ SY128 @ ( powerset @ SV77 ) ) )
| ( ( subset_intersection2 @ SV77 @ SY127 @ SY127 )
= SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1129,plain,
! [SV78: $i] :
( ( ! [SY129: $i] :
~ ( ~ ( ~ ( element @ SV78 @ ( powerset @ SY129 ) )
| ( subset @ SV78 @ SY129 ) )
| ~ ( ~ ( subset @ SV78 @ SY129 )
| ( element @ SV78 @ ( powerset @ SY129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1130,plain,
( ( ~ ( ( sK2_SY67 != sK1_A ) )
| ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1131,plain,
! [SV79: $i] :
( ( ~ ~ ( empty @ SV79 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( element @ SY130 @ ( powerset @ SV79 ) )
| ~ ~ ( empty @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1132,plain,
! [SV80: $i] :
( ( ! [SY131: $i,SY132: $i] :
( ~ ~ ( ~ ( in @ SV80 @ SY131 )
| ~ ( element @ SY131 @ ( powerset @ SY132 ) ) )
| ( element @ SV80 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1133,plain,
! [SV81: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ~ ~ ( ~ ( element @ SY133 @ ( powerset @ SV81 ) )
| ~ ( element @ SY134 @ ( powerset @ SV81 ) ) )
| ( ( subset_intersection2 @ SV81 @ SY133 @ SY134 )
= ( subset_intersection2 @ SV81 @ SY134 @ SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1134,plain,
! [SV82: $i] :
( ( ~ ! [SY135: $i] :
~ ( element @ SY135 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1135,plain,
! [SV83: $i] :
( ( ~ ( finite @ SV83 )
| ! [SY136: $i] :
( ~ ( element @ SY136 @ ( powerset @ SV83 ) )
| ( finite @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1136,plain,
! [SV84: $i] :
( ( ! [SY137: $i] :
( ~ ! [SY138: $i] :
( ~ ( in @ SY138 @ SV84 )
| ( in @ SY138 @ SY137 ) )
| ( element @ SV84 @ ( powerset @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1137,plain,
! [SV85: $i] :
( ( ! [SY139: $i] :
( ~ ( element @ SY139 @ ( powerset @ SV85 ) )
| ( element @ ( subset_complement @ SV85 @ SY139 ) @ ( powerset @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1138,plain,
! [SV86: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ~ ~ ( ~ ( element @ SY140 @ ( powerset @ SV86 ) )
| ~ ( element @ SY141 @ ( powerset @ SV86 ) ) )
| ( element @ ( subset_union2 @ SV86 @ SY140 @ SY141 ) @ ( powerset @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1139,plain,
! [SV87: $i] :
( ( ! [SY142: $i,SY143: $i] :
( ~ ~ ( ~ ( element @ SY142 @ ( powerset @ SV87 ) )
| ~ ( element @ SY143 @ ( powerset @ SV87 ) ) )
| ( element @ ( subset_intersection2 @ SV87 @ SY142 @ SY143 ) @ ( powerset @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1140,plain,
! [SV88: $i] :
( ( ! [SY144: $i] :
( ~ ( element @ SY144 @ ( powerset @ SV88 ) )
| ( ( subset_complement @ SV88 @ ( subset_complement @ SV88 @ SY144 ) )
= SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1141,plain,
! [SV89: $i] :
( ( ! [SY145: $i] :
( ~ ( element @ SY145 @ ( powerset @ ( powerset @ SV89 ) ) )
| ( ( complements_of_subsets @ SV89 @ ( complements_of_subsets @ SV89 @ SY145 ) )
= SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1142,plain,
! [SV90: $i] :
( ( ! [SY146: $i,SY147: $i] :
( ~ ~ ( ~ ( element @ SY146 @ ( powerset @ SV90 ) )
| ~ ( element @ SY147 @ ( powerset @ SV90 ) ) )
| ( element @ ( subset_difference @ SV90 @ SY146 @ SY147 ) @ ( powerset @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1143,plain,
! [SV64: $i] :
( ( empty @ ( powerset @ SV64 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1144,plain,
! [SV66: $i] :
( ( ! [SY113: $i] :
~ ~ ( ~ ( element @ SY113 @ ( powerset @ SV66 ) )
| ~ ( empty @ SY113 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1145,plain,
! [SV67: $i,SV91: $i] :
( ( ~ ( element @ SV91 @ SV67 )
| ~ ( ~ ( ~ ( proper_element @ SV91 @ SV67 )
| ( SV91
!= ( union @ SV67 ) ) )
| ~ ( ~ ( ( SV91
!= ( union @ SV67 ) ) )
| ( proper_element @ SV91 @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1146,plain,
! [SV68: $i,SV92: $i] :
( ( ! [SY148: $i] :
( ~ ~ ( ~ ( element @ SV92 @ ( powerset @ SV68 ) )
| ~ ( element @ SY148 @ ( powerset @ SV68 ) ) )
| ( ( subset_union2 @ SV68 @ SV92 @ SV92 )
= SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1147,plain,
! [SV69: $i,SV93: $i] :
( ( ! [SY149: $i] :
( ~ ~ ( ~ ( element @ SV93 @ ( powerset @ SV69 ) )
| ~ ( element @ SY149 @ ( powerset @ SV69 ) ) )
| ( ( subset_union2 @ SV69 @ SV93 @ SY149 )
= ( subset_union2 @ SV69 @ SY149 @ SV93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1148,plain,
! [SV70: $i] :
( ( ! [SY119: $i] :
~ ~ ( ~ ( element @ SY119 @ ( powerset @ SV70 ) )
| ~ ~ ( proper_element @ SY119 @ ( powerset @ SV70 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1149,plain,
! [SV71: $i] :
( ( ( ~ ( v1_membered @ SV71 ) )
= $true )
| ( ( ! [SY120: $i] :
( ~ ( element @ SY120 @ ( powerset @ SV71 ) )
| ( v1_membered @ SY120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1150,plain,
! [SV72: $i,SV94: $i] :
( ( ~ ( element @ SV94 @ ( powerset @ ( powerset @ SV72 ) ) )
| ( element @ ( complements_of_subsets @ SV72 @ SV94 ) @ ( powerset @ ( powerset @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1151,plain,
! [SV73: $i,SV95: $i] :
( ( ~ ( element @ SV95 @ ( powerset @ ( powerset @ SV73 ) ) )
| ( element @ ( union_of_subsets @ SV73 @ SV95 ) @ ( powerset @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1152,plain,
! [SV74: $i,SV96: $i] :
( ( ~ ( element @ SV96 @ ( powerset @ ( powerset @ SV74 ) ) )
| ( element @ ( meet_of_subsets @ SV74 @ SV96 ) @ ( powerset @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1153,plain,
! [SV97: $i,SV75: $i] :
( ( ~ ( in @ SV75 @ SV97 )
| ( element @ SV75 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1154,plain,
! [SV76: $i,SV98: $i] :
( ( ~ ( element @ SV98 @ ( powerset @ SV76 ) )
| ! [SY150: $i] :
( ~ ( in @ SY150 @ SV98 )
| ( in @ SY150 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1155,plain,
! [SV77: $i,SV99: $i] :
( ( ! [SY151: $i] :
( ~ ~ ( ~ ( element @ SV99 @ ( powerset @ SV77 ) )
| ~ ( element @ SY151 @ ( powerset @ SV77 ) ) )
| ( ( subset_intersection2 @ SV77 @ SV99 @ SV99 )
= SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1156,plain,
! [SV100: $i,SV78: $i] :
( ( ~ ( ~ ( ~ ( element @ SV78 @ ( powerset @ SV100 ) )
| ( subset @ SV78 @ SV100 ) )
| ~ ( ~ ( subset @ SV78 @ SV100 )
| ( element @ SV78 @ ( powerset @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1157,plain,
( ( ~ ( ( sK2_SY67 != sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1158,plain,
( ( proper_element @ sK2_SY67 @ ( powerset @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1159,plain,
! [SV79: $i] :
( ( ( ~ ~ ( empty @ SV79 ) )
= $true )
| ( ( ~ ! [SY130: $i] :
~ ~ ( ~ ( element @ SY130 @ ( powerset @ SV79 ) )
| ~ ~ ( empty @ SY130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1160,plain,
! [SV101: $i,SV80: $i] :
( ( ! [SY152: $i] :
( ~ ~ ( ~ ( in @ SV80 @ SV101 )
| ~ ( element @ SV101 @ ( powerset @ SY152 ) ) )
| ( element @ SV80 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1161,plain,
! [SV81: $i,SV102: $i] :
( ( ! [SY153: $i] :
( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV81 ) )
| ~ ( element @ SY153 @ ( powerset @ SV81 ) ) )
| ( ( subset_intersection2 @ SV81 @ SV102 @ SY153 )
= ( subset_intersection2 @ SV81 @ SY153 @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1162,plain,
! [SV82: $i] :
( ( ! [SY135: $i] :
~ ( element @ SY135 @ SV82 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1163,plain,
! [SV83: $i] :
( ( ( ~ ( finite @ SV83 ) )
= $true )
| ( ( ! [SY136: $i] :
( ~ ( element @ SY136 @ ( powerset @ SV83 ) )
| ( finite @ SY136 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1164,plain,
! [SV103: $i,SV84: $i] :
( ( ~ ! [SY154: $i] :
( ~ ( in @ SY154 @ SV84 )
| ( in @ SY154 @ SV103 ) )
| ( element @ SV84 @ ( powerset @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1165,plain,
! [SV85: $i,SV104: $i] :
( ( ~ ( element @ SV104 @ ( powerset @ SV85 ) )
| ( element @ ( subset_complement @ SV85 @ SV104 ) @ ( powerset @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1166,plain,
! [SV86: $i,SV105: $i] :
( ( ! [SY155: $i] :
( ~ ~ ( ~ ( element @ SV105 @ ( powerset @ SV86 ) )
| ~ ( element @ SY155 @ ( powerset @ SV86 ) ) )
| ( element @ ( subset_union2 @ SV86 @ SV105 @ SY155 ) @ ( powerset @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1167,plain,
! [SV87: $i,SV106: $i] :
( ( ! [SY156: $i] :
( ~ ~ ( ~ ( element @ SV106 @ ( powerset @ SV87 ) )
| ~ ( element @ SY156 @ ( powerset @ SV87 ) ) )
| ( element @ ( subset_intersection2 @ SV87 @ SV106 @ SY156 ) @ ( powerset @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1168,plain,
! [SV88: $i,SV107: $i] :
( ( ~ ( element @ SV107 @ ( powerset @ SV88 ) )
| ( ( subset_complement @ SV88 @ ( subset_complement @ SV88 @ SV107 ) )
= SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1169,plain,
! [SV89: $i,SV108: $i] :
( ( ~ ( element @ SV108 @ ( powerset @ ( powerset @ SV89 ) ) )
| ( ( complements_of_subsets @ SV89 @ ( complements_of_subsets @ SV89 @ SV108 ) )
= SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1170,plain,
! [SV90: $i,SV109: $i] :
( ( ! [SY157: $i] :
( ~ ~ ( ~ ( element @ SV109 @ ( powerset @ SV90 ) )
| ~ ( element @ SY157 @ ( powerset @ SV90 ) ) )
| ( element @ ( subset_difference @ SV90 @ SV109 @ SY157 ) @ ( powerset @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1171,plain,
! [SV66: $i] :
( ( ~ ~ ( ~ ( element @ ( sK8_SY113 @ SV66 ) @ ( powerset @ SV66 ) )
| ~ ( empty @ ( sK8_SY113 @ SV66 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1144]) ).
thf(1172,plain,
! [SV67: $i,SV91: $i] :
( ( ( ~ ( element @ SV91 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV91 @ SV67 )
| ( SV91
!= ( union @ SV67 ) ) )
| ~ ( ~ ( ( SV91
!= ( union @ SV67 ) ) )
| ( proper_element @ SV91 @ SV67 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1173,plain,
! [SV110: $i,SV68: $i,SV92: $i] :
( ( ~ ~ ( ~ ( element @ SV92 @ ( powerset @ SV68 ) )
| ~ ( element @ SV110 @ ( powerset @ SV68 ) ) )
| ( ( subset_union2 @ SV68 @ SV92 @ SV92 )
= SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1174,plain,
! [SV111: $i,SV69: $i,SV93: $i] :
( ( ~ ~ ( ~ ( element @ SV93 @ ( powerset @ SV69 ) )
| ~ ( element @ SV111 @ ( powerset @ SV69 ) ) )
| ( ( subset_union2 @ SV69 @ SV93 @ SV111 )
= ( subset_union2 @ SV69 @ SV111 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1175,plain,
! [SV70: $i] :
( ( ~ ~ ( ~ ( element @ ( sK9_SY119 @ SV70 ) @ ( powerset @ SV70 ) )
| ~ ~ ( proper_element @ ( sK9_SY119 @ SV70 ) @ ( powerset @ SV70 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1148]) ).
thf(1176,plain,
! [SV71: $i] :
( ( ( v1_membered @ SV71 )
= $false )
| ( ( ! [SY120: $i] :
( ~ ( element @ SY120 @ ( powerset @ SV71 ) )
| ( v1_membered @ SY120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1177,plain,
! [SV72: $i,SV94: $i] :
( ( ( ~ ( element @ SV94 @ ( powerset @ ( powerset @ SV72 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV72 @ SV94 ) @ ( powerset @ ( powerset @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1178,plain,
! [SV73: $i,SV95: $i] :
( ( ( ~ ( element @ SV95 @ ( powerset @ ( powerset @ SV73 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV73 @ SV95 ) @ ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1179,plain,
! [SV74: $i,SV96: $i] :
( ( ( ~ ( element @ SV96 @ ( powerset @ ( powerset @ SV74 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV74 @ SV96 ) @ ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1180,plain,
! [SV97: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV97 ) )
= $true )
| ( ( element @ SV75 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1181,plain,
! [SV76: $i,SV98: $i] :
( ( ( ~ ( element @ SV98 @ ( powerset @ SV76 ) ) )
= $true )
| ( ( ! [SY150: $i] :
( ~ ( in @ SY150 @ SV98 )
| ( in @ SY150 @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1182,plain,
! [SV112: $i,SV77: $i,SV99: $i] :
( ( ~ ~ ( ~ ( element @ SV99 @ ( powerset @ SV77 ) )
| ~ ( element @ SV112 @ ( powerset @ SV77 ) ) )
| ( ( subset_intersection2 @ SV77 @ SV99 @ SV99 )
= SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1183,plain,
! [SV100: $i,SV78: $i] :
( ( ~ ( ~ ( element @ SV78 @ ( powerset @ SV100 ) )
| ( subset @ SV78 @ SV100 ) )
| ~ ( ~ ( subset @ SV78 @ SV100 )
| ( element @ SV78 @ ( powerset @ SV100 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1184,plain,
( ( sK2_SY67 != sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1157]) ).
thf(1185,plain,
! [SV79: $i] :
( ( ( ~ ( empty @ SV79 ) )
= $false )
| ( ( ~ ! [SY130: $i] :
~ ~ ( ~ ( element @ SY130 @ ( powerset @ SV79 ) )
| ~ ~ ( empty @ SY130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1186,plain,
! [SV113: $i,SV101: $i,SV80: $i] :
( ( ~ ~ ( ~ ( in @ SV80 @ SV101 )
| ~ ( element @ SV101 @ ( powerset @ SV113 ) ) )
| ( element @ SV80 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1187,plain,
! [SV114: $i,SV81: $i,SV102: $i] :
( ( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV81 ) )
| ~ ( element @ SV114 @ ( powerset @ SV81 ) ) )
| ( ( subset_intersection2 @ SV81 @ SV102 @ SV114 )
= ( subset_intersection2 @ SV81 @ SV114 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1188,plain,
! [SV82: $i] :
( ( ~ ( element @ ( sK10_SY135 @ SV82 ) @ SV82 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1162]) ).
thf(1189,plain,
! [SV83: $i] :
( ( ( finite @ SV83 )
= $false )
| ( ( ! [SY136: $i] :
( ~ ( element @ SY136 @ ( powerset @ SV83 ) )
| ( finite @ SY136 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1190,plain,
! [SV103: $i,SV84: $i] :
( ( ( ~ ! [SY154: $i] :
( ~ ( in @ SY154 @ SV84 )
| ( in @ SY154 @ SV103 ) ) )
= $true )
| ( ( element @ SV84 @ ( powerset @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1164]) ).
thf(1191,plain,
! [SV85: $i,SV104: $i] :
( ( ( ~ ( element @ SV104 @ ( powerset @ SV85 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV85 @ SV104 ) @ ( powerset @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1192,plain,
! [SV115: $i,SV86: $i,SV105: $i] :
( ( ~ ~ ( ~ ( element @ SV105 @ ( powerset @ SV86 ) )
| ~ ( element @ SV115 @ ( powerset @ SV86 ) ) )
| ( element @ ( subset_union2 @ SV86 @ SV105 @ SV115 ) @ ( powerset @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1193,plain,
! [SV116: $i,SV87: $i,SV106: $i] :
( ( ~ ~ ( ~ ( element @ SV106 @ ( powerset @ SV87 ) )
| ~ ( element @ SV116 @ ( powerset @ SV87 ) ) )
| ( element @ ( subset_intersection2 @ SV87 @ SV106 @ SV116 ) @ ( powerset @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1194,plain,
! [SV88: $i,SV107: $i] :
( ( ( ~ ( element @ SV107 @ ( powerset @ SV88 ) ) )
= $true )
| ( ( ( subset_complement @ SV88 @ ( subset_complement @ SV88 @ SV107 ) )
= SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1195,plain,
! [SV89: $i,SV108: $i] :
( ( ( ~ ( element @ SV108 @ ( powerset @ ( powerset @ SV89 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV89 @ ( complements_of_subsets @ SV89 @ SV108 ) )
= SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1196,plain,
! [SV117: $i,SV90: $i,SV109: $i] :
( ( ~ ~ ( ~ ( element @ SV109 @ ( powerset @ SV90 ) )
| ~ ( element @ SV117 @ ( powerset @ SV90 ) ) )
| ( element @ ( subset_difference @ SV90 @ SV109 @ SV117 ) @ ( powerset @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1197,plain,
! [SV66: $i] :
( ( ~ ( ~ ( element @ ( sK8_SY113 @ SV66 ) @ ( powerset @ SV66 ) )
| ~ ( empty @ ( sK8_SY113 @ SV66 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1171]) ).
thf(1198,plain,
! [SV67: $i,SV91: $i] :
( ( ( element @ SV91 @ SV67 )
= $false )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV91 @ SV67 )
| ( SV91
!= ( union @ SV67 ) ) )
| ~ ( ~ ( ( SV91
!= ( union @ SV67 ) ) )
| ( proper_element @ SV91 @ SV67 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1199,plain,
! [SV110: $i,SV68: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ( element @ SV92 @ ( powerset @ SV68 ) )
| ~ ( element @ SV110 @ ( powerset @ SV68 ) ) ) )
= $true )
| ( ( ( subset_union2 @ SV68 @ SV92 @ SV92 )
= SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1200,plain,
! [SV111: $i,SV69: $i,SV93: $i] :
( ( ( ~ ~ ( ~ ( element @ SV93 @ ( powerset @ SV69 ) )
| ~ ( element @ SV111 @ ( powerset @ SV69 ) ) ) )
= $true )
| ( ( ( subset_union2 @ SV69 @ SV93 @ SV111 )
= ( subset_union2 @ SV69 @ SV111 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1201,plain,
! [SV70: $i] :
( ( ~ ( ~ ( element @ ( sK9_SY119 @ SV70 ) @ ( powerset @ SV70 ) )
| ~ ~ ( proper_element @ ( sK9_SY119 @ SV70 ) @ ( powerset @ SV70 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1175]) ).
thf(1202,plain,
! [SV71: $i,SV118: $i] :
( ( ( ~ ( element @ SV118 @ ( powerset @ SV71 ) )
| ( v1_membered @ SV118 ) )
= $true )
| ( ( v1_membered @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1203,plain,
! [SV72: $i,SV94: $i] :
( ( ( element @ SV94 @ ( powerset @ ( powerset @ SV72 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV72 @ SV94 ) @ ( powerset @ ( powerset @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1204,plain,
! [SV73: $i,SV95: $i] :
( ( ( element @ SV95 @ ( powerset @ ( powerset @ SV73 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV73 @ SV95 ) @ ( powerset @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1205,plain,
! [SV74: $i,SV96: $i] :
( ( ( element @ SV96 @ ( powerset @ ( powerset @ SV74 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV74 @ SV96 ) @ ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1206,plain,
! [SV97: $i,SV75: $i] :
( ( ( in @ SV75 @ SV97 )
= $false )
| ( ( element @ SV75 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1207,plain,
! [SV76: $i,SV98: $i] :
( ( ( element @ SV98 @ ( powerset @ SV76 ) )
= $false )
| ( ( ! [SY150: $i] :
( ~ ( in @ SY150 @ SV98 )
| ( in @ SY150 @ SV76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1208,plain,
! [SV112: $i,SV77: $i,SV99: $i] :
( ( ( ~ ~ ( ~ ( element @ SV99 @ ( powerset @ SV77 ) )
| ~ ( element @ SV112 @ ( powerset @ SV77 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV77 @ SV99 @ SV99 )
= SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1209,plain,
! [SV100: $i,SV78: $i] :
( ( ~ ( ~ ( element @ SV78 @ ( powerset @ SV100 ) )
| ( subset @ SV78 @ SV100 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1183]) ).
thf(1210,plain,
! [SV100: $i,SV78: $i] :
( ( ~ ( ~ ( subset @ SV78 @ SV100 )
| ( element @ SV78 @ ( powerset @ SV100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1183]) ).
thf(1211,plain,
( ( sK2_SY67 = sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1212,plain,
! [SV79: $i] :
( ( ( empty @ SV79 )
= $true )
| ( ( ~ ! [SY130: $i] :
~ ~ ( ~ ( element @ SY130 @ ( powerset @ SV79 ) )
| ~ ~ ( empty @ SY130 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1185]) ).
thf(1213,plain,
! [SV113: $i,SV101: $i,SV80: $i] :
( ( ( ~ ~ ( ~ ( in @ SV80 @ SV101 )
| ~ ( element @ SV101 @ ( powerset @ SV113 ) ) ) )
= $true )
| ( ( element @ SV80 @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1214,plain,
! [SV114: $i,SV81: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV81 ) )
| ~ ( element @ SV114 @ ( powerset @ SV81 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV81 @ SV102 @ SV114 )
= ( subset_intersection2 @ SV81 @ SV114 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1215,plain,
! [SV82: $i] :
( ( element @ ( sK10_SY135 @ SV82 ) @ SV82 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1216,plain,
! [SV83: $i,SV119: $i] :
( ( ( ~ ( element @ SV119 @ ( powerset @ SV83 ) )
| ( finite @ SV119 ) )
= $true )
| ( ( finite @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1217,plain,
! [SV103: $i,SV84: $i] :
( ( ( ! [SY154: $i] :
( ~ ( in @ SY154 @ SV84 )
| ( in @ SY154 @ SV103 ) ) )
= $false )
| ( ( element @ SV84 @ ( powerset @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1218,plain,
! [SV85: $i,SV104: $i] :
( ( ( element @ SV104 @ ( powerset @ SV85 ) )
= $false )
| ( ( element @ ( subset_complement @ SV85 @ SV104 ) @ ( powerset @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1219,plain,
! [SV115: $i,SV86: $i,SV105: $i] :
( ( ( ~ ~ ( ~ ( element @ SV105 @ ( powerset @ SV86 ) )
| ~ ( element @ SV115 @ ( powerset @ SV86 ) ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV86 @ SV105 @ SV115 ) @ ( powerset @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1220,plain,
! [SV116: $i,SV87: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( element @ SV106 @ ( powerset @ SV87 ) )
| ~ ( element @ SV116 @ ( powerset @ SV87 ) ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV87 @ SV106 @ SV116 ) @ ( powerset @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1221,plain,
! [SV88: $i,SV107: $i] :
( ( ( element @ SV107 @ ( powerset @ SV88 ) )
= $false )
| ( ( ( subset_complement @ SV88 @ ( subset_complement @ SV88 @ SV107 ) )
= SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1222,plain,
! [SV89: $i,SV108: $i] :
( ( ( element @ SV108 @ ( powerset @ ( powerset @ SV89 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV89 @ ( complements_of_subsets @ SV89 @ SV108 ) )
= SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1223,plain,
! [SV117: $i,SV90: $i,SV109: $i] :
( ( ( ~ ~ ( ~ ( element @ SV109 @ ( powerset @ SV90 ) )
| ~ ( element @ SV117 @ ( powerset @ SV90 ) ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV90 @ SV109 @ SV117 ) @ ( powerset @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1224,plain,
! [SV66: $i] :
( ( ~ ( element @ ( sK8_SY113 @ SV66 ) @ ( powerset @ SV66 ) )
| ~ ( empty @ ( sK8_SY113 @ SV66 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1225,plain,
! [SV67: $i,SV91: $i] :
( ( ( ~ ( ~ ( proper_element @ SV91 @ SV67 )
| ( SV91
!= ( union @ SV67 ) ) )
| ~ ( ~ ( ( SV91
!= ( union @ SV67 ) ) )
| ( proper_element @ SV91 @ SV67 ) ) )
= $false )
| ( ( element @ SV91 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1226,plain,
! [SV110: $i,SV68: $i,SV92: $i] :
( ( ( ~ ( ~ ( element @ SV92 @ ( powerset @ SV68 ) )
| ~ ( element @ SV110 @ ( powerset @ SV68 ) ) ) )
= $false )
| ( ( ( subset_union2 @ SV68 @ SV92 @ SV92 )
= SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1227,plain,
! [SV111: $i,SV69: $i,SV93: $i] :
( ( ( ~ ( ~ ( element @ SV93 @ ( powerset @ SV69 ) )
| ~ ( element @ SV111 @ ( powerset @ SV69 ) ) ) )
= $false )
| ( ( ( subset_union2 @ SV69 @ SV93 @ SV111 )
= ( subset_union2 @ SV69 @ SV111 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1228,plain,
! [SV70: $i] :
( ( ~ ( element @ ( sK9_SY119 @ SV70 ) @ ( powerset @ SV70 ) )
| ~ ~ ( proper_element @ ( sK9_SY119 @ SV70 ) @ ( powerset @ SV70 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1229,plain,
! [SV71: $i,SV118: $i] :
( ( ( ~ ( element @ SV118 @ ( powerset @ SV71 ) ) )
= $true )
| ( ( v1_membered @ SV118 )
= $true )
| ( ( v1_membered @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1230,plain,
! [SV76: $i,SV98: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV98 )
| ( in @ SV120 @ SV76 ) )
= $true )
| ( ( element @ SV98 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1231,plain,
! [SV112: $i,SV77: $i,SV99: $i] :
( ( ( ~ ( ~ ( element @ SV99 @ ( powerset @ SV77 ) )
| ~ ( element @ SV112 @ ( powerset @ SV77 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV77 @ SV99 @ SV99 )
= SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1232,plain,
! [SV100: $i,SV78: $i] :
( ( ~ ( element @ SV78 @ ( powerset @ SV100 ) )
| ( subset @ SV78 @ SV100 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1233,plain,
! [SV100: $i,SV78: $i] :
( ( ~ ( subset @ SV78 @ SV100 )
| ( element @ SV78 @ ( powerset @ SV100 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1234,plain,
! [SV79: $i] :
( ( ( ! [SY130: $i] :
~ ~ ( ~ ( element @ SY130 @ ( powerset @ SV79 ) )
| ~ ~ ( empty @ SY130 ) ) )
= $false )
| ( ( empty @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1235,plain,
! [SV113: $i,SV101: $i,SV80: $i] :
( ( ( ~ ( ~ ( in @ SV80 @ SV101 )
| ~ ( element @ SV101 @ ( powerset @ SV113 ) ) ) )
= $false )
| ( ( element @ SV80 @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1236,plain,
! [SV114: $i,SV81: $i,SV102: $i] :
( ( ( ~ ( ~ ( element @ SV102 @ ( powerset @ SV81 ) )
| ~ ( element @ SV114 @ ( powerset @ SV81 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV81 @ SV102 @ SV114 )
= ( subset_intersection2 @ SV81 @ SV114 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1237,plain,
! [SV83: $i,SV119: $i] :
( ( ( ~ ( element @ SV119 @ ( powerset @ SV83 ) ) )
= $true )
| ( ( finite @ SV119 )
= $true )
| ( ( finite @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1238,plain,
! [SV84: $i,SV103: $i] :
( ( ( ~ ( in @ ( sK11_SY154 @ SV103 @ SV84 ) @ SV84 )
| ( in @ ( sK11_SY154 @ SV103 @ SV84 ) @ SV103 ) )
= $false )
| ( ( element @ SV84 @ ( powerset @ SV103 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1217]) ).
thf(1239,plain,
! [SV115: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( ~ ( element @ SV105 @ ( powerset @ SV86 ) )
| ~ ( element @ SV115 @ ( powerset @ SV86 ) ) ) )
= $false )
| ( ( element @ ( subset_union2 @ SV86 @ SV105 @ SV115 ) @ ( powerset @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1240,plain,
! [SV116: $i,SV87: $i,SV106: $i] :
( ( ( ~ ( ~ ( element @ SV106 @ ( powerset @ SV87 ) )
| ~ ( element @ SV116 @ ( powerset @ SV87 ) ) ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV87 @ SV106 @ SV116 ) @ ( powerset @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1241,plain,
! [SV117: $i,SV90: $i,SV109: $i] :
( ( ( ~ ( ~ ( element @ SV109 @ ( powerset @ SV90 ) )
| ~ ( element @ SV117 @ ( powerset @ SV90 ) ) ) )
= $false )
| ( ( element @ ( subset_difference @ SV90 @ SV109 @ SV117 ) @ ( powerset @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1242,plain,
! [SV66: $i] :
( ( ~ ( element @ ( sK8_SY113 @ SV66 ) @ ( powerset @ SV66 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1224]) ).
thf(1243,plain,
! [SV66: $i] :
( ( ~ ( empty @ ( sK8_SY113 @ SV66 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1224]) ).
thf(1244,plain,
! [SV67: $i,SV91: $i] :
( ( ( ~ ( ~ ( proper_element @ SV91 @ SV67 )
| ( SV91
!= ( union @ SV67 ) ) ) )
= $false )
| ( ( element @ SV91 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1225]) ).
thf(1245,plain,
! [SV67: $i,SV91: $i] :
( ( ( ~ ( ~ ( ( SV91
!= ( union @ SV67 ) ) )
| ( proper_element @ SV91 @ SV67 ) ) )
= $false )
| ( ( element @ SV91 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1225]) ).
thf(1246,plain,
! [SV110: $i,SV68: $i,SV92: $i] :
( ( ( ~ ( element @ SV92 @ ( powerset @ SV68 ) )
| ~ ( element @ SV110 @ ( powerset @ SV68 ) ) )
= $true )
| ( ( ( subset_union2 @ SV68 @ SV92 @ SV92 )
= SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1247,plain,
! [SV111: $i,SV69: $i,SV93: $i] :
( ( ( ~ ( element @ SV93 @ ( powerset @ SV69 ) )
| ~ ( element @ SV111 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( ( subset_union2 @ SV69 @ SV93 @ SV111 )
= ( subset_union2 @ SV69 @ SV111 @ SV93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1248,plain,
! [SV70: $i] :
( ( ~ ( element @ ( sK9_SY119 @ SV70 ) @ ( powerset @ SV70 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1228]) ).
thf(1249,plain,
! [SV70: $i] :
( ( ~ ~ ( proper_element @ ( sK9_SY119 @ SV70 ) @ ( powerset @ SV70 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1228]) ).
thf(1250,plain,
! [SV71: $i,SV118: $i] :
( ( ( element @ SV118 @ ( powerset @ SV71 ) )
= $false )
| ( ( v1_membered @ SV118 )
= $true )
| ( ( v1_membered @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1251,plain,
! [SV76: $i,SV98: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV98 ) )
= $true )
| ( ( in @ SV120 @ SV76 )
= $true )
| ( ( element @ SV98 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1252,plain,
! [SV112: $i,SV77: $i,SV99: $i] :
( ( ( ~ ( element @ SV99 @ ( powerset @ SV77 ) )
| ~ ( element @ SV112 @ ( powerset @ SV77 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV77 @ SV99 @ SV99 )
= SV99 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1231]) ).
thf(1253,plain,
! [SV100: $i,SV78: $i] :
( ( ( ~ ( element @ SV78 @ ( powerset @ SV100 ) ) )
= $true )
| ( ( subset @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1254,plain,
! [SV100: $i,SV78: $i] :
( ( ( ~ ( subset @ SV78 @ SV100 ) )
= $true )
| ( ( element @ SV78 @ ( powerset @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1255,plain,
! [SV79: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK12_SY130 @ SV79 ) @ ( powerset @ SV79 ) )
| ~ ~ ( empty @ ( sK12_SY130 @ SV79 ) ) ) )
= $false )
| ( ( empty @ SV79 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1234]) ).
thf(1256,plain,
! [SV113: $i,SV101: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV101 )
| ~ ( element @ SV101 @ ( powerset @ SV113 ) ) )
= $true )
| ( ( element @ SV80 @ SV113 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1257,plain,
! [SV114: $i,SV81: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV81 ) )
| ~ ( element @ SV114 @ ( powerset @ SV81 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV81 @ SV102 @ SV114 )
= ( subset_intersection2 @ SV81 @ SV114 @ SV102 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1258,plain,
! [SV83: $i,SV119: $i] :
( ( ( element @ SV119 @ ( powerset @ SV83 ) )
= $false )
| ( ( finite @ SV119 )
= $true )
| ( ( finite @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1259,plain,
! [SV84: $i,SV103: $i] :
( ( ( ~ ( in @ ( sK11_SY154 @ SV103 @ SV84 ) @ SV84 ) )
= $false )
| ( ( element @ SV84 @ ( powerset @ SV103 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1260,plain,
! [SV84: $i,SV103: $i] :
( ( ( in @ ( sK11_SY154 @ SV103 @ SV84 ) @ SV103 )
= $false )
| ( ( element @ SV84 @ ( powerset @ SV103 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1261,plain,
! [SV115: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( element @ SV105 @ ( powerset @ SV86 ) )
| ~ ( element @ SV115 @ ( powerset @ SV86 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV86 @ SV105 @ SV115 ) @ ( powerset @ SV86 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1239]) ).
thf(1262,plain,
! [SV116: $i,SV87: $i,SV106: $i] :
( ( ( ~ ( element @ SV106 @ ( powerset @ SV87 ) )
| ~ ( element @ SV116 @ ( powerset @ SV87 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV87 @ SV106 @ SV116 ) @ ( powerset @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1240]) ).
thf(1263,plain,
! [SV117: $i,SV90: $i,SV109: $i] :
( ( ( ~ ( element @ SV109 @ ( powerset @ SV90 ) )
| ~ ( element @ SV117 @ ( powerset @ SV90 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV90 @ SV109 @ SV117 ) @ ( powerset @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1264,plain,
! [SV66: $i] :
( ( element @ ( sK8_SY113 @ SV66 ) @ ( powerset @ SV66 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1242]) ).
thf(1265,plain,
! [SV66: $i] :
( ( empty @ ( sK8_SY113 @ SV66 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1266,plain,
! [SV67: $i,SV91: $i] :
( ( ( ~ ( proper_element @ SV91 @ SV67 )
| ( SV91
!= ( union @ SV67 ) ) )
= $true )
| ( ( element @ SV91 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1267,plain,
! [SV67: $i,SV91: $i] :
( ( ( ~ ( ( SV91
!= ( union @ SV67 ) ) )
| ( proper_element @ SV91 @ SV67 ) )
= $true )
| ( ( element @ SV91 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1268,plain,
! [SV110: $i,SV68: $i,SV92: $i] :
( ( ( ~ ( element @ SV92 @ ( powerset @ SV68 ) ) )
= $true )
| ( ( ~ ( element @ SV110 @ ( powerset @ SV68 ) ) )
= $true )
| ( ( ( subset_union2 @ SV68 @ SV92 @ SV92 )
= SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1246]) ).
thf(1269,plain,
! [SV111: $i,SV69: $i,SV93: $i] :
( ( ( ~ ( element @ SV93 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( ~ ( element @ SV111 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( ( subset_union2 @ SV69 @ SV93 @ SV111 )
= ( subset_union2 @ SV69 @ SV111 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1270,plain,
! [SV70: $i] :
( ( element @ ( sK9_SY119 @ SV70 ) @ ( powerset @ SV70 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1248]) ).
thf(1271,plain,
! [SV70: $i] :
( ( ~ ( proper_element @ ( sK9_SY119 @ SV70 ) @ ( powerset @ SV70 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1272,plain,
! [SV76: $i,SV98: $i,SV120: $i] :
( ( ( in @ SV120 @ SV98 )
= $false )
| ( ( in @ SV120 @ SV76 )
= $true )
| ( ( element @ SV98 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1273,plain,
! [SV112: $i,SV77: $i,SV99: $i] :
( ( ( ~ ( element @ SV99 @ ( powerset @ SV77 ) ) )
= $true )
| ( ( ~ ( element @ SV112 @ ( powerset @ SV77 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV77 @ SV99 @ SV99 )
= SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1274,plain,
! [SV100: $i,SV78: $i] :
( ( ( element @ SV78 @ ( powerset @ SV100 ) )
= $false )
| ( ( subset @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1275,plain,
! [SV100: $i,SV78: $i] :
( ( ( subset @ SV78 @ SV100 )
= $false )
| ( ( element @ SV78 @ ( powerset @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1276,plain,
! [SV79: $i] :
( ( ( ~ ( ~ ( element @ ( sK12_SY130 @ SV79 ) @ ( powerset @ SV79 ) )
| ~ ~ ( empty @ ( sK12_SY130 @ SV79 ) ) ) )
= $true )
| ( ( empty @ SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1255]) ).
thf(1277,plain,
! [SV113: $i,SV101: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV101 ) )
= $true )
| ( ( ~ ( element @ SV101 @ ( powerset @ SV113 ) ) )
= $true )
| ( ( element @ SV80 @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1278,plain,
! [SV114: $i,SV81: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV81 ) ) )
= $true )
| ( ( ~ ( element @ SV114 @ ( powerset @ SV81 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV81 @ SV102 @ SV114 )
= ( subset_intersection2 @ SV81 @ SV114 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1279,plain,
! [SV84: $i,SV103: $i] :
( ( ( in @ ( sK11_SY154 @ SV103 @ SV84 ) @ SV84 )
= $true )
| ( ( element @ SV84 @ ( powerset @ SV103 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1259]) ).
thf(1280,plain,
! [SV115: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( element @ SV105 @ ( powerset @ SV86 ) ) )
= $true )
| ( ( ~ ( element @ SV115 @ ( powerset @ SV86 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV86 @ SV105 @ SV115 ) @ ( powerset @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1281,plain,
! [SV116: $i,SV87: $i,SV106: $i] :
( ( ( ~ ( element @ SV106 @ ( powerset @ SV87 ) ) )
= $true )
| ( ( ~ ( element @ SV116 @ ( powerset @ SV87 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV87 @ SV106 @ SV116 ) @ ( powerset @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1282,plain,
! [SV117: $i,SV90: $i,SV109: $i] :
( ( ( ~ ( element @ SV109 @ ( powerset @ SV90 ) ) )
= $true )
| ( ( ~ ( element @ SV117 @ ( powerset @ SV90 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV90 @ SV109 @ SV117 ) @ ( powerset @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1283,plain,
! [SV67: $i,SV91: $i] :
( ( ( ~ ( proper_element @ SV91 @ SV67 ) )
= $true )
| ( ( SV91
!= ( union @ SV67 ) )
= $true )
| ( ( element @ SV91 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1284,plain,
! [SV67: $i,SV91: $i] :
( ( ( ~ ( ( SV91
!= ( union @ SV67 ) ) ) )
= $true )
| ( ( proper_element @ SV91 @ SV67 )
= $true )
| ( ( element @ SV91 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1285,plain,
! [SV110: $i,SV68: $i,SV92: $i] :
( ( ( element @ SV92 @ ( powerset @ SV68 ) )
= $false )
| ( ( ~ ( element @ SV110 @ ( powerset @ SV68 ) ) )
= $true )
| ( ( ( subset_union2 @ SV68 @ SV92 @ SV92 )
= SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1286,plain,
! [SV111: $i,SV69: $i,SV93: $i] :
( ( ( element @ SV93 @ ( powerset @ SV69 ) )
= $false )
| ( ( ~ ( element @ SV111 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( ( subset_union2 @ SV69 @ SV93 @ SV111 )
= ( subset_union2 @ SV69 @ SV111 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1287,plain,
! [SV70: $i] :
( ( proper_element @ ( sK9_SY119 @ SV70 ) @ ( powerset @ SV70 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1288,plain,
! [SV112: $i,SV77: $i,SV99: $i] :
( ( ( element @ SV99 @ ( powerset @ SV77 ) )
= $false )
| ( ( ~ ( element @ SV112 @ ( powerset @ SV77 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV77 @ SV99 @ SV99 )
= SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1289,plain,
! [SV79: $i] :
( ( ( ~ ( element @ ( sK12_SY130 @ SV79 ) @ ( powerset @ SV79 ) )
| ~ ~ ( empty @ ( sK12_SY130 @ SV79 ) ) )
= $false )
| ( ( empty @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1290,plain,
! [SV113: $i,SV101: $i,SV80: $i] :
( ( ( in @ SV80 @ SV101 )
= $false )
| ( ( ~ ( element @ SV101 @ ( powerset @ SV113 ) ) )
= $true )
| ( ( element @ SV80 @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1291,plain,
! [SV114: $i,SV81: $i,SV102: $i] :
( ( ( element @ SV102 @ ( powerset @ SV81 ) )
= $false )
| ( ( ~ ( element @ SV114 @ ( powerset @ SV81 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV81 @ SV102 @ SV114 )
= ( subset_intersection2 @ SV81 @ SV114 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1292,plain,
! [SV115: $i,SV86: $i,SV105: $i] :
( ( ( element @ SV105 @ ( powerset @ SV86 ) )
= $false )
| ( ( ~ ( element @ SV115 @ ( powerset @ SV86 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV86 @ SV105 @ SV115 ) @ ( powerset @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1293,plain,
! [SV116: $i,SV87: $i,SV106: $i] :
( ( ( element @ SV106 @ ( powerset @ SV87 ) )
= $false )
| ( ( ~ ( element @ SV116 @ ( powerset @ SV87 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV87 @ SV106 @ SV116 ) @ ( powerset @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1294,plain,
! [SV117: $i,SV90: $i,SV109: $i] :
( ( ( element @ SV109 @ ( powerset @ SV90 ) )
= $false )
| ( ( ~ ( element @ SV117 @ ( powerset @ SV90 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV90 @ SV109 @ SV117 ) @ ( powerset @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1295,plain,
! [SV67: $i,SV91: $i] :
( ( ( proper_element @ SV91 @ SV67 )
= $false )
| ( ( SV91
!= ( union @ SV67 ) )
= $true )
| ( ( element @ SV91 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1296,plain,
! [SV67: $i,SV91: $i] :
( ( ( SV91
!= ( union @ SV67 ) )
= $false )
| ( ( proper_element @ SV91 @ SV67 )
= $true )
| ( ( element @ SV91 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1297,plain,
! [SV92: $i,SV68: $i,SV110: $i] :
( ( ( element @ SV110 @ ( powerset @ SV68 ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ SV68 ) )
= $false )
| ( ( ( subset_union2 @ SV68 @ SV92 @ SV92 )
= SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1298,plain,
! [SV93: $i,SV69: $i,SV111: $i] :
( ( ( element @ SV111 @ ( powerset @ SV69 ) )
= $false )
| ( ( element @ SV93 @ ( powerset @ SV69 ) )
= $false )
| ( ( ( subset_union2 @ SV69 @ SV93 @ SV111 )
= ( subset_union2 @ SV69 @ SV111 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1299,plain,
! [SV99: $i,SV77: $i,SV112: $i] :
( ( ( element @ SV112 @ ( powerset @ SV77 ) )
= $false )
| ( ( element @ SV99 @ ( powerset @ SV77 ) )
= $false )
| ( ( ( subset_intersection2 @ SV77 @ SV99 @ SV99 )
= SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1300,plain,
! [SV79: $i] :
( ( ( ~ ( element @ ( sK12_SY130 @ SV79 ) @ ( powerset @ SV79 ) ) )
= $false )
| ( ( empty @ SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1301,plain,
! [SV79: $i] :
( ( ( ~ ~ ( empty @ ( sK12_SY130 @ SV79 ) ) )
= $false )
| ( ( empty @ SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1302,plain,
! [SV80: $i,SV113: $i,SV101: $i] :
( ( ( element @ SV101 @ ( powerset @ SV113 ) )
= $false )
| ( ( in @ SV80 @ SV101 )
= $false )
| ( ( element @ SV80 @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1303,plain,
! [SV102: $i,SV81: $i,SV114: $i] :
( ( ( element @ SV114 @ ( powerset @ SV81 ) )
= $false )
| ( ( element @ SV102 @ ( powerset @ SV81 ) )
= $false )
| ( ( ( subset_intersection2 @ SV81 @ SV102 @ SV114 )
= ( subset_intersection2 @ SV81 @ SV114 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1304,plain,
! [SV105: $i,SV86: $i,SV115: $i] :
( ( ( element @ SV115 @ ( powerset @ SV86 ) )
= $false )
| ( ( element @ SV105 @ ( powerset @ SV86 ) )
= $false )
| ( ( element @ ( subset_union2 @ SV86 @ SV105 @ SV115 ) @ ( powerset @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1305,plain,
! [SV106: $i,SV87: $i,SV116: $i] :
( ( ( element @ SV116 @ ( powerset @ SV87 ) )
= $false )
| ( ( element @ SV106 @ ( powerset @ SV87 ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV87 @ SV106 @ SV116 ) @ ( powerset @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1306,plain,
! [SV109: $i,SV90: $i,SV117: $i] :
( ( ( element @ SV117 @ ( powerset @ SV90 ) )
= $false )
| ( ( element @ SV109 @ ( powerset @ SV90 ) )
= $false )
| ( ( element @ ( subset_difference @ SV90 @ SV109 @ SV117 ) @ ( powerset @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1307,plain,
! [SV67: $i,SV91: $i] :
( ( ( SV91
= ( union @ SV67 ) )
= $false )
| ( ( proper_element @ SV91 @ SV67 )
= $false )
| ( ( element @ SV91 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1308,plain,
! [SV67: $i,SV91: $i] :
( ( ( SV91
= ( union @ SV67 ) )
= $true )
| ( ( proper_element @ SV91 @ SV67 )
= $true )
| ( ( element @ SV91 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1296]) ).
thf(1309,plain,
! [SV79: $i] :
( ( ( element @ ( sK12_SY130 @ SV79 ) @ ( powerset @ SV79 ) )
= $true )
| ( ( empty @ SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1310,plain,
! [SV79: $i] :
( ( ( ~ ( empty @ ( sK12_SY130 @ SV79 ) ) )
= $true )
| ( ( empty @ SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1301]) ).
thf(1311,plain,
! [SV79: $i] :
( ( ( empty @ ( sK12_SY130 @ SV79 ) )
= $false )
| ( ( empty @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1312,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1034,1311,1309,1308,1307,1306,1305,1304,1303,1302,1299,1298,1297,1287,1279,1275,1274,1272,1270,1265,1264,1260,1258,1250,1222,1221,1218,1215,1211,1206,1205,1204,1203,1158,1143,1116,1114,1113,1112,1084,1070,1069,1068,1067,1066,1060,1059,1058,1056,1055,1053,1052,1051,1050,1048,1047,1046,1045,1044,1043,1042,1041,1039,1038,1037,1036,1035]) ).
thf(1313,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1312,1025]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU354+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:14:51 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.65/1.34 ......
% 6.65/1.34
% 6.65/1.34 No.of.Axioms: 58
% 6.65/1.34
% 6.65/1.34 Length.of.Defs: 0
% 6.65/1.34
% 6.65/1.34 Contains.Choice.Funs: false
% 6.65/1.34 ........................
% 6.65/1.34
% 6.65/1.34 ********************************
% 6.65/1.34 * All subproblems solved! *
% 6.65/1.34 ********************************
% 6.65/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:59,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:1312,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.65/1.34
% 6.65/1.34 %**** Beginning of derivation protocol ****
% 6.65/1.34 % SZS output start CNFRefutation
% See solution above
% 6.65/1.35
% 6.65/1.35 %**** End of derivation protocol ****
% 6.65/1.35 %**** no. of clauses in derivation: 702 ****
% 6.65/1.35 %**** clause counter: 1312 ****
% 6.65/1.35
% 6.65/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:59,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:1312,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------