%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU355+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 212.41s 35.65s
% Output : CNFRefutation 212.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 137
% Syntax : Number of formulae : 1589 ( 712 unt; 0 typ; 0 def)
% Number of atoms : 11525 (4036 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 20871 (4281 ~;3435 |; 202 &;12528 @)
% ( 69 <=>; 356 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 191 ( 188 usr; 8 con; 0-6 aty)
% Number of variables : 3446 ( 0 ^;3422 !; 24 ?;3446 :)
% 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_SY260,type,
sK10_SY260: $i > $i ).
thf(tp_sK11_SY305,type,
sK11_SY305: $i > $i ).
thf(tp_sK12_SY314,type,
sK12_SY314: $i > $i ).
thf(tp_sK13_SY384,type,
sK13_SY384: $i > $i ).
thf(tp_sK14_SY283,type,
sK14_SY283: $i > $i ).
thf(tp_sK15_SY380,type,
sK15_SY380: $i > $i > $i > $i ).
thf(tp_sK16_SY383,type,
sK16_SY383: $i > $i > $i > $i ).
thf(tp_sK17_SY344,type,
sK17_SY344: $i > $i > $i ).
thf(tp_sK18_SY391,type,
sK18_SY391: $i > $i > $i ).
thf(tp_sK19_SY390,type,
sK19_SY390: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY252,type,
sK5_SY252: $i > $i ).
thf(tp_sK6_SY276,type,
sK6_SY276: $i > $i ).
thf(tp_sK7_SY329,type,
sK7_SY329: $i > $i ).
thf(tp_sK8_SY348,type,
sK8_SY348: $i > $i > $i ).
thf(tp_sK9_SY256,type,
sK9_SY256: $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(5,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(8,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(10,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(13,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(15,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( related_reflexive @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_orders_2) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( element @ C @ A )
& ( element @ D @ B ) )
=> ( ( ordered_pair_as_product_element @ A @ B @ C @ D )
= ( ordered_pair @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(66,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(73,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(76,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tex_2) ).
thf(77,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(87,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(92,axiom,
? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_orders_2) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(124,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(166,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(168,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(180,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(187,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(194,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(197,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(198,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( element @ ( the_topology @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
thf(199,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(202,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(203,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(207,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(209,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(211,axiom,
$true,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(228,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(229,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ( element @ ( bottom_of_semilattstr @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(231,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(232,axiom,
$true,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(238,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(239,axiom,
$true,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(241,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(244,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(245,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(247,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(248,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(249,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(250,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(251,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(256,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(257,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(259,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(261,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(262,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(263,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(264,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pre_topc) ).
thf(265,axiom,
! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).
thf(266,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(267,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(270,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(271,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( element @ C @ A )
& ( element @ D @ B ) )
=> ( element @ ( ordered_pair_as_product_element @ A @ B @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(273,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( meet_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_lattice3) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( join_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_lattice3) ).
thf(276,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(282,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice3) ).
thf(290,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice3) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(301,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( antisymmetric_relstr @ A )
<=> ( is_antisymmetric_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_orders_2) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(308,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( transitive_relstr @ A )
<=> ( is_transitive_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_orders_2) ).
thf(324,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(333,axiom,
! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(337,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier_subset @ A )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_pre_topc) ).
thf(346,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(352,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier @ A )
<=> ( empty @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( quasi_total @ C @ A @ B )
<=> ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( ( quasi_total @ C @ A @ B )
<=> ( C = empty_set ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
thf(382,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_grcat_1) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(420,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_arytm_3) ).
thf(423,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(424,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(429,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).
thf(430,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).
thf(434,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(464,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(465,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(469,axiom,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
thf(476,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(485,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(510,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(514,axiom,
! [A: $i] :
( ( lower_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( ( bottom_of_semilattstr @ ( boole_lattice @ A ) )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_lattice3) ).
thf(515,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(538,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(540,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( below @ ( boole_lattice @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lattice3) ).
thf(548,axiom,
! [A: $i] :
( ( ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ D ) )
=> ( related @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_orders_2) ).
thf(554,axiom,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ B ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_orders_2) ).
thf(573,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(611,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_tops_2) ).
thf(652,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
thf(655,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(660,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
thf(661,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(669,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(671,conjecture,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ empty_set @ B )
& ( relstr_element_smaller @ A @ empty_set @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).
thf(672,negated_conjecture,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ empty_set @ B )
& ( relstr_element_smaller @ A @ empty_set @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[671]) ).
thf(673,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ empty_set @ B )
& ( relstr_element_smaller @ A @ empty_set @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[672]) ).
thf(674,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(675,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(676,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(677,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(678,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(679,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(680,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(681,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(682,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(683,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(684,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( related_reflexive @ A @ B @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(685,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(686,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(687,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(688,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(689,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(690,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( element @ C @ A )
& ( element @ D @ B ) )
=> ( ( ordered_pair_as_product_element @ A @ B @ C @ D )
= ( ordered_pair @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(691,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(692,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(693,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(694,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(695,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(696,plain,
( ( ? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(697,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(698,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(699,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(700,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(701,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(702,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(703,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(704,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(705,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(706,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(707,plain,
$true = $true,
inference(unfold_def,[status(thm)],[197]) ).
thf(708,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( element @ ( the_topology @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(709,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(710,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(711,plain,
$true = $true,
inference(unfold_def,[status(thm)],[202]) ).
thf(712,plain,
$true = $true,
inference(unfold_def,[status(thm)],[203]) ).
thf(713,plain,
$true = $true,
inference(unfold_def,[status(thm)],[207]) ).
thf(714,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(715,plain,
$true = $true,
inference(unfold_def,[status(thm)],[211]) ).
thf(716,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(717,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(718,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(719,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(720,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(721,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(722,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(723,plain,
$true = $true,
inference(unfold_def,[status(thm)],[228]) ).
thf(724,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ( element @ ( bottom_of_semilattstr @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(725,plain,
$true = $true,
inference(unfold_def,[status(thm)],[231]) ).
thf(726,plain,
$true = $true,
inference(unfold_def,[status(thm)],[232]) ).
thf(727,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(728,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(729,plain,
$true = $true,
inference(unfold_def,[status(thm)],[238]) ).
thf(730,plain,
$true = $true,
inference(unfold_def,[status(thm)],[239]) ).
thf(731,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(732,plain,
$true = $true,
inference(unfold_def,[status(thm)],[241]) ).
thf(733,plain,
$true = $true,
inference(unfold_def,[status(thm)],[244]) ).
thf(734,plain,
$true = $true,
inference(unfold_def,[status(thm)],[245]) ).
thf(735,plain,
$true = $true,
inference(unfold_def,[status(thm)],[247]) ).
thf(736,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(737,plain,
$true = $true,
inference(unfold_def,[status(thm)],[249]) ).
thf(738,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(739,plain,
$true = $true,
inference(unfold_def,[status(thm)],[251]) ).
thf(740,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(741,plain,
$true = $true,
inference(unfold_def,[status(thm)],[256]) ).
thf(742,plain,
$true = $true,
inference(unfold_def,[status(thm)],[257]) ).
thf(743,plain,
$true = $true,
inference(unfold_def,[status(thm)],[259]) ).
thf(744,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(745,plain,
$true = $true,
inference(unfold_def,[status(thm)],[261]) ).
thf(746,plain,
$true = $true,
inference(unfold_def,[status(thm)],[262]) ).
thf(747,plain,
$true = $true,
inference(unfold_def,[status(thm)],[263]) ).
thf(748,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(749,plain,
( ( ! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(750,plain,
$true = $true,
inference(unfold_def,[status(thm)],[266]) ).
thf(751,plain,
$true = $true,
inference(unfold_def,[status(thm)],[267]) ).
thf(752,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(753,plain,
$true = $true,
inference(unfold_def,[status(thm)],[270]) ).
thf(754,plain,
$true = $true,
inference(unfold_def,[status(thm)],[271]) ).
thf(755,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( element @ C @ A )
& ( element @ D @ B ) )
=> ( element @ ( ordered_pair_as_product_element @ A @ B @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(756,plain,
$true = $true,
inference(unfold_def,[status(thm)],[273]) ).
thf(757,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( meet_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(758,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( join_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(759,plain,
$true = $true,
inference(unfold_def,[status(thm)],[276]) ).
thf(760,plain,
( ( ! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(761,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(762,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ C @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(763,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(764,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( antisymmetric_relstr @ A )
<=> ( is_antisymmetric_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(765,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(766,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( transitive_relstr @ A )
<=> ( is_transitive_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(767,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(768,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(769,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(770,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier_subset @ A )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(771,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(772,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier @ A )
<=> ( empty @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(773,plain,
( ( ! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(774,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( quasi_total @ C @ A @ B )
<=> ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( ( quasi_total @ C @ A @ B )
<=> ( C = empty_set ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(775,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(776,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(777,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(778,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(779,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(780,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(781,plain,
( ( ! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(782,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(783,plain,
( ( ! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(784,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(785,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(786,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(787,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(788,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(789,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(790,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(791,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(792,plain,
( ( ! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(793,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(794,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(795,plain,
( ( ! [A: $i] :
( ( lower_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( ( bottom_of_semilattstr @ ( boole_lattice @ A ) )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(796,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(797,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(798,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(799,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( below @ ( boole_lattice @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(800,plain,
( ( ! [A: $i] :
( ( ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ D ) )
=> ( related @ A @ B @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(801,plain,
( ( ! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ B ) )
=> ( B = C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(802,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(803,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(804,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(805,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(806,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(807,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(808,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(809,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(810,plain,
( ( ( rel_str @ sK1_A )
=> ! [SY217: $i] :
( ( element @ SY217 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ empty_set @ SY217 )
& ( relstr_element_smaller @ sK1_A @ empty_set @ SY217 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[673]) ).
thf(811,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[810]) ).
thf(812,plain,
( ( ! [SY217: $i] :
( ( element @ SY217 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ empty_set @ SY217 )
& ( relstr_element_smaller @ sK1_A @ empty_set @ SY217 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[810]) ).
thf(813,plain,
( ( ~ ! [SY217: $i] :
( ( element @ SY217 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ empty_set @ SY217 )
& ( relstr_element_smaller @ sK1_A @ empty_set @ SY217 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[812]) ).
thf(814,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(815,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(816,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(817,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(818,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(819,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(820,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(821,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(822,plain,
( ( ! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ B ) )
=> ( B = C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(823,plain,
( ( ! [A: $i] :
( ( ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ D ) )
=> ( related @ A @ B @ D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(824,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ ( boole_lattice @ A ) ) )
=> ( ( below @ ( boole_lattice @ A ) @ B @ C )
<=> ( subset @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(825,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(826,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(827,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(828,plain,
( ( ! [A: $i] :
( ( lower_bounded_semilattstr @ ( boole_lattice @ A ) )
& ( ( bottom_of_semilattstr @ ( boole_lattice @ A ) )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(829,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(830,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(831,plain,
( ( ! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(832,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(833,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(834,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(835,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(836,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(837,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(838,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(839,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(840,plain,
( ( ! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(841,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(842,plain,
( ( ! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(843,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(844,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(845,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(846,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)],[777]) ).
thf(847,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)],[776]) ).
thf(848,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(849,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( quasi_total @ C @ A @ B )
<=> ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( ( quasi_total @ C @ A @ B )
<=> ( C = empty_set ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(850,plain,
( ( ! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(851,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier @ A )
<=> ( empty @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(852,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(853,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( empty_carrier_subset @ A )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(854,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(855,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(856,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(857,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( transitive_relstr @ A )
<=> ( is_transitive_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(858,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(859,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( antisymmetric_relstr @ A )
<=> ( is_antisymmetric_in @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(860,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(861,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ C @ D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(862,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(863,plain,
( ( ! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(864,plain,
$true = $true,
inference(copy,[status(thm)],[759]) ).
thf(865,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( join_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(866,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( meet_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(867,plain,
$true = $true,
inference(copy,[status(thm)],[756]) ).
thf(868,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( element @ C @ A )
& ( element @ D @ B ) )
=> ( element @ ( ordered_pair_as_product_element @ A @ B @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(869,plain,
$true = $true,
inference(copy,[status(thm)],[754]) ).
thf(870,plain,
$true = $true,
inference(copy,[status(thm)],[753]) ).
thf(871,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(872,plain,
$true = $true,
inference(copy,[status(thm)],[751]) ).
thf(873,plain,
$true = $true,
inference(copy,[status(thm)],[750]) ).
thf(874,plain,
( ( ! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(875,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( empty_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(876,plain,
$true = $true,
inference(copy,[status(thm)],[747]) ).
thf(877,plain,
$true = $true,
inference(copy,[status(thm)],[746]) ).
thf(878,plain,
$true = $true,
inference(copy,[status(thm)],[745]) ).
thf(879,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( interior @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(880,plain,
$true = $true,
inference(copy,[status(thm)],[743]) ).
thf(881,plain,
$true = $true,
inference(copy,[status(thm)],[742]) ).
thf(882,plain,
$true = $true,
inference(copy,[status(thm)],[741]) ).
thf(883,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(884,plain,
$true = $true,
inference(copy,[status(thm)],[739]) ).
thf(885,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(886,plain,
$true = $true,
inference(copy,[status(thm)],[737]) ).
thf(887,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(888,plain,
$true = $true,
inference(copy,[status(thm)],[735]) ).
thf(889,plain,
$true = $true,
inference(copy,[status(thm)],[734]) ).
thf(890,plain,
$true = $true,
inference(copy,[status(thm)],[733]) ).
thf(891,plain,
$true = $true,
inference(copy,[status(thm)],[732]) ).
thf(892,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(893,plain,
$true = $true,
inference(copy,[status(thm)],[730]) ).
thf(894,plain,
$true = $true,
inference(copy,[status(thm)],[729]) ).
thf(895,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(896,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)],[727]) ).
thf(897,plain,
$true = $true,
inference(copy,[status(thm)],[726]) ).
thf(898,plain,
$true = $true,
inference(copy,[status(thm)],[725]) ).
thf(899,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A ) )
=> ( element @ ( bottom_of_semilattstr @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(900,plain,
$true = $true,
inference(copy,[status(thm)],[723]) ).
thf(901,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(902,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(903,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)],[720]) ).
thf(904,plain,
( ( ! [A: $i,B: $i] :
( ( ( top_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( element @ ( topstr_closure @ A @ B ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(905,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(906,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)],[717]) ).
thf(907,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(908,plain,
$true = $true,
inference(copy,[status(thm)],[715]) ).
thf(909,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(910,plain,
$true = $true,
inference(copy,[status(thm)],[713]) ).
thf(911,plain,
$true = $true,
inference(copy,[status(thm)],[712]) ).
thf(912,plain,
$true = $true,
inference(copy,[status(thm)],[711]) ).
thf(913,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(914,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(915,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( element @ ( the_topology @ A ) @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(916,plain,
$true = $true,
inference(copy,[status(thm)],[707]) ).
thf(917,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(copy,[status(thm)],[706]) ).
thf(918,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(919,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[704]) ).
thf(920,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(921,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(922,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(923,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)],[700]) ).
thf(924,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)],[699]) ).
thf(925,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(926,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)],[697]) ).
thf(927,plain,
( ( ? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(928,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(929,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(930,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(931,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(932,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(933,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ( element @ C @ A )
& ( element @ D @ B ) )
=> ( ( ordered_pair_as_product_element @ A @ B @ C @ D )
= ( ordered_pair @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(934,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(935,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(936,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(937,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(938,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(939,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( related_reflexive @ A @ B @ B ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(940,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(941,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(942,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(943,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(944,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(945,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(946,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(947,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(948,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(949,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(950,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(951,plain,
( ( ~ ! [SY217: $i] :
( ( element @ SY217 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ empty_set @ SY217 )
& ( relstr_element_smaller @ sK1_A @ empty_set @ SY217 ) ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(952,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_intersection2 @ SX0 @ SX1 @ SX2 )
= ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[936]) ).
thf(953,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( rel_str @ SX0 )
| ~ ( strict_rel_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[927]) ).
thf(954,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( element @ ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[895]) ).
thf(955,plain,
( ( ! [SX0: $i] :
( ~ ( top_str @ SX0 )
| ( element @ ( the_topology @ SX0 ) @ ( powerset @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[915]) ).
thf(956,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( related @ SX0 @ SX1 @ SX2 )
| ~ ( related @ SX0 @ SX2 @ SX1 ) )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[822]) ).
thf(957,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( top_str @ SX0 )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ( element @ ( topstr_closure @ SX0 @ SX1 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[904]) ).
thf(958,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ( ( relation_dom @ SX0 )
= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[836]) ).
thf(959,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)],[847]) ).
thf(960,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ SX1 )
= ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[858]) ).
thf(961,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( identity_on_carrier @ SX0 )
= ( identity_as_relation_of @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[848]) ).
thf(962,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( ~ ( relstr_set_smaller @ sK1_A @ empty_set @ SX0 )
| ~ ( relstr_element_smaller @ sK1_A @ empty_set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[951]) ).
thf(963,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( ( subset_complement @ SX0 @ ( subset_complement @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[925]) ).
thf(964,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ~ ~ ( ~ ( ( SX1 != empty_set ) )
| ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) )
| ( SX1 != empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[819]) ).
thf(965,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)],[924]) ).
thf(966,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[815]) ).
thf(967,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( union_of_subsets @ SX0 @ SX1 )
= ( union @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[935]) ).
thf(968,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ( SX0 != empty_set ) )
| ~ ( ~ ( ( SX1
!= ( set_meet @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
| ~ ( ( SX0 != empty_set )
| ~ ( ~ ( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) )
| ~ ( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[850]) ).
thf(969,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( element @ ( empty_carrier_subset @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[875]) ).
thf(970,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( ~ ( ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( related @ SX0 @ SX2 @ SX3 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( related @ SX0 @ SX2 @ SX3 ) )
| ( relstr_element_smaller @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[861]) ).
thf(971,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[947]) ).
thf(972,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[860]) ).
thf(973,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != empty_set ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( subset_complement @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[831]) ).
thf(974,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[818]) ).
thf(975,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[929]) ).
thf(976,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( top_str @ SX0 )
| ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) ) )
| ( element @ ( interior @ SX0 @ SX1 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[879]) ).
thf(977,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( meet_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[905]) ).
thf(978,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[949]) ).
thf(979,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( latt_str @ SX0 ) )
| ( element @ ( join_of_latt_set @ SX0 @ SX1 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[865]) ).
thf(980,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[931]) ).
thf(981,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[941]) ).
thf(982,plain,
( ( ~ ! [SX0: $i] :
~ ( rel_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[917]) ).
thf(983,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1 != empty_set ) )
| ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[830]) ).
thf(984,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( latt_str @ SX0 ) )
| ( element @ ( meet_of_latt_set @ SX0 @ SX1 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[866]) ).
thf(985,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ! [SX1: $i,SX2: $i] :
~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[833]) ).
thf(986,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( meet_of_subsets @ SX0 @ SX1 )
= ( set_meet @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[937]) ).
thf(987,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( reflexive_relstr @ SX0 ) )
| ~ ( rel_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( related_reflexive @ SX0 @ SX1 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[939]) ).
thf(988,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ~ ( empty @ SX1 ) )
| ~ ( element @ SX2 @ SX0 ) )
| ~ ( element @ SX3 @ SX1 ) )
| ( element @ ( ordered_pair_as_product_element @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( cartesian_product2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[868]) ).
thf(989,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( empty_carrier_subset @ SX0 )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[853]) ).
thf(990,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( element @ ( cast_as_carrier_subset @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[885]) ).
thf(991,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[841]) ).
thf(992,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)],[906]) ).
thf(993,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[845]) ).
thf(994,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[816]) ).
thf(995,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[837]) ).
thf(996,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( join_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( element @ ( join @ SX0 @ SX1 @ SX2 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[871]) ).
thf(997,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[918]) ).
thf(998,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[909]) ).
thf(999,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( empty @ SX0 )
| ~ ( ~ ( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) )
| ~ ( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[854]) ).
thf(1000,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( cast_as_carrier_subset @ SX0 )
= ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[820]) ).
thf(1001,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_union2 @ SX0 @ SX1 @ SX2 )
= ( set_union2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[934]) ).
thf(1002,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ( ( cast_as_carrier_subset @ SX0 )
= ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[856]) ).
thf(1003,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( element @ SX2 @ ( powerset @ SX0 ) ) )
| ( ( subset_difference @ SX0 @ SX1 @ SX2 )
= ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[938]) ).
thf(1004,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[852]) ).
thf(1005,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( v1_xcmplx_0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[839]) ).
thf(1006,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ( relation @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[844]) ).
thf(1007,plain,
( ( ! [SX0: $i] :
~ ( ~ ( lower_bounded_semilattstr @ ( boole_lattice @ SX0 ) )
| ( ( bottom_of_semilattstr @ ( boole_lattice @ SX0 ) )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[828]) ).
thf(1008,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ~ ( ~ ( ~ ( ( SX1 != empty_set )
| ( SX0 = empty_set ) )
| ~ ( ~ ( ~ ( quasi_total @ SX2 @ SX0 @ SX1 )
| ( SX0
= ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) ) )
| ~ ( ( SX0
!= ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) )
| ( quasi_total @ SX2 @ SX0 @ SX1 ) ) ) )
| ~ ( ( SX1 != empty_set )
| ( SX0 = empty_set )
| ~ ( ~ ( ~ ( quasi_total @ SX2 @ SX0 @ SX1 )
| ( SX2 = empty_set ) )
| ~ ( ( SX2 != empty_set )
| ( quasi_total @ SX2 @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[849]) ).
thf(1009,plain,
( ( ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ~ ( ~ ( v1_xcmplx_0 @ SX1 )
| ~ ( v1_xreal_0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[840]) ).
thf(1010,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[919]) ).
thf(1011,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[914]) ).
thf(1012,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[817]) ).
thf(1013,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ~ ( ~ ( in @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[832]) ).
thf(1014,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)],[903]) ).
thf(1015,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)],[855]) ).
thf(1016,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( strict_rel_str @ SX0 )
| ( SX0
= ( rel_str_of @ ( the_carrier @ SX0 ) @ ( the_InternalRel @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[838]) ).
thf(1017,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX1 )
| ~ ( epsilon_connected @ SX1 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[843]) ).
thf(1018,plain,
( ( ! [SX0: $i] :
( ( singleton @ SX0 )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[814]) ).
thf(1019,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( related @ SX0 @ SX3 @ SX2 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( related @ SX0 @ SX3 @ SX2 ) )
| ( relstr_set_smaller @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[862]) ).
thf(1020,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( ~ ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) )
| ~ ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[863]) ).
thf(1021,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( transitive_relstr @ SX0 )
| ~ ( rel_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( related @ SX0 @ SX1 @ SX2 )
| ~ ( related @ SX0 @ SX2 @ SX3 ) )
| ( related @ SX0 @ SX1 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[823]) ).
thf(1022,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[928]) ).
thf(1023,plain,
( ( ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ~ ( v1_membered @ SX1 )
| ~ ( v2_membered @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[842]) ).
thf(1024,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)],[896]) ).
thf(1025,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ( ~ ( empty_carrier @ SX0 )
| ( empty @ ( the_carrier @ SX0 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SX0 ) )
| ( empty_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[851]) ).
thf(1026,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ( ~ ( antisymmetric_relstr @ SX0 )
| ( is_antisymmetric_in @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) )
| ( antisymmetric_relstr @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[859]) ).
thf(1027,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)],[907]) ).
thf(1028,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)],[945]) ).
thf(1029,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[827]) ).
thf(1030,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ ( boole_lattice @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ ( boole_lattice @ SX0 ) ) )
| ~ ( ~ ( ~ ( below @ ( boole_lattice @ SX0 ) @ SX1 @ SX2 )
| ( subset @ SX1 @ SX2 ) )
| ~ ( ~ ( subset @ SX1 @ SX2 )
| ( below @ ( boole_lattice @ SX0 ) @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[824]) ).
thf(1031,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[932]) ).
thf(1032,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( meet_semilatt_str @ SX0 ) )
| ( element @ ( bottom_of_semilattstr @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[899]) ).
thf(1033,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( union_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[902]) ).
thf(1034,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[922]) ).
thf(1035,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[835]) ).
thf(1036,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ( ~ ( transitive_relstr @ SX0 )
| ( is_transitive_in @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) ) )
| ~ ( ~ ( is_transitive_in @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) )
| ( transitive_relstr @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[857]) ).
thf(1037,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 ) )
| ~ ( empty @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[920]) ).
thf(1038,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SX0 )
| ~ ( meet_semilatt_str @ SX0 ) )
| ~ ( element @ SX1 @ ( the_carrier @ SX0 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) ) )
| ( element @ ( meet @ SX0 @ SX1 @ SX2 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[883]) ).
thf(1039,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[826]) ).
thf(1040,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[948]) ).
thf(1041,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)],[846]) ).
thf(1042,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ~ ( empty @ SX1 ) )
| ~ ( element @ SX2 @ SX0 ) )
| ~ ( element @ SX3 @ SX1 ) )
| ( ( ordered_pair_as_product_element @ SX0 @ SX1 @ SX2 @ SX3 )
= ( ordered_pair @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[933]) ).
thf(1043,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[943]) ).
thf(1044,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( element @ ( subset_complement @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[892]) ).
thf(1045,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[829]) ).
thf(1046,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)],[926]) ).
thf(1047,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[930]) ).
thf(1048,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)],[923]) ).
thf(1049,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( element @ ( relation_rng_as_subset @ SX0 @ SX1 @ SX2 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[901]) ).
thf(1050,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ~ ( ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) )
| ( SX1 != SX0 ) )
| ~ ( ~ ( ( SX1 != SX0 ) )
| ( proper_element @ SX1 @ ( powerset @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[834]) ).
thf(1051,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( element @ SX2 @ ( powerset @ ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[913]) ).
thf(1052,plain,
! [SV1: $i] :
( ( subset @ empty_set @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1053,plain,
! [SV2: $i] :
( ( element @ ( k1_pcomps_1 @ SV2 ) @ ( powerset @ ( powerset @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1054,plain,
! [SV3: $i] :
( ( element @ ( cast_to_subset @ SV3 ) @ ( powerset @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1055,plain,
! [SV4: $i] :
( ( ( set_union2 @ SV4 @ empty_set )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1056,plain,
! [SV5: $i] :
( ( ( set_intersection2 @ SV5 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1057,plain,
! [SV6: $i] :
( ( ( set_difference @ SV6 @ empty_set )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1058,plain,
! [SV7: $i] :
( ( ( set_difference @ empty_set @ SV7 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1059,plain,
! [SV8: $i] :
( ( ! [SY218: $i,SY219: $i] :
( ~ ~ ( ~ ( element @ SY218 @ ( powerset @ SV8 ) )
| ~ ( element @ SY219 @ ( powerset @ SV8 ) ) )
| ( ( subset_intersection2 @ SV8 @ SY218 @ SY219 )
= ( set_intersection2 @ SY218 @ SY219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1060,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( rel_str @ SX0 )
| ~ ( strict_rel_str @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1061,plain,
! [SV9: $i] :
( ( ! [SY220: $i,SY221: $i] :
( ~ ( relation_of2 @ SY221 @ SV9 @ SY220 )
| ( element @ ( relation_dom_as_subset @ SV9 @ SY220 @ SY221 ) @ ( powerset @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1062,plain,
! [SV10: $i] :
( ( ~ ( top_str @ SV10 )
| ( element @ ( the_topology @ SV10 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1063,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( antisymmetric_relstr @ SV11 )
| ~ ( rel_str @ SV11 ) )
| ! [SY222: $i] :
( ~ ( element @ SY222 @ ( the_carrier @ SV11 ) )
| ! [SY223: $i] :
( ~ ( element @ SY223 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY222 @ SY223 )
| ~ ( related @ SV11 @ SY223 @ SY222 ) )
| ( SY222 = SY223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1064,plain,
! [SV12: $i] :
( ( ! [SY224: $i] :
( ~ ~ ( ~ ( top_str @ SV12 )
| ~ ( element @ SY224 @ ( powerset @ ( the_carrier @ SV12 ) ) ) )
| ( element @ ( topstr_closure @ SV12 @ SY224 ) @ ( powerset @ ( the_carrier @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1065,plain,
! [SV13: $i] :
( ( ~ ( relation @ SV13 )
| ~ ( ( ( relation_dom @ SV13 )
= empty_set )
| ( ( relation_rng @ SV13 )
= empty_set ) )
| ( SV13 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1066,plain,
! [SV14: $i] :
( ( ! [SY225: $i,SY226: $i] :
( ~ ~ ( ~ ( element @ SY225 @ ( powerset @ SV14 ) )
| ~ ( element @ SY226 @ ( powerset @ SV14 ) ) )
| ( ( subset_intersection2 @ SV14 @ SY225 @ SY226 )
= ( subset_intersection2 @ SV14 @ SY226 @ SY225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1067,plain,
! [SV15: $i] :
( ( ! [SY227: $i] :
( ~ ( element @ SY227 @ ( powerset @ SV15 ) )
| ( ( subset_complement @ SV15 @ SY227 )
= ( set_difference @ SV15 @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1068,plain,
! [SV16: $i] :
( ( ~ ( one_sorted_str @ SV16 )
| ( ( identity_on_carrier @ SV16 )
= ( identity_as_relation_of @ ( the_carrier @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1069,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( ~ ( relstr_set_smaller @ sK1_A @ empty_set @ SX0 )
| ~ ( relstr_element_smaller @ sK1_A @ empty_set @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1070,plain,
! [SV17: $i] :
( ( ! [SY228: $i] :
( ~ ( element @ SY228 @ ( powerset @ SV17 ) )
| ( ( subset_complement @ SV17 @ ( subset_complement @ SV17 @ SY228 ) )
= SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1071,plain,
! [SV18: $i] :
( ( ! [SY229: $i] :
( ~ ( element @ SY229 @ ( powerset @ ( powerset @ SV18 ) ) )
| ~ ( ~ ~ ~ ( ~ ( ( SY229 != empty_set ) )
| ( ( complements_of_subsets @ SV18 @ SY229 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV18 @ SY229 )
!= empty_set ) )
| ( SY229 != empty_set ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1072,plain,
! [SV19: $i] :
( ( ! [SY230: $i,SY231: $i] :
( ~ ~ ( ~ ( element @ SY230 @ ( powerset @ SV19 ) )
| ~ ( element @ SY231 @ ( powerset @ SV19 ) ) )
| ( ( subset_intersection2 @ SV19 @ SY230 @ SY230 )
= SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1073,plain,
! [SV20: $i] :
( ( ! [SY232: $i] :
~ ( ~ ( ( ( set_difference @ SV20 @ SY232 )
!= empty_set )
| ( subset @ SV20 @ SY232 ) )
| ~ ( ~ ( subset @ SV20 @ SY232 )
| ( ( set_difference @ SV20 @ SY232 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1074,plain,
! [SV21: $i] :
( ( ! [SY233: $i] :
( ~ ( element @ SY233 @ ( powerset @ ( powerset @ SV21 ) ) )
| ( ( union_of_subsets @ SV21 @ SY233 )
= ( union @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1075,plain,
! [SV22: $i] :
( ( ! [SY234: $i] :
~ ( ~ ( ~ ( ( SV22 != empty_set ) )
| ~ ( ~ ( ( SY234
!= ( set_meet @ SV22 ) )
| ! [SY235: $i] :
~ ( ~ ( ~ ( in @ SY235 @ SY234 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY235 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY235 @ SY237 ) )
| ( in @ SY235 @ SY234 ) ) ) )
| ~ ( ~ ! [SY238: $i] :
~ ( ~ ( ~ ( in @ SY238 @ SY234 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY238 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY238 @ SY240 ) )
| ( in @ SY238 @ SY234 ) ) )
| ( SY234
= ( set_meet @ SV22 ) ) ) ) )
| ~ ( ( SV22 != empty_set )
| ~ ( ~ ( ( SY234
!= ( set_meet @ SV22 ) )
| ( SY234 = empty_set ) )
| ~ ( ( SY234 != empty_set )
| ( SY234
= ( set_meet @ SV22 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1076,plain,
! [SV23: $i] :
( ( ~ ( one_sorted_str @ SV23 )
| ( element @ ( empty_carrier_subset @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1077,plain,
! [SV24: $i] :
( ( ~ ( rel_str @ SV24 )
| ! [SY241: $i,SY242: $i] :
( ~ ( element @ SY242 @ ( the_carrier @ SV24 ) )
| ~ ( ~ ( ~ ( relstr_element_smaller @ SV24 @ SY241 @ SY242 )
| ! [SY243: $i] :
( ~ ( element @ SY243 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY243 @ SY241 )
| ( related @ SV24 @ SY242 @ SY243 ) ) )
| ~ ( ~ ! [SY244: $i] :
( ~ ( element @ SY244 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY244 @ SY241 )
| ( related @ SV24 @ SY242 @ SY244 ) )
| ( relstr_element_smaller @ SV24 @ SY241 @ SY242 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1078,plain,
! [SV25: $i] :
( ( ! [SY245: $i,SY246: $i] :
( ~ ~ ( ~ ( in @ SV25 @ SY245 )
| ~ ( element @ SY245 @ ( powerset @ SY246 ) ) )
| ( element @ SV25 @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1079,plain,
! [SV26: $i] :
( ( ! [SY247: $i] :
~ ( ~ ( ~ ( disjoint @ SV26 @ SY247 )
| ( ( set_intersection2 @ SV26 @ SY247 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV26 @ SY247 )
!= empty_set )
| ( disjoint @ SV26 @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1080,plain,
! [SV27: $i] :
( ( ~ ( ( SV27 != empty_set ) )
| ! [SY248: $i] :
( ~ ( element @ SY248 @ ( powerset @ SV27 ) )
| ! [SY249: $i] :
( ~ ( element @ SY249 @ SV27 )
| ~ ~ ( in @ SY249 @ SY248 )
| ( in @ SY249 @ ( subset_complement @ SV27 @ SY248 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1081,plain,
! [SV28: $i] :
( ( ! [SY250: $i] :
( ~ ! [SY251: $i] :
( ~ ( in @ SY251 @ SV28 )
| ( in @ SY251 @ SY250 ) )
| ( element @ SV28 @ ( powerset @ SY250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1082,plain,
! [SV29: $i] :
( ( ~ ! [SY252: $i] :
~ ~ ( ~ ( element @ SY252 @ ( powerset @ SV29 ) )
| ~ ( empty @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1083,plain,
! [SV30: $i] :
( ( ! [SY253: $i] :
( ~ ~ ( ~ ( top_str @ SV30 )
| ~ ( element @ SY253 @ ( powerset @ ( the_carrier @ SV30 ) ) ) )
| ( element @ ( interior @ SV30 @ SY253 ) @ ( powerset @ ( the_carrier @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1084,plain,
! [SV31: $i] :
( ( ! [SY254: $i] :
( ~ ( element @ SY254 @ ( powerset @ ( powerset @ SV31 ) ) )
| ( element @ ( meet_of_subsets @ SV31 @ SY254 ) @ ( powerset @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1085,plain,
! [SV32: $i] :
( ( ~ ( empty @ SV32 )
| ( SV32 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1086,plain,
! [SV33: $i] :
( ( ! [SY255: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SV33 )
| ~ ( latt_str @ SV33 ) )
| ( element @ ( join_of_latt_set @ SV33 @ SY255 ) @ ( the_carrier @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1087,plain,
! [SV34: $i] :
( ( ~ ~ ( empty @ SV34 )
| ~ ! [SY256: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY256 @ ( powerset @ SV34 ) )
| ~ ~ ( empty @ SY256 ) )
| ~ ( finite @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1088,plain,
! [SV35: $i] :
( ( ! [SY257: $i] :
( ~ ( in @ SV35 @ SY257 )
| ( element @ SV35 @ SY257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1089,plain,
( ( ! [SX0: $i] :
~ ( rel_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1090,plain,
! [SV36: $i] :
( ( ! [SY258: $i] :
( ~ ( element @ SY258 @ ( powerset @ ( powerset @ SV36 ) ) )
| ~ ~ ( ~ ( ( SY258 != empty_set ) )
| ( ( complements_of_subsets @ SV36 @ SY258 )
!= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1091,plain,
! [SV37: $i] :
( ( ! [SY259: $i] :
( ~ ~ ( ~ ~ ( empty_carrier @ SV37 )
| ~ ( latt_str @ SV37 ) )
| ( element @ ( meet_of_latt_set @ SV37 @ SY259 ) @ ( the_carrier @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1092,plain,
! [SV38: $i] :
( ( ~ ( relation @ SV38 )
| ~ ! [SY260: $i,SY261: $i] :
~ ( in @ ( ordered_pair @ SY260 @ SY261 ) @ SV38 )
| ( SV38 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1093,plain,
! [SV39: $i] :
( ( ! [SY262: $i] :
( ~ ( element @ SY262 @ ( powerset @ ( powerset @ SV39 ) ) )
| ( ( meet_of_subsets @ SV39 @ SY262 )
= ( set_meet @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1094,plain,
! [SV40: $i] :
( ( ! [SY263: $i,SY264: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) )
| ~ ( element @ SY263 @ ( the_carrier @ SV40 ) ) )
| ~ ( element @ SY264 @ ( the_carrier @ SV40 ) ) )
| ( related_reflexive @ SV40 @ SY263 @ SY263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1095,plain,
! [SV41: $i] :
( ( ! [SY265: $i,SY266: $i,SY267: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SY265 ) )
| ~ ( element @ SY266 @ SV41 ) )
| ~ ( element @ SY267 @ SY265 ) )
| ( element @ ( ordered_pair_as_product_element @ SV41 @ SY265 @ SY266 @ SY267 ) @ ( cartesian_product2 @ SV41 @ SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1096,plain,
! [SV42: $i] :
( ( ~ ( one_sorted_str @ SV42 )
| ( ( empty_carrier_subset @ SV42 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1097,plain,
! [SV43: $i] :
( ( ~ ( one_sorted_str @ SV43 )
| ( element @ ( cast_as_carrier_subset @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1098,plain,
! [SV44: $i] :
( ( ~ ( v1_membered @ SV44 )
| ! [SY268: $i] :
( ~ ( element @ SY268 @ ( powerset @ SV44 ) )
| ( v1_membered @ SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1099,plain,
! [SV45: $i] :
( ( ! [SY269: $i,SY270: $i] :
( ~ ~ ( ~ ( element @ SY269 @ ( powerset @ SV45 ) )
| ~ ( element @ SY270 @ ( powerset @ SV45 ) ) )
| ( element @ ( subset_difference @ SV45 @ SY269 @ SY270 ) @ ( powerset @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1100,plain,
! [SV46: $i] :
( ( ~ ( finite @ SV46 )
| ! [SY271: $i] :
( ~ ( element @ SY271 @ ( powerset @ SV46 ) )
| ( finite @ SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1101,plain,
! [SV47: $i] :
( ( ! [SY272: $i] :
( ~ ( element @ SY272 @ ( powerset @ SV47 ) )
| ! [SY273: $i] :
( ~ ( in @ SY273 @ SY272 )
| ( in @ SY273 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1102,plain,
! [SV48: $i] :
( ( ~ ( relation @ SV48 )
| ~ ( ~ ( ( ( relation_dom @ SV48 )
!= empty_set )
| ( ( relation_rng @ SV48 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV48 )
!= empty_set )
| ( ( relation_dom @ SV48 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1103,plain,
! [SV49: $i] :
( ( ! [SY274: $i,SY275: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) )
| ~ ( element @ SY274 @ ( the_carrier @ SV49 ) ) )
| ~ ( element @ SY275 @ ( the_carrier @ SV49 ) ) )
| ( element @ ( join @ SV49 @ SY274 @ SY275 ) @ ( the_carrier @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1104,plain,
! [SV50: $i] :
( ( ~ ! [SY276: $i] :
~ ( element @ SY276 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1105,plain,
! [SV51: $i] :
( ( ~ ( rel_str @ SV51 )
| ( one_sorted_str @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1106,plain,
! [SV52: $i] :
( ( ! [SY277: $i] :
~ ( ~ ( ~ ~ ( empty @ SV52 )
| ~ ( ~ ( ~ ( element @ SY277 @ SV52 )
| ( in @ SY277 @ SV52 ) )
| ~ ( ~ ( in @ SY277 @ SV52 )
| ( element @ SY277 @ SV52 ) ) ) )
| ~ ( ~ ( empty @ SV52 )
| ~ ( ~ ( ~ ( element @ SY277 @ SV52 )
| ( empty @ SY277 ) )
| ~ ( ~ ( empty @ SY277 )
| ( element @ SY277 @ SV52 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1107,plain,
! [SV53: $i] :
( ( ~ ( one_sorted_str @ SV53 )
| ( ( cast_as_carrier_subset @ SV53 )
= ( the_carrier @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1108,plain,
! [SV54: $i] :
( ( ! [SY278: $i,SY279: $i] :
( ~ ~ ( ~ ( element @ SY278 @ ( powerset @ SV54 ) )
| ~ ( element @ SY279 @ ( powerset @ SV54 ) ) )
| ( ( subset_union2 @ SV54 @ SY278 @ SY279 )
= ( set_union2 @ SY278 @ SY279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1109,plain,
! [SV55: $i] :
( ( ~ ( one_sorted_str @ SV55 )
| ( ( cast_as_carrier_subset @ SV55 )
= ( the_carrier @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1110,plain,
! [SV56: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ~ ~ ( ~ ( element @ SY280 @ ( powerset @ SV56 ) )
| ~ ( element @ SY281 @ ( powerset @ SV56 ) ) )
| ( ( subset_difference @ SV56 @ SY280 @ SY281 )
= ( set_difference @ SY280 @ SY281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1111,plain,
! [SV57: $i] :
( ( ~ ( ~ ( ( SV57 != empty_set )
| ! [SY282: $i] :
~ ( in @ SY282 @ SV57 ) )
| ~ ( ~ ! [SY283: $i] :
~ ( in @ SY283 @ SV57 )
| ( SV57 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1112,plain,
! [SV58: $i] :
( ( ~ ( v1_membered @ SV58 )
| ! [SY284: $i] :
( ~ ( element @ SY284 @ SV58 )
| ( v1_xcmplx_0 @ SY284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1113,plain,
! [SV59: $i] :
( ( ! [SY285: $i,SY286: $i] :
( ~ ( element @ SY286 @ ( powerset @ ( cartesian_product2 @ SV59 @ SY285 ) ) )
| ( relation @ SY286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1114,plain,
! [SV60: $i] :
( ( ~ ( ~ ( lower_bounded_semilattstr @ ( boole_lattice @ SV60 ) )
| ( ( bottom_of_semilattstr @ ( boole_lattice @ SV60 ) )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1115,plain,
! [SV61: $i] :
( ( ! [SY287: $i,SY288: $i] :
( ~ ( relation_of2_as_subset @ SY288 @ SV61 @ SY287 )
| ~ ( ~ ( ~ ( ( SY287 != empty_set )
| ( SV61 = empty_set ) )
| ~ ( ~ ( ~ ( quasi_total @ SY288 @ SV61 @ SY287 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SY287 @ SY288 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SY287 @ SY288 ) )
| ( quasi_total @ SY288 @ SV61 @ SY287 ) ) ) )
| ~ ( ( SY287 != empty_set )
| ( SV61 = empty_set )
| ~ ( ~ ( ~ ( quasi_total @ SY288 @ SV61 @ SY287 )
| ( SY288 = empty_set ) )
| ~ ( ( SY288 != empty_set )
| ( quasi_total @ SY288 @ SV61 @ SY287 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1116,plain,
! [SV62: $i] :
( ( ~ ( v2_membered @ SV62 )
| ! [SY289: $i] :
( ~ ( element @ SY289 @ SV62 )
| ~ ( ~ ( v1_xcmplx_0 @ SY289 )
| ~ ( v1_xreal_0 @ SY289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1117,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1118,plain,
! [SV63: $i] :
( ( ~ ( rel_str @ SV63 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SV63 ) @ ( the_carrier @ SV63 ) @ ( the_carrier @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1119,plain,
! [SV64: $i] :
( ( ! [SY290: $i] :
~ ( ~ ( ~ ( subset @ SV64 @ ( singleton @ SY290 ) )
| ( SV64 = empty_set )
| ( SV64
= ( singleton @ SY290 ) ) )
| ~ ( ~ ( ( SV64 = empty_set )
| ( SV64
= ( singleton @ SY290 ) ) )
| ( subset @ SV64 @ ( singleton @ SY290 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1120,plain,
! [SV65: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ~ ( element @ SY292 @ ( powerset @ SV65 ) )
| ~ ~ ( ~ ( in @ SY291 @ ( subset_complement @ SV65 @ SY292 ) )
| ~ ( in @ SY291 @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1121,plain,
! [SV66: $i] :
( ( ! [SY293: $i,SY294: $i] :
( ~ ~ ( ~ ( element @ SY293 @ ( powerset @ SV66 ) )
| ~ ( element @ SY294 @ ( powerset @ SV66 ) ) )
| ( element @ ( subset_intersection2 @ SV66 @ SY293 @ SY294 ) @ ( powerset @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1122,plain,
! [SV67: $i] :
( ( ! [SY295: $i] :
( ~ ( element @ SY295 @ SV67 )
| ~ ( ~ ( ~ ( proper_element @ SY295 @ SV67 )
| ( SY295
!= ( union @ SV67 ) ) )
| ~ ( ~ ( ( SY295
!= ( union @ SV67 ) ) )
| ( proper_element @ SY295 @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1123,plain,
! [SV68: $i] :
( ( ~ ( rel_str @ SV68 )
| ~ ( strict_rel_str @ SV68 )
| ( SV68
= ( rel_str_of @ ( the_carrier @ SV68 ) @ ( the_InternalRel @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1124,plain,
! [SV69: $i] :
( ( ~ ( ordinal @ SV69 )
| ! [SY296: $i] :
( ~ ( element @ SY296 @ SV69 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SY296 )
| ~ ( epsilon_connected @ SY296 ) )
| ~ ( ordinal @ SY296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1125,plain,
! [SV70: $i] :
( ( ( singleton @ SV70 )
!= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1126,plain,
! [SV71: $i] :
( ( ~ ( rel_str @ SV71 )
| ! [SY297: $i,SY298: $i] :
( ~ ( element @ SY298 @ ( the_carrier @ SV71 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SV71 @ SY297 @ SY298 )
| ! [SY299: $i] :
( ~ ( element @ SY299 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY299 @ SY297 )
| ( related @ SV71 @ SY299 @ SY298 ) ) )
| ~ ( ~ ! [SY300: $i] :
( ~ ( element @ SY300 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY300 @ SY297 )
| ( related @ SV71 @ SY300 @ SY298 ) )
| ( relstr_set_smaller @ SV71 @ SY297 @ SY298 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1127,plain,
! [SV72: $i] :
( ( ! [SY301: $i] :
( ~ ( relation_of2 @ SY301 @ SV72 @ SV72 )
| ~ ( ~ ( strict_rel_str @ ( rel_str_of @ SV72 @ SY301 ) )
| ~ ( rel_str @ ( rel_str_of @ SV72 @ SY301 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1128,plain,
! [SV73: $i] :
( ( ~ ~ ( ~ ( transitive_relstr @ SV73 )
| ~ ( rel_str @ SV73 ) )
| ! [SY302: $i] :
( ~ ( element @ SY302 @ ( the_carrier @ SV73 ) )
| ! [SY303: $i] :
( ~ ( element @ SY303 @ ( the_carrier @ SV73 ) )
| ! [SY304: $i] :
( ~ ( element @ SY304 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SY302 @ SY303 )
| ~ ( related @ SV73 @ SY303 @ SY304 ) )
| ( related @ SV73 @ SY302 @ SY304 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1129,plain,
! [SV74: $i] :
( ( ~ ~ ( empty @ SV74 )
| ~ ! [SY305: $i] :
~ ~ ( ~ ( element @ SY305 @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ SY305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1130,plain,
! [SV75: $i] :
( ( ~ ( v2_membered @ SV75 )
| ! [SY306: $i] :
( ~ ( element @ SY306 @ ( powerset @ SV75 ) )
| ~ ( ~ ( v1_membered @ SY306 )
| ~ ( v2_membered @ SY306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1131,plain,
! [SV76: $i] :
( ( ! [SY307: $i,SY308: $i] :
( ~ ~ ( ~ ( element @ SY307 @ ( powerset @ SV76 ) )
| ~ ( element @ SY308 @ ( powerset @ SV76 ) ) )
| ( element @ ( subset_union2 @ SV76 @ SY307 @ SY308 ) @ ( powerset @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1132,plain,
! [SV77: $i] :
( ( ~ ( one_sorted_str @ SV77 )
| ~ ( ~ ( ~ ( empty_carrier @ SV77 )
| ( empty @ ( the_carrier @ SV77 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV77 ) )
| ( empty_carrier @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1133,plain,
! [SV78: $i] :
( ( ~ ( rel_str @ SV78 )
| ~ ( ~ ( ~ ( antisymmetric_relstr @ SV78 )
| ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) )
| ( antisymmetric_relstr @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1134,plain,
! [SV79: $i] :
( ( ! [SY309: $i] :
( ~ ( element @ SY309 @ ( powerset @ ( powerset @ SV79 ) ) )
| ( element @ ( complements_of_subsets @ SV79 @ SY309 ) @ ( powerset @ ( powerset @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1135,plain,
! [SV80: $i] :
( ( ! [SY310: $i] :
~ ( ~ ( ~ ( element @ SV80 @ ( powerset @ SY310 ) )
| ( subset @ SV80 @ SY310 ) )
| ~ ( ~ ( subset @ SV80 @ SY310 )
| ( element @ SV80 @ ( powerset @ SY310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1136,plain,
! [SV81: $i] :
( ( ! [SY311: $i] :
~ ( ~ ( ~ ( subset @ SV81 @ ( singleton @ SY311 ) )
| ( SV81 = empty_set )
| ( SV81
= ( singleton @ SY311 ) ) )
| ~ ( ~ ( ( SV81 = empty_set )
| ( SV81
= ( singleton @ SY311 ) ) )
| ( subset @ SV81 @ ( singleton @ SY311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1137,plain,
! [SV82: $i] :
( ( ! [SY312: $i] :
( ~ ( element @ SY312 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
| ! [SY313: $i] :
( ~ ( element @ SY313 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
| ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV82 ) @ SY312 @ SY313 )
| ( subset @ SY312 @ SY313 ) )
| ~ ( ~ ( subset @ SY312 @ SY313 )
| ( below @ ( boole_lattice @ SV82 ) @ SY312 @ SY313 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1138,plain,
! [SV83: $i] :
( ( ~ ~ ( empty @ SV83 )
| ~ ! [SY314: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY314 @ ( powerset @ SV83 ) )
| ~ ~ ( empty @ SY314 ) )
| ~ ( finite @ SY314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1139,plain,
! [SV84: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV84 )
| ~ ( meet_semilatt_str @ SV84 ) )
| ( element @ ( bottom_of_semilattstr @ SV84 ) @ ( the_carrier @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1140,plain,
! [SV85: $i] :
( ( ! [SY315: $i] :
( ~ ( element @ SY315 @ ( powerset @ ( powerset @ SV85 ) ) )
| ( element @ ( union_of_subsets @ SV85 @ SY315 ) @ ( powerset @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1141,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1142,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1143,plain,
! [SV86: $i] :
( ( ~ ( rel_str @ SV86 )
| ~ ( ~ ( ~ ( transitive_relstr @ SV86 )
| ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) ) )
| ~ ( ~ ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) )
| ( transitive_relstr @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1144,plain,
! [SV87: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV87 )
| ~ ( one_sorted_str @ SV87 ) )
| ~ ( empty @ ( the_carrier @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1145,plain,
! [SV88: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) )
| ~ ( element @ SY316 @ ( the_carrier @ SV88 ) ) )
| ~ ( element @ SY317 @ ( the_carrier @ SV88 ) ) )
| ( element @ ( meet @ SV88 @ SY316 @ SY317 ) @ ( the_carrier @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1146,plain,
! [SV89: $i] :
( ( ! [SY318: $i] :
~ ( ~ ( ( ( set_difference @ SV89 @ SY318 )
!= empty_set )
| ( subset @ SV89 @ SY318 ) )
| ~ ( ~ ( subset @ SV89 @ SY318 )
| ( ( set_difference @ SV89 @ SY318 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1147,plain,
! [SV90: $i] :
( ( ! [SY319: $i,SY320: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV90 @ SY319 )
| ~ ( element @ SY319 @ ( powerset @ SY320 ) ) )
| ~ ( empty @ SY320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1148,plain,
! [SV91: $i] :
( ( ! [SY321: $i,SY322: $i] :
( ~ ~ ( ~ ( element @ SY321 @ ( powerset @ SV91 ) )
| ~ ( element @ SY322 @ ( powerset @ SV91 ) ) )
| ( ( subset_union2 @ SV91 @ SY321 @ SY322 )
= ( subset_union2 @ SV91 @ SY322 @ SY321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1149,plain,
! [SV92: $i] :
( ( ! [SY323: $i,SY324: $i,SY325: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SY323 ) )
| ~ ( element @ SY324 @ SV92 ) )
| ~ ( element @ SY325 @ SY323 ) )
| ( ( ordered_pair_as_product_element @ SV92 @ SY323 @ SY324 @ SY325 )
= ( ordered_pair @ SY324 @ SY325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1150,plain,
! [SV93: $i] :
( ( ! [SY326: $i] :
( ~ ( element @ SV93 @ SY326 )
| ( empty @ SY326 )
| ( in @ SV93 @ SY326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1151,plain,
! [SV94: $i] :
( ( ! [SY327: $i] :
( ~ ( element @ SY327 @ ( powerset @ SV94 ) )
| ( element @ ( subset_complement @ SV94 @ SY327 ) @ ( powerset @ SV94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1152,plain,
! [SV95: $i] :
( ( ~ ( subset @ SV95 @ empty_set )
| ( SV95 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1153,plain,
! [SV96: $i] :
( ( ! [SY328: $i] :
( ~ ( element @ SY328 @ ( powerset @ ( powerset @ SV96 ) ) )
| ( ( complements_of_subsets @ SV96 @ ( complements_of_subsets @ SV96 @ SY328 ) )
= SY328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1154,plain,
! [SV97: $i] :
( ( ~ ! [SY329: $i] :
~ ~ ( ~ ( element @ SY329 @ ( powerset @ SV97 ) )
| ~ ~ ( proper_element @ SY329 @ ( powerset @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1155,plain,
! [SV98: $i] :
( ( ! [SY330: $i,SY331: $i] :
( ~ ~ ( ~ ( element @ SY330 @ ( powerset @ SV98 ) )
| ~ ( element @ SY331 @ ( powerset @ SV98 ) ) )
| ( ( subset_union2 @ SV98 @ SY330 @ SY330 )
= SY330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1156,plain,
! [SV99: $i] :
( ( ! [SY332: $i,SY333: $i] :
( ~ ( relation_of2 @ SY333 @ SV99 @ SY332 )
| ( element @ ( relation_rng_as_subset @ SV99 @ SY332 @ SY333 ) @ ( powerset @ SY332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1157,plain,
! [SV100: $i] :
( ( ! [SY334: $i] :
( ~ ( element @ SY334 @ ( powerset @ SV100 ) )
| ~ ( ~ ( ~ ( proper_element @ SY334 @ ( powerset @ SV100 ) )
| ( SY334 != SV100 ) )
| ~ ( ~ ( ( SY334 != SV100 ) )
| ( proper_element @ SY334 @ ( powerset @ SV100 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1158,plain,
! [SV101: $i] :
( ( ! [SY335: $i,SY336: $i] :
( ~ ( relation_of2_as_subset @ SY336 @ SV101 @ SY335 )
| ( element @ SY336 @ ( powerset @ ( cartesian_product2 @ SV101 @ SY335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1159,plain,
! [SV8: $i,SV102: $i] :
( ( ! [SY337: $i] :
( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV8 ) )
| ~ ( element @ SY337 @ ( powerset @ SV8 ) ) )
| ( ( subset_intersection2 @ SV8 @ SV102 @ SY337 )
= ( set_intersection2 @ SV102 @ SY337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1160,plain,
( ( ~ ~ ( ~ ( rel_str @ sK2_SX0 )
| ~ ( strict_rel_str @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1060]) ).
thf(1161,plain,
! [SV103: $i,SV9: $i] :
( ( ! [SY338: $i] :
( ~ ( relation_of2 @ SY338 @ SV9 @ SV103 )
| ( element @ ( relation_dom_as_subset @ SV9 @ SV103 @ SY338 ) @ ( powerset @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1162,plain,
! [SV10: $i] :
( ( ( ~ ( top_str @ SV10 ) )
= $true )
| ( ( element @ ( the_topology @ SV10 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1163,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( antisymmetric_relstr @ SV11 )
| ~ ( rel_str @ SV11 ) ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( element @ SY222 @ ( the_carrier @ SV11 ) )
| ! [SY223: $i] :
( ~ ( element @ SY223 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY222 @ SY223 )
| ~ ( related @ SV11 @ SY223 @ SY222 ) )
| ( SY222 = SY223 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1164,plain,
! [SV104: $i,SV12: $i] :
( ( ~ ~ ( ~ ( top_str @ SV12 )
| ~ ( element @ SV104 @ ( powerset @ ( the_carrier @ SV12 ) ) ) )
| ( element @ ( topstr_closure @ SV12 @ SV104 ) @ ( powerset @ ( the_carrier @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1165,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( ( ( relation_dom @ SV13 )
= empty_set )
| ( ( relation_rng @ SV13 )
= empty_set ) )
| ( SV13 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1166,plain,
! [SV14: $i,SV105: $i] :
( ( ! [SY339: $i] :
( ~ ~ ( ~ ( element @ SV105 @ ( powerset @ SV14 ) )
| ~ ( element @ SY339 @ ( powerset @ SV14 ) ) )
| ( ( subset_intersection2 @ SV14 @ SV105 @ SY339 )
= ( subset_intersection2 @ SV14 @ SY339 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1167,plain,
! [SV15: $i,SV106: $i] :
( ( ~ ( element @ SV106 @ ( powerset @ SV15 ) )
| ( ( subset_complement @ SV15 @ SV106 )
= ( set_difference @ SV15 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1168,plain,
! [SV16: $i] :
( ( ( ~ ( one_sorted_str @ SV16 ) )
= $true )
| ( ( ( identity_on_carrier @ SV16 )
= ( identity_as_relation_of @ ( the_carrier @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1169,plain,
( ( ~ ( element @ sK3_SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK3_SX0 )
| ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1069]) ).
thf(1170,plain,
! [SV17: $i,SV107: $i] :
( ( ~ ( element @ SV107 @ ( powerset @ SV17 ) )
| ( ( subset_complement @ SV17 @ ( subset_complement @ SV17 @ SV107 ) )
= SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1171,plain,
! [SV18: $i,SV108: $i] :
( ( ~ ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
| ~ ( ~ ~ ~ ( ~ ( ( SV108 != empty_set ) )
| ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ( SV108 != empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1172,plain,
! [SV19: $i,SV109: $i] :
( ( ! [SY340: $i] :
( ~ ~ ( ~ ( element @ SV109 @ ( powerset @ SV19 ) )
| ~ ( element @ SY340 @ ( powerset @ SV19 ) ) )
| ( ( subset_intersection2 @ SV19 @ SV109 @ SV109 )
= SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1173,plain,
! [SV110: $i,SV20: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV20 @ SV110 )
!= empty_set )
| ( subset @ SV20 @ SV110 ) )
| ~ ( ~ ( subset @ SV20 @ SV110 )
| ( ( set_difference @ SV20 @ SV110 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1174,plain,
! [SV21: $i,SV111: $i] :
( ( ~ ( element @ SV111 @ ( powerset @ ( powerset @ SV21 ) ) )
| ( ( union_of_subsets @ SV21 @ SV111 )
= ( union @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1175,plain,
! [SV112: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( ( SV22 != empty_set ) )
| ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) )
| ~ ( ~ ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) )
| ~ ( ( SV22 != empty_set )
| ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1176,plain,
! [SV23: $i] :
( ( ( ~ ( one_sorted_str @ SV23 ) )
= $true )
| ( ( element @ ( empty_carrier_subset @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1177,plain,
! [SV24: $i] :
( ( ( ~ ( rel_str @ SV24 ) )
= $true )
| ( ( ! [SY241: $i,SY242: $i] :
( ~ ( element @ SY242 @ ( the_carrier @ SV24 ) )
| ~ ( ~ ( ~ ( relstr_element_smaller @ SV24 @ SY241 @ SY242 )
| ! [SY243: $i] :
( ~ ( element @ SY243 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY243 @ SY241 )
| ( related @ SV24 @ SY242 @ SY243 ) ) )
| ~ ( ~ ! [SY244: $i] :
( ~ ( element @ SY244 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY244 @ SY241 )
| ( related @ SV24 @ SY242 @ SY244 ) )
| ( relstr_element_smaller @ SV24 @ SY241 @ SY242 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1178,plain,
! [SV113: $i,SV25: $i] :
( ( ! [SY347: $i] :
( ~ ~ ( ~ ( in @ SV25 @ SV113 )
| ~ ( element @ SV113 @ ( powerset @ SY347 ) ) )
| ( element @ SV25 @ SY347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1179,plain,
! [SV114: $i,SV26: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV26 @ SV114 )
| ( ( set_intersection2 @ SV26 @ SV114 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV26 @ SV114 )
!= empty_set )
| ( disjoint @ SV26 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1180,plain,
! [SV27: $i] :
( ( ( ~ ( ( SV27 != empty_set ) ) )
= $true )
| ( ( ! [SY248: $i] :
( ~ ( element @ SY248 @ ( powerset @ SV27 ) )
| ! [SY249: $i] :
( ~ ( element @ SY249 @ SV27 )
| ~ ~ ( in @ SY249 @ SY248 )
| ( in @ SY249 @ ( subset_complement @ SV27 @ SY248 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1181,plain,
! [SV115: $i,SV28: $i] :
( ( ~ ! [SY348: $i] :
( ~ ( in @ SY348 @ SV28 )
| ( in @ SY348 @ SV115 ) )
| ( element @ SV28 @ ( powerset @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1182,plain,
! [SV29: $i] :
( ( ! [SY252: $i] :
~ ~ ( ~ ( element @ SY252 @ ( powerset @ SV29 ) )
| ~ ( empty @ SY252 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1183,plain,
! [SV116: $i,SV30: $i] :
( ( ~ ~ ( ~ ( top_str @ SV30 )
| ~ ( element @ SV116 @ ( powerset @ ( the_carrier @ SV30 ) ) ) )
| ( element @ ( interior @ SV30 @ SV116 ) @ ( powerset @ ( the_carrier @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1184,plain,
! [SV31: $i,SV117: $i] :
( ( ~ ( element @ SV117 @ ( powerset @ ( powerset @ SV31 ) ) )
| ( element @ ( meet_of_subsets @ SV31 @ SV117 ) @ ( powerset @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1185,plain,
! [SV32: $i] :
( ( ( ~ ( empty @ SV32 ) )
= $true )
| ( ( SV32 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1186,plain,
! [SV118: $i,SV33: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV33 )
| ~ ( latt_str @ SV33 ) )
| ( element @ ( join_of_latt_set @ SV33 @ SV118 ) @ ( the_carrier @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1187,plain,
! [SV34: $i] :
( ( ( ~ ~ ( empty @ SV34 ) )
= $true )
| ( ( ~ ! [SY256: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY256 @ ( powerset @ SV34 ) )
| ~ ~ ( empty @ SY256 ) )
| ~ ( finite @ SY256 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1188,plain,
! [SV119: $i,SV35: $i] :
( ( ~ ( in @ SV35 @ SV119 )
| ( element @ SV35 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1189,plain,
( ( ~ ( rel_str @ sK4_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1089]) ).
thf(1190,plain,
! [SV36: $i,SV120: $i] :
( ( ~ ( element @ SV120 @ ( powerset @ ( powerset @ SV36 ) ) )
| ~ ~ ( ~ ( ( SV120 != empty_set ) )
| ( ( complements_of_subsets @ SV36 @ SV120 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1191,plain,
! [SV121: $i,SV37: $i] :
( ( ~ ~ ( ~ ~ ( empty_carrier @ SV37 )
| ~ ( latt_str @ SV37 ) )
| ( element @ ( meet_of_latt_set @ SV37 @ SV121 ) @ ( the_carrier @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1192,plain,
! [SV38: $i] :
( ( ( ~ ( relation @ SV38 ) )
= $true )
| ( ( ~ ! [SY260: $i,SY261: $i] :
~ ( in @ ( ordered_pair @ SY260 @ SY261 ) @ SV38 )
| ( SV38 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1193,plain,
! [SV39: $i,SV122: $i] :
( ( ~ ( element @ SV122 @ ( powerset @ ( powerset @ SV39 ) ) )
| ( ( meet_of_subsets @ SV39 @ SV122 )
= ( set_meet @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1194,plain,
! [SV123: $i,SV40: $i] :
( ( ! [SY349: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) )
| ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
| ~ ( element @ SY349 @ ( the_carrier @ SV40 ) ) )
| ( related_reflexive @ SV40 @ SV123 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1195,plain,
! [SV124: $i,SV41: $i] :
( ( ! [SY350: $i,SY351: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) )
| ~ ( element @ SY350 @ SV41 ) )
| ~ ( element @ SY351 @ SV124 ) )
| ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SY350 @ SY351 ) @ ( cartesian_product2 @ SV41 @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1196,plain,
! [SV42: $i] :
( ( ( ~ ( one_sorted_str @ SV42 ) )
= $true )
| ( ( ( empty_carrier_subset @ SV42 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1197,plain,
! [SV43: $i] :
( ( ( ~ ( one_sorted_str @ SV43 ) )
= $true )
| ( ( element @ ( cast_as_carrier_subset @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1198,plain,
! [SV44: $i] :
( ( ( ~ ( v1_membered @ SV44 ) )
= $true )
| ( ( ! [SY268: $i] :
( ~ ( element @ SY268 @ ( powerset @ SV44 ) )
| ( v1_membered @ SY268 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1199,plain,
! [SV45: $i,SV125: $i] :
( ( ! [SY352: $i] :
( ~ ~ ( ~ ( element @ SV125 @ ( powerset @ SV45 ) )
| ~ ( element @ SY352 @ ( powerset @ SV45 ) ) )
| ( element @ ( subset_difference @ SV45 @ SV125 @ SY352 ) @ ( powerset @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1200,plain,
! [SV46: $i] :
( ( ( ~ ( finite @ SV46 ) )
= $true )
| ( ( ! [SY271: $i] :
( ~ ( element @ SY271 @ ( powerset @ SV46 ) )
| ( finite @ SY271 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1201,plain,
! [SV47: $i,SV126: $i] :
( ( ~ ( element @ SV126 @ ( powerset @ SV47 ) )
| ! [SY353: $i] :
( ~ ( in @ SY353 @ SV126 )
| ( in @ SY353 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1202,plain,
! [SV48: $i] :
( ( ( ~ ( relation @ SV48 ) )
= $true )
| ( ( ~ ( ~ ( ( ( relation_dom @ SV48 )
!= empty_set )
| ( ( relation_rng @ SV48 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV48 )
!= empty_set )
| ( ( relation_dom @ SV48 )
= empty_set ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1203,plain,
! [SV127: $i,SV49: $i] :
( ( ! [SY354: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) )
| ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
| ~ ( element @ SY354 @ ( the_carrier @ SV49 ) ) )
| ( element @ ( join @ SV49 @ SV127 @ SY354 ) @ ( the_carrier @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1204,plain,
! [SV50: $i] :
( ( ! [SY276: $i] :
~ ( element @ SY276 @ SV50 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1205,plain,
! [SV51: $i] :
( ( ( ~ ( rel_str @ SV51 ) )
= $true )
| ( ( one_sorted_str @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1206,plain,
! [SV128: $i,SV52: $i] :
( ( ~ ( ~ ( ~ ~ ( empty @ SV52 )
| ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( in @ SV128 @ SV52 ) )
| ~ ( ~ ( in @ SV128 @ SV52 )
| ( element @ SV128 @ SV52 ) ) ) )
| ~ ( ~ ( empty @ SV52 )
| ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( empty @ SV128 ) )
| ~ ( ~ ( empty @ SV128 )
| ( element @ SV128 @ SV52 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1207,plain,
! [SV53: $i] :
( ( ( ~ ( one_sorted_str @ SV53 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV53 )
= ( the_carrier @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1208,plain,
! [SV54: $i,SV129: $i] :
( ( ! [SY355: $i] :
( ~ ~ ( ~ ( element @ SV129 @ ( powerset @ SV54 ) )
| ~ ( element @ SY355 @ ( powerset @ SV54 ) ) )
| ( ( subset_union2 @ SV54 @ SV129 @ SY355 )
= ( set_union2 @ SV129 @ SY355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1209,plain,
! [SV55: $i] :
( ( ( ~ ( one_sorted_str @ SV55 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV55 )
= ( the_carrier @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1210,plain,
! [SV56: $i,SV130: $i] :
( ( ! [SY356: $i] :
( ~ ~ ( ~ ( element @ SV130 @ ( powerset @ SV56 ) )
| ~ ( element @ SY356 @ ( powerset @ SV56 ) ) )
| ( ( subset_difference @ SV56 @ SV130 @ SY356 )
= ( set_difference @ SV130 @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1211,plain,
! [SV57: $i] :
( ( ~ ( ( SV57 != empty_set )
| ! [SY282: $i] :
~ ( in @ SY282 @ SV57 ) )
| ~ ( ~ ! [SY283: $i] :
~ ( in @ SY283 @ SV57 )
| ( SV57 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1212,plain,
! [SV58: $i] :
( ( ( ~ ( v1_membered @ SV58 ) )
= $true )
| ( ( ! [SY284: $i] :
( ~ ( element @ SY284 @ SV58 )
| ( v1_xcmplx_0 @ SY284 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1213,plain,
! [SV131: $i,SV59: $i] :
( ( ! [SY357: $i] :
( ~ ( element @ SY357 @ ( powerset @ ( cartesian_product2 @ SV59 @ SV131 ) ) )
| ( relation @ SY357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1214,plain,
! [SV60: $i] :
( ( ~ ( lower_bounded_semilattstr @ ( boole_lattice @ SV60 ) )
| ( ( bottom_of_semilattstr @ ( boole_lattice @ SV60 ) )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1215,plain,
! [SV132: $i,SV61: $i] :
( ( ! [SY358: $i] :
( ~ ( relation_of2_as_subset @ SY358 @ SV61 @ SV132 )
| ~ ( ~ ( ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set ) )
| ~ ( ~ ( ~ ( quasi_total @ SY358 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SY358 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SY358 ) )
| ( quasi_total @ SY358 @ SV61 @ SV132 ) ) ) )
| ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set )
| ~ ( ~ ( ~ ( quasi_total @ SY358 @ SV61 @ SV132 )
| ( SY358 = empty_set ) )
| ~ ( ( SY358 != empty_set )
| ( quasi_total @ SY358 @ SV61 @ SV132 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1216,plain,
! [SV62: $i] :
( ( ( ~ ( v2_membered @ SV62 ) )
= $true )
| ( ( ! [SY289: $i] :
( ~ ( element @ SY289 @ SV62 )
| ~ ( ~ ( v1_xcmplx_0 @ SY289 )
| ~ ( v1_xreal_0 @ SY289 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1217,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1218,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1219,plain,
! [SV63: $i] :
( ( ( ~ ( rel_str @ SV63 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV63 ) @ ( the_carrier @ SV63 ) @ ( the_carrier @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1220,plain,
! [SV133: $i,SV64: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV64 @ ( singleton @ SV133 ) )
| ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) )
| ~ ( ~ ( ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) )
| ( subset @ SV64 @ ( singleton @ SV133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1221,plain,
! [SV134: $i,SV65: $i] :
( ( ! [SY359: $i] :
( ~ ( element @ SY359 @ ( powerset @ SV65 ) )
| ~ ~ ( ~ ( in @ SV134 @ ( subset_complement @ SV65 @ SY359 ) )
| ~ ( in @ SV134 @ SY359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1222,plain,
! [SV66: $i,SV135: $i] :
( ( ! [SY360: $i] :
( ~ ~ ( ~ ( element @ SV135 @ ( powerset @ SV66 ) )
| ~ ( element @ SY360 @ ( powerset @ SV66 ) ) )
| ( element @ ( subset_intersection2 @ SV66 @ SV135 @ SY360 ) @ ( powerset @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1223,plain,
! [SV67: $i,SV136: $i] :
( ( ~ ( element @ SV136 @ SV67 )
| ~ ( ~ ( ~ ( proper_element @ SV136 @ SV67 )
| ( SV136
!= ( union @ SV67 ) ) )
| ~ ( ~ ( ( SV136
!= ( union @ SV67 ) ) )
| ( proper_element @ SV136 @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1224,plain,
! [SV68: $i] :
( ( ( ~ ( rel_str @ SV68 ) )
= $true )
| ( ( ~ ( strict_rel_str @ SV68 )
| ( SV68
= ( rel_str_of @ ( the_carrier @ SV68 ) @ ( the_InternalRel @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1225,plain,
! [SV69: $i] :
( ( ( ~ ( ordinal @ SV69 ) )
= $true )
| ( ( ! [SY296: $i] :
( ~ ( element @ SY296 @ SV69 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SY296 )
| ~ ( epsilon_connected @ SY296 ) )
| ~ ( ordinal @ SY296 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1226,plain,
! [SV70: $i] :
( ( ( singleton @ SV70 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1227,plain,
! [SV71: $i] :
( ( ( ~ ( rel_str @ SV71 ) )
= $true )
| ( ( ! [SY297: $i,SY298: $i] :
( ~ ( element @ SY298 @ ( the_carrier @ SV71 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SV71 @ SY297 @ SY298 )
| ! [SY299: $i] :
( ~ ( element @ SY299 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY299 @ SY297 )
| ( related @ SV71 @ SY299 @ SY298 ) ) )
| ~ ( ~ ! [SY300: $i] :
( ~ ( element @ SY300 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY300 @ SY297 )
| ( related @ SV71 @ SY300 @ SY298 ) )
| ( relstr_set_smaller @ SV71 @ SY297 @ SY298 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1228,plain,
! [SV72: $i,SV137: $i] :
( ( ~ ( relation_of2 @ SV137 @ SV72 @ SV72 )
| ~ ( ~ ( strict_rel_str @ ( rel_str_of @ SV72 @ SV137 ) )
| ~ ( rel_str @ ( rel_str_of @ SV72 @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1229,plain,
! [SV73: $i] :
( ( ( ~ ~ ( ~ ( transitive_relstr @ SV73 )
| ~ ( rel_str @ SV73 ) ) )
= $true )
| ( ( ! [SY302: $i] :
( ~ ( element @ SY302 @ ( the_carrier @ SV73 ) )
| ! [SY303: $i] :
( ~ ( element @ SY303 @ ( the_carrier @ SV73 ) )
| ! [SY304: $i] :
( ~ ( element @ SY304 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SY302 @ SY303 )
| ~ ( related @ SV73 @ SY303 @ SY304 ) )
| ( related @ SV73 @ SY302 @ SY304 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1230,plain,
! [SV74: $i] :
( ( ( ~ ~ ( empty @ SV74 ) )
= $true )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( element @ SY305 @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ SY305 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1231,plain,
! [SV75: $i] :
( ( ( ~ ( v2_membered @ SV75 ) )
= $true )
| ( ( ! [SY306: $i] :
( ~ ( element @ SY306 @ ( powerset @ SV75 ) )
| ~ ( ~ ( v1_membered @ SY306 )
| ~ ( v2_membered @ SY306 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1232,plain,
! [SV76: $i,SV138: $i] :
( ( ! [SY361: $i] :
( ~ ~ ( ~ ( element @ SV138 @ ( powerset @ SV76 ) )
| ~ ( element @ SY361 @ ( powerset @ SV76 ) ) )
| ( element @ ( subset_union2 @ SV76 @ SV138 @ SY361 ) @ ( powerset @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1233,plain,
! [SV77: $i] :
( ( ( ~ ( one_sorted_str @ SV77 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( empty_carrier @ SV77 )
| ( empty @ ( the_carrier @ SV77 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV77 ) )
| ( empty_carrier @ SV77 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1234,plain,
! [SV78: $i] :
( ( ( ~ ( rel_str @ SV78 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( antisymmetric_relstr @ SV78 )
| ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) )
| ( antisymmetric_relstr @ SV78 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1235,plain,
! [SV79: $i,SV139: $i] :
( ( ~ ( element @ SV139 @ ( powerset @ ( powerset @ SV79 ) ) )
| ( element @ ( complements_of_subsets @ SV79 @ SV139 ) @ ( powerset @ ( powerset @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1236,plain,
! [SV140: $i,SV80: $i] :
( ( ~ ( ~ ( ~ ( element @ SV80 @ ( powerset @ SV140 ) )
| ( subset @ SV80 @ SV140 ) )
| ~ ( ~ ( subset @ SV80 @ SV140 )
| ( element @ SV80 @ ( powerset @ SV140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1237,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV81 @ ( singleton @ SV141 ) )
| ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) )
| ~ ( ~ ( ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) )
| ( subset @ SV81 @ ( singleton @ SV141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1238,plain,
! [SV82: $i,SV142: $i] :
( ( ~ ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
| ! [SY362: $i] :
( ~ ( element @ SY362 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
| ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SY362 )
| ( subset @ SV142 @ SY362 ) )
| ~ ( ~ ( subset @ SV142 @ SY362 )
| ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SY362 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1239,plain,
! [SV83: $i] :
( ( ( ~ ~ ( empty @ SV83 ) )
= $true )
| ( ( ~ ! [SY314: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY314 @ ( powerset @ SV83 ) )
| ~ ~ ( empty @ SY314 ) )
| ~ ( finite @ SY314 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1240,plain,
! [SV84: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV84 )
| ~ ( meet_semilatt_str @ SV84 ) ) )
= $true )
| ( ( element @ ( bottom_of_semilattstr @ SV84 ) @ ( the_carrier @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1241,plain,
! [SV85: $i,SV143: $i] :
( ( ~ ( element @ SV143 @ ( powerset @ ( powerset @ SV85 ) ) )
| ( element @ ( union_of_subsets @ SV85 @ SV143 ) @ ( powerset @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1242,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1141]) ).
thf(1243,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1141]) ).
thf(1244,plain,
( ( ( relation_dom @ empty_set )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1142]) ).
thf(1245,plain,
( ( ( relation_rng @ empty_set )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1142]) ).
thf(1246,plain,
! [SV86: $i] :
( ( ( ~ ( rel_str @ SV86 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( transitive_relstr @ SV86 )
| ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) ) )
| ~ ( ~ ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) )
| ( transitive_relstr @ SV86 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1247,plain,
! [SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV87 )
| ~ ( one_sorted_str @ SV87 ) ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1248,plain,
! [SV144: $i,SV88: $i] :
( ( ! [SY363: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) )
| ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
| ~ ( element @ SY363 @ ( the_carrier @ SV88 ) ) )
| ( element @ ( meet @ SV88 @ SV144 @ SY363 ) @ ( the_carrier @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1249,plain,
! [SV145: $i,SV89: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV89 @ SV145 )
!= empty_set )
| ( subset @ SV89 @ SV145 ) )
| ~ ( ~ ( subset @ SV89 @ SV145 )
| ( ( set_difference @ SV89 @ SV145 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1250,plain,
! [SV146: $i,SV90: $i] :
( ( ! [SY364: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV90 @ SV146 )
| ~ ( element @ SV146 @ ( powerset @ SY364 ) ) )
| ~ ( empty @ SY364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1251,plain,
! [SV91: $i,SV147: $i] :
( ( ! [SY365: $i] :
( ~ ~ ( ~ ( element @ SV147 @ ( powerset @ SV91 ) )
| ~ ( element @ SY365 @ ( powerset @ SV91 ) ) )
| ( ( subset_union2 @ SV91 @ SV147 @ SY365 )
= ( subset_union2 @ SV91 @ SY365 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1252,plain,
! [SV148: $i,SV92: $i] :
( ( ! [SY366: $i,SY367: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) )
| ~ ( element @ SY366 @ SV92 ) )
| ~ ( element @ SY367 @ SV148 ) )
| ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SY366 @ SY367 )
= ( ordered_pair @ SY366 @ SY367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1253,plain,
! [SV149: $i,SV93: $i] :
( ( ~ ( element @ SV93 @ SV149 )
| ( empty @ SV149 )
| ( in @ SV93 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1254,plain,
! [SV94: $i,SV150: $i] :
( ( ~ ( element @ SV150 @ ( powerset @ SV94 ) )
| ( element @ ( subset_complement @ SV94 @ SV150 ) @ ( powerset @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1255,plain,
! [SV95: $i] :
( ( ( ~ ( subset @ SV95 @ empty_set ) )
= $true )
| ( ( SV95 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1256,plain,
! [SV96: $i,SV151: $i] :
( ( ~ ( element @ SV151 @ ( powerset @ ( powerset @ SV96 ) ) )
| ( ( complements_of_subsets @ SV96 @ ( complements_of_subsets @ SV96 @ SV151 ) )
= SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1257,plain,
! [SV97: $i] :
( ( ! [SY329: $i] :
~ ~ ( ~ ( element @ SY329 @ ( powerset @ SV97 ) )
| ~ ~ ( proper_element @ SY329 @ ( powerset @ SV97 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1258,plain,
! [SV98: $i,SV152: $i] :
( ( ! [SY368: $i] :
( ~ ~ ( ~ ( element @ SV152 @ ( powerset @ SV98 ) )
| ~ ( element @ SY368 @ ( powerset @ SV98 ) ) )
| ( ( subset_union2 @ SV98 @ SV152 @ SV152 )
= SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1259,plain,
! [SV153: $i,SV99: $i] :
( ( ! [SY369: $i] :
( ~ ( relation_of2 @ SY369 @ SV99 @ SV153 )
| ( element @ ( relation_rng_as_subset @ SV99 @ SV153 @ SY369 ) @ ( powerset @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1260,plain,
! [SV100: $i,SV154: $i] :
( ( ~ ( element @ SV154 @ ( powerset @ SV100 ) )
| ~ ( ~ ( ~ ( proper_element @ SV154 @ ( powerset @ SV100 ) )
| ( SV154 != SV100 ) )
| ~ ( ~ ( ( SV154 != SV100 ) )
| ( proper_element @ SV154 @ ( powerset @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1261,plain,
! [SV155: $i,SV101: $i] :
( ( ! [SY370: $i] :
( ~ ( relation_of2_as_subset @ SY370 @ SV101 @ SV155 )
| ( element @ SY370 @ ( powerset @ ( cartesian_product2 @ SV101 @ SV155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1262,plain,
! [SV156: $i,SV8: $i,SV102: $i] :
( ( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV8 ) )
| ~ ( element @ SV156 @ ( powerset @ SV8 ) ) )
| ( ( subset_intersection2 @ SV8 @ SV102 @ SV156 )
= ( set_intersection2 @ SV102 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1263,plain,
( ( ~ ( ~ ( rel_str @ sK2_SX0 )
| ~ ( strict_rel_str @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1264,plain,
! [SV103: $i,SV9: $i,SV157: $i] :
( ( ~ ( relation_of2 @ SV157 @ SV9 @ SV103 )
| ( element @ ( relation_dom_as_subset @ SV9 @ SV103 @ SV157 ) @ ( powerset @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1265,plain,
! [SV10: $i] :
( ( ( top_str @ SV10 )
= $false )
| ( ( element @ ( the_topology @ SV10 ) @ ( powerset @ ( powerset @ ( the_carrier @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1266,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( antisymmetric_relstr @ SV11 )
| ~ ( rel_str @ SV11 ) ) )
= $false )
| ( ( ! [SY222: $i] :
( ~ ( element @ SY222 @ ( the_carrier @ SV11 ) )
| ! [SY223: $i] :
( ~ ( element @ SY223 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY222 @ SY223 )
| ~ ( related @ SV11 @ SY223 @ SY222 ) )
| ( SY222 = SY223 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1267,plain,
! [SV104: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( top_str @ SV12 )
| ~ ( element @ SV104 @ ( powerset @ ( the_carrier @ SV12 ) ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV12 @ SV104 ) @ ( powerset @ ( the_carrier @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1164]) ).
thf(1268,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ~ ( ( ( relation_dom @ SV13 )
= empty_set )
| ( ( relation_rng @ SV13 )
= empty_set ) )
| ( SV13 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1269,plain,
! [SV158: $i,SV14: $i,SV105: $i] :
( ( ~ ~ ( ~ ( element @ SV105 @ ( powerset @ SV14 ) )
| ~ ( element @ SV158 @ ( powerset @ SV14 ) ) )
| ( ( subset_intersection2 @ SV14 @ SV105 @ SV158 )
= ( subset_intersection2 @ SV14 @ SV158 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1270,plain,
! [SV15: $i,SV106: $i] :
( ( ( ~ ( element @ SV106 @ ( powerset @ SV15 ) ) )
= $true )
| ( ( ( subset_complement @ SV15 @ SV106 )
= ( set_difference @ SV15 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1271,plain,
! [SV16: $i] :
( ( ( one_sorted_str @ SV16 )
= $false )
| ( ( ( identity_on_carrier @ SV16 )
= ( identity_as_relation_of @ ( the_carrier @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1272,plain,
( ( ~ ( element @ sK3_SX0 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1273,plain,
( ( ~ ( ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK3_SX0 )
| ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1274,plain,
! [SV17: $i,SV107: $i] :
( ( ( ~ ( element @ SV107 @ ( powerset @ SV17 ) ) )
= $true )
| ( ( ( subset_complement @ SV17 @ ( subset_complement @ SV17 @ SV107 ) )
= SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1275,plain,
! [SV18: $i,SV108: $i] :
( ( ( ~ ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ~ ( ~ ( ( SV108 != empty_set ) )
| ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ( SV108 != empty_set ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1276,plain,
! [SV159: $i,SV19: $i,SV109: $i] :
( ( ~ ~ ( ~ ( element @ SV109 @ ( powerset @ SV19 ) )
| ~ ( element @ SV159 @ ( powerset @ SV19 ) ) )
| ( ( subset_intersection2 @ SV19 @ SV109 @ SV109 )
= SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1277,plain,
! [SV110: $i,SV20: $i] :
( ( ~ ( ( ( set_difference @ SV20 @ SV110 )
!= empty_set )
| ( subset @ SV20 @ SV110 ) )
| ~ ( ~ ( subset @ SV20 @ SV110 )
| ( ( set_difference @ SV20 @ SV110 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1278,plain,
! [SV21: $i,SV111: $i] :
( ( ( ~ ( element @ SV111 @ ( powerset @ ( powerset @ SV21 ) ) ) )
= $true )
| ( ( ( union_of_subsets @ SV21 @ SV111 )
= ( union @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1279,plain,
! [SV112: $i,SV22: $i] :
( ( ~ ( ~ ( ( SV22 != empty_set ) )
| ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) )
| ~ ( ~ ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) )
| ~ ( ( SV22 != empty_set )
| ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1280,plain,
! [SV23: $i] :
( ( ( one_sorted_str @ SV23 )
= $false )
| ( ( element @ ( empty_carrier_subset @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1281,plain,
! [SV24: $i] :
( ( ( rel_str @ SV24 )
= $false )
| ( ( ! [SY241: $i,SY242: $i] :
( ~ ( element @ SY242 @ ( the_carrier @ SV24 ) )
| ~ ( ~ ( ~ ( relstr_element_smaller @ SV24 @ SY241 @ SY242 )
| ! [SY243: $i] :
( ~ ( element @ SY243 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY243 @ SY241 )
| ( related @ SV24 @ SY242 @ SY243 ) ) )
| ~ ( ~ ! [SY244: $i] :
( ~ ( element @ SY244 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY244 @ SY241 )
| ( related @ SV24 @ SY242 @ SY244 ) )
| ( relstr_element_smaller @ SV24 @ SY241 @ SY242 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1282,plain,
! [SV160: $i,SV113: $i,SV25: $i] :
( ( ~ ~ ( ~ ( in @ SV25 @ SV113 )
| ~ ( element @ SV113 @ ( powerset @ SV160 ) ) )
| ( element @ SV25 @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1283,plain,
! [SV114: $i,SV26: $i] :
( ( ~ ( ~ ( disjoint @ SV26 @ SV114 )
| ( ( set_intersection2 @ SV26 @ SV114 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV26 @ SV114 )
!= empty_set )
| ( disjoint @ SV26 @ SV114 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1284,plain,
! [SV27: $i] :
( ( ( SV27 != empty_set )
= $false )
| ( ( ! [SY248: $i] :
( ~ ( element @ SY248 @ ( powerset @ SV27 ) )
| ! [SY249: $i] :
( ~ ( element @ SY249 @ SV27 )
| ~ ~ ( in @ SY249 @ SY248 )
| ( in @ SY249 @ ( subset_complement @ SV27 @ SY248 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1285,plain,
! [SV115: $i,SV28: $i] :
( ( ( ~ ! [SY348: $i] :
( ~ ( in @ SY348 @ SV28 )
| ( in @ SY348 @ SV115 ) ) )
= $true )
| ( ( element @ SV28 @ ( powerset @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1286,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ( element @ ( sK5_SY252 @ SV29 ) @ ( powerset @ SV29 ) )
| ~ ( empty @ ( sK5_SY252 @ SV29 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1182]) ).
thf(1287,plain,
! [SV116: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( top_str @ SV30 )
| ~ ( element @ SV116 @ ( powerset @ ( the_carrier @ SV30 ) ) ) ) )
= $true )
| ( ( element @ ( interior @ SV30 @ SV116 ) @ ( powerset @ ( the_carrier @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1288,plain,
! [SV31: $i,SV117: $i] :
( ( ( ~ ( element @ SV117 @ ( powerset @ ( powerset @ SV31 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV31 @ SV117 ) @ ( powerset @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1289,plain,
! [SV32: $i] :
( ( ( empty @ SV32 )
= $false )
| ( ( SV32 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1290,plain,
! [SV118: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV33 )
| ~ ( latt_str @ SV33 ) ) )
= $true )
| ( ( element @ ( join_of_latt_set @ SV33 @ SV118 ) @ ( the_carrier @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1291,plain,
! [SV34: $i] :
( ( ( ~ ( empty @ SV34 ) )
= $false )
| ( ( ~ ! [SY256: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY256 @ ( powerset @ SV34 ) )
| ~ ~ ( empty @ SY256 ) )
| ~ ( finite @ SY256 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1292,plain,
! [SV119: $i,SV35: $i] :
( ( ( ~ ( in @ SV35 @ SV119 ) )
= $true )
| ( ( element @ SV35 @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1293,plain,
( ( rel_str @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1294,plain,
! [SV36: $i,SV120: $i] :
( ( ( ~ ( element @ SV120 @ ( powerset @ ( powerset @ SV36 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV120 != empty_set ) )
| ( ( complements_of_subsets @ SV36 @ SV120 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1295,plain,
! [SV121: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV37 )
| ~ ( latt_str @ SV37 ) ) )
= $true )
| ( ( element @ ( meet_of_latt_set @ SV37 @ SV121 ) @ ( the_carrier @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1296,plain,
! [SV38: $i] :
( ( ( relation @ SV38 )
= $false )
| ( ( ~ ! [SY260: $i,SY261: $i] :
~ ( in @ ( ordered_pair @ SY260 @ SY261 ) @ SV38 )
| ( SV38 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1297,plain,
! [SV39: $i,SV122: $i] :
( ( ( ~ ( element @ SV122 @ ( powerset @ ( powerset @ SV39 ) ) ) )
= $true )
| ( ( ( meet_of_subsets @ SV39 @ SV122 )
= ( set_meet @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1298,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) )
| ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
| ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
| ( related_reflexive @ SV40 @ SV123 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1299,plain,
! [SV162: $i,SV124: $i,SV41: $i] :
( ( ! [SY371: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) )
| ~ ( element @ SV162 @ SV41 ) )
| ~ ( element @ SY371 @ SV124 ) )
| ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SY371 ) @ ( cartesian_product2 @ SV41 @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1300,plain,
! [SV42: $i] :
( ( ( one_sorted_str @ SV42 )
= $false )
| ( ( ( empty_carrier_subset @ SV42 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1301,plain,
! [SV43: $i] :
( ( ( one_sorted_str @ SV43 )
= $false )
| ( ( element @ ( cast_as_carrier_subset @ SV43 ) @ ( powerset @ ( the_carrier @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1302,plain,
! [SV44: $i] :
( ( ( v1_membered @ SV44 )
= $false )
| ( ( ! [SY268: $i] :
( ~ ( element @ SY268 @ ( powerset @ SV44 ) )
| ( v1_membered @ SY268 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1303,plain,
! [SV163: $i,SV45: $i,SV125: $i] :
( ( ~ ~ ( ~ ( element @ SV125 @ ( powerset @ SV45 ) )
| ~ ( element @ SV163 @ ( powerset @ SV45 ) ) )
| ( element @ ( subset_difference @ SV45 @ SV125 @ SV163 ) @ ( powerset @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1304,plain,
! [SV46: $i] :
( ( ( finite @ SV46 )
= $false )
| ( ( ! [SY271: $i] :
( ~ ( element @ SY271 @ ( powerset @ SV46 ) )
| ( finite @ SY271 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1305,plain,
! [SV47: $i,SV126: $i] :
( ( ( ~ ( element @ SV126 @ ( powerset @ SV47 ) ) )
= $true )
| ( ( ! [SY353: $i] :
( ~ ( in @ SY353 @ SV126 )
| ( in @ SY353 @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1306,plain,
! [SV48: $i] :
( ( ( relation @ SV48 )
= $false )
| ( ( ~ ( ~ ( ( ( relation_dom @ SV48 )
!= empty_set )
| ( ( relation_rng @ SV48 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV48 )
!= empty_set )
| ( ( relation_dom @ SV48 )
= empty_set ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1307,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) )
| ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
| ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
| ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1308,plain,
! [SV50: $i] :
( ( ~ ( element @ ( sK6_SY276 @ SV50 ) @ SV50 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1204]) ).
thf(1309,plain,
! [SV51: $i] :
( ( ( rel_str @ SV51 )
= $false )
| ( ( one_sorted_str @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1310,plain,
! [SV128: $i,SV52: $i] :
( ( ~ ( ~ ~ ( empty @ SV52 )
| ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( in @ SV128 @ SV52 ) )
| ~ ( ~ ( in @ SV128 @ SV52 )
| ( element @ SV128 @ SV52 ) ) ) )
| ~ ( ~ ( empty @ SV52 )
| ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( empty @ SV128 ) )
| ~ ( ~ ( empty @ SV128 )
| ( element @ SV128 @ SV52 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1311,plain,
! [SV53: $i] :
( ( ( one_sorted_str @ SV53 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV53 )
= ( the_carrier @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1312,plain,
! [SV165: $i,SV54: $i,SV129: $i] :
( ( ~ ~ ( ~ ( element @ SV129 @ ( powerset @ SV54 ) )
| ~ ( element @ SV165 @ ( powerset @ SV54 ) ) )
| ( ( subset_union2 @ SV54 @ SV129 @ SV165 )
= ( set_union2 @ SV129 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1313,plain,
! [SV55: $i] :
( ( ( one_sorted_str @ SV55 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV55 )
= ( the_carrier @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1314,plain,
! [SV166: $i,SV56: $i,SV130: $i] :
( ( ~ ~ ( ~ ( element @ SV130 @ ( powerset @ SV56 ) )
| ~ ( element @ SV166 @ ( powerset @ SV56 ) ) )
| ( ( subset_difference @ SV56 @ SV130 @ SV166 )
= ( set_difference @ SV130 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1315,plain,
! [SV57: $i] :
( ( ~ ( ( SV57 != empty_set )
| ! [SY282: $i] :
~ ( in @ SY282 @ SV57 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1211]) ).
thf(1316,plain,
! [SV57: $i] :
( ( ~ ( ~ ! [SY283: $i] :
~ ( in @ SY283 @ SV57 )
| ( SV57 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1211]) ).
thf(1317,plain,
! [SV58: $i] :
( ( ( v1_membered @ SV58 )
= $false )
| ( ( ! [SY284: $i] :
( ~ ( element @ SY284 @ SV58 )
| ( v1_xcmplx_0 @ SY284 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1318,plain,
! [SV131: $i,SV59: $i,SV167: $i] :
( ( ~ ( element @ SV167 @ ( powerset @ ( cartesian_product2 @ SV59 @ SV131 ) ) )
| ( relation @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1319,plain,
! [SV60: $i] :
( ( ~ ( lower_bounded_semilattstr @ ( boole_lattice @ SV60 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1214]) ).
thf(1320,plain,
! [SV60: $i] :
( ( ( bottom_of_semilattstr @ ( boole_lattice @ SV60 ) )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1214]) ).
thf(1321,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ~ ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
| ~ ( ~ ( ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set ) )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
| ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) )
| ~ ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1322,plain,
! [SV62: $i] :
( ( ( v2_membered @ SV62 )
= $false )
| ( ( ! [SY289: $i] :
( ~ ( element @ SY289 @ SV62 )
| ~ ( ~ ( v1_xcmplx_0 @ SY289 )
| ~ ( v1_xreal_0 @ SY289 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1323,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1217]) ).
thf(1324,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1218]) ).
thf(1325,plain,
! [SV63: $i] :
( ( ( rel_str @ SV63 )
= $false )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV63 ) @ ( the_carrier @ SV63 ) @ ( the_carrier @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1326,plain,
! [SV133: $i,SV64: $i] :
( ( ~ ( ~ ( subset @ SV64 @ ( singleton @ SV133 ) )
| ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) )
| ~ ( ~ ( ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) )
| ( subset @ SV64 @ ( singleton @ SV133 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1327,plain,
! [SV134: $i,SV65: $i,SV169: $i] :
( ( ~ ( element @ SV169 @ ( powerset @ SV65 ) )
| ~ ~ ( ~ ( in @ SV134 @ ( subset_complement @ SV65 @ SV169 ) )
| ~ ( in @ SV134 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1328,plain,
! [SV170: $i,SV66: $i,SV135: $i] :
( ( ~ ~ ( ~ ( element @ SV135 @ ( powerset @ SV66 ) )
| ~ ( element @ SV170 @ ( powerset @ SV66 ) ) )
| ( element @ ( subset_intersection2 @ SV66 @ SV135 @ SV170 ) @ ( powerset @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1329,plain,
! [SV67: $i,SV136: $i] :
( ( ( ~ ( element @ SV136 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV136 @ SV67 )
| ( SV136
!= ( union @ SV67 ) ) )
| ~ ( ~ ( ( SV136
!= ( union @ SV67 ) ) )
| ( proper_element @ SV136 @ SV67 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1330,plain,
! [SV68: $i] :
( ( ( rel_str @ SV68 )
= $false )
| ( ( ~ ( strict_rel_str @ SV68 )
| ( SV68
= ( rel_str_of @ ( the_carrier @ SV68 ) @ ( the_InternalRel @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1331,plain,
! [SV69: $i] :
( ( ( ordinal @ SV69 )
= $false )
| ( ( ! [SY296: $i] :
( ~ ( element @ SY296 @ SV69 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SY296 )
| ~ ( epsilon_connected @ SY296 ) )
| ~ ( ordinal @ SY296 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1332,plain,
! [SV71: $i] :
( ( ( rel_str @ SV71 )
= $false )
| ( ( ! [SY297: $i,SY298: $i] :
( ~ ( element @ SY298 @ ( the_carrier @ SV71 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SV71 @ SY297 @ SY298 )
| ! [SY299: $i] :
( ~ ( element @ SY299 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY299 @ SY297 )
| ( related @ SV71 @ SY299 @ SY298 ) ) )
| ~ ( ~ ! [SY300: $i] :
( ~ ( element @ SY300 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY300 @ SY297 )
| ( related @ SV71 @ SY300 @ SY298 ) )
| ( relstr_set_smaller @ SV71 @ SY297 @ SY298 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1333,plain,
! [SV72: $i,SV137: $i] :
( ( ( ~ ( relation_of2 @ SV137 @ SV72 @ SV72 ) )
= $true )
| ( ( ~ ( ~ ( strict_rel_str @ ( rel_str_of @ SV72 @ SV137 ) )
| ~ ( rel_str @ ( rel_str_of @ SV72 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1334,plain,
! [SV73: $i] :
( ( ( ~ ( ~ ( transitive_relstr @ SV73 )
| ~ ( rel_str @ SV73 ) ) )
= $false )
| ( ( ! [SY302: $i] :
( ~ ( element @ SY302 @ ( the_carrier @ SV73 ) )
| ! [SY303: $i] :
( ~ ( element @ SY303 @ ( the_carrier @ SV73 ) )
| ! [SY304: $i] :
( ~ ( element @ SY304 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SY302 @ SY303 )
| ~ ( related @ SV73 @ SY303 @ SY304 ) )
| ( related @ SV73 @ SY302 @ SY304 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1335,plain,
! [SV74: $i] :
( ( ( ~ ( empty @ SV74 ) )
= $false )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( element @ SY305 @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ SY305 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1336,plain,
! [SV75: $i] :
( ( ( v2_membered @ SV75 )
= $false )
| ( ( ! [SY306: $i] :
( ~ ( element @ SY306 @ ( powerset @ SV75 ) )
| ~ ( ~ ( v1_membered @ SY306 )
| ~ ( v2_membered @ SY306 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1337,plain,
! [SV171: $i,SV76: $i,SV138: $i] :
( ( ~ ~ ( ~ ( element @ SV138 @ ( powerset @ SV76 ) )
| ~ ( element @ SV171 @ ( powerset @ SV76 ) ) )
| ( element @ ( subset_union2 @ SV76 @ SV138 @ SV171 ) @ ( powerset @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1338,plain,
! [SV77: $i] :
( ( ( one_sorted_str @ SV77 )
= $false )
| ( ( ~ ( ~ ( ~ ( empty_carrier @ SV77 )
| ( empty @ ( the_carrier @ SV77 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV77 ) )
| ( empty_carrier @ SV77 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1339,plain,
! [SV78: $i] :
( ( ( rel_str @ SV78 )
= $false )
| ( ( ~ ( ~ ( ~ ( antisymmetric_relstr @ SV78 )
| ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) )
| ( antisymmetric_relstr @ SV78 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1340,plain,
! [SV79: $i,SV139: $i] :
( ( ( ~ ( element @ SV139 @ ( powerset @ ( powerset @ SV79 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV79 @ SV139 ) @ ( powerset @ ( powerset @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1341,plain,
! [SV140: $i,SV80: $i] :
( ( ~ ( ~ ( element @ SV80 @ ( powerset @ SV140 ) )
| ( subset @ SV80 @ SV140 ) )
| ~ ( ~ ( subset @ SV80 @ SV140 )
| ( element @ SV80 @ ( powerset @ SV140 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1342,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( ~ ( subset @ SV81 @ ( singleton @ SV141 ) )
| ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) )
| ~ ( ~ ( ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) )
| ( subset @ SV81 @ ( singleton @ SV141 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1343,plain,
! [SV82: $i,SV142: $i] :
( ( ( ~ ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) ) )
= $true )
| ( ( ! [SY362: $i] :
( ~ ( element @ SY362 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
| ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SY362 )
| ( subset @ SV142 @ SY362 ) )
| ~ ( ~ ( subset @ SV142 @ SY362 )
| ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SY362 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1344,plain,
! [SV83: $i] :
( ( ( ~ ( empty @ SV83 ) )
= $false )
| ( ( ~ ! [SY314: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY314 @ ( powerset @ SV83 ) )
| ~ ~ ( empty @ SY314 ) )
| ~ ( finite @ SY314 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1345,plain,
! [SV84: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV84 )
| ~ ( meet_semilatt_str @ SV84 ) ) )
= $false )
| ( ( element @ ( bottom_of_semilattstr @ SV84 ) @ ( the_carrier @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1346,plain,
! [SV85: $i,SV143: $i] :
( ( ( ~ ( element @ SV143 @ ( powerset @ ( powerset @ SV85 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV85 @ SV143 ) @ ( powerset @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1347,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1242]) ).
thf(1348,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1349,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1350,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1351,plain,
! [SV86: $i] :
( ( ( rel_str @ SV86 )
= $false )
| ( ( ~ ( ~ ( ~ ( transitive_relstr @ SV86 )
| ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) ) )
| ~ ( ~ ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) )
| ( transitive_relstr @ SV86 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1352,plain,
! [SV87: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV87 )
| ~ ( one_sorted_str @ SV87 ) ) )
= $false )
| ( ( ~ ( empty @ ( the_carrier @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1353,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) )
| ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
| ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
| ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1354,plain,
! [SV145: $i,SV89: $i] :
( ( ~ ( ( ( set_difference @ SV89 @ SV145 )
!= empty_set )
| ( subset @ SV89 @ SV145 ) )
| ~ ( ~ ( subset @ SV89 @ SV145 )
| ( ( set_difference @ SV89 @ SV145 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1355,plain,
! [SV173: $i,SV146: $i,SV90: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV90 @ SV146 )
| ~ ( element @ SV146 @ ( powerset @ SV173 ) ) )
| ~ ( empty @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1356,plain,
! [SV174: $i,SV91: $i,SV147: $i] :
( ( ~ ~ ( ~ ( element @ SV147 @ ( powerset @ SV91 ) )
| ~ ( element @ SV174 @ ( powerset @ SV91 ) ) )
| ( ( subset_union2 @ SV91 @ SV147 @ SV174 )
= ( subset_union2 @ SV91 @ SV174 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1357,plain,
! [SV175: $i,SV148: $i,SV92: $i] :
( ( ! [SY372: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) )
| ~ ( element @ SV175 @ SV92 ) )
| ~ ( element @ SY372 @ SV148 ) )
| ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SY372 )
= ( ordered_pair @ SV175 @ SY372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1358,plain,
! [SV149: $i,SV93: $i] :
( ( ( ~ ( element @ SV93 @ SV149 ) )
= $true )
| ( ( ( empty @ SV149 )
| ( in @ SV93 @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1359,plain,
! [SV94: $i,SV150: $i] :
( ( ( ~ ( element @ SV150 @ ( powerset @ SV94 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV94 @ SV150 ) @ ( powerset @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1360,plain,
! [SV95: $i] :
( ( ( subset @ SV95 @ empty_set )
= $false )
| ( ( SV95 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1361,plain,
! [SV96: $i,SV151: $i] :
( ( ( ~ ( element @ SV151 @ ( powerset @ ( powerset @ SV96 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV96 @ ( complements_of_subsets @ SV96 @ SV151 ) )
= SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1362,plain,
! [SV97: $i] :
( ( ~ ~ ( ~ ( element @ ( sK7_SY329 @ SV97 ) @ ( powerset @ SV97 ) )
| ~ ~ ( proper_element @ ( sK7_SY329 @ SV97 ) @ ( powerset @ SV97 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1257]) ).
thf(1363,plain,
! [SV176: $i,SV98: $i,SV152: $i] :
( ( ~ ~ ( ~ ( element @ SV152 @ ( powerset @ SV98 ) )
| ~ ( element @ SV176 @ ( powerset @ SV98 ) ) )
| ( ( subset_union2 @ SV98 @ SV152 @ SV152 )
= SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1364,plain,
! [SV153: $i,SV99: $i,SV177: $i] :
( ( ~ ( relation_of2 @ SV177 @ SV99 @ SV153 )
| ( element @ ( relation_rng_as_subset @ SV99 @ SV153 @ SV177 ) @ ( powerset @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1365,plain,
! [SV100: $i,SV154: $i] :
( ( ( ~ ( element @ SV154 @ ( powerset @ SV100 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV154 @ ( powerset @ SV100 ) )
| ( SV154 != SV100 ) )
| ~ ( ~ ( ( SV154 != SV100 ) )
| ( proper_element @ SV154 @ ( powerset @ SV100 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1366,plain,
! [SV155: $i,SV101: $i,SV178: $i] :
( ( ~ ( relation_of2_as_subset @ SV178 @ SV101 @ SV155 )
| ( element @ SV178 @ ( powerset @ ( cartesian_product2 @ SV101 @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1367,plain,
! [SV156: $i,SV8: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( element @ SV102 @ ( powerset @ SV8 ) )
| ~ ( element @ SV156 @ ( powerset @ SV8 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV8 @ SV102 @ SV156 )
= ( set_intersection2 @ SV102 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1368,plain,
( ( ~ ( rel_str @ sK2_SX0 )
| ~ ( strict_rel_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1369,plain,
! [SV103: $i,SV9: $i,SV157: $i] :
( ( ( ~ ( relation_of2 @ SV157 @ SV9 @ SV103 ) )
= $true )
| ( ( element @ ( relation_dom_as_subset @ SV9 @ SV103 @ SV157 ) @ ( powerset @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1264]) ).
thf(1370,plain,
! [SV11: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV11 )
| ~ ( rel_str @ SV11 ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( element @ SY222 @ ( the_carrier @ SV11 ) )
| ! [SY223: $i] :
( ~ ( element @ SY223 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY222 @ SY223 )
| ~ ( related @ SV11 @ SY223 @ SY222 ) )
| ( SY222 = SY223 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1266]) ).
thf(1371,plain,
! [SV104: $i,SV12: $i] :
( ( ( ~ ( ~ ( top_str @ SV12 )
| ~ ( element @ SV104 @ ( powerset @ ( the_carrier @ SV12 ) ) ) ) )
= $false )
| ( ( element @ ( topstr_closure @ SV12 @ SV104 ) @ ( powerset @ ( the_carrier @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1372,plain,
! [SV13: $i] :
( ( ( ~ ( ( ( relation_dom @ SV13 )
= empty_set )
| ( ( relation_rng @ SV13 )
= empty_set ) ) )
= $true )
| ( ( SV13 = empty_set )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1373,plain,
! [SV158: $i,SV14: $i,SV105: $i] :
( ( ( ~ ~ ( ~ ( element @ SV105 @ ( powerset @ SV14 ) )
| ~ ( element @ SV158 @ ( powerset @ SV14 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV14 @ SV105 @ SV158 )
= ( subset_intersection2 @ SV14 @ SV158 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1269]) ).
thf(1374,plain,
! [SV15: $i,SV106: $i] :
( ( ( element @ SV106 @ ( powerset @ SV15 ) )
= $false )
| ( ( ( subset_complement @ SV15 @ SV106 )
= ( set_difference @ SV15 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1375,plain,
( ( element @ sK3_SX0 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1272]) ).
thf(1376,plain,
( ( ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK3_SX0 )
| ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1377,plain,
! [SV17: $i,SV107: $i] :
( ( ( element @ SV107 @ ( powerset @ SV17 ) )
= $false )
| ( ( ( subset_complement @ SV17 @ ( subset_complement @ SV17 @ SV107 ) )
= SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1378,plain,
! [SV18: $i,SV108: $i] :
( ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ( ~ ( ( SV108 != empty_set ) )
| ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ( SV108 != empty_set ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1379,plain,
! [SV159: $i,SV19: $i,SV109: $i] :
( ( ( ~ ~ ( ~ ( element @ SV109 @ ( powerset @ SV19 ) )
| ~ ( element @ SV159 @ ( powerset @ SV19 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV19 @ SV109 @ SV109 )
= SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1380,plain,
! [SV110: $i,SV20: $i] :
( ( ~ ( ( ( set_difference @ SV20 @ SV110 )
!= empty_set )
| ( subset @ SV20 @ SV110 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1277]) ).
thf(1381,plain,
! [SV110: $i,SV20: $i] :
( ( ~ ( ~ ( subset @ SV20 @ SV110 )
| ( ( set_difference @ SV20 @ SV110 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1277]) ).
thf(1382,plain,
! [SV21: $i,SV111: $i] :
( ( ( element @ SV111 @ ( powerset @ ( powerset @ SV21 ) ) )
= $false )
| ( ( ( union_of_subsets @ SV21 @ SV111 )
= ( union @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1383,plain,
! [SV112: $i,SV22: $i] :
( ( ~ ( ~ ( ( SV22 != empty_set ) )
| ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) )
| ~ ( ~ ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1279]) ).
thf(1384,plain,
! [SV112: $i,SV22: $i] :
( ( ~ ( ( SV22 != empty_set )
| ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1279]) ).
thf(1385,plain,
! [SV179: $i,SV24: $i] :
( ( ( ! [SY373: $i] :
( ~ ( element @ SY373 @ ( the_carrier @ SV24 ) )
| ~ ( ~ ( ~ ( relstr_element_smaller @ SV24 @ SV179 @ SY373 )
| ! [SY374: $i] :
( ~ ( element @ SY374 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY374 @ SV179 )
| ( related @ SV24 @ SY373 @ SY374 ) ) )
| ~ ( ~ ! [SY375: $i] :
( ~ ( element @ SY375 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY375 @ SV179 )
| ( related @ SV24 @ SY373 @ SY375 ) )
| ( relstr_element_smaller @ SV24 @ SV179 @ SY373 ) ) ) ) )
= $true )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1386,plain,
! [SV160: $i,SV113: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( in @ SV25 @ SV113 )
| ~ ( element @ SV113 @ ( powerset @ SV160 ) ) ) )
= $true )
| ( ( element @ SV25 @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1387,plain,
! [SV114: $i,SV26: $i] :
( ( ~ ( ~ ( disjoint @ SV26 @ SV114 )
| ( ( set_intersection2 @ SV26 @ SV114 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1388,plain,
! [SV114: $i,SV26: $i] :
( ( ~ ( ( ( set_intersection2 @ SV26 @ SV114 )
!= empty_set )
| ( disjoint @ SV26 @ SV114 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1389,plain,
! [SV27: $i] :
( ( ( SV27 = empty_set )
= $true )
| ( ( ! [SY248: $i] :
( ~ ( element @ SY248 @ ( powerset @ SV27 ) )
| ! [SY249: $i] :
( ~ ( element @ SY249 @ SV27 )
| ~ ~ ( in @ SY249 @ SY248 )
| ( in @ SY249 @ ( subset_complement @ SV27 @ SY248 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1284]) ).
thf(1390,plain,
! [SV115: $i,SV28: $i] :
( ( ( ! [SY348: $i] :
( ~ ( in @ SY348 @ SV28 )
| ( in @ SY348 @ SV115 ) ) )
= $false )
| ( ( element @ SV28 @ ( powerset @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1391,plain,
! [SV29: $i] :
( ( ~ ( ~ ( element @ ( sK5_SY252 @ SV29 ) @ ( powerset @ SV29 ) )
| ~ ( empty @ ( sK5_SY252 @ SV29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1286]) ).
thf(1392,plain,
! [SV116: $i,SV30: $i] :
( ( ( ~ ( ~ ( top_str @ SV30 )
| ~ ( element @ SV116 @ ( powerset @ ( the_carrier @ SV30 ) ) ) ) )
= $false )
| ( ( element @ ( interior @ SV30 @ SV116 ) @ ( powerset @ ( the_carrier @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1393,plain,
! [SV31: $i,SV117: $i] :
( ( ( element @ SV117 @ ( powerset @ ( powerset @ SV31 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV31 @ SV117 ) @ ( powerset @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1394,plain,
! [SV118: $i,SV33: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV33 )
| ~ ( latt_str @ SV33 ) ) )
= $false )
| ( ( element @ ( join_of_latt_set @ SV33 @ SV118 ) @ ( the_carrier @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1395,plain,
! [SV34: $i] :
( ( ( empty @ SV34 )
= $true )
| ( ( ~ ! [SY256: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY256 @ ( powerset @ SV34 ) )
| ~ ~ ( empty @ SY256 ) )
| ~ ( finite @ SY256 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1291]) ).
thf(1396,plain,
! [SV119: $i,SV35: $i] :
( ( ( in @ SV35 @ SV119 )
= $false )
| ( ( element @ SV35 @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1397,plain,
! [SV36: $i,SV120: $i] :
( ( ( element @ SV120 @ ( powerset @ ( powerset @ SV36 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV120 != empty_set ) )
| ( ( complements_of_subsets @ SV36 @ SV120 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1398,plain,
! [SV121: $i,SV37: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV37 )
| ~ ( latt_str @ SV37 ) ) )
= $false )
| ( ( element @ ( meet_of_latt_set @ SV37 @ SV121 ) @ ( the_carrier @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1399,plain,
! [SV38: $i] :
( ( ( ~ ! [SY260: $i,SY261: $i] :
~ ( in @ ( ordered_pair @ SY260 @ SY261 ) @ SV38 ) )
= $true )
| ( ( SV38 = empty_set )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1400,plain,
! [SV39: $i,SV122: $i] :
( ( ( element @ SV122 @ ( powerset @ ( powerset @ SV39 ) ) )
= $false )
| ( ( ( meet_of_subsets @ SV39 @ SV122 )
= ( set_meet @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1401,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) )
| ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
| ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1402,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) )
| ~ ( element @ SV162 @ SV41 ) )
| ~ ( element @ SV180 @ SV124 ) )
| ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1403,plain,
! [SV44: $i,SV181: $i] :
( ( ( ~ ( element @ SV181 @ ( powerset @ SV44 ) )
| ( v1_membered @ SV181 ) )
= $true )
| ( ( v1_membered @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1404,plain,
! [SV163: $i,SV45: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ( element @ SV125 @ ( powerset @ SV45 ) )
| ~ ( element @ SV163 @ ( powerset @ SV45 ) ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV45 @ SV125 @ SV163 ) @ ( powerset @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1303]) ).
thf(1405,plain,
! [SV46: $i,SV182: $i] :
( ( ( ~ ( element @ SV182 @ ( powerset @ SV46 ) )
| ( finite @ SV182 ) )
= $true )
| ( ( finite @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1406,plain,
! [SV47: $i,SV126: $i] :
( ( ( element @ SV126 @ ( powerset @ SV47 ) )
= $false )
| ( ( ! [SY353: $i] :
( ~ ( in @ SY353 @ SV126 )
| ( in @ SY353 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1407,plain,
! [SV48: $i] :
( ( ( ~ ( ( ( relation_dom @ SV48 )
!= empty_set )
| ( ( relation_rng @ SV48 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV48 )
!= empty_set )
| ( ( relation_dom @ SV48 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1408,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) )
| ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
| ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1307]) ).
thf(1409,plain,
! [SV50: $i] :
( ( element @ ( sK6_SY276 @ SV50 ) @ SV50 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1308]) ).
thf(1410,plain,
! [SV128: $i,SV52: $i] :
( ( ~ ( ~ ~ ( empty @ SV52 )
| ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( in @ SV128 @ SV52 ) )
| ~ ( ~ ( in @ SV128 @ SV52 )
| ( element @ SV128 @ SV52 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1411,plain,
! [SV128: $i,SV52: $i] :
( ( ~ ( ~ ( empty @ SV52 )
| ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( empty @ SV128 ) )
| ~ ( ~ ( empty @ SV128 )
| ( element @ SV128 @ SV52 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1412,plain,
! [SV165: $i,SV54: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ( element @ SV129 @ ( powerset @ SV54 ) )
| ~ ( element @ SV165 @ ( powerset @ SV54 ) ) ) )
= $true )
| ( ( ( subset_union2 @ SV54 @ SV129 @ SV165 )
= ( set_union2 @ SV129 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1413,plain,
! [SV166: $i,SV56: $i,SV130: $i] :
( ( ( ~ ~ ( ~ ( element @ SV130 @ ( powerset @ SV56 ) )
| ~ ( element @ SV166 @ ( powerset @ SV56 ) ) ) )
= $true )
| ( ( ( subset_difference @ SV56 @ SV130 @ SV166 )
= ( set_difference @ SV130 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1414,plain,
! [SV57: $i] :
( ( ( SV57 != empty_set )
| ! [SY282: $i] :
~ ( in @ SY282 @ SV57 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1315]) ).
thf(1415,plain,
! [SV57: $i] :
( ( ~ ! [SY283: $i] :
~ ( in @ SY283 @ SV57 )
| ( SV57 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1316]) ).
thf(1416,plain,
! [SV58: $i,SV183: $i] :
( ( ( ~ ( element @ SV183 @ SV58 )
| ( v1_xcmplx_0 @ SV183 ) )
= $true )
| ( ( v1_membered @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1417,plain,
! [SV131: $i,SV59: $i,SV167: $i] :
( ( ( ~ ( element @ SV167 @ ( powerset @ ( cartesian_product2 @ SV59 @ SV131 ) ) ) )
= $true )
| ( ( relation @ SV167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1418,plain,
! [SV60: $i] :
( ( lower_bounded_semilattstr @ ( boole_lattice @ SV60 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1319]) ).
thf(1419,plain,
! [SV60: $i] :
( ( ( bottom_of_semilattstr @ ( boole_lattice @ SV60 ) )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1320]) ).
thf(1420,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set ) )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
| ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) )
| ~ ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1421,plain,
! [SV62: $i,SV184: $i] :
( ( ( ~ ( element @ SV184 @ SV62 )
| ~ ( ~ ( v1_xcmplx_0 @ SV184 )
| ~ ( v1_xreal_0 @ SV184 ) ) )
= $true )
| ( ( v2_membered @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1422,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1423,plain,
! [SV133: $i,SV64: $i] :
( ( ~ ( ~ ( subset @ SV64 @ ( singleton @ SV133 ) )
| ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1326]) ).
thf(1424,plain,
! [SV133: $i,SV64: $i] :
( ( ~ ( ~ ( ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) )
| ( subset @ SV64 @ ( singleton @ SV133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1326]) ).
thf(1425,plain,
! [SV134: $i,SV65: $i,SV169: $i] :
( ( ( ~ ( element @ SV169 @ ( powerset @ SV65 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( in @ SV134 @ ( subset_complement @ SV65 @ SV169 ) )
| ~ ( in @ SV134 @ SV169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1426,plain,
! [SV170: $i,SV66: $i,SV135: $i] :
( ( ( ~ ~ ( ~ ( element @ SV135 @ ( powerset @ SV66 ) )
| ~ ( element @ SV170 @ ( powerset @ SV66 ) ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV66 @ SV135 @ SV170 ) @ ( powerset @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1427,plain,
! [SV67: $i,SV136: $i] :
( ( ( element @ SV136 @ SV67 )
= $false )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV136 @ SV67 )
| ( SV136
!= ( union @ SV67 ) ) )
| ~ ( ~ ( ( SV136
!= ( union @ SV67 ) ) )
| ( proper_element @ SV136 @ SV67 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1428,plain,
! [SV68: $i] :
( ( ( ~ ( strict_rel_str @ SV68 ) )
= $true )
| ( ( SV68
= ( rel_str_of @ ( the_carrier @ SV68 ) @ ( the_InternalRel @ SV68 ) ) )
= $true )
| ( ( rel_str @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1429,plain,
! [SV69: $i,SV185: $i] :
( ( ( ~ ( element @ SV185 @ SV69 )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV185 )
| ~ ( epsilon_connected @ SV185 ) )
| ~ ( ordinal @ SV185 ) ) )
= $true )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1430,plain,
! [SV186: $i,SV71: $i] :
( ( ( ! [SY376: $i] :
( ~ ( element @ SY376 @ ( the_carrier @ SV71 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SV71 @ SV186 @ SY376 )
| ! [SY377: $i] :
( ~ ( element @ SY377 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY377 @ SV186 )
| ( related @ SV71 @ SY377 @ SY376 ) ) )
| ~ ( ~ ! [SY378: $i] :
( ~ ( element @ SY378 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY378 @ SV186 )
| ( related @ SV71 @ SY378 @ SY376 ) )
| ( relstr_set_smaller @ SV71 @ SV186 @ SY376 ) ) ) ) )
= $true )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1431,plain,
! [SV72: $i,SV137: $i] :
( ( ( relation_of2 @ SV137 @ SV72 @ SV72 )
= $false )
| ( ( ~ ( ~ ( strict_rel_str @ ( rel_str_of @ SV72 @ SV137 ) )
| ~ ( rel_str @ ( rel_str_of @ SV72 @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1432,plain,
! [SV73: $i] :
( ( ( ~ ( transitive_relstr @ SV73 )
| ~ ( rel_str @ SV73 ) )
= $true )
| ( ( ! [SY302: $i] :
( ~ ( element @ SY302 @ ( the_carrier @ SV73 ) )
| ! [SY303: $i] :
( ~ ( element @ SY303 @ ( the_carrier @ SV73 ) )
| ! [SY304: $i] :
( ~ ( element @ SY304 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SY302 @ SY303 )
| ~ ( related @ SV73 @ SY303 @ SY304 ) )
| ( related @ SV73 @ SY302 @ SY304 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1433,plain,
! [SV74: $i] :
( ( ( empty @ SV74 )
= $true )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( element @ SY305 @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ SY305 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1434,plain,
! [SV75: $i,SV187: $i] :
( ( ( ~ ( element @ SV187 @ ( powerset @ SV75 ) )
| ~ ( ~ ( v1_membered @ SV187 )
| ~ ( v2_membered @ SV187 ) ) )
= $true )
| ( ( v2_membered @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1435,plain,
! [SV171: $i,SV76: $i,SV138: $i] :
( ( ( ~ ~ ( ~ ( element @ SV138 @ ( powerset @ SV76 ) )
| ~ ( element @ SV171 @ ( powerset @ SV76 ) ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV76 @ SV138 @ SV171 ) @ ( powerset @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1436,plain,
! [SV77: $i] :
( ( ( ~ ( ~ ( empty_carrier @ SV77 )
| ( empty @ ( the_carrier @ SV77 ) ) )
| ~ ( ~ ( empty @ ( the_carrier @ SV77 ) )
| ( empty_carrier @ SV77 ) ) )
= $false )
| ( ( one_sorted_str @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1437,plain,
! [SV78: $i] :
( ( ( ~ ( ~ ( antisymmetric_relstr @ SV78 )
| ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) )
| ( antisymmetric_relstr @ SV78 ) ) )
= $false )
| ( ( rel_str @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1438,plain,
! [SV79: $i,SV139: $i] :
( ( ( element @ SV139 @ ( powerset @ ( powerset @ SV79 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV79 @ SV139 ) @ ( powerset @ ( powerset @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1439,plain,
! [SV140: $i,SV80: $i] :
( ( ~ ( ~ ( element @ SV80 @ ( powerset @ SV140 ) )
| ( subset @ SV80 @ SV140 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1440,plain,
! [SV140: $i,SV80: $i] :
( ( ~ ( ~ ( subset @ SV80 @ SV140 )
| ( element @ SV80 @ ( powerset @ SV140 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1441,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( ~ ( subset @ SV81 @ ( singleton @ SV141 ) )
| ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1442,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( ~ ( ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) )
| ( subset @ SV81 @ ( singleton @ SV141 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1443,plain,
! [SV82: $i,SV142: $i] :
( ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false )
| ( ( ! [SY362: $i] :
( ~ ( element @ SY362 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
| ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SY362 )
| ( subset @ SV142 @ SY362 ) )
| ~ ( ~ ( subset @ SV142 @ SY362 )
| ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SY362 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1444,plain,
! [SV83: $i] :
( ( ( empty @ SV83 )
= $true )
| ( ( ~ ! [SY314: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY314 @ ( powerset @ SV83 ) )
| ~ ~ ( empty @ SY314 ) )
| ~ ( finite @ SY314 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1344]) ).
thf(1445,plain,
! [SV84: $i] :
( ( ( ~ ~ ( empty_carrier @ SV84 )
| ~ ( meet_semilatt_str @ SV84 ) )
= $true )
| ( ( element @ ( bottom_of_semilattstr @ SV84 ) @ ( the_carrier @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1345]) ).
thf(1446,plain,
! [SV85: $i,SV143: $i] :
( ( ( element @ SV143 @ ( powerset @ ( powerset @ SV85 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV85 @ SV143 ) @ ( powerset @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1447,plain,
! [SV86: $i] :
( ( ( ~ ( ~ ( transitive_relstr @ SV86 )
| ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) ) )
| ~ ( ~ ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) )
| ( transitive_relstr @ SV86 ) ) )
= $false )
| ( ( rel_str @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1448,plain,
! [SV87: $i] :
( ( ( ~ ~ ( empty_carrier @ SV87 )
| ~ ( one_sorted_str @ SV87 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1352]) ).
thf(1449,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) )
| ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
| ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1450,plain,
! [SV145: $i,SV89: $i] :
( ( ~ ( ( ( set_difference @ SV89 @ SV145 )
!= empty_set )
| ( subset @ SV89 @ SV145 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1451,plain,
! [SV145: $i,SV89: $i] :
( ( ~ ( ~ ( subset @ SV89 @ SV145 )
| ( ( set_difference @ SV89 @ SV145 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1452,plain,
! [SV173: $i,SV146: $i,SV90: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV90 @ SV146 )
| ~ ( element @ SV146 @ ( powerset @ SV173 ) ) )
| ~ ( empty @ SV173 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1453,plain,
! [SV174: $i,SV91: $i,SV147: $i] :
( ( ( ~ ~ ( ~ ( element @ SV147 @ ( powerset @ SV91 ) )
| ~ ( element @ SV174 @ ( powerset @ SV91 ) ) ) )
= $true )
| ( ( ( subset_union2 @ SV91 @ SV147 @ SV174 )
= ( subset_union2 @ SV91 @ SV174 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1454,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) )
| ~ ( element @ SV175 @ SV92 ) )
| ~ ( element @ SV188 @ SV148 ) )
| ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1455,plain,
! [SV149: $i,SV93: $i] :
( ( ( element @ SV93 @ SV149 )
= $false )
| ( ( ( empty @ SV149 )
| ( in @ SV93 @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1456,plain,
! [SV94: $i,SV150: $i] :
( ( ( element @ SV150 @ ( powerset @ SV94 ) )
= $false )
| ( ( element @ ( subset_complement @ SV94 @ SV150 ) @ ( powerset @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1457,plain,
! [SV96: $i,SV151: $i] :
( ( ( element @ SV151 @ ( powerset @ ( powerset @ SV96 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV96 @ ( complements_of_subsets @ SV96 @ SV151 ) )
= SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1458,plain,
! [SV97: $i] :
( ( ~ ( ~ ( element @ ( sK7_SY329 @ SV97 ) @ ( powerset @ SV97 ) )
| ~ ~ ( proper_element @ ( sK7_SY329 @ SV97 ) @ ( powerset @ SV97 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1459,plain,
! [SV176: $i,SV98: $i,SV152: $i] :
( ( ( ~ ~ ( ~ ( element @ SV152 @ ( powerset @ SV98 ) )
| ~ ( element @ SV176 @ ( powerset @ SV98 ) ) ) )
= $true )
| ( ( ( subset_union2 @ SV98 @ SV152 @ SV152 )
= SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1460,plain,
! [SV153: $i,SV99: $i,SV177: $i] :
( ( ( ~ ( relation_of2 @ SV177 @ SV99 @ SV153 ) )
= $true )
| ( ( element @ ( relation_rng_as_subset @ SV99 @ SV153 @ SV177 ) @ ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1364]) ).
thf(1461,plain,
! [SV100: $i,SV154: $i] :
( ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV154 @ ( powerset @ SV100 ) )
| ( SV154 != SV100 ) )
| ~ ( ~ ( ( SV154 != SV100 ) )
| ( proper_element @ SV154 @ ( powerset @ SV100 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1462,plain,
! [SV155: $i,SV101: $i,SV178: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV178 @ SV101 @ SV155 ) )
= $true )
| ( ( element @ SV178 @ ( powerset @ ( cartesian_product2 @ SV101 @ SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1463,plain,
! [SV156: $i,SV8: $i,SV102: $i] :
( ( ( ~ ( ~ ( element @ SV102 @ ( powerset @ SV8 ) )
| ~ ( element @ SV156 @ ( powerset @ SV8 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV8 @ SV102 @ SV156 )
= ( set_intersection2 @ SV102 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1464,plain,
( ( ~ ( rel_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1465,plain,
( ( ~ ( strict_rel_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1466,plain,
! [SV103: $i,SV9: $i,SV157: $i] :
( ( ( relation_of2 @ SV157 @ SV9 @ SV103 )
= $false )
| ( ( element @ ( relation_dom_as_subset @ SV9 @ SV103 @ SV157 ) @ ( powerset @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1467,plain,
! [SV11: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV11 ) )
= $true )
| ( ( ~ ( rel_str @ SV11 ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( element @ SY222 @ ( the_carrier @ SV11 ) )
| ! [SY223: $i] :
( ~ ( element @ SY223 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY222 @ SY223 )
| ~ ( related @ SV11 @ SY223 @ SY222 ) )
| ( SY222 = SY223 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1370]) ).
thf(1468,plain,
! [SV104: $i,SV12: $i] :
( ( ( ~ ( top_str @ SV12 )
| ~ ( element @ SV104 @ ( powerset @ ( the_carrier @ SV12 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV12 @ SV104 ) @ ( powerset @ ( the_carrier @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1371]) ).
thf(1469,plain,
! [SV13: $i] :
( ( ( ( ( relation_dom @ SV13 )
= empty_set )
| ( ( relation_rng @ SV13 )
= empty_set ) )
= $false )
| ( ( SV13 = empty_set )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1470,plain,
! [SV158: $i,SV14: $i,SV105: $i] :
( ( ( ~ ( ~ ( element @ SV105 @ ( powerset @ SV14 ) )
| ~ ( element @ SV158 @ ( powerset @ SV14 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV14 @ SV105 @ SV158 )
= ( subset_intersection2 @ SV14 @ SV158 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1471,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK3_SX0 ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK3_SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1472,plain,
! [SV18: $i,SV108: $i] :
( ( ( ~ ~ ~ ( ~ ( ( SV108 != empty_set ) )
| ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ( SV108 != empty_set ) ) )
= $false )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1473,plain,
! [SV159: $i,SV19: $i,SV109: $i] :
( ( ( ~ ( ~ ( element @ SV109 @ ( powerset @ SV19 ) )
| ~ ( element @ SV159 @ ( powerset @ SV19 ) ) ) )
= $false )
| ( ( ( subset_intersection2 @ SV19 @ SV109 @ SV109 )
= SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1474,plain,
! [SV110: $i,SV20: $i] :
( ( ( ( set_difference @ SV20 @ SV110 )
!= empty_set )
| ( subset @ SV20 @ SV110 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1380]) ).
thf(1475,plain,
! [SV110: $i,SV20: $i] :
( ( ~ ( subset @ SV20 @ SV110 )
| ( ( set_difference @ SV20 @ SV110 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1381]) ).
thf(1476,plain,
! [SV112: $i,SV22: $i] :
( ( ~ ( ( SV22 != empty_set ) )
| ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) )
| ~ ( ~ ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1383]) ).
thf(1477,plain,
! [SV112: $i,SV22: $i] :
( ( ( SV22 != empty_set )
| ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1384]) ).
thf(1478,plain,
! [SV179: $i,SV24: $i,SV189: $i] :
( ( ( ~ ( element @ SV189 @ ( the_carrier @ SV24 ) )
| ~ ( ~ ( ~ ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
| ! [SY379: $i] :
( ~ ( element @ SY379 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY379 @ SV179 )
| ( related @ SV24 @ SV189 @ SY379 ) ) )
| ~ ( ~ ! [SY380: $i] :
( ~ ( element @ SY380 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY380 @ SV179 )
| ( related @ SV24 @ SV189 @ SY380 ) )
| ( relstr_element_smaller @ SV24 @ SV179 @ SV189 ) ) ) )
= $true )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1479,plain,
! [SV160: $i,SV113: $i,SV25: $i] :
( ( ( ~ ( ~ ( in @ SV25 @ SV113 )
| ~ ( element @ SV113 @ ( powerset @ SV160 ) ) ) )
= $false )
| ( ( element @ SV25 @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1480,plain,
! [SV114: $i,SV26: $i] :
( ( ~ ( disjoint @ SV26 @ SV114 )
| ( ( set_intersection2 @ SV26 @ SV114 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1387]) ).
thf(1481,plain,
! [SV114: $i,SV26: $i] :
( ( ( ( set_intersection2 @ SV26 @ SV114 )
!= empty_set )
| ( disjoint @ SV26 @ SV114 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1388]) ).
thf(1482,plain,
! [SV27: $i,SV190: $i] :
( ( ( ~ ( element @ SV190 @ ( powerset @ SV27 ) )
| ! [SY381: $i] :
( ~ ( element @ SY381 @ SV27 )
| ~ ~ ( in @ SY381 @ SV190 )
| ( in @ SY381 @ ( subset_complement @ SV27 @ SV190 ) ) ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1483,plain,
! [SV28: $i,SV115: $i] :
( ( ( ~ ( in @ ( sK8_SY348 @ SV115 @ SV28 ) @ SV28 )
| ( in @ ( sK8_SY348 @ SV115 @ SV28 ) @ SV115 ) )
= $false )
| ( ( element @ SV28 @ ( powerset @ SV115 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1390]) ).
thf(1484,plain,
! [SV29: $i] :
( ( ~ ( element @ ( sK5_SY252 @ SV29 ) @ ( powerset @ SV29 ) )
| ~ ( empty @ ( sK5_SY252 @ SV29 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1485,plain,
! [SV116: $i,SV30: $i] :
( ( ( ~ ( top_str @ SV30 )
| ~ ( element @ SV116 @ ( powerset @ ( the_carrier @ SV30 ) ) ) )
= $true )
| ( ( element @ ( interior @ SV30 @ SV116 ) @ ( powerset @ ( the_carrier @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1392]) ).
thf(1486,plain,
! [SV118: $i,SV33: $i] :
( ( ( ~ ~ ( empty_carrier @ SV33 )
| ~ ( latt_str @ SV33 ) )
= $true )
| ( ( element @ ( join_of_latt_set @ SV33 @ SV118 ) @ ( the_carrier @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1394]) ).
thf(1487,plain,
! [SV34: $i] :
( ( ( ! [SY256: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY256 @ ( powerset @ SV34 ) )
| ~ ~ ( empty @ SY256 ) )
| ~ ( finite @ SY256 ) ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1488,plain,
! [SV36: $i,SV120: $i] :
( ( ( ~ ( ~ ( ( SV120 != empty_set ) )
| ( ( complements_of_subsets @ SV36 @ SV120 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV120 @ ( powerset @ ( powerset @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1489,plain,
! [SV121: $i,SV37: $i] :
( ( ( ~ ~ ( empty_carrier @ SV37 )
| ~ ( latt_str @ SV37 ) )
= $true )
| ( ( element @ ( meet_of_latt_set @ SV37 @ SV121 ) @ ( the_carrier @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1398]) ).
thf(1490,plain,
! [SV38: $i] :
( ( ( ! [SY260: $i,SY261: $i] :
~ ( in @ ( ordered_pair @ SY260 @ SY261 ) @ SV38 ) )
= $false )
| ( ( SV38 = empty_set )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1491,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) )
| ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
| ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) ) )
= $false )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1492,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) )
| ~ ( element @ SV162 @ SV41 ) )
| ~ ( element @ SV180 @ SV124 ) ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1493,plain,
! [SV44: $i,SV181: $i] :
( ( ( ~ ( element @ SV181 @ ( powerset @ SV44 ) ) )
= $true )
| ( ( v1_membered @ SV181 )
= $true )
| ( ( v1_membered @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1494,plain,
! [SV163: $i,SV45: $i,SV125: $i] :
( ( ( ~ ( ~ ( element @ SV125 @ ( powerset @ SV45 ) )
| ~ ( element @ SV163 @ ( powerset @ SV45 ) ) ) )
= $false )
| ( ( element @ ( subset_difference @ SV45 @ SV125 @ SV163 ) @ ( powerset @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1495,plain,
! [SV46: $i,SV182: $i] :
( ( ( ~ ( element @ SV182 @ ( powerset @ SV46 ) ) )
= $true )
| ( ( finite @ SV182 )
= $true )
| ( ( finite @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1496,plain,
! [SV47: $i,SV126: $i,SV191: $i] :
( ( ( ~ ( in @ SV191 @ SV126 )
| ( in @ SV191 @ SV47 ) )
= $true )
| ( ( element @ SV126 @ ( powerset @ SV47 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1497,plain,
! [SV48: $i] :
( ( ( ~ ( ( ( relation_dom @ SV48 )
!= empty_set )
| ( ( relation_rng @ SV48 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1498,plain,
! [SV48: $i] :
( ( ( ~ ( ( ( relation_rng @ SV48 )
!= empty_set )
| ( ( relation_dom @ SV48 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1499,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) )
| ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
| ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) ) )
= $false )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1500,plain,
! [SV128: $i,SV52: $i] :
( ( ~ ~ ( empty @ SV52 )
| ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( in @ SV128 @ SV52 ) )
| ~ ( ~ ( in @ SV128 @ SV52 )
| ( element @ SV128 @ SV52 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1410]) ).
thf(1501,plain,
! [SV128: $i,SV52: $i] :
( ( ~ ( empty @ SV52 )
| ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( empty @ SV128 ) )
| ~ ( ~ ( empty @ SV128 )
| ( element @ SV128 @ SV52 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1411]) ).
thf(1502,plain,
! [SV165: $i,SV54: $i,SV129: $i] :
( ( ( ~ ( ~ ( element @ SV129 @ ( powerset @ SV54 ) )
| ~ ( element @ SV165 @ ( powerset @ SV54 ) ) ) )
= $false )
| ( ( ( subset_union2 @ SV54 @ SV129 @ SV165 )
= ( set_union2 @ SV129 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1503,plain,
! [SV166: $i,SV56: $i,SV130: $i] :
( ( ( ~ ( ~ ( element @ SV130 @ ( powerset @ SV56 ) )
| ~ ( element @ SV166 @ ( powerset @ SV56 ) ) ) )
= $false )
| ( ( ( subset_difference @ SV56 @ SV130 @ SV166 )
= ( set_difference @ SV130 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1504,plain,
! [SV57: $i] :
( ( ( SV57 != empty_set )
= $true )
| ( ( ! [SY282: $i] :
~ ( in @ SY282 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1414]) ).
thf(1505,plain,
! [SV57: $i] :
( ( ( ~ ! [SY283: $i] :
~ ( in @ SY283 @ SV57 ) )
= $true )
| ( ( SV57 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1506,plain,
! [SV58: $i,SV183: $i] :
( ( ( ~ ( element @ SV183 @ SV58 ) )
= $true )
| ( ( v1_xcmplx_0 @ SV183 )
= $true )
| ( ( v1_membered @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1507,plain,
! [SV131: $i,SV59: $i,SV167: $i] :
( ( ( element @ SV167 @ ( powerset @ ( cartesian_product2 @ SV59 @ SV131 ) ) )
= $false )
| ( ( relation @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1508,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false )
| ( ( ~ ( ~ ( ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set ) )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
| ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) )
| ~ ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1509,plain,
! [SV62: $i,SV184: $i] :
( ( ( ~ ( element @ SV184 @ SV62 ) )
= $true )
| ( ( ~ ( ~ ( v1_xcmplx_0 @ SV184 )
| ~ ( v1_xreal_0 @ SV184 ) ) )
= $true )
| ( ( v2_membered @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1510,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1422]) ).
thf(1511,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1422]) ).
thf(1512,plain,
! [SV133: $i,SV64: $i] :
( ( ~ ( subset @ SV64 @ ( singleton @ SV133 ) )
| ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1423]) ).
thf(1513,plain,
! [SV133: $i,SV64: $i] :
( ( ~ ( ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) )
| ( subset @ SV64 @ ( singleton @ SV133 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1424]) ).
thf(1514,plain,
! [SV134: $i,SV65: $i,SV169: $i] :
( ( ( element @ SV169 @ ( powerset @ SV65 ) )
= $false )
| ( ( ~ ~ ( ~ ( in @ SV134 @ ( subset_complement @ SV65 @ SV169 ) )
| ~ ( in @ SV134 @ SV169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1515,plain,
! [SV170: $i,SV66: $i,SV135: $i] :
( ( ( ~ ( ~ ( element @ SV135 @ ( powerset @ SV66 ) )
| ~ ( element @ SV170 @ ( powerset @ SV66 ) ) ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV66 @ SV135 @ SV170 ) @ ( powerset @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1516,plain,
! [SV67: $i,SV136: $i] :
( ( ( ~ ( ~ ( proper_element @ SV136 @ SV67 )
| ( SV136
!= ( union @ SV67 ) ) )
| ~ ( ~ ( ( SV136
!= ( union @ SV67 ) ) )
| ( proper_element @ SV136 @ SV67 ) ) )
= $false )
| ( ( element @ SV136 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1517,plain,
! [SV68: $i] :
( ( ( strict_rel_str @ SV68 )
= $false )
| ( ( SV68
= ( rel_str_of @ ( the_carrier @ SV68 ) @ ( the_InternalRel @ SV68 ) ) )
= $true )
| ( ( rel_str @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1518,plain,
! [SV69: $i,SV185: $i] :
( ( ( ~ ( element @ SV185 @ SV69 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV185 )
| ~ ( epsilon_connected @ SV185 ) )
| ~ ( ordinal @ SV185 ) ) )
= $true )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1429]) ).
thf(1519,plain,
! [SV186: $i,SV71: $i,SV192: $i] :
( ( ( ~ ( element @ SV192 @ ( the_carrier @ SV71 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
| ! [SY382: $i] :
( ~ ( element @ SY382 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY382 @ SV186 )
| ( related @ SV71 @ SY382 @ SV192 ) ) )
| ~ ( ~ ! [SY383: $i] :
( ~ ( element @ SY383 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY383 @ SV186 )
| ( related @ SV71 @ SY383 @ SV192 ) )
| ( relstr_set_smaller @ SV71 @ SV186 @ SV192 ) ) ) )
= $true )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1520,plain,
! [SV137: $i,SV72: $i] :
( ( ( ~ ( strict_rel_str @ ( rel_str_of @ SV72 @ SV137 ) )
| ~ ( rel_str @ ( rel_str_of @ SV72 @ SV137 ) ) )
= $false )
| ( ( relation_of2 @ SV137 @ SV72 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1521,plain,
! [SV73: $i] :
( ( ( ~ ( transitive_relstr @ SV73 ) )
= $true )
| ( ( ~ ( rel_str @ SV73 ) )
= $true )
| ( ( ! [SY302: $i] :
( ~ ( element @ SY302 @ ( the_carrier @ SV73 ) )
| ! [SY303: $i] :
( ~ ( element @ SY303 @ ( the_carrier @ SV73 ) )
| ! [SY304: $i] :
( ~ ( element @ SY304 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SY302 @ SY303 )
| ~ ( related @ SV73 @ SY303 @ SY304 ) )
| ( related @ SV73 @ SY302 @ SY304 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1522,plain,
! [SV74: $i] :
( ( ( ! [SY305: $i] :
~ ~ ( ~ ( element @ SY305 @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ SY305 ) ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1523,plain,
! [SV75: $i,SV187: $i] :
( ( ( ~ ( element @ SV187 @ ( powerset @ SV75 ) ) )
= $true )
| ( ( ~ ( ~ ( v1_membered @ SV187 )
| ~ ( v2_membered @ SV187 ) ) )
= $true )
| ( ( v2_membered @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1524,plain,
! [SV171: $i,SV76: $i,SV138: $i] :
( ( ( ~ ( ~ ( element @ SV138 @ ( powerset @ SV76 ) )
| ~ ( element @ SV171 @ ( powerset @ SV76 ) ) ) )
= $false )
| ( ( element @ ( subset_union2 @ SV76 @ SV138 @ SV171 ) @ ( powerset @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1525,plain,
! [SV77: $i] :
( ( ( ~ ( ~ ( empty_carrier @ SV77 )
| ( empty @ ( the_carrier @ SV77 ) ) ) )
= $false )
| ( ( one_sorted_str @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1526,plain,
! [SV77: $i] :
( ( ( ~ ( ~ ( empty @ ( the_carrier @ SV77 ) )
| ( empty_carrier @ SV77 ) ) )
= $false )
| ( ( one_sorted_str @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1527,plain,
! [SV78: $i] :
( ( ( ~ ( ~ ( antisymmetric_relstr @ SV78 )
| ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) ) ) )
= $false )
| ( ( rel_str @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1437]) ).
thf(1528,plain,
! [SV78: $i] :
( ( ( ~ ( ~ ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) )
| ( antisymmetric_relstr @ SV78 ) ) )
= $false )
| ( ( rel_str @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1437]) ).
thf(1529,plain,
! [SV140: $i,SV80: $i] :
( ( ~ ( element @ SV80 @ ( powerset @ SV140 ) )
| ( subset @ SV80 @ SV140 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1530,plain,
! [SV140: $i,SV80: $i] :
( ( ~ ( subset @ SV80 @ SV140 )
| ( element @ SV80 @ ( powerset @ SV140 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1531,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( subset @ SV81 @ ( singleton @ SV141 ) )
| ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1441]) ).
thf(1532,plain,
! [SV141: $i,SV81: $i] :
( ( ~ ( ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) )
| ( subset @ SV81 @ ( singleton @ SV141 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1442]) ).
thf(1533,plain,
! [SV142: $i,SV82: $i,SV193: $i] :
( ( ( ~ ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
| ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 )
| ( subset @ SV142 @ SV193 ) )
| ~ ( ~ ( subset @ SV142 @ SV193 )
| ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 ) ) ) )
= $true )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1534,plain,
! [SV83: $i] :
( ( ( ! [SY314: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY314 @ ( powerset @ SV83 ) )
| ~ ~ ( empty @ SY314 ) )
| ~ ( finite @ SY314 ) ) )
= $false )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1535,plain,
! [SV84: $i] :
( ( ( ~ ~ ( empty_carrier @ SV84 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV84 ) )
= $true )
| ( ( element @ ( bottom_of_semilattstr @ SV84 ) @ ( the_carrier @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1536,plain,
! [SV86: $i] :
( ( ( ~ ( ~ ( transitive_relstr @ SV86 )
| ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) ) ) )
= $false )
| ( ( rel_str @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1537,plain,
! [SV86: $i] :
( ( ( ~ ( ~ ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) )
| ( transitive_relstr @ SV86 ) ) )
= $false )
| ( ( rel_str @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1538,plain,
! [SV87: $i] :
( ( ( ~ ~ ( empty_carrier @ SV87 ) )
= $true )
| ( ( ~ ( one_sorted_str @ SV87 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1539,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) )
| ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
| ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) ) )
= $false )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1540,plain,
! [SV145: $i,SV89: $i] :
( ( ( ( set_difference @ SV89 @ SV145 )
!= empty_set )
| ( subset @ SV89 @ SV145 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1541,plain,
! [SV145: $i,SV89: $i] :
( ( ~ ( subset @ SV89 @ SV145 )
| ( ( set_difference @ SV89 @ SV145 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1451]) ).
thf(1542,plain,
! [SV173: $i,SV146: $i,SV90: $i] :
( ( ~ ~ ( ~ ( in @ SV90 @ SV146 )
| ~ ( element @ SV146 @ ( powerset @ SV173 ) ) )
| ~ ( empty @ SV173 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1543,plain,
! [SV174: $i,SV91: $i,SV147: $i] :
( ( ( ~ ( ~ ( element @ SV147 @ ( powerset @ SV91 ) )
| ~ ( element @ SV174 @ ( powerset @ SV91 ) ) ) )
= $false )
| ( ( ( subset_union2 @ SV91 @ SV147 @ SV174 )
= ( subset_union2 @ SV91 @ SV174 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1544,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) )
| ~ ( element @ SV175 @ SV92 ) )
| ~ ( element @ SV188 @ SV148 ) ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1545,plain,
! [SV93: $i,SV149: $i] :
( ( ( empty @ SV149 )
= $true )
| ( ( in @ SV93 @ SV149 )
= $true )
| ( ( element @ SV93 @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1546,plain,
! [SV97: $i] :
( ( ~ ( element @ ( sK7_SY329 @ SV97 ) @ ( powerset @ SV97 ) )
| ~ ~ ( proper_element @ ( sK7_SY329 @ SV97 ) @ ( powerset @ SV97 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1547,plain,
! [SV176: $i,SV98: $i,SV152: $i] :
( ( ( ~ ( ~ ( element @ SV152 @ ( powerset @ SV98 ) )
| ~ ( element @ SV176 @ ( powerset @ SV98 ) ) ) )
= $false )
| ( ( ( subset_union2 @ SV98 @ SV152 @ SV152 )
= SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1548,plain,
! [SV153: $i,SV99: $i,SV177: $i] :
( ( ( relation_of2 @ SV177 @ SV99 @ SV153 )
= $false )
| ( ( element @ ( relation_rng_as_subset @ SV99 @ SV153 @ SV177 ) @ ( powerset @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1549,plain,
! [SV100: $i,SV154: $i] :
( ( ( ~ ( ~ ( proper_element @ SV154 @ ( powerset @ SV100 ) )
| ( SV154 != SV100 ) )
| ~ ( ~ ( ( SV154 != SV100 ) )
| ( proper_element @ SV154 @ ( powerset @ SV100 ) ) ) )
= $false )
| ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1550,plain,
! [SV155: $i,SV101: $i,SV178: $i] :
( ( ( relation_of2_as_subset @ SV178 @ SV101 @ SV155 )
= $false )
| ( ( element @ SV178 @ ( powerset @ ( cartesian_product2 @ SV101 @ SV155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1462]) ).
thf(1551,plain,
! [SV156: $i,SV8: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV8 ) )
| ~ ( element @ SV156 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV8 @ SV102 @ SV156 )
= ( set_intersection2 @ SV102 @ SV156 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1463]) ).
thf(1552,plain,
( ( rel_str @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1553,plain,
( ( strict_rel_str @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1465]) ).
thf(1554,plain,
! [SV11: $i] :
( ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( ~ ( rel_str @ SV11 ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( element @ SY222 @ ( the_carrier @ SV11 ) )
| ! [SY223: $i] :
( ~ ( element @ SY223 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY222 @ SY223 )
| ~ ( related @ SV11 @ SY223 @ SY222 ) )
| ( SY222 = SY223 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1555,plain,
! [SV104: $i,SV12: $i] :
( ( ( ~ ( top_str @ SV12 ) )
= $true )
| ( ( ~ ( element @ SV104 @ ( powerset @ ( the_carrier @ SV12 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV12 @ SV104 ) @ ( powerset @ ( the_carrier @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1556,plain,
! [SV13: $i] :
( ( ( ( relation_dom @ SV13 )
= empty_set )
= $false )
| ( ( SV13 = empty_set )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1469]) ).
thf(1557,plain,
! [SV13: $i] :
( ( ( ( relation_rng @ SV13 )
= empty_set )
= $false )
| ( ( SV13 = empty_set )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1469]) ).
thf(1558,plain,
! [SV158: $i,SV14: $i,SV105: $i] :
( ( ( ~ ( element @ SV105 @ ( powerset @ SV14 ) )
| ~ ( element @ SV158 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV14 @ SV105 @ SV158 )
= ( subset_intersection2 @ SV14 @ SV158 @ SV105 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1559,plain,
( ( ( relstr_set_smaller @ sK1_A @ empty_set @ sK3_SX0 )
= $false )
| ( ( ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK3_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1560,plain,
! [SV18: $i,SV108: $i] :
( ( ( ~ ~ ~ ( ~ ( ( SV108 != empty_set ) )
| ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1561,plain,
! [SV108: $i,SV18: $i] :
( ( ( ~ ~ ~ ( ~ ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ( SV108 != empty_set ) ) )
= $false )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1562,plain,
! [SV159: $i,SV19: $i,SV109: $i] :
( ( ( ~ ( element @ SV109 @ ( powerset @ SV19 ) )
| ~ ( element @ SV159 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV19 @ SV109 @ SV109 )
= SV109 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1473]) ).
thf(1563,plain,
! [SV110: $i,SV20: $i] :
( ( ( ( set_difference @ SV20 @ SV110 )
!= empty_set )
= $true )
| ( ( subset @ SV20 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1564,plain,
! [SV110: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV110 ) )
= $true )
| ( ( ( set_difference @ SV20 @ SV110 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1475]) ).
thf(1565,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ( ( SV22 != empty_set ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) )
| ~ ( ~ ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1476]) ).
thf(1566,plain,
! [SV112: $i,SV22: $i] :
( ( ( SV22 != empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1477]) ).
thf(1567,plain,
! [SV179: $i,SV24: $i,SV189: $i] :
( ( ( ~ ( element @ SV189 @ ( the_carrier @ SV24 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
| ! [SY379: $i] :
( ~ ( element @ SY379 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY379 @ SV179 )
| ( related @ SV24 @ SV189 @ SY379 ) ) )
| ~ ( ~ ! [SY380: $i] :
( ~ ( element @ SY380 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY380 @ SV179 )
| ( related @ SV24 @ SV189 @ SY380 ) )
| ( relstr_element_smaller @ SV24 @ SV179 @ SV189 ) ) ) )
= $true )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1478]) ).
thf(1568,plain,
! [SV160: $i,SV113: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV113 )
| ~ ( element @ SV113 @ ( powerset @ SV160 ) ) )
= $true )
| ( ( element @ SV25 @ SV160 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1569,plain,
! [SV114: $i,SV26: $i] :
( ( ( ~ ( disjoint @ SV26 @ SV114 ) )
= $true )
| ( ( ( set_intersection2 @ SV26 @ SV114 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1570,plain,
! [SV114: $i,SV26: $i] :
( ( ( ( set_intersection2 @ SV26 @ SV114 )
!= empty_set )
= $true )
| ( ( disjoint @ SV26 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1481]) ).
thf(1571,plain,
! [SV27: $i,SV190: $i] :
( ( ( ~ ( element @ SV190 @ ( powerset @ SV27 ) ) )
= $true )
| ( ( ! [SY381: $i] :
( ~ ( element @ SY381 @ SV27 )
| ~ ~ ( in @ SY381 @ SV190 )
| ( in @ SY381 @ ( subset_complement @ SV27 @ SV190 ) ) ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1482]) ).
thf(1572,plain,
! [SV28: $i,SV115: $i] :
( ( ( ~ ( in @ ( sK8_SY348 @ SV115 @ SV28 ) @ SV28 ) )
= $false )
| ( ( element @ SV28 @ ( powerset @ SV115 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1573,plain,
! [SV28: $i,SV115: $i] :
( ( ( in @ ( sK8_SY348 @ SV115 @ SV28 ) @ SV115 )
= $false )
| ( ( element @ SV28 @ ( powerset @ SV115 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1574,plain,
! [SV29: $i] :
( ( ~ ( element @ ( sK5_SY252 @ SV29 ) @ ( powerset @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1575,plain,
! [SV29: $i] :
( ( ~ ( empty @ ( sK5_SY252 @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1576,plain,
! [SV116: $i,SV30: $i] :
( ( ( ~ ( top_str @ SV30 ) )
= $true )
| ( ( ~ ( element @ SV116 @ ( powerset @ ( the_carrier @ SV30 ) ) ) )
= $true )
| ( ( element @ ( interior @ SV30 @ SV116 ) @ ( powerset @ ( the_carrier @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1577,plain,
! [SV118: $i,SV33: $i] :
( ( ( ~ ~ ( empty_carrier @ SV33 ) )
= $true )
| ( ( ~ ( latt_str @ SV33 ) )
= $true )
| ( ( element @ ( join_of_latt_set @ SV33 @ SV118 ) @ ( the_carrier @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1578,plain,
! [SV34: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK9_SY256 @ SV34 ) @ ( powerset @ SV34 ) )
| ~ ~ ( empty @ ( sK9_SY256 @ SV34 ) ) )
| ~ ( finite @ ( sK9_SY256 @ SV34 ) ) ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1487]) ).
thf(1579,plain,
! [SV36: $i,SV120: $i] :
( ( ( ~ ( ( SV120 != empty_set ) )
| ( ( complements_of_subsets @ SV36 @ SV120 )
!= empty_set ) )
= $true )
| ( ( element @ SV120 @ ( powerset @ ( powerset @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1488]) ).
thf(1580,plain,
! [SV121: $i,SV37: $i] :
( ( ( ~ ~ ( empty_carrier @ SV37 ) )
= $true )
| ( ( ~ ( latt_str @ SV37 ) )
= $true )
| ( ( element @ ( meet_of_latt_set @ SV37 @ SV121 ) @ ( the_carrier @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1581,plain,
! [SV38: $i] :
( ( ( ! [SY384: $i] :
~ ( in @ ( ordered_pair @ ( sK10_SY260 @ SV38 ) @ SY384 ) @ SV38 ) )
= $false )
| ( ( SV38 = empty_set )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1490]) ).
thf(1582,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) )
| ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
| ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1491]) ).
thf(1583,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) )
| ~ ( element @ SV162 @ SV41 ) )
| ~ ( element @ SV180 @ SV124 ) ) )
= $false )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1584,plain,
! [SV44: $i,SV181: $i] :
( ( ( element @ SV181 @ ( powerset @ SV44 ) )
= $false )
| ( ( v1_membered @ SV181 )
= $true )
| ( ( v1_membered @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1585,plain,
! [SV163: $i,SV45: $i,SV125: $i] :
( ( ( ~ ( element @ SV125 @ ( powerset @ SV45 ) )
| ~ ( element @ SV163 @ ( powerset @ SV45 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV45 @ SV125 @ SV163 ) @ ( powerset @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1494]) ).
thf(1586,plain,
! [SV46: $i,SV182: $i] :
( ( ( element @ SV182 @ ( powerset @ SV46 ) )
= $false )
| ( ( finite @ SV182 )
= $true )
| ( ( finite @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1587,plain,
! [SV47: $i,SV126: $i,SV191: $i] :
( ( ( ~ ( in @ SV191 @ SV126 ) )
= $true )
| ( ( in @ SV191 @ SV47 )
= $true )
| ( ( element @ SV126 @ ( powerset @ SV47 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1588,plain,
! [SV48: $i] :
( ( ( ( ( relation_dom @ SV48 )
!= empty_set )
| ( ( relation_rng @ SV48 )
= empty_set ) )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1589,plain,
! [SV48: $i] :
( ( ( ( ( relation_rng @ SV48 )
!= empty_set )
| ( ( relation_dom @ SV48 )
= empty_set ) )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1590,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) )
| ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
| ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1499]) ).
thf(1591,plain,
! [SV128: $i,SV52: $i] :
( ( ( ~ ~ ( empty @ SV52 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( in @ SV128 @ SV52 ) )
| ~ ( ~ ( in @ SV128 @ SV52 )
| ( element @ SV128 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1592,plain,
! [SV128: $i,SV52: $i] :
( ( ( ~ ( empty @ SV52 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( empty @ SV128 ) )
| ~ ( ~ ( empty @ SV128 )
| ( element @ SV128 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1593,plain,
! [SV165: $i,SV54: $i,SV129: $i] :
( ( ( ~ ( element @ SV129 @ ( powerset @ SV54 ) )
| ~ ( element @ SV165 @ ( powerset @ SV54 ) ) )
= $true )
| ( ( ( subset_union2 @ SV54 @ SV129 @ SV165 )
= ( set_union2 @ SV129 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1502]) ).
thf(1594,plain,
! [SV166: $i,SV56: $i,SV130: $i] :
( ( ( ~ ( element @ SV130 @ ( powerset @ SV56 ) )
| ~ ( element @ SV166 @ ( powerset @ SV56 ) ) )
= $true )
| ( ( ( subset_difference @ SV56 @ SV130 @ SV166 )
= ( set_difference @ SV130 @ SV166 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1595,plain,
! [SV57: $i] :
( ( ( SV57 = empty_set )
= $false )
| ( ( ! [SY282: $i] :
~ ( in @ SY282 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1596,plain,
! [SV57: $i] :
( ( ( ! [SY283: $i] :
~ ( in @ SY283 @ SV57 ) )
= $false )
| ( ( SV57 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1597,plain,
! [SV58: $i,SV183: $i] :
( ( ( element @ SV183 @ SV58 )
= $false )
| ( ( v1_xcmplx_0 @ SV183 )
= $true )
| ( ( v1_membered @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1598,plain,
! [SV168: $i,SV61: $i,SV132: $i] :
( ( ( ~ ( ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set ) )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
| ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) )
| ~ ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) ) )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1599,plain,
! [SV62: $i,SV184: $i] :
( ( ( element @ SV184 @ SV62 )
= $false )
| ( ( ~ ( ~ ( v1_xcmplx_0 @ SV184 )
| ~ ( v1_xreal_0 @ SV184 ) ) )
= $true )
| ( ( v2_membered @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1600,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1510]) ).
thf(1601,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1511]) ).
thf(1602,plain,
! [SV133: $i,SV64: $i] :
( ( ( ~ ( subset @ SV64 @ ( singleton @ SV133 ) ) )
= $true )
| ( ( ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1603,plain,
! [SV133: $i,SV64: $i] :
( ( ( ~ ( ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) ) )
= $true )
| ( ( subset @ SV64 @ ( singleton @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1604,plain,
! [SV169: $i,SV65: $i,SV134: $i] :
( ( ( ~ ( ~ ( in @ SV134 @ ( subset_complement @ SV65 @ SV169 ) )
| ~ ( in @ SV134 @ SV169 ) ) )
= $false )
| ( ( element @ SV169 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1605,plain,
! [SV170: $i,SV66: $i,SV135: $i] :
( ( ( ~ ( element @ SV135 @ ( powerset @ SV66 ) )
| ~ ( element @ SV170 @ ( powerset @ SV66 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV66 @ SV135 @ SV170 ) @ ( powerset @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1515]) ).
thf(1606,plain,
! [SV67: $i,SV136: $i] :
( ( ( ~ ( ~ ( proper_element @ SV136 @ SV67 )
| ( SV136
!= ( union @ SV67 ) ) ) )
= $false )
| ( ( element @ SV136 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1516]) ).
thf(1607,plain,
! [SV67: $i,SV136: $i] :
( ( ( ~ ( ~ ( ( SV136
!= ( union @ SV67 ) ) )
| ( proper_element @ SV136 @ SV67 ) ) )
= $false )
| ( ( element @ SV136 @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1516]) ).
thf(1608,plain,
! [SV69: $i,SV185: $i] :
( ( ( element @ SV185 @ SV69 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV185 )
| ~ ( epsilon_connected @ SV185 ) )
| ~ ( ordinal @ SV185 ) ) )
= $true )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1609,plain,
! [SV186: $i,SV71: $i,SV192: $i] :
( ( ( ~ ( element @ SV192 @ ( the_carrier @ SV71 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
| ! [SY382: $i] :
( ~ ( element @ SY382 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY382 @ SV186 )
| ( related @ SV71 @ SY382 @ SV192 ) ) )
| ~ ( ~ ! [SY383: $i] :
( ~ ( element @ SY383 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY383 @ SV186 )
| ( related @ SV71 @ SY383 @ SV192 ) )
| ( relstr_set_smaller @ SV71 @ SV186 @ SV192 ) ) ) )
= $true )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1610,plain,
! [SV137: $i,SV72: $i] :
( ( ( ~ ( strict_rel_str @ ( rel_str_of @ SV72 @ SV137 ) ) )
= $false )
| ( ( relation_of2 @ SV137 @ SV72 @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1520]) ).
thf(1611,plain,
! [SV137: $i,SV72: $i] :
( ( ( ~ ( rel_str @ ( rel_str_of @ SV72 @ SV137 ) ) )
= $false )
| ( ( relation_of2 @ SV137 @ SV72 @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1520]) ).
thf(1612,plain,
! [SV73: $i] :
( ( ( transitive_relstr @ SV73 )
= $false )
| ( ( ~ ( rel_str @ SV73 ) )
= $true )
| ( ( ! [SY302: $i] :
( ~ ( element @ SY302 @ ( the_carrier @ SV73 ) )
| ! [SY303: $i] :
( ~ ( element @ SY303 @ ( the_carrier @ SV73 ) )
| ! [SY304: $i] :
( ~ ( element @ SY304 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SY302 @ SY303 )
| ~ ( related @ SV73 @ SY303 @ SY304 ) )
| ( related @ SV73 @ SY302 @ SY304 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1613,plain,
! [SV74: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK11_SY305 @ SV74 ) @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ ( sK11_SY305 @ SV74 ) ) ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1522]) ).
thf(1614,plain,
! [SV75: $i,SV187: $i] :
( ( ( element @ SV187 @ ( powerset @ SV75 ) )
= $false )
| ( ( ~ ( ~ ( v1_membered @ SV187 )
| ~ ( v2_membered @ SV187 ) ) )
= $true )
| ( ( v2_membered @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1615,plain,
! [SV171: $i,SV76: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ ( powerset @ SV76 ) )
| ~ ( element @ SV171 @ ( powerset @ SV76 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV76 @ SV138 @ SV171 ) @ ( powerset @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1524]) ).
thf(1616,plain,
! [SV77: $i] :
( ( ( ~ ( empty_carrier @ SV77 )
| ( empty @ ( the_carrier @ SV77 ) ) )
= $true )
| ( ( one_sorted_str @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1617,plain,
! [SV77: $i] :
( ( ( ~ ( empty @ ( the_carrier @ SV77 ) )
| ( empty_carrier @ SV77 ) )
= $true )
| ( ( one_sorted_str @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1618,plain,
! [SV78: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV78 )
| ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) ) )
= $true )
| ( ( rel_str @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1527]) ).
thf(1619,plain,
! [SV78: $i] :
( ( ( ~ ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) )
| ( antisymmetric_relstr @ SV78 ) )
= $true )
| ( ( rel_str @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1528]) ).
thf(1620,plain,
! [SV140: $i,SV80: $i] :
( ( ( ~ ( element @ SV80 @ ( powerset @ SV140 ) ) )
= $true )
| ( ( subset @ SV80 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1529]) ).
thf(1621,plain,
! [SV140: $i,SV80: $i] :
( ( ( ~ ( subset @ SV80 @ SV140 ) )
= $true )
| ( ( element @ SV80 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1622,plain,
! [SV141: $i,SV81: $i] :
( ( ( ~ ( subset @ SV81 @ ( singleton @ SV141 ) ) )
= $true )
| ( ( ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1623,plain,
! [SV141: $i,SV81: $i] :
( ( ( ~ ( ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) ) )
= $true )
| ( ( subset @ SV81 @ ( singleton @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1624,plain,
! [SV142: $i,SV82: $i,SV193: $i] :
( ( ( ~ ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 )
| ( subset @ SV142 @ SV193 ) )
| ~ ( ~ ( subset @ SV142 @ SV193 )
| ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 ) ) ) )
= $true )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1533]) ).
thf(1625,plain,
! [SV83: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK12_SY314 @ SV83 ) @ ( powerset @ SV83 ) )
| ~ ~ ( empty @ ( sK12_SY314 @ SV83 ) ) )
| ~ ( finite @ ( sK12_SY314 @ SV83 ) ) ) )
= $false )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1534]) ).
thf(1626,plain,
! [SV84: $i] :
( ( ( ~ ( empty_carrier @ SV84 ) )
= $false )
| ( ( ~ ( meet_semilatt_str @ SV84 ) )
= $true )
| ( ( element @ ( bottom_of_semilattstr @ SV84 ) @ ( the_carrier @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1627,plain,
! [SV86: $i] :
( ( ( ~ ( transitive_relstr @ SV86 )
| ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) ) )
= $true )
| ( ( rel_str @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1536]) ).
thf(1628,plain,
! [SV86: $i] :
( ( ( ~ ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) )
| ( transitive_relstr @ SV86 ) )
= $true )
| ( ( rel_str @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1537]) ).
thf(1629,plain,
! [SV87: $i] :
( ( ( ~ ( empty_carrier @ SV87 ) )
= $false )
| ( ( ~ ( one_sorted_str @ SV87 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1630,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) )
| ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
| ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1631,plain,
! [SV145: $i,SV89: $i] :
( ( ( ( set_difference @ SV89 @ SV145 )
!= empty_set )
= $true )
| ( ( subset @ SV89 @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1632,plain,
! [SV145: $i,SV89: $i] :
( ( ( ~ ( subset @ SV89 @ SV145 ) )
= $true )
| ( ( ( set_difference @ SV89 @ SV145 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1633,plain,
! [SV173: $i,SV146: $i,SV90: $i] :
( ( ( ~ ~ ( ~ ( in @ SV90 @ SV146 )
| ~ ( element @ SV146 @ ( powerset @ SV173 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1542]) ).
thf(1634,plain,
! [SV174: $i,SV91: $i,SV147: $i] :
( ( ( ~ ( element @ SV147 @ ( powerset @ SV91 ) )
| ~ ( element @ SV174 @ ( powerset @ SV91 ) ) )
= $true )
| ( ( ( subset_union2 @ SV91 @ SV147 @ SV174 )
= ( subset_union2 @ SV91 @ SV174 @ SV147 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1543]) ).
thf(1635,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) )
| ~ ( element @ SV175 @ SV92 ) )
| ~ ( element @ SV188 @ SV148 ) ) )
= $false )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1636,plain,
! [SV97: $i] :
( ( ~ ( element @ ( sK7_SY329 @ SV97 ) @ ( powerset @ SV97 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1637,plain,
! [SV97: $i] :
( ( ~ ~ ( proper_element @ ( sK7_SY329 @ SV97 ) @ ( powerset @ SV97 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1638,plain,
! [SV176: $i,SV98: $i,SV152: $i] :
( ( ( ~ ( element @ SV152 @ ( powerset @ SV98 ) )
| ~ ( element @ SV176 @ ( powerset @ SV98 ) ) )
= $true )
| ( ( ( subset_union2 @ SV98 @ SV152 @ SV152 )
= SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1639,plain,
! [SV100: $i,SV154: $i] :
( ( ( ~ ( ~ ( proper_element @ SV154 @ ( powerset @ SV100 ) )
| ( SV154 != SV100 ) ) )
= $false )
| ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1549]) ).
thf(1640,plain,
! [SV100: $i,SV154: $i] :
( ( ( ~ ( ~ ( ( SV154 != SV100 ) )
| ( proper_element @ SV154 @ ( powerset @ SV100 ) ) ) )
= $false )
| ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1549]) ).
thf(1641,plain,
! [SV156: $i,SV8: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( ~ ( element @ SV156 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV8 @ SV102 @ SV156 )
= ( set_intersection2 @ SV102 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1642,plain,
! [SV11: $i] :
( ( ( rel_str @ SV11 )
= $false )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( ! [SY222: $i] :
( ~ ( element @ SY222 @ ( the_carrier @ SV11 ) )
| ! [SY223: $i] :
( ~ ( element @ SY223 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY222 @ SY223 )
| ~ ( related @ SV11 @ SY223 @ SY222 ) )
| ( SY222 = SY223 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1643,plain,
! [SV104: $i,SV12: $i] :
( ( ( top_str @ SV12 )
= $false )
| ( ( ~ ( element @ SV104 @ ( powerset @ ( the_carrier @ SV12 ) ) ) )
= $true )
| ( ( element @ ( topstr_closure @ SV12 @ SV104 ) @ ( powerset @ ( the_carrier @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1644,plain,
! [SV158: $i,SV14: $i,SV105: $i] :
( ( ( ~ ( element @ SV105 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( ~ ( element @ SV158 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV14 @ SV105 @ SV158 )
= ( subset_intersection2 @ SV14 @ SV158 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1645,plain,
( ( ( relstr_element_smaller @ sK1_A @ empty_set @ sK3_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ empty_set @ sK3_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1646,plain,
! [SV18: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ( ( SV108 != empty_set ) )
| ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) ) )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1560]) ).
thf(1647,plain,
! [SV108: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ( SV108 != empty_set ) ) )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1648,plain,
! [SV159: $i,SV19: $i,SV109: $i] :
( ( ( ~ ( element @ SV109 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( ~ ( element @ SV159 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV19 @ SV109 @ SV109 )
= SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1649,plain,
! [SV110: $i,SV20: $i] :
( ( ( ( set_difference @ SV20 @ SV110 )
= empty_set )
= $false )
| ( ( subset @ SV20 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1650,plain,
! [SV110: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV110 )
= $false )
| ( ( ( set_difference @ SV20 @ SV110 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1651,plain,
! [SV112: $i,SV22: $i] :
( ( ( SV22 != empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) )
| ~ ( ~ ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1652,plain,
! [SV112: $i,SV22: $i] :
( ( ( SV22 = empty_set )
= $false )
| ( ( ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1653,plain,
! [SV179: $i,SV24: $i,SV189: $i] :
( ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
| ! [SY379: $i] :
( ~ ( element @ SY379 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY379 @ SV179 )
| ( related @ SV24 @ SV189 @ SY379 ) ) )
| ~ ( ~ ! [SY380: $i] :
( ~ ( element @ SY380 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY380 @ SV179 )
| ( related @ SV24 @ SV189 @ SY380 ) )
| ( relstr_element_smaller @ SV24 @ SV179 @ SV189 ) ) ) )
= $true )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1654,plain,
! [SV160: $i,SV113: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV113 ) )
= $true )
| ( ( ~ ( element @ SV113 @ ( powerset @ SV160 ) ) )
= $true )
| ( ( element @ SV25 @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1655,plain,
! [SV114: $i,SV26: $i] :
( ( ( disjoint @ SV26 @ SV114 )
= $false )
| ( ( ( set_intersection2 @ SV26 @ SV114 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1656,plain,
! [SV114: $i,SV26: $i] :
( ( ( ( set_intersection2 @ SV26 @ SV114 )
= empty_set )
= $false )
| ( ( disjoint @ SV26 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1657,plain,
! [SV27: $i,SV190: $i] :
( ( ( element @ SV190 @ ( powerset @ SV27 ) )
= $false )
| ( ( ! [SY381: $i] :
( ~ ( element @ SY381 @ SV27 )
| ~ ~ ( in @ SY381 @ SV190 )
| ( in @ SY381 @ ( subset_complement @ SV27 @ SV190 ) ) ) )
= $true )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1658,plain,
! [SV28: $i,SV115: $i] :
( ( ( in @ ( sK8_SY348 @ SV115 @ SV28 ) @ SV28 )
= $true )
| ( ( element @ SV28 @ ( powerset @ SV115 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1572]) ).
thf(1659,plain,
! [SV29: $i] :
( ( element @ ( sK5_SY252 @ SV29 ) @ ( powerset @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1660,plain,
! [SV29: $i] :
( ( empty @ ( sK5_SY252 @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1661,plain,
! [SV116: $i,SV30: $i] :
( ( ( top_str @ SV30 )
= $false )
| ( ( ~ ( element @ SV116 @ ( powerset @ ( the_carrier @ SV30 ) ) ) )
= $true )
| ( ( element @ ( interior @ SV30 @ SV116 ) @ ( powerset @ ( the_carrier @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1662,plain,
! [SV118: $i,SV33: $i] :
( ( ( ~ ( empty_carrier @ SV33 ) )
= $false )
| ( ( ~ ( latt_str @ SV33 ) )
= $true )
| ( ( element @ ( join_of_latt_set @ SV33 @ SV118 ) @ ( the_carrier @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1663,plain,
! [SV34: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK9_SY256 @ SV34 ) @ ( powerset @ SV34 ) )
| ~ ~ ( empty @ ( sK9_SY256 @ SV34 ) ) )
| ~ ( finite @ ( sK9_SY256 @ SV34 ) ) ) )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1664,plain,
! [SV36: $i,SV120: $i] :
( ( ( ~ ( ( SV120 != empty_set ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV36 @ SV120 )
!= empty_set )
= $true )
| ( ( element @ SV120 @ ( powerset @ ( powerset @ SV36 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1665,plain,
! [SV121: $i,SV37: $i] :
( ( ( ~ ( empty_carrier @ SV37 ) )
= $false )
| ( ( ~ ( latt_str @ SV37 ) )
= $true )
| ( ( element @ ( meet_of_latt_set @ SV37 @ SV121 ) @ ( the_carrier @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1666,plain,
! [SV38: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_SY260 @ SV38 ) @ ( sK13_SY384 @ SV38 ) ) @ SV38 ) )
= $false )
| ( ( SV38 = empty_set )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1581]) ).
thf(1667,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) )
| ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1668,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) )
| ~ ( element @ SV162 @ SV41 ) )
| ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1583]) ).
thf(1669,plain,
! [SV163: $i,SV45: $i,SV125: $i] :
( ( ( ~ ( element @ SV125 @ ( powerset @ SV45 ) ) )
= $true )
| ( ( ~ ( element @ SV163 @ ( powerset @ SV45 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV45 @ SV125 @ SV163 ) @ ( powerset @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1670,plain,
! [SV47: $i,SV126: $i,SV191: $i] :
( ( ( in @ SV191 @ SV126 )
= $false )
| ( ( in @ SV191 @ SV47 )
= $true )
| ( ( element @ SV126 @ ( powerset @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1671,plain,
! [SV48: $i] :
( ( ( ( relation_dom @ SV48 )
!= empty_set )
= $true )
| ( ( ( relation_rng @ SV48 )
= empty_set )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1672,plain,
! [SV48: $i] :
( ( ( ( relation_rng @ SV48 )
!= empty_set )
= $true )
| ( ( ( relation_dom @ SV48 )
= empty_set )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1673,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) )
| ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) ) )
= $true )
| ( ( ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1674,plain,
! [SV128: $i,SV52: $i] :
( ( ( ~ ( empty @ SV52 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( in @ SV128 @ SV52 ) )
| ~ ( ~ ( in @ SV128 @ SV52 )
| ( element @ SV128 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1675,plain,
! [SV128: $i,SV52: $i] :
( ( ( empty @ SV52 )
= $false )
| ( ( ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( empty @ SV128 ) )
| ~ ( ~ ( empty @ SV128 )
| ( element @ SV128 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1676,plain,
! [SV165: $i,SV54: $i,SV129: $i] :
( ( ( ~ ( element @ SV129 @ ( powerset @ SV54 ) ) )
= $true )
| ( ( ~ ( element @ SV165 @ ( powerset @ SV54 ) ) )
= $true )
| ( ( ( subset_union2 @ SV54 @ SV129 @ SV165 )
= ( set_union2 @ SV129 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1677,plain,
! [SV166: $i,SV56: $i,SV130: $i] :
( ( ( ~ ( element @ SV130 @ ( powerset @ SV56 ) ) )
= $true )
| ( ( ~ ( element @ SV166 @ ( powerset @ SV56 ) ) )
= $true )
| ( ( ( subset_difference @ SV56 @ SV130 @ SV166 )
= ( set_difference @ SV130 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1678,plain,
! [SV57: $i,SV194: $i] :
( ( ( ~ ( in @ SV194 @ SV57 ) )
= $true )
| ( ( SV57 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1679,plain,
! [SV57: $i] :
( ( ( ~ ( in @ ( sK14_SY283 @ SV57 ) @ SV57 ) )
= $false )
| ( ( SV57 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1596]) ).
thf(1680,plain,
! [SV168: $i,SV61: $i,SV132: $i] :
( ( ( ~ ( ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set ) )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) ) )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1681,plain,
! [SV168: $i,SV61: $i,SV132: $i] :
( ( ( ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) )
| ~ ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) ) )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1682,plain,
! [SV62: $i,SV184: $i] :
( ( ( ~ ( v1_xcmplx_0 @ SV184 )
| ~ ( v1_xreal_0 @ SV184 ) )
= $false )
| ( ( element @ SV184 @ SV62 )
= $false )
| ( ( v2_membered @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1683,plain,
! [SV133: $i,SV64: $i] :
( ( ( subset @ SV64 @ ( singleton @ SV133 ) )
= $false )
| ( ( ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1684,plain,
! [SV133: $i,SV64: $i] :
( ( ( ( SV64 = empty_set )
| ( SV64
= ( singleton @ SV133 ) ) )
= $false )
| ( ( subset @ SV64 @ ( singleton @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1685,plain,
! [SV169: $i,SV65: $i,SV134: $i] :
( ( ( ~ ( in @ SV134 @ ( subset_complement @ SV65 @ SV169 ) )
| ~ ( in @ SV134 @ SV169 ) )
= $true )
| ( ( element @ SV169 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1686,plain,
! [SV170: $i,SV66: $i,SV135: $i] :
( ( ( ~ ( element @ SV135 @ ( powerset @ SV66 ) ) )
= $true )
| ( ( ~ ( element @ SV170 @ ( powerset @ SV66 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV66 @ SV135 @ SV170 ) @ ( powerset @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1687,plain,
! [SV67: $i,SV136: $i] :
( ( ( ~ ( proper_element @ SV136 @ SV67 )
| ( SV136
!= ( union @ SV67 ) ) )
= $true )
| ( ( element @ SV136 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1606]) ).
thf(1688,plain,
! [SV67: $i,SV136: $i] :
( ( ( ~ ( ( SV136
!= ( union @ SV67 ) ) )
| ( proper_element @ SV136 @ SV67 ) )
= $true )
| ( ( element @ SV136 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1689,plain,
! [SV69: $i,SV185: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV185 )
| ~ ( epsilon_connected @ SV185 ) )
| ~ ( ordinal @ SV185 ) )
= $false )
| ( ( element @ SV185 @ SV69 )
= $false )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1690,plain,
! [SV186: $i,SV71: $i,SV192: $i] :
( ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
| ! [SY382: $i] :
( ~ ( element @ SY382 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY382 @ SV186 )
| ( related @ SV71 @ SY382 @ SV192 ) ) )
| ~ ( ~ ! [SY383: $i] :
( ~ ( element @ SY383 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY383 @ SV186 )
| ( related @ SV71 @ SY383 @ SV192 ) )
| ( relstr_set_smaller @ SV71 @ SV186 @ SV192 ) ) ) )
= $true )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1691,plain,
! [SV137: $i,SV72: $i] :
( ( ( strict_rel_str @ ( rel_str_of @ SV72 @ SV137 ) )
= $true )
| ( ( relation_of2 @ SV137 @ SV72 @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1610]) ).
thf(1692,plain,
! [SV137: $i,SV72: $i] :
( ( ( rel_str @ ( rel_str_of @ SV72 @ SV137 ) )
= $true )
| ( ( relation_of2 @ SV137 @ SV72 @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1693,plain,
! [SV73: $i] :
( ( ( rel_str @ SV73 )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( ! [SY302: $i] :
( ~ ( element @ SY302 @ ( the_carrier @ SV73 ) )
| ! [SY303: $i] :
( ~ ( element @ SY303 @ ( the_carrier @ SV73 ) )
| ! [SY304: $i] :
( ~ ( element @ SY304 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SY302 @ SY303 )
| ~ ( related @ SV73 @ SY303 @ SY304 ) )
| ( related @ SV73 @ SY302 @ SY304 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1694,plain,
! [SV74: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_SY305 @ SV74 ) @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ ( sK11_SY305 @ SV74 ) ) ) )
= $true )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1613]) ).
thf(1695,plain,
! [SV75: $i,SV187: $i] :
( ( ( ~ ( v1_membered @ SV187 )
| ~ ( v2_membered @ SV187 ) )
= $false )
| ( ( element @ SV187 @ ( powerset @ SV75 ) )
= $false )
| ( ( v2_membered @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1696,plain,
! [SV171: $i,SV76: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ ( powerset @ SV76 ) ) )
= $true )
| ( ( ~ ( element @ SV171 @ ( powerset @ SV76 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV76 @ SV138 @ SV171 ) @ ( powerset @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1697,plain,
! [SV77: $i] :
( ( ( ~ ( empty_carrier @ SV77 ) )
= $true )
| ( ( empty @ ( the_carrier @ SV77 ) )
= $true )
| ( ( one_sorted_str @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1698,plain,
! [SV77: $i] :
( ( ( ~ ( empty @ ( the_carrier @ SV77 ) ) )
= $true )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( one_sorted_str @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1699,plain,
! [SV78: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV78 ) )
= $true )
| ( ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) )
= $true )
| ( ( rel_str @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1618]) ).
thf(1700,plain,
! [SV78: $i] :
( ( ( ~ ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV78 )
= $true )
| ( ( rel_str @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1619]) ).
thf(1701,plain,
! [SV140: $i,SV80: $i] :
( ( ( element @ SV80 @ ( powerset @ SV140 ) )
= $false )
| ( ( subset @ SV80 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1620]) ).
thf(1702,plain,
! [SV140: $i,SV80: $i] :
( ( ( subset @ SV80 @ SV140 )
= $false )
| ( ( element @ SV80 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1703,plain,
! [SV141: $i,SV81: $i] :
( ( ( subset @ SV81 @ ( singleton @ SV141 ) )
= $false )
| ( ( ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1704,plain,
! [SV141: $i,SV81: $i] :
( ( ( ( SV81 = empty_set )
| ( SV81
= ( singleton @ SV141 ) ) )
= $false )
| ( ( subset @ SV81 @ ( singleton @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1705,plain,
! [SV142: $i,SV82: $i,SV193: $i] :
( ( ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 )
| ( subset @ SV142 @ SV193 ) )
| ~ ( ~ ( subset @ SV142 @ SV193 )
| ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 ) ) ) )
= $true )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1706,plain,
! [SV83: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK12_SY314 @ SV83 ) @ ( powerset @ SV83 ) )
| ~ ~ ( empty @ ( sK12_SY314 @ SV83 ) ) )
| ~ ( finite @ ( sK12_SY314 @ SV83 ) ) ) )
= $true )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1625]) ).
thf(1707,plain,
! [SV84: $i] :
( ( ( empty_carrier @ SV84 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV84 ) )
= $true )
| ( ( element @ ( bottom_of_semilattstr @ SV84 ) @ ( the_carrier @ SV84 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1708,plain,
! [SV86: $i] :
( ( ( ~ ( transitive_relstr @ SV86 ) )
= $true )
| ( ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) )
= $true )
| ( ( rel_str @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1709,plain,
! [SV86: $i] :
( ( ( ~ ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) ) )
= $true )
| ( ( transitive_relstr @ SV86 )
= $true )
| ( ( rel_str @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1710,plain,
! [SV87: $i] :
( ( ( empty_carrier @ SV87 )
= $true )
| ( ( ~ ( one_sorted_str @ SV87 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1711,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) )
| ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) ) )
= $true )
| ( ( ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1712,plain,
! [SV145: $i,SV89: $i] :
( ( ( ( set_difference @ SV89 @ SV145 )
= empty_set )
= $false )
| ( ( subset @ SV89 @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1713,plain,
! [SV145: $i,SV89: $i] :
( ( ( subset @ SV89 @ SV145 )
= $false )
| ( ( ( set_difference @ SV89 @ SV145 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1714,plain,
! [SV173: $i,SV146: $i,SV90: $i] :
( ( ( ~ ( ~ ( in @ SV90 @ SV146 )
| ~ ( element @ SV146 @ ( powerset @ SV173 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1715,plain,
! [SV174: $i,SV91: $i,SV147: $i] :
( ( ( ~ ( element @ SV147 @ ( powerset @ SV91 ) ) )
= $true )
| ( ( ~ ( element @ SV174 @ ( powerset @ SV91 ) ) )
= $true )
| ( ( ( subset_union2 @ SV91 @ SV147 @ SV174 )
= ( subset_union2 @ SV91 @ SV174 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1634]) ).
thf(1716,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) )
| ~ ( element @ SV175 @ SV92 ) )
| ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1717,plain,
! [SV97: $i] :
( ( element @ ( sK7_SY329 @ SV97 ) @ ( powerset @ SV97 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1718,plain,
! [SV97: $i] :
( ( ~ ( proper_element @ ( sK7_SY329 @ SV97 ) @ ( powerset @ SV97 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1719,plain,
! [SV176: $i,SV98: $i,SV152: $i] :
( ( ( ~ ( element @ SV152 @ ( powerset @ SV98 ) ) )
= $true )
| ( ( ~ ( element @ SV176 @ ( powerset @ SV98 ) ) )
= $true )
| ( ( ( subset_union2 @ SV98 @ SV152 @ SV152 )
= SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1638]) ).
thf(1720,plain,
! [SV100: $i,SV154: $i] :
( ( ( ~ ( proper_element @ SV154 @ ( powerset @ SV100 ) )
| ( SV154 != SV100 ) )
= $true )
| ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1639]) ).
thf(1721,plain,
! [SV100: $i,SV154: $i] :
( ( ( ~ ( ( SV154 != SV100 ) )
| ( proper_element @ SV154 @ ( powerset @ SV100 ) ) )
= $true )
| ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1640]) ).
thf(1722,plain,
! [SV156: $i,SV8: $i,SV102: $i] :
( ( ( element @ SV102 @ ( powerset @ SV8 ) )
= $false )
| ( ( ~ ( element @ SV156 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV8 @ SV102 @ SV156 )
= ( set_intersection2 @ SV102 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1723,plain,
! [SV11: $i,SV195: $i] :
( ( ( ~ ( element @ SV195 @ ( the_carrier @ SV11 ) )
| ! [SY385: $i] :
( ~ ( element @ SY385 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SV195 @ SY385 )
| ~ ( related @ SV11 @ SY385 @ SV195 ) )
| ( SV195 = SY385 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1724,plain,
! [SV12: $i,SV104: $i] :
( ( ( element @ SV104 @ ( powerset @ ( the_carrier @ SV12 ) ) )
= $false )
| ( ( top_str @ SV12 )
= $false )
| ( ( element @ ( topstr_closure @ SV12 @ SV104 ) @ ( powerset @ ( the_carrier @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1725,plain,
! [SV158: $i,SV14: $i,SV105: $i] :
( ( ( element @ SV105 @ ( powerset @ SV14 ) )
= $false )
| ( ( ~ ( element @ SV158 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV14 @ SV105 @ SV158 )
= ( subset_intersection2 @ SV14 @ SV158 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1726,plain,
! [SV18: $i,SV108: $i] :
( ( ( ~ ( ~ ( ( SV108 != empty_set ) )
| ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1727,plain,
! [SV108: $i,SV18: $i] :
( ( ( ~ ( ~ ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ( SV108 != empty_set ) ) )
= $false )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1728,plain,
! [SV159: $i,SV19: $i,SV109: $i] :
( ( ( element @ SV109 @ ( powerset @ SV19 ) )
= $false )
| ( ( ~ ( element @ SV159 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV19 @ SV109 @ SV109 )
= SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1729,plain,
! [SV112: $i,SV22: $i] :
( ( ( SV22 = empty_set )
= $true )
| ( ( ~ ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) )
| ~ ( ~ ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) )
| ( SV112
= ( set_meet @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1651]) ).
thf(1730,plain,
! [SV22: $i,SV112: $i] :
( ( ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ( SV112 = empty_set ) )
| ~ ( ( SV112 != empty_set )
| ( SV112
= ( set_meet @ SV22 ) ) ) )
= $false )
| ( ( SV22 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1731,plain,
! [SV189: $i,SV179: $i,SV24: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
| ! [SY379: $i] :
( ~ ( element @ SY379 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY379 @ SV179 )
| ( related @ SV24 @ SV189 @ SY379 ) ) )
| ~ ( ~ ! [SY380: $i] :
( ~ ( element @ SY380 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY380 @ SV179 )
| ( related @ SV24 @ SV189 @ SY380 ) )
| ( relstr_element_smaller @ SV24 @ SV179 @ SV189 ) ) )
= $false )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1732,plain,
! [SV160: $i,SV113: $i,SV25: $i] :
( ( ( in @ SV25 @ SV113 )
= $false )
| ( ( ~ ( element @ SV113 @ ( powerset @ SV160 ) ) )
= $true )
| ( ( element @ SV25 @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1654]) ).
thf(1733,plain,
! [SV190: $i,SV27: $i,SV196: $i] :
( ( ( ~ ( element @ SV196 @ SV27 )
| ~ ~ ( in @ SV196 @ SV190 )
| ( in @ SV196 @ ( subset_complement @ SV27 @ SV190 ) ) )
= $true )
| ( ( element @ SV190 @ ( powerset @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(1734,plain,
! [SV30: $i,SV116: $i] :
( ( ( element @ SV116 @ ( powerset @ ( the_carrier @ SV30 ) ) )
= $false )
| ( ( top_str @ SV30 )
= $false )
| ( ( element @ ( interior @ SV30 @ SV116 ) @ ( powerset @ ( the_carrier @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1735,plain,
! [SV118: $i,SV33: $i] :
( ( ( empty_carrier @ SV33 )
= $true )
| ( ( ~ ( latt_str @ SV33 ) )
= $true )
| ( ( element @ ( join_of_latt_set @ SV33 @ SV118 ) @ ( the_carrier @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1736,plain,
! [SV34: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_SY256 @ SV34 ) @ ( powerset @ SV34 ) )
| ~ ~ ( empty @ ( sK9_SY256 @ SV34 ) ) )
| ~ ( finite @ ( sK9_SY256 @ SV34 ) ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1737,plain,
! [SV36: $i,SV120: $i] :
( ( ( SV120 != empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV36 @ SV120 )
!= empty_set )
= $true )
| ( ( element @ SV120 @ ( powerset @ ( powerset @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1738,plain,
! [SV121: $i,SV37: $i] :
( ( ( empty_carrier @ SV37 )
= $true )
| ( ( ~ ( latt_str @ SV37 ) )
= $true )
| ( ( element @ ( meet_of_latt_set @ SV37 @ SV121 ) @ ( the_carrier @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1739,plain,
! [SV38: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_SY260 @ SV38 ) @ ( sK13_SY384 @ SV38 ) ) @ SV38 )
= $true )
| ( ( SV38 = empty_set )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1666]) ).
thf(1740,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) )
| ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) ) )
= $false )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1741,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) )
| ~ ( element @ SV162 @ SV41 ) ) )
= $true )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1668]) ).
thf(1742,plain,
! [SV163: $i,SV45: $i,SV125: $i] :
( ( ( element @ SV125 @ ( powerset @ SV45 ) )
= $false )
| ( ( ~ ( element @ SV163 @ ( powerset @ SV45 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV45 @ SV125 @ SV163 ) @ ( powerset @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1743,plain,
! [SV48: $i] :
( ( ( ( relation_dom @ SV48 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV48 )
= empty_set )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1744,plain,
! [SV48: $i] :
( ( ( ( relation_rng @ SV48 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV48 )
= empty_set )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1745,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) )
| ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) ) )
= $false )
| ( ( ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1746,plain,
! [SV128: $i,SV52: $i] :
( ( ( empty @ SV52 )
= $true )
| ( ( ~ ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( in @ SV128 @ SV52 ) )
| ~ ( ~ ( in @ SV128 @ SV52 )
| ( element @ SV128 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1747,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( empty @ SV128 ) )
| ~ ( ~ ( empty @ SV128 )
| ( element @ SV128 @ SV52 ) ) )
= $false )
| ( ( empty @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1748,plain,
! [SV165: $i,SV54: $i,SV129: $i] :
( ( ( element @ SV129 @ ( powerset @ SV54 ) )
= $false )
| ( ( ~ ( element @ SV165 @ ( powerset @ SV54 ) ) )
= $true )
| ( ( ( subset_union2 @ SV54 @ SV129 @ SV165 )
= ( set_union2 @ SV129 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1749,plain,
! [SV166: $i,SV56: $i,SV130: $i] :
( ( ( element @ SV130 @ ( powerset @ SV56 ) )
= $false )
| ( ( ~ ( element @ SV166 @ ( powerset @ SV56 ) ) )
= $true )
| ( ( ( subset_difference @ SV56 @ SV130 @ SV166 )
= ( set_difference @ SV130 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1750,plain,
! [SV57: $i,SV194: $i] :
( ( ( in @ SV194 @ SV57 )
= $false )
| ( ( SV57 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1751,plain,
! [SV57: $i] :
( ( ( in @ ( sK14_SY283 @ SV57 ) @ SV57 )
= $true )
| ( ( SV57 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1752,plain,
! [SV168: $i,SV61: $i,SV132: $i] :
( ( ( ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set ) )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1753,plain,
! [SV168: $i,SV61: $i,SV132: $i] :
( ( ( ( SV132 != empty_set )
| ( SV61 = empty_set )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) )
| ~ ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1754,plain,
! [SV62: $i,SV184: $i] :
( ( ( ~ ( v1_xcmplx_0 @ SV184 ) )
= $false )
| ( ( element @ SV184 @ SV62 )
= $false )
| ( ( v2_membered @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1755,plain,
! [SV62: $i,SV184: $i] :
( ( ( ~ ( v1_xreal_0 @ SV184 ) )
= $false )
| ( ( element @ SV184 @ SV62 )
= $false )
| ( ( v2_membered @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1756,plain,
! [SV133: $i,SV64: $i] :
( ( ( SV64 = empty_set )
= $true )
| ( ( SV64
= ( singleton @ SV133 ) )
= $true )
| ( ( subset @ SV64 @ ( singleton @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1757,plain,
! [SV133: $i,SV64: $i] :
( ( ( SV64 = empty_set )
= $false )
| ( ( subset @ SV64 @ ( singleton @ SV133 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1684]) ).
thf(1758,plain,
! [SV133: $i,SV64: $i] :
( ( ( SV64
= ( singleton @ SV133 ) )
= $false )
| ( ( subset @ SV64 @ ( singleton @ SV133 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1684]) ).
thf(1759,plain,
! [SV169: $i,SV65: $i,SV134: $i] :
( ( ( ~ ( in @ SV134 @ ( subset_complement @ SV65 @ SV169 ) ) )
= $true )
| ( ( ~ ( in @ SV134 @ SV169 ) )
= $true )
| ( ( element @ SV169 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1685]) ).
thf(1760,plain,
! [SV170: $i,SV66: $i,SV135: $i] :
( ( ( element @ SV135 @ ( powerset @ SV66 ) )
= $false )
| ( ( ~ ( element @ SV170 @ ( powerset @ SV66 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV66 @ SV135 @ SV170 ) @ ( powerset @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1761,plain,
! [SV67: $i,SV136: $i] :
( ( ( ~ ( proper_element @ SV136 @ SV67 ) )
= $true )
| ( ( SV136
!= ( union @ SV67 ) )
= $true )
| ( ( element @ SV136 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1762,plain,
! [SV67: $i,SV136: $i] :
( ( ( ~ ( ( SV136
!= ( union @ SV67 ) ) ) )
= $true )
| ( ( proper_element @ SV136 @ SV67 )
= $true )
| ( ( element @ SV136 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1763,plain,
! [SV69: $i,SV185: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV185 )
| ~ ( epsilon_connected @ SV185 ) ) )
= $false )
| ( ( element @ SV185 @ SV69 )
= $false )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1689]) ).
thf(1764,plain,
! [SV69: $i,SV185: $i] :
( ( ( ~ ( ordinal @ SV185 ) )
= $false )
| ( ( element @ SV185 @ SV69 )
= $false )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1689]) ).
thf(1765,plain,
! [SV192: $i,SV186: $i,SV71: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
| ! [SY382: $i] :
( ~ ( element @ SY382 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY382 @ SV186 )
| ( related @ SV71 @ SY382 @ SV192 ) ) )
| ~ ( ~ ! [SY383: $i] :
( ~ ( element @ SY383 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY383 @ SV186 )
| ( related @ SV71 @ SY383 @ SV192 ) )
| ( relstr_set_smaller @ SV71 @ SV186 @ SV192 ) ) )
= $false )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1766,plain,
! [SV73: $i,SV197: $i] :
( ( ( ~ ( element @ SV197 @ ( the_carrier @ SV73 ) )
| ! [SY386: $i] :
( ~ ( element @ SY386 @ ( the_carrier @ SV73 ) )
| ! [SY387: $i] :
( ~ ( element @ SY387 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SV197 @ SY386 )
| ~ ( related @ SV73 @ SY386 @ SY387 ) )
| ( related @ SV73 @ SV197 @ SY387 ) ) ) )
= $true )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(1767,plain,
! [SV74: $i] :
( ( ( ~ ( element @ ( sK11_SY305 @ SV74 ) @ ( powerset @ SV74 ) )
| ~ ~ ( empty @ ( sK11_SY305 @ SV74 ) ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1768,plain,
! [SV75: $i,SV187: $i] :
( ( ( ~ ( v1_membered @ SV187 ) )
= $false )
| ( ( element @ SV187 @ ( powerset @ SV75 ) )
= $false )
| ( ( v2_membered @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1769,plain,
! [SV75: $i,SV187: $i] :
( ( ( ~ ( v2_membered @ SV187 ) )
= $false )
| ( ( element @ SV187 @ ( powerset @ SV75 ) )
= $false )
| ( ( v2_membered @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1770,plain,
! [SV171: $i,SV76: $i,SV138: $i] :
( ( ( element @ SV138 @ ( powerset @ SV76 ) )
= $false )
| ( ( ~ ( element @ SV171 @ ( powerset @ SV76 ) ) )
= $true )
| ( ( element @ ( subset_union2 @ SV76 @ SV138 @ SV171 ) @ ( powerset @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1771,plain,
! [SV77: $i] :
( ( ( empty_carrier @ SV77 )
= $false )
| ( ( empty @ ( the_carrier @ SV77 ) )
= $true )
| ( ( one_sorted_str @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1772,plain,
! [SV77: $i] :
( ( ( empty @ ( the_carrier @ SV77 ) )
= $false )
| ( ( empty_carrier @ SV77 )
= $true )
| ( ( one_sorted_str @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1773,plain,
! [SV78: $i] :
( ( ( antisymmetric_relstr @ SV78 )
= $false )
| ( ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) )
= $true )
| ( ( rel_str @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1774,plain,
! [SV78: $i] :
( ( ( is_antisymmetric_in @ ( the_InternalRel @ SV78 ) @ ( the_carrier @ SV78 ) )
= $false )
| ( ( antisymmetric_relstr @ SV78 )
= $true )
| ( ( rel_str @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1775,plain,
! [SV141: $i,SV81: $i] :
( ( ( SV81 = empty_set )
= $true )
| ( ( SV81
= ( singleton @ SV141 ) )
= $true )
| ( ( subset @ SV81 @ ( singleton @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1776,plain,
! [SV141: $i,SV81: $i] :
( ( ( SV81 = empty_set )
= $false )
| ( ( subset @ SV81 @ ( singleton @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1777,plain,
! [SV141: $i,SV81: $i] :
( ( ( SV81
= ( singleton @ SV141 ) )
= $false )
| ( ( subset @ SV81 @ ( singleton @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1778,plain,
! [SV193: $i,SV142: $i,SV82: $i] :
( ( ( ~ ( ~ ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 )
| ( subset @ SV142 @ SV193 ) )
| ~ ( ~ ( subset @ SV142 @ SV193 )
| ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 ) ) )
= $false )
| ( ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1779,plain,
! [SV83: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK12_SY314 @ SV83 ) @ ( powerset @ SV83 ) )
| ~ ~ ( empty @ ( sK12_SY314 @ SV83 ) ) )
| ~ ( finite @ ( sK12_SY314 @ SV83 ) ) )
= $false )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1780,plain,
! [SV84: $i] :
( ( ( meet_semilatt_str @ SV84 )
= $false )
| ( ( empty_carrier @ SV84 )
= $true )
| ( ( element @ ( bottom_of_semilattstr @ SV84 ) @ ( the_carrier @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1781,plain,
! [SV86: $i] :
( ( ( transitive_relstr @ SV86 )
= $false )
| ( ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) )
= $true )
| ( ( rel_str @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(1782,plain,
! [SV86: $i] :
( ( ( is_transitive_in @ ( the_InternalRel @ SV86 ) @ ( the_carrier @ SV86 ) )
= $false )
| ( ( transitive_relstr @ SV86 )
= $true )
| ( ( rel_str @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1783,plain,
! [SV87: $i] :
( ( ( one_sorted_str @ SV87 )
= $false )
| ( ( empty_carrier @ SV87 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1784,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) )
| ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) ) )
= $false )
| ( ( ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1785,plain,
! [SV173: $i,SV146: $i,SV90: $i] :
( ( ( ~ ( in @ SV90 @ SV146 )
| ~ ( element @ SV146 @ ( powerset @ SV173 ) ) )
= $true )
| ( ( ~ ( empty @ SV173 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1786,plain,
! [SV174: $i,SV91: $i,SV147: $i] :
( ( ( element @ SV147 @ ( powerset @ SV91 ) )
= $false )
| ( ( ~ ( element @ SV174 @ ( powerset @ SV91 ) ) )
= $true )
| ( ( ( subset_union2 @ SV91 @ SV147 @ SV174 )
= ( subset_union2 @ SV91 @ SV174 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1787,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) )
| ~ ( element @ SV175 @ SV92 ) ) )
= $true )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(1788,plain,
! [SV97: $i] :
( ( proper_element @ ( sK7_SY329 @ SV97 ) @ ( powerset @ SV97 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1789,plain,
! [SV176: $i,SV98: $i,SV152: $i] :
( ( ( element @ SV152 @ ( powerset @ SV98 ) )
= $false )
| ( ( ~ ( element @ SV176 @ ( powerset @ SV98 ) ) )
= $true )
| ( ( ( subset_union2 @ SV98 @ SV152 @ SV152 )
= SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1790,plain,
! [SV100: $i,SV154: $i] :
( ( ( ~ ( proper_element @ SV154 @ ( powerset @ SV100 ) ) )
= $true )
| ( ( SV154 != SV100 )
= $true )
| ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1791,plain,
! [SV100: $i,SV154: $i] :
( ( ( ~ ( ( SV154 != SV100 ) ) )
= $true )
| ( ( proper_element @ SV154 @ ( powerset @ SV100 ) )
= $true )
| ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(1792,plain,
! [SV102: $i,SV8: $i,SV156: $i] :
( ( ( element @ SV156 @ ( powerset @ SV8 ) )
= $false )
| ( ( element @ SV102 @ ( powerset @ SV8 ) )
= $false )
| ( ( ( subset_intersection2 @ SV8 @ SV102 @ SV156 )
= ( set_intersection2 @ SV102 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1793,plain,
! [SV11: $i,SV195: $i] :
( ( ( ~ ( element @ SV195 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ! [SY385: $i] :
( ~ ( element @ SY385 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SV195 @ SY385 )
| ~ ( related @ SV11 @ SY385 @ SV195 ) )
| ( SV195 = SY385 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1794,plain,
! [SV105: $i,SV14: $i,SV158: $i] :
( ( ( element @ SV158 @ ( powerset @ SV14 ) )
= $false )
| ( ( element @ SV105 @ ( powerset @ SV14 ) )
= $false )
| ( ( ( subset_intersection2 @ SV14 @ SV105 @ SV158 )
= ( subset_intersection2 @ SV14 @ SV158 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1795,plain,
! [SV18: $i,SV108: $i] :
( ( ( ~ ( ( SV108 != empty_set ) )
| ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1796,plain,
! [SV108: $i,SV18: $i] :
( ( ( ~ ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) )
| ( SV108 != empty_set ) )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1797,plain,
! [SV109: $i,SV19: $i,SV159: $i] :
( ( ( element @ SV159 @ ( powerset @ SV19 ) )
= $false )
| ( ( element @ SV109 @ ( powerset @ SV19 ) )
= $false )
| ( ( ( subset_intersection2 @ SV19 @ SV109 @ SV109 )
= SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1798,plain,
! [SV22: $i,SV112: $i] :
( ( ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) )
| ~ ( ~ ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) )
| ( SV112
= ( set_meet @ SV22 ) ) ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1799,plain,
! [SV22: $i,SV112: $i] :
( ( ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ( SV112 = empty_set ) ) )
= $false )
| ( ( SV22 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1730]) ).
thf(1800,plain,
! [SV22: $i,SV112: $i] :
( ( ( ~ ( ( SV112 != empty_set )
| ( SV112
= ( set_meet @ SV22 ) ) ) )
= $false )
| ( ( SV22 = empty_set )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1730]) ).
thf(1801,plain,
! [SV189: $i,SV179: $i,SV24: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
| ! [SY379: $i] :
( ~ ( element @ SY379 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY379 @ SV179 )
| ( related @ SV24 @ SV189 @ SY379 ) ) ) )
= $false )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1802,plain,
! [SV189: $i,SV179: $i,SV24: $i] :
( ( ( ~ ( ~ ! [SY380: $i] :
( ~ ( element @ SY380 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY380 @ SV179 )
| ( related @ SV24 @ SV189 @ SY380 ) )
| ( relstr_element_smaller @ SV24 @ SV179 @ SV189 ) ) )
= $false )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1803,plain,
! [SV25: $i,SV160: $i,SV113: $i] :
( ( ( element @ SV113 @ ( powerset @ SV160 ) )
= $false )
| ( ( in @ SV25 @ SV113 )
= $false )
| ( ( element @ SV25 @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1804,plain,
! [SV190: $i,SV27: $i,SV196: $i] :
( ( ( ~ ( element @ SV196 @ SV27 ) )
= $true )
| ( ( ~ ~ ( in @ SV196 @ SV190 )
| ( in @ SV196 @ ( subset_complement @ SV27 @ SV190 ) ) )
= $true )
| ( ( element @ SV190 @ ( powerset @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1805,plain,
! [SV118: $i,SV33: $i] :
( ( ( latt_str @ SV33 )
= $false )
| ( ( empty_carrier @ SV33 )
= $true )
| ( ( element @ ( join_of_latt_set @ SV33 @ SV118 ) @ ( the_carrier @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1806,plain,
! [SV34: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_SY256 @ SV34 ) @ ( powerset @ SV34 ) )
| ~ ~ ( empty @ ( sK9_SY256 @ SV34 ) ) ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1807,plain,
! [SV34: $i] :
( ( ( ~ ( finite @ ( sK9_SY256 @ SV34 ) ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1808,plain,
! [SV36: $i,SV120: $i] :
( ( ( SV120 = empty_set )
= $true )
| ( ( ( complements_of_subsets @ SV36 @ SV120 )
!= empty_set )
= $true )
| ( ( element @ SV120 @ ( powerset @ ( powerset @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(1809,plain,
! [SV121: $i,SV37: $i] :
( ( ( latt_str @ SV37 )
= $false )
| ( ( empty_carrier @ SV37 )
= $true )
| ( ( element @ ( meet_of_latt_set @ SV37 @ SV121 ) @ ( the_carrier @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1810,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) )
| ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1811,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) )
| ~ ( element @ SV162 @ SV41 ) ) )
= $false )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1812,plain,
! [SV125: $i,SV45: $i,SV163: $i] :
( ( ( element @ SV163 @ ( powerset @ SV45 ) )
= $false )
| ( ( element @ SV125 @ ( powerset @ SV45 ) )
= $false )
| ( ( element @ ( subset_difference @ SV45 @ SV125 @ SV163 ) @ ( powerset @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1813,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) )
| ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(1814,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( in @ SV128 @ SV52 ) )
| ~ ( ~ ( in @ SV128 @ SV52 )
| ( element @ SV128 @ SV52 ) ) )
= $false )
| ( ( empty @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1815,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( empty @ SV128 ) ) )
= $false )
| ( ( empty @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1747]) ).
thf(1816,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( ~ ( empty @ SV128 )
| ( element @ SV128 @ SV52 ) ) )
= $false )
| ( ( empty @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1747]) ).
thf(1817,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( element @ SV165 @ ( powerset @ SV54 ) )
= $false )
| ( ( element @ SV129 @ ( powerset @ SV54 ) )
= $false )
| ( ( ( subset_union2 @ SV54 @ SV129 @ SV165 )
= ( set_union2 @ SV129 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1818,plain,
! [SV130: $i,SV56: $i,SV166: $i] :
( ( ( element @ SV166 @ ( powerset @ SV56 ) )
= $false )
| ( ( element @ SV130 @ ( powerset @ SV56 ) )
= $false )
| ( ( ( subset_difference @ SV56 @ SV130 @ SV166 )
= ( set_difference @ SV130 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1819,plain,
! [SV168: $i,SV61: $i,SV132: $i] :
( ( ( ~ ( ( SV132 != empty_set )
| ( SV61 = empty_set ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1752]) ).
thf(1820,plain,
! [SV168: $i,SV61: $i,SV132: $i] :
( ( ( SV132 != empty_set )
= $true )
| ( ( ( SV61 = empty_set )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) )
| ~ ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(1821,plain,
! [SV62: $i,SV184: $i] :
( ( ( v1_xcmplx_0 @ SV184 )
= $true )
| ( ( element @ SV184 @ SV62 )
= $false )
| ( ( v2_membered @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(1822,plain,
! [SV62: $i,SV184: $i] :
( ( ( v1_xreal_0 @ SV184 )
= $true )
| ( ( element @ SV184 @ SV62 )
= $false )
| ( ( v2_membered @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1755]) ).
thf(1823,plain,
! [SV169: $i,SV65: $i,SV134: $i] :
( ( ( in @ SV134 @ ( subset_complement @ SV65 @ SV169 ) )
= $false )
| ( ( ~ ( in @ SV134 @ SV169 ) )
= $true )
| ( ( element @ SV169 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1824,plain,
! [SV135: $i,SV66: $i,SV170: $i] :
( ( ( element @ SV170 @ ( powerset @ SV66 ) )
= $false )
| ( ( element @ SV135 @ ( powerset @ SV66 ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV66 @ SV135 @ SV170 ) @ ( powerset @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1825,plain,
! [SV67: $i,SV136: $i] :
( ( ( proper_element @ SV136 @ SV67 )
= $false )
| ( ( SV136
!= ( union @ SV67 ) )
= $true )
| ( ( element @ SV136 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1826,plain,
! [SV67: $i,SV136: $i] :
( ( ( SV136
!= ( union @ SV67 ) )
= $false )
| ( ( proper_element @ SV136 @ SV67 )
= $true )
| ( ( element @ SV136 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1827,plain,
! [SV69: $i,SV185: $i] :
( ( ( ~ ( ~ ( epsilon_transitive @ SV185 )
| ~ ( epsilon_connected @ SV185 ) ) )
= $true )
| ( ( element @ SV185 @ SV69 )
= $false )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1763]) ).
thf(1828,plain,
! [SV69: $i,SV185: $i] :
( ( ( ordinal @ SV185 )
= $true )
| ( ( element @ SV185 @ SV69 )
= $false )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(1829,plain,
! [SV192: $i,SV186: $i,SV71: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
| ! [SY382: $i] :
( ~ ( element @ SY382 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY382 @ SV186 )
| ( related @ SV71 @ SY382 @ SV192 ) ) ) )
= $false )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1765]) ).
thf(1830,plain,
! [SV192: $i,SV186: $i,SV71: $i] :
( ( ( ~ ( ~ ! [SY383: $i] :
( ~ ( element @ SY383 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY383 @ SV186 )
| ( related @ SV71 @ SY383 @ SV192 ) )
| ( relstr_set_smaller @ SV71 @ SV186 @ SV192 ) ) )
= $false )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1765]) ).
thf(1831,plain,
! [SV73: $i,SV197: $i] :
( ( ( ~ ( element @ SV197 @ ( the_carrier @ SV73 ) ) )
= $true )
| ( ( ! [SY386: $i] :
( ~ ( element @ SY386 @ ( the_carrier @ SV73 ) )
| ! [SY387: $i] :
( ~ ( element @ SY387 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SV197 @ SY386 )
| ~ ( related @ SV73 @ SY386 @ SY387 ) )
| ( related @ SV73 @ SV197 @ SY387 ) ) ) )
= $true )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1832,plain,
! [SV74: $i] :
( ( ( ~ ( element @ ( sK11_SY305 @ SV74 ) @ ( powerset @ SV74 ) ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1833,plain,
! [SV74: $i] :
( ( ( ~ ~ ( empty @ ( sK11_SY305 @ SV74 ) ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1834,plain,
! [SV75: $i,SV187: $i] :
( ( ( v1_membered @ SV187 )
= $true )
| ( ( element @ SV187 @ ( powerset @ SV75 ) )
= $false )
| ( ( v2_membered @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1768]) ).
thf(1835,plain,
! [SV75: $i,SV187: $i] :
( ( ( v2_membered @ SV187 )
= $true )
| ( ( element @ SV187 @ ( powerset @ SV75 ) )
= $false )
| ( ( v2_membered @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1836,plain,
! [SV138: $i,SV76: $i,SV171: $i] :
( ( ( element @ SV171 @ ( powerset @ SV76 ) )
= $false )
| ( ( element @ SV138 @ ( powerset @ SV76 ) )
= $false )
| ( ( element @ ( subset_union2 @ SV76 @ SV138 @ SV171 ) @ ( powerset @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1837,plain,
! [SV193: $i,SV142: $i,SV82: $i] :
( ( ( ~ ( ~ ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 )
| ( subset @ SV142 @ SV193 ) ) )
= $false )
| ( ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1838,plain,
! [SV82: $i,SV193: $i,SV142: $i] :
( ( ( ~ ( ~ ( subset @ SV142 @ SV193 )
| ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 ) ) )
= $false )
| ( ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1839,plain,
! [SV83: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK12_SY314 @ SV83 ) @ ( powerset @ SV83 ) )
| ~ ~ ( empty @ ( sK12_SY314 @ SV83 ) ) ) )
= $false )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1779]) ).
thf(1840,plain,
! [SV83: $i] :
( ( ( ~ ( finite @ ( sK12_SY314 @ SV83 ) ) )
= $false )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1779]) ).
thf(1841,plain,
! [SV87: $i] :
( ( ( empty @ ( the_carrier @ SV87 ) )
= $false )
| ( ( empty_carrier @ SV87 )
= $true )
| ( ( one_sorted_str @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1842,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) )
| ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1784]) ).
thf(1843,plain,
! [SV173: $i,SV146: $i,SV90: $i] :
( ( ( ~ ( in @ SV90 @ SV146 ) )
= $true )
| ( ( ~ ( element @ SV146 @ ( powerset @ SV173 ) ) )
= $true )
| ( ( ~ ( empty @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(1844,plain,
! [SV147: $i,SV91: $i,SV174: $i] :
( ( ( element @ SV174 @ ( powerset @ SV91 ) )
= $false )
| ( ( element @ SV147 @ ( powerset @ SV91 ) )
= $false )
| ( ( ( subset_union2 @ SV91 @ SV147 @ SV174 )
= ( subset_union2 @ SV91 @ SV174 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1845,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) )
| ~ ( element @ SV175 @ SV92 ) ) )
= $false )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1846,plain,
! [SV152: $i,SV98: $i,SV176: $i] :
( ( ( element @ SV176 @ ( powerset @ SV98 ) )
= $false )
| ( ( element @ SV152 @ ( powerset @ SV98 ) )
= $false )
| ( ( ( subset_union2 @ SV98 @ SV152 @ SV152 )
= SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1847,plain,
! [SV100: $i,SV154: $i] :
( ( ( proper_element @ SV154 @ ( powerset @ SV100 ) )
= $false )
| ( ( SV154 != SV100 )
= $true )
| ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(1848,plain,
! [SV100: $i,SV154: $i] :
( ( ( SV154 != SV100 )
= $false )
| ( ( proper_element @ SV154 @ ( powerset @ SV100 ) )
= $true )
| ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1849,plain,
! [SV11: $i,SV195: $i] :
( ( ( element @ SV195 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( ! [SY385: $i] :
( ~ ( element @ SY385 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SV195 @ SY385 )
| ~ ( related @ SV11 @ SY385 @ SV195 ) )
| ( SV195 = SY385 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1850,plain,
! [SV18: $i,SV108: $i] :
( ( ( ~ ( ( SV108 != empty_set ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1795]) ).
thf(1851,plain,
! [SV108: $i,SV18: $i] :
( ( ( ~ ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set ) ) )
= $true )
| ( ( SV108 != empty_set )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(1852,plain,
! [SV22: $i,SV112: $i] :
( ( ( ~ ( ( SV112
!= ( set_meet @ SV22 ) )
| ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1798]) ).
thf(1853,plain,
! [SV22: $i,SV112: $i] :
( ( ( ~ ( ~ ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) )
| ( SV112
= ( set_meet @ SV22 ) ) ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1798]) ).
thf(1854,plain,
! [SV22: $i,SV112: $i] :
( ( ( ( SV112
!= ( set_meet @ SV22 ) )
| ( SV112 = empty_set ) )
= $true )
| ( ( SV22 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1799]) ).
thf(1855,plain,
! [SV22: $i,SV112: $i] :
( ( ( ( SV112 != empty_set )
| ( SV112
= ( set_meet @ SV22 ) ) )
= $true )
| ( ( SV22 = empty_set )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1856,plain,
! [SV189: $i,SV179: $i,SV24: $i] :
( ( ( ~ ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
| ! [SY379: $i] :
( ~ ( element @ SY379 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY379 @ SV179 )
| ( related @ SV24 @ SV189 @ SY379 ) ) )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1857,plain,
! [SV189: $i,SV179: $i,SV24: $i] :
( ( ( ~ ! [SY380: $i] :
( ~ ( element @ SY380 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY380 @ SV179 )
| ( related @ SV24 @ SV189 @ SY380 ) )
| ( relstr_element_smaller @ SV24 @ SV179 @ SV189 ) )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1858,plain,
! [SV190: $i,SV27: $i,SV196: $i] :
( ( ( element @ SV196 @ SV27 )
= $false )
| ( ( ~ ~ ( in @ SV196 @ SV190 )
| ( in @ SV196 @ ( subset_complement @ SV27 @ SV190 ) ) )
= $true )
| ( ( element @ SV190 @ ( powerset @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1859,plain,
! [SV34: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_SY256 @ SV34 ) @ ( powerset @ SV34 ) )
| ~ ~ ( empty @ ( sK9_SY256 @ SV34 ) ) ) )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1860,plain,
! [SV34: $i] :
( ( ( finite @ ( sK9_SY256 @ SV34 ) )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1861,plain,
! [SV120: $i,SV36: $i] :
( ( ( ( complements_of_subsets @ SV36 @ SV120 )
= empty_set )
= $false )
| ( ( SV120 = empty_set )
= $true )
| ( ( element @ SV120 @ ( powerset @ ( powerset @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1862,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(1863,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) )
| ~ ( element @ SV162 @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1864,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) ) )
= $true )
| ( ( ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(1865,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( ~ ( element @ SV128 @ SV52 )
| ( in @ SV128 @ SV52 ) ) )
= $false )
| ( ( empty @ SV52 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1814]) ).
thf(1866,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( ~ ( in @ SV128 @ SV52 )
| ( element @ SV128 @ SV52 ) ) )
= $false )
| ( ( empty @ SV52 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1814]) ).
thf(1867,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( element @ SV128 @ SV52 )
| ( empty @ SV128 ) )
= $true )
| ( ( empty @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1868,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( empty @ SV128 )
| ( element @ SV128 @ SV52 ) )
= $true )
| ( ( empty @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(1869,plain,
! [SV168: $i,SV61: $i,SV132: $i] :
( ( ( ( SV132 != empty_set )
| ( SV61 = empty_set ) )
= $false )
| ( ( ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1870,plain,
! [SV168: $i,SV61: $i,SV132: $i] :
( ( ( SV132 = empty_set )
= $false )
| ( ( ( SV61 = empty_set )
| ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) )
| ~ ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1871,plain,
! [SV65: $i,SV169: $i,SV134: $i] :
( ( ( in @ SV134 @ SV169 )
= $false )
| ( ( in @ SV134 @ ( subset_complement @ SV65 @ SV169 ) )
= $false )
| ( ( element @ SV169 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1872,plain,
! [SV67: $i,SV136: $i] :
( ( ( SV136
= ( union @ SV67 ) )
= $false )
| ( ( proper_element @ SV136 @ SV67 )
= $false )
| ( ( element @ SV136 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(1873,plain,
! [SV67: $i,SV136: $i] :
( ( ( SV136
= ( union @ SV67 ) )
= $true )
| ( ( proper_element @ SV136 @ SV67 )
= $true )
| ( ( element @ SV136 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1826]) ).
thf(1874,plain,
! [SV69: $i,SV185: $i] :
( ( ( ~ ( epsilon_transitive @ SV185 )
| ~ ( epsilon_connected @ SV185 ) )
= $false )
| ( ( element @ SV185 @ SV69 )
= $false )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1875,plain,
! [SV192: $i,SV186: $i,SV71: $i] :
( ( ( ~ ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
| ! [SY382: $i] :
( ~ ( element @ SY382 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY382 @ SV186 )
| ( related @ SV71 @ SY382 @ SV192 ) ) )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1829]) ).
thf(1876,plain,
! [SV192: $i,SV186: $i,SV71: $i] :
( ( ( ~ ! [SY383: $i] :
( ~ ( element @ SY383 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY383 @ SV186 )
| ( related @ SV71 @ SY383 @ SV192 ) )
| ( relstr_set_smaller @ SV71 @ SV186 @ SV192 ) )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1830]) ).
thf(1877,plain,
! [SV73: $i,SV197: $i] :
( ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( ! [SY386: $i] :
( ~ ( element @ SY386 @ ( the_carrier @ SV73 ) )
| ! [SY387: $i] :
( ~ ( element @ SY387 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SV197 @ SY386 )
| ~ ( related @ SV73 @ SY386 @ SY387 ) )
| ( related @ SV73 @ SV197 @ SY387 ) ) ) )
= $true )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(1878,plain,
! [SV74: $i] :
( ( ( element @ ( sK11_SY305 @ SV74 ) @ ( powerset @ SV74 ) )
= $true )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1832]) ).
thf(1879,plain,
! [SV74: $i] :
( ( ( ~ ( empty @ ( sK11_SY305 @ SV74 ) ) )
= $true )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1833]) ).
thf(1880,plain,
! [SV193: $i,SV142: $i,SV82: $i] :
( ( ( ~ ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 )
| ( subset @ SV142 @ SV193 ) )
= $true )
| ( ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1881,plain,
! [SV82: $i,SV193: $i,SV142: $i] :
( ( ( ~ ( subset @ SV142 @ SV193 )
| ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 ) )
= $true )
| ( ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1838]) ).
thf(1882,plain,
! [SV83: $i] :
( ( ( ~ ( ~ ( element @ ( sK12_SY314 @ SV83 ) @ ( powerset @ SV83 ) )
| ~ ~ ( empty @ ( sK12_SY314 @ SV83 ) ) ) )
= $true )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1839]) ).
thf(1883,plain,
! [SV83: $i] :
( ( ( finite @ ( sK12_SY314 @ SV83 ) )
= $true )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1840]) ).
thf(1884,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) ) )
= $true )
| ( ( ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(1885,plain,
! [SV173: $i,SV146: $i,SV90: $i] :
( ( ( in @ SV90 @ SV146 )
= $false )
| ( ( ~ ( element @ SV146 @ ( powerset @ SV173 ) ) )
= $true )
| ( ( ~ ( empty @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(1886,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) )
| ~ ( element @ SV175 @ SV92 ) )
= $true )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(1887,plain,
! [SV100: $i,SV154: $i] :
( ( ( SV154 = SV100 )
= $false )
| ( ( proper_element @ SV154 @ ( powerset @ SV100 ) )
= $false )
| ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1888,plain,
! [SV100: $i,SV154: $i] :
( ( ( SV154 = SV100 )
= $true )
| ( ( proper_element @ SV154 @ ( powerset @ SV100 ) )
= $true )
| ( ( element @ SV154 @ ( powerset @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1889,plain,
! [SV195: $i,SV11: $i,SV198: $i] :
( ( ( ~ ( element @ SV198 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SV195 @ SV198 )
| ~ ( related @ SV11 @ SV198 @ SV195 ) )
| ( SV195 = SV198 ) )
= $true )
| ( ( element @ SV195 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(1890,plain,
! [SV18: $i,SV108: $i] :
( ( ( SV108 != empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1891,plain,
! [SV108: $i,SV18: $i] :
( ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set )
= $false )
| ( ( SV108 != empty_set )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1892,plain,
! [SV22: $i,SV112: $i] :
( ( ( ( SV112
!= ( set_meet @ SV22 ) )
| ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1852]) ).
thf(1893,plain,
! [SV22: $i,SV112: $i] :
( ( ( ~ ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) )
| ( SV112
= ( set_meet @ SV22 ) ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(1894,plain,
! [SV22: $i,SV112: $i] :
( ( ( SV112
!= ( set_meet @ SV22 ) )
= $true )
| ( ( SV112 = empty_set )
= $true )
| ( ( SV22 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(1895,plain,
! [SV22: $i,SV112: $i] :
( ( ( SV112 != empty_set )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(1896,plain,
! [SV189: $i,SV179: $i,SV24: $i] :
( ( ( ~ ( relstr_element_smaller @ SV24 @ SV179 @ SV189 ) )
= $true )
| ( ( ! [SY379: $i] :
( ~ ( element @ SY379 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY379 @ SV179 )
| ( related @ SV24 @ SV189 @ SY379 ) ) )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(1897,plain,
! [SV189: $i,SV179: $i,SV24: $i] :
( ( ( ~ ! [SY380: $i] :
( ~ ( element @ SY380 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY380 @ SV179 )
| ( related @ SV24 @ SV189 @ SY380 ) ) )
= $true )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1857]) ).
thf(1898,plain,
! [SV27: $i,SV190: $i,SV196: $i] :
( ( ( ~ ~ ( in @ SV196 @ SV190 ) )
= $true )
| ( ( in @ SV196 @ ( subset_complement @ SV27 @ SV190 ) )
= $true )
| ( ( element @ SV196 @ SV27 )
= $false )
| ( ( element @ SV190 @ ( powerset @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(1899,plain,
! [SV34: $i] :
( ( ( ~ ( element @ ( sK9_SY256 @ SV34 ) @ ( powerset @ SV34 ) )
| ~ ~ ( empty @ ( sK9_SY256 @ SV34 ) ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1900,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) ) )
= $false )
| ( ( ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1901,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) ) )
= $true )
| ( ( ~ ( element @ SV162 @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(1902,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) ) )
= $false )
| ( ( ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(1903,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( element @ SV128 @ SV52 )
| ( in @ SV128 @ SV52 ) )
= $true )
| ( ( empty @ SV52 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1865]) ).
thf(1904,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ SV52 )
| ( element @ SV128 @ SV52 ) )
= $true )
| ( ( empty @ SV52 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1866]) ).
thf(1905,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( element @ SV128 @ SV52 ) )
= $true )
| ( ( empty @ SV128 )
= $true )
| ( ( empty @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(1906,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( empty @ SV128 ) )
= $true )
| ( ( element @ SV128 @ SV52 )
= $true )
| ( ( empty @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(1907,plain,
! [SV61: $i,SV168: $i,SV132: $i] :
( ( ( SV132 != empty_set )
= $false )
| ( ( ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(1908,plain,
! [SV132: $i,SV168: $i,SV61: $i] :
( ( ( SV61 = empty_set )
= $false )
| ( ( ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(1909,plain,
! [SV132: $i,SV168: $i,SV61: $i] :
( ( ( SV61 = empty_set )
= $true )
| ( ( ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) )
| ~ ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
= $true )
| ( ( SV132 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(1910,plain,
! [SV69: $i,SV185: $i] :
( ( ( ~ ( epsilon_transitive @ SV185 ) )
= $false )
| ( ( element @ SV185 @ SV69 )
= $false )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1911,plain,
! [SV69: $i,SV185: $i] :
( ( ( ~ ( epsilon_connected @ SV185 ) )
= $false )
| ( ( element @ SV185 @ SV69 )
= $false )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1912,plain,
! [SV192: $i,SV186: $i,SV71: $i] :
( ( ( ~ ( relstr_set_smaller @ SV71 @ SV186 @ SV192 ) )
= $true )
| ( ( ! [SY382: $i] :
( ~ ( element @ SY382 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY382 @ SV186 )
| ( related @ SV71 @ SY382 @ SV192 ) ) )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(1913,plain,
! [SV192: $i,SV186: $i,SV71: $i] :
( ( ( ~ ! [SY383: $i] :
( ~ ( element @ SY383 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY383 @ SV186 )
| ( related @ SV71 @ SY383 @ SV192 ) ) )
= $true )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(1914,plain,
! [SV197: $i,SV73: $i,SV199: $i] :
( ( ( ~ ( element @ SV199 @ ( the_carrier @ SV73 ) )
| ! [SY388: $i] :
( ~ ( element @ SY388 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SV197 @ SV199 )
| ~ ( related @ SV73 @ SV199 @ SY388 ) )
| ( related @ SV73 @ SV197 @ SY388 ) ) )
= $true )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(1915,plain,
! [SV74: $i] :
( ( ( empty @ ( sK11_SY305 @ SV74 ) )
= $false )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1916,plain,
! [SV193: $i,SV142: $i,SV82: $i] :
( ( ( ~ ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 ) )
= $true )
| ( ( subset @ SV142 @ SV193 )
= $true )
| ( ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(1917,plain,
! [SV82: $i,SV193: $i,SV142: $i] :
( ( ( ~ ( subset @ SV142 @ SV193 ) )
= $true )
| ( ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 )
= $true )
| ( ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(1918,plain,
! [SV83: $i] :
( ( ( ~ ( element @ ( sK12_SY314 @ SV83 ) @ ( powerset @ SV83 ) )
| ~ ~ ( empty @ ( sK12_SY314 @ SV83 ) ) )
= $false )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(1919,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) ) )
= $false )
| ( ( ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1920,plain,
! [SV90: $i,SV173: $i,SV146: $i] :
( ( ( element @ SV146 @ ( powerset @ SV173 ) )
= $false )
| ( ( in @ SV90 @ SV146 )
= $false )
| ( ( ~ ( empty @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1921,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) ) )
= $true )
| ( ( ~ ( element @ SV175 @ SV92 ) )
= $true )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(1922,plain,
! [SV195: $i,SV11: $i,SV198: $i] :
( ( ( ~ ( element @ SV198 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( related @ SV11 @ SV195 @ SV198 )
| ~ ( related @ SV11 @ SV198 @ SV195 ) )
| ( SV195 = SV198 ) )
= $true )
| ( ( element @ SV195 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(1923,plain,
! [SV18: $i,SV108: $i] :
( ( ( SV108 = empty_set )
= $true )
| ( ( ( complements_of_subsets @ SV18 @ SV108 )
!= empty_set )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1890]) ).
thf(1924,plain,
! [SV108: $i,SV18: $i] :
( ( ( ( complements_of_subsets @ SV18 @ SV108 )
= empty_set )
= $true )
| ( ( SV108 != empty_set )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(1925,plain,
! [SV22: $i,SV112: $i] :
( ( ( SV112
!= ( set_meet @ SV22 ) )
= $true )
| ( ( ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(1926,plain,
! [SV22: $i,SV112: $i] :
( ( ( ~ ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(1927,plain,
! [SV22: $i,SV112: $i] :
( ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV112 = empty_set )
= $true )
| ( ( SV22 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(1928,plain,
! [SV22: $i,SV112: $i] :
( ( ( SV112 = empty_set )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1929,plain,
! [SV189: $i,SV179: $i,SV24: $i] :
( ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $false )
| ( ( ! [SY379: $i] :
( ~ ( element @ SY379 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY379 @ SV179 )
| ( related @ SV24 @ SV189 @ SY379 ) ) )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(1930,plain,
! [SV189: $i,SV179: $i,SV24: $i] :
( ( ( ! [SY380: $i] :
( ~ ( element @ SY380 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SY380 @ SV179 )
| ( related @ SV24 @ SV189 @ SY380 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(1931,plain,
! [SV27: $i,SV190: $i,SV196: $i] :
( ( ( ~ ( in @ SV196 @ SV190 ) )
= $false )
| ( ( in @ SV196 @ ( subset_complement @ SV27 @ SV190 ) )
= $true )
| ( ( element @ SV196 @ SV27 )
= $false )
| ( ( element @ SV190 @ ( powerset @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(1932,plain,
! [SV34: $i] :
( ( ( ~ ( element @ ( sK9_SY256 @ SV34 ) @ ( powerset @ SV34 ) ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1933,plain,
! [SV34: $i] :
( ( ( ~ ~ ( empty @ ( sK9_SY256 @ SV34 ) ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1934,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
| ~ ( rel_str @ SV40 ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(1935,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) ) )
= $false )
| ( ( ~ ( element @ SV162 @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(1936,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( ~ ~ ( empty_carrier @ SV49 )
| ~ ( join_semilatt_str @ SV49 ) )
= $true )
| ( ( ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(1937,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( element @ SV128 @ SV52 ) )
= $true )
| ( ( in @ SV128 @ SV52 )
= $true )
| ( ( empty @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(1938,plain,
! [SV52: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ SV52 ) )
= $true )
| ( ( element @ SV128 @ SV52 )
= $true )
| ( ( empty @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(1939,plain,
! [SV52: $i,SV128: $i] :
( ( ( element @ SV128 @ SV52 )
= $false )
| ( ( empty @ SV128 )
= $true )
| ( ( empty @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(1940,plain,
! [SV52: $i,SV128: $i] :
( ( ( empty @ SV128 )
= $false )
| ( ( element @ SV128 @ SV52 )
= $true )
| ( ( empty @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(1941,plain,
! [SV61: $i,SV168: $i,SV132: $i] :
( ( ( SV132 = empty_set )
= $true )
| ( ( ~ ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1907]) ).
thf(1942,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) )
= $false )
| ( ( SV61 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(1943,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) )
| ~ ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) )
= $false )
| ( ( SV61 = empty_set )
= $true )
| ( ( SV132 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(1944,plain,
! [SV69: $i,SV185: $i] :
( ( ( epsilon_transitive @ SV185 )
= $true )
| ( ( element @ SV185 @ SV69 )
= $false )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(1945,plain,
! [SV69: $i,SV185: $i] :
( ( ( epsilon_connected @ SV185 )
= $true )
| ( ( element @ SV185 @ SV69 )
= $false )
| ( ( ordinal @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1911]) ).
thf(1946,plain,
! [SV192: $i,SV186: $i,SV71: $i] :
( ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $false )
| ( ( ! [SY382: $i] :
( ~ ( element @ SY382 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY382 @ SV186 )
| ( related @ SV71 @ SY382 @ SV192 ) ) )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(1947,plain,
! [SV192: $i,SV186: $i,SV71: $i] :
( ( ( ! [SY383: $i] :
( ~ ( element @ SY383 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SY383 @ SV186 )
| ( related @ SV71 @ SY383 @ SV192 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(1948,plain,
! [SV197: $i,SV73: $i,SV199: $i] :
( ( ( ~ ( element @ SV199 @ ( the_carrier @ SV73 ) ) )
= $true )
| ( ( ! [SY388: $i] :
( ~ ( element @ SY388 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SV197 @ SV199 )
| ~ ( related @ SV73 @ SV199 @ SY388 ) )
| ( related @ SV73 @ SV197 @ SY388 ) ) )
= $true )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(1949,plain,
! [SV193: $i,SV142: $i,SV82: $i] :
( ( ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 )
= $false )
| ( ( subset @ SV142 @ SV193 )
= $true )
| ( ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(1950,plain,
! [SV82: $i,SV193: $i,SV142: $i] :
( ( ( subset @ SV142 @ SV193 )
= $false )
| ( ( below @ ( boole_lattice @ SV82 ) @ SV142 @ SV193 )
= $true )
| ( ( element @ SV193 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false )
| ( ( element @ SV142 @ ( the_carrier @ ( boole_lattice @ SV82 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(1951,plain,
! [SV83: $i] :
( ( ( ~ ( element @ ( sK12_SY314 @ SV83 ) @ ( powerset @ SV83 ) ) )
= $false )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1918]) ).
thf(1952,plain,
! [SV83: $i] :
( ( ( ~ ~ ( empty @ ( sK12_SY314 @ SV83 ) ) )
= $false )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1918]) ).
thf(1953,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( ~ ~ ( empty_carrier @ SV88 )
| ~ ( meet_semilatt_str @ SV88 ) )
= $true )
| ( ( ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(1954,plain,
! [SV146: $i,SV90: $i,SV173: $i] :
( ( ( empty @ SV173 )
= $false )
| ( ( in @ SV90 @ SV146 )
= $false )
| ( ( element @ SV146 @ ( powerset @ SV173 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(1955,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) ) )
= $false )
| ( ( ~ ( element @ SV175 @ SV92 ) )
= $true )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(1956,plain,
! [SV195: $i,SV11: $i,SV198: $i] :
( ( ( element @ SV198 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( ~ ~ ( ~ ( related @ SV11 @ SV195 @ SV198 )
| ~ ( related @ SV11 @ SV198 @ SV195 ) )
| ( SV195 = SV198 ) )
= $true )
| ( ( element @ SV195 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1957,plain,
! [SV108: $i,SV18: $i] :
( ( ( ( complements_of_subsets @ SV18 @ SV108 )
= empty_set )
= $false )
| ( ( SV108 = empty_set )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(1958,plain,
! [SV18: $i,SV108: $i] :
( ( ( SV108 = empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV18 @ SV108 )
= empty_set )
= $true )
| ( ( element @ SV108 @ ( powerset @ ( powerset @ SV18 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(1959,plain,
! [SV22: $i,SV112: $i] :
( ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( ! [SY341: $i] :
~ ( ~ ( ~ ( in @ SY341 @ SV112 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV22 )
| ( in @ SY341 @ SY236 ) ) )
| ~ ( ~ ! [SY237: $i] :
( ~ ( in @ SY237 @ SV22 )
| ( in @ SY341 @ SY237 ) )
| ( in @ SY341 @ SV112 ) ) ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(1960,plain,
! [SV22: $i,SV112: $i] :
( ( ( ! [SY344: $i] :
~ ( ~ ( ~ ( in @ SY344 @ SV112 )
| ! [SY239: $i] :
( ~ ( in @ SY239 @ SV22 )
| ( in @ SY344 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV22 )
| ( in @ SY344 @ SY240 ) )
| ( in @ SY344 @ SV112 ) ) ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(1961,plain,
! [SV189: $i,SV179: $i,SV24: $i,SV200: $i] :
( ( ( ~ ( element @ SV200 @ ( the_carrier @ SV24 ) )
| ~ ( in @ SV200 @ SV179 )
| ( related @ SV24 @ SV189 @ SV200 ) )
= $true )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $false )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(1962,plain,
! [SV24: $i,SV179: $i,SV189: $i] :
( ( ( ~ ( element @ ( sK15_SY380 @ SV189 @ SV179 @ SV24 ) @ ( the_carrier @ SV24 ) )
| ~ ( in @ ( sK15_SY380 @ SV189 @ SV179 @ SV24 ) @ SV179 )
| ( related @ SV24 @ SV189 @ ( sK15_SY380 @ SV189 @ SV179 @ SV24 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1930]) ).
thf(1963,plain,
! [SV27: $i,SV190: $i,SV196: $i] :
( ( ( in @ SV196 @ SV190 )
= $true )
| ( ( in @ SV196 @ ( subset_complement @ SV27 @ SV190 ) )
= $true )
| ( ( element @ SV196 @ SV27 )
= $false )
| ( ( element @ SV190 @ ( powerset @ SV27 ) )
= $false )
| ( ( SV27 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1931]) ).
thf(1964,plain,
! [SV34: $i] :
( ( ( element @ ( sK9_SY256 @ SV34 ) @ ( powerset @ SV34 ) )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1932]) ).
thf(1965,plain,
! [SV34: $i] :
( ( ( ~ ( empty @ ( sK9_SY256 @ SV34 ) ) )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1933]) ).
thf(1966,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) ) )
= $true )
| ( ( ~ ( rel_str @ SV40 ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(1967,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( ~ ~ ( empty @ SV41 )
| ~ ~ ( empty @ SV124 ) )
= $true )
| ( ( ~ ( element @ SV162 @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1935]) ).
thf(1968,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( ~ ~ ( empty_carrier @ SV49 ) )
= $true )
| ( ( ~ ( join_semilatt_str @ SV49 ) )
= $true )
| ( ( ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(1969,plain,
! [SV52: $i,SV128: $i] :
( ( ( element @ SV128 @ SV52 )
= $false )
| ( ( in @ SV128 @ SV52 )
= $true )
| ( ( empty @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(1970,plain,
! [SV52: $i,SV128: $i] :
( ( ( in @ SV128 @ SV52 )
= $false )
| ( ( element @ SV128 @ SV52 )
= $true )
| ( ( empty @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(1971,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
| ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) )
= $false )
| ( ( SV132 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(1972,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) ) )
= $false )
| ( ( SV61 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(1973,plain,
! [SV168: $i,SV132: $i,SV61: $i] :
( ( ( ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) )
= $false )
| ( ( SV61 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(1974,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) ) )
= $false )
| ( ( SV61 = empty_set )
= $true )
| ( ( SV132 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(1975,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) )
= $false )
| ( ( SV61 = empty_set )
= $true )
| ( ( SV132 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(1976,plain,
! [SV192: $i,SV186: $i,SV71: $i,SV201: $i] :
( ( ( ~ ( element @ SV201 @ ( the_carrier @ SV71 ) )
| ~ ( in @ SV201 @ SV186 )
| ( related @ SV71 @ SV201 @ SV192 ) )
= $true )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $false )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(1977,plain,
! [SV71: $i,SV186: $i,SV192: $i] :
( ( ( ~ ( element @ ( sK16_SY383 @ SV192 @ SV186 @ SV71 ) @ ( the_carrier @ SV71 ) )
| ~ ( in @ ( sK16_SY383 @ SV192 @ SV186 @ SV71 ) @ SV186 )
| ( related @ SV71 @ ( sK16_SY383 @ SV192 @ SV186 @ SV71 ) @ SV192 ) )
= $false )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1947]) ).
thf(1978,plain,
! [SV197: $i,SV73: $i,SV199: $i] :
( ( ( element @ SV199 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( ! [SY388: $i] :
( ~ ( element @ SY388 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SV197 @ SV199 )
| ~ ( related @ SV73 @ SV199 @ SY388 ) )
| ( related @ SV73 @ SV197 @ SY388 ) ) )
= $true )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(1979,plain,
! [SV83: $i] :
( ( ( element @ ( sK12_SY314 @ SV83 ) @ ( powerset @ SV83 ) )
= $true )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1951]) ).
thf(1980,plain,
! [SV83: $i] :
( ( ( ~ ( empty @ ( sK12_SY314 @ SV83 ) ) )
= $true )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(1981,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( ~ ~ ( empty_carrier @ SV88 ) )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV88 ) )
= $true )
| ( ( ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(1982,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( ~ ~ ( empty @ SV92 )
| ~ ~ ( empty @ SV148 ) )
= $true )
| ( ( ~ ( element @ SV175 @ SV92 ) )
= $true )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1955]) ).
thf(1983,plain,
! [SV198: $i,SV195: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( related @ SV11 @ SV195 @ SV198 )
| ~ ( related @ SV11 @ SV198 @ SV195 ) ) )
= $true )
| ( ( SV195 = SV198 )
= $true )
| ( ( element @ SV198 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV195 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(1984,plain,
! [SV22: $i,SV112: $i,SV202: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV202 @ SV112 )
| ! [SY389: $i] :
( ~ ( in @ SY389 @ SV22 )
| ( in @ SV202 @ SY389 ) ) )
| ~ ( ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV22 )
| ( in @ SV202 @ SY390 ) )
| ( in @ SV202 @ SV112 ) ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(1985,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
| ! [SY391: $i] :
( ~ ( in @ SY391 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY391 ) ) )
| ~ ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) ) ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1960]) ).
thf(1986,plain,
! [SV189: $i,SV179: $i,SV24: $i,SV200: $i] :
( ( ( ~ ( element @ SV200 @ ( the_carrier @ SV24 ) ) )
= $true )
| ( ( ~ ( in @ SV200 @ SV179 )
| ( related @ SV24 @ SV189 @ SV200 ) )
= $true )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $false )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(1987,plain,
! [SV24: $i,SV179: $i,SV189: $i] :
( ( ( ~ ( element @ ( sK15_SY380 @ SV189 @ SV179 @ SV24 ) @ ( the_carrier @ SV24 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1962]) ).
thf(1988,plain,
! [SV24: $i,SV179: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK15_SY380 @ SV189 @ SV179 @ SV24 ) @ SV179 )
| ( related @ SV24 @ SV189 @ ( sK15_SY380 @ SV189 @ SV179 @ SV24 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1962]) ).
thf(1989,plain,
! [SV34: $i] :
( ( ( empty @ ( sK9_SY256 @ SV34 ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(1990,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) ) )
= $false )
| ( ( ~ ( rel_str @ SV40 ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(1991,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( ~ ~ ( empty @ SV41 ) )
= $true )
| ( ( ~ ~ ( empty @ SV124 ) )
= $true )
| ( ( ~ ( element @ SV162 @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1967]) ).
thf(1992,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( ~ ( empty_carrier @ SV49 ) )
= $false )
| ( ( ~ ( join_semilatt_str @ SV49 ) )
= $true )
| ( ( ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(1993,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) ) )
= $false )
| ( ( SV132 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(1994,plain,
! [SV168: $i,SV132: $i,SV61: $i] :
( ( ( ~ ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) ) )
= $false )
| ( ( SV132 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(1995,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
= $true )
| ( ( SV61 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1972]) ).
thf(1996,plain,
! [SV168: $i,SV132: $i,SV61: $i] :
( ( ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) )
= $true )
| ( ( SV61 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1973]) ).
thf(1997,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV168 = empty_set ) )
= $true )
| ( ( SV61 = empty_set )
= $true )
| ( ( SV132 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(1998,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ( SV168 != empty_set )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) )
= $true )
| ( ( SV61 = empty_set )
= $true )
| ( ( SV132 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1975]) ).
thf(1999,plain,
! [SV192: $i,SV186: $i,SV71: $i,SV201: $i] :
( ( ( ~ ( element @ SV201 @ ( the_carrier @ SV71 ) ) )
= $true )
| ( ( ~ ( in @ SV201 @ SV186 )
| ( related @ SV71 @ SV201 @ SV192 ) )
= $true )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $false )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2000,plain,
! [SV71: $i,SV186: $i,SV192: $i] :
( ( ( ~ ( element @ ( sK16_SY383 @ SV192 @ SV186 @ SV71 ) @ ( the_carrier @ SV71 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1977]) ).
thf(2001,plain,
! [SV71: $i,SV186: $i,SV192: $i] :
( ( ( ~ ( in @ ( sK16_SY383 @ SV192 @ SV186 @ SV71 ) @ SV186 )
| ( related @ SV71 @ ( sK16_SY383 @ SV192 @ SV186 @ SV71 ) @ SV192 ) )
= $false )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1977]) ).
thf(2002,plain,
! [SV199: $i,SV197: $i,SV73: $i,SV203: $i] :
( ( ( ~ ( element @ SV203 @ ( the_carrier @ SV73 ) )
| ~ ~ ( ~ ( related @ SV73 @ SV197 @ SV199 )
| ~ ( related @ SV73 @ SV199 @ SV203 ) )
| ( related @ SV73 @ SV197 @ SV203 ) )
= $true )
| ( ( element @ SV199 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2003,plain,
! [SV83: $i] :
( ( ( empty @ ( sK12_SY314 @ SV83 ) )
= $false )
| ( ( empty @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2004,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( ~ ( empty_carrier @ SV88 ) )
= $false )
| ( ( ~ ( meet_semilatt_str @ SV88 ) )
= $true )
| ( ( ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2005,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( ~ ~ ( empty @ SV92 ) )
= $true )
| ( ( ~ ~ ( empty @ SV148 ) )
= $true )
| ( ( ~ ( element @ SV175 @ SV92 ) )
= $true )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1982]) ).
thf(2006,plain,
! [SV198: $i,SV195: $i,SV11: $i] :
( ( ( ~ ( ~ ( related @ SV11 @ SV195 @ SV198 )
| ~ ( related @ SV11 @ SV198 @ SV195 ) ) )
= $false )
| ( ( SV195 = SV198 )
= $true )
| ( ( element @ SV198 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV195 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2007,plain,
! [SV22: $i,SV112: $i,SV202: $i] :
( ( ( ~ ( ~ ( in @ SV202 @ SV112 )
| ! [SY389: $i] :
( ~ ( in @ SY389 @ SV22 )
| ( in @ SV202 @ SY389 ) ) )
| ~ ( ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV22 )
| ( in @ SV202 @ SY390 ) )
| ( in @ SV202 @ SV112 ) ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2008,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
| ! [SY391: $i] :
( ~ ( in @ SY391 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY391 ) ) )
| ~ ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2009,plain,
! [SV189: $i,SV179: $i,SV24: $i,SV200: $i] :
( ( ( element @ SV200 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( ~ ( in @ SV200 @ SV179 )
| ( related @ SV24 @ SV189 @ SV200 ) )
= $true )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $false )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2010,plain,
! [SV24: $i,SV179: $i,SV189: $i] :
( ( ( element @ ( sK15_SY380 @ SV189 @ SV179 @ SV24 ) @ ( the_carrier @ SV24 ) )
= $true )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1987]) ).
thf(2011,plain,
! [SV24: $i,SV179: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK15_SY380 @ SV189 @ SV179 @ SV24 ) @ SV179 ) )
= $false )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2012,plain,
! [SV179: $i,SV189: $i,SV24: $i] :
( ( ( related @ SV24 @ SV189 @ ( sK15_SY380 @ SV189 @ SV179 @ SV24 ) )
= $false )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2013,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ~ ( empty_carrier @ SV40 )
| ~ ( reflexive_relstr @ SV40 ) )
= $true )
| ( ( ~ ( rel_str @ SV40 ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1990]) ).
thf(2014,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( ~ ( empty @ SV41 ) )
= $false )
| ( ( ~ ~ ( empty @ SV124 ) )
= $true )
| ( ( ~ ( element @ SV162 @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1991]) ).
thf(2015,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( empty_carrier @ SV49 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV49 ) )
= $true )
| ( ( ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1992]) ).
thf(2016,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 )
| ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) ) )
= $true )
| ( ( SV132 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1993]) ).
thf(2017,plain,
! [SV168: $i,SV132: $i,SV61: $i] :
( ( ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
| ( quasi_total @ SV168 @ SV61 @ SV132 ) )
= $true )
| ( ( SV132 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1994]) ).
thf(2018,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 ) )
= $true )
| ( ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
= $true )
| ( ( SV61 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2019,plain,
! [SV168: $i,SV132: $i,SV61: $i] :
( ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
= $true )
| ( ( quasi_total @ SV168 @ SV61 @ SV132 )
= $true )
| ( ( SV61 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2020,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 ) )
= $true )
| ( ( SV168 = empty_set )
= $true )
| ( ( SV61 = empty_set )
= $true )
| ( ( SV132 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2021,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( SV168 != empty_set )
= $true )
| ( ( quasi_total @ SV168 @ SV61 @ SV132 )
= $true )
| ( ( SV61 = empty_set )
= $true )
| ( ( SV132 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2022,plain,
! [SV192: $i,SV186: $i,SV71: $i,SV201: $i] :
( ( ( element @ SV201 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( ~ ( in @ SV201 @ SV186 )
| ( related @ SV71 @ SV201 @ SV192 ) )
= $true )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $false )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2023,plain,
! [SV71: $i,SV186: $i,SV192: $i] :
( ( ( element @ ( sK16_SY383 @ SV192 @ SV186 @ SV71 ) @ ( the_carrier @ SV71 ) )
= $true )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2000]) ).
thf(2024,plain,
! [SV71: $i,SV186: $i,SV192: $i] :
( ( ( ~ ( in @ ( sK16_SY383 @ SV192 @ SV186 @ SV71 ) @ SV186 ) )
= $false )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2001]) ).
thf(2025,plain,
! [SV186: $i,SV192: $i,SV71: $i] :
( ( ( related @ SV71 @ ( sK16_SY383 @ SV192 @ SV186 @ SV71 ) @ SV192 )
= $false )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2001]) ).
thf(2026,plain,
! [SV199: $i,SV197: $i,SV73: $i,SV203: $i] :
( ( ( ~ ( element @ SV203 @ ( the_carrier @ SV73 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( related @ SV73 @ SV197 @ SV199 )
| ~ ( related @ SV73 @ SV199 @ SV203 ) )
| ( related @ SV73 @ SV197 @ SV203 ) )
= $true )
| ( ( element @ SV199 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2027,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( empty_carrier @ SV88 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV88 ) )
= $true )
| ( ( ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2004]) ).
thf(2028,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( ~ ( empty @ SV92 ) )
= $false )
| ( ( ~ ~ ( empty @ SV148 ) )
= $true )
| ( ( ~ ( element @ SV175 @ SV92 ) )
= $true )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2029,plain,
! [SV198: $i,SV195: $i,SV11: $i] :
( ( ( ~ ( related @ SV11 @ SV195 @ SV198 )
| ~ ( related @ SV11 @ SV198 @ SV195 ) )
= $true )
| ( ( SV195 = SV198 )
= $true )
| ( ( element @ SV198 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV195 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2030,plain,
! [SV22: $i,SV112: $i,SV202: $i] :
( ( ( ~ ( ~ ( in @ SV202 @ SV112 )
| ! [SY389: $i] :
( ~ ( in @ SY389 @ SV22 )
| ( in @ SV202 @ SY389 ) ) ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2007]) ).
thf(2031,plain,
! [SV112: $i,SV202: $i,SV22: $i] :
( ( ( ~ ( ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV22 )
| ( in @ SV202 @ SY390 ) )
| ( in @ SV202 @ SV112 ) ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2007]) ).
thf(2032,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
| ! [SY391: $i] :
( ~ ( in @ SY391 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY391 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2033,plain,
! [SV189: $i,SV24: $i,SV179: $i,SV200: $i] :
( ( ( ~ ( in @ SV200 @ SV179 ) )
= $true )
| ( ( related @ SV24 @ SV189 @ SV200 )
= $true )
| ( ( element @ SV200 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $false )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2034,plain,
! [SV24: $i,SV179: $i,SV189: $i] :
( ( ( in @ ( sK15_SY380 @ SV189 @ SV179 @ SV24 ) @ SV179 )
= $true )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $true )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2035,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ~ ( empty_carrier @ SV40 ) )
= $true )
| ( ( ~ ( reflexive_relstr @ SV40 ) )
= $true )
| ( ( ~ ( rel_str @ SV40 ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2013]) ).
thf(2036,plain,
! [SV180: $i,SV162: $i,SV124: $i,SV41: $i] :
( ( ( empty @ SV41 )
= $true )
| ( ( ~ ~ ( empty @ SV124 ) )
= $true )
| ( ( ~ ( element @ SV162 @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2014]) ).
thf(2037,plain,
! [SV164: $i,SV127: $i,SV49: $i] :
( ( ( join_semilatt_str @ SV49 )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( ~ ( element @ SV127 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2038,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( ~ ( quasi_total @ SV168 @ SV61 @ SV132 ) )
= $true )
| ( ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
= $true )
| ( ( SV132 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2039,plain,
! [SV168: $i,SV132: $i,SV61: $i] :
( ( ( SV61
!= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
= $true )
| ( ( quasi_total @ SV168 @ SV61 @ SV132 )
= $true )
| ( ( SV132 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2040,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( quasi_total @ SV168 @ SV61 @ SV132 )
= $false )
| ( ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
= $true )
| ( ( SV61 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2041,plain,
! [SV168: $i,SV132: $i,SV61: $i] :
( ( ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
= $false )
| ( ( quasi_total @ SV168 @ SV61 @ SV132 )
= $true )
| ( ( SV61 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2042,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( quasi_total @ SV168 @ SV61 @ SV132 )
= $false )
| ( ( SV168 = empty_set )
= $true )
| ( ( SV61 = empty_set )
= $true )
| ( ( SV132 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2043,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( SV168 = empty_set )
= $false )
| ( ( quasi_total @ SV168 @ SV61 @ SV132 )
= $true )
| ( ( SV61 = empty_set )
= $true )
| ( ( SV132 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2044,plain,
! [SV192: $i,SV71: $i,SV186: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ SV186 ) )
= $true )
| ( ( related @ SV71 @ SV201 @ SV192 )
= $true )
| ( ( element @ SV201 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $false )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2022]) ).
thf(2045,plain,
! [SV71: $i,SV186: $i,SV192: $i] :
( ( ( in @ ( sK16_SY383 @ SV192 @ SV186 @ SV71 ) @ SV186 )
= $true )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $true )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2024]) ).
thf(2046,plain,
! [SV199: $i,SV197: $i,SV73: $i,SV203: $i] :
( ( ( element @ SV203 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( ~ ~ ( ~ ( related @ SV73 @ SV197 @ SV199 )
| ~ ( related @ SV73 @ SV199 @ SV203 ) )
| ( related @ SV73 @ SV197 @ SV203 ) )
= $true )
| ( ( element @ SV199 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2047,plain,
! [SV172: $i,SV144: $i,SV88: $i] :
( ( ( meet_semilatt_str @ SV88 )
= $false )
| ( ( empty_carrier @ SV88 )
= $true )
| ( ( ~ ( element @ SV144 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2048,plain,
! [SV188: $i,SV175: $i,SV148: $i,SV92: $i] :
( ( ( empty @ SV92 )
= $true )
| ( ( ~ ~ ( empty @ SV148 ) )
= $true )
| ( ( ~ ( element @ SV175 @ SV92 ) )
= $true )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2028]) ).
thf(2049,plain,
! [SV198: $i,SV195: $i,SV11: $i] :
( ( ( ~ ( related @ SV11 @ SV195 @ SV198 ) )
= $true )
| ( ( ~ ( related @ SV11 @ SV198 @ SV195 ) )
= $true )
| ( ( SV195 = SV198 )
= $true )
| ( ( element @ SV198 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV195 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2029]) ).
thf(2050,plain,
! [SV22: $i,SV112: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV112 )
| ! [SY389: $i] :
( ~ ( in @ SY389 @ SV22 )
| ( in @ SV202 @ SY389 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2030]) ).
thf(2051,plain,
! [SV112: $i,SV202: $i,SV22: $i] :
( ( ( ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV22 )
| ( in @ SV202 @ SY390 ) )
| ( in @ SV202 @ SV112 ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2052,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
| ! [SY391: $i] :
( ~ ( in @ SY391 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY391 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2053,plain,
! [SV189: $i,SV24: $i,SV179: $i,SV200: $i] :
( ( ( in @ SV200 @ SV179 )
= $false )
| ( ( related @ SV24 @ SV189 @ SV200 )
= $true )
| ( ( element @ SV200 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( relstr_element_smaller @ SV24 @ SV179 @ SV189 )
= $false )
| ( ( element @ SV189 @ ( the_carrier @ SV24 ) )
= $false )
| ( ( rel_str @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2054,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( ~ ( empty_carrier @ SV40 ) )
= $false )
| ( ( ~ ( reflexive_relstr @ SV40 ) )
= $true )
| ( ( ~ ( rel_str @ SV40 ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2055,plain,
! [SV180: $i,SV162: $i,SV41: $i,SV124: $i] :
( ( ( ~ ( empty @ SV124 ) )
= $false )
| ( ( empty @ SV41 )
= $true )
| ( ( ~ ( element @ SV162 @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2056,plain,
! [SV164: $i,SV49: $i,SV127: $i] :
( ( ( element @ SV127 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( join_semilatt_str @ SV49 )
= $false )
| ( ( ~ ( element @ SV164 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2057,plain,
! [SV132: $i,SV61: $i,SV168: $i] :
( ( ( quasi_total @ SV168 @ SV61 @ SV132 )
= $false )
| ( ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
= $true )
| ( ( SV132 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2058,plain,
! [SV168: $i,SV132: $i,SV61: $i] :
( ( ( SV61
= ( relation_dom_as_subset @ SV61 @ SV132 @ SV168 ) )
= $false )
| ( ( quasi_total @ SV168 @ SV61 @ SV132 )
= $true )
| ( ( SV132 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV168 @ SV61 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2059,plain,
! [SV192: $i,SV71: $i,SV186: $i,SV201: $i] :
( ( ( in @ SV201 @ SV186 )
= $false )
| ( ( related @ SV71 @ SV201 @ SV192 )
= $true )
| ( ( element @ SV201 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( relstr_set_smaller @ SV71 @ SV186 @ SV192 )
= $false )
| ( ( element @ SV192 @ ( the_carrier @ SV71 ) )
= $false )
| ( ( rel_str @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2060,plain,
! [SV203: $i,SV199: $i,SV197: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ( related @ SV73 @ SV197 @ SV199 )
| ~ ( related @ SV73 @ SV199 @ SV203 ) ) )
= $true )
| ( ( related @ SV73 @ SV197 @ SV203 )
= $true )
| ( ( element @ SV203 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV199 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2061,plain,
! [SV172: $i,SV88: $i,SV144: $i] :
( ( ( element @ SV144 @ ( the_carrier @ SV88 ) )
= $false )
| ( ( empty_carrier @ SV88 )
= $true )
| ( ( meet_semilatt_str @ SV88 )
= $false )
| ( ( ~ ( element @ SV172 @ ( the_carrier @ SV88 ) ) )
= $true )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2062,plain,
! [SV188: $i,SV175: $i,SV92: $i,SV148: $i] :
( ( ( ~ ( empty @ SV148 ) )
= $false )
| ( ( empty @ SV92 )
= $true )
| ( ( ~ ( element @ SV175 @ SV92 ) )
= $true )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2063,plain,
! [SV198: $i,SV195: $i,SV11: $i] :
( ( ( related @ SV11 @ SV195 @ SV198 )
= $false )
| ( ( ~ ( related @ SV11 @ SV198 @ SV195 ) )
= $true )
| ( ( SV195 = SV198 )
= $true )
| ( ( element @ SV198 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV195 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2064,plain,
! [SV22: $i,SV112: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV112 ) )
= $true )
| ( ( ! [SY389: $i] :
( ~ ( in @ SY389 @ SV22 )
| ( in @ SV202 @ SY389 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2065,plain,
! [SV112: $i,SV202: $i,SV22: $i] :
( ( ( ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV22 )
| ( in @ SV202 @ SY390 ) ) )
= $true )
| ( ( in @ SV202 @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2051]) ).
thf(2066,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) )
= $false )
| ( ( ~ ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2052]) ).
thf(2067,plain,
! [SV112: $i,SV22: $i] :
( ( ( ! [SY391: $i] :
( ~ ( in @ SY391 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY391 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2052]) ).
thf(2068,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( empty_carrier @ SV40 )
= $true )
| ( ( ~ ( reflexive_relstr @ SV40 ) )
= $true )
| ( ( ~ ( rel_str @ SV40 ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2069,plain,
! [SV180: $i,SV162: $i,SV41: $i,SV124: $i] :
( ( ( empty @ SV124 )
= $true )
| ( ( empty @ SV41 )
= $true )
| ( ( ~ ( element @ SV162 @ SV41 ) )
= $true )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2055]) ).
thf(2070,plain,
! [SV127: $i,SV49: $i,SV164: $i] :
( ( ( element @ SV164 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( join_semilatt_str @ SV49 )
= $false )
| ( ( empty_carrier @ SV49 )
= $true )
| ( ( element @ SV127 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( element @ ( join @ SV49 @ SV127 @ SV164 ) @ ( the_carrier @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2071,plain,
! [SV203: $i,SV199: $i,SV197: $i,SV73: $i] :
( ( ( ~ ( ~ ( related @ SV73 @ SV197 @ SV199 )
| ~ ( related @ SV73 @ SV199 @ SV203 ) ) )
= $false )
| ( ( related @ SV73 @ SV197 @ SV203 )
= $true )
| ( ( element @ SV203 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV199 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2072,plain,
! [SV144: $i,SV88: $i,SV172: $i] :
( ( ( element @ SV172 @ ( the_carrier @ SV88 ) )
= $false )
| ( ( meet_semilatt_str @ SV88 )
= $false )
| ( ( empty_carrier @ SV88 )
= $true )
| ( ( element @ SV144 @ ( the_carrier @ SV88 ) )
= $false )
| ( ( element @ ( meet @ SV88 @ SV144 @ SV172 ) @ ( the_carrier @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2073,plain,
! [SV188: $i,SV175: $i,SV92: $i,SV148: $i] :
( ( ( empty @ SV148 )
= $true )
| ( ( empty @ SV92 )
= $true )
| ( ( ~ ( element @ SV175 @ SV92 ) )
= $true )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2062]) ).
thf(2074,plain,
! [SV195: $i,SV198: $i,SV11: $i] :
( ( ( related @ SV11 @ SV198 @ SV195 )
= $false )
| ( ( related @ SV11 @ SV195 @ SV198 )
= $false )
| ( ( SV195 = SV198 )
= $true )
| ( ( element @ SV198 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV195 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( antisymmetric_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2075,plain,
! [SV22: $i,SV112: $i,SV202: $i] :
( ( ( in @ SV202 @ SV112 )
= $false )
| ( ( ! [SY389: $i] :
( ~ ( in @ SY389 @ SV22 )
| ( in @ SV202 @ SY389 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2076,plain,
! [SV112: $i,SV202: $i,SV22: $i] :
( ( ( ! [SY390: $i] :
( ~ ( in @ SY390 @ SV22 )
| ( in @ SV202 @ SY390 ) ) )
= $false )
| ( ( in @ SV202 @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2077,plain,
! [SV112: $i,SV22: $i] :
( ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
= $true )
| ( ( ~ ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2066]) ).
thf(2078,plain,
! [SV22: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK18_SY391 @ SV112 @ SV22 ) @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ ( sK18_SY391 @ SV112 @ SV22 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2067]) ).
thf(2079,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( reflexive_relstr @ SV40 )
= $false )
| ( ( empty_carrier @ SV40 )
= $true )
| ( ( ~ ( rel_str @ SV40 ) )
= $true )
| ( ( ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2080,plain,
! [SV180: $i,SV124: $i,SV41: $i,SV162: $i] :
( ( ( element @ SV162 @ SV41 )
= $false )
| ( ( empty @ SV41 )
= $true )
| ( ( empty @ SV124 )
= $true )
| ( ( ~ ( element @ SV180 @ SV124 ) )
= $true )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2081,plain,
! [SV203: $i,SV199: $i,SV197: $i,SV73: $i] :
( ( ( ~ ( related @ SV73 @ SV197 @ SV199 )
| ~ ( related @ SV73 @ SV199 @ SV203 ) )
= $true )
| ( ( related @ SV73 @ SV197 @ SV203 )
= $true )
| ( ( element @ SV203 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV199 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2082,plain,
! [SV188: $i,SV148: $i,SV92: $i,SV175: $i] :
( ( ( element @ SV175 @ SV92 )
= $false )
| ( ( empty @ SV92 )
= $true )
| ( ( empty @ SV148 )
= $true )
| ( ( ~ ( element @ SV188 @ SV148 ) )
= $true )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2083,plain,
! [SV112: $i,SV202: $i,SV22: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV22 )
| ( in @ SV202 @ SV204 ) )
= $true )
| ( ( in @ SV202 @ SV112 )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2084,plain,
! [SV22: $i,SV202: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK19_SY390 @ SV112 @ SV202 @ SV22 ) @ SV22 )
| ( in @ SV202 @ ( sK19_SY390 @ SV112 @ SV202 @ SV22 ) ) )
= $false )
| ( ( in @ SV202 @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2076]) ).
thf(2085,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) )
= $false )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2086,plain,
! [SV22: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK18_SY391 @ SV112 @ SV22 ) @ SV22 ) )
= $false )
| ( ( ~ ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2078]) ).
thf(2087,plain,
! [SV112: $i,SV22: $i] :
( ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ ( sK18_SY391 @ SV112 @ SV22 ) )
= $false )
| ( ( ~ ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2078]) ).
thf(2088,plain,
! [SV161: $i,SV123: $i,SV40: $i] :
( ( ( rel_str @ SV40 )
= $false )
| ( ( empty_carrier @ SV40 )
= $true )
| ( ( reflexive_relstr @ SV40 )
= $false )
| ( ( ~ ( element @ SV123 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2089,plain,
! [SV162: $i,SV41: $i,SV124: $i,SV180: $i] :
( ( ( element @ SV180 @ SV124 )
= $false )
| ( ( empty @ SV124 )
= $true )
| ( ( empty @ SV41 )
= $true )
| ( ( element @ SV162 @ SV41 )
= $false )
| ( ( element @ ( ordered_pair_as_product_element @ SV41 @ SV124 @ SV162 @ SV180 ) @ ( cartesian_product2 @ SV41 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2090,plain,
! [SV203: $i,SV199: $i,SV197: $i,SV73: $i] :
( ( ( ~ ( related @ SV73 @ SV197 @ SV199 ) )
= $true )
| ( ( ~ ( related @ SV73 @ SV199 @ SV203 ) )
= $true )
| ( ( related @ SV73 @ SV197 @ SV203 )
= $true )
| ( ( element @ SV203 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV199 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2081]) ).
thf(2091,plain,
! [SV175: $i,SV92: $i,SV148: $i,SV188: $i] :
( ( ( element @ SV188 @ SV148 )
= $false )
| ( ( empty @ SV148 )
= $true )
| ( ( empty @ SV92 )
= $true )
| ( ( element @ SV175 @ SV92 )
= $false )
| ( ( ( ordered_pair_as_product_element @ SV92 @ SV148 @ SV175 @ SV188 )
= ( ordered_pair @ SV175 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2092,plain,
! [SV112: $i,SV202: $i,SV22: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV22 ) )
= $true )
| ( ( in @ SV202 @ SV204 )
= $true )
| ( ( in @ SV202 @ SV112 )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2083]) ).
thf(2093,plain,
! [SV22: $i,SV202: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK19_SY390 @ SV112 @ SV202 @ SV22 ) @ SV22 ) )
= $false )
| ( ( in @ SV202 @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2084]) ).
thf(2094,plain,
! [SV22: $i,SV112: $i,SV202: $i] :
( ( ( in @ SV202 @ ( sK19_SY390 @ SV112 @ SV202 @ SV22 ) )
= $false )
| ( ( in @ SV202 @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2084]) ).
thf(2095,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) ) )
= $false )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2096,plain,
! [SV112: $i,SV22: $i] :
( ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
= $false )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2097,plain,
! [SV22: $i,SV112: $i] :
( ( ( in @ ( sK18_SY391 @ SV112 @ SV22 ) @ SV22 )
= $true )
| ( ( ~ ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2086]) ).
thf(2098,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) )
= $false )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ ( sK18_SY391 @ SV112 @ SV22 ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2099,plain,
! [SV161: $i,SV40: $i,SV123: $i] :
( ( ( element @ SV123 @ ( the_carrier @ SV40 ) )
= $false )
| ( ( reflexive_relstr @ SV40 )
= $false )
| ( ( empty_carrier @ SV40 )
= $true )
| ( ( rel_str @ SV40 )
= $false )
| ( ( ~ ( element @ SV161 @ ( the_carrier @ SV40 ) ) )
= $true )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2088]) ).
thf(2100,plain,
! [SV203: $i,SV199: $i,SV197: $i,SV73: $i] :
( ( ( related @ SV73 @ SV197 @ SV199 )
= $false )
| ( ( ~ ( related @ SV73 @ SV199 @ SV203 ) )
= $true )
| ( ( related @ SV73 @ SV197 @ SV203 )
= $true )
| ( ( element @ SV203 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV199 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2101,plain,
! [SV112: $i,SV202: $i,SV22: $i,SV204: $i] :
( ( ( in @ SV204 @ SV22 )
= $false )
| ( ( in @ SV202 @ SV204 )
= $true )
| ( ( in @ SV202 @ SV112 )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2102,plain,
! [SV22: $i,SV202: $i,SV112: $i] :
( ( ( in @ ( sK19_SY390 @ SV112 @ SV202 @ SV22 ) @ SV22 )
= $true )
| ( ( in @ SV202 @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $false )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2093]) ).
thf(2103,plain,
! [SV112: $i,SV22: $i] :
( ( ( ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) ) )
= $true )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2095]) ).
thf(2104,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 ) )
= $false )
| ( ( in @ ( sK18_SY391 @ SV112 @ SV22 ) @ SV22 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2105,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) ) )
= $false )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ ( sK18_SY391 @ SV112 @ SV22 ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2098]) ).
thf(2106,plain,
! [SV112: $i,SV22: $i] :
( ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
= $false )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ ( sK18_SY391 @ SV112 @ SV22 ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2098]) ).
thf(2107,plain,
! [SV123: $i,SV40: $i,SV161: $i] :
( ( ( element @ SV161 @ ( the_carrier @ SV40 ) )
= $false )
| ( ( rel_str @ SV40 )
= $false )
| ( ( empty_carrier @ SV40 )
= $true )
| ( ( reflexive_relstr @ SV40 )
= $false )
| ( ( element @ SV123 @ ( the_carrier @ SV40 ) )
= $false )
| ( ( related_reflexive @ SV40 @ SV123 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2108,plain,
! [SV197: $i,SV203: $i,SV199: $i,SV73: $i] :
( ( ( related @ SV73 @ SV199 @ SV203 )
= $false )
| ( ( related @ SV73 @ SV197 @ SV199 )
= $false )
| ( ( related @ SV73 @ SV197 @ SV203 )
= $true )
| ( ( element @ SV203 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV199 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( element @ SV197 @ ( the_carrier @ SV73 ) )
= $false )
| ( ( transitive_relstr @ SV73 )
= $false )
| ( ( rel_str @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2109,plain,
! [SV112: $i,SV22: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV205 ) )
= $true )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2110,plain,
! [SV112: $i,SV22: $i] :
( ( ( ~ ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) ) )
= $false )
| ( ( in @ ( sK18_SY391 @ SV112 @ SV22 ) @ SV22 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2104]) ).
thf(2111,plain,
! [SV112: $i,SV22: $i] :
( ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
= $false )
| ( ( in @ ( sK18_SY391 @ SV112 @ SV22 ) @ SV22 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2104]) ).
thf(2112,plain,
! [SV112: $i,SV22: $i] :
( ( ( ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) ) )
= $true )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ ( sK18_SY391 @ SV112 @ SV22 ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2105]) ).
thf(2113,plain,
! [SV112: $i,SV22: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ SV22 ) )
= $true )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV205 )
= $true )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2114,plain,
! [SV112: $i,SV22: $i] :
( ( ( ! [SY392: $i] :
( ~ ( in @ SY392 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SY392 ) ) )
= $true )
| ( ( in @ ( sK18_SY391 @ SV112 @ SV22 ) @ SV22 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2110]) ).
thf(2115,plain,
! [SV112: $i,SV22: $i,SV206: $i] :
( ( ( ~ ( in @ SV206 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV206 ) )
= $true )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ ( sK18_SY391 @ SV112 @ SV22 ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2116,plain,
! [SV112: $i,SV22: $i,SV205: $i] :
( ( ( in @ SV205 @ SV22 )
= $false )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV205 )
= $true )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2117,plain,
! [SV112: $i,SV22: $i,SV207: $i] :
( ( ( ~ ( in @ SV207 @ SV22 )
| ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV207 ) )
= $true )
| ( ( in @ ( sK18_SY391 @ SV112 @ SV22 ) @ SV22 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2118,plain,
! [SV112: $i,SV22: $i,SV206: $i] :
( ( ( ~ ( in @ SV206 @ SV22 ) )
= $true )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV206 )
= $true )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ ( sK18_SY391 @ SV112 @ SV22 ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2119,plain,
! [SV112: $i,SV22: $i,SV207: $i] :
( ( ( ~ ( in @ SV207 @ SV22 ) )
= $true )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV207 )
= $true )
| ( ( in @ ( sK18_SY391 @ SV112 @ SV22 ) @ SV22 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2117]) ).
thf(2120,plain,
! [SV112: $i,SV22: $i,SV206: $i] :
( ( ( in @ SV206 @ SV22 )
= $false )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV206 )
= $true )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ ( sK18_SY391 @ SV112 @ SV22 ) )
= $false )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2121,plain,
! [SV112: $i,SV22: $i,SV207: $i] :
( ( ( in @ SV207 @ SV22 )
= $false )
| ( ( in @ ( sK17_SY344 @ SV22 @ SV112 ) @ SV207 )
= $true )
| ( ( in @ ( sK18_SY391 @ SV112 @ SV22 ) @ SV22 )
= $true )
| ( ( SV112
= ( set_meet @ SV22 ) )
= $true )
| ( ( SV22 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2122,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[821,2121,2120,2116,2111,2108,2107,2106,2102,2101,2096,2094,2091,2089,2074,2072,2070,2059,2058,2057,2053,2045,2043,2042,2041,2040,2034,2025,2023,2012,2010,2003,1989,1979,1970,1969,1964,1963,1958,1957,1954,1950,1949,1945,1944,1940,1939,1928,1927,1915,1888,1887,1883,1878,1873,1872,1871,1861,1860,1846,1844,1841,1836,1835,1834,1828,1824,1822,1821,1818,1817,1812,1809,1805,1803,1797,1794,1792,1788,1782,1781,1780,1777,1776,1775,1774,1773,1772,1771,1758,1757,1756,1751,1750,1744,1743,1739,1734,1724,1717,1713,1712,1702,1701,1692,1691,1670,1660,1659,1658,1656,1655,1650,1649,1645,1601,1600,1597,1586,1584,1573,1557,1556,1553,1552,1550,1548,1545,1517,1507,1466,1457,1456,1446,1438,1419,1418,1409,1400,1396,1393,1382,1377,1375,1374,1360,1350,1349,1348,1347,1325,1324,1313,1311,1309,1301,1300,1293,1289,1280,1271,1265,1226,1058,1057,1056,1055,1054,1053,1052,950,921,916,912,911,910,908,900,898,897,894,893,891,890,889,888,886,884,882,881,880,878,877,876,873,872,870,869,867,864]) ).
thf(2123,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU355+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n016.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 15:20:29 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 212.41/35.65 ......
% 212.41/35.65
% 212.41/35.65 No.of.Axioms: 136
% 212.41/35.65
% 212.41/35.65 Length.of.Defs: 0
% 212.41/35.65
% 212.41/35.65 Contains.Choice.Funs: false
% 212.41/35.65 .....................................................
% 212.41/35.65
% 212.41/35.65 ********************************
% 212.41/35.65 * All subproblems solved! *
% 212.41/35.65 ********************************
% 212.41/35.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:137,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:2122,loop_count:0,foatp_calls:1,translation:fof_full)
% 212.41/35.65
% 212.41/35.65 %**** Beginning of derivation protocol ****
% 212.41/35.65 % SZS output start CNFRefutation
% See solution above
% 212.41/35.67
% 212.41/35.67 %**** End of derivation protocol ****
% 212.41/35.67 %**** no. of clauses in derivation: 1589 ****
% 212.41/35.67 %**** clause counter: 2122 ****
% 212.41/35.67
% 212.41/35.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:137,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:2122,loop_count:0,foatp_calls:1,translation:fof_full)
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